Randomness in Evolution: Valid and Invalid Usage

[cyborg]

This page is a good one to see more detail on the algorithmic argument:

http://www.cs.umaine.edu/~chaitin/sciamer.html

[sol invictus]

No. You cannot compress a random sequence with any algorithm and gain any reduction in information required to express it.


Let's do an example. Suppose you claim the sequence 10 is random. Well, here's my compression algorithm:

input output
10 |||| 0
00 |||| 1
01 |||| 00
11 |||| 10

This algorithm compresses 10 and 00, but not 01 or 11 - so it is perfectly consistent with the theorem you quoted (of course), but it also compresses the sequence you claimed was random.

Now, because I specified an algorithm that can handle any input losslessly, it took a while. But I can also simply do this:

input |||| output
anything | 0

That compresses any sequence.

Now, you wanted an algorithm to produce a sequence... that's easy too. Here's a very short algorithm: produce a random (or pseudo-random, doesn't matter) sequence of 1's and 0's. Eventually the given sequence will be produced. :)

EDIT - another one is an algorithm that just produces every possible sequence of increasing numbers of bits, like 0, 1, 00, 01 10, 11, 000, 001, 010, 011, 100, etc. Very easy to specify, and will produce any finite sequence.

[Dancing David]

I never said it was.

"Artic foxes are white because of mutation" does not follow my from my statement about the importance of mutation as a component of evolution. Evolution explains alot more than why your eye colour from last generation to this one.

By the way, if I recall hazel eyes are blend of the co-dominant brown and blue. Thus your eyes as compared to your parent is purely hereditary. But the blue gene your parents have is believed to be a recent mutation, so their hazel eyes are the result of mutation and selection. They can not be said to be caused by just mutation, ro just selection.

Link (http://www.dailymail.co.uk/pages/live/articles/technology/technology.html?in_page_id=1965&in_article_id=511473)

So your parents eyes were hazel because of mutation ... and selection, recombination, drift,....

Walt


Hi Walt, thanks for the response!

I will remind you that what you said was "It ain't evolution as we know it without mutation."

Now the deal is that alelle combinations and the control genes for growth can be very important in the variability of traits.

Hazel eye are caused by the combination of double dominant green with the dominant brown, blue is the double recessive. So green is double gree, hazel is green:brown , brown can be double brown or brown:blue.

The point being that regardless of the ontology of the variation, there can be and is variation that is not dependant upon mutation. Which is the point I was trying to make and the other two posters and perhaps you seem to want to ignore.

But to say that this requires the mutational accident would be like saying that all penecillin based antibiotic are dependant upon the accident of the mold growth.

Which is nonsesne, of course the trait was needed and accidentaly noticed.

However the groth of the mol in solution vats of great size, the refinement of the material to extract the penecilling and the concentration of the active agent are all very deliberate and very controlled.

So what is the 'more' important part, the fortuitous discovery or the deliberate development of the mediaction, to say that modern antibiotics are all 'accidental' because they were discovered by 'accident' is exactly comparable to saying all natural selection is 'random' because it has a'random' element.

Is the treatment of a severe bacterial infection and sepsis really accidental?

[cyborg]

That compresses any sequence.

YOU HAVE NOT INCLUDED THE SIZE OF THE ALGORITHM IN YOUR CLAIM THAT THE SEQUENCE IS COMPRESSED.

Need I point this out yet again?

[sol invictus]

YOU HAVE NOT INCLUDED THE SIZE OF THE ALGORITHM IN YOUR CLAIM THAT THE SEQUENCE IS COMPRESSED.

Need I point this out yet again?

You seem to be rather confused.

First, the algorithm I gave is clearly more or less as simple as is possible. Moreover I described it in one short sentence, which bounds its complexity, and it compresses ANY sequence no matter what the length is.

Second, the complexity of a compression algorithm isn't usually the point. If I had an algorithm that could compress any sequence losslessly it would violate the theorem you quoted above, regardless of how complex the algorithm itself was. That theorem has nothing to do with the complexity of the algorithm - it simply proves that no such algorithm exists.

[cyborg]

You seem to be rather confused.

I am not.

First, the algorithm I gave is clearly more or less as simple as is possible.

It is not simple enough to have a size of zero.

Second, the complexity of a compression algorithm isn't usually the point.

It is here.

You are trying to prove that a sequence can be compressed arbitrarially by playing language tricks. You have not understood the point of the definition - you have to include this information. You do not get to magic up zero bit length algorithms that hide arbitrary bit length data.

[sol invictus]

It is not simple enough to have a size of zero.

Look - the case of sequences with very few bits is both trivial and uninteresting for these purposes. Obviously we are not going to be able to decide whether 10 is a random sequence, as opposed to 01 or 11 for example. The interesting cases are sequences with many bits.

You are trying to prove that a sequence can be compressed arbitrarially by playing language tricks. You have not understood the point of the definition - you have to include this information. You do not get to magic up zero bit length algorithms that hide arbitrary bit length data.

Nonsense. I've given you an algorithm, which I described in one short English sentence, which can compress any sequence - no matter how many bits it contains - down to one bit. The information required to specify my algorithm is obviously bounded, but the sequences it will compress are not. So your definition does not suffice.

[jimbob]

ETA: Cyborg, If you used a compression algorithm on the works of Shakespeare, so that it could be compressed no further, then by your definition isn't the result a random number?

If not why?

If you said that no general algorithm could compress all random signals, and in general, random signals do not compress much, then I would agree with you.

But that can't be what you are claiming. Because I could say that no general algorithm could compress multiple results of the snooker ball example, which you claim is nonrandom for some reason.

[cyborg]

Look - the case of sequences with very few bits is both trivial and uninteresting for these purposes. Obviously we are not going to be able to decide whether 10 is a random sequence, as opposed to 01 or 11 for example. The interesting cases are sequences with many bits.

Yes they are trivial cases but this is simply about getting you to accept the principal of the thing and abandon the language trickery you have latched onto.

If you won't accept the trivialities then it's pointless dealing with larger cases.

Do you or do you not understand why it is invalid to pretend you have compressed information down to a single bit if you need to have that information represented in full in the algorithm for decompressing the data?

I don't understand why this disconnect is occuring: if I specify the algorithm:

1|print 101101110111000010110101011101001111010010100001

To compress:

101101110111000010110101011101001111010010100001

And then give it the input:

1

Then the number of bits I have encoded this sequence to is 49 at the very minimum - assuming no bits to describe the "print" part of the algorithm. I have gained absolutely nothing but shifting the input into the algorithm.

Shifting input into the algorithm DOES NOT WORK because we consider the complexity of the algorithm and input.

Algorithm AND input.

Nonsense. I've given you an algorithm, which I described in one short English sentence, which can compress any sequence - no matter how many bits it contains - down to one bit.

This?

EDIT - another one is an algorithm that just produces every possible sequence of increasing numbers of bits, like 0, 1, 00, 01 10, 11, 000, 001, 010, 011, 100, etc. Very easy to specify, and will produce any finite sequence.

And how do you propose to specify which sequence this algorithm is to produce without ending up back where you started?

[cyborg]

But that can't be what you are claiming. Because I could say that no general algorithm could compress multiple results of the snooker ball example, which you claim is nonrandom for some reason.

I did not say it is "non-random" - I said it is trivially easy to create a deterministic set of data from a random source and then have the same results time and time again.

The important part of an interacting system is not whether or not some behaviour is "random" or "non-random" - that is mathematically undecidable (see the link) - the important part is the deterministic relationships - i.e. what things will have a causal effect on other things and conversly what things will not have a causal effect on other things.

[sol invictus]

I don't understand why this disconnect is occuring: if I specify the algorithm:
<snip>


Sure, but that bears little resemblance to the algorithm I proposed - which is to send ALL input sequences to 1.

And how do you propose to specify which sequence this algorithm is to produce without ending up back where you started?

That's your problem - or rather a problem with your proposed definition - not mine.

[jimbob]

the important part is the deterministic relationships - i.e. what things will have a causal effect on other things and conversly what things will not have a causal effect on other things.

I'd agree with that. ETA: but how do you determine this? Its the first collison deterministic? yes, its the n'th collision deterministic? yes with respect to its immediate predescessors, but no with respect to the first, if n is more than 12. There have been no other external inputs, so the result of the nth impact isn't determined by the (n-12)th impact. The 12th impact and beyond are random.


Biology is more complex than snooker balls, so with more random influences


However if you are discussing a chaotic system, you might be able to describe the feedback loops both positive and negative, but you won't be able to descibe what the effects of these will be beyond a certain time in the future.

In the snooker ball case, we hypothetically knowe the inputs to the theoretical (quantum) resolution. We know the laws of motion governing the balls. We can easily know what happens after the first impact... and second... but not the twelfth. There have been no further external inputs.

In biological systems I am saying it would be theoretically impossible to say that owlet x will breed successfully, because all the traits might be in its favour, as events could overtake it. These events will have immediate causes, but mixed up with them will be random causes.

You can obviously predict some failures with 100% accuracy, the sterile etc...

Do you see what I am saying that if the fitness environment is chaotic, then it will also be subject to random changes (probably over long ttimescales relative to a human lifetime, but short relative to life's tenure on Earth)?

A single mutation could spread, and completely alter the fitness environment for many organisms. A slight change in the structure of H5N1 might be a catastrophic demonstration of that. Without modern medicine, there could be a strong selective pressure arising on humanity from one slight change to a virus.

[cyborg]

Sure, but that bears little resemblance to the algorithm I proposed - which is to send ALL input sequences to 1.

Which fails for the reasons below.

That's your problem - or rather a problem with your proposed definition - not mine.

Well no it's not. You're not thinking it through.

It's all very well saying, "here's a program that prints all sequences so it's infinitely compressive!" but that's a set of sequences, not a sequence. It is not of the same type so it doesn't fall under the definition.

To fall under the definition it would be have to be a sequence such as:

0100011011000001010011100101110111...

Which is the concatenation of the sequences of those sets and is a sequence under its own right.

One and only one sequence encoded by an algorithm and its input.

Your "solution" is like you asking me to compress a file and me returning your algorithm and saying:

"Well, it'll generate your file eventually - it's your problem figuring out when that is."

Not acceptable.

[jimbob]

What about the perfectly compressed works of Shakespere?

Wouldn't that be a random sequence by your definiton Cyborg?

ETA: Wuithout the algorithm I'd agree that it would be indistinguishable from a random sequence.

[cyborg]

What about the perfectly compressed works of Shakespere?

Wouldn't that be a random sequence by that definition?

Yes it would - what are you trying to say?

[mijopaalmc]

Yes it would - what are you trying to say?

Possibly that such a definition doesn't make a meaningful distinction between random and non-random.

One would think that since so many people have insisted that my definition of random is meaningless that you would be more careful in coming up with your own.

[cyborg]

Possibly that such a definition doesn't make a meaningful distinction between random and non-random.

I fail to see how. Compressed data is not expanded data. Shakespere's Compressed works are not Shakespere's Uncompressed works.

One would think that since so many people have insisted that my definition of random is meaningless that you would be more careful in coming up with your own.

It's not exactly "my own" definition.

[sol invictus]

Which fails for the reasons below.


What reasons? I gave you an algorithm that compresses all sequences, no matter what the length, to one bit. And it doesn't take many bits to specify. That's a clear counterexample to what you were claiming.

As for generating a given sequence, I can do that as well - just define that sequence to be "1", and the algorithm outputs "1".

I think perhaps the best way to see that your definition cannot possibly work is to think of these sequences as representing numbers written in binary. Then each sequence is just some integer. But it is clearly ridiculous to make a rule that calls some integers random, and some not.

[Belz...]

Sol: Cyborg is right, you can't claim to compress data indefinitely without taking into account the algorithm itself.

Cyborg: Sol is right, you can't compress data at all without SOME algorithm, without which the entire idea is nonsensical.

Can't we just all get along ? ;)

[sol invictus]

Sol: Cyborg is right, you can't claim to compress data indefinitely without taking into account the algorithm itself.


Well, one correct statement is the one cyborg quoted above - that you can't losslessly compress every sequence of a given size. But remove the "lossless" or the "every" and there's no statement.

I've continued this discussion because there is a good idea here. I agree with cyborg that when sequences are hard to compress they are close to random. I would have phrased it in terms Shannon entropy (a sequence of N bits is random if its Shannon entropy is maximized), but that's very similar. In fact I've discussed that on this forum in the past.

But all of these definitions rely on limits - I don't think there's any way to define any of them properly for a finite sequence, or a finite quantity of data. If I'm wrong, I'd like to know how to do it. And incidentally if there is a way, it would define an unambiguous method for measuring information in the genome and give the lie to the creationists that say mutations can't increase information.

[jimbob]

I fail to see how. Compressed data is not expanded data. Shakespere's Compressed works are not Shakespere's Uncompressed works.


Are you saying that the uncompressed works of Shakespere are nonrandom, whilst the compressed works aren't?

If you were arguing that information with no redundancy would look indistinguishable from random noise, then I would agree with you. However that isn't what you are saying, you are saying that it is random.

A pretty odd type of random as, by your definition, Shakespere's uncompressed works aren't random, yet you apply a deterministic algorithm that would always give the same result, and this result is random by your definition.

[cyborg]

What reasons? I gave you an algorithm that compresses all sequences, no matter what the length, to one bit. And it doesn't take many bits to specify. That's a clear counterexample to what you were claiming.

Please re-read what I said carefully. Your types are wrong. It doesn't do the job for the reason I explained.

As for generating a given sequence, I can do that as well - just define that sequence to be "1", and the algorithm outputs "1".

Eh?
But it is clearly ridiculous to make a rule that calls some integers random, and some not.

That is not the rule. Please read the link on the undecidablility of that proposition. We can only really compare the "randomness" of our finite analyses - we can't ever prove randomness.

[cyborg]

A pretty odd type of random as, by your definition, Shakespere's uncompressed works aren't random, yet you apply a deterministic algorithm that would always give the same result, and this result is random by your definition.

If I randomly constructed a Java program then it would be a deterministic algorithm inspite of this. You are mixing up the difference between the algorithm and the representation of the algorithm.

Say I had the works represented in ASCII and I wanted to compress them. Because in ASCII the 8th bit of a standard character is always 0 I can reduce the size of any standard ASCII file by an eighth by simply removing this bit. This sequence, however, would most likely still be compressable and hence would not be "random", but it would be more "random" than the original file because there is less potential to compress it as there is less redundancy in the file.

Now as you have both rightly seen the meaning of this analysis increases with the size of the sequences you are considering. So the works of Shakespere would certainly not be considered random as they can likely be compressed by a dictionary algorithm by quite a high percentage. The compressed file should be considered random because if it is not there is still redundancy to exploit. (Not the action remember, the representation).

The compressed file and the uncompressed file can both be said to be equivalent algorithms. So we are interested in minimal algorithms to produce a sequence - and we should expect the representation of those minimal algorithms to not be producable by an algorithm itself. (Which is smaller).

[Dancing David]

Wow, know what, Shakespeare is evolving into a random sequence. Du_u_ude.

And the perscription of antibiotics is random.

[sol invictus]

Please re-read what I said carefully. Your types are wrong. It doesn't do the job for the reason I explained.


Sorry cyborg - I did re-read it, and I really don't understand what you're saying. It doesn't coincide with the link you gave (as far as I can tell). I don't see the point in discussing this further with you, particularly in this thread. When I have time I'll start a new one about randomness.

[cyborg]

Sorry cyborg - I did re-read it, and I really don't understand what you're saying.

A set of sequences is not a sequence - the output you are producing is not type valid. If you are saying: "the algorithm keeps producing sequences actually," then it's not a terminating algorithm and hence it doesn't encode a particular sequence - 0, 1, 00, 01 etc... can only be considered "scratch" results - working memory. There has to be a definite result.

[sol invictus]

A set of sequences is not a sequence - the output you are producing is not type valid. If you are saying: "the algorithm keeps producing sequences actually," then it's not a terminating algorithm and hence it doesn't encode a particular sequence - 0, 1, 00, 01 etc... can only be considered "scratch" results - working memory. There has to be a definite result.

But... your comment (the one my post responded to) was about my proposed compression algorithm, not the production algorithm.

We're obviously not on the same page here. Like I said, there is no point in continuing this conversation.

[jimbob]

I still say that you have it backwards Cyborg.

If you remove all redundant information from a datastream, the result will be fully compressed. It would look like random noise, as any patterns in the data could be compressed further. However it would not be random noise, as it would contain useful information.

Your approach is useless, as you define Shakespear's uncompressed works as norandom, yet a perfectly compressed version of the same works as random*. Whilst at the same time you also seem to think that the results of a chaotic system are nonrandom.

In other words the output of system where identical inputs can produce significantly different and diverging results can be nonrandom (according to you), whilst one where the same inputs will always produce the same outputs, and produce a "random" output from a nonrandom input, even though you can transform thise outputs in both directions and always get the same results.


*I'll grant you pseudorandom, in that it won't be predictible, but it isn't random.

[jimbob]

Back to the OP:

Cyborg:


the important part is the deterministic relationships - i.e. what things will have a causal effect on other things and conversly what things will not have a causal effect on other things.I'd agree with that. ETA: but how do you determine this? Its the first collison deterministic? yes, its the n'th collision deterministic? yes with respect to its immediate predescessors, but no with respect to the first, if n is more than 12. There have been no other external inputs, so the result of the nth impact isn't determined by the (n-12)th impact. The 12th impact and beyond are random.


Biology is more complex than snooker balls, so with more random influences


However if you are discussing a chaotic system, you might be able to describe the feedback loops both positive and negative, but you won't be able to descibe what the effects of these will be beyond a certain time in the future.

In the snooker ball case, we hypothetically knowe the inputs to the theoretical (quantum) resolution. We know the laws of motion governing the balls. We can easily know what happens after the first impact... and second... but not the twelfth. There have been no further external inputs.

In biological systems I am saying it would be theoretically impossible to say that owlet x will breed successfully, because all the traits might be in its favour, as events could overtake it. These events will have immediate causes, but mixed up with them will be random causes.

You can obviously predict some failures with 100% accuracy, the sterile etc...

Do you see what I am saying that if the fitness environment is chaotic, then it will also be subject to random changes (probably over long ttimescales relative to a human lifetime, but short relative to life's tenure on Earth)?

A single mutation could spread, and completely alter the fitness environment for many organisms. A slight change in the structure of H5N1 might be a catastrophic demonstration of that. Without modern medicine, there could be a strong selective pressure arising on humanity from one slight change to a virus.

[cyborg]

However it would not be random noise, as it would contain useful information.

What is useful information you should realise is a matter of interpretation.

Your approach is useless, as you define Shakespear's uncompressed works as norandom, yet a perfectly compressed version of the same works as random*. Whilst at the same time you also seem to think that the results of a chaotic system are nonrandom.

For one thing you have talked of chaotic systems as being determinstic so I don't get what your point is here.

On the other you seem to have completely missed the point that if you can construct an equivalent representation for a sequence which is a small ratio of it then the sequence in question would be considered "non-random". If the sequence you have constructed to represent wouldn't be considered "random" then it's not a minimal sequence.

I don't really know how else to get you to understand that there is a difference between representation and expression.

In other words the output of system where identical inputs can produce significantly different and diverging results can be nonrandom (according to you), whilst one where the same inputs will always produce the same outputs, and produce a "random" output from a nonrandom input, even though you can transform thise outputs in both directions and always get the same results.

You have completely failed to grasp the concept here.

[articulett]

Cyborg, he has been failing to grasp the concept and repeating the same inanities for over a year... Like Mijo, he is convinced that it's because he understands more than everyone else (including actual experts)... it isn't ever, ever going to change. He cannot grasp it.

He is so muddled in his understanding that I don't think he can actually convey a comprehensible understanding of evolution to anyone... ever. It's garbled and jumping tenses and mixing the model for specific examples.

For what it's worth, you are clear to me. I have no idea if the same old people are clear to anyone... or if they are even clear to each other. Jimbobs whole "identical inputs"/different outputs is so convoluted, because he's not talking about IDENTICAL inputs at all... he tosses in a new variable or an event and that isn't identical and then says that it makes the outcome probabilistic per his non sequitur of an example. If this life wasn't "destined" (whatever that means) because some random thing could have affected the outcome -- then, to jimbob, evolution is random. To Mijo it's random so long as random things (described as "anything to do with probability) are involved in natural selection.

It's whacked. It's nonsense. You try to hard to make a dent in the impenetrable. Their descriptions could apply equally to poker... and it would be equally as garbled and uninformative as to what poker is or how the game is played as it is to evolution.

[jimbob]

Cyborg, with no redundant information it would look like random noise, but not be; every time you uncompress it, it turns into Shakespere, every time you attempt to uncompress random noise it turns into random noise. That is a difference.

Are you disagreeing with the statement that chaotic systems produce random outputs over long timescales? I have said that over short timescales, chaotic systems are (maybe I didn't add sufficiently) deterministic, that is true, but over long timescales, although they depend on previous conditions, slight errors get magnified untli you go far enough forward, and accurate prediction would require an accuracy at the quantum level. Beyond this point, the output is not only unpredictible with respect to the initial conditions it is random because it is determined in part by future random events.

Articulett, could you explian what Cyborg means to me please? I thought I understood, but disagreed with, his point, but now I have no idea.


Articulettt, my contention is quite simple. Many biological systems are chaotic; natural selection certainly is affected by chaotic systems, for example the weather. In fact natural selection has all the hallmarks of a chaotic system. In other words it is random, because what reproduces is governed in part by chance. This is a long-term randomness is a fundamental aspect of chaotic systems, and is uncontroversial.

Over long timescales, this chaotic nature mean that the direction of evolution is likely to change randomly. A single mutation in a disease can and does cause a vast change in the selective pressures affecting a population. This is a random change in "direction".

[cyborg]

Cyborg, with no redundant information it would look like random noise, but not be; every time you uncompress it, it turns into Shakespere, every time you attempt to uncompress random noise it turns into random noise. That is a difference.

That's a pretty bold statement: you're telling me there's no interpretation under which I could take "real" random noise and turn it into "meaningful" information.

I don't know what magic mathematical function it is that you have that can distinguish "real" random noise from "fake" random noise but I'd like to see it.

(I.e. if you can't see that this is mathematically impossible you will never correct your understanding).

[jimbob]

So if you run the uncompression algorithm on random noise you expect to get meaningful information?

Should you try some other algorithm, the compressed works of Shakespere could very well produce a random-seeming result. However we are talking about using a known decompression algorithm, and that is highly unlikely* to produce anything meaningful on a similar sized random stream of numbers.

There is implicit information within the random noise, which concerns the distribution of the random noise.



*The whole argument about monkeys and typewriters, and entropy can show this. A google search on Project Gutenberg, shows that the text when zipped is 2.15 Mb. Now this won't be perfect compression, but gives an idea, about 17 mbits.

Even if the compressed works were "only" 2 million bits long this is still 2^(2million) possible combintations. I feel confident in saying that that particular arrangement of bits won't happen by chance.

[cyborg]

So if you run the uncompression algorithm on random noise you expect to get meaningful information?

You haven't read this carefully: there is no "the" uncompression algorithm.

[Dancing David]

All use of antibiotics based upon pennecillin is accidental because the original discovery was accidental.

:D

[mijopaalmc]

All use of antibiotics based upon pennecillin is accidental because the original discovery was accidental.

:D

Your point?

[jimbob]

All use of antibiotics based upon pennecillin is accidental because the original discovery was accidental.

The use isn't accidental, but there was a sudden random alteration in the fitness landscape for certain disease-causing bacteria that occured as a consequence of the discovery of antibiotics and their subsequent use.

It isn't one of the best examples of evolutionary direction being altered by random events, but you could argue that it an example.

[jimbob]

So if you run the uncompression algorithm on random noise you expect to get meaningful information?

You haven't read this carefully: there is no "the" uncompression algorithm.


Er yes there is:

Look - the case of sequences with very few bits is both trivial and uninteresting for these purposes. Obviously we are not going to be able to decide whether 10 is a random sequence, as opposed to 01 or 11 for example. The interesting cases are sequences with many bits.

Yes they are trivial cases but this is simply about getting you to accept the principal of the thing and abandon the language trickery you have latched onto.

If you won't accept the trivialities then it's pointless dealing with larger cases.

Do you or do you not understand why it is invalid to pretend you have compressed information down to a single bit if you need to have that information represented in full in the algorithm for decompressing the data?

I don't understand why this disconnect is occuring: if I specify the algorithm:

1|print 101101110111000010110101011101001111010010100001

To compress:

101101110111000010110101011101001111010010100001

And then give it the input:

1

Then the number of bits I have encoded this sequence to is 49 at the very minimum - assuming no bits to describe the "print" part of the algorithm. I have gained absolutely nothing but shifting the input into the algorithm.

Shifting input into the algorithm DOES NOT WORK because we consider the complexity of the algorithm and input.

Algorithm AND input.

Nonsense. I've given you an algorithm, which I described in one short English sentence, which can compress any sequence - no matter how many bits it contains - down to one bit.

This?

EDIT - another one is an algorithm that just produces every possible sequence of increasing numbers of bits, like 0, 1, 00, 01 10, 11, 000, 001, 010, 011, 100, etc. Very easy to specify, and will produce any finite sequence.

And how do you propose to specify which sequence this algorithm is to produce without ending up back where you started?


Do you or do you not understand why it is invalid to pretend you have compressed information down to a single bit if you need to have that information represented in full in the algorithm for decompressing the data?

You have been arguing that you do know the decompression algorithm.

So if a randomly generated sequence of 2million bits was able to be compressed, even slightly, it wouldn't be random?

You need to reread any information theory lecture notes you have.



You can't predict what the next number in a random sequence will be.

If you can predict what the next set of numbers will be in a sequence then you don't need the sequence, so the information is redundant, this means that you can compress information until you can't predict what the numbers will be.

This does mean that perfectly compressed data is unpredictable. It does not mean that it is impossible to analyse a sequence of previously generated random data and compress it. There will be (random) patterns in the random data and these could be compressed.

[jimbob]

Dancing David, do you see my point that chance events do not only affect the selection of idividuals, but also the direction of evolution, and over long timescales, will mean that the direction of evolution has changed randomly?

[cyborg]

Er yes there is:

I cannot fathom why you have highlighted the parts you have - at all.

You have been arguing that you do know the decompression algorithm.

No - I've said that the information comprising the algorithm must be included with any input when declaring what any sequence is encoded to. That does not fix the behaviour of the algorithm.

It does not mean that it is impossible to analyse a sequence of previously generated random data and compress it. There will be (random) patterns in the random data and these could be compressed.

And you know that your random generator is random how now?

Oh right, it's because it generates random data... except when it doesn't. Then it's still random because it's a random generator. Because you said it is.

That's a big FAIL on grasping the point.

[jimbob]

And you know that your random generator is random how now?

Oh right, it's because it generates random data... except when it doesn't. Then it's still random because it's a random generator. Because you said it is.

That's a big FAIL on grasping the point.

Lottery machines, are probably sufficiently random due to the same chaotic equations for snooker balls. Number of counts of a geiger counter in a short-enough timeframe would also be random. You would have to use numbers generated by some physical sequence, but that isn't a coneceptual problem.

A simple analogy:

If a die is shaken two million times, it would not be surprising to see patterns in the results. These could be quite possibly compressed. Just because a number is generated by a random process, doesn't mean it can't be compressed. A sequence of one million sixes is just as likely (1:6^2million) as any other particular sequence; the order is important if you are turning the sequence into a single number.

[cyborg]

These could be quite possibly compressed.

You will inevitably have patterns - because a pattern can be as short as "11" or "00" etc...

You could even have really long runs. And they might be compressable.

But you have to deal with the entire sequence.

As the rule of thumb for compression is that for every increase in compression you can make in one area there will be another area which will decrease in the compression you can have. You can't get around the entropy of the sequence.

It is absolutely no good if there is a compressable sequence if compressing it requires you expand other sequences. This is why attempting to compress random sequences generally fails and it is the trap you have fallen into here.

[jimbob]

Here (http://foxmath.blogspot.com/2007/03/196-patterns-with-winzip.html) is a discussion about compression of random bitstreams:

Note that the random data is less compressible than the data which the author claims is nonrandom. However it is still compressible.

This whole discussion about whether compressible data is random or nopt has little bearing on the OP or the use of the term random in evolution.

I object to the term "nonrandom", which implies "inevitable".

Back to the OP:

Do you understand my point about chaotic systems having random outcomes over long timescales?

I have said that in stable environments, you might not need to discuss randomness, and the word "random" might be confusing; however I see no difficulty in simply saying the truth by adding the phrase "tend(s) to".

At first glance it seems reasonable to state that evolution doesn't need chaotic systems to work, however any implimentation that I can think of will have the replicators altering each other's fitness environment, i.e. there would be many positive feedback loops, so I'd think evoultionary systems would all be chaotic, although I am not certain.

Could you tell me how your approach is remotely helpful for discussing evolutionary history, it is more complex, and it doesn't reflect reality.

[cyborg]

I object to the term "nonrandom", which implies "inevitable".

This is your problem, not mine.

[jimbob]

And the rest of the post?

[articulett]

Why does "nonrandom" imply inevitable to you, jimbob, when it comes to evolution? Is a poker hand inevitable? You've already agreed that's it's akin to evolution as far as the first part being "random" and the second part (playing the game) being probabilistic.

We'd describe Poker by saying the cards are dealt randomly and then the outcome of the game is determined by how the game is played. We'd describe evolution by saying the mutations happen randomly, but the outcome is determined by natural selection. The details as to "how the game is played" , like the details of "natural selection", are more important than "probabilities" in conveying understanding of the process, right?

Why are you hearing something that isn't there in the description of evolution as given by the experts? You don't seem to hear it when we talk about Poker.

[cyborg]

And the rest of the post?

What would be the point?

[Walter Wayne]

Hi Walt, thanks for the response!

I will remind you that what you said was "It ain't evolution as we know it without mutation."

Now the deal is that alelle combinations and the control genes for growth can be very important in the variability of traits.

Hazel eye are caused by the combination of double dominant green with the dominant brown, blue is the double recessive. So green is double gree, hazel is green:brown , brown can be double brown or brown:blue.

The point being that regardless of the ontology of the variation, there can be and is variation that is not dependant upon mutation. Which is the point I was trying to make and the other two posters and perhaps you seem to want to ignore.
I am not ignoring those posters, I am disagreeing with them.

The variation you point to, how did that come about? Yes, natural selection will cause variation by changing the frequencies of alleles, and possibly new combinations of alleles. How ever, if the frequency of one particular allele is 0, it will remain there.

Evolution, as we know it, not only explains such things as the different breeds of dog. In is the uniting factor of biology, it describes how we are related to the platypus and every other organism. Evolution without mutation does not explain the descent from prokaryote to all the species today. In others, evolution without mutation is not evolution as we know it.

Walt

[jimbob]

Indeed, Walter Wayne, Without mutation, multicellular organisms wouldn't have arisn. (Actually given the chemistry of DNA and RNA, it would also be impossible for there to have been no mutation).

Why does "nonrandom" imply inevitable to you, jimbob, when it comes to evolution? Is a poker hand inevitable? You've already agreed that's it's akin to evolution as far as the first part being "random" and the second part (playing the game) being probabilistic.

A better analogy might be a game maybe akin to dungeons and dragons, where the traits modulate how lucky an organism needs to be to reproduce. That is still a poor analogy, but getting closer.

A game of poker, where every so often (very rarely) the rules change slightly, so different hands are strong, and where sometimes weak hands can beat strong ones...


We'd describe Poker by saying the cards are dealt randomly and then the outcome of the game is determined by how the game is played. We'd describe evolution by saying the mutations happen randomly, but the outcome is determined by natural selection. The details as to "how the game is played" , like the details of "natural selection", are more important than "probabilities" in conveying understanding of the process, right?

Fair enough, but I am pointing out that natural selection is probabilistic, i.e. an organism could seem "fit" but fail to reproduce due to bad luck (a gust of wind at the wrong time). It makes little sense to claim that that organism wasn't really "fit" because that doesn't really agree with observation.

A real example:


Barn Owls could have (say) 12 chicks per parent.
In some areas the population of barn owls is stable.
This means that on average, one offspring per parent reproduces.
Most owlets will be similar to their parents.

I would argue that once you have removed "runts" or other grossly unfit owlets, most would be fairly similar, so an "average" owlet might have (say) a 10% chance of reproducing.

This means that any individual beneficial trait is unlikely to spread. However, over the entire population, some will do so. It also means that deleterious traits are likely to die out very quickly. A 10 % increase in "fitness" gives an 11% chance of reproducing, whilst a 10% decrease gives a 9% chance of reproducing.

Chance is more important in determining which owlets survive than subtle differences in traits. That doesn't mean that you can't assess which traits are beneficial, but at that level of detail, you need a probabilistic treatment of natural selection.


How do you describe what, "a selective pressure of as little as 1:1000" actually means without invoking probabilities?

Again, I wonder if this is a semantic difference over the worrd "random".

I think it is misleading to describe any chaotic system as "nonrandom", as over long enough timescales the behaviour is random.

Evolutionary algorithms can have a nonrandom selection, and are good examples for describing how powerful evolutionis. However, as soon as you are dealing with biological evolution (or indeed imperfect self-replication*) there are multiple feedback loops and the system is almost certainly chaotic, which will certainly be random over long timescales.


*e.g. biological evolution.

[articulett]

The way you describe it sounds muddled... the same way it sounds muddle to say that Poker is played probabilistically. It's not wrong. It's just that the information you are conveying with your continual need to focus on probabilities in evolution is equally as misleading and uninformative as focusing on such in regards to explaining what poker is.

Yes, probabilities are involved... but ... your focus there makes you fail at conveying useful meaning. I imagine you'd be equally as maddening if you were trying to teach Poker to people and kept saying-- "it's random, because it's based on probabilities because you can never tell how a hand will be played and the same hands can be played different ways".

You truly are that vague and muddled sounding on a much more important topic than Poker... and you are muddled in a way that makes you sound more like Behe than the experts who teach the concept to many.

[jimbob]

What is muddled about the barn-owl example?


Barn Owls could have (say) 12 chicks per parent.
In some areas the population of barn owls is stable.
This means that on average, one offspring per parent reproduces.
Most owlets will be similar to their parents.

I would argue that once you have removed "runts" or other grossly unfit owlets, most would be fairly similar, so an "average" owlet might have (say) a 10% chance of reproducing.

This means that any individual beneficial trait is unlikely to spread. However, over the entire population, some will do so. It also means that deleterious traits are likely to die out very quickly. A 10 % increase in "fitness" gives an 11% chance of reproducing, whilst a 10% decrease gives a 9% chance of reproducing.

Chance is more important in determining which owlets survive than subtle differences in traits. That doesn't mean that you can't assess which traits are beneficial, but at that level of detail, you need a probabilistic treatment of natural selection.

Especially the point that "Chance is more important in determining which owlets survive than subtle differences in traits."

Do you agree or disagree with this statement?

ETA:

How do you describe what, "a selective pressure of as little as 1:1000" actually means without invoking probabilities?

[articulett]

Why do you need to when discussing evolution... it's the aggregate of beneficial traits multiplied exponentially over time that matters to the equation... just like winning multiple poker hands makes someone a winner--

The DNA that gets itself copied the most--whatever the reasons-- determinisn, chance, or something you wouldn't call either-- are the winners in evolution. Coding for life forms that are fecund is a pretty good strategy as far as DNA getting copied. Inserting your DNA into a vector works well for ervs. There's a whole bunch of techniques that have evolved, because THEY COULD... and they success was self replicating...

You just seem to always want to jump into the middle of specific example in order to call evolution random or probabilistic. Your owl example doesn't describe evolution... it illustrates (in a sort of muddy way )that there are selective pressures that humans might consider random... but those selection pressures ("random" or not) still determine who will go on to the next round. The selection process (no matter how it happens) culls from the pool of randomness. To confuse it with the pool of randomness makes you sound like someone who would describe playing poker using a barn owl population growth analogy.

Your need to describe things in terms of possibilities makes it so that you are only making sense in your head. To everyone else, you are saying a muddled mouthful of nothingness and confusing the definition or model for a specific example, therein.

If someone asked you what a grocery store is-- you wouldn't bend over back wards to make sure you used "random" or "probability" in the descriptor. You wouldn't focus on probabilities... you wouldn't describe a single example as though that was "the descriptor" (rather than "an example") of grocery stores.

Yet, for evolution, you just keep going on the same loop. Why? You make those exact errors (or whatever you want to call them) in your description. It's not "wrong". But who would insist on telling people what Poker or Grocery Stores or what anything is by insisting on defining it in regards to probability??? Why must you?

Creationists do this for evolution so that they can pretend that scientists think that "this all came about by chance"-- the 747 straw man. I really don't know why you keep doing it. But I find it bizarre, to say the least. It's like Mijo. Maybe someone somewhere understands you and your motivation or thinks you are clear. I'm pretty sure that I'm describing what I hear from you the way most experts on the subject would.

Why would someone insist on describing evolution the way known creationists are known to muddle? Why would they continually prefer such an explanation when the experts who have taught many have provided such eloquent examples?

[Beerina]

Here is a thread to discuss how the word "random" applies, or does not apply, to the Theory of Evolution, depending on how you define the word, and stuff like that.

Your thoughts?

"Random" is mis-used by anti-evolutionists to suggest rearranging a bunch of atoms or molecules randomly, and, boing! Out pops a frog or bird or human.

Which, of course, is statistically rediculous.


With respect to evolution, there are several areas of "randomness". But first, what does "randomness" buy for evolution?

It buys a way to alter the organism, which may be beneficial in the environment (whether the environment is changing or not), or detrimental, or completely and rapidly deadly as some defect, like a hole in the heart.

In more mathematical terms, think of the organism as being like a point on a flat sheet with dimples and mountains in it. It's similar to those demonstrations of gravity and black holes with huge dents in it that the steel ball rolls around and around and down into. The point on that grid for the organism corresponds to its current set of features as it developed and lived its life.

When the organism has a child that's different, it's like another point a little bit away from the first point. It may be nearer a hill or nearer a valley. We will assume for now a hill is a good development and a valley a bad one.

So if the new point is on a hill, it will probably survive slightly better, and thus have more children, also near to it, some even further up the hill. And those children have even more, based on how far they are up the hill. Soon the average of the whole population is centered around the top of the hill.

If it's further down a valley, it has a harder time surviving and reproducing, and thus fewer children, and thus less impact on future generations.


So far so good.

Now back to randomness. The "randomness" of an adaptation would correspond roughly to how far a child's point might be from its parent's on this hill-and-mountain grid plane.


There are several kinds of random changes:

1. Chemical errors caused by molecules like those in DNA not splitting and recombining "properly". This is a physical system after all, and **** happens.

2. Errors due to radiation that causes #1, or, even worse, causes an atom of one element to spontaneously transform to an atom of another, throwing off the DNA chemistry.

3. Sexual reproduction -- swapping of DNA slices between two successful organisms. Certain aspects are randomized in a very structured way, such as this or that bone length, other features, chemistry of the liver, etc.


The first two "random" changes are fairly rare, and also are probably far more likely to generate a seriously disabled or stillborn child when they do occur. As such, they would move the population's average point across that hill-and-valley plane much more slowly.

The last, sexual reproduction (which itself evolved) can scour this plane far, far more quickly. "Slightly taller, slightly smaller, slightly different chemistry, etc." can make noticeable and rapid changes that impact successful reproduction much more quickly. This is why humans could turn wolves into a hundred breeds of cutie-pie dogs in a few thousand years, or grass and berries into corn and tomatoes, for that matter.


In summary, "randomness" in evolution means the rate at which the species scours this "hill and valley" plane through the generations. There are several ways to introduce change into the next generation, with sexual reproduction scouring this grid plane far faster than old-school random mutations (which creationists misuse, suggesting it's the only thing at work).

The development of intelligence allows even faster scouring of this space as it added immensly to the survival capacity of species. It invents treatments and cures that shift the survival "point" up the hill, away from where the pure DNA would suggest the child organism should be.

And human-level intelligence, when it gets around to inventing custom-designed genes, will turn the speed of scouring into a rocket. We will be able to directly set the point of the next "child" wherever we like.

[jimbob]

Why do you need to when discussing evolution... it's the aggregate of beneficial traits multiplied exponentially over time that matters to the equation... just like winning multiple poker hands makes someone a winner--

The DNA that gets itself copied the most--whatever the reasons-- determinisn, chance, or something you wouldn't call either-- are the winners in evolution. Coding for life forms that are fecund is a pretty good strategy as far as DNA getting copied. Inserting your DNA into a vector works well for ervs. There's a whole bunch of techniques that have evolved, because THEY COULD... and they success was self replicating...

The OP was when it was valid to talk about randomness in discussing evolution.

I contend that my barn-owl example above is a perfectly valid area of discussion, and a situation where a probabilistic treatment is appropriate.


You just seem to always want to jump into the middle of specific example in order to call evolution random or probabilistic. Your owl example doesn't describe evolution... it illustrates (in a sort of muddy way )that there are selective pressures that humans might consider random... but those selection pressures ("random" or not) still determine who will go on to the next round. The selection process (no matter how it happens) culls from the pool of randomness. To confuse it with the pool of randomness makes you sound like someone who would describe playing poker using a barn owl population growth analogy.

Firstly the barn owl example was an example, not an analogy. This is an important difference. The example was a description of how natural selection actually works in practice.

I apologise for sounding slightly rude here, but this is where I suspect there is a slight cultural difference.

To me, "the pool of randomness" sounds unclear and muddy. As I said before, and with the numerical examples, to illustrate this, there is a differnce between the "type of randomness" in mutation and natural selection. I wouldn't describe natural selection as hapazard, but would be happy to describe mutation as haphazard. I also wouldn't describe mutation as probabilistic, because "haphazard", conveys a slightly different nuance.


As you are probably aware, I am a physicist by training and an engineer by profession. There are manu aspects of the device development that require statistical treatments of the results (chip-yields being the obvious one).

Putting numbers on scenerios and working out the implications is one thing that most engineers are particularly happy with; in fact I would say it is one of the most important aspects to "thinking like an engineer" (some engineers mightn't do this, but then they should consider a different career).

To me, and other people with a background in physical sciences, the numbers are not muddy; indeed, an appropriate quantitive treatment is superior to a qualitative treatment by virtue of describing the system more fully, and simply.

Of course this only works in a situation where people are happy using numbers in this manner, but I would contend that the opposite approach (which you seem to be happier with) hides important aspects, as you are either forced into inaccurate generalisations, or very long explanations.


Your need to describe things in terms of possibilities makes it so that you are only making sense in your head. To everyone else, you are saying a muddled mouthful of nothingness and confusing the definition or model for a specific example, therein.

To you maybe, but I doubt that other people find this so confusing.

It is one example, but this is simply an illustration of the general principle. If you work through the numbers, you find that this is the situation for the vast majority of organisms in the vast majority of situations. The numbers might be different, but I think that there is an important conclusion that can be drawn.

This is that: With the exception of 'abnormal' offspring, differences in fitness are less important than chance in determining which individual organisms actually reproduce. Overall in the population, 'unfit traits' will vanish quickly, and some 'fit traits' will proliferate, but many 'fit traits' will fail, simply due to chance. .

Further to that, if you are talking about stable ecosystems, and moderate timescales, with suitable populations, you can then ignore randomness, as organisms will evolve that are adapted to their envitronment. You can even make statements that particular adaptations will tend to evolve in particular enviornments. Again without mentioning randomness. However This is only one part of evolution.

Over long timescales, the chaotic nature of the ecosystem will begin to have an effect, and the selective pressures, i.e. the direction of evolution will be subject to random change.



If someone asked you what a grocery store is-- you wouldn't bend over back wards to make sure you used "random" or "probability" in the descriptor. You wouldn't focus on probabilities... you wouldn't describe a single example as though that was "the descriptor" (rather than "an example") of grocery stores.

Yet, for evolution, you just keep going on the same loop. Why? You make those exact errors (or whatever you want to call them) in your description. It's not "wrong". But who would insist on telling people what Poker or Grocery Stores or what anything is by insisting on defining it in regards to probability??? Why must you?

I am not sure what you are gatting at here, I really can't see where I have made any "errors", or how you can avoid a probabilistic treatment.

Both Dawkins and Maynard Smith write about "selective advantage" and quantify them. How do you use a selective advantage of 1:1000 without a probabilistic tratment?

I'm sorry if you did answer this question, buyt I can't actually see it anywhere.

Maybe suitable for a primary-school explanation


Creationists do this for evolution so that they can pretend that scientists think that "this all came about by chance"-- the 747 straw man. I really don't know why you keep doing it. But I find it bizarre, to say the least. It's like Mijo. Maybe someone somewhere understands you and your motivation or thinks you are clear. I'm pretty sure that I'm describing what I hear from you the way most experts on the subject would.

Why would someone insist on describing evolution the way known creationists are known to muddle? Why would they continually prefer such an explanation when the experts who have taught many have provided such eloquent examples?

You have equated technological development to evolution, which is what Dembski is in favour of. Please show me a creationist using my arguments.

Why would someone insist on describing evolution the way known creationists are known to muddle?

[articulett]

No Jimbob... I think I'm bowing out... you are impenetrable.

Yes, I was very clear... as is Dawkins and many experts I quoted on how the evolution of technology, design, language, etc. is akin to evolution of genomes... they are both information systems that are copied in units that are then modified such that the whole "evolves" over time--the environment selects (DETERMINES) what "memes" evolve over time... whether those memes are airplane designs, computer languages, or technological advances. Cyborg understand me. Dawkins uses the terminology. My students understand. I find them all clearer on the subject and brighter than you. This is NOT what Dembski says and repeating that he does over and over along with his muddled quote on the subject is only convincing you. No one but you thinks Dembski is saying what I have said. All the experts understand well what I am talking about. As do most of the forum members here. I'm not making stuff up... I am quoting those who taught me-- who teach others... who understand the subject. You are pulling stuff out of your ass and pretending to have expertise. And multiple people have called you on it.

Like Earthborn, and Mijo, please don't "sum up" what you think I'm saying. My words speak quite well for themselves. And your straw men sound like all your explanations... muddled and imagining expertise that no one but you seems to see-- and unfixable, to boot. You don't understand my words. So don't paraphrase them and assume you've understood and that you are explaining something to someone else. We've not shown that you have any special ability at explaining, understanding, nor analogies-- have we? As far as I can tell, your expertise on these subjects is in your head.

You are mad at me... but I and cyborg and many have spent a lot of careful detailed time trying to show you where you are muddled sounding and why you sound like Behe and why the experts are so much clearer than you... and why your summation of what others are saying is wrong-- stupid, even... misleading... just like your description of evolution. You can fix it... but as far as I can tell no one but you thinks you are clearer or making more sense than the actual experts--which have been oft quoted-- yet you never really read them.

And yet you read and quote Demski and imagine that he's making sense and that he's saying what I'm saying. HMMM....

Does anyone other than Mijo share this delusion of yours? Just curious. I think I'll stick with the actual experts. They seem so much smarter, comprehensible, and even more humble than you. I don't care what your job is or your imagined expertise. You suck at explaining and describing evolution. You don't seem to really understand it. My high school students could probably explain it much more clearly than you. Yes probabilities matter-- but stick to the way the experts describe things... I've quoted multiple experts. I've also quoted Behe. I can't imagine why one would prefer to sound so much like the latter than the former and your semantics and tangents haven't clarified. WHO are you clearer to-- about what exactly?

You get to win (in your head) as always--by getting the last word. But it still doesn't make you clear, right, or educable on the subject. --And you go back on my ignore list, because you fling straw men and play that self serving ego building game where you are winning points in a conversation that no one but you seems to be having or understanding. I don't know how to fix that. I don't think it is fixable. I just think you and Mijo (and few others) have a need to get the last word and that last word must be on par with Behe's description of evolution as "random" or "scientists think this all came about randomly".

I'd wonder if the problem was me, but this is such a character trait of creationists who pretend they are not creationists, that I"m more than certain the problem is you. And I have yet to see anyone who has this random fixation as strong as Behe (and you do) change.

[jimbob]

Articulett I am going to respond to your post, because you obviously were addressing comments at me.

Unlike you, I have never claimed to be an expert, simply numerate. Most of your posts seem to contain allusions to what other people say, but precious few actual arguments, or detailed rebuttals of points.

Here is an example of your muddled thinking, part of the post is hidden for ease of reading. You don't seem to grasp the fundamental difference between Darwinian evolution as occurs in biology, and colloquial use of the word "evolution" in everyday speach.


Jim-Bob...
in the nozzle example--you could have weird artifacts or stupid engineers that occasionally through out models that were better and it would change nothing about the definition...the evolution...what evolution is. You are using these kinds of examples to say that selection is "probabalistic" or non-random... Do you understand how these examples are tangential to the definition as to what IS going on... moreover... this doesn't mean they've come up with the best possible design or that one of the one's they discarded might have something that worked better somewhere along the evolutionary process had they kept it. You and mijo are confusing this sort of tangential detail so that you can define evolution as random. Whether it's the nozzle or the life form--it's evolving based on information that has proven successful before. That's it. Cities evolve...everyone who comes through it is involved in the design...the people who settled first have no idea what will evolve--the people adding homes or business or communities are building on what has evolved up to the present. Obsolete buildings are destroyed. Roads are widened. Cell phone towers are added. No single person is more complex than the city itself just as no single person is more complex than the internet.
Both evolve based on what is there to build upon...what worked before...what "stuck around"... all participants are designers of the evolving entity.

All life forms today are the result of eons of successful reproductions. All ecosystems today are the result of unplanned co-evolving of environment and the organisms that inhabit them. As much as you might think people are designing things like Jet fighters--they aren't designing them from scratch--they are using info. that worked before and recombining it or altering it to see if something better results. INFORMATION...changes "randomly"--the results are then culled so that the best (or luckiest, or prickliest, or worst tasting, or most anti-biotic resistant, or horniest, or most useful) survive.

All human knowledge has evolved on knowledge accumulated by humans past and present. All life forms have evolved based on accumulated information of histories "successes".

In case you miss the fundamental difference: cities do not "evolve" in the darwinian sense.

Not all iterative development processes are evolution.

I think I was getting you and Cyborg muddled up, he said that aircraft designs evolve. You said that cities evolve.

Nope. Aircraft do not evolve. They sit around or they get flown around.

Aircraft designs are a different matter.

If anything, classical design techniques (i.e. not using evolutionary algrithms) might have some common features with lamarckian evolution, but this is a theory of evolution that was discredited by darwinian evolution. It is pretty poor to pretend that this is similar to biological evolution.

[jimbob]

You get to win (in your head) as always--by getting the last word. But it still doesn't make you clear, right, or educable on the subject. --And you go back on my ignore list, because you fling straw men and play that self serving ego building game where you are winning points in a conversation that no one but you seems to be having or understanding. I don't know how to fix that. I don't think it is fixable. I just think you and Mijo (and few others) have a need to get the last word and that last word must be on par with Behe's description of evolution as "random" or "scientists think this all came about randomly".

I'd wonder if the problem was me, but this is such a character trait of creationists who pretend they are not creationists, that I"m more than certain the problem is you. And I have yet to see anyone who has this random fixation as strong as Behe (and you do) change.


The same could be said of you with more justification:

"I am going to direct this post at and say that I am putting you on ignore, so in my head I do have the last word"

I also mentioned Dembski, bacause I got a little bored of your insinuating (without evidence) that I sounded like Behe. Whilst you have talked about the "evolution" of manmade artifacts (cities) and Dembski talks about "technological evolution".

[cyborg]

I still don't think you know what Lamarckian evolution is - it isn't the "opposite" of Darwinian evolution in that it is somehow "directed" by "non-randomness," rather the idea was that morphogenic change in an individual was inheritable - i.e. if you change your body by working out then the improvements you've made to your body are heritable traits.

[jimbob]

The organism changed in response to the environment and this change was transmitted to its offspring.

The giraffe wanted to reach high up branches, so it stretched its neck so its offspring had longer necks.

The prototype aircraft showed weakness in part of its fusalage, so the next design iteration was strengthened in this area.

Completely unlike darwinian evolution.

Evolutionary algorithms, however do have similarities.

[cyborg]

The organism changed in response to the environment and this change was transmitted to its offspring.

Completely unlike darwinian evolution.

Well no actually - it is not "completely" unlike darwinian evolution. Change "organism" for "population" and "its" for "their".

Evolutionary algorithms, however do have similarities.

Except that the determinism of the algorithm constructs a fatalistic scenario that makes you uncomfortable right?

[jimbob]

The organism changed in response to the environment and this change was transmitted to its offspring.

Completely unlike darwinian evolution.

Well no actually - it is not "completely" unlike darwinian evolution. Change "organism" for "population" and "its" for "their".

Why is this valid?


Evolutionary algorithms, however do have similarities.

Except that the determinism of the algorithm constructs a fatalistic scenario that makes you uncomfortable right?
That is one of the diffeerences, however there are also obvious similarities that are lacking in classical design with "intelligently directed" alterations.

When you debug a computer programme, do you randomly change the code, or do you look at the errors and try to work out what you need to change, and how?


An evolutionary algorithm would make random alterations and breed from the code examples that performed closest to the requirements. This is obviously closer to darwinian evolution than classical design methodologies, but it isn't darwinian evolution, as it the selection criteria have been intelligently chosen so that the result is something that meets the predefined performance requirements.

With imperfect self-replication, where the imperfection is random, darwininan evolution will follow. Also the offspring of the replicators will alter the fitness landscape for the other replicators, so there are complex feedback loops, and the fitness landscape is will be chaotic. In other words it could well be stable for long periods of time, but will be subject to random changes.

This is what happens in evolution, and is inherent in any system of imperfect self-replicaton with the imperfections being random.

"Chaotic" is probably a better word than random, but chaotic systems are random over long enough timescales.

[cyborg]

Why is this valid?

Why isn't it?

When you debug a computer programme, do you randomly change the code, or do you look at the errors and try to work out what you need to change, and how?

Straw man noted.

the selection criteria have been intelligently chosen so that the result is something that meets the predefined performance requirements.

YES OR NO:

Selection criteria must be intelligently chosen.

This is what happens in evolution, and is inherent in any system of imperfect self-replicaton with the imperfections being random.

Well no - because as you've refused to acknowledge for metaphysical rather than mathematical reasons the "randomness" of the "imperfections" is totally irrelevant to the behaviour of the system.

"Chaotic" is probably a better word than random, but chaotic systems are random over long enough timescales.

I see for you "random" is a synonym for "not fatalistic" - even when the mathematics demands otherwise.

[articulett]

genomes are equivalent to other forms of information in regards to the analogy-- whether computer code, product design, or technological specifications... phenotypes compete in the environment as do other products of information whereby the ones that are best at getting their information copied (per whatever reasons) have information that gets to evolve and code for future "designs".

What evolves is determined by the information that gets copied the most. Who cares if the information changes randomly or purposefully or some weird combination of both or through artificial selection or asteroids or radiation or floods? The resulting products can only be selected by the surviving and best replicating information--whether it's DNA or qwerty keyboard designs.

Jimbob is ever confusing the code for the thing it codes for. In Lamarkian evolution, Giraffes would somehow "know" to grow longer necks... that's how it looks to humans... but what happens is that those without longer necks don't produce as many offspring compared to their longer necked herd members who have a competition advantage in food acquisition and mating opportunities-- and thus more opportunities to pass on those longer necked genes as well as subsequent neck lengthening mutations.

Lamarkian evolution would be if you tricked an airplane in a way and airplanes began to start appearing with those traits even though nothing or no one selected for tweaks to the design specifications so that they could appear with those traits.

A species dies the same species they are born. Some or all of their genomic information may be copied and tweaked in the process... it may be copied a little or a lot-- the more it's copied, the greater the chance for that copied bit of information to become a part of an evolving species or organism. This is true with language, airplane designs, computer languages, computer programs, etc. When it comes to copying things other than genes, humans are the replicators and the "mutators" and the selectors for the most part-- We evolved brains that evolved to be information users.

In my opinion, religion and creationism hijack these tendencies to spread themselves (the information that makes up the "belief system")... just like gonorrhea harnesses the human sex drive to spread itself (the information in it's genes).

It sterilizes their vectors so they can't copy their own genes/memes-- instead they are stuck propagating the info. in the clever interloper.

(my clarification is for anyone who actually wants to know what Jim is referring to regarding his straw man interpretation of my views... I don't think Jim is really communicating with anyone however... his expertise on the subject appears to exist entirely in his head.)

[jimbob]

The organism changed in response to the environment and this change was transmitted to its offspring.

Completely unlike darwinian evolution.

Well no actually - it is not "completely" unlike darwinian evolution. Change "organism" for "population" and "its" for "their".


Why is this valid?
Why isn't it?
Because you changed the mechanism.

[cyborg]

Because you changed the mechanism.

No, I changed the plurarity.

[jimbob]

Why is this valid?

Why isn't it?

When you debug a computer programme, do you randomly change the code, or do you look at the errors and try to work out what you need to change, and how?

Straw man noted.

How is that a straw man: I am arguing that technological development is not a good analogy for darwinina evolution because the mechanisms are significantly different. The example is an example of how this differs from an evolutionary approach in a particular field of technical development. I could have chosen many others but it was not a weakened or absurd statement of your argument, but an example where the tow processes differ.

the selection criteria have been intelligently chosen so that the result is something that meets the predefined performance requirements.

YES OR NO:

Selection criteria must be intelligently chosen.

Yes, that was my point. In evolutionary algorithms there are intelligently chosen selection criteria. In darwinian evolution there are no externally applied selection criteria, simply success or failure in reproduction (or self-replication).

This is what happens in evolution, and is inherent in any system of imperfect self-replicaton with the imperfections being random.

Well no - because as you've refused to acknowledge for metaphysical rather than mathematical reasons the "randomness" of the "imperfections" is totally irrelevant to the behaviour of the system.

"Chaotic" is probably a better word than random, but chaotic systems are random over long enough timescales.

I see for you "random" is a synonym for "not fatalistic" - even when the mathematics demands otherwise.

I don't really understand your point here:

The compressed works of Shakespere are no more nor less random than the uncompressed works. A process where the outcome is significantly altered by random events is random.

[Wowbagger]

If we accept evolution as a chaotic system, like the weather, I am willing to agree that the word "random", when defined appropriately in the context of chaotic systems, is another valid usage of the word.

Trying to read through Jimbob's posts, he may or may not have described everything effectively. But, does anyone generally disagree with the above statement?

[cyborg]

Yes, that was my point. In evolutionary algorithms there are intelligently chosen selection criteria

You didn't answer my question.

YES OR NO:

Selection criteria must be intelligently chosen.

[jimbob]

This is a derail, but you seem quite insistent, even though this has been covered before.

In technological development not biological evolution, if you want to use a genetic algorithm to develop something useful, then you need to
impose a set of selection criteria so that the result meets the requirement specifications.

You could use an evolutionary algorithm to choose what the requirements are, however all you are doing is shifting your choice of selection criteria, as you then need to decide on the criteria for the original evolutionary algorithm.

So in any realistic example of technological development that I can think of, you do need to assign selection criteria, or you will not have an evolutionary algorithm.

In biological evolution this is not the case. If a self-replicating system manages to self-replicate, then it is obviously adequately adapted to its environment. It has "passed" the "selection test". This is all that natural selection is. A self-replicating system that fails to replicate will not produce any descendants to evolve further.

Simple application of Malthusian reasoning will show that self-replicating systems are going to be subject to natural selection, as, if nothing else limits their population growth, they will eventually be limited by resources. If the self-replication is imperfect, then the variants that are "fitter" will thrive at the expense of those that are less well-adapted. This is not just akin to Darwinian evolution, it is Darwinian evolution.

I have answered your question several times, now are you going to answer mine about how the phrase "a selective advantage of 1:1000" is not part of a probabilistic treatment of natural selection?

[cyborg]

You could use an evolutionary algorithm to choose what the requirements are,

I could use many, many things: is it necessary that they are all of intelligent design?

I have answered your question several times,

No you have not - you've answered the question you want to answer.

now are you going to answer mine about how the phrase "a selective advantage of 1:1000" is not part of a probabilistic treatment of natural selection?

No I am not because it is a probabilsitic treatment of natural selection.

The emphasis is on "treatment". The emphasis is on knowing the difference between a model and the thing it is modelling. You seem to insist you can know the difference or that it is even meaningful.

[zosima]

If we accept evolution as a chaotic system, like the weather, I am willing to agree that the word "random", when defined appropriately in the context of chaotic systems, is another valid usage of the word.

Trying to read through Jimbob's posts, he may or may not have described everything effectively. But, does anyone generally disagree with the above statement?

Chaotic systems are systems that can often appear random, but are actually deterministic. Or in other words, they are only as random as their inputs. In fact many chaotic are incredibly orderly. For example:
http://www.wolframscience.com/nksonline/page-151

In example (d) Wolfram demonstrates a shift map, which demonstrates chaotic behavior despite being a very simple operation. So it is wrong to say chaotic systems are random, it might be reasonable to say chaotic systems appear random. This means that what the "evolution is random" argument comes down to(if evolution is chaotic) is whether the initial conditions are random.

Also a definition from upenn physics
http://www.physics.upenn.edu/courses/gladney/mathphys/subsection3_2_5.html
We state that systems are chaotic if they:
1. are deterministic through description by mathematical rules.
2. have mathematical descriptions which are nonlinear in some way.

The evolution is random people generally like to note that biological/ecological systems are complex, perform a bait and switch over to evolution is chaotic. If they don't stop there with the chaos = random, they'll say "of course the initial conditions were random because quantum interactions are probabilistic". Of course this is the probability to random bait and switch, but even if we buy that probabilistic systems are random, this doesn't mean that the system is necessarily sensitive to quantum randomness. Quantum fluctuations cancel out on macroscopic levels, leading to the orderly laws that scientists thought were the whole story for many years. In other words, The tendency to magnify disorder in an input can only do so up to the resolution of the input and there is absolutely no reason to think the resolution will be that high.

Of course I don't even think there is strong evidence that evolution is chaotic. If we look at the evidence and listen to the experts, it seems the story is the process and path of evolution is orderly and regular, but that it has a long history and has been subject to a lot of external pressures. This makes for complex results.

[Wowbagger]

Chaotic systems are systems that can often appear random, If something appears to be random, it could be a handy shortcut to just call it "random", when such shortcuts are acceptable.

The sun does not literally rise in the sky, it only appears that way, and yet we can say "sunrise" as a handy shortcut.

[articulett]

yeah... but Mijo and jimbob are pretending they are being "more accurate"-- not taking verbal shortcuts to best sum up a phenomena.

[mijopaalmc]

yeah... but Mijo and jimbob are pretending they are being "more accurate"-- not taking verbal shortcuts to best sum up a phenomena.

But you haven't actually provided any evidence that the reasons you say that evolution is non-random actually arise from an underlying non-random. Instead, you have equivocated as to your usage of "determine" and "determined" in such a way that every process described by a well-defined set of rules becomes non-random.

[zosima]

@Mijo
I'm confused as to why you think the burden of proof would fall upon the people claiming that evolution is non-random. Articulett has really hammered home the fact that the scientific community of evolutionary biologists considers evolution non-random.

Beyond that ,all the science that evolution is dependent upon involves laws that are uniform, predictable, and regular. Even on the smallest level biological systems are incredibly reliable. Individual cells survive for 10s or 100s of years without malfunction. Viruses, much smaller than cells, reliably invade cells and modify their behavior predictably.

These points alone should establish a burden for you to provide evidence and/or a well-reasoned and clear argument as to why we shouldn't accept the opinions of the authorities on the subject; authorities who happen to be much better educated on and much more familiar with this topic than any of us. You'll have to show us why we should disregard the intuition that the reliability of biological systems makes them appear mechanistic;rule-abiding;non-random.

Beyond that, insisting that evolution is random, despite the weight of evidence, is tantamount to Hume's argument against induction; that the 1001st duck could always be black. A belief that chafes against the fundamental underpinnings of logic.

If you want to make a point that persuades then you'll have to show how evolution and its results are random and not merely complex.

I outlined one such argument, that I would find persuasive, in my previous post. If you can prove that evolution is a chaotic process that takes a random input, I would be persuaded.

[zosima]

Mijo:
To extend on my point about random processes and chaos,

We've seen an example of a non-chaotic process that is dependent upon random inputs; the smoke detector. A system with microscopic components that have random behavior that is significant to the behavior of the system as a whole, but which does not have random macroscopic behavior.

Why not explain how evolution is somehow different than the smoke detector? That would be more persuasive than insisting that the smoke detector is random.

[mijopaalmc]

zosima-

I have already explained that evolution and the smoke detector are identical situations. A random process leads to orderly behavior over long periods of time. This however does not mean that radioactive decay is not a random process. Similarly, just because the aggregate processes of evolution such as mutation and natural selection have the orderly results we observe in evolution does not mean that mutation or natural selection are not themselves as individual processes are not random.

[Dancing David]

The recent use of antibiotics to treat people with septic infections is accidental because the discovery of penecillin is accidental.

[articulett]

Seatbelts saving lives in accidents is random because you can't predict before hand whether a seat belt will save your life or harm it or do neither.

Seatbelts saving lives in accidents is random, because accidents are random and accidental.

I can speak in creationist doublespeak too.

(Having random components does not a random process make.)

[zosima]

zosima-

I have already explained that evolution and the smoke detector are identical situations. A random process leads to orderly behavior over long periods of time. This however does not mean that radioactive decay is not a random process. Similarly, just because the aggregate processes of evolution such as mutation and natural selection have the orderly results we observe in evolution does not mean that mutation or natural selection are not themselves as individual processes are not random.

Okay, I suppose you could continue to insist the smoke detector is random and persuade no one. Thats cool too. Have fun with that. :D

[mijopaalmc]

Okay, I suppose you could continue to insist the smoke detector is random and persuade no one. Thats cool too. Have fun with that. :D

But I am not saying that the operation of an ionization smoke detector is random; I am saying that the operation of an ionization smoke detector is orderly and based on random events. Similarly, evolution itself is orderly but natural selection and mutation are random.

Non-random simply implies that evolution is a deterministic process, a phenomenon which has never been observed.

[Earthborn]

(Having random components does not a random process make.)What does make a process random?

[mijopaalmc]

What does make a process random?

Yeah...it doesn't sound like she (or perhaps anyone who is arguing that evolution is nonrandom) thinks that random processes can have orderly results.

[zosima]

Yeah...it doesn't sound like she (or perhaps anyone who is arguing that evolution is nonrandom) thinks that random processes can have orderly results.

From wikitionary:
Statistical Randomness:
"the property of a numeric sequence of containing no recognizable patterns or regularities; exemplified in the results of an ideal die roll."

Or as I mentioned many posts ago: uncorrelated and uniformly distributed.

A smoke detector is a non-random system that takes a random input(or inputs more accurately). For all intents and purposes it is deterministic.

As there are recognizable patterns and regularities, it is clear that evolution, even individual selections in evolution are non-random. The more interesting argument that some people have been having with Jimbob, is whether evolution is deterministic or not. Which I think has fair arguments on both sides.

The mistake you seem to be making, over and over and over, again, is to assume that because you think evolution is not-deterministic that this implies that evolution is random.

This is a common mistake made in introductory logic classes.
If X->~Y this does not mean that ~X->Y
Above: Let X mean deterministic and Y mean random.

If a system is deterministic it is not random, but if a system is not deterministic it is not necessarily random.

(more commonly this fallacy is stated X->Y does not imply that ~X->~Y)

[Earthborn]

From wikitionary:
Statistical Randomness:
"the property of a numeric sequence of containing no recognizable patterns or regularities; exemplified in the results of an ideal die roll."You may have noticed that I ask what a random process is. A process may produce a numeric sequence, but it is not the same thing as a numeric sequence.

[articulett]

There really aren't such things as random processes... stochastic processes which contain random inputs are sometimes called "random processes"-- but it's not the process itself that is random. The fact that something is a "process" means that it has direction... If you call something random just because parts are random... then every process is a random process-- child birth, film developing, puberty, reproduction, making lasagna, getting a diploma, seatbelt studies, the mechanisms of fire alarm activation--

Random process is about as useful as a "variable process" or an "upside-down process" or a "magical process"- it doesn't really mean anything, and when it comes to reproduction and exponential growth of the best reproducers, it is completely uninformative and only used by creationists.

Sure, randomness can lead to order... but the order in evolution and the appearance of design, doesn't come from randomness (as stated repeatedly by actual experts and those who teach the subject)-- that's more like spiral galaxies and spheres-- the order in evolution comes from natural selection. And nobody but a creationist obfuscates understanding of natural selection by needing to call it "random". It's muddled and laughable. It makes you sound like a creationist. It had no meaning and confuses more than it clarifies.

But of course, you are sure you know more than the experts... just like Behe. And all this explaining will fail to penetrate.

I shake my head at the folly.

[zosima]

You may have noticed that I ask what a random process is. A process may produce a numeric sequence, but it is not the same thing as a numeric sequence.

I tend to agree with Articulett, I don't think the idea of a random process is particularly meaningful. If you see a reason to distinguish between a random process and a statistically random sequence feel free to illuminate me.

In addition to what Articulett has already said, some things that make me thing the distinction is not meaningful are:

#1 we are talking about evolution, a theory that is characterized by statistical knowledge accumulated by biologists and ecologists. Since the theory derives from statistical knowledge, I think the statistical definition is appropriate.

#2 Theorems in computer science and mathematics indicate that the distinction between a process and a sequence of numbers is unnecessary. For example, see Godel Numbering, all ideas that are expressible in mathematical symbols are encoded as a sequence of numbers. So we might say that a random process is a random sequence of Godel Number's(or Number) over a basis that characterizes the features of a system we care about.

So why do think that such a distinction is meaningful and what exactly is the nature of that distinction?

[Wowbagger]

A process can have some random* components, but that does NOT make the whole process, itself, random.
(*however you define the word)


Mutations may or may not be random (depending on how you define the word), but assuming they are random, for a moment: That still says nothing about selection, which would still be non-random.

(A theoretical process, in which every step is completely random, could be called a random process, though at that point the word "process" would hardly make sense.)

[mijopaalmc]

Since so many people are so sure that I don't understand probability theory, I would like them to explain exactly where I am misunderstanding it particularly with respect to the relationship between predictability and randomness.

[zosima]

Since so many people are so sure that I don't understand probability theory, I would like them to explain exactly where I am misunderstanding it particularly with respect to the relationship between predictability and randomness.

Here's my response:


From wikitionary:
Statistical Randomness:
"the property of a numeric sequence of containing no recognizable patterns or regularities; exemplified in the results of an ideal die roll."

Or as I mentioned many posts ago: uncorrelated and uniformly distributed.

A smoke detector is a non-random system that takes a random input(or inputs more accurately). For all intents and purposes it is deterministic.

As there are recognizable patterns and regularities, it is clear that evolution, even individual selections in evolution are non-random. The more interesting argument that some people have been having with Jimbob, is whether evolution is deterministic or not. Which I think has fair arguments on both sides.

The mistake you seem to be making, over and over and over, again, is to assume that because you think evolution is not-deterministic that this implies that evolution is random.

This is a common mistake made in introductory logic classes.
If X->~Y this does not mean that ~X->Y
Above: Let X mean deterministic and Y mean random.

If a system is deterministic it is not random, but if a system is not deterministic it is not necessarily random.

(more commonly this fallacy is stated X->Y does not imply that ~X->~Y)


It identifies the fallacy and the correct definition of random.

Any process that has a non-uniform probability distribution will exhibit statistical regularities which makes it non-random. Continuous probability distributions that are not a dirac delta will not be deterministic. A system can be both non-uniform and not a dirac delta. Thus neither random nor deterministic. Your mistake is to call a non-deterministic system 'random'.

The interesting argument with evolution isn't whether it is random or deterministic. Strictly speaking, it cannot be random because the fact that complex structures develop constitutes a regularity that prevents a fit to the definition of randomness. Also strictly speaking, the only way it can be deterministic is if the universe is determined; An issue that is not specific to evolution.

The interesting question is how much do the fundamental variables have to be changed to create a significant difference on some timescale. Will a butterfly flapping its wings change the entire fate of a species? Will evolution still converge to the same result even if we pound the planet with meteors?

Arguing over whether evolution is random is a boring semantic argument anyway.

[mijopaalmc]

zosima-

The fatal flaw in you argument is that systems that have uniform probabilities also exhibit statistical regularity. I have pointed this out to you before:

zosima-

If I were wrong about randomness and predictability, larger sample sizes would not in most cases increase the power of statistical tests. Also, you would not be able to say that each number on standard, fair, six-sided die would come up roughly one sixth of the time or that the arithmetic mean of a series of rolls would be approximately 3.5. Moreover, you would not be able to say that, as the number of rolls increased, the proportion of each number coming up to the total number of rolls would approach one sixth or that the arithmetic mean of a series of rolls would approach 3.5.

Why do you refuse to address in as a counterexample to you central premise?

[Walter Wayne]

There really aren't such things as random processes... stochastic processes which contain random inputs are sometimes called "random processes"-- but it's not the process itself that is random. The fact that something is a "process" means that it has direction... If you call something random just because parts are random... then every process is a random process-- child birth, film developing, puberty, reproduction, making lasagna, getting a diploma, seatbelt studies, the mechanisms of fire alarm activation--

Random process is about as useful as a "variable process" or an "upside-down process" or a "magical process"- it doesn't really mean anything, and when it comes to reproduction and exponential growth of the best reproducers, it is completely uninformative and only used by creationists.

Sure, randomness can lead to order... but the order in evolution and the appearance of design, doesn't come from randomness (as stated repeatedly by actual experts and those who teach the subject)-- that's more like spiral galaxies and spheres-- the order in evolution comes from natural selection. And nobody but a creationist obfuscates understanding of natural selection by needing to call it "random". It's muddled and laughable. It makes you sound like a creationist. It had no meaning and confuses more than it clarifies.

There is a lot of misinformation in that post. The inputs are not what make a process stochastic, but the nature of the internal workings. That is, given the same input (whether that input was generated randomly or not), a process that goes to the same state(s) is a determistic one. A process where the future states indeterminant based on the inputs is stochastic.

Wether the output or state of the system is/appears random is dependent on the nature of the system. A simple system like a fire detector, will be a stochastic system will be for all intents and purposes determistic, even if technically a random system. A simple system like a random number generator, where noise is measured and a steam of ones and zeros is produced based on that noise is random.

There have been numerous qualities of evolution that make very distinct from the fire alarm mechanism. They've been discussed at length in other threads.

Walt

[Walter Wayne]

Here's my response:



It identifies the fallacy and the correct definition of random.

Any process that has a non-uniform probability distribution will exhibit statistical regularities which makes it non-random. Continuous probability distributions that are not a dirac delta will not be deterministic. A system can be both non-uniform and not a dirac delta. Thus neither random nor deterministic. Your mistake is to call a non-deterministic system 'random'.

The interesting argument with evolution isn't whether it is random or deterministic. Strictly speaking, it cannot be random because the fact that complex structures develop constitutes a regularity that prevents a fit to the definition of randomness. Also strictly speaking, the only way it can be deterministic is if the universe is determined; An issue that is not specific to evolution.

The interesting question is how much do the fundamental variables have to be changed to create a significant difference on some timescale. Will a butterfly flapping its wings change the entire fate of a species? Will evolution still converge to the same result even if we pound the planet with meteors?

Arguing over whether evolution is random is a boring semantic argument anyway.
It actually gives a definition of a random sequence, and an incorrect one at that. For one, a sequence generated by an ideal die may, actually probably will, have a bias, and there is a possibility (though unlikely for very long sequences) that it will have discernable patterns.

People in everyday use do not exclusively use random for equiprobably things. People in the physical sciences use it for other probability distributions as well, as do statisticians and mathematicians.

Walt

[zosima]

zosima-

The fatal flaw in you argument is that systems that have uniform probabilities also exhibit statistical regularity.


The wikitionary definition cites a die roll, which is uniformly distributed and uncorrelated. In the definition I mention, not only must the distribution be uniform but it must also be uncorrelated.

Is the type of statistical regularity you're talking about what you state in the example below? If yes I'll address it, but if it is something else, please do illuminate me.


Why do you refuse to address in as a counterexample to you central premise?

I told you why I wouldn't address it when you first posted it. Because it was off-topic in the thread you posted it in. Of course you made me ask you to post it in the right spot 3-4 times before you got the point, but...I'm pretty used to that by now. But I'll address your point now that you've pasted it into the correct thread. That said, I'm surprised I have to explain such a basic point to someone who professes so much knowledge about statistics.

If I roll a single die, all outcomes are equally likely. That single roll is random.
We the properties of that variable are not the same as the properties of other variables. For example the expected value(probability weighted mean) is not random, in fact, it is a constant. The probability 1/6 is also constant and non-random. You are conflating regularity in the values of the statistics with what these statistics tell us about potential regularities in the system. Notice that the official definition above cites an individual die roll not dice rolls, which become necessary for statistical regularities. This is the very crux of the point that has been made in this thread. A system made out of random components can have a sum behavior that is not random. That is the point of the law-of-large numbers.

A good way of thinking about it is this:

Ask yourself whether it is possible to come up with a strategy for a 'game' that will win you money on the long run. If you can do better than breaking even then it is not random.(Assuming the odds are fair)

If the game is guess the number when a die is rolled and a win pays out 5:1. There is no strategy that I can pick that will ever make me do better than average
This is a random game. Guessing 3.5 or 1/6 isn't going to get you anywhere, in fact these numbers aren't even part of the game.

If the game is guess the sum of two dice and it pays out 11:1 If my strategy is guess 7 I'll do better than even.
If the game is guess the mean within +- .5 after 10,000 rolls, I'd do well to guess 3.5 (With some appropriate payout, the pattern being n-1:1 payout, where n is the number of outcomes)

Now to understand why the constraint of being uncorrelated and uniform is placed. Imagine betting on the outcome of every 6th roll in a series. If it is a normal die(uncorrelated and uniform) I can't expect to do any better than even on this game, regardless of strategy. If it is a weighted die(non-uniform) lets say that there is a 50% chance of a 1 and a 10% chance for all other outcomes. (With a 5:1 payout) If my strategy is play 1, I'm going to expect to win money.

Here's another system, lets say we have a die that always rolls 1 the first time you roll it, 2 the second, 3 the third, 4 the 4th and 5 the 5th, 6 the 6th and 1 the 7th...
This system has a uniform distribution, but the correlation in the system makes it non-random. If I'm playing the game where I get to bet every 6th roll, I'll do well to play 6 as my strategy and expect to win money.

Each of these games are different. The fact that they all involve a die does not make them all random, but they are all probabilistic. The reason I can't win money betting on individual values of the ideal die is because it is random. There is no strategy that is better than any other. The reason I can win money when betting on the mean is because the mean is non-random. But no matter how much money I win betting on the mean, I'll never be able to make money betting on the ideal die.


It actually gives a definition of a random sequence, and an incorrect one at that. For one, a sequence generated by an ideal die may, actually probably will, have a bias, and there is a possibility (though unlikely for very long sequences) that it will have discernable patterns.

People in everyday use do not exclusively use random for equiprobably things. People in the physical sciences use it for other probability distributions as well, as do statisticians and mathematicians.


An ideal die will not have a bias. Although a finite sequence may vary from the expected value. It does not take a very long sequence at all for it be without patterns. We can only be 100% sure about the properties of a theoretical system. There is always the possibility that a real world system or a finite random sequence, will not appear to be so. To tell me that is a trivial, non-constructive objection, and it doesn't change anything about the issue at hand.

If you don't like that definition use the definition I've provided: uniform and uncorrelated. I provide a detailed explanation above. The explanation also dovetails with an interpretation of 'people in everyday use'. Although If you're talking about what everyday people think random is(whatever that means) then there is really no sense in discussing it, because what everyday people think is going to vary heavily from person to person and culture to culture. Moreover evidence indicates that everyday people have huge misconceptions about evolution so do we really care what they think random is and whether that applies to evolution? What scientists call a non-random probability distribution random? The ones on TV?

Finally, If you happen to have a definition of random that isn't just exclaiming that random is a synonym for non-deterministic, I'd be interested in hearing it.

[Walter Wayne]

An ideal die will not have a bias. Although a finite sequence may vary from the expected value. It does not take a very long sequence at all for it be without patterns. We can only be 100% sure about the properties of a theoretical system. The problem is your definition doesn't mention a process, like the rolling of an ideal die. It mentions the property of a sequence. Second it is a wiki, and one with zero discussion. Get me a more authoratative source.

[zosima]

The problem is your definition doesn't mention a process, like the rolling of an ideal die. It mentions the property of a sequence. Second it is a wiki, and one with zero discussion. Get me a more authoratative source.

#1 I welcome a better definition, you haven't provided one and I've defended the logic behind my definition in detail. In absense of reasoned opposition I don't need anything more authoritative.

#2 I think the idea of having no patterns, being unpredictable is more colloquial than the more rigorous definition I've been providing. That is uniform and uncorrelated

#3 The distinction between a process and a sequence of numbers in this context is not significant. The measurements that are taken of a system at different times will constitute a sequence of numbers that will describe the state vector of the system. If the numbers are random that indicates the system is random.

#4 Its already been addressed why random process is not even really a significant distinction. If you disagree, once again I ask you to define a random process in a meaningful way.

#5 None of the points that I've made have relied on the authority of Wiktionary.

[articulett]

It doesn't matter your sources, zosima-- they imagine themselves smarter than them. I gave them a peer reviewed paper that said "evolution is not random"-- but to them it must be... the same people... spouting the same nothingness for the same unknown reasons.

To them, it must be "correct" (whatever that means) to say that "scientists think that all this came about randomly". Scientists, of course, don't say that.

But it's the favorite straw of creationists for some reason... and so all semantic burble leads back to the "evolution is random" nothingness.

[mijopaalmc]

Here are some easily accessible definitions of "determinsitic" and "stochastic" with citation to other published works:

Determistic (http://mathworld.wolfram.com/Deterministic.html)

A Turing machine is called deterministic if there is always at most one instruction associated with a given present internal state/tape state pair $(q,s)$. Otherwise, it is called nondeterministic (Itô 1987, p. 137).

In prediction theory, let ${X_t}$ be a weakly stationary process, and let $M_t(X)$ be a subspace spanned by the $X_s$ (with $s\leq{t}$). $If M_t(X)$ is independent of t so that $M_t(X)=M(X)$ for every $t$, then ${X_t}$ is said to be deterministic (Itô 1987, p. 1463).

Stochastic (http://mathworld.wolfram.com/Stochastic.html)


Stochastic is synonymous with "random." The word is of Greek origin and means "pertaining to chance" (Parzen 1962, p. 7). It is used to indicate that a particular subject is seen from point of view of randomness. Stochastic is often used as counterpart of the word "deterministic," which means that random phenomena are not involved. Therefore, stochastic models are based on random trials, while deterministic models always produce the same output for a given starting condition.

[zosima]

Here are some easily accessible definitions of "determinsitic" and "stochastic" with citation to other published works:

Thanks for the info Mijo.

:)

[articulett]

Thanks for the info Mijo.

:)

If you play semantic scavenger hunt and extrapolate correctly, you, too, might finally understand that evolution is random.

And then you'd be as smart as Mijo.

[jimbob]

There is a lot of misinformation in that post. The inputs are not what make a process stochastic, but the nature of the internal workings. That is, given the same input (whether that input was generated randomly or not), a process that goes to the same state(s) is a determistic one. A process where the future states indeterminant based on the inputs is stochastic.

Wether the output or state of the system is/appears random is dependent on the nature of the system. A simple system like a fire detector, will be a stochastic system will be for all intents and purposes determistic, even if technically a random system. A simple system like a random number generator, where noise is measured and a steam of ones and zeros is produced based on that noise is random.

There have been numerous qualities of evolution that make very distinct from the fire alarm mechanism. They've been discussed at length in other threads.

Walt

Indeed, and the biggest difference is that an ionisation smoke detector is not a chaotic system. A slight difference in the decay rate leads to a slight difference in the ionisation current, which leads to a slight difference in teh "apparent" smoke density ant the output signal. A slight difference in the gain (transconductance) in the amplifying transistor similarly leads to a slight difference in the sensitivity of the detector, so this is compensated for during factory testing.

With the smoke detector slight differences in inputs lead to slight differences in outputs.

With chaotic, and other divergent systems, slight differences in inputs lead to vastly different outcomes, and the differences increase over time.

This seems to be what happens in ecosystems. Many biological systems exhibit chotic behaviour, and the consensus is that the weather does too. There are lots of positive feedback loops in biological evolution and this means that disruptive mutations can significantly affect the fitnes landscape for other organisms and alter the course of evolution.

The emergence of grasses mighe have been one. On a smaller level, but significant for the survival of millions of individuals, the mutation that made spanish flu so deadly was another.

[Walter Wayne]

#1 I welcome a better definition, you haven't provided one and I've defended the logic behind my definition in detail. In absense of reasoned opposition I don't need anything more authoritative.
Random: having a state or value depends on chance.
#2 I think the idea of having no patterns, being unpredictable is more colloquial than the more rigorous definition I've been providing. That is uniform and uncorrelatedSo you can predict the sum of two die rolls? That isn't uniform. You can predict the position of someone on a snakes and later board on the second turn, after seeing the result of their first turn? That is correlated with the result of the first term.
#3 The distinction between a process and a sequence of numbers in this context is not significant. The measurements that are taken of a system at different times will constitute a sequence of numbers that will describe the state vector of the system. If the numbers are random that indicates the system is random.But if you define whether a process is random by observing only the sequence produced, a sequence of randomly generated numbers may produce a non-uniform distribution. A determistic process can also produce unbiased sequences.
#4 Its already been addressed why random process is not even really a significant distinction. If you disagree, once again I ask you to define a random process in a meaningful way.
In other posts, I've pointed out the difference between technically random, and random with significant variation. I am not simply arguing that evolution is merely technically random, I've have mentioned that several times before.

[nitpick]Just because every physical process may be technically random, doesn't mean the definition isn't meaningful. During the period of classical physics, they were people who thought physical processes were technically determisitic. Determistic still meant something. But this is just a derail. [nitpick]
#5 None of the points that I've made have relied on the authority of Wiktionary.

Walt

[zosima]

Random: having a state or value depends on chance.
So you can predict the sum of two die rolls? That isn't uniform. You can predict the position of someone on a snakes and later board on the second turn, after seeing the result of their first turn? That is correlated with the result of the first term.


You can predict the sum of two die rolls with better than an accuracy better than random chance. If you provide a confidence interval, you can provide an exact prediction.

I'm sorry I don't understand the 'snakes and later board' example.


But if you define whether a process is random by observing only the sequence produced, a sequence of randomly generated numbers may produce a non-uniform distribution. A determistic process can also produce unbiased sequences.


Both these examples go to my point about theoretical vs best fits to the real world. I'm not arguing that these systems can't be deceptive. We often make mistakes in science and fit a model that later appears wrong in light of more evidence. Given enough data, the nature of each of the systems means that they'll both approach the correct definition given enough data.

For example, a pseudorandom number generator will always eventually give its self away because it necessarily has cycles. After a certain period it will begin to repeat and be obviously deterministic.


On your second point
In other posts, I've pointed out the difference between technically random, and random with significant variation. I am not simply arguing that evolution is merely technically random, I've have mentioned that several times before.


Could you elaborate? I'm not sure what you mean by this.


[nitpick]Just because every physical process may be technically random, doesn't mean the definition isn't meaningful. During the period of classical physics, they were people who thought physical processes were technically determisitic. Determistic still meant something. But this is just a derail. [nitpick]


I'll agree its meaningful, but that sort of randomness wouldn't apply meaningfully to evolution, in the sense that it would apply equally and trivially to everything if true. In other words it is outside the scope of this discussion.

Also I don't think quantum effects are random, they are probabilistic.
To generate a true random bit from the outcome of a non-uniform quantum effect you need to run the process twice, but switch what counts for true and false in each trial. You only count the result, if they agree, if they don't you run two more trials. (There are other techniques, but they all involve more than one trial)


Indeed, and the biggest difference is that an ionisation smoke detector is not a chaotic system. A slight difference in the decay rate leads to a slight difference in the ionisation current, which leads to a slight difference in teh "apparent" smoke density ant the output signal. A slight difference in the gain (transconductance) in the amplifying transistor similarly leads to a slight difference in the sensitivity of the detector, so this is compensated for during factory testing.

With the smoke detector slight differences in inputs lead to slight differences in outputs.

Agreed. With the qualification that the output isn't a slight difference in measured signal, it is strictly 'smoke or no'.


With chaotic, and other divergent systems, slight differences in inputs lead to vastly different outcomes, and the differences increase over time.


With the qualification that the system needs to be sensitive to the changes in the input.


This seems to be what happens in ecosystems. Many biological systems exhibit chotic behaviour, and the consensus is that the weather does too. There are lots of positive feedback loops in biological evolution and this means that disruptive mutations can significantly affect the fitnes landscape for other organisms and alter the course of evolution.

The emergence of grasses mighe have been one. On a smaller level, but significant for the survival of millions of individuals, the mutation that made spanish flu so deadly was another.


I've got a couple of points here.

#1 Just to be clear I understand this to be from the perspective of the 'history of evolution' or 'path of evolution'. If we're talking about evolution in the sense of how a species change in response to changes in its environment(which may or may not be chaotic or random) this point is inapplicable. (Ie doesn't apply to the argument made from Baysian logic some pages back)

#2 The 'consensus' I got from the 'chaotic' thread was that the jury was still out with respect to whether weather was chaotic. Moreover the 'consensus' I got was that we couldn't tell if a system was chaotic unless we are talking about a mathematical model and are in agreement about its quality of fit to the evidence.

#3 I appreciate your intuition on these issues, but is there any reason you believe these systems are chaotic?

#4 How do you know that these systems are not just complex?

#5 How do you know that, if these systems are chaotic, that they are sensitive to random inputs?

#6 What do you contend these inputs are?

#7 How do you know that these systems are not constrained by negative feedback in the form of energy limitations and physical landscape for ecosystems, in terms of intertia,viscosity, and energy for weather.

#8 What are the relative scales of the development rate of 'disruptive mutations' vs 'positive feedback' in speciation. How do we know the scales are comparable?

#9 How do we know that this 'positive feedback' doesn't just affect the speed at which the solution is generated and not the substantive result of the solution.

Your assertions are all well and good, but they're just as hand-wavy as your assertions about chaos theory which were quite vigorously shot down. Unless you can answer these questions with evidence and reason, really all you are saying is that despite the testament of people in the field, you have the strong personal conviction, a feeling, that the results of evolution involve significant chaotic effects. Which, IMO, is terribly unpersuasive.

[zosima]

An example of my skepticism wrt chaos. While many systems in nature might seem to have exponential growth in their error, many curves in nature that look like exponential curves end up being sigmoidal. While they exhibit have a large derivative near the normalized origin, resource limitations ultimately end up reducing the growth rate to 0.

Bacterial populations are an excellent example. Initially they don't increase so quickly in absolute terms because there aren't very many of them they quickly accelerate their growth peaks as they begin to compete for resources then quickly decelerates to a steady state. Their population v time curve looks like a sigmoid, the derivative looks like a normal distribution.

Why exclude this possibility?

[articulett]

Moreover-- the exponential growth allows for more variety to select from-- more potential "winners" in the evolution game. That's the essence of the Evolution--not how "randomly" this variety was acquired!

[mijopaalmc]

If you play semantic scavenger hunt and extrapolate correctly, you, too, might finally understand that evolution is random.

And then you'd be as smart as Mijo.

So insisting that people use the proper and rigorous scientific is playing "semantic scavenger hunt"?

The definitions I provided are widely accepted by mathematicians, statisticians, physical scientists, and biologists of many different stripes.

Why can't evolutionary biologists (as you choose to portray them) standardize their terminology?

[Wowbagger]

Moreover-- the exponential growth allows for more variety to select from-- more potential "winners" in the evolution game. That's the essence of the Evolution--not how "randomly" this variety was acquired! That's a good summary of the point of this thread, I think.

Why can't evolutionary biologists (as you choose to portray them) standardize their terminology? They do! But, just like mathematicians, statisticians, physical scientists, etc., the standard terms are adjusted according to the context of the study.

[mijopaalmc]

They do! But, just like mathematicians, statisticians, physical scientists, etc., the standard terms are adjusted according to the context of the study.

Uh....the other definitions by which evolutionary biologists claim evolution is not random are not consistent with the understanding of randomness needed to meaningfully practice statistics and to use statistical analysis to demonstrate that evolution does occur.

[Wowbagger]

Uh....the other definitions by which evolutionary biologists claim evolution is not random are not consistent with the understanding of randomness needed to meaningfully practice statistics and to use statistical analysis to demonstrate that evolution does occur.Who said they are not consistent?

Maybe they are, but are only relevant to certain aspects, or certain models of evolution; not the whole entire thing. Selection is non-random, by practically any definition of the word, for one thing... and that is true no matter how random (or not) mutations happen to be.

[articulett]

What Mijo just said actually doesn't mean anything at all. It's like Tom Cruise saying "there's no such thing as a chemical imbalance". It's garble disguised as a statement of fact. It has no actual meaning or relevance.

[zosima]

Uh....the other definitions by which evolutionary biologists claim evolution is not random are not consistent with the understanding of randomness needed to meaningfully practice statistics and to use statistical analysis to demonstrate that evolution does occur.

You provided some definitions. You didn't connect the dots. I honestly don't see how the definitions you provided support your point. So at this point you're conceding the central claim, while defining terms that are tangentially related.

But please do go on defining words. You've missed quite a few.

[articulett]

Evolutionists, geneticists, Bayesian Staticians, etc. all understand evolution, Dawkins, why evolution is not random, and-- despite Mijo's exclamation to the contrary-- they also "meaningfully practice statistics" and can "use statistical analysis to demonstrate that evolution does occur".

They cannot find coherency in the words of people like Mijo, however, and note that many creationists have a need to focus on randomness in evolution to avoid the accumulated exponential benefit leading to the appearance of design due to natural selection. That's why we keep them out of the classroom and don't attempt to engage them in rational discussions on the topic.

How the variety comes about is not as important as what is selected and multiplied from the assorted varieties. You can desribe evolution in stunning detail without ever having to use the word random or understand a thing about Mijo's vague definition of "random" as "having anything to do with probabilities and/or containing anything that has to do with probabilities."

[mijopaalmc]

double post

[mijopaalmc]

Who said they are not consistent?

Maybe they are, but are only relevant to certain aspects, or certain models of evolution; not the whole entire thing. Selection is non-random, by practically any definition of the word, for one thing... and that is true no matter how random (or not) mutations happen to be.

Uh....the only definition of "random" that I can find that doesn't describe natural selection is "[o]f or relating to an event in which all outcomes are equally likely". (The definition that zosima provided isn't actually a definition that I have seen anyone use because even random processes can display regularity.)

Unfortunately, defining "random" as "equiprobable" (as is done in the above definition) violates the fundamental assumptions of statistical analysis, namely that variations that are due completely to taking two different samples from the same population can somehow be distinguished from variations due to taking two different samples from two different populations. To do this, a statistic is calculated for the sample and then compared to a distribution of the statistic to determine how likely it is that the difference between the samples is due to more than just the intrinsic variation due to sampling.

Obviously, in order for statistical inference to make any meaningful, this statististical methodology (which is slightly modified if we switch from frequentist statistics to Bayesian statistics, but it is still fundamentally based on probability) assumes that that the sample statistic can take on several values and that the value of the sample statistic is somehow dependent upon the sample taken. Thus, we return to the need for a much more inclusive definition of "random" than "equiprobable", because the sample statistic can vary even when there is no actual meaningful variation between the samples.

[zosima]

Uh....the only definition of "random" that I can find that doesn't describe natural selection is "[o]f or relating to an event in which all outcomes are equally likely". (The definition that zosima provided isn't actually a definition that I have seen anyone use because even random processes can display regularity.)



Thats great Mijo, whenever someone provides a detailed deconstruction of your argument switch topics and ignore it completely, great strategy from the perspective of maximizing obfuscation but not in terms of identifying truth or coming to consensus. Do you even read more than the first line of anyone's posts?


Unfortunately, defining "random" as "equiprobable" (as is done in the above definition) violates the fundamental assumptions of statistical analysis, namely that variations that are due completely to taking two different samples from the same population can somehow be distinguished from variations due to taking two different samples from two different populations. To do this, a statistic is calculated for the sample and then compared to a distribution of the statistic to determine how likely it is that the difference between the samples is due to more than just the intrinsic variation due to sampling.

Obviously, in order for statistical inference to make any meaningful, this statististical methodology (which is slightly modified if we switch from frequentist statistics to Bayesian statistics, but it is still fundamentally based on probability) assumes that that the sample statistic can take on several values and that the value of the sample statistic is somehow dependent upon the sample taken. Thus, we return to the need for a much more inclusive definition of "random" than "equiprobable", because the sample statistic can vary even when there is no actual meaningful variation between the samples.

#1 You've done this before. Once again you make the following logic.
Scientists use statistics.
Statistics involve the use of modeling with a 'random variable'
Random variable has the word 'random' in it.
Thus we can conclude that the systems modeled with statistics are random.

#2 You do realize that you are not only saying that evolution is random with this argument, but also that all empirical sciences are random? This means chemistry is random, biology is random, physics is random. Why make such a big deal about evolution?

#3 Using a 'random variable' is a modeling technique, it says nothing about the system it models. This is the same mistake you make when you assume that since we can calculate constant statistics describing a system(ie mean) that this regularity in the statistic implies a regularity in the system. It does not.

#4 You continue to characterize the definition of random I've provided as 'equiprobable' (ie uniformly distributed). That misses the second part of the definition uncorrelated. Thus it misses the point. I provide extensive examples as to how both constraints are necessary 2 posts ago.

#5 You make the jump from noting that the variable doesn't always assume the same value to the jump that it is random. That does not follow, all the follows is that it is not determinate. Any deviation in the statistics of the variable from uniformly distributed and uncorrelated is considered a deviation from random.

Conclusion: Your argument is flawed. The bottom line is that a variable that is uncorrelated and uniform is one such that there is no regularity. No matter how many observations I make I will never gather any information that will allow me to predict the next value. That is random. 'Things modeled with statistics' is not a definition of random, it is not even informative.

[articulett]

What Zosima said-- and double... it's what every smart person or anyone who understand the topic is saying. No one is following you, Mijo. Your expertise exists only in your imagination. Evolution is "random" only in your imagination.

Having random components does not a random process make! Nor does having "probabilities" or "being related to statistics". Just because you've learned to tie everything having to do with evolution to the word "random" doesn't mean that you are saying anything useful or informative to anyone unless their desire is to to obfuscate understanding of natural selection. No one who understands evolution conveys it by calling random. Unless you have some peer reviewed scientific evidence we are unaware of where some scientist of some import is saying "evolution is random". Not your extrapolation... those words.

But I admire your self important and self congratulating circularity and Zosima's careful deconstruction of your "breathtaking inanity". Really, I can't tell your dialogue from the Behe court transcript. Amazing. :D

[jimbob]

Back a couple of posts:

You could use an evolutionary algorithm to choose what the requirements are,

I could use many, many things: is it necessary that they are all of intelligent design?

This is a digression, I suggest that if you want to pursue it further it should go in the "intelligent evolution" thread.

However I can't see any useful system where the selection criteria have been chosen randomly. They might not have been chosen directly by an intelligent agency, but by other system that hadf been intellignetly designed. For example maybe the key performance parameters had been decided upon by a neural net, or maybe an evolutionary algorithm. Although I doubt this has actually happened in any real engineering.

If you want to meet the performance specification, then you need to define what the goal of the evolutionary algorithm is.

If there was a self-replicating system, one wouldn't need to do this, better self-replicators would evolve.



I have answered your question several times,

No you have not - you've answered the question you want to answer.

I can't think of a way that evoultionary algorithms a could be used without intelligently set goals in technological development to produce something useful, and I think that this is because they can't. Can you give a realistic example as to how they could?


now are you going to answer mine about how the phrase "a selective advantage of 1:1000" is not part of a probabilistic treatment of natural selection?

No I am not because it is a probabilsitic treatment of natural selection.

The emphasis is on "treatment". The emphasis is on knowing the difference between a model and the thing it is modelling. You seem to insist you can know the difference or that it is even meaningful.


The OP was where it was appropriate to use "randomness" when discussing evolution. You now seem to be implicitly accepting that probabilistic treatments are used implicitly by evolutionary biologists, are you now claiming that this treatment is wrong because it is "only a model"?

Are you claiming that chance deoes not influence which cod-fry survives and reproduces. That this reproductive is already predetermined at spawning?

If you state that chance does have a role, then the probabilistic treatment is valid because chance has a role. If chance does not play a role, then the probabilistic treatment is only a demonstration of our imperfect knowledge.

My position is the scientifically conventional one, which is accepted by most bioplogists, yours seems to be obsolete, and based on the 19th Century knowledge and assumptions (Laplacian determinism).

I say that which individual cod-fry reproduces is heavily influenced by chance.

1-million spawn, stable (or falling) population, so fewer than one repoducing adult from each parent. Two parents, so less than a 1:500,000 chance of reproducing.

Most of these cod spawn will be very similar to each other and their parents, yet on average two survive and reproduce.

Remember this post earlier in the thread, which does confirm my view that over the timescales of life, there are chance events influincing natural selection:


ETA:

Sol agrees with you Jimbob, but I won't edit out what i just said. I will continue to think about why I feel it doesn't matter and see if I can restate my thought.

It's OK to disagree with me! :) Sometimes I'm even wrong :jaw-dropp.

I think QM events can strongly affect chaotic systems after relatively short amounts of time. I'm pretty sure 99% of physicists would agree with me.

I don't think it's useful to distinguish between "random" and "unpredictable" when we're discussing physical processes. I'm not sure how many physicists would agree with me on that (although I think I could convince them).

But none of that prevents us from predicting with extremely high confidence that July in Saskatoon will be warmer than January in Saskatoon. As they say - "weather is chaotic, but climate is predictable" (or something along those lines). As for evolution, it has both weather-like and climate-like aspects.

ETA, and this one:


However as the response is determined under indentical sets of events indentical sets of responses occur.

cyborg, I think jimbob's point is that in the Copenhagen interpretation of QM the statement I quoted above is just not correct. Identical circumstances do not lead to identical responses.

The only thing which is determined by the theory are probabilities, and furthermore it can be demonstrated that the probabilistic nature is not due to our ignorance - it is an intrinsic part of the theory. So according to that, the world is truly random at a microscopic level.

[Wowbagger]

Really, I can't tell your dialogue from the Behe court transcript. Amazing.Well, now you're just being cruel!

[Walter Wayne]

You can predict the sum of two die rolls with better than an accuracy better than random chance.No your prediction will be exactly what would be predicted by random chance.
You mean you can predict it more accurately than a random variable that was uniform on the 2 to 12 interval. You are using your definition to justify your definition to justify your definition.

Second, there are probability distributions that will be predicted with less accuracy than a uniform distribution. The sum of two dice example is just one example of a non-uniform distribution. Try the same with some bi-modal or multi-modal distributions and you will find the same isn't true.

If you provide a confidence interval, you can provide an exact prediction.
Prediction for one die roll: 3.5 +/-2.5
Appears with a confidence interval I can supply an exact prediction on uniform probability as well.

I'm sorry I don't understand the 'snakes and later board' example.On snake and ladders, or any board game where movement is determined by die roll. Your position after your turn is correlated with your position at the beginning of the turn. It still isn't predictable. Especially true in games like trivial pursuit where the number of rolls in a turn is variable. Correlation doesn't necessarily make things predictable.

Both these examples go to my point about theoretical vs best fits to the real world. I'm not arguing that these systems can't be deceptive. We often make mistakes in science and fit a model that later appears wrong in light of more evidence. Given enough data, the nature of each of the systems means that they'll both approach the correct definition given enough data.

For example, a pseudorandom number generator will always eventually give its self away because it necessarily has cycles. After a certain period it will begin to repeat and be obviously deterministic.Hmmm, it is possible to make a pseudo-random number generator that won't give itself away. For example, if we want a random string of 1s and 0s ...

1. The next number in the sequence is the number that would minimize the entropy of the sequence to this point.
2. If added a "1" or a "0" both result in the same entropy, then choose 0.
Could you elaborate? I'm not sure what you mean by this.
I won't go into great detail, as there are examples across several threads already.

An example of technically random process that isn't random in most practical senses is the decay of a chunk of radioactive material is an example of a random process where the result is random in only the most technical sense of the word. Individual atoms decay at random interval, but after one half-life passes your prediction of the amount of material left will be accurate to an incredible precision.

This is in contrast to say, a random number generator, which compares random noise to a threshold values, and generates a high (1) or low (0) based on the result. The system is not only technical random, but random also at the macro-level.

This is what I mean by the difference between things which are only technically random, and those things which are random in a practical sense.
I'll agree its meaningful, but that sort of randomness wouldn't apply meaningfully to evolution, in the sense that it would apply equally and trivially to everything if true. In other words it is outside the scope of this discussion.

Also I don't think quantum effects are random, they are probabilistic.
To generate a true random bit from the outcome of a non-uniform quantum effect you need to run the process twice, but switch what counts for true and false in each trial. You only count the result, if they agree, if they don't you run two more trials. (There are other techniques, but they all involve more than one trial)First, to generate a "bit" that is random and without bias, all you need is a distribution where the median lies between two possibilities. For example, with the roll of one die I can generate "0" bit on a roll of less than 3.5 and "1" otherwise. With the sum of two roll I can't simply because the median, 7, might come up. But on the sum of 3 dice I can generate a bit based on whether the result is above or below 10.5.

Walt

[mijopaalmc]

Thats great Mijo, whenever someone provides a detailed deconstruction of your argument switch topics and ignore it completely, great strategy from the perspective of maximizing obfuscation but not in terms of identifying truth or coming to consensus. Do you even read more than the first line of anyone's posts?

Actually, this describes your modus operandi much more closely. You provided a definition of "random" that didn't take some of the oldest and most basic concepts in probability theory and statistics into account and therefore is invalid in so far as it does not describe most systems that could be described as random.

#1 You've done this before. Once again you make the following logic.
Scientists use statistics.
Statistics involve the use of modeling with a 'random variable'
Random variable has the word 'random' in it.
Thus we can conclude that the systems modeled with statistics are random.

#2 You do realize that you are not only saying that evolution is random with this argument, but also that all empirical sciences are random? This means chemistry is random, biology is random, physics is random. Why make such a big deal about evolution?

#3 Using a 'random variable' is a modeling technique, it says nothing about the system it models. This is the same mistake you make when you assume that since we can calculate constant statistics describing a system(ie mean) that this regularity in the statistic implies a regularity in the system. It does not.

#4 You continue to characterize the definition of random I've provided as 'equiprobable' (ie uniformly distributed). That misses the second part of the definition uncorrelated. Thus it misses the point. I provide extensive examples as to how both constraints are necessary 2 posts ago.

#5 You make the jump from noting that the variable doesn't always assume the same value to the jump that it is random. That does not follow, all the follows is that it is not determinate. Any deviation in the statistics of the variable from uniformly distributed and uncorrelated is considered a deviation from random.

Unfortunately, that is not my reasoning. I recognize that there seems to be some sort of cognitive break between the description of evolution as non-random and the practice of statistics within evolutionary biology. The former insists that anything that is uniformly distributed, independent, and uncorrelated is random, whereas the latter allows for those conditions and makes statements about how likely it is to expect such things given the characteristics of the data.

Conclusion: Your argument is flawed. The bottom line is that a variable that is uncorrelated and uniform is one such that there is no regularity. No matter how many observations I make I will never gather any information that will allow me to predict the next value. That is random. 'Things modeled with statistics' is not a definition of random, it is not even informative.

Correction: your straw man representation of my argument is flawed.

Even data that is generated by a random (equiprobable) process can, if the sample is small enough, display bias, correlation, or dependence. Similarly, small sample data that is generated by a process that is biased, correlated, or dependent can lack those properties. Thus, it becomes essential to develop methods to detect these and other properties that exist beyond the artifacts of sampling.

[cyborg]

This is a digression, I suggest that if you want to pursue it further it should go in the "intelligent evolution" thread.

No.

However I can't see any useful system where the selection criteria have been chosen randomly.

Non-answer.

They might not have been chosen directly by an intelligent agency, but by other system that hadf been intellignetly designed. For example maybe the key performance parameters had been decided upon by a neural net, or maybe an evolutionary algorithm. Although I doubt this has actually happened in any real engineering.

You're making things up about the system I've never even implied.

If you want to meet the performance specification, then you need to define what the goal of the evolutionary algorithm is.

There is no performance specification. You're making things up.

If there was a self-replicating system, one wouldn't need to do this, better self-replicators would evolve.

You've never been able to come to terms with the concept that "self-replication" is simply a different abstract representation in a computer system that has no extrinsic meaning making any attempt to explain why this is completely irrelevant to the behaviour of the system as a whole a waste of my time.

I can't think of a way that evoultionary algorithms a could be used without intelligently set goals in technological development to produce something useful, and I think that this is because they can't.

Your lack of imagination is your problem.

Can you give a realistic example as to how they could?

No - because any system I describe you would invent parts never described for it that would in your mind make it invalid in some legalistic sense.

The first part you'll never come to accept is that a describing a "useful" product is a matter of who is arbitrating "useful" and will be different under different contexts.

The OP was where it was appropriate to use "randomness" when discussing evolution. You now seem to be implicitly accepting that probabilistic treatments are used implicitly by evolutionary biologists, are you now claiming that this treatment is wrong because it is "only a model"?

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

Are you claiming that chance deoes not influence which cod-fry survives and reproduces. That this reproductive is already predetermined at spawning?

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

If you state that chance does have a role, then the probabilistic treatment is valid because chance has a role. If chance does not play a role, then the probabilistic treatment is only a demonstration of our imperfect knowledge.

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

My position is the scientifically conventional one, which is accepted by most bioplogists, yours seems to be obsolete, and based on the 19th Century knowledge and assumptions (Laplacian determinism).

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

I say that which individual cod-fry reproduces is heavily influenced by chance.

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

1-million spawn, stable (or falling) population, so fewer than one repoducing adult from each parent. Two parents, so less than a 1:500,000 chance of reproducing.

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

Most of these cod spawn will be very similar to each other and their parents, yet on average two survive and reproduce.

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

Remember this post earlier in the thread, which does confirm my view that over the timescales of life, there are chance events influincing natural selection:

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

I have wasted my time. What a fun ten minutes.

[articulett]

Well, now you're just being cruel!

Perhaps. But I am also correct, as anyone who has read the transcript will probably attest. I defy to clarify a difference. It's all about muddying understanding using the word random to make it sound like scientists think this all happened randomly... (which people find implausible... and so god seems like a possible alternative.) Once you understand natural selection-- the god concept seems increasing unlikely. Natural Selection is a much more coherent explanation for what we observe.

[zosima]

You mean you can predict it more accurately than a random variable that was uniform on the 2 to 12 interval. You are using your definition to justify your definition to justify your definition.

Lets hear a strategy to do better than even betting on a uniform uncorrelated die. I'm saying with this definition it corresponds well to our intuitions.
If the system is non-uniform and/or correlated we can talk about likely outcomes. It is saying that the definition is logical and consistent.
It would be absolutely silly for me to say my example of random makes sense according to your definition of random.

Which incidentally, you still haven't bothered to provide. Is that ever going to happen? In absence of an alternative to compare it to, my definition is still the best one available.


Second, there are probability distributions that will be predicted with less accuracy than a uniform distribution. The sum of two dice example is just one example of a non-uniform distribution. Try the same with some bi-modal or multi-modal distributions and you will find the same isn't true.


You're going to need to be clear about what isn't true about bi-modal distributions. As I understand it, I can do better making predictions about a bi-modal distribution than a uniform one. I'm certain I'd rather be betting on a horse race where I knew the horses were bi-modally distributed rather than uniformly.


Prediction for one die roll: 3.5 +/-2.5
Appears with a confidence interval I can supply an exact prediction on uniform probability as well.

Yes, but you have noticed that your confidence covers the entire interval. I can either interpret that statement as a trivial platitude or as saying that you have no idea what outcome there will be. You might as well say, 'I can predict exactly that there will be some value'. Nice prediction, but I'd hardly say it supports your case.


On snake and ladders, or any board game where movement is determined by die roll. Your position after your turn is correlated with your position at the beginning of the turn. It still isn't predictable. Especially true in games like trivial pursuit where the number of rolls in a turn is variable. Correlation doesn't necessarily make things predictable.


You make a mistake here. Lets say the game has progressed for some time, I'm on position 70 on the board and I'm rolling one 6 sided die. The only outcomes are 71-76, the capacity to predict that it isn't going to be 68 and that it isn't going to be 77 tells us nothing because those are impossible outcomes. In other words, the outcome of the die roll is uncorrelated with the previous rolls. In a game like this you'd actually have to remap the meaning of the symbols on the die depending on previous rolls to create a correlation.


Hmmm, it is possible to make a pseudo-random number generator that won't give itself away. For example, if we want a random string of 1s and 0s ...

1. The next number in the sequence is the number that would minimize the entropy of the sequence to this point.
2. If added a "1" or a "0" both result in the same entropy, then choose 0.


It is a fundamental result from discrete number theory. I suggest you brush up on your math.

You haven't really explained your algorithm, but there is a reason they are called 'pseudo-random' if your algorithm worked you could patent it and create a true random number generator. But there is a theorem that prevents you from going back and definitively calculating the entropy of the sequence. Read up on Kolmogorov complexity
Or If I'm wrong you can patent your algorithm or you can tell me and I'll patent it.




An example of technically random process that isn't random in most practical senses is the decay of a chunk of radioactive material is an example of a random process where the result is random in only the most technical sense of the word. Individual atoms decay at random interval, but after one half-life passes your prediction of the amount of material left will be accurate to an incredible precision.

Well it sure seems like you're spending a lot of time arguing about 'technically random' processes. Care to make an argument about why evolution is macroscopically random? It seems like Jimbob is the only one still making macroscopic arguments.

It sure seems like what you're saying is that systems with random components can be macroscopically non-random, with this example. So how about you explain how you can tell the difference between the two in the macroscopic world?


First, to generate a "bit" that is random and without bias, all you need is a distribution where the median lies between two possibilities. For example, with the roll of one die I can generate "0" bit on a roll of less than 3.5 and "1" otherwise. With the sum of two roll I can't simply because the median, 7, might come up. But on the sum of 3 dice I can generate a bit based on whether the result is above or below 10.5.


I guess I was thinking about continuous wavefunction distributions. If the distribution is continuous and the median will always be a potential outcome in the distribution. So it will always take two trials over a continuous distribution. If its a discrete distribution, I'll concede the point that you can get a bit in one trial, if the median is not a possible outcome.

Of course, this is a digression from my digression. But the bottom line is that to get a random bit from a skewed distribution you need to use a function that unskews the distribution. Otherwise your outcome will not be random

To conclude:
Walter, If you want to make a point about the macroscopic randomness of evolution why don't you: #1 Propose a definition of random that you think we can agree with. #2 Start talking about evolution.

Then we can drop all these technicalities.


Actually, this describes your modus operandi much more closely. You provided a definition of "random" that didn't take some of the oldest and most basic concepts in probability theory and statistics into account and therefore is invalid in so far as it does not describe most systems that could be described as random.

Interesting claim, but you don't provide any warrants, any reasons, the logic behind your point. Which is the converse of what I was claiming that you don't address the logical and cogent points made by others. This is the 'broken record' strategy of communication. If you don't explain the details of your claim and ignore the details of other people's claims it only obfuscates, because you are deliberately resisting 'getting to the bottom of' the issue. Of course if you realize you are wrong, but are just to stubborn to admit it, then obfuscation is a good way to go.

But where could I possibly find evidence of this claim??? Maybe I'll look to your next sentence?


Unfortunately, that is not my reasoning. I recognize that there seems to be some sort of cognitive break between the description of evolution as non-random and the practice of statistics within evolutionary biology. The former insists that anything that is uniformly distributed, independent, and uncorrelated is random, whereas the latter allows for those conditions and makes statements about how likely it is to expect such things given the characteristics of the data.


I make five separate points, you lump them together and respond 'that is not my reasoning' . No its not your reasoning, it is my reasoning. The onus is upon you to address my reasoning or concede the point.

The icing on the cake, is that you fall back on the 'evolutionary biologists don't understand the consequences of their statistics'. To the contrary, you don't understand the consequences of their statistics.


Even data that is generated by a random (equiprobable) process can, if the sample is small enough, display bias, correlation, or dependence. Similarly, small sample data that is generated by a process that is biased, correlated, or dependent can lack those properties. Thus, it becomes essential to develop methods to detect these and other properties that exist beyond the artifacts of sampling.
[/QUOTE]



Correction: your straw man representation of my argument is flawed.


Correction: Mijo's correction has turned correct into incorrect.

I make my conclusion from 5 separate arguments.(and about 12 in the post before that) Your reasoning is flawed. You do not address the reasoning. You don't even explain why you think it is a straw-man.


Even data that is generated by a random (equiprobable) process can, if the sample is small enough, display bias, correlation, or dependence. Similarly, small sample data that is generated by a process that is biased, correlated, or dependent can lack those properties. Thus, it becomes essential to develop methods to detect these and other properties that exist beyond the artifacts of sampling.

Again: making assertions without evidence. Also 1-5 in the previous post still apply. Most specifically #3 conflations of the methods with the model and the model with the physical world

I address this in detail ~4 posts ago in my discussion with Walter Wayne. Do try to keep up Mijo.

[articulett]

Look, Jim bob couldn't get the nozzle example. Or even the mixed nut example. In a can of mixed nuts, the biggest nuts (the Brazil nuts) end up on top giving the appearance that the company is trying to trick you into thinking there are more Brazil nuts than there are. However, it's just a seeming "design" due to natural selection. Little nuts fall between the spaces towards the bottom because they can. It doesn't matter whether the nuts are place in randomly or how they got mixed or what the variety is... the principal of SELECTION is the same. If you want to understand why the Brazil nuts are on top... you don't need to know about randomness nor probabilities-- just the selection process. If you want to know why things look designed, when they are manifestly not designed-- you must understand natural selection-- you don't need to understand a thing about assorted definitions of random or how they apply to the process at all. You JUST NEED to know the SELECTION PROCESS-- gravity and amount and size of open spaces in the container allowing for stuff to fall downwards.

Why anyone who wasn't a creationist would want to obscure understanding of this process by needing to use a reference to randomness or probabilities is beyond me.

Jimbob-- Why are the Brazil nuts on top?

(And Zosima... in the other thread I provided multiple peer reviewed works and sources that describe "random" pretty much as you have-- there is no professional source that has ever been provided that uses Mijo's bizarrely vague definition of "anything containing anything having to do with probabilities".)

Your assessment is absolutely correct-- as you know... it's coherent and concise and you gather up the goal posts as fast as he moves them-- but it's a no win. Mijo NEEDS evolution to be random. So does Walter Wayne and Jim bob. They were doing the same muddled bizarre pedantry over a year ago, and nothing has changed. Nothing. In their heads they are more expert than the experts. And I expect they all think they sound smarter than each other. I don't think any of them are following each other or that any of them are making sense to anyone other than themselves. They cannot sum up what scientists and others are saying without making it into a pscyho straw man... and there is no evidence that they even understand the very basics of evolution much less that they could convey the concept to anyone.

And yet, they continue on with the pedantry. There's a link on the front page to the Dover Transcript. And if you are ever in the mood to see a stunning recreation of this conversation (and something reminiscent of conversations you will soon learn to recognize as "creationist conversations"-- read Behe on cross examination. )

Others understand you. No one understand the self appointed experts. You understand the experts. No one understands Mijo, Jimbob, nor Walter Wayne from what I can tell.

[zosima]

Look, Jim bob couldn't get the nozzle example. Or even the mixed nut example. In a can of mixed nuts, the biggest nuts (the Brazil nuts end up on top giving the appearance that the company is trying to trick you into thinking there are more Brazil nuts than there are.) However, it's just a seeming "design" due to natural selection. Little nuts fall between the spaces towards the bottom because they can. It doesn't matter whether the nuts are place in randomly or how they got mixed or what the variety is... the principal of SELECTION is the same. If you want to understand why the Brazil nuts are on top... you don't need to know about randomness nor probabilities-- just the selection process. If you want to know why thing look designed, when they are manifestly not designed-- you must understand natural selection-- you don't need to understand a thing about assorted definitions of random or how they apply to the process at all. You JUST NEED to know the SELECTION PROCESS-- gravity and amount and size of open spaces in the container allowing for stuff to fall downwards.

Why anyone who wasn't a creationist would want to obscure understanding of this process by needing to use a reference to randomness or probabilities is beyond me.

Jimbob-- Why are the Brazil nuts on top?

But to his credit: He is on topic. ;)

That said, I can empathize with your frustration.

[articulett]

But to his credit: He is on topic. ;)

That said, I can empathize with your frustration.

Kind of... he and Walter are better than Mijo... but they have their own weird "obfuscation points" and they are the same as last year. Jimbob want to say that evolution is random because you can't predict what will be selected... he jumps tenses mid game. We don't know which nuts are going to be exactly were either-- but we can recognize a pattern.

And nuts don't pass on their features to offspring allowing the most selected to multiply exponentially while the unselected disappear.

And read the addition I added to my post above yours. I just want you to have someone applauding your coherence and intelligence. The self appointed experts never will--they are too sure of their own rightness. But others read and learn. ;)

[zosima]

Kind of... he and Walter are better than Mijo... but they have their own weird "obfuscation points" and they are the same as last year. Jimbob want to say that evolution is random because you can't predict what will be selected... he jumps tenses mid game. We don't know which nuts are going to be exactly were either-- but we can recognize a pattern.

And nuts don't pass on their features to offspring allowing the most selected to multiply exponentially while the unselected disappear.

And read the addition I added to my post above yours. I just want you to have someone applauding your coherence and intelligence. The self appointed experts never will--they are too sure of their own rightness. But others read and learn. ;)

Thanks, (-:

Speaking of obfuscation,
I foresee a lot of opportunities for fun if we conflate the topic and the speaker in this discussion about nuts. :)

[articulett]

Yes... the possibility for dual meaning could make for interesting conversation. Cyborg and I tried to pin them down with Poker before... but you know how it is... whenever you make a point, they ignore you, move the goal post, state an irrelevancy, and fling an ad hom.

No one would describe poker as a game of randomness even thought randomeness plays a role. No one would describe the Brazil Nuts on top "plot" as random... if they actually wanted to convey information as to why the nuts are on top.

Nutty nuts nutters.

You just have to be able to appreciate irony, the woo tactic of repetition without saying anything, and the potential fodder for parody. I have to put them on ignore, because they've been saying the same nothing for over a year. I just pop in to read the responses--... okay, and to enjoy cyborg's zingers and occasionally try to illuminate in case someone is confused and actually wants to understand what is and isn't random about evolution --and why scientists say the most important part is "natural selection" which some scientists refer to as "nonrandom", "the opposite of random", "biased" or even "determined".

[Wowbagger]

Well, since we've lost our marbles on the other thread (http://forums.randi.org/showpost.php?p=2692157&postcount=1039), we might as well go nuts, here.

[articulett]

I will never bathe in that muck again.

I only peek in for entertainment purposes now.

Ugh... they were saying the same nonsense at exactly this same time last year. Tons dropped in to try different ways of answering Mijo's OP and explaining what was nonrandom about evolution-- but still not a clue amongst them.

[mijopaalmc]

I will never bathe in that muck again.

I only peek in for entertainment purposes now.

You seem to have been doing an excellent job of wallowing here, seeing as how you are the sixth most frequent post in this thread with 63 posts or ~14% of the total posts. Interestingly enough, that is about a post a day (some of them fairly extensive and content-laden).

Are you really claiming that you are remaining above the fray?

[mijopaalmc]

I will never bathe in that muck again.

I only peek in for entertainment purposes now.

Ugh... they were saying the same nonsense at exactly this same time last year. Tons dropped in to try different ways of answering Mijo's OP and explaining what was nonrandom about evolution-- but still not a clue amongst them.

And you blatantly ignored the people who disagreed with you, especially Schneibster who did some really thorough line-by-line refutations of your claims.

[Walter Wayne]

...

Which incidentally, you still haven't bothered to provide. Is that ever going to happen? In absence of an alternative to compare it to, my definition is still the best one available.

...

See post #853 (though pardon my grammatical mistake).

Edited to add: and as for your insistence on uniformity, look up poisson distributed random variables, gaussian distributed random variables, binomially distributed random variables ...

[zosima]

See post #853 (though pardon my grammatical mistake).


"Random: having a state or value depends on chance."

So then you're saying that everything is random? In legal terminology this has a fatal flaw known as no bright line. From this definition there is no way to tell what it doesn't apply to. In other words, to define a term that applies to everything doesn't communicate any information because you know just as much about whatever you are talking about before or after it was said.

Just to go through some examples:

An ideal die roll: random.
An ideal die is rolled, but unrevealed to me. Its result: random.
66% chance that after switching doors, that I win in Monty hall: random.
99.999% chance that I won't be struck by lighting: random
99.9999999999999999999999999999% chance that I won't teleport across the room: random
physics,chemistry, biology: random


Gee, I'll be surprised if this post even makes it up on the forum, who knows the electrons in my computer might tunnel. I mean whether it gets posted or not is completely random.

I figure'd you would provide something better than that....care to defend this silliness? Or could you explain why you don't just post "this is random" in every thread, and insist on duking it out in the evolution thread?


Edited to add: and as for your insistence on uniformity, look up poisson distributed random variables, gaussian distributed random variables, binomially distributed random variables ...

Note that these distributions are statistics that can result from many samples of processes. If the process is truly random any individual sample is #1 uncorrelated, #2 uniform.

Here's an old response about conflating the method of investigation with the topic of investigation(originally to mijo):


So thanks for finally getting around to answering my question. Let me summarize your argument. Evolution is modeled using random variables. The term 'random variable' has the word random in its name. Thus evolutionary biologist are wrong to call evolution non-random. I think its pretty easy to see the flaw in this argument. The technique of using random variables to model our imperfect knowledge of a process doesn't say anything about the process itself. For example in the Monty Hall problem we use random variables to describe the probability of winning, but the actual process is predetermined. Nothing changes because of the way we model it. It seems obvious to me that there is a difference between a random variable and a random process. Evolution as a science uses the former, evolution is not the latter. We're done.

[mijopaalmc]

Edited to add: and as for your insistence on uniformity, look up poisson distributed random variables, gaussian distributed random variables, binomially distributed random variables ...

I asked articulett the same question many times before in the first thread devoted to this topic. She simply never answered the question, claimed I was obfuscating, and hemmed and hawed about how algebra contained random variables (http://forums.randi.org/showthread.php?postid=2725470#post2725470) (a tactic which she has repeated throughout the duration of these threads):

http://forums.randi.org/showthread.php?postid=2727501#post2727501
http://forums.randi.org/showthread.php?postid=2731372#post2731372
http://forums.randi.org/showthread.php?postid=3357723#post3357723
http://forums.randi.org/showthread.php?postid=3576893#post3576893

Basically the idea that random variable don't have to be uniformly distributed to be labeled "random" is something that seems to confound those who argue that evolution is non-random.

[mijopaalmc]

zosima-

The Monty Hall problem is trivial from the perspective from the person set the prize4s behind the doors, but that is not the perspective from which the problem is analyzed, namely that of the person who is playing the game.

Are you claiming that there is an entity that has predetermined the fates of all living thing on earth like that person who set the prizes perdetermines their location?

[Wowbagger]

Basically the idea that random variable don't have to be uniformly distributed to be labeled "random" is something that seems to confound those who argue that evolution is non-random.I think the problem, basically, is that this fact is not relevant when calling Evolution random or not. Evolution may have random elements in its models, and those elements may not have uniformly distributed variables; but that does not mean the whole thing is random! Only those parts, in those models.
And, that applies to other sciences, as well.

[zosima]

I asked articulett the same question many times before in the first thread devoted to this topic. She simply never answered the question, claimed I was obfuscating, and hemmed and hawed about how algebra contained random variables (http://forums.randi.org/showthread.php?postid=2725470#post2725470) (a tactic which she has repeated throughout the duration of these threads):

http://forums.randi.org/showthread.php?postid=2727501#post2727501
http://forums.randi.org/showthread.php?postid=2731372#post2731372
http://forums.randi.org/showthread.php?postid=3357723#post3357723
http://forums.randi.org/showthread.php?postid=3576893#post3576893

Basically the idea that random variable don't have to be uniformly distributed to be labeled "random" is something that seems to confound those who argue that evolution is non-random.

Mijo why don't you respond to the points I've made and the questions I've asked you? This is a discussion that I'm having with Walter. He's clearly much more intelligent, knowledgeable, and reasonable. So, If he makes a coherent response, which I'm quite sure he will, I'll respond to his objections. I'm even open to the possibility that a the statistics of a random process could have a different distribution than I've suggested, if I'm persuaded. I'm not open to the possibility that a random process can have any distribution. Until you fix your record player, I'm not open to anything you have to say.

Your failure to maintain topic continuity, has denied you the right to an on topic response. So please go back to the kiddy table to play with the other children, or alternatively demonstrate a little insight.

[mijopaalmc]

I think the problem, basically, is that this fact is not relevant when calling Evolution random or not. Evolution may have random elements in its models, and those elements may not have uniformly distributed variables; but that does not mean the whole thing is random! Only those parts, in those models.
And, that applies to other sciences, as well.

OK, I realize that there is a valid distinction between the process itself and the mathematical models that describe it and I agree that "random" and "non-random" may only meaningfully describe the mathematical models. However, if you are going to describe a mathematical model with random portions, then mathematically speaking to whole system is random. This is a non-negotiable point as we are describing a mathematical process and mathematically speaking any Borel-measurable function (which includes all elementary functions learned from primary school to elementary vector calculus) of a random variable is itself a random variable and the mathematical definition of a random process is a family of random variable defined of the same probability space. This is also why I am often frustrated with articulett when she insist that definition of random I am using makes algebra random, because the variables in the kind of algebra she is talking are not the random variables of probability and statistics, because they are merely values that you plug into a function and not functions in their own right as random variables are.

[zosima]

OK, I realize that there is a valid distinction between the process itself and the mathematical models that describe it and I agree that "random" and "non-random" may only meaningfully describe the mathematical models. However, if you are going to describe a mathematical model with random portions, then mathematically speaking to whole system is random. This is a non-negotiable point as we are describing a mathematical process and mathematically speaking any Borel-measurable function (which includes all elementary functions learned from primary school to elementary vector calculus) of a random variable is itself a random variable and the mathematical definition of a random process is a family of random variable defined of the same probability space. This is also why I am often frustrated with articulett when she insist that definition of random I am using makes algebra random, because the variables in the kind of algebra she is talking are not the random variables of probability and statistics, because they are merely values that you plug into a function and not functions in their own right as random variables are.

Wrong, but please do try again.

f(x) = 0*x+c

[mijopaalmc]

Mijo why don't you respond to the points I've made and the questions I've asked you? This is a discussion that I'm having with Walter. He's clearly much more intelligent, knowledgeable, and reasonable. So, If he makes a coherent response, which I'm quite sure he will, I'll respond to his objections. I'm even open to the possibility that a the statistics of a random process could have a different distribution than I've suggested, if I'm persuaded. I'm not open to the possibility that a random process can have any distribution. Until you fix your record player, I'm not open to anything you have to say.

Your failure to maintain topic continuity, has denied you the right to an on topic response. So please go back to the kiddy table to play with the other children, or alternatively demonstrate a little insight.

My, my, aren't you imperious and petulant?

I can talk to whomever I want on this thread about what ever I want as long it is on topic, and, since one of the subtopics is a meaningful definition of "random", articulett equivocation and misapplication of the definition of "random" I provided is right on track.

Anyway, if we stick to describing mathematical models of evolution, your insistence that random processes be uniformly distributed and uncorrelated is unnecessarily restrictive. For instance, Gaussian processes (http://en.wikipedia.org/wiki/Gaussian_process) can involve any random variables as long as any finite linear combinations is also Gaussian, autoregressive moving average processes (http://en.wikipedia.org/wiki/Autoregressive_moving_average_model) show correlation between time intervals, and mixing processes (http://en.wikipedia.org/wiki/Topological_mixing#Mixing_in_stochastic_processes) show statistical dependence.

[mijopaalmc]

Wrong, but please do try again.

f(x) = 0*x+c

Obviously, you don't know what a trivial case is.

[zosima]

Obviously, you don't know what a trivial case is.

Sure I do, it is a counter-example to a bad definition, that takes no effort. Now if I had to think about it my counter-example would be pathological, but still acceptable. Just a post ago this was 'non-negotiable' , but now you make exceptions for what you term trivial examples. This is just another way of saying, "you're wrong".



As to my petulance. I can't have you just making up mathematics as you go along, and then try to trick people into believing it by trying to sound authoritative. As to all the other silliness you chose to make up, I'm not worrying about it. You've given up on trying to have a discussion, and I wouldn't want to be overdressed to the party.

But just as a friendly warning I would recommend you avoid straying towards mathematics. You do remember that business with 'almost surely' where you demonstrated you didn't understand the cardinality of a set don't you?

[zosima]

Edited to add: and as for your insistence on uniformity, look up poisson distributed random variables, gaussian distributed random variables, binomially distributed random variables ...

To better clarify my point. If there are going to constitute examples of non-uniform random systems, you need to explain why they should be considered random. I don't think the fact that they use of the term 'random variable' is persuasive either.

#1 Random variable is used with distributions that are clearly not random. For example, I could have a dirac delta random variable. Ie a function with a dirac delta that is centered upon 0. It is a distribution over a random variable, but it is also only has one possible outcome. We could do the same thing over a discrete distribution as well.(In case you want to pick some nits)
Still, we would be talking about a random variable, yet a non-random system. Is the dirac delta function also random? Where do you draw the line?

#2 Probability distributions represent statistics of systems, but the systems they describe may or may not be random. For example, I can generate a binomial distribution by rolling a die many times over a number of trials and counting the numbers as they come up. Alternatively, I could write a computer program that will either return 1-6 with exactly the same frequency as the die returned the values, but in some sorted order. Both could generate a statistical fit that might be described by the binomial distribution. The computer would be deterministic and clearly so, the die would not.

#3 The Distributions themselves are not random at all. For example, if I want to generate a normal distribution, all I have to do is evaluate the probability density function for the normal distribution.(I'm not going to write it out here) This is a simple and deterministic mathematical operation. If you think that the particular distributions that you've mentioned happen to describe random processes, you're going to have to explain why, 'cause I don't see any reason why it should be assumed.

We can deduce from these examples, that the fact that these distributions involve random variables, does not imply that the system is random or deterministic. This means any definition of random is going to be one that either ignores these distributions entirely, or defines specific characteristics of the distribution that indicate that it is describing a system that is random or not.


From a perspective that jives more closely with human intuitions. I think the term random is not so binary as just 'random or not'. It would be more accurate to talk about how random a system is. A system with a uniformly distributed and uncorrelated output is as ideal a random system as you can get. A system that always outputs the same value or same sequence of values is as deterministic as you can get. A system somewhere in between will be mixed in character. If a die is .00001% more likely to roll a 6 than the other numbers, it is still mostly random, and if a system that always has the same output changes it with .00001% it is still mostly deterministic.

If you don't agree with this, please tell me, why does the use of probability distributions to describe systems make them random? Or alternatively what probability distributions describe random systems?

[cyborg]

Alternatively, I could write a computer program that will either return 1-6 with exactly the same frequency as the die returned the values, but in some sorted order. Both could generate a statistical fit that might be described by the binomial distribution. The computer would be deterministic and clearly so, the die would not.

Despite my best efforts nothing has managed to persuade anyone of the issue of making an authouritive a posteriori statement about the definitive randomness of a source.

The fact that any finite arbitrary sequence one could care to choose can be produced by an entirely deterministic mechanism doesn't seem to have slotted any cog into a new positions as far as the consequence of that fact when it comes to making bold statements about the mechanism of a system that isn't fully interrogatable.

[jimbob]

Yes... the possibility for dual meaning could make for interesting conversation. Cyborg and I tried to pin them down with Poker before... but you know how it is... whenever you make a point, they ignore you, move the goal post, state an irrelevancy, and fling an ad hom.

No one would describe poker as a game of randomness even thought randomeness plays a role. No one would describe the Brazil Nuts on top "plot" as random... if they actually wanted to convey information as to why the nuts are on top.

Nutty nuts nutters.

You just have to be able to appreciate irony, the woo tactic of repetition without saying anything, and the potential fodder for parody. I have to put them on ignore, because they've been saying the same nothing for over a year. I just pop in to read the responses--... okay, and to enjoy cyborg's zingers and occasionally try to illuminate in case someone is confused and actually wants to understand what is and isn't random about evolution --and why scientists say the most important part is "natural selection" which some scientists refer to as "nonrandom", "the opposite of random", "biased" or even "determined".

You mean like this post?

This is a digression, I suggest that if you want to pursue it further it should go in the "intelligent evolution" thread.

No.

However I can't see any useful system where the selection criteria have been chosen randomly.

Non-answer.

They might not have been chosen directly by an intelligent agency, but by other system that hadf been intellignetly designed. For example maybe the key performance parameters had been decided upon by a neural net, or maybe an evolutionary algorithm. Although I doubt this has actually happened in any real engineering.

You're making things up about the system I've never even implied.


If you want to meet the performance specification, then you need to define what the goal of the evolutionary algorithm is.

There is no performance specification. You're making things up.

If there was a self-replicating system, one wouldn't need to do this, better self-replicators would evolve.

You've never been able to come to terms with the concept that "self-replication" is simply a different abstract representation in a computer system that has no extrinsic meaning making any attempt to explain why this is completely irrelevant to the behaviour of the system as a whole a waste of my time.

I can't think of a way that evoultionary algorithms a could be used without intelligently set goals in technological development to produce something useful, and I think that this is because they can't.

Your lack of imagination is your problem.

Can you give a realistic example as to how they could?

No - because any system I describe you would invent parts never described for it that would in your mind make it invalid in some legalistic sense.

The first part you'll never come to accept is that a describing a "useful" product is a matter of who is arbitrating "useful" and will be different under different contexts.

The OP was where it was appropriate to use "randomness" when discussing evolution. You now seem to be implicitly accepting that probabilistic treatments are used implicitly by evolutionary biologists, are you now claiming that this treatment is wrong because it is "only a model"?

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

Are you claiming that chance deoes not influence which cod-fry survives and reproduces. That this reproductive is already predetermined at spawning?

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

If you state that chance does have a role, then the probabilistic treatment is valid because chance has a role. If chance does not play a role, then the probabilistic treatment is only a demonstration of our imperfect knowledge.

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

My position is the scientifically conventional one, which is accepted by most bioplogists, yours seems to be obsolete, and based on the 19th Century knowledge and assumptions (Laplacian determinism).

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

I say that which individual cod-fry reproduces is heavily influenced by chance.

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

1-million spawn, stable (or falling) population, so fewer than one repoducing adult from each parent. Two parents, so less than a 1:500,000 chance of reproducing.

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

Most of these cod spawn will be very similar to each other and their parents, yet on average two survive and reproduce.

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

Remember this post earlier in the thread, which does confirm my view that over the timescales of life, there are chance events influincing natural selection:

I've explained the concept several times and you don't get it. Repeating myself would be a waste of time.

I have wasted my time. What a fun ten minutes.



As far as I can see Cyborg has failed to answer my points.

I had two main points:

Firstly I said that without self-replication, you need to define some selection criteria. If you want to achieve anything useful, then these criteria have to be ultimately the result of an intelligent agency.

With self-replication, then natural selection follows; without self-replication, you need artificial selection. A single valid counterexample would invalidate my assertion, but Cyborg hasn't provided one, nor has he(?) even alluded to one.

Secondly The OP asked when it was valid to use "randomness" in discussingf evolution. I pointed out that "selective advantage" is a probabilistic ttreatment of natural selection. Cyborg's answer wasn't that it isn't a probabilisic treatment, but that it is only a "treatment" of natural selection. I disagree that it is "only" a treatment of natural selection, for the reasons given earlier in the post, but even if it were only a "treatment", it is still the approach used in evolutionary biology. If this is the case, why is it invalid when discussing evolution, when biologists use it?

Articulett, why is a discussion of a "selective advantage of as little as 1 in 1000" not a probabilistic approach?

[cyborg]

Firstly I said that without self-replication, you need to define some selection criteria.

Impossible to discuss with you for aforementioned reasons of your inability to cognate the nature of "self-replication".

If you want to achieve anything useful, then these criteria have to be ultimately the result of an intelligent agency.

Impossible to discuss with you for aforementioned reasons of your inability to cognate the nature of "useful".

A single valid counterexample would invalidate my assertion, but Cyborg hasn't provided one, nor has he(?) even alluded to one.

You won't and haven't read so there's no point.

Secondly The OP asked when it was valid to use "randomness" in discussingf evolution. I pointed out that "selective advantage" is a probabilistic ttreatment of natural selection. Cyborg's answer wasn't that it isn't a probabilisic treatment, but that it is only a "treatment" of natural selection. I disagree that it is "only" a treatment of natural selection, for the reasons given earlier in the post, but even if it were only a "treatment", it is still the approach used in evolutionary biology. If this is the case, why is it invalid when discussing evolution, when biologists use it?

Inpenitrable.

[articulett]

I like the nut example-- It's a good analogy... though Jimbob and Mijo suck at analogies as evidenced by this and other threads.

The "Brazil Nut plot theorists" i.e.(creationists) have a vested interest in people believing that the Brazil nuts on top are part of a plot to make it look like there are more nuts than they are.

Their technique is to laugh off the scientists and say, "they think those nuts just got there randomly-- ha what are the odds of that... they don't understand how statistically improbable that is!"

People hearing this will say, "how is it the Brazil nuts could just randomly end up on top every time?? Those scientists are full of crap".

But no scientist is saying the nuts got there randomly. There may be randomness involved... but the Brazil nuts don't end up on top randomly. We understand the principals and once anyone else did, they'd see how laughable the "Brazil nut plot" is.

And they'd see what Behe, Jim-Bob, Mijo, and Walter Wayne are doing as well. They need evolution to be random so that the "Brazil nut plot" looks more plausible. At least that's what I see. What else could it be? Isn't their goal obfuscation and a need to tie everything to random and "get the last word"-- even if they don't "know" that is what they are doing? What else do they imagine they are accomplishing? How are they not being like the "Brazil Nut Plot" theorists of my analogy?

And so they aim to deride those who are clear on the simple facts because the simple facts not only make people aware of how there is no Brazil nut plot... but also just how dishonest obfuscatory the Brazil Nut conspirators are.

The Brazil Nut conspirators must obfuscate the real understanding of the "Brazil nuts on top" for themselves and everyone else... lest people comprehend what's really going on, and just how full of BS those who speak on behalf of the nut conspiracy are. In the process they spread a bigotry against those who would do and can explain and would explain the concept to anyone who was actually interested in the truth.

[jimbob]

Random: having a state or value depends on chance.
So you can predict the sum of two die rolls? That isn't uniform. You can predict the position of someone on a snakes and later board on the second turn, after seeing the result of their first turn? That is correlated with the result of the first term.


You can predict the sum of two die rolls with better than an accuracy better than random chance. If you provide a confidence interval, you can provide an exact prediction.

I'm sorry I don't understand the 'snakes and later board' example.

I think Walter Wayne was saying that it is like a drunkard's walk, the whole trajectory is random, but depends on the past history.





Indeed, and the biggest difference is that an ionisation smoke detector is not a chaotic system. A slight difference in the decay rate leads to a slight difference in the ionisation current, which leads to a slight difference in teh "apparent" smoke density ant the output signal. A slight difference in the gain (transconductance) in the amplifying transistor similarly leads to a slight difference in the sensitivity of the detector, so this is compensated for during factory testing.

With the smoke detector slight differences in inputs lead to slight differences in outputs.

Agreed. With the qualification that the output isn't a slight difference in measured signal, it is strictly 'smoke or no'.


<nitpick>some smoke detectors do produce an oputput that is a "level of smoke" which is returned to the controller, wheich then assesses whether the whol system is indicitive of a dangerous fire or a false alarm. For example ambient pollution, or cigarette smoke. In the industry, these are termed smoke "sensors" rather than "detctors" which do only have an alarm/non-alarm output, I have previously worked in (in the fire "detector" and "sensor" development area). </nitpick>




I've got a couple of points here.

#1 Just to be clear I understand this to be from the perspective of the 'history of evolution' or 'path of evolution'. If we're talking about evolution in the sense of how a species change in response to changes in its environment(which may or may not be chaotic or random) this point is inapplicable. (Ie doesn't apply to the argument made from Baysian logic some pages back)

True, and this is where I think a lot of the differences lie.

I have said that in a stable environment, and over a long enough time, then you don't need to invoke randomness. This does cover a lot of examples used when discussing how evolution works, for example the advantage of sight.

I would still argue that the particular adaptations could still be random, e.g. compound eye vs simple eye, position of the retina etc... but the adaptation to the environment would be there.


However this stable environment is only a subset of the situations where evoution occurs, even if it is the simplest to understand.

#2 The 'consensus' I got from the 'chaotic' thread was that the jury was still out with respect to whether weather was chaotic. Moreover the 'consensus' I got was that we couldn't tell if a system was chaotic unless we are talking about a mathematical model and are in agreement about its quality of fit to the evidence.


There is quite a bit of evidence that it is chaotic, but that is why I started the other thread...



#3 I appreciate your intuition on these issues, but is there any reason you believe these systems are chaotic?

#4 How do you know that these systems are not just complex?

Positive feedback loops tend to produce unstable systems, indeed they are often used to produce oscillators. Ecosystems have lots of positive feedback loops, which would predispose the system to chaotic behaviour.


#5 How do you know that, if these systems are chaotic, that they are sensitive to random inputs?

Because that is how the maths works out. If they depend on position or momentum, they will eventually depend on quantum effects.


#6 What do you contend these inputs are?

Anything that affects the reproductive success of an organism, so including: the weather, asteroid strikes (rarely), competition, availability of mates, fertility, predation, parasites, food supply, territory, water supply, volcanoes (rarely), lightning strikes, etc...

There are many positive feedback loops, one has been hypothesised for the non-recovery of the grand bannks cod fishery. The simple analysis being that the reduced adult cod population has reduced the predation of smaller fish. These smaller fish, in turn prey on the young cod fry. The reduced predation of the smaller fish has increased the predation of the cod-fry, which in turn acts to keep the cod population down.


#7 How do you know that these systems are not constrained by negative feedback in the form of energy limitations and physical landscape for ecosystems, in terms of intertia,viscosity, and energy for weather.

#8 What are the relative scales of the development rate of 'disruptive mutations' vs 'positive feedback' in speciation. How do we know the scales are comparable?

There are obviously negative feedback loops involved in ecosystems as well as positive ones, however looking at the history of evoution

I don't get your question here. "Disruptive" mutations are rare, but they can be significant. If you are talking about geological timescales, then random events become more important in affecting how the developmetnal course of the ecosystem.

If the ecosystem starts to change, then (almost by definition) the organisms in that environment will be less well adapted to the altering environment than they would have been to the previous, stable environment. This would mean that variations are more likely to be eneficial than when the organisms were well-adapted.

Some of the positive feedbaclk loops would be those that frive the evolution of symbiotic relationships, where particular flowers and insects co-evolve.

Earlier on, I described the course of evolution as similar in some respects to a river system, these are often chaotic, and the course can seem stable for long times, but they can also change suddenly. If the topography is steep the change is less likely, if the gradients are shallow, then change is more likely. Similarly, in locally flat regions of the fitness landscape, or minor "saddles", slight changes could tip the evolution of the organism's descendents down different routes.


#9 How do we know that this 'positive feedback' doesn't just affect the speed at which the solution is generated and not the substantive result of the solution.

Your assertions are all well and good, but they're just as hand-wavy as your assertions about chaos theory which were quite vigorously shot down. Unless you can answer these questions with evidence and reason, really all you are saying is that despite the testament of people in the field, you have the strong personal conviction, a feeling, that the results of evolution involve significant chaotic effects. Which, IMO, is terribly unpersuasive.


There is plenty of evidence for discussion of chaotic behaviour in population dynamics and in other areas relevant to evolution.

I would also disagree that the assertions were "vigorously" shot down. I still contend that most physicists think that the timescales for quantum uncertainty to affect the weather is quite short. When I studied physics, the consensus seemed to be about 6-weeks. My very naive treatment of the numbers came to a conclusion that was not vastly different. Life has existed for over 3-billion years, so that is the sort of timescale that would be needed if random events didn't affect natural selection affecting the weather.

[mijopaalmc]

I like the nut example-- It's a good analogy... though Jimbob and Mijo suck at analogies as evidenced by this and other threads.

The "Brazil Nut plot theorists" i.e.(creationists) have a vested interest in people believing that the Brazil nuts on top are part of a plot to make it look like there are more nuts than they are.

Their technique is to laugh off the scientists and say, "they think those nuts just got there randomly-- ha what are the odds of that... they don't understand how statistically improbable that is!"

People hearing this will say, "how is it the Brazil nuts could just randomly end up on top every time?? Those scientists are full of crap".

But no scientist is saying the nuts got there randomly. There may be randomness involved... but the Brazil nuts don't end up on top randomly. We understand the principals and once anyone else did, they'd see how laughable the "Brazil nut plot" is.

And they'd see what Behe, Jim-Bob, Mijo, and Walter Wayne are doing as well. They need evolution to be random so that the "Brazil nut plot" looks more plausible. At least that's what I see. What else could it be? Isn't their goal obfuscation and a need to tie everything to random and "get the last word"-- even if they don't "know" that is what they are doing? What else do they imagine they are accomplishing? How are they not being like the "Brazil Nut Plot" theorists of my analogy?

And so they aim to deride those who are clear on the simple facts because the simple facts not only make people aware of how there is no Brazil nut plot... but also just how dishonest obfuscatory the Brazil Nut conspirators are.

The Brazil Nut conspirators must obfuscate the real understanding of the "Brazil nuts on top" for themselves and everyone else... lest people comprehend what's really going on, and just how full of BS those who speak on behalf of the nut conspiracy are. In the process they spread a bigotry against those who would do and can explain and would explain the concept to anyone who was actually interested in the truth.

The only problem with articutett's attempt at a summary of our views* is that it doesn't even begin to come close to an accurate portrayal of out views. Our views are that even if the movements of the nuts are completely random, processes such as the infill and close packing of smaller particles behind the bigger particles would force them to the top. There is no room, even implicitly, for a guiding intelligence (supernatural or otherwise) to conspire to put the Brazil nuts at the top.

I would really like to know why articulett insists on misrepresent people's positions if her position is as strong as she says it is.

*jimbob and Walter Wayne, let me know if you don't agree with anything I said.

[zosima]

I think Walter Wayne was saying that it is like a drunkard's walk, the whole trajectory is random, but depends on the past history.
I get that. In the same way that the density or temperature of a gas is non-random so is the sum of the dice. Even though each particle may be in a random walk or each die may be behaving randomly. Density is actually an exact analogy, it is the integral(sum) over the energy distribution.


<nitpick>some smoke detectors do produce an oputput that is a "level of smoke" which is returned to the controller, wheich then assesses whether the whol system is indicitive of a dangerous fire or a false alarm. For example ambient pollution, or cigarette smoke. In the industry, these are termed smoke "sensors" rather than "detctors" which do only have an alarm/non-alarm output, I have previously worked in (in the fire "detector" and "sensor" development area). </nitpick>
It doesn't really matter if some are. The smoke detector is a counter example, thus there only need to exist one smoke detector that has binary output to prove the point. You might as well have said that it could be a spark plug. It wouldn't make a difference to the logic of the point.


I have said that in a stable environment, and over a long enough time, then you don't need to invoke randomness. This does cover a lot of examples used when discussing how evolution works, for example the advantage of sight.

I would still argue that the particular adaptations could still be random, e.g. compound eye vs simple eye, position of the retina etc... but the adaptation to the environment would be there.

However this stable environment is only a subset of the situations where evoution occurs, even if it is the simplest to understand.


#1 See the punctuated equilibrium example. I brought that up first and I'm not sure why you don't consider that persuasive evidence. It shows that in response to change the species changes quickly and reliably. What this point means is that evolution is driven by the environment.

#2 The punctuated equilibrium argument dovetails well with the explanations for the variation in eyes. Compound eyes support the evolutionary strategy of insects. Survival via multiplicity and redundancy. Simple eyes like ocelli show up in spiders, which generally do not require good vision. Their niche requires them to be able to sense creatures in their web, and quite unsurprisingly they have very high sensitivity to vibration. This example if anything is a testament to the non-randomness of evolution.

#3 For there to be any sort of spontaneous randomness a species needs to be in a situation where the environment favors either of two possible mutations equally and these mutations have to be comparably likely. Th evidence that this sort of spontaneous bifurcation happens is non-existent and the math indicates that it is vanishingly unlikely. For your example to make sense it would have to be reasonably probable that a snail could spontaneously generate a compound eye. Of course, this is exactly what doesn't happen in evolution, although it is the sort of thinking that creationists employ. It is this very sort of contradiction that indicates that evolution must be non-random.

#4 If your claim is that the path of evolution is random, it simply reduces to the claim that history(or prehistory) is random. So, if you could, do you think you could start saying that rather than singling out evolution as being somehow different than the claim that comets are random? It would save people a lot of time in 'spotting the crackpot' so to speak.


There is quite a bit of evidence that it is chaotic, but that is why I started the other thread...

You may think this, but there was by no means a consensus in the other thread. I was disputing your claim that this was somehow the consensus. Moreover, it seemed to me that many of the people who were most familiar with the topic tended to disagree.


Positive feedback loops tend to produce unstable systems, indeed they are often used to produce oscillators. Ecosystems have lots of positive feedback loops, which would predispose the system to chaotic behaviour.

Okey dokey. Once again you provide your intuitions. What positive feedback loops? The assertion that ecosystems have 'lots of positive feedback loops' is at best a hunch.

Moreover, I double checked with a friend of mine who knows a lot more about control systems than probably anyone on this board and he verified what I was pretty sure is already true. Whether or not a system has positive feedback loops says nothing about whether the system is stable, unstable, chaotic, or not chaotic. A system with positive feedback loops can be characterized with a differential equation. Upon solving this equation whether the system is stable or not depends upon what the poles of the solution happen to be. Not surprisingly this is almost exactly the same claim as the one made by CoolSkeptic in the chaos thread. You must be able to characterize the system to determine whether its chaotic.

Also what aspect of ecosystems do you assert is chaotic? As I understand it an ecosystem quickly approaches a Nash equilibrium. The aspects of game theory that dominate ecological science indicate regularity. For example, dawkins talks about how the distribution of sexes in a species is described reliably by a game theoretical approach.


Because that is how the maths works out. If they depend on position or momentum, they will eventually depend on quantum effects.


Um.....you are going to have to show me that math, because I think you are completely wrong. For example...I can calculate the position of a bullet after a certain amount of time from the momentum of the rifle during recoil, and the mass of the bullet. Change in any of the parameters leads to a linear change in the output. Thus the system is neither chaotic, nor unstable. Moreover it involves no quantum terms.

x = t*(p/m)

x = position
t = time
p = momentum
m = mass


Anything that affects the reproductive success of an organism, so including: the weather, asteroid strikes (rarely), competition, availability of mates, fertility, predation, parasites, food supply, territory, water supply, volcanoes (rarely), lightning strikes, etc...


Nice laundry list....here is my laundry list response:
Lightning:only affects individuals, averages on level of species
Weather,Water supply: effects last much shorter periods of time than even individual creatures. Ie averages on the time scale of species existence.
Competition,availability,fertility, predation,parasites,food supply, territory: Described with a non-chaotic, non-random nash equilibrium.
Volcanos, Asteroid strikes: only random in the sense that 'the sun rising tomorrow' is random.

Of course, again, these arguments reduce to history being random as well


There are many positive feedback loops, one has been hypothesised for the non-recovery of the grand bannks cod fishery. The simple analysis being that the reduced adult cod population has reduced the predation of smaller fish. These smaller fish, in turn prey on the young cod fry. The reduced predation of the smaller fish has increased the predation of the cod-fry, which in turn acts to keep the cod population down.

Right....see my explanation on positive feedback. This example is perfect, this predation cycle drives down the cod population until either #1 the cod go extinct or #2 it stabilizes due to decreased food supply for small fish. Stable Equilibrium Not Chaos


There are obviously negative feedback loops involved in ecosystems as well as positive ones, however looking at the history of evoution

Looking at the history of evolution what? Most systems in the biological world eventually reach a resource constraint, ie negative feedback, thus a system with positive feedback eventually moves into a negative state and the system stabilizes. Of course....see my previous analysis about how your preoccupation with feedback loops is irrelevant.


I don't get your question here. "Disruptive" mutations are rare, but they can be significant. If you are talking about geological timescales, then random events become more important in affecting how the developmetnal course of the ecosystem.

If the ecosystem starts to change, then (almost by definition) the organisms in that environment will be less well adapted to the altering environment than they would have been to the previous, stable environment. This would mean that variations are more likely to be eneficial than when the organisms were well-adapted.

Some of the positive feedbaclk loops would be those that frive the evolution of symbiotic relationships, where particular flowers and insects co-evolve.


My point is you have no idea how frequent these mutations are. My point is that if you look at the rate of birth and mutation in organisms we have reason to think that disruptive mutations are virtually certain on a geological time scale, even though they may be improbable on the scale of a generation.

For example, Gould has an example in the structure of evolutionary theory with a proto-lungfish. This creature starts as a fish with no lungs, there is a drought(ie weather effect), the environment dries up, the fish evolves lungs, the drought ends the lungs quickly become vestigial and disappear. There is another drought, again the fish evolves lungs, again the drought ends and the lungs disappear. This happens over and over in the fossil record. You would think that lungs are an incredibly disruptive mutation, but it turns out that on a geological timescale, for that organism they were not. In fact, their development was inevitable.


Earlier on, I described the course of evolution as similar in some respects to a river system, these are often chaotic, and the course can seem stable for long times, but they can also change suddenly. If the topography is steep the change is less likely, if the gradients are shallow, then change is more likely. Similarly, in locally flat regions of the fitness landscape, or minor "saddles", slight changes could tip the evolution of the organism's descendents down different routes.


I remember this, but it is an example divorced from the theory and reality of evolution. Gould talks about this as well. In places that have a flat landscape the diversity of the gene pool increase to the point that additional mutations stop the creature from breeding with itself. If this cannot occur it cannot spread any further. Moreover the landscape is constrained by resource(energy) limitations in the environment. So there will always be resistance to moving away from the nash equilibrium and 'meandering' around the fitness landscape. The organism can only change when the fitness landscape changes.



I would also disagree that the assertions were "vigorously" shot down. I still contend that most physicists think that the timescales for quantum uncertainty to affect the weather is quite short. When I studied physics, the consensus seemed to be about 6-weeks. My very naive treatment of the numbers came to a conclusion that was not vastly different. Life has existed for over 3-billion years, so that is the sort of timescale that would be needed if random events didn't affect natural selection affecting the weather.

There certainly wasn't 'consensus' but it seemed like the people who were most knowledgeable suggested you learn some math. As to where that 6-weeks number comes from, as was noted in the other thread, unless you've got a secret model of weather you haven't published, then you are pulling that number out of your posterior.

Moreover these vague claims about weather don't prove anything about evolution, unless you are making the very non-mainstream claim that quantum effects are significant in climate. A rain storm isn't going to have any effect on a species, even a hurricane. You don't hear about any extinctions from those sorts of events, because even if we can't predict the specific time and strength, they happen several times every year and species are hardened against them. So how does weather even matter at all? Could you provide a concrete scenario.

As to 3-billion years...you are doing the analysis backwards. The longer the period of time the more likely that all different configurations are tried and any randomness averages out. (ie many hurricanes/monsoons per year)

[articulett]

Beautifully stated Zosima. Really. Elegant. Clear. Concise. Accurate. And specifically tailored to jimbob. But don't expect it to make a dent with him. Just revel in the impenetrability coupled with the imagined expertise. You will learn to recognize it in it's many different forms. It's not fixable-- but others read and learn and your skin gets thickened in the process as does your own understanding of what Dawkins et. al. are actually saying and why the self appointed experts aren't really saying anything at all.

[sphenisc]

I think Walter Wayne was saying that it is like a drunkard's walk, the whole trajectory is random, but depends on the past history.


Talking of which...

http://www.bbc.co.uk/radio4/science/thematerialworld.shtml

This week’s Material World includes an interview with Dr. Leonard Mlodinow, Computation and Neural Systems, California Institute of Technology (Caltech), whose new book is The Drunkard’s Walk: How Randomness Rules Our Lives (Allen Lane).

Use the "Listen again" feature to hear the programme and find out how a real scientist defines random. :)

[zosima]

Beautifully stated Zosima. Really. Elegant. Clear. Concise. Accurate. And specifically tailored to jimbob. But don't expect it to make a dent with him. Just revel in the impenetrability coupled with the imagined expertise. You will learn to recognize it in it's many different forms. It's not fixable-- but others read and learn and your skin gets thickened in the process as does your own understanding of what Dawkins et. al. are actually saying and why the self appointed experts aren't really saying anything at all.

:blush: Thanks, I do feel like I'm learning something from this even if it seems like some of my fellow forum-goers' ideas aren't really evolving.(lol, I can't help it with the corny jokes) At the very least, this discussion might convince someone to read a book by an expert on the subject.

[Earthborn]

This week’s Material World includes an interview with Dr. Leonard Mlodinow, Computation and Neural Systems, California Institute of Technology (Caltech), whose new book is The Drunkard’s Walk: How Randomness Rules Our Lives (Allen Lane).Speaking of drunkard's walks, this interview (http://www.pbs.org/newshour/gergen/november96/gould.htm) with Stephen Jay Gould is also interesting. And speaking of how randomness rules our lives, this website (http://bioinfo.med.utoronto.ca/Evolution_by_Accident/Evolution_by_Accident.html) by evolutionary biologist Laurence A. Moran -- author of "Evolution by Accident" -- is also on topic. Neither one appears particularly afraid to call evolution "random".

[Dancing David]

All treatment with antibiotics is acidental since penecillin was discovered by accident.

All modern surgery is WWII since most of it was developed there.

[mijopaalmc]

All treatment with antibiotics is acidental since penecillin was discovered by accident.

All modern surgery is WWII since most of it was developed there.

Nice straw men!

[zosima]

Speaking of drunkard's walks, this interview (http://www.pbs.org/newshour/gergen/november96/gould.htm) with Stephen Jay Gould is also interesting. And speaking of how randomness rules our lives, this website (http://bioinfo.med.utoronto.ca/Evolution_by_Accident/Evolution_by_Accident.html) by evolutionary biologist Laurence A. Moran -- author of "Evolution by Accident" -- is also on topic. Neither one appears particularly afraid to call evolution "random".

Those are neat articles, thanks for the links. I don't think I would disagree largely with either of them.

As Moran states evolution is as random as history is random, which I certainly wouldn't disagree with. (In fact, I said exactly that in my last post.) Moreover, the claim that evolution is 'random' in the sense that it is unpredictable is indisputable(unless someone wants to start predicting the course of history.) Incidentally, this is the definition that Moran uses for random.

The only real issue I might take is with Moran's characterization of genetic drift, which seems a bit antiquated. If you look at explanations of genetic drift they always start with a 50/50 distribution of alleles in a gene pool. If the distribution is not 50/50 and genetic drift is significant, because the population is small, it reliably drives the allele with smaller frequency out of the gene pool. If genetic drift is insignificant, because the population is large, then it takes a back seat to natural selection. This is the reasoning that causes evolutionary theorists to favor the importance of selection over drift. This is particularly true with new mutations. Since mutations with small frequencies tend to be drifted out of the gene pool, a new mutation can never drift its way into significance.(or at least such an outcome is vanishingly improbable) It must be favored by selection to ever reach a significant frequency.

Insofar as Gould's interview is concerned, I'd recommend not reading too much into Gould's attempt to explain a random walk to the masses. Especially since he's making the point in the context of trying convince people that the progressivist view of evolution in wrong. Gould describes evolution as almost exactly analogous to a gas. It reliably expands to fill the space available to it, despite the unpredictable behavior of its individual elements. This is life filling all available ecological niche's. Gould too would argue that any 'random' elements are the arguments that fundamentally change the ecological landscape. These things are the punctuation in his punctuated equilibrium theory. In fact, in his last work, he saw evolution as nearly completely driven by external pressures, with a species not evolving unless some event comes along to 'pop the balloon' so to speak.

I think the issues being argued in this thread are:
#1 whether or not evolution is a chaotic process.
#2 whether any probabilistic system is random.

[articulett]

Speaking of drunkard's walks, this interview (http://www.pbs.org/newshour/gergen/november96/gould.htm) with Stephen Jay Gould is also interesting. And speaking of how randomness rules our lives, this website (http://bioinfo.med.utoronto.ca/Evolution_by_Accident/Evolution_by_Accident.html) by evolutionary biologist Laurence A. Moran -- author of "Evolution by Accident" -- is also on topic. Neither one appears particularly afraid to call evolution "random".
The point? Both make a concerted effort to point out that natural selection is not random.

Neither are as good at conveying the information as folks like PZ Myers who are very aware of the commonest confusion people have along with why creationist like to obfuscate understanding with the term. No evolutionist is adverse to the term random. It's the misuse designed to confuse understanding of the main part of evolution-- Darwin's theory-- the thing that shows how things look designed-- NATURAL SELECTION.

http://scienceblogs.com/pharyngula/2008/06/a_good_question.php#comments


Get it? I thought not. I'm sure your scientists would have no problems using the term random in describing the Brazil nuts on top scenario. But they would be extra careful of using the term in a way that could be all to easily extrapolated to mean the "Brazil nut plot" was likely. Get it? Or do you suck at analogies like Mijo and Jimbob?

Here's more about fabulous creationist obfuscation on this very point as if you were actually interested in what scientists are actually saying on the topic and why they would never describe evolution in the way Mijo, Behe, or Jimbob is:


http://scienceblogs.com/pharyngula/2008/06/local_boy_gets_obnoxious.php#comments

It all depends on your goal of course. If obfuscation is your goal or to make everyone aware of the randomness involved in evolution (as though that part isn't obvious)-- then be my guest.

Knock yourself out... you can use the terms and definitions that people who actually communicate to others use... or you can imagine that somehow you are doing so and that you are conveying something of value to someone other than yourself.

[Wowbagger]

However, if you are going to describe a mathematical model with random portions, then mathematically speaking to whole system is random.Okay, if you want to define random to include "any model in which any portion is random", then that's your business.

But, to science, that is an incredibly useless definition. In order to render such models as more powerful tools for discovery, it seems it is better to think of them as "not entirely random".

[mijopaalmc]

The point?

What's the point of explaining it to you, since you are so obviously and willfully ignoring it.

Both make a concerted effort to point out that natural selection is not random.

That may be true, but Moran's piece in particular also made concerted effort to point out that natural selection is not the only process at work in evolution, that other processes than natural selection may be more important to the the overall process of evolution than natural selection, and that, probably most importantly of all, natural selection's being non-random does not make evolution itself non random.

[mijopaalmc]

Okay, if you want to define random to include "any model in which any portion is random", then that's your business.

But, to science, that is an incredibly useless definition. In order to render such models as more powerful tools for discovery, it seems it is better to think of them as "not entirely random".

I'm sorry but this comment seems to imply an incredible ignorance of the last 85 years of research into the stochastic modeling of evolution. For reviews of this research you should consult:

Stochastic Models of Evolution in Genetics, Ecology and Linguistics (http://arxiv.org/PS_cache/cond-mat/pdf/0703/0703478v1.pdf)


Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology (http://mmbr.asm.org/cgi/content/full/65/1/151.pdf)

Note in particular how the deterministic behavior that articulett and other cherish so much can be described the limiting behaviors of the stochastic models in large populations and over long periods of time.

[zosima]

Okay, if you want to define random to include "any model in which any portion is random", then that's your business.

But, to science, that is an incredibly useless definition. In order to render such models as more powerful tools for discovery, it seems it is better to think of them as "not entirely random".

Not only is it useless, it is also wrong. Mijo conceded my counter-example; going from this point being 'non-negotiable' to negotiable. Mijo's statement only holds true insofar as all the examples that disprove his definition are ignored.
Then again that is not so different than the strategy Mijo applies to all the points he makes. So I suppose it is not surprising.

[articulett]

Not only is it useless, it is also wrong. Mijo conceded my counter-example; going from this point being 'non-negotiable' to negotiable. Mijo's statement only holds true insofar as all the examples that disprove his definition are ignored.
Then again that is not so different than the strategy Mijo applies to all the points he makes. So I suppose it is not surprising.

Nor is it random... :)

[mijopaalmc]

Not only is it useless, it is also wrong. Mijo conceded my counter-example; going from this point being 'non-negotiable' to negotiable.

I did not actually concede your "counter-example"; I just never adequately responded to it. (Somehow I think that no response would be adequate to convince you that that you do in fact not understand the basic concepts of probability theory, because you seemed to have decided that I am a priori wrong.)

Your example is in fact a random variable, just as all measurable functions of random variables are. In essence, just because one event has a probability of 1 doesn't make the distribution non-random because other events still exist they just happen with a probability of zero.

[Wowbagger]

I wonder if Mijo could give us a clear-cut example of how defining evolution as "entirely random" could yield more new discoveries, vs. defining it as "NOT entirely random".

He can take his time, if he needs to. I am attending a conference most of this weekend, and won't be browsing here, much, in the next few days, anyway.

Actual examples are preferred. But, hypothetical, "in principal" examples would be acceptable, as long as the point is relatively clear.

[articulett]

Natural selection takes the very best of the "random" strands of DNA and multiplies them exponentially... giving them more tickets in the winning mutation lottery to be selected in a later environment. At the same time, it immediately wipes out the most deleterious stretches of DNA so they never have a chance to mutate.

THIS is the very essence as to how things become ordered... how they appear so amazingly designed. This is not the essence of how planets and galaxies and non replicating systems get the appearance of design. And this is not random to anyone but a creationist or someone confused by a creationist.

Having random components does not a random process make.

(Wowbagger... have fun at your humanist conference... looking forward to your insights on the forum and at TAM)

[mijopaalmc]

I wonder if Mijo could give us a clear-cut example of how defining evolution as "entirely random" could yield more new discoveries, vs. defining it as "NOT entirely random".

See, I understand that distinction you are trying to make here, but I don't find it of very much utility, to people who understand probability theory. Processes that contain random elements are by definition random. Where the idea of something being "entirely" random comes from seems to be the conflation of randomness with fairness (i.e., equiprobability).

He can take his time, if he needs to. I am attending a conference most of this weekend, and won't be browsing here, much, in the next few days, anyway.

I am also in a similar situation. I will be helping a friend move across the country so I will not be checking the forum for a about a week.

[zosima]

I did not actually concede your "counter-example"; I just never adequately responded to it. (Somehow I think that no response would be adequate to convince you that that you do in fact not understand the basic concepts of probability theory, because you seemed to have decided that I am a priori wrong.)

#1 As far as I am concerned running away from a strong objection to a fallacious claim is concession, or perhaps somewhat worse than concession. This is particularly true for you insofar as you have a habit of showing complete amnesia to the points that 'sink your battleship'.

#2 I don't think you are a priori wrong about evolution, I think you are a posteriori wrong. Insofar as science is an empirical study, your claims about evolution are proven wrong by evidence. Although, admittedly, your claims about mathematics are a priori wrong.
Speaking of false claims about mathematics....


Your example is in fact a random variable, just as all measurable functions of random variables are. In essence, just because one event has a probability of 1 doesn't make the distribution non-random because other events still exist they just happen with a probability of zero.

#1 This is the 'almost surely' business... we went over this before and you still seem to be missing the point. This claim about the possibility existing with a vanishingly small probability is only true if the function I provided( f(x)=0*x+c) involves a random variable defined over a field with an uncountably large number of elements(like the reals or the complex numbers) if the distribution is defined over a finite field or a countably infinite field(like the rationals or the natural numbers) then the probability of the outcome is exactly 0. Thus my counter example is definitely correct if defined over a finite field, like the non-negative integers modulo 7.

#2 Since evolution involves a discrete number of individuals, it will never correspond to the idealized models of the reals or the complex numbers. It will always exhibit behavior over a finite field. So your objection above, specifically doesn't apply to evolution.

#3 This ignores the fact that a probability distribution over the reals with a dirac delta in it, is not random at all, but simply not-deterministic or not probable. If a model involves a significant random variable the term that is often used technically is stochastic. Stochastic is not freely interchangeable with random. Models with random components may be Stochastic, but not all Stochastic models have random components. The components may be probabilistic, but behave in ways that deviate significantly from random.

#4 The paper you cited actually makes my point incredibly well. Stochastic Models of Evolution in Genetics, Ecology, and, Genetics, being a technical paper, takes extreme care in their use of terms. The authors call models that have significant probabilistic components stochastic. They call events that are not deterministic probabilistic and they only use random when they are talking about events that are uniformly distributed and uncorrelated.

For example:
A haploid or randomly-mating diploid population evolving this way is ofter referred to as an ideal population. In reality, individuals do not mate at random, and there is often a preference, or requirement, for mating to occur between or within different classes of individuals.

#1 They say it perfectly, a preference(or non-uniformity in choice) is a deviation from random. Game. Set. Match.

#2 The authors also make my point about genetic drift powerfully in equation 136, which describes whether a new mutation can become dominant in a population via genetic drift. What the equation shows is that the trait cannot be neutral or disadvantageous and increase in frequency via drift. It must have a selective advantage to increase in frequency. This confirms the intuition that gene frequencies will not drift without the help of selection.

#3 All the points you make, rely on somehow claiming that the statistics of a model at the limit must necessarily be random if a model has random components. The whole reason for looking at the behavior of a model at the limit is to be able to divine the regularities in the model despite any noise in the system. Your point has been been refuted dozens of times in this thread. See my example from the moments of a gas with a Boltzmann energy distribution if you are still confused about this point.

[zosima]

See, I understand that distinction you are trying to make here, but I don't find it of very much utility, to people who understand probability theory. Processes that contain random elements are by definition random. Where the idea of something being "entirely" random comes from seems to be the conflation of randomness with fairness (i.e., equiprobability).


#1 You still don't give any example of how the definition is any more useful. You just make some vague inference that people who disagree with you don't understand probability. Which incidentally, flies in the face of just about every mathematical example to try to bring into the discussion.

#2 Again the characterization of the definition of random as only equiprobable is missing the point. It is both uniformly distributed and uncorrelated.

#3 Imagining that this has anything to do with fairness demonstrates just how poorly you really do understand the subject matter at hand. This has nothing to do with fairness. It has to do with predictability. That is why the correlation constraint is just as important as uniformity. Several posts back I went through how with these two constraints you can guarantee a variable is unpredictable.

#4 An equivalent mis-characterization of your point would be something like "your confusion seems to come from conflation of randomness and politeness". Ie it is a complete non sequitur

[articulett]

Bingo!

His arguments are coming from his a**posterior.

He is a Brazil not conspiracist trying to say that scientists think the nuts just got there randomly... he knows that this makes the plot about" people purposefully putting the big nuts on top to make people believe there are more" is more believable if they think that scientists think... that the nuts just "randomly" end up on top and/or people just happen to "randomly" open nut cans where the Brazil nut happened to have "randomly" risen.

The point is to keep people from understanding why time and gravity are selection forces (NATURAL SELECTION) that will ensure that the little nuts fall through the holes while the big nuts stay afloat... thus making it extremely unlikely that you will ever have a canister of mixed nuts where the nuts look evenly mixed. The more "natural selection"--the more the uneven the distribution. Natural selection is a nonrandom filter that gives a weird impression of purposeful design or intent at times in the brains of those who evolved to notice design, meaning, patterns, and intent-- even when they aren't there.

[mijopaalmc]

Bingo!

His arguments are coming from his a**posterior.

He is a Brazil not conspiracist trying to say that scientists think the nuts just got there randomly... he knows that this make the plot about people purposefully putting the big nuts on top to make people believe there are more is more believable if they think that scientists think... that the nuts just "randomly" end up on top and/or people just happen to randomly open nut cans where the Brazil nut happened to have randomly risen.

The point is to keep people from understanding why time and gravity are selection forces (NATURAL SELECTION) that will ensure that the little nuts fall through the holes while the big nuts stay afloat... thus making it extremely unlikely that you will ever have a canister of mixed nuts where the nuts look evenly mixed. The more "natural selection"--the more the uneven the distribution. Natural selection is a nonrandom filter that gives a weird impression of purposeful design or intent at times in the brains of those who evolved to notice design, meaning, patterns, and intent-- even when they aren't there.

You are ignoring the fact that the assuming that the nuts move about randomly does not preclude the infilling and close packing of the smaller nuts below the bigger ones biasing the movement of the bigger nuts to the top of the can. Simply saying that the process has orderly long-term result doesn't mean that any of the component processes are non-random.

[articulett]

I think all the smart folks know that understanding of natural selection is inversely related to belief in god. I am quite certain all the focus on randomness is to make sure that people do not understand natural selection. Whether it's why Brazil Nuts are on top or the way life seems to look amazingly well designed-- Natural Selection is by far the best, most satisfying, and most useful explanation... and it puts all woo to shame. Understanding it, helps us understand how our mind tricks itself... and it puts us on the look out for other naturalistic explanations we had become unaware of.

[jimbob]

The only problem with articutett's attempt at a summary of our views* is that it doesn't even begin to come close to an accurate portrayal of out views. Our views are that even if the movements of the nuts are completely random, processes such as the infill and close packing of smaller particles behind the bigger particles would force them to the top. There is no room, even implicitly, for a guiding intelligence (supernatural or otherwise) to conspire to put the Brazil nuts at the top.

I would really like to know why articulett insists on misrepresent people's positions if her position is as strong as she says it is.

*jimbob and Walter Wayne, let me know if you don't agree with anything I said.


Actually the brazil nut fairys could do this, but the outcome wouldn't be random because a probabilistic tresatment shows a drift in one direction. This differes to evolution, where the direction of drift alters.

Articulett, do you accept that when evolutionary biologists describe "a selective pressure of as little as 0.1%" they are using a probabilistic treatment to describe natural selection?

[Dancing David]

Nice straw men!

Takes one to know one! ;)

Oh straw master, evolution is random since it relies on random processes.

I would say it is a mix of random and causal.

[articulett]

I know... you got to love the irony in that one. The ones who imagine themselves experts at logical fallacies seem to be utterly blind to how much they rely on them (logical fallacies) --and really not much else -to support whatever points they imagine themselves to be making.

For fun, check out some of the Dover transcript...
http://www.talkorigins.org/faqs/dover/day12pm.html for example...

note Behe's usage and obfuscation of the word random...
Zosima, I suspect you will experience deja vu.

[Wowbagger]

See, I understand that distinction you are trying to make here, but I don't find it of very much utility, to people who understand probability theory.Uh, wait a minute... weren't you the one trying to push the distinction?


Processes that contain random elements are by definition random.And, I asked you how does that statement help us make more new discoveries about life, vs. accepting the process as "not entirely random"?

But, forget the word "entirely" since it seems to confuse us a bit. Evolutionary biologists more often refer to the process of Evolution as "non-random". Why do you think that is?

If we were to call the process random, in the way you describe, you have to describe how that would help us make more powerful discoveries about life, than the descriptions evolutionary biologists are currently using.

And, please, keep your description as clear-cut as possible.


Where the idea of something being "entirely" random comes from seems to be the conflation of randomness with fairness (i.e., equiprobability). I did not mean to imply equiprobability in my use of the word "entirely". I meant it in the context you described: Calling a process with only some random elements as [entirely] random. Instead of non-random or partly-random or "not entirely random", etc.

[Mitchell314]

Would chaotic be better than random in this sense?

[zosima]

Would chaotic be better than random in this sense?

Chaotic would be better, if evolution were chaotic. But whether or not chaos is important or necessary to evolution is certainly not to be taken for granted, and is an issue of much debate in this thread, as well as others.

So if you have evidence that evolution is chaotic please do present it. But just so we don't reiterate a lot of ground that has already been covered, you might want to reread the discussion that jimbob and I have had in this thread and the 'chaotic systems & repeatability' thread. 'Cause if you start talking about quantum mechanics and butterflies flapping their wings during hurricanes I'm going to facepalm so hard its not even funny.
http://kevinchiu.org/emote/facepalm.jpg
http://www.forumammo.com/cpg/albums/userpics/10071/picard-no-facepalm.jpg

[Mitchell314]

Okay, so the motion of molecules are chaotic. But one can reasonably determine the motion the overall object.

Organisms are molecules, species are the fluids composed of them. But the Brownian motion overtime changes how these different 'fluids' interact, even though the individual motions are by themselves somewhat chaotic (indifferent). Over time, the individual nuances have form, though any particular...um...thingamajig and any point in time is seemingly, well, the R word.

Or something like that. Go with Psychohistory if you will. And don't step on butterflies, so philosophers and mathematicians won't be nondeterministically nudged to bother us about them.

[zosima]

Okay, so the motion of molecules are chaotic. But one can reasonably determine the motion the overall object.

Organisms are molecules, species are the fluids composed of them. But the Brownian motion overtime changes how these different 'fluids' interact, even though the individual motions are by themselves somewhat chaotic (indifferent). Over time, the individual nuances have form, though any particular...um...thingamajig and any point in time is seemingly, well, the R word.

Or something like that. Go with Psychohistory if you will. And don't step on butterflies, so philosophers and mathematicians won't be nondeterministically nudged to bother us about them.

We've talked about this pretty thoroughly already. So just scan through the tons of other posts, and you can role play that you were actually writing for whichever side you agree with.

[Wowbagger]

Actually, that highlights one of the problems with this thread: There are tons of other posts on here, and no one, not even I who started this, is probably going to read and sort through every single one of them.

It might be best just to summarize the discussion, to answer new questions. And, perhaps provide links to more info: Either other posts or other web sites. Whatever.

[zosima]

Actually, that highlights one of the problems with this thread: There are tons of other posts on here, and no one, not even I who started this, is probably going to read and sort through every single one of them.

It might be best just to summarize the discussion, to answer new questions. And, perhaps provide links to more info: Either other posts or other web sites. Whatever.

Ya, It would be hard for me to fairly summarize the position, seeing as how I tend towards the deterministic extreme.

I think the issue of chaos was covered pretty well in the other thread that I referenced though. I think it got resolved in a somewhat more technical fashion.

With respect to both randomness & chaos no one is arguing that they don't exist and that they aren't important parts of all sorts of natural processes.

But any sort of the claim that evolution is uniquely random(or chaotic) needs to show either (1) that there is some macroscopic characteristic of evolutionary processes that makes it random or chaotic. or (2) that we have strong reason to believe that microscopic random or chaotic processes will actually have macroscopic random effects.

So the claim that living things are made up of fluids which are governed by Brownian motion is, at this point, both unoriginal and insufficient.

I personally think, that people automatically assuming that these microscopic characteristics scale up to the macroscopic level, missed a fundamental point in their scientific education. If anything,study of Brownian motion in physics or chemistry, demonstrates exactly the opposite, that random microscopic behavior cancels and that the macroscopic behavior of these systems is incredibly regular.

Moreover, to characterize the cellular machinery of a cell as some sort of crapshoot is missing a fundamental point of biology. Cells perform specialized tasks for sometimes as long as hundred years without failure. During replication unwinding the DNA causes the molecules to experience significant torques as it occurs incredibly quickly, and yet these systems are still reliable for many generations within an organism and across generations.

So I guess I see waving ones hands and looking at it as all random as intellectually lazy, basically assuming we know as much as we can know, when the fact of the matter is that the longer we look the more we find rules and laws and regularities that govern living systems.

[Mitchell314]

Metaphors are wonderful things only if everybody knows what they are.

And I was talking about the Brownian motion as an analogy. Why pick at an analogy at the wrong end?

[zosima]

Metaphors are wonderful things only if everybody knows what they are.

And I was talking about the Brownian motion as an analogy. Why pick at an analogy at the wrong end?

Why pick an analogy?

[sphenisc]

Actually, that highlights one of the problems with this thread: There are tons of other posts on here, and no one, not even I who started this, is probably going to read and sort through every single one of them.



A random sample would probably do.

:duck:

[jimbob]

Ya, It would be hard for me to fairly summarize the position, seeing as how I tend towards the deterministic extreme.

I think the issue of chaos was covered pretty well in the other thread that I referenced though. I think it got resolved in a somewhat more technical fashion.

With respect to both randomness & chaos no one is arguing that they don't exist and that they aren't important parts of all sorts of natural processes.

But any sort of the claim that evolution is uniquely random(or chaotic) needs to show either (1) that there is some macroscopic characteristic of evolutionary processes that makes it random or chaotic. or (2) that we have strong reason to believe that microscopic random or chaotic processes will actually have macroscopic random effects.




Many (most) phsicists would argue that chaotic systems are influenced on the macrosocpic level by quantum effects:



It's OK to disagree with me! :) Sometimes I'm even wrong :jaw-dropp.

I think QM events can strongly affect chaotic systems after relatively short amounts of time. I'm pretty sure 99% of physicists would agree with me.

I don't think it's useful to distinguish between "random" and "unpredictable" when we're discussing physical processes. I'm not sure how many physicists would agree with me on that (although I think I could convince them).

But none of that prevents us from predicting with extremely high confidence that July in Saskatoon will be warmer than January in Saskatoon. As they say - "weather is chaotic, but climate is predictable" (or something along those lines). As for evolution, it has both weather-like and climate-like aspects.

And the important feature is that over long timescale the random factors become more not less important.

The most extreme example I can think of is that many Near Earth Objects have chaotic orbits. These are unpredictible over the long term, partly because far enough in the future the orbital path hasn't been determined.

An example that isn't a NEO is Pluto, where the orbit is unpredictible beyond 2-million years. Now if we increased our measurement resolution, this could be increased; but far enough in the future this is influenced by random factors.

The course of evolution, and the shape of ecosystems is heavily influenced by the history, and an asteroid impact tends to have a severe effect.

This is an extreme example, but still valid.

Over longer timescales, rare events are more likely.

At the other end of the scale, a slinght mutation in the influenza virus killed millions of people. The random mutation in the flu virus suddenly created a new selective pressure on humans for a short while.

Black squirrels (http://www.bbc.co.uk/theoneshow/article/2008/05/eh_blacksquirrel.shtml) seem to be the result of a mutation of grey squirrels, and semed to have been first reported in England in 1912.

This variant tends to be more successful than a grey squirrel, and so they have been spreading at the expense of grey squirrels. Now the numbers of black squirrels are sufficient that you could talk about a slective advantage, and ignore random factors. In 1912 this would not be the case, as the small popuolation (initially one individual) would have been vulnerable to chance* events. As the grey squirrel population is not increasing fourfold every year, we can be confident that most squirrels fail to reproduce. Even though the black squirrel had a higher chance of reproducing, the odds were still agianst that particular mutation spreading.


*I would argue that these truly are "chance" events, others might argue that they were actually somehow predetermined, however they are in principle unpredictible.

[zosima]

Many (most) phsicists would argue that chaotic systems are influenced on the macrosocpic level by quantum effects:

1. Again, appeal to authority is not persuasive when the quotes you use do not include either the persons reasoning, and you cannot defend any reasoning the sensibly supports your claims.

2. This is not particularly persuasive at the point which you can't articulate why in the "chaos & repeatability" thread. In fact, you ran away when I demonstrated the huge contradiction that your claims entail. You are losing every battle, but somehow trying to claim you are winning the war.

3. Also note, that you are making inferences, that Sol does not claim. He does not say that every chaotic system is affected by QM. Nor does he claim that any system always will be. All he claims is that it is possible. Jumping from the possibility existing to the claim that all chaotic systems are influenced by QM all the time his a monumental stretch.

4. You've never shown that evolution is chaotic. In fact, I believe in my last post in the chaotic thread I showed that by your definition of chaotic ecology is definitely not chaotic. You never responded, so I have to assume you agree. At any rate, you are grasping at straws here.


And the important feature is that over long timescale the random factors become more not less important.

The most extreme example I can think of is that many Near Earth Objects have chaotic orbits. These are unpredictible over the long term, partly because far enough in the future the orbital path hasn't been determined.

An example that isn't a NEO is Pluto, where the orbit is unpredictible beyond 2-million years. Now if we increased our measurement resolution, this could be increased; but far enough in the future this is influenced by random factors.


1. Being specificity of the positioning of the planet and other large gravitational bodies, is not the same as being influenced by quarks. As far as I know, there is going to be just as much vacuum fluctuation on one side of Pluto as the other. Again. It is a huge stretch to go from solar sized bodies to the influence of single quarks and leptons.

2. If the effects were to be significant it would take longer than the life of the universe for them to be significant. We get 2 million years of accuracy with the predictions we can make now. Lets assume we get 1 meter of accuracy today(which is generous, it is probably much worse than that). Planc's length is: 1.616 252 × 10e-35 meters. Which means it would take 2e6/1.616 252e-35 meters. That is 2e41years. That is longer than even the longest estimates for how long it will take for heat death of the universe. Incidentally, the orbit will have decayed due to tidal forces long before then as well.

3. If other non-quantum events intervene prior to the 2e41 years it will take for quantum effects to be significant, then quantum effects will not be significant. For example the non-quantum effect of the andromeda galaxy colliding into ours will show up in only 2.5 billion years from now.

4. This is what I was talking about with respect to effective granularity. Whether randomness exists or not, it is not necessarily an input to a chaotic system. Assuming it is, justifying it with hand-waving, and failing to do even the simplest calculations to verify your claims, is what I mean by being 'intellectually lazy'



The course of evolution, and the shape of ecosystems is heavily influenced by the history, and an asteroid impact tends to have a severe effect.

This is an extreme example, but still valid.

Over longer timescales, rare events are more likely.


Again, more handwaving, more claims without justification. No reason to believe QM is significant. Also conflation of rare events and random events. Finally your claim reduces to the claim that history/prehistory is random, not that evolution is
random. That is fine if you want to characterize our limited knowledge as randomness, but as I said above, I just consider it lazy. The more we learn, the less 'random' things appear.


Black squirrels (http://www.bbc.co.uk/theoneshow/article/2008/05/eh_blacksquirrel.shtml) seem to be the result of a mutation of grey squirrels, and semed to have been first reported in England in 1912.

This variant tends to be more successful than a grey squirrel, and so they have been spreading at the expense of grey squirrels. Now the numbers of black squirrels are sufficient that you could talk about a slective advantage, and ignore random factors. In 1912 this would not be the case, as the small popuolation (initially one individual) would have been vulnerable to chance* events. As the grey squirrel population is not increasing fourfold every year, we can be confident that most squirrels fail to reproduce. Even though the black squirrel had a higher chance of reproducing, the odds were still agianst that particular mutation spreading.


That is a huge amount of extrapolation from a few sentences of pop-sci article. Do a little bit of research on black and grey squirrels and we learn that they did not develop from a single random mutation but are common to the Americas. Where they developed as part of a long evolutionary process. http://en.wikipedia.org/wiki/Black_Squirrel

Also from your article:
"At the time when grey squirrels were new to the UK, black squirrels started to be noticed on a Hertfordshire common. The first sighting is believed to be as early as 1912."
This quote seems to claim simultaneous introduction of black & grey squirrels. As the wikipedia article shows. Black & Grey squirrels have differential success depending on geography. So a population of black & grey squirrels was introduced to the UK, and the subtype that was most appropriate for the UK became dominant. So the only thing that you might characterize as random is the introduction, but that was probably by humans. So do want to call human behavior random? Do you want to call it directed? Either way it is not an issue that is particular to evolution in nature.

[articulett]

Why pick an analogy?
And if so, why not my Brazil nut analogy. So simple and visual and... it has nuts!

[Mitchell314]

Why pick an analogy?

Because it's cheap and easy. The third dimension was explained to Mr. A. Square by analogy. Isn't natural philosophy sometimes easier understood by relations to other more readily understood concepts?

[zosima]

Because it's cheap and easy. The third dimension was explained to Mr. A. Square by analogy. Isn't natural philosophy sometimes easier understood by relations to other more readily understood concepts?

An analogy is fine if you are using it to define a term. An analogy is not sufficient to make claims about the properties of a system, if you intend the analogy to 'stand in for the system'

Maybe I should say "why pick a bad analogy?", If species are fluids okay.... but they are not. The differences between a fluid and a species are large enough that you will never be able to prove anything or make a persuasive claim with it. The simple claim that a species is somehow a fluid is so incredibly under-defined that it doesn't establish any claim. For example Is an evolutionary fluid a fluid with Laminar flow or Turbulent Flow? Is it Viscid or Inviscid? Can I apply the Navier-Stokes equations to solve evolutionary problems? Is it a compressible or incompressible fluid? More like a liquid or more like a gas? Is it frozen in flux? What shape container does it fill? How do I interpret, mass,pressure, density, temperature, momentum, velocity for an 'evolutionary fluid'? By the time you've answered all these questions, you could have made significant progress reasoning about the question directly. Oh yes, and when it comes down to it, there are huge outstanding questions about fluids themselves that we can't answer. So why not pick a system we can reason about?

So is your analogy accurate? No. Does it share some properties with evolution? Perhaps. Can we apply conclusions about your fluids to evolution? Not Bloody Likely.

[Mitchell314]

When I use an analogy, I don't mean to include the unsaid baggage. I assumed other people do the same thing. So if that's not the case, then I'm sorry.

So to be thorough and explicit: I don't want to include all the baggage of analogies that I'm not talking about. There, problem solved. Let's move on to more productive talk, such as something related to the topic and not misunderstandings in the nuances of the English language. Unless it has become of fashion to speak of Science and Mathematics in verse.

[zosima]

When I use an analogy, I don't mean to include the unsaid baggage. I assumed other people do the same thing. So if that's not the case, then I'm sorry.

So to be thorough and explicit: I don't want to include all the baggage of analogies that I'm not talking about. There, problem solved. Let's move on to more productive talk, such as something related to the topic and not misunderstandings in the nuances of the English language. Unless it has become of fashion to speak of Science and Mathematics in verse.

What you consider baggage others may not. But I think verse would definitely be a step in the wrong direction from analogy. Generally, an explicit, perhaps even mathematical example, is a good way to make a claim, but if you don't have one...I'm hoping this thread will just die. All points have been made in triplicate.

[articulett]

Reading this thread is like seeing Zosima the Buck defending his territory as the young bucks step up with the bravado to challenge and fail gently but firmly every time. For all I know Zosima is younger than his challengers-- but he understand physics and he understands logic and he understands how to convey information so that this non-expert in physics understands. And he understands what the experts in biology are saying and is able to convey that understanding to most anyone except those most in need of thinking themselves as superior "explainers".

Just my opinion, of course.

*applause and whistles from sidelines*

[Walter Wayne]

Sorry for the delay. The combination of being busy and interent outage means I haven't addressed some things in a bit.

"Random: having a state or value depends on chance."

So then you're saying that everything is random? In legal terminology this has a fatal flaw known as no bright line. From this definition there is no way to tell what it doesn't apply to. In other words, to define a term that applies to everything doesn't communicate any information because you know just as much about whatever you are talking about before or after it was said.
First, if you want a laymen's definition, expect "no bright line" for anything that lies along a continuum. Your also interpreted it without the context of my other posts, where I explicit mentioned that some things are only random in the most technical sense of the word.
Note that these distributions are statistics that can result from many samples of processes. If the process is truly random any individual sample is #1 uncorrelated, #2 uniform.
Again, random does not mean uniform or uncorrelated. From statistics, the field you mentioned:

Simple random sampling: The one most are familair with.
Each sample is unbiased, and uncorrelated. Though to be precise, most often used is simple random sampling without replacement is unbiased, but does have some correlation, though usually small.

Systematic random sampling: Involves taking every nth member of the population. For example if you wanted to sample 400 of the 17470 members of these board, you would generate an unbiased number between 1 and 43, and then sample that member on your list, and every 43rd member after that.

Stratified random sampling: Used often in political polls. This involves dividing the population into strata or classes and then sampling from with in each of them. So you could do independent surveys of low-income, middle-income and high-income families to make sure that your sample doesn't accidently miss one class. Your sample is no longer uncorrelated (and may be biased depending on the particular brand of stratified random sampling you use).

Random does not mean uniformly distributed and uncorrelated.

To better clarify my point. If there are going to constitute examples of non-uniform random systems, you need to explain why they should be considered random. I don't think the fact that they use of the term 'random variable' is persuasive either.

#1 Random variable is used with distributions that are clearly not random. For example, I could have a dirac delta random variable. Ie a function with a dirac delta that is centered upon 0. It is a distribution over a random variable, but it is also only has one possible outcome. We could do the same thing over a discrete distribution as well.(In case you want to pick some nits)
Still, we would be talking about a random variable, yet a non-random system. Is the dirac delta function also random? Where do you draw the line?

How does, "having a value depending on chance", or "not being predictable" or "not determined by past state" correspond to a dirac-delta function?

#2 Probability distributions represent statistics of systems, but the systems they describe may or may not be random. For example, I can generate a binomial distribution by rolling a die many times over a number of trials and counting the numbers as they come up. Alternatively, I could write a computer program that will either return 1-6 with exactly the same frequency as the die returned the values, but in some sorted order. Both could generate a statistical fit that might be described by the binomial distribution. The computer would be deterministic and clearly so, the die would not.There is a difference between a population distribution, and probability distribution, and you appear to be conflating the two here. If I look at the sides of my fair-die, I will see the population distibution. 1 side with 1 pip, I side with 2 pips, ... etc. If I take a fair single sample of that population (by rolling the die), the probability distribution of that sample will be equal to the relative population distribution of the die. That last bit is the foundation of how simple random sampling works.
#3 The Distributions themselves are not random at all. For example, if I want to generate a normal distribution, all I have to do is evaluate the probability density function for the normal distribution.(I'm not going to write it out here) This is a simple and deterministic mathematical operation. If you think that the particular distributions that you've mentioned happen to describe random processes, you're going to have to explain why, 'cause I don't see any reason why it should be assumed.I am not sure what that has to do with. A uniform distribution is also describle in the same manner. For discrete uniform distributions the probability of a possible outcome is 1 in the total number of outcomes.
From a perspective that jives more closely with human intuitions. I think the term random is not so binary as just 'random or not'. It would be more accurate to talk about how random a system is. A system with a uniformly distributed and uncorrelated output is as ideal a random system as you can get. A system that always outputs the same value or same sequence of values is as deterministic as you can get.
...
I agree with this, which is why I mentioned the difference between random in only a technical sense compared to one that is random "in practice."

Walt

[zosima]

Sorry for the delay. The combination of being busy and interent outage means I haven't addressed some things in a bit.
Its good to see you back. :)


First, if you want a laymen's definition, expect "no bright line" for anything that lies along a continuum. Your also interpreted it without the context of my other posts, where I explicit mentioned that some things are only random in the most technical sense of the word.

Well, we might be able to come to some sort of agreement with respect to things lying on the continuum so I'll come back to that at the end.

It seems to me that you start talking about this idea of 'technically random' whenever you are having problems with whatever definition you put forward, but as far as I can tell your definition of 'random' and 'technically random' are identical. They are both "having a state or value depends on chance" which both assign the term random to things that are clearly not random.

Also, I'm not sure how you appointed yourself the arbiter of the definition of technically random, but that seems to be the claim we're disputing at the moment. (If we were talking about practically random we wouldn't be talking about definitions and statistics, we'd be talking about the processes of evolution.)


Again, random does not mean uniform or uncorrelated. From statistics, the field you mentioned:

Simple random sampling: The one most are familair with.
Each sample is unbiased, and uncorrelated. Though to be precise, most often used is simple random sampling without replacement is unbiased, but does have some correlation, though usually small.

Systematic random sampling: Involves taking every nth member of the population. For example if you wanted to sample 400 of the 17470 members of these board, you would generate an unbiased number between 1 and 43, and then sample that member on your list, and every 43rd member after that.

Stratified random sampling: Used often in political polls. This involves dividing the population into strata or classes and then sampling from with in each of them. So you could do independent surveys of low-income, middle-income and high-income families to make sure that your sample doesn't accidently miss one class. Your sample is no longer uncorrelated (and may be biased depending on the particular brand of stratified random sampling you use).


1. You have identified some techniques for identifying samples. The first one is the only one actually called random sampling. You did the same thing with distributions, where you inserted random into the name to try to support your point. So these would normally be called, 'simple random sampling','systematic sampling', and 'stratified sampling', in the same way that you started calling the distribution 'Poisson random distribution', 'Normal random distribution', etc....They are normally called the 'Poisson distribution'
and the 'Normal Distribution'

2. Note that these practical techniques to get samples that are random, they are not perfect, the failures you mention(like small correlations) represent deviations from the ideal(random)

3. Clearly depending on what they are sampling their results may differ significantly from random(they may only get one result,)
This point being to distinguish patterns in their outcome from patterns in sampling.

4. I thought it noteworthy at the point when anyone in statistics would say 'random number between 1 and 43' You say 'unbiased'. That is telling insofar as you are manipulating your descriptions to prevent them from displaying exactly the characteristics that ideal randomness shows.

5. These techniques can be random samples, if we know something about the structure of what we are sampling so we add no information via a lack of uniformity of selection or a correlation between selections. For example we would get a random sampling via a systematic sampling if we knew that the order of the objects we were sampling was uncorrelated with the values that we were sampling from those objects. A second example: We use stratified sampling, when we know that there is sufficient heterogeneity in our overall population such that it could bias our sample(ie create a strong correlation between our samples, or eliminate uniformity because one subgroup is much larger than others)


How does, "having a value depending on chance", or "not being predictable" or "not determined by past state" correspond to a dirac-delta function?


I made this example about a dirac-delta when you were talking about 'Poisson Random Distributions'(actually called Poisson Distributions) ie inferring that any distribution over a statistical variable is random. The 'dirac delta random distribution' disproves this suggestion.

Also, as Mijo reminds us so frequently, if the dirac-delta function is defined over the reals or the complex numbers we can never quite be sure that it won't have another outcome. This means that we can construct examples with a dirac-delta that are completely opposed to our intuitions insofar as they are completely predictable and yet still dependent on chance.


There is a difference between a population distribution, and probability distribution, and you appear to be conflating the two here. If I look at the sides of my fair-die, I will see the population distibution. 1 side with 1 pip, I side with 2 pips, ... etc. If I take a fair single sample of that population (by rolling the die), the probability distribution of that sample will be equal to the relative population distribution of the die. That last bit is the foundation of how simple random sampling works.

I'm sorry if this wasn't clear, but this is the point I was trying to demonstrate to you, with this example. That there is difference and the fact that we use a Gaussian distribution to model a process does not necessarily mean the population that produced it is random. Even if you do call it a "Gaussian random distribution".



I am not sure what that has to do with. A uniform distribution is also describle in the same manner. For discrete uniform distributions the probability of a possible outcome is 1 in the total number of outcomes.

This point was also a response to your laundry list of distributions. The point is similar: the distribution is separate from the process. I think that is why the necessity of no correlation is so crucial as well. You may get statistical distributions similar the ones you mention when you randomly sample a random event many times, especially if you are summing the outcomes. But the distribution of a single random event will never be distributed that way.

ETA: all these statistical techniques that you and mijo keep bringing up may have random in the name, but "Random Distributions", "Random Variables", "Random Samples" all can be used in combination with a variety of different random and non-random processes. The commonality that they have, is that it assumes that they are unbiased with respect to the way they are generated. In other words, they clearly reflect the nature of the process itself, because the sampling or generative process itself is ideally uncorrelated and uniform. To try to claim that all the processes they describe are also random is clearly a mistake or even that they are necessarily the statistics of random processes. The only process that is ideally random is the uncorrelated and uniform one.


I agree with this, which is why I mentioned the difference between random in only a technical sense compared to one that is random "in practice."

Walt

Again, your technical definition and your practical definition are indistinguishable. It seems like the definition you advocate alternates between "anything that is not determinate" and "systems described using statistics", "practical", and "technical"


I'd like to move on to this idea of a continuum to see if we can find some common ground:
If your 'technical' definition is 'anything that is not determinate' then there is no way to define a spectrum. Where is the far end of the spectrum, the end that is opposite determinate, anchored? Under your definition all answers to that question are equally good. Is the pure random end of the spectrum a Poisson distribution? or a Gaussian distribution? A Chi-Sq distribution?

If we use uniformly distributed and uncorrelated as the definition then we have a clear and singular answer. We would say that a flat, horizontal, uniform distribution is the ideally random distribution of a single event. The distribution of an ideally deterministic single event would be a vertical, dirac-delta distribution. One end is vertical, one end is horizontal, they fall on opposite ends of a spectrum. Anything that falls in between would be a deviation from ideal randomness and a deviation from ideal determinism.
For multiple events we would want to calculate the correlation between a sequence of samples, (with value on the y axis and sample number on the x)
If the correlation is 1.0 the sequence is ideally deterministic, if the correlation is 0.0 the sequence is ideally random.

Incidentally, that is why I call use this definition of 'technically random' in the same way that I don't call any events that have a distribution different than the dirac-delta 'technically determinate'

[Mitchell314]

What you consider baggage others may not. But I think verse would definitely be a step in the wrong direction from analogy. Generally, an explicit, perhaps even mathematical example, is a good way to make a claim, but if you don't have one...I'm hoping this thread will just die. All points have been made in triplicate.

For the love of the Gods! Metaphor then. It's now a blasted metaphor. The verse statement was a joke. How could it not be?

Mathematical claim: Random relative to whom? Deterministic relative to whom? Is it plausible to say we can map out the future of the evolution of most species? Is there some black box mathematical function that spits the genetic code of some animal's ancestors millions of years ago? Is there a computer program that can accurately predict who'll be what at any given time?

[zosima]

For the love of the Gods! Metaphor then. It's now a blasted metaphor. The verse statement was a joke. How could it not be?

It really seems like you didn't even skim the body of available posts. Not even the recent ones. You make some vague analogy to Brownian motion, an analogy that has been repeated over and over and over in this thread. How do you expect me to respond? I think I have every reason to be impatient.


Mathematical claim: Random relative to whom? Deterministic relative to whom? Is it plausible to say we can map out the future of the evolution of most species? Is there some black box mathematical function that spits the genetic code of some animal's ancestors millions of years ago? Is there a computer program that can accurately predict who'll be what at any given time?

All I meant to say, is that I would appreciate it if you make a claim that is precise and original.

With your questions you're asking me to rewrite and/or summarize the many things that people have already said, when the record is right in front of you face. Generally when complete strangers ask me to engage in time consuming tasks, my generosity is limited. So please, do the research yourself and read the thread.

[Mitchell314]

Alright then, refresh me on determinism is relative to whom? Who is the observer? Omniscient space-faring beings, or people like us with our limited knowledge on the biosphere?

In order for us to be determined about a natural system, we need sufficient knowledge. If we don't, then it may appear to be chaotic. Given that we are immersed in the system, we are even more limited. Our current empirical knowledge does not give us the privilege to declare evolution deterministic to us. We need more data, better understandings of evolution and always will to better understand.

[zosima]

Alright then, refresh me on determinism is relative to whom? Who is the observer? Omniscient space-faring beings, or people like us with our limited knowledge on the biosphere?

I guess it depends, there is no one consensus.


In order for us to be determined about a natural system, we need sufficient knowledge. If we don't, then it may appear to be chaotic. Given that we are immersed in the system, we are even more limited. Our current empirical knowledge does not give us the privilege to declare evolution deterministic to us. We need more data, better understandings of evolution and always will to better understand.

I agree with that. We don't know for sure until we get more evidence. This is particularly true when it comes to understanding whether a system is chaotic or not.

I think most people have been arguing from the perspective of what omniscient beings might know, although some people seem to claim that human use of probabilistic models implies that the system is random, without the need for additional inquiry.

I think some of the arguments that are important to answering this question have to do with the rate of mutation in a species, the importance of drift relative to selection, the significance of punctuated equilibrium, whether change is generated spontaneously, how we interpret infinitesimally improbable events and what chaotic systems, if any, serve as inputs to the process of evolution.

Pretty much all of these have been touched on, but knowledge and interpretations vary wildly.

[articulett]

And there seems to be a pretty good explanation amongst experts that while it makes sense to call mutations random (though they aren't strictly so) because they happen without respect to how they will fix the organism they code for, natural selection determines which of these mutations will multiply exponentially (having the chance to accumulate more mutations) and which will die out)--this is the essence of evolution... and this accounts for evolved complexity and seeming design when there is no intent behind the process.

[jimbob]

1. Again, appeal to authority is not persuasive when the quotes you use do not include either the persons reasoning, and you cannot defend any reasoning the sensibly supports your claims.


I wasn't exactly appealing to authority; when I took my physics degree, the consensus was that chaotic systems quickly required resolution down to the quantum level to make predictions. I suspect that Sol Invictus is a little more current than me, but he had confirmed that the consensus hasn't changed much.

Here is one of the other posts that I was looking for (why restate something that someone else has written lucidly?)

Originally Posted by shemp
Since on any given throw, we don’t know in advance which of these values the dice will add up to, we say that the result is random. However, I say that the result is not random. Instead, I say that the result is predetermined by the conditions of the throw (such as the position of the dice in the thrower’s hand, the speed of the throw, the spin placed on the dice by the throw, the quality of the felt on the table, the hardness of the table, the hardness of the rail at the end of the table, the temperature of the dice, various qualities of the surrounding air [such as temperature, humidity, and air movement], along with other possible intangibles). The throw only appears to be random to the observer because he does not have all of this information and the capability to process it to determine the outcome of the throw.
I disagree, and most physicists would, too. Ultimately, the outcome of the throw is based not only upon random quantum phenomena, but upon values that are in principle unmeasurable; that is, not merely we cannot measure them, but they do not in principle have a determined value. The values of variables that depend upon them, therefore, are stochastic probability distributions, whose individual outcomes cannot be predicted from any prior knowledge of the state of the system, no matter how detailed. At any of numerous critical moments during the throw, the outcome of the dice roll can be influenced by a single quantum event, which is in principle truly random.

One might constrain particular throws; for example, it is possible that a sufficiently skilled thrower could alter the probability to favor some outcomes over others. Or the dice can be loaded, increasing the probability of certain outcomes. One will never, however, no matter how fine the control, absolutely determine the outcome. It is in principle impossible to do so under the laws of physics our universe operates on.

Originally Posted by shemp
So is there really no randomness in the non-quantum world? I think there is not. I think that every action at this level is predetermined by the physical conditions preceding it. This would mean that non-quantum randomness is merely an interpretation that we use to explain these actions.
We have shown (to a certainty of over two hundred standard deviations, a truly astounding level of certainty) by experiment that indeterminate (uncertain in the sense of Heisenberg's Uncertainty Principle) quantum values are not merely unmeasurable, but in fact cannot have a definite value. The experiment is called the Aspect Experiment; you can find a discussion of this experiment on this forum by searching on that term. It is therefore incorrect, even if you do maintain that every quantum action is predetermined by physical conditions, to state that the outcome is determinate; that is impossible, since the physical conditions are not merely unmeasurable but nonexistent.

Originally Posted by shemp
1. Is there really randomness in the macro, non-quantum world, or is it just an illusion and a lack of information and computing power?
According to the outcome of experiments, there really is randomness in the non-quantum world, and it springs from:

Originally Posted by shemp
2. Similarly, is there really randomness in the quantum world?
Yes, again, according to the outcome of experiments.

Originally Posted by shemp
3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?
It is not a sharp line, but there are areas that are definitely on one side or definitely on the other. As has been stated, the line is somewhere above the size of a molecule. The proof of this is an experiment that appears to contradict the Second Law of Thermodynamics, but confirms a derivation of that Law known as the Fluctuation Theorem. Details are available upon request; I'll have to google it up, and if you just want to argue philosophy, it's not worth my while. If you're interested in the hard evidence, I can provide it.

Originally Posted by shemp
4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?
On that, I have an opinion, but it is not grounded in the previous questions. I'll therefore answer (out of order) that I don't know whether it can, and I don't know if it is.

And another link (http://findarticles.com/p/articles/mi_m1200/is_n14_v138/ai_8986262) discussing how classical chotic systems are affected by quantum uncertainty:

Ronald F. Fox of the Georgia Institute of Technology in Atlanta and his colleagues have taken a different tack. They looked at the behavior of a special, hypothetical physical system that could be treated either as a purely classical problem -- in which case it would display chaos -- or as a quantum problem. By comparing how the system's quantum version varies depending on whether the corresponding classical version shows chaotic behavior, the researchers hoped to identify characteristics of the quantum system that could be tied to chaotic behavior in the classical system.

"We found that there is such a property," Fox says.

In a quantum system, the Heisenberg uncertainty principle determines how precisely two variables -- such as position and momentum -- can be defined simultaneously. At the same time, a given variable has a certain probability distribution representing the range of values it may have. When the corresponding classical system is chaotic, Fox and his collaborators find that this probability distribution, initially as narrow as the uncertainty principle allows, becomes extremely broad, growing exponentially as the system evolves. "For a classical object, one normally thinks of these quantum fluctuations [expressed by the probability distribution] as very, very small and ignorable," Fox says. "We argue that when the dynamics is chaotic, these quantum fluctuations grow very large."


Not forgetting the earlier link discuissing billard balls From my OP on the other thread:

Here (http://physicaplus.org.il/articles2/barrow_eng.html) is a discussion about a very simple system (from the Israel physical society)

You can apply this rule to snooker balls as well as molecules. One knows from bitter experience that snooker or pool exhibits sensitive dependence on initial conditions: a slight miscue of the cue-ball produces a big miss! If the balls are bouncing around a frictionless snooker table in a perfect vacuum (otherwise they will just stop moving after one or two collisions) then we might typically have d=1 metre and r=3 cm, so our map is qn+1 = 3qn. The growth in recoil angle uncertainty in the trajectory of a ball as it bounces off other balls is therefore pretty dramatic. In fact, if you hit the ball as accurately as Heisenberg's quantum Uncertainty Principle allows any physical process to be determined by observation, then only about 12 collisions are needed to amplify this uncertainty up to more than 90 degrees!

Twenty-four collisions ahead, and there are twelve sets of collisions where the accuracy required would be beyond the uncertainty principle.

I did give my reasons for stating how I came up with a rough figure for how long far in advance you might be able to predict weather. Athough these figures were rough and based on the simplifing assumptions that I stated, the rough result tallied pretty well with the couple of months that I understood was the best guess when I was an undergraduate.

1. Being specificity of the positioning of the planet and other large gravitational bodies, is not the same as being influenced by quarks. As far as I know, there is going to be just as much vacuum fluctuation on one side of Pluto as the other. Again. It is a huge stretch to go from solar sized bodies to the influence of single quarks and leptons.

2. If the effects were to be significant it would take longer than the life of the universe for them to be significant. We get 2 million years of accuracy with the predictions we can make now. Lets assume we get 1 meter of accuracy today(which is generous, it is probably much worse than that). Planc's length is: 1.616 252 × 10e-35 meters. Which means it would take 2e6/1.616 252e-35 meters. That is 2e41years. That is longer than even the longest estimates for how long it will take for heat death of the universe. Incidentally, the orbit will have decayed due to tidal forces long before then as well.

3. If other non-quantum events intervene prior to the 2e41 years it will take for quantum effects to be significant, then quantum effects will not be significant. For example the non-quantum effect of the andromeda galaxy colliding into ours will show up in only 2.5 billion years from now.

4. This is what I was talking about with respect to effective granularity. Whether randomness exists or not, it is not necessarily an input to a chaotic system. Assuming it is, justifying it with hand-waving, and failing to do even the simplest calculations to verify your claims, is what I mean by being 'intellectually lazy'

So there are other factors that also make it unpredictible. I dinn't deny that. I am saying that even if these factors didn't exist, the system itself contains enough sensitivity to initial conditions to make its behaviour undetermined beyond a certain timescale.


That is a huge amount of extrapolation from a few sentences of pop-sci article. Do a little bit of research on black and grey squirrels and we learn that they did not develop from a single random mutation but are common to the Americas. Where they developed as part of a long evolutionary process. http://en.wikipedia.org/wiki/Black_Squirrel

Also from your article:
"At the time when grey squirrels were new to the UK, black squirrels started to be noticed on a Hertfordshire common. The first sighting is believed to be as early as 1912."
This quote seems to claim simultaneous introduction of black & grey squirrels. As the wikipedia article shows. Black & Grey squirrels have differential success depending on geography. So a population of black & grey squirrels was introduced to the UK, and the subtype that was most appropriate for the UK became dominant. So the only thing that you might characterize as random is the introduction, but that was probably by humans. So do want to call human behavior random? Do you want to call it directed? Either way it is not an issue that is particular to evolution in nature.

Was there a small initial population of black squirrels in England in 1912? Were they lucky to breed? Why isn't random human action not an evolutionary force?

The discovery of penicillin was an accident. That has had a massive effect on the subsequent evolution of many bacteria populations. Why isn't that another random factor?

[sphenisc]

An analogy is fine if you are using it to define a term. An analogy is not sufficient to make claims about the properties of a system, if you intend the analogy to 'stand in for the system'

Maybe I should say "why pick a bad analogy?", If species are fluids okay.... but they are not. The differences between a fluid and a species are large enough that you will never be able to prove anything or make a persuasive claim with it. The simple claim that a species is somehow a fluid is so incredibly under-defined that it doesn't establish any claim. For example Is an evolutionary fluid a fluid with Laminar flow or Turbulent Flow? Is it Viscid or Inviscid? Can I apply the Navier-Stokes equations to solve evolutionary problems? Is it a compressible or incompressible fluid? More like a liquid or more like a gas? Is it frozen in flux? What shape container does it fill? How do I interpret, mass,pressure, density, temperature, momentum, velocity for an 'evolutionary fluid'? By the time you've answered all these questions, you could have made significant progress reasoning about the question directly. Oh yes, and when it comes down to it, there are huge outstanding questions about fluids themselves that we can't answer. So why not pick a system we can reason about?

So is your analogy accurate? No. Does it share some properties with evolution? Perhaps. Can we apply conclusions about your fluids to evolution? Not Bloody Likely.

I take it you didn't enjoy "River out of Eden" much.

[jimbob]

And there seems to be a pretty good explanation amongst experts that while it makes sense to call mutations random (though they aren't strictly so) because they happen without respect to how they will fix the organism they code for, natural selection determines which of these mutations will multiply exponentially (having the chance to accumulate more mutations) and which will die out)--this is the essence of evolution... and this accounts for evolved complexity and seeming design when there is no intent behind the process.

And these experts also implicitally (and sometimes explicitally) use probabilistic treatments of natural selection.

From the extended phenotype (http://books.google.com/books?hl=en&lr=&id=FY2XEa_ul7cC&oi=fnd&pg=PA1&dq=probabilistic+natural+selection+dawkins&ots=HGLViEX4V9&sig=mETbXiZN4u1y6lWz-nX0u7wvIVU#PPA33,M1):

"A selection pressure as weak as 1 in 1000 would take only a few thousand generations to push an initially rare mutation to fixation".

"If the selection pressure we are discussing is very strong, that is if one replicator makes its posessors very much more likely to survive than its alleles do "

Dawkins invokes a probabilistic treatment, as he would have to, given his background.

Articulett, how is this not a probabilistic treatment of natural selection?

[cyborg]

Articulett, how is this not a probabilistic treatment of natural selection?

Jimbob - how do you not get that a probabilistic treatment doesn't necessitate an acuasal relationship?

[articulett]

And jimbob... I've explained my point a thousand times. The nuts get to the top through probabilities, I supposed... but that IS irrelevant to understanding how they always seem to end up there. And I have you on ignore. Don't bother asking me leading questions you cannot comprehend the answer to anyhow. That is mijo-esque. I've been there; done that. You can have the last word. I refuse to let you inflict it on me, however.

(Your obfuscation regarding probabilities is fantastic, however, if you don't really want people to understand the basic science that ensures that the big nuts will settle on top... if, instead, you hope that they'll be open to the idea that there is a plot amongst nut sellers to make it look like there are more big nuts then there actually are. kudos.)

[Wowbagger]

Dawkins invokes a probabilistic treatment, as he would have to, given his background.

Articulett, how is this not a probabilistic treatment of natural selection?(My answer to this question might be considered a severe oversimplification. So, if anyone else on the thread wants to correct me or expand upon it, please do so: )

Perhaps the easiest way to think about it, is that the probability ultimately doesn't matter. The non-randomness of selection would allow the adaptation (or mutation) to propagate under an enormous range of possibilities and probabilities. If a selection pressure is as weak as 1 in 1000 or as strong as 999 in 1000: the adaptation would eventually fixate in the species.

Perhaps the timing would be different, but the outcome would still be empirically predictable.

[zosima]

I wasn't exactly appealing to authority; when I took my physics degree, the consensus was that chaotic systems quickly required resolution down to the quantum level to make predictions. I suspect that Sol Invictus is a little more current than me, but he had confirmed that the consensus hasn't changed much.
Apparently you didn't learn too much....do you have any conception of how large a number 2e41 years is?


Here is one of the other posts that I was looking for (why restate something that someone else has written lucidly?)

Especially when you seem incapable of making your points lucidly.


And another link (http://findarticles.com/p/articles/mi_m1200/is_n14_v138/ai_8986262) discussing how classical chotic systems are affected by quantum uncertainty:

You seem to be missing the point here Jimbo. Some classical systems may interact with quantum systems. All the examples of other people making 'authoritative claims' involve people claiming that it is possible for quantum interactions between classical systems and quantum systems.

You make the huge mistake of assuming that all classical systems will interact with chaotic systems. Do you really not understand various levels of granularity? It seems like we had identified the point exactly in the other chaos thread. In case you forgot....Not all chaotic systems are sensitive to quantum effects. Macroscopic systems may or may be chaotic and if they are chaotic, and whether they are QM sensitive varies, but a general rule of thumb is that the further removed they are from QM in scale, the less likely it is that QM is going to be significant. When I say insignificant, I mean that the probability of the outcome of the system being changed by quantum effects in the entire history of universe is less than nanoscopic.

At this point you might as well be talking about how likely it is for all my molecules to quantum teleport across the room. Both the arguments have the same form:

Jimbo: QM says that it is always possible that the molecules in your body could simultaneously teleport across the room.
Me: Yes, but statistics indicates that it will never happen.
Jimbo: Well look here, I found this article where a real scientist(omg!) says that particles quantum teleport all the time.
Me: I just did the calculation and it shows that the probability of many particles teleporting simultaneously in the lifespan of a billion,billion,billion,billion universes is less than one.
Jimbo: Yeah, but it could still happen
Me: *Facepalm/Wheeps for the educational system of whatever country jimbo is from*


Not forgetting the earlier link discuissing billard balls From my OP on the other thread:


We also came up with some other facts from that thread lets see, what were they?
#1 Billiard balls in the real world will never be QM sensitive because of friction.
#2 Technically, only mathematical systems can be truly chaotic.
#3 Being committed to the fact that chaotic systems can exist in the real world, commits oneself to the fact that chaotic systems will have various degrees of granularity(or sensitivity to effects on different scales).


I did give my reasons for stating how I came up with a rough figure for how long far in advance you might be able to predict weather. Athough these figures were rough and based on the simplifing assumptions that I stated, the rough result tallied pretty well with the couple of months that I understood was the best guess when I was an undergraduate.

The problem with the math used was that it was wrong. You used a model that no credible scientist would even shake a stick at. You assumed that since the quality of the met-office weather model improved by a factor of 3 over 20 years, that if you just gave a more detailed input to that model that it could produce as accurate a prediction as you want.

They're using a discrete computational model. Do you have any idea how silly and inappropriate linear extrapolation is? Do you realize that at some point no amount of rainfall accuracy is going to help predictions. Do you have any idea how complex rainfall models are? Do you even understand the details of Met Office's model? This wasn't just a few simplifying assumptions, this was making things up. You don't get to make those assumptions unless you have good reason and you certainly don't, especially when you claim these models are non-linear. Ie why would you make linear assumptions about their capacity to predict?

This would be like me saying: "Republicans won the presidential election by -500K votes in 2000, and they won by 3M votes in 2004, thus I can accurately predict that the republicans will win the 2008 presidential election by 7M votes."

There is a certain point when simplifying assumptions go from helpful to daft. You went way passed that point with your example.



So there are other factors that also make it unpredictible. I dinn't deny that. I am saying that even if these factors didn't exist, the system itself contains enough sensitivity to initial conditions to make its behaviour undetermined beyond a certain timescale.


It becomes undetermined about 2e41 years after the heat death of the universe. Assuming nothing intervenes. Do you understand how big this number is? Lets assume that the heat death of the universe occurs at 1e40 years(it is probably closer to 1e20). Then how many years will it be before your orbit is sensitive to quantum effects? 1.9e41....Your claims are assine. 2e41 years after the sun has burned out, 2e41 years after the Andromeda galaxy has collided with ours. Quantum uncertainty will never show up, because pluto will have collided with something before then, a decidedly un-quantum effect.

Actually, before quantum uncertainty in the initial conditions is significant Pluto's protons and neutrons will have decayed into their constituent quantum particles.

Was there a small initial population of black squirrels in England in 1912? Were they lucky to breed? Why isn't random human action not an evolutionary force?

We know there was some initial population. We know that the black squirrels came from the Americas because they were related. We know they bred and became successful because they were well suited to the environment. You would have a stronger case if the Grey squirrels became successful, as they were poorly suited to the environment. As it is, what happened is exactly what a deterministic theory would predict.

When we first started talking about this I made the statement unambiguously that when it comes to human action all bets are off. The reason I say that is because discussion whether human behavior is more inane than the discussion we are currently having. Are you really trying to tell me that you know who introduced those squirrels and what their reasoning was?


The discovery of penicillin was an accident. That has had a massive effect on the subsequent evolution of many bacteria populations. Why isn't that another random factor?

Again, you really want to talk about human motivations? The best you'll get out of this line of discussion is that humans are random, but I think most people will be less likely to concede that point than they will evolution. I can only assume that you are pursuing this because you've failed to establish your claim via any more rational lines of inquiry.

Moreover are you claiming that you know that no one else would have developed antibiotics if it hadn't been discovered when it was? If you can predict alternate histories, then nothing is random, so you lose or you lose.

Also:
"The discovery of penicillin is attributed to Scottish scientist Sir Alexander Fleming in 1928 and the development of penicillin for use as a medicine is attributed to the Australian Nobel Laureate Howard Walter Florey.
However, several others had noted earlier the bacteriostatic effects of Penicillium: The first published reference appears to have been in 1875, when it was reported to the Royal Society in London by John Tyndall[1]. Ernest Duchesne documented it in his 1897 paper; however it was not accepted by the Institut Pasteur because of his young age. In March 2000, doctors at the San Juan de Dios Hospital in San Jose (Costa Rica) published manuscripts belonging to the Costa Rican scientist and medical doctor Clodomiro (Clorito) Picado Twight (1887-1944). The manuscripts explained Picado's experiences between 1915 and 1927 about the inhibitory actions of the fungi of genera Penic. Clorito Picado had reported his discovery to the Paris Academy of Sciences, yet did not patent it, even though his investigation had started years before Fleming's."

Simultaneity in human discovery is common. Especially because there is evidence that penicillin been noted elsewhere, I have strong reason to believe its discovery was inevitable.

One final point. Why did you disappear from the chaos thread? It seemed we were making some real progress until you decided to flee.

[Jorghnassen]

Oh, 24 pages of pointless bickering. Let me solve half of that dilemma: when creationists and "intelligent design" people use the word "random" to describe evolution, they are using it wrong.

[Mitchell314]

Oh, 24 pages of pointless bickering. Let me solve half of that dilemma: when creationists and "intelligent design" people use the word "random" to describe evolution, they are using it wrong.

More like when they are describing evolution, they are using it wrong.

When you have random or arbitrarily indifferent behaviors, and some actions are more preferred than others, then the thingamajig inhabitants will seem to use the more preferred action. And if the current actions are reflected on previous ones, then you may get evolution (biological or not).

Whether or not you believe this, if you are easily entertained and know how to write code, then you can play around with this. Write in a class for a dot and make a bunch of them. Make them move around randomly with some directions better than others. Like up or down, or towards/away the mouse if you have the right lib. If you get it right and you're patient, you'll see random become predictable.

[zosima]

More like when they are describing evolution, they are using it wrong.

When you have random or arbitrarily indifferent behaviors, and some actions are more preferred than others, then the thingamajig inhabitants will seem to use the more preferred action. And if the current actions are reflected on previous ones, then you may get evolution (biological or not).

Whether or not you believe this, if you are easily entertained and know how to write code, then you can play around with this. Write in a class for a dot and make a bunch of them. Make them move around randomly with some directions better than others. Like up or down, or towards/away the mouse if you have the right lib. If you get it right and you're patient, you'll see random become predictable.

You're getting close to the central issue that people have been bickering over. For the moment I'll suspend all the practical objections that I might make about pseudo-random number generators, and we'll assume that your dot class is 'random'. I've got three questions.

1. When you make some directions 'better' than others, you are skewing the distribution of the random numbers your program produced. If the random number generator naturally produced numbers with that distribution you would probably think there was something wrong with it, yes?

2. What if you used exactly specified a set of floating point precision numbers. For some set of specified floating precision numbers you will get some rounding error in the insignificant digits when multiplying. Do you consider this random?

3. For this third one, let us presume that your dot is, in fact, random. So you have a system(or program) made up of random dots, You would also call the overall behavior of your program random? Despite the fact that those dots(plural), reliably follow the mouse?

All of these questions are very much central to the discussion in this thread.

Incidentally, this dot program you describe sounds an awful lot like a program for the Mac dashboard.....

[articulett]

Yes indeed... Is a random number or random pattern generator, random itself?

Nope. Having random components, does not a random process make. :)

[jimbob]

Zosima, I know enough to recognise that a digital computer simulation of a chaotic system is not in itself a chaotic syatem.

And that an analogue computer simulation is.

The digital simulation contains numbers that have been translated into high or low voltages on transistors, patterns of these voltages are then altered to duplicate the mathematical operations being performed on them. This is no more a chaotic physical system than a pen-and-pencil calcuation of these numbers.

[zosima]

Zosima, I know enough to recognise that a digital computer simulation of a chaotic system is not in itself a chaotic syatem.


Seriously It seems you are missing something fundamental, and all this arguing is getting to be less fun. So I'll type up a mathematical explanation of how these systems work later tonight. If you have a degree in physics and you still remember the math it required to get this degree, then you should have no trouble understanding what I'm saying. Unless you have some new, and highly creative objection after that point, we're done whether you agree or not.

I'll type it up in ~6 hours.

In case you're curious. The highlights will be this: #1 only mathematical models can be truly chaotic. #2 analog,pencil-and-paper,and digital physical systems, can all approximate chaotic systems equally well. #3 Any chaotic model applied to a natural system will, at best, be chaotic on some finite time/distance interval after which it will cease to be chaotic. #4 Any chaotic model when applied to a natural system will have a minimum sensitivity to perturbation.

[Wowbagger]

Oh, 24 pages of pointless bickering. Let me solve half of that dilemma: when creationists and "intelligent design" people use the word "random" to describe evolution, they are using it wrong.That might work as an approximate rule of thumb. But, there will be occasional exceptions on both sides.

[Walter Wayne]

Its good to see you back. :)
Good to be back and have some time to post.

Well, we might be able to come to some sort of agreement with respect to things lying on the continuum so I'll come back to that at the end.

It seems to me that you start talking about this idea of 'technically random' whenever you are having problems with whatever definition you put forward, but as far as I can tell your definition of 'random' and 'technically random' are identical. They are both "having a state or value depends on chance" which both assign the term random to things that are clearly not random.
I have given some examples of things that lie in both categories. Gas pressure being due to the number and momentum of particles hitting the container, will vary as you measure it, but to such a small extent that it is only technically random, but not practically so.

Compare that to a simple random number generator, where a noise source is compared to a reference voltage, and depending on the result a logical high ("1") or logical low ("0") is output. The resulting string of 1s and 0s is random in both senses, not just technically but also in practice.

Also, I'm not sure how you appointed yourself the arbiter of the definition of technically random, but that seems to be the claim we're disputing at the moment. (If we were talking about practically random we wouldn't be talking about definitions and statistics, we'd be talking about the processes of evolution.)



1. You have identified some techniques for identifying samples. The first one is the only one actually called random sampling. You did the same thing with distributions, where you inserted random into the name to try to support your point. So these would normally be called, 'simple random sampling','systematic sampling', and 'stratified sampling', in the same way that you started calling the distribution 'Poisson random distribution', 'Normal random distribution', etc....They are normally called the 'Poisson distribution'
and the 'Normal Distribution'
I want to get the definition of random out of the way, since it is useless to discuss how it applies to evolution as long as we are on different. Second I haven't appointed myself arbiter, the examples I gave about aren't ones I supplied.

Not true, random sampling is different that simple random sampling. Wikipedia doesn't do a bad job of explaining it. From the end of the first paragraph ...

This process and technique is known as Simple Random Sampling, and should not be confused with Random Sampling.

And you can look at both definitions at wikipedia, and note that one of the examples they give of random sample is a stratified sample.

Actually, you can find "gaussian random distribution" in text books and on the web. If you look up "gaussian random" in google you will find articles, several technical, on gaussian random distribution or generating gaussian random numbers.

Stats book talk about random numbers having a non-uniform distribution, stochastic books do, my computer science text book on numerical methods discussing generating non-uniformly distributed random numbers using the transform and acceptance-rejection methods.

I haven't simply added random to these, and have not appointed myself an arbiter.

2. Note that these practical techniques to get samples that are random, they are not perfect, the failures you mention(like small correlations) represent deviations from the ideal(random)

3. Clearly depending on what they are sampling their results may differ significantly from random(they may only get one result,)
This point being to distinguish patterns in their outcome from patterns in sampling.

4. I thought it noteworthy at the point when anyone in statistics would say 'random number between 1 and 43' You say 'unbiased'. That is telling insofar as you are manipulating your descriptions to prevent them from displaying exactly the characteristics that ideal randomness shows.

5. These techniques can be random samples, if we know something about the structure of what we are sampling so we add no information via a lack of uniformity of selection or a correlation between selections. For example we would get a random sampling via a systematic sampling if we knew that the order of the objects we were sampling was uncorrelated with the values that we were sampling from those objects. A second example: We use stratified sampling, when we know that there is sufficient heterogeneity in our overall population such that it could bias our sample(ie create a strong correlation between our samples, or eliminate uniformity because one subgroup is much larger than others)
2. As I pointed out, random sample and simple random sample do not mean the same thing.

3. Sure, if there is no variance in the population being sampled, then the outcome of sampling will be determined.

4. Of course I didn't use the word random there. It's stupid to use a word whose definition we are discussing in a position that would lead to ambiguity. And since random doesn't mean uniform as pointed out previously, it would be down right wrong. There was no manipulating, because random was the wrong word for the occassion.

5. I don't think you said what you wanted to there, as simple-random sample and random sample are not the same.

I made this example about a dirac-delta when you were talking about 'Poisson Random Distributions'(actually called Poisson Distributions) ie inferring that any distribution over a statistical variable is random. The 'dirac delta random distribution' disproves this suggestion.
Poisson distribution can be population distributions or random distributions.

Also, as Mijo reminds us so frequently, if the dirac-delta function is defined over the reals or the complex numbers we can never quite be sure that it won't have another outcome. This means that we can construct examples with a dirac-delta that are completely opposed to our intuitions insofar as they are completely predictable and yet still dependent on chance.
I don't agree with Mijo on that, though I haven't followed that line of argument much.

When one definies a probability function over the reals, the function is the probability density function, and you can get the probability of the result being on any interval by intergrating the probability density over that interval. If the density function is delta-dirac(x-k), then any interval not including k will have probability 0. Any interval including k will have probability 1. That seems about as certain as can be.
I'm sorry if this wasn't clear, but this is the point I was trying to demonstrate to you, with this example. That there is difference and the fact that we use a Gaussian distribution to model a process does not necessarily mean the population that produced it is random. Even if you do call it a "Gaussian random distribution".

This point was also a response to your laundry list of distributions. The point is similar: the distribution is separate from the process. I think that is why the necessity of no correlation is so crucial as well. You may get statistical distributions similar the ones you mention when you randomly sample a random event many times, especially if you are summing the outcomes. But the distribution of a single random event will never be distributed that way.
The distribution of thermal noise is approximately gaussian. If you sample the voltage on a resistor, the probability distribution of that single sample is gaussian.
ETA: all these statistical techniques that you and mijo keep bringing up may have random in the name, but "Random Distributions", "Random Variables", "Random Samples" all can be used in combination with a variety of different random and non-random processes. The commonality that they have, is that it assumes that they are unbiased with respect to the way they are generated. In other words, they clearly reflect the nature of the process itself, because the sampling or generative process itself is ideally uncorrelated and uniform. To try to claim that all the processes they describe are also random is clearly a mistake or even that they are necessarily the statistics of random processes. The only process that is ideally random is the uncorrelated and uniform one.
No, there is no assumption that they are unbiased in the way they are formed. However, if you wanted to measure such a process and get an accurate picture, an unbiased sampling is the best way to go about finding the processes bias.
Again, your technical definition and your practical definition are indistinguishable. It seems like the definition you advocate alternates between "anything that is not determinate" and "systems described using statistics", "practical", and "technical"
No more so that the term technical and practical are indistinguishable. I've given examples above and elsewhere.

I'd like to move on to this idea of a continuum to see if we can find some common ground:
If your 'technical' definition is 'anything that is not determinate' then there is no way to define a spectrum. Where is the far end of the spectrum, the end that is opposite determinate, anchored? Under your definition all answers to that question are equally good. Is the pure random end of the spectrum a Poisson distribution? or a Gaussian distribution? A Chi-Sq distribution?
Technically something that is random can have any distribution that doesn't have a variance of 0. Determistic system can have similar distributions. What is important in the technical defintion is that one can get different results for the same starting conditions.

If we use uniformly distributed and uncorrelated as the definition then we have a clear and singular answer. We would say that a flat, horizontal, uniform distribution is the ideally random distribution of a single event. The distribution of an ideally deterministic single event would be a vertical, dirac-delta distribution. One end is vertical, one end is horizontal, they fall on opposite ends of a spectrum. Anything that falls in between would be a deviation from ideal randomness and a deviation from ideal determinism.
For multiple events we would want to calculate the correlation between a sequence of samples, (with value on the y axis and sample number on the x)
If the correlation is 1.0 the sequence is ideally deterministic, if the correlation is 0.0 the sequence is ideally random.
1. I get a clear answer as well.

2. How are you calculating the correlation, by the standard equation I assume?

3. Non-uniform distributions will generate correlations of 0 as well as uniform ones. They would just have to be independent of the sampling process. If your numbering samples in the order you take them it would be sufficient that the process be independent of time.

4. Deterministic systems can produce correlations of 0. If you periodically asked me for a number, and I give alternating 1s and 0s you will get an incredibly low correlation to the sample N. Compare that to a random (your definition) string of bits.

Walt

P.S. If I have time before leaving for vegas I will give some examples of how heredity or self-correlation in a system can make it more un-predictable. Depending on how much time I have, I might go into those traits of evolution that do make it distinctly different from some of the common random systems like gas pressure, fire detectors, etc.

[zosima]

Zosima, I know enough to recognise that a digital computer simulation of a chaotic system is not in itself a chaotic syatem.



he highlights will be this: #1 only mathematical models can be truly chaotic. #2 analog,pencil-and-paper,and digital physical systems, can all approximate chaotic systems equally well. #3 Any chaotic model applied to a natural system will, at best, be chaotic on some finite time/distance interval after which it will cease to be chaotic. #4 Any chaotic model when applied to a natural system will have a minimum sensitivity to perturbation.

The simplest way to define a system's sensitivity to initial conditions mathematically via a Lyapunov exponent. Heres how it works:

Imagine a function:
$$U(t)$$
We can define the error of the system as:
$$\delta U(t) = \parallel U_{1}(t) - U_{2}(t)\parallel$$
Then we can write an expression exponential error growth as follows:
$$\delta U(t) = \delta U(0) e^{\lambda t} \hspace{2 mm} for \hspace{2 mm} \lambda > 0$$
Constant error:
$$\delta U(t) = \delta U(0) e^{\lambda t} \hspace{2 mm} for \hspace{2 mm} \lambda = 0$$
Decreasing error(stability):
$$\delta U(t) = \delta U(0) e^{\lambda t} \hspace{2 mm} for \hspace{2 mm} \lambda < 0$$

A couple of things become clear from this definition. #1 Error between two different solutions must be able to grow indefinitely. If the error growth stops the system is no longer chaotic on that interval. #2 Whether a system is chaotic by some definition depends on how we define our norm.

For example, its clear that if we use a euclidean norm to describe the error in a theoretical orbital system its clear from conservation of angular momentum that the greatest error growth we could have in the system is:
$$\delta U(t) = t \Sigma v$$
If we're talking about a population system then its error growth follows from the exponential growth description:
$$\delta P(t) = | P(0)_{1} e^{r t} \hspace{2 mm} - \hspace{2 mm} P(0)_{2} e^{r t} |$$
Since the difference between two exponentials is an exponential we can be sure it will meet the exponential sensitivity condition.

For some systems we might be concerned with the error growth within some bounded region. For those we might use a more probabilistic norm, but for our purposes it doesn't really matter.

From these definitions it is clear we can have a discrete system that meets this definition. For example:
$$U(t) = c4^{t}$$
Defined over the non-negative integers.

The problem with chaos is physical systems is that they cannot have growth that is exponential forever. Eventually the system will be bounded from above. For example, eventually a population system will run out of resources for growth, an orbital system(with a probabilistic norm) will either collapse into its center of mass or be thrown apart(due to the specific solution of the system, or tidal forces), an analog computational system will reach a maximal wavelength(constrained by energy), a digital computer will run out of memory, a pencil and paper system will run out of patience.

So a system can only be truly chaotic in a theoretical world where the system can run forever and has an infinite amount of resources. That's #1

Now #2 follows from our definition. Any system that exhibits growth and has a norm has the capacity to show this particular sensitivity. If that norm over two particular versions of that system grows exponentially it meets our definition of exponential error growth. A digital system can use the number of megabytes it takes to store a particular state(or difference in states), a pen and paper system can use the time it takes to write down an answer, an analog system can use the amplitude of a waveform. The particular representation doesn't matter. Look up iterative maps, for more examples on discrete computational chaotic systems.

#3 Follows from #1. A physical system will exhibit exponential error growth until it exhausts its resources, then it will cease to be chaotic. For example a system of billiard balls loses energy to heat from the elasticity of collisions. Eventually the balls cease to move and the error becomes constant.

#4 For the condition of exponential error growth to be met:
$$U(t) = \parallel U_{1}(t) - U_{2}(t)\parallel \neq 0$$
Otherwise:
$$\delta U(t) = 0 e^{\lambda t} = 0$$

This means that under our chosen norm we have to be able to resolve a difference. Our norm could be a stepwise norm...for example:
$$\delta U(t) = \lfloor U_{1} - U_{2} \rfloor $$

In a physical bounded system with a probabilistic norm the difference will always be bounded, at minimum, by Planc's distance, but often at a level above that. Here are some examples:

In a bounded system with a probabilistic norm, this means the difference in state needs to be resolvable over the noise in the system. (As the probability of the system is constant below this point). This can be thermal noise in a particulate system. Or imperfections in the material of an analog system. In a genetic system this might be the genetic difference required to create a phenotypical change. In a computational system this might be the number of RS bits required to protect against cosmic rays. In a population system this might be the difference in predator fitness required to kill one more prey.

So here's the conclusion. Physical systems are only an approximation of chaotic systems. Any physical modality can admit to a chaotic model.
If you want to claim that a physical system is chaotic you need to #1 provide a mathematical model of that system. #2 identify the norm under which it is chaotic. #3 Identify the range over which it is expected to exhibit chaotic behavior. #4 Identify the initial conditions and demonstrate that the difference between them is non-zero under this norm. #5 Provide evidence that said model is a good fit. What you don't need to do is, #1 wave hands, #2 not provide model that meets criteria above, #3 misquote/post claims without warrants.

[articulett]

And for those less physics inclined, I did once provide this article about the difference between randomness and chaos: http://www.newscientist.com/article.ns?id=dn11858

Non-random behaviour

Brembs and colleagues analysed the resulting flight records using increasingly sophisticated models of random behaviour. Were the flies' decisions random, like the result of a coin flip? No. Did they fit a coin-flip model in which the probability of "heads" varied randomly? Again, no.

Nor could they be explained by a series of random inputs, or a series of random inputs combined in non-random ways.

Instead, the researchers found that the flies' behaviour bears the hallmark of chaos – a non-random process that is nevertheless unpredictable, like the weather. No one has yet been able to adequately explain how chaos arises.

Chaotic advantage

The chaotic control gives flies' flight a spontaneity that might be evolutionarily advantageous when searching for food, say, or when a female tries to avoid an unwanted male. And, unlike true randomness, evolution can fine-tune the level of this spontaneity, Brembs says.


Understanding the terms you are using and making sure your audience understands is the first step of clear communication and useful modeling. But if obfuscation is your goal, use language however it pleases you to do so. Words can mean whatever you want them to me if you have a "higher purpose".

[jimbob]

Why isn't this an example of a random evolutionary event:

From New Scientist (http://www.newscientist.com/channel/life/dn14094-bacteria-make-major-evolutionary-shift-in-the-lab.html)

Mostly, the patterns Lenski saw were similar in each separate population. All 12 evolved larger cells, for example, as well as faster growth rates on the glucose they were fed, and lower peak population densities.

But sometime around the 31,500th generation, something dramatic happened in just one of the populations – the bacteria suddenly acquired the ability to metabolise citrate, a second nutrient in their culture medium that E. coli normally cannot use.

Indeed, the inability to use citrate is one of the traits by which bacteriologists distinguish E. coli from other species. The citrate-using mutants increased in population size and diversity.





In the meantime, the experiment stands as proof that evolution does not always lead to the best possible outcome (http://www.newscientist.com/channel/life/dn13620-evolution-24-myths-and-misconceptions.html). Instead, a chance event can sometimes open evolutionary doors for one population that remain forever closed to other populations with different histories.

That argument that a chance event can open (or close) evoloutionary "doors") has been part of my argument, although I talked about "niches".


Inotice that articulett is claiming to have put me on ignore again:

And jimbob... I've explained my point a thousand times. The nuts get to the top through probabilities, I supposed... but that IS irrelevant to understanding how they always seem to end up there. And I have you on ignore. Don't bother asking me leading questions you cannot comprehend the answer to anyhow. That is mijo-esque. I've been there; done that. You can have the last word. I refuse to let you inflict it on me, however.

(Your obfuscation regarding probabilities is fantastic, however, if you don't really want people to understand the basic science that ensures that the big nuts will settle on top... if, instead, you hope that they'll be open to the idea that there is a plot amongst nut sellers to make it look like there are more big nuts then there actually are. kudos.)


I say that Dawkins in the Extended Phenotype uses a probabilistic treatment of natural selection.

What is the alternative "nonprobabilistic" treatment?

That is obviously somehow a dishonest question.

[articulett]

For some life forms, they evolved to try something new or different when the old stuff isn't working...

[zosima]

I have given some examples of things that lie in both categories. Gas pressure being due to the number and momentum of particles hitting the container, will vary as you measure it, but to such a small extent that it is only technically random, but not practically so.

1. This is the central point of contention. I would agree that it is not wrong to call any individual particle in the gas 'technically random', or just 'random'. But the moments of the gas are neither practically nor technically random. As you say the number and the momentum of the particles is the cause of pressure. In an idealized closed container(no particle leakage,inelastic collisions,& rigid walls) the number of particles and their momentum will be strictly constant. (Due to the fact that the container is closed and due to conservation of momentum) So technically it is non-random and non-varying.
For example, pressure is:
P = Nm(vrms)2/3V
N the number of particles.(constant due to closure)
Vrms is the mean of the distribution(constant due to conservation of momentum)
m is the sum over the mass of the system(constant due to closure and conservation)
V is volume, (system wide constant)
I will note that practically there will be variation. Practically, the gas will leak energy/momentum into the walls of the container and it will radiate the energy out of the system from there. This will cause a steady decline in temperature.

2. It sounds like you're saying that the system is 'technically random' because there may be some variation in the insignificant digits of the measured moments of a gas. This is equivalent to saying everything is technically random. The is no physical entity that can be measured to infinite precision and there will always be 'quantum variation'. Thus the definition you put forth is devoid of meaning.(A definition that applies to everything equally fails to communicate information, see Shannon information entropy, if you are confused on this point.)

3. Also, no measurement will be to infinite precision. Discussions of any physical quantity need to be put in the context of some experimental method. If our instrument cannot measure down to an accuracy that we see any variation, then it is fair to call that system non-random and deterministic, insofar as our experiment is concerned. If we can measure a small variation in the measurement, we need to be careful how we phrase our statements about the system. We might be say the system is not a completely deterministic, that it has no variation in the significant digits, and that it has variation in the insignificant digits. If there is no pattern in this variation(uniform and uncorrelated) we might say there is random variation in the insignificant digits of our measurement. It would be folly to call the whole system random or even variable if the significant digits of our measurement are constant.


Compare that to a simple random number generator, where a noise source is compared to a reference voltage, and depending on the result a logical high ("1") or logical low ("0") is output. The resulting string of 1s and 0s is random in both senses, not just technically but also in practice.


Practically yes, technically maybe. Actually, at one time it was not uncommon to find systematic variation in a physical measurement used for a random number generator that was thought secure. That is actually part of the reason that software moved to pseudo-random number generators. They ended up being less random than noise based physical measurements. Although, admittedly technology has improved and cryptographic necessity has brought back the importance of random numbers generated from physical systems these days.


I want to get the definition of random out of the way, since it is useless to discuss how it applies to evolution as long as we are on different. Second I haven't appointed myself arbiter, the examples I gave about aren't ones I supplied.
What I refer to is your tendency to shift to the claim that "well whatever points you're making the system is still technically random". The points I've been making apply to both your definitions, so you can't logically regress to another nearly identical definition that you name more authoritatively.


Not true, random sampling is different that simple random sampling. Wikipedia doesn't do a bad job of explaining it. From the end of the first paragraph ...

This process and technique is known as Simple Random Sampling, and should not be confused with Random Sampling.

And you can look at both definitions at wikipedia, and note that one of the examples they give of random sample is a stratified sample.

Actually, you can find "gaussian random distribution" in text books and on the web. If you look up "gaussian random" in google you will find articles, several technical, on gaussian random distribution or generating gaussian random numbers.

The point I'm trying to make is not that it is wrong to have random in the name, but to point out that its presence in the name doesn't add to your claim. For example, you seem to make a big deal about the fact the that the
word 'random' is in a 'gaussian random distribution'. As you so aptly mention further down in your post, it is not the distribution that is random. In fact, a gaussian distribution is entirely deterministic.
Gpdf = (1/sqrt(2*pi))*exp(-x2/2)
(This is with a mean of 0 and a variance of 1)
The fact is that a large number of measurements may often be modeled with a Gaussian distribution due to the central limit theorem. We might call this a population or a sample distribution, depending on context.


Stats book talk about random numbers having a non-uniform distribution, stochastic books do, my computer science text book on numerical methods discussing generating non-uniformly distributed random numbers using the transform and acceptance-rejection methods.


Yet a random number generator that isn't uniformly distributed is considered non-random in computer science. A cryptographic random number generator that isn't uniformly distributed is no random number generator at all. Stats books talk about 'random variables' having non-uniform distributions and we've already mentioned that they consider distributions like the dirac-delta to be distributions over random variables as well.

If we want this conversation to go until infinity we can both go and mine all our textbooks and all the scientific literature for examples that support both our cases. The bottom line is that the use of the term isn't going to be consistent from author to author, researcher to researcher, field to field, etc... So which usage should we choose? I would assert strongly that the definition of practitioners in the field of evolution is most applicable, and we've already heard the top minds in the field denying randomness in evolution.


2. As I pointed out, random sample and simple random sample do not mean the same thing.

Yes this was addressed above, I'm not sure how this denies that fact that deviations: correlations, skews, etc... are a deviation from randomness.


3. Sure, if there is no variance in the population being sampled, then the outcome of sampling will be determined.

Exactly the point. For example, in the last post you mention 'Systematic Random Sampling', but insofar as SRS is a deterministic process, it is non-random. And you've just agreed that the object being sampled is not necessarily random either.

So why is the word 'random' in the name at all? What is its meaning? It is talking about the capacity of the technique to create neither bias, nor correlation in the sampled distribution. If the samples themselves are uniformly distributed and uncorrelated(in the appropriate variable space of the problem) they will do exactly that. In that way a random sampling technique can form an accurate impression of the object being studied. This corresponds well to the definition I put forth. Whereas the definition of random as non-zero variance doesn't seem to explain this usage at all.

Exactly which technique needs to be used depends a lot of the object of study. We might use a systematic technique if we know the objects of interest are in a unordered(randomly ordered) list. We might use stratified sampling, when we believe there is a numerical or representational bias between groups. (For example in a survey by phone certain groups may be more likely to have a telephone, so if we want to eliminate this skew in our sampling, we would do well to sample the different groups separately and then recombine appropriately.)


4. Of course I didn't use the word random there. It's stupid to use a word whose definition we are discussing in a position that would lead to ambiguity. And since random doesn't mean uniform as pointed out previously, it would be down right wrong. There was no manipulating, because random was the wrong word for the occassion.

I thought it interesting. A uniform and uncorrelated number is exactly what you were talking about. Under my definition there would be no ambiguity. It certainly would be called random in any technical description. It only becomes ambiguous when the advocated definition is so broad that the original word is depleted of meaning.


5. I don't think you said what you wanted to there, as simple-random sample and random sample are not the same.

I do understand the difference. 'simple random sample' v 'all other types of random sampling' is a false dichotomy. If you didn't understand my previous explanation, my other one above may be clearer. The basic idea is that the technique ought to be selected to eliminate bias and correlation from the sampling process itself. Practically other variables will be optimized as well when deciding on a technique. For example, cost, speed, practicality, error. A systematic sample can be much easier to implement if its usage is not problematic.



Poisson distribution can be population distributions or random distributions.

I don't think you are using these terms quite correctly, or at least you are twisting 'random distribution' to somehow put it into opposition to 'population distribution' to support your definition. You were much clearer in the previous post when you distinguished between 'probability distribution' (or 'sample distribution') and 'sample distribution'

But I get that a population and sample can both have a Poisson distribution.



I don't agree with Mijo on that, though I haven't followed that line of argument much.

When one definies a probability function over the reals, the function is the probability density function, and you can get the probability of the result being on any interval by intergrating the probability density over that interval. If the density function is delta-dirac(x-k), then any interval not including k will have probability 0. Any interval including k will have probability 1. That seems about as certain as can be.


Hey now. You're arguing my points now. That the moments(or partial moments) of a system are constant and regular. This is integral is exactly what we do when we calculate the characteristic moments of a gas(density, velocity,temperature, pressure, etc...) and they are exact.

The point is that if you are looking at any particular solution of a sample distribution over the reals, you cannot necessarily be sure that the value will be the expected, regardless of the distribution. Only almost sure. What this means is that if we use a non-zero variance definition of random, there is not even a theoretical way to be certain a system is non-random. Although, I would tend to agree that this sort of digression is a bit of a red-herring.


The distribution of thermal noise is approximately gaussian. If you sample the voltage on a resistor, the probability distribution of that single sample is gaussian.

Yep thats noise alright. This is just a regression of the gas issue discussed above. The voltage is a function of temperature, and that follows from the random motion of individual molecules. It is governed by the central limit theorem and is not random(remember OHM's law). The single sample would only be random if it didn't tend toward that limit.(as per my stated definition of random)


No, there is no assumption that they are unbiased in the way they are formed. However, if you wanted to measure such a process and get an accurate picture, an unbiased sampling is the best way to go about finding the processes bias.

This is covered in detail above.


No more so that the term technical and practical are indistinguishable. I've given examples above and elsewhere.

You distinguish by saying that 'practically random' has more 'variance than technically random' . That is the only commonality in your distinction. That is just another way for you to say "I reserve to draw the distinction wherever suites my purposes"



Technically something that is random can have any distribution that doesn't have a variance of 0. Determistic system can have similar distributions. What is important in the technical defintion is that one can get different results for the same starting conditions.

Two bad meaningless definitions. I've addressed them both, but I've hit the first a little more explicitly. So I'm just going to address the second one here.

1. The terms 'different' and 'same' are ambiguous. Since no starting conditions are ever the same, there is no identical repeatability and no way to to tell if a system is random or not under this definition. Also the contrary point is true for the result. All results are necessarily different. You couldn't even design an experiment that can test this in theory as you can never measure to infinite precision whether the starts are the same and the ends are different.

2. This claims that random is synonymous with non-deterministic, clearly they are not. We can actually construct a thought experiment that proves this point. Imagine a phenomenon. We're in thought experiment land, though, so lets imagine we can control for every variable and actually get identical conditions. Our first measurement will be 1 or 0 with some probability and every subsequent measurement in the system for that session will be the negation of the previous value:
$$System: S(t) $$
$$p(S(0)) = .5$$
$$S(t-1) = 0 \Rightarrow S(t) = 1$$
$$S(t-1) = 1 \Rightarrow S(t) = 0$$
So is this system random or deterministic? We've stipulated that we control for all variables so we're in the same conditions, yet our first measurement may be 1 or it may be 0, we don't know. Yet after we measure that first value the system behaves in a completely reliable way. The answer seems to be that neither explanation is entirely adequate and we would more accurately call this intermediate system a mixed system or a non-deterministic(also non-random) system. You might argue that this thought experiment is unrealistic, that it is impossible because it postulates an uncaused event and the observer divides the sequences of measurements into sessions, but this is not too different from a quantum experiment testing bell's inequality, where the observer collapses the waveform, so an initial probabilistic measurement determines the system. It necessarily excludes this same-start different result definition.


1. I get a clear answer as well.

I think you miss by point. What I'm saying is that there are tons of systems that seem to fall between random and determinate. The definition I have creates a spectrum(on two dimensions) by placing uniform and uncorrelated
on one extreme and singular(dirac) and correlated on the other extreme. This organizes our conceptual space over a continuous field.(RxR) It allows us to situate the intermediate examples in the appropriate locations in the space. This is an advantage. Your definition has a certain binary quality such that it is unable to properly situate intermediate cases so that they agree with our intuitions. This is a disadvantage.


2. How are you calculating the correlation, by the standard equation I assume?

No I'm talking about lack of correlation in a more fundamental sense. In all senses really. For example there is a certain class of pseudo-random number generators that seemed to show lack of correlation and uniformity. In other words it seemed to produce random numbers. What was later discovered was that if the numbers were plotted in a high-dimensional space they would form clear and identifiable bands. So I don't think any single definition of correlation is sufficient.


3. Non-uniform distributions will generate correlations of 0 as well as uniform ones. They would just have to be independent of the sampling process. If your numbering samples in the order you take them it would be sufficient that the process be independent of time.

If (un)correlation followed from uniformity or uniformity from (un) correlation, I wouldn't require two constraints to describe random. I would just mention the more primary. Only both together create random.


4. Deterministic systems can produce correlations of 0. If you periodically asked me for a number, and I give alternating 1s and 0s you will get an incredibly low correlation to the sample N. Compare that to a random (your definition) string of bits.


See my example above, that any single correlation algorithm is inadequate.
If you plot your alternating 1s and 0s over the appropriate choice of basis a correlation will show.

Just to conclude, I'm getting kind of bored of this discussion.
In the interests of expediency, I'd like to try to work at a compromise. Really since a definition is based upon usage and common usage is based upon a consensus understanding of language, as long as either one of us(or mijo) is willing to assert their definition regardless of evidence to the contrary we're never going to be done. So it might be best for us to start looking for a compromise definition and stop asserting the universal truth of our definition. Since usage will vary(as I mention above) it seems kind of silly to insist that there is one correct definition. The definition is whatever people agree is should be and different groups will have come to different agreements. So what definition practical, technical or not, is appropriate to this discussion?

[jimbob]

For some life forms, they evolved to try something new or different when the old stuff isn't working...

I take issue with virtually every word in that post.

Firstly:

Organisms do not evolve "to" do anything. Nor do they "try" things.

Secondly:

If the "old stuff" wasn't working, they would become extinct.

A random variation increased the reproductive success of holders of this variation, and so the new variation spread. If the holders of the variation (mutation) are still competing with organisms without this mutation, then their success will reduce the reproductive success of organisms without the mutation.

[Mitchell314]

You're getting close to the central issue that people have been bickering over. For the moment I'll suspend all the practical objections that I might make about pseudo-random number generators, and we'll assume that your dot class is 'random'. I've got three questions.

1. When you make some directions 'better' than others, you are skewing the distribution of the random numbers your program produced. If the random number generator naturally produced numbers with that distribution you would probably think there was something wrong with it, yes?


Sorry about that. I've come up with a slightly better one on my calc. Pretty much, have an initial random behavior, and then (not affecting the randomness or semi-randomness) fuzzily show preference. That might be making a do over or something. The end result may not be fully random (and will become more...deterministic over time if you get it right). But the initial behaviors are. Or you can have previous behaviors give rise to new chaotic (I'm tired of saying random) behavior. Such as evolving feet for better survival, while giving the ability for drunks to aimlessly wander around.

I found a cool applet that had four simple "amoeba" wander around. They had four genetic traits: Speed, size, angular speed, and stinger length. The rules were that if an amoeba was stung, it died and was replaced by the killer, with random tiny mutations. The whole system evolves, and differently when I ran it; predominately going the route of wide ones with short, slow stingers; or small ones with fast stingers far out. Then again, you may point out that natural ecosystems are vastly more complex, cells have much more traits, and aren't simple 2d geometric primitives.


2. What if you used exactly specified a set of floating point precision numbers. For some set of specified floating precision numbers you will get some rounding error in the insignificant digits when multiplying. Do you consider this random?


My program used only integers (TI-83 SE+). Rounding may - in some instances - appear random. It depends on implementation. Some physics engines can appear random due to poorly handled rounding. I don't consider it random, though if I experience it through black-box implementation of a program, it might seem random.


3. For this third one, let us presume that your dot is, in fact, random. So you have a system(or program) made up of random dots, You would also call the overall behavior of your program random? Despite the fact that those dots(plural), reliably follow the mouse?


No...yes...no...ish. It's randomish, but normally in this program, it will pretty much settle and buzz around the mouse. Overall, it starts here and ends up here, and follows rules (go towards X) regardless of how. When I watched the dot frame by frame (a little less than .5 fps for ten dots), it was all over the place. After a while, it did get to where I wanted it to go (top left). The direction was random (The calculator is good with whatever seed it uses), but if the direction wasn't up-left, then it did a re-roll and settled for that. A light breeze, but a breeze nonetheless. For me, there was definite movement in a minute.


All of these questions are very much central to the discussion in this thread.

Incidentally, this dot program you describe sounds an awful lot like a program for the Mac dashboard.....

Actually, this was just a curiosity I played around with when I just started learning how to code. A purely random coincidence. And this isn't the only program dealing with this nature.

Hey, I was bored. Roaming dots are fun.

[Dancing David]

Zosima, I know enough to recognise that a digital computer simulation of a chaotic system is not in itself a chaotic syatem.


OOOOkay, um, what is a chaotic simulation then, like a strange attractor?

Wow.

And that an analogue computer simulation is.

The digital simulation contains numbers that have been translated into high or low voltages on transistors, patterns of these voltages are then altered to duplicate the mathematical operations being performed on them. This is no more a chaotic physical system than a pen-and-pencil calcuation of these numbers.

And what produces bifurcation and the mandlebrot set, pointless semantics.

Start with the weather random number generator and you will get chaos.

[Dancing David]

I take issue with virtually every word in that post.

Firstly:

Organisms do not evolve "to" do anything. Nor do they "try" things.

Secondly:

If the "old stuff" wasn't working, they would become extinct.

A random variation increased the reproductive success of holders of this variation, and so the new variation spread. If the holders of the variation (mutation) are still competing with organisms without this mutation, then their success will reduce the reproductive success of organisms without the mutation.

I agree many organisism do not evolve 'to do things'.
I take exception with many of your words.

Um variation need not be random, but please continue to abuse the term variation. There are means of variation that are not 'random', but whatever.

[articulett]

When I say the organism "evolved to", most people understand that those with the propensity in the genes preferentially survived and reproduced. When we say duck's corkscrew shaped members evolved to fit in the reproductive tracts of females discouraging rape... then I trust that all people who actually understand evolution understand that these are the environmental forces which "naturally selected" the genes coding for these traits.

I don't expect a creationist to understand or agree with anything I say. They can't. It spoils what they want to believe about their self appointed expertise in whatever it is they imagine themselves to be experts in.

[Wowbagger]

There are means of variation that are not 'random', but whatever.I agree. But, it does depend on how you define 'random'.

[Wowbagger]

One of the problems with the language of evolutionary biologists, is that they tend to say things like "evolved in order to...", or "calculates resources for optimal whatever...", but it is important to understand that they do not literally mean it when they say that!

Biologists do not literally mean that birds whip out calculators, to figure out how much yolk to distribute into how many eggs, to achieve optimal survival of the progeny. But, that genes evolved to hone the ability, "instinctually", within the bird's body.

However, biologists will still use such verbiage, as a shortcut, when talking amongst other biologists (and somtimes to the public, under the mistaken belief that they will "get it"), because it's just easier to say "birds calculate egg yolk distribution" instead of rambling on about what actually happens. Other biologists will "get it".

[articulett]

I think that no matter how you define random... there are means of variation that aren't.

But I shan't play the "defining random" game any more. I quoted definitions from peer reviewed sources. Those claiming evolution is random have not. They keep claiming their vague definition is the "technically correct" whatever that means... I guess by their own imagined expert authority anything that contains any randomness IS random and/or anything related to probability and/or that contains any part related to probability is random.

On my planet, that makes random a completely useless word unless your goal is to obfuscate understanding of evolution so as not to convey how natural selection works.

[lenny]

For some life forms, they evolved to try something new or different when the old stuff isn't working...

ummm, did you really mean that?

wouldn't you expect the vast majority if things to just go extinct if it turns out "the old stuff isn't working"? evolution on demand sounds, well, a bit miraculous.

[lenny]

2. What if you used exactly specified a set of floating point precision numbers. For some set of specified floating precision numbers you will get some rounding error in the insignificant digits when multiplying. Do you consider this random?


no, it is not random. and how does it help us to introduce "rounding error"?

a chaotic mathematical system simulated on a digital computer is just a many to one map on the integers. nothing random, and in "error" only if one mistakenly identifies the simulation with the thing simlutated (an exact calculation). as a mere simlulation it can still yield interesting robust insights.

do you disagree with jimbob's analog/digital distinction?

[Prometheus]

ummm, did you really mean that?

wouldn't you expect the vast majority if things to just go extinct if it turns out "the old stuff isn't working"? evolution on demand sounds, well, a bit miraculous.

Not evolution on demand, but evolved adaptability.

[articulett]

ummm, did you really mean that?

wouldn't you expect the vast majority if things to just go extinct if it turns out "the old stuff isn't working"? evolution on demand sounds, well, a bit miraculous.

Yes... I meant it, and it followed an article I quoted and I also explained what I meant. It's not "evolution on demand". It's evolution with a brain coded for "spontaneity"... read what I actually said and referenced before commenting if you want your opinions respected. Otherwise, you appear jerkish to me.

[articulett]

Not evolution on demand, but evolved adaptability.

Thanks.

[zosima]

no, it is not random. and how does it help us to introduce "rounding error"?
I wasn't intending it as an argument. Mitchell is new to this thread, and he introduced an example that I wanted to understand, and I wanted to understand how he felt about the whole random issue. Different people, on this thread might answer it different ways, and their answers tell me things. But issues of numerical stability are incredibly important.

Rounding error on a digital system is generally a deterministic process that is very difficult to model. So it tells me if Mitchell is a random=unpredictable, or a random='fundamentally random' fellow.


a chaotic mathematical system simulated on a digital computer is just a many to one map on the integers. nothing random, and in "error" only if one mistakenly identifies the simulation with the thing simlutated (an exact calculation). as a mere simlulation it can still yield interesting robust insights.

A chaotic system is:
1. Deterministic.
2. A purely mathematical construct.

I don't really want to argue about this, I've really talked to enough on this thread already. Just read my older posts, if you're curious about my position.


do you disagree with jimbob's analog/digital distinction?

Absolutely. It demonstrates jimbo's fundamental misunderstanding of what constitutes a chaotic system.

If you want an example try learning about the logistic map. It is an extremely common chaotic model that is completely closed under the integers. There are numerous other chaotic equations that are completely discrete as well.

My position is that any physical instantiation of a chaotic system is only going to fit the mathematical model ideal approximately. The only reason I can see that Jimbo is supporting this analog/digital distinction, is because it limits us to examples that are harder to reason about precisely, and thus makes it easier for him to wave his hands into his conclusion.

But seriously,I can't take the time to explain all this. If you are still confused I've laid everything out in detail in my previous posts. There is nothing more that I can say that hasn't already been said there.

[Dancing David]

When I say the organism "evolved to", most people understand that those with the propensity in the genes preferentially survived and reproduced. When we say duck's corkscrew shaped members evolved to fit in the reproductive tracts of females discouraging rape... then I trust that all people who actually understand evolution understand that these are the environmental forces which "naturally selected" the genes coding for these traits.

I don't expect a creationist to understand or agree with anything I say. They can't. It spoils what they want to believe about their self appointed expertise in whatever it is they imagine themselves to be experts in.


I understand that, and I was not faulting you, more the extreme fine point drawing of some people and avoiding the trap of determinism.

I agree with you and understand your arguments. I understand what you are saying but the others, wow...

[Dancing David]

I agree. But, it does depend on how you define 'random'.


Like 'dog' and 'tree' an idiomatic self referencing symbolic exchange that looses meaning when some people forget about the consensus of communication and stop trying to exchange ideas.

[mijopaalmc]

Absolutely. It demonstrates jimbo's fundamental misunderstanding of what constitutes a chaotic system. It sounds like both ya'll have a fuzzy, hand-wavy, pop-sci understanding of how these things work.

If you want an education, try learning about the logistic map. It is an extremely common chaotic model that is completely closed under the integers. There are numerous other chaotic equations that are completely discrete as well.

But seriously, I'm not gonna take the time to explain this to you. If you are still confused I've laid everything out in detail in my previous posts. There is nothing more that I can say that hasn't already been said there.

If you are going to criticize someone's knowledge of chaotic systems you might want to review your own. First off, the the logistic map may be closed under the integers (i.e., any integer input yields an integer output), but it not chaotic on the integers, because the integers do not form a dense set of perioduic orbits, a defining element of chaos.

[zosima]

If you are going to criticize someone's knowledge of chaotic systems you might want to review your own. First off, the the logistic map may be closed under the integers (i.e., any integer input yields an integer output), but it not chaotic on the integers, because the integers do not form a dense set of perioduic orbits, a defining element of chaos.

Yeah, I edited that language out of my post(before mijo reposted what I said) because I realized that I was a little annoyed and had used language that was too strong. So I apologize.

But my claim is correct. The logistic map is chaotic over the integers, you are incorrect. Write a program yourself, you'll see it cycling even in one dimension around 0. (Just to be sure I just tested it out with r=5 and x(0) = 7)

Moreover, there are plenty of other discrete chaotic systems. (Probably there are an infinite number) I would recommend this book if you are still confused:
http://www.amazon.com/exec/obidos/ASIN/1584880023/ref=nosim/weisstein-20
What's the book called? Discrete Chaos

ETA: Also here's an example from Wolfram's Mathworld: http://demonstrations.wolfram.com/DiscreteLogisticEquation/
The actual output is normalized between [0,1] for the purpose of plotting.(it is easier to see, 'cause don't need to rescale the plot every time you perform a step). The name of the example "Discrete Logistic Equation" Do you ever get sick of being wrong Mijo?

[mijopaalmc]

The logistic map is chaotic over the integers, you are incorrect. Write a program yourself, you'll see it cycling even in one dimension around 0. (Just to be sure I just tested it out with r=5 and x(0) = 7)

Moreover, there are plenty of other discrete chaotic systems. (Probably there are an infinite number) I would recommend this book if you are still confused:
http://www.amazon.com/exec/obidos/ASIN/1584880023/ref=nosim/weisstein-20
What's the book called? Discrete Chaos

ETA: Also here's an example from Wolfram's Mathworld: http://demonstrations.wolfram.com/DiscreteLogisticEquation/
The actual output is normalized between [0,1] for the purpose of plotting.(it is easier to see, 'cause don't need to rescale the plot every time you perform a step). The name of the example "Discrete Logistic Equation" Do you ever get sick of being wrong Mijo?

Actually, yet again it is you who is wrong. The logistic map on the integers contains only stable fixed points between 1 and 4 and unstable points for intergers greater than 4. It does not contain any periodic orbits, let alone are the periodic orbits dense in the integers. The logistic map on the integers is therefore not chaotic on the integers, at least according to Robert Devaney's definition of a chaotic dynamical system (http://books.google.com/books?id=CjAnY99LwTgC&printsec=frontcover#PPA50,M1).

[Vorticity]

...
If you want an example try learning about the logistic map. It is an extremely common chaotic model that is completely closed under the integers. There are numerous other chaotic equations that are completely discrete as well.
...

I've been trying very hard to stay out of this futile thread, but I thought I'd jump in here with a quick note. The current disagreement over the logistic map seems to be resulting from some confusion over terms.

The logistic map is a discrete dynamical system which is usually written as:

$x_{n+1} = r x_n(1-x_n)$

zosima, when you say that the logistic map is "closed under the integers", what do you mean. To me, for a map defined as

$x_{n+1} = f(x_n)

to be "closed under the integers", that would mean that when $x_n$ is an integer, then $f(x_n)$ is such that $x_{n+1}$ is always an integer as well.

For arbitrary, real $r$, it is clear that the logistic map does not satisfy this criterion, although this is the case if $r$ is an integer.

However, in the next sentence, you say "There are numerous other chaotic equations that are completely discrete as well." (Bolding mine) This wording suggests to me that you are equating the property of being discrete (i.e. possessing a discrete independent variable) with the property of being closed under the integers. In fact, these are two different properties.

While for certain initial conditions and certain values of $r$ (e.g. for $r = 1$), it is undeniably the case that the logistic map is chaotic, it is certainly not the case for integer-valued initial conditions.

[Vorticity]

But my claim is correct. The logistic map is chaotic over the integers, you are incorrect. Write a program yourself, you'll see it cycling even in one dimension around 0. (Just to be sure I just tested it out with r=5 and x(0) = 7)

Unless we're having some huge confusion over definitions, then I'm baffled.

I just wrote a program and tried it with these values. The logistic map does not display chaos for these values of r and x(0). It shoots off to negative infinity.

ETA: Also here's an example from Wolfram's Mathworld: http://demonstrations.wolfram.com/DiscreteLogisticEquation/
The actual output is normalized between [0,1] for the purpose of plotting.(it is easier to see, 'cause don't need to rescale the plot every time you perform a step).

It is not normalized. It wasn't necessary.

For 0 <= r <= 4, the interval [0,1] is closed under the standard logistic map.

That is why they constrain their initial condition to be between 0 and 1, and also they constrain their parameter lambda (which is equivalent to r) to be between 0 and 4.

The name of the example "Discrete Logistic Equation" Do you ever get sick of being wrong Mijo?
Careful.

Although this is to a certain extent a confusion over nomenclature, as far as I can tell, mijo is much closer to being right than you are: The logistic map with integer r (and so closed under the integers) is, in fact, NOT chaotic with integer initial conditions.


By the way, an interesting side note, since we're speaking tangentially about probability:

For r = 4, the logistic map has an invariant measure p(x) on [0,1], where
$p(x) = \frac{1}{\pi\sqrt{x(1-x)}}$

[mijopaalmc]

zosima, when you say that the logistic map is "closed under the integers", what do you mean. To me, for a map defined as

$x_{n+1} = f(x_n)

to be "closed under the integers", that would mean that when $x_n$ is an integer, then $f(x_n)$ is such that $x_{n+1}$ is always an integer as well.

For arbitrary, real $r$, it is clear that the logistic map does not satisfy this criterion, although this is the case if $r$ is an integer.

However, in the next sentence, you say "There are numerous other chaotic equations that are completely discrete as well." (Bolding mine) This wording suggests to me that you are equating the property of being discrete (i.e. possessing a discrete independent variable) with the property of being closed under the integers. In fact, these are two different properties.

Yeah, this was something that also confused me about zosima's post. I interpreted the property of being "closed under the integers" as being the property of algebraic closure you described above. As you also noted this propert say nothing about the discreteness or continuity of the dynmical system, which, as far as I understand, pertains to the "number" of iterations (i.e., compositions of the time evolution function). This is in generally more rigorously explained as the group action of the integers (in the discrete case) or the reals (in the continuous case) on a manifold, and, as far as I understand, is roughly analogous to indexing random variables to a competely ordered set for stochastic processes.

[jimbob]

For some life forms, they evolved to try something new or different when the old stuff isn't working...
I take issue with virtually every word in that post.

Firstly:

Organisms do not evolve "to" do anything. Nor do they "try" things.

Secondly:

If the "old stuff" wasn't working, they would become extinct.

A random variation increased the reproductive success of holders of this variation, and so the new variation spread. If the holders of the variation (mutation) are still competing with organisms without this mutation, then their success will reduce the reproductive success of organisms without the mutation.

I agree many organisism do not evolve 'to do things'.
I take exception with many of your words.

Um variation need not be random, but please continue to abuse the term variation. There are means of variation that are not 'random', but whatever.

Dancing David,

It wasn't just the Evolved to... part. It was what they were evolving to do. It would still be wrong to say.
For some life forms, they evolved to try and tried something new or different when the old stuff isn't working...

Lets change it again to make it less wrong:

For some life forms, they evolved to try and "tried" something new or different reproduced better than the old stuff (which initially still worked sufficiently to produce reproducing offspring otherwise there wouldn't be any descendents) when the old stuff isn't working...



The original statement is almost 100% wrong. It is also a disagreement I had with articulet when she equated aspects of technical development to evolution.

Humans can, and do learn from mistakes. Evolution can only "learn" from success.

The post above articulett, which I suspect she was responding to concerned a single populationof e.coli that evolved citrate metabolism.


The vast majority of organisms reproduce asexually most of the time. Variation in such a situation (ignoring lateral gene transfer) is due to mutation.

[zosima]

Unless we're having some huge confusion over definitions, then I'm baffled.

I just wrote a program and tried it with these values. The logistic map does not display chaos for these values of r and x(0). It shoots off to negative infinity.


Well my initial claim was with respect to whether digital systems can be chaotic. So it does shoot off to negative infinity. But then it rolls around and oscillates chaotically, so technically, I'm describing it over a finite field.

Also, I am making the claim that r must also be an integer. So I'm not just talking about discrete time, I'm talking about a completely discrete system. If R is rational it is trivially not closed under the integers. (Or a finite field)


It is not normalized. It wasn't necessary.

For 0 <= r <= 4, the interval [0,1] is closed under the standard logistic map.

That is why they constrain their initial condition to be between 0 and 1, and also they constrain their parameter lambda (which is equivalent to r) to be between 0 and 4.


You are right about that. That sort of normalized plotting is a technique applied elsewhere is NKS I'd figured thats what they were doing there, so I stand corrected.

But even that being the case a normalized plot(dividing by some reasonable guarantee of an upper bound, or moding the output), will demonstrate the chaotic behavior of the map with large x. If you want to say that I've applied a modulus to plot the output,thats fine. Its also seems to be 'tangential' at best, as you would put it. It fits the definition of chaotic insofar as it has exponential error growth from neighboring starting conditions( the fundamental feature in the discussion of evolution.). Really, the discussion is about the broader question of unpredictability in systems, and often chaotic systems are being used to stand in for unpredictable systems. Constraining a system to fall within some bounded region seems to me to be an irrelevant constraint to this discussion.

But what I'm most concerned with is proving that a digital system can constitute a chaotic system just as well as an analog system of equivalent precision. I'm certainly not saying that any of the chaotic properties of the function follow from the function being defined over the integers, only that they are not inconsistent.

If you take issue with the logistic map there are plenty of other systems that would prove my point. Moreover rational numbers within a digital system would be a sufficient field to make proofs about chaos in digital systems

[mijopaalmc]

Also, I am making the claim that r must also be an integer. So I'm not just talking about discrete time, I'm talking about a completely discrete system. If R is rational it is trivially not closed under the integers. (Or a finite field)

But when r is restricted to the integers, the dynamical system is not chaotic, as there are no periodic orbits and periodic orbits are an essential element of chaos.

Constraining a system to fall within some bounded region seems to me to be an irrelevant constraint to this discussion.

As far as I have read in textbooks about chaos, chaotic maps are maps of sets in to themselves. Outside of some bounded interval ([0,1] in the case of the logistic, any intial interval will eventually not map into itself.

If you take issue with the logistic map there are plenty of other systems that would prove my point. Moreover rational numbers within a digital system would be a sufficient field to make proofs about chaos in digital systems

Nice assertions. Would you care to back them up with some actual examples?

[zosima]

But when r is restricted to the integers, the dynamical system is not chaotic, as there are no periodic orbits and periodic orbits are an essential element of chaos.

That is an excellent repetition of your claim, it doesn't seem like you've included any new content. The definition that I've been using insofar as evolution is concerned is exponential error growth. Restricting to periodic orbits necessarily excludes numerous systems that need to be part of the evolution discussion. For example, the pool(snooker) balls, would be chaotic in the sense of exponential error growth, but not in the sense that they ever have periodic orbits. Moreover, if we use your definition, then it is guaranteed that evolution has nothing to do with chaos, as evolution doesn't have periodic orbits. So the definition you've provided, while perhaps useful in limiting certain mathematical investigations, is self-defeating when applied to the topic at hand, whereas exponential error growth is a perfectly sufficient definition. Why should we restrict chaotic systems to periodic orbits? Is there any reasoning behind this claim?


As far as I have read in textbooks about chaos, chaotic maps are maps of sets in to themselves.

Okay, if that is the constraint you are placing, then closure under the integers was sufficient in the first place.


Outside of some bounded interval ([0,1] in the case of the logistic, any intial interval will eventually not map into itself.


You're wrong. r = .1, x = 10, will map into itself an infinite number of times, on the bounded region [-10,10], although this particular solution will not be chaotic. There actually is a set of solutions that have this property. r = .01, x = 100 [-100,100] r = .001,x = 1000,[-1000,1000] so, technically, there are an infinite number of bounded solutions outside of the interval [0,1] that map onto themselves indefinitely yet do not converge to 0(or ever enter the region [0,1])

Also I've already mentioned this but you seem to have missed it, if we're working with a finite set of integers or we do a normalized plot, it shows just as much chaotic oscillation as any other system. It is just a question of how you visualize the erratic and unpredictable behavior of the output.


Nice assertions. Would you care to back them up with some actual examples?

y = 2*x mod z over the integers is a classical example.(z prime != 2)
Over the rationals: y = 2*x mod 1.0

Both digital and analog systems will make numerical approximations from the mathematical ideal, which has been my contention from the start, and thus they are both equivalent approximations.

ETA: Moreover, if we restrict the discussion to only systems that have dense periodic orbits, it essentially concedes the issue of randomness in evolution. Chaotic systems under your definition are generally subject to noise induced order. This eliminates the possibility of any large scale randomness in evolution.

[jimbob]

Both digital and analog systems will make numerical approximations from the mathematical ideal, which has been my contention from the start, and thus they are both equivalent approximations.


No they are not.

An analogue computer does not make numerical approximations. It is a physical model of a system, with one type of physical quantity replacing another, for example using an LCR circuit to model the oscillations of a mass on a spring. If you made two analogue computer simulations of chaotic system, they will diverge, by virtue of them not having identical starting conditions.

If you made two digital computer simulations of chaotic system, they will not dverge, if you set the initial numbers and precision to be the same.

The computer is a physical system, but a computer simulation is not a physical chaotic system.

Physically, assuming that you are using a computer with CMOS logic, the computer simulation consists of a set of tranistors with their gate voltages either "high" or "low" and their drain voltages either "high" or "low". (The computer simulaiton could also be made on a babbage-engine, or on a valve computer, or any other type of computer that could be made). In all these systems, as you say, there is a numerical approximation to solving the chaotic equations. And a "mapping" of these results to some form of output system.

An analogue system aims to be a physical analogue of the system that is modelled, so there is no numerical approximation. In other words, a chaotic analogue simulation will be chaotic, but obviously its behaviour will diverge from that of the system it is modelling because it is a different chaotic system.

[zosima]

No they are not.

An analogue computer does not make numerical approximations. It is a physical model of a system, with one type of physical quantity replacing another, for example using an LCR circuit to model the oscillations of a mass on a spring. If you made two analogue computer simulations of chaotic system, they will diverge, by virtue of them not having identical starting conditions.

The computer is a physical system, but a computer simulation is not a physical chaotic system.

Physically, assuming that you are using a computer with CMOS logic, the computer simulation consists of a set of tranistors with their gate voltages either "high" or "low" and their drain voltages either "high" or "low". (The computer simulaiton could also be made on a babbage-engine, or on a valve computer, or any other type of computer that could be made). In all these systems, as you say, there is a numerical approximation to solving the chaotic equations. And a "mapping" of these results to some form of output system.

An analogue system aims to be a physical analogue of the system that is modelled, so there is no numerical approximation. In other words, a chaotic analogue simulation will be chaotic, but obviously its behaviour will diverge from that of the system it is modelling because it is a different chaotic system.


Your claim that the behavior of the computer itself is not 'truly chaotic' is demonstrably false. See: http://mathworld.wolfram.com/ShadowingTheorem.html
QED: Computers can be chaotic.

But really, all you are really saying is that if a computer is a physical simulation of something else, then it can only approximate that thing. It is trivially true that in a simulation the simulator is not the simulatee. If I use an RC oscillator to simulate a spring(in analog) it will also only be an approximate simulation of the spring. Moreover there is numerical approximation in any analog system. It has finite resolution limited by the size of its components(although this might be smaller than computer components), moreover its resolution is limited practically by noise and the accuracy with which we can measure its output. The reason we use computers to do simulations and not analog systems is because they are more accurate not less.


If you made two digital computer simulations of chaotic system, they will not dverge, if you set the initial numbers and precision to be the same.

Technically, since chaotic systems are deterministic, you are now making the case that digital systems are better simulations of chaotic systems than analog systems. I think it is your confusion over this point that has leading you astray since the beginning.

@Mijo: If you are looking for more periodic chaotic systems over integers here are some more examples.

x(0)=-2
y(0)= 4

x(n+1) = 1 - y(n) + |x(n)|
y(n+1) = x(n)

And:

x(0)=1
y(0)=-2

x(n+1) = 1 -x(n)^2 + y(n)
y(n+1) = x(n)