How “random” is “randomness”?

[shemp]

How “random” is “randomness”?

Let’s start here, with the page that got me to start thinking about this question:

Schrödinger's cat

Quote:

Schrödinger wrote:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

The idea, of course, is to tie the existence of the cat to a “random” 50/50 probability. In the Wikipedia article, four interpretations are given: The Copenhagen interpretation, in which a superposition of states collapses when observed; Everett’s many-worlds interpretation, in which the universe splits into two, one where the cat is alive and the other where the cat is dead; the Ensemble interpretation, which denies that the concept of “wave function” exists in the real world and is merely an abstract mathematical concept; and the Objective collapse theories, which state that wave function collapse occurs not when an observer intervenes, but occurs either randomly or when some arbitrary physical threshold is reached.

I wonder if the real problem with interpretations of the Schrödinger's cat thought experiment is with the concept of “randomness”. Just how “random” is “randomness”?

Take, for example, the game of Craps. In theory, if the dice are not “loaded”, the chance of the dice coming up with the values 2-12 is:

2: 1/36
3: 2/36
4: 3/36
5: 4/36
6: 5/36
7: 6/36
8: 5/36
9: 4/36
10: 3/36
11: 2/36
12: 1/36

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.

We can make similar arguments for games such as, for example, roulette or tossing a coin. We can calculate probabilities for these games, but there is really nothing random about them. The outcomes are predetermined by the physical conditions, but nobody has the ability to calculate the information to determine the outcome. Perhaps, given enough information, time and computing power, one could determine the outcome of a coin toss or a roulette spin in advance.

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. Of course, this brings free will into question. If there is no randomness at this level, is there no free will? Is our consciousness only a product of the physical conditions within our brains?

Then, of course, we can ask ourselves, “Is there any randomness even at the quantum level?” Or is quantum-level randomness just a perception caused by a lack of information and computing power? I’m sure this question has been addressed many times, but I’m not a professional in this area, and I’m sure there are compelling arguments pro and con.

OK, let’s cut to the chase, sum things up, and pose the questions I’d like some answers to (or at least debate on, if there are no clear-cut answers):

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?

2. Similarly, is there really randomness in the quantum world?

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

[DanishDynamite]

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?

In the macro-world there is no true randomness with 99.9999999999999999999999 and some % probability.

Quote:

2. Similarly, is there really randomness in the quantum world?

To the best of our knowledge, yes. Hence, the reason the above number is not 100%.

Quote:

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

Philosophically, nowhere. In practice, somewhere above molecular size.

Quote:

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

Depends what you mean by "free will".

[shemp]

Originally Posted by DanishDynamite

Depends what you mean by "free will".

When confronted with two or more choices, do I have the "free will" to make the choice, or is my decision controlled by physical circumstances in my brain?

[SirPhilip]

Originally Posted by DanishDynamite

In the macro-world there is no true randomness with 99.9999999999999999999999 and some % probability.

Curious. Does that apply beyond the event horizon of black holes?

[rcronk]

In English, the definitions of random and arbitrary seem to have mushed into meaning pretty much the same thing.

In cryptography and computing, for example, randomness means that each option appears equally, like picking 1000 numbers from 1 to 10 and each of the 10 options come up statistically the same number of times. In computing, pseudo-random number generators use previously generated numbers as input to the next number that's generated.

Arbitrariness means that each number picked does not have any connection with previous numbers. So if I were to pick 1000 numbers from 1 to 10, we couldn't say anything about the distribution of the numbers because they aren't derived from anything.

Computers can't create an arbitrary number because the number has to come from somewhere. The only attempt to create "real" arbitrary numbers in computing was to hang an antenna out of the box and have it pick up "random" noise from the universe and use that - but that's not random or arbitrary, it's created from sources that are just too complicated to track down. I guess it could be called pseudo-arbitrary.

A funny result of the above definitions is that 1,2,3,4,5,6,7,8,9,10 is a random list because each item appears statistically the same number of times. Most people seem to think that random means mixed up or shuffled in such a way that it seems arbitrary. The number PI is actually statistically random as all numbers appear in it statistically the same number of times for a given set (like the first billion digits, for example).

I think this all might have something to do with "free will" if you mean that free will is a decision that a person makes that's not based on anything but what the person "wants" to do at that moment - coming from somewhere within them that isn't deterministic or dependent upon anything else. It would seem that people's decisions are in fact affected by their experiences up to that point, but who knows if there's something inside a person that affects that decision that doesn't have anything to do with their experiences up to that point.

This is also something I've been struggling with lately and I'm not sure where to take the logic of it from here. The paradox I'm faced with is that I believe in an omniscient God but I also believe in free will, or the ability for me to do whatever I want to do. I don't believe in predetermination (that I'm following a predetermined script) but I do believe that God knows what's going to happen with my choices in the future.

Any ideas people here have would be very helpful to me. And please don't bash me for believing in God, I'm really just looking for some more ideas about how to resolve this apparent paradox and get a little closer to the truth of reality. Thanks.

[blobru]

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?

Regular dice behave statistically because no one is skillful enough to account for all the intangibles you list -- a lot of crap artists out there, but no one's that good! -- so they 'cancel out' in any large sample.

Quote:

2. Similarly, is there really randomness in the quantum world?

For quantum craps, there don't seem to be any intangibles* in play. The "dice" are purely statistical. (*not sure about the "Objective collapse" interpretation though)

Quote:

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

Philosophically, I would just draw the distinction between observed randomness (craps) and theoretical randomness (quanta).

Quote:

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

Don't think there's a necessary connection. A random will isn't any more "free" than a determinist will really. Its actions are just harder to predict.

Determinist will: brain state A --> action z always (100% of the time).
Random will: brain state A --> action z (40% of the time), y (30%), x (20%), w (10%); for example.

But "free" will I think means something like...
Free will: brain state A --> (???) --> action z,y,x,w... (question: can the observed actions of a "free will" follow a statistical pattern?)

In other words, (???) = some intermediate unknown state that doesn't obey macro-physical (deterministic) or micro-physical (probabilistic) laws.
I've seen some philosophers argue that "free" will is an emergent property of the complex physical system that is our brain and body, in other words that (???) = 'emergent property', but I can't say I understand them too well. It seems to me that for authentic "free" will you'd really need something like a self-governed source that transcends physics, causa sui, i.e., a "soul"(?)

[Schneibster]

Originally Posted by rcronk

please don't bash me for believing in God, I'm really just looking for some more ideas about how to resolve this apparent paradox and get a little closer to the truth of reality.

Well, no promises I won't tell you things that will challenge your faith, perhaps more than a bit- but at least I'll try to be civil, and I won't attack it deliberately; it's just that I don't see much way to talk about this from a standpoint that includes the possibility of the existence of an omniscient individual. So if you can be tolerant of that, I can at least try to remain civil. Full disclosure: I am an atheist, and I have been most of my life- I tried religion once in my early adulthood, and just couldn't handle how much it made me feel like a hypocrite. If that doesn't scare you off, read on.

Originally Posted by rcronk

In English, the definitions of random and arbitrary seem to have mushed into meaning pretty much the same thing.

From the standpoint of casual language, you may be correct, though I'm not as sure about it as you seem to be. These concepts can be amazingly slippery when discussed with someone not aware of the formal definitions.

From a formal standpoint, they are very different. "Random" means a value that cannot be predicted by what has come before; it may (and in most cases does) indicate a value that is the outcome of a stochastic process, that is, a process that has a probability distribution among the possible results. Such a process, if repeated a large number of times, will show a limited number of possible outcomes that occur at various probabilities. "Arbitrary," on the other hand, means a value that need not be connected to what has come before, but might or might not be. While this may only appear to be a shade of difference, in formal usage, one would talk about how a function would behave given an arbitrary input value if one were discussing the function pedantically, and how it would behave given a random input value if one were discussing the conclusions that can be derived from that function if it describes the consequences of a random process.

Originally Posted by rcronk

In cryptography and computing, for example, randomness means that each option appears equally, like picking 1000 numbers from 1 to 10 and each of the 10 options come up statistically the same number of times. In computing, pseudo-random number generators use previously generated numbers as input to the next number that's generated.

Arbitrariness means that each number picked does not have any connection with previous numbers. So if I were to pick 1000 numbers from 1 to 10, we couldn't say anything about the distribution of the numbers because they aren't derived from anything.

Having done a fair bit of cryptographic coding, I note that you have confused a test for randomness with randomness itself. Also, your definition of arbitrariness seems a little more like a definition of how to get randomness, not what randomness actually is; if you, for example, hit a paintbrush against your hand in front of a crowd, and ask everyone who did not get paint on them to pick a number from one to ten, the numbers they picked would be both random and arbitrary; the people chosen would be arbitrarily chosen, upon random criteria. (Assuming they did not all jump up and beat the tar out of you. )

Randomness can be tested by checking that the occurrence of outcomes conforms to the expected probability distribution. That is, if the statistical universe is 1,000 picks of a number from 1 to 10, one should find equal numbers of each; whereas if the statistical universe is 1,000 decays of a photon of 1.02MeV energy into two particles, one should find almost all of the decays have resulted in the pair production of an electron and a positron, but just a few have come out as an electron neutrino and electron antineutrino. The probability distribution of arbitrary picks over a range of numbers should yield equal probability for each number; however, the probability distribution of photon decays does not yield equal probabilities of each outcome. A process, therefore, that conforms to the test of its probability distribution is a random process; but it is not the test that determines the randomness, it is the character or nature of the process that determines it.

It is a common misconception that "random" means "equal probability of all outcomes;" actually, it does not. They might have unequal probabilities, as any gambler can tell you, but still be random.

It is a further misconception that anything that is random cannot be deterministic. In fact, processes whose outcomes conform to a probability distribution are completely deterministic. One will not, after all, see the gamma ray photon decay into a nitrogen nucleus; that has zero probability, since it would violate conservation of mass-energy. The gamma ray photon can only decay in a certain limited number of ways, and it is certain (i.e. predetermined) that it will choose one of them every single time. Equally, if one asks that a number between 1 and 20 be picked, and discards every choice that is not between 1 and 20, then all the numbers picked and not discarded will be between 1 and 20, and this too is predetermined.

It is the individual photon decay, or the individual choice of a number, that is random. Note, however, that the individual photon decay is, as far as we can tell, truly random; whereas the individual number choices may or may not be truly random; for example, some people may have a favorite number (whatever that might mean) that is within the range, and if given the choice will always pick that number; the choice, for them, then, would be deterministic, but still arbitrary from the point of view of a person asking for number selections from their arbitrary choice of people to ask.

Originally Posted by rcronk

Computers can't create an arbitrary number because the number has to come from somewhere. The only attempt to create "real" arbitrary numbers in computing was to hang an antenna out of the box and have it pick up "random" noise from the universe and use that - but that's not random or arbitrary, it's created from sources that are just too complicated to track down. I guess it could be called pseudo-arbitrary.

Actually, you can buy devices that use "Johnson thermal semiconductor shot noise" to generate random numbers. These devices use the occurrence or non-occurrence of a random quantum event within a set period to determine whether the next bit output is a one or a zero. With judicious choice of the parameters of the junction, and the bit clock, one gets equal numbers of ones and zeros over the long haul, with no chance of predicting whether any particular bit is going to be a zero or a one. (I have vastly oversimplified the design of such devices, but I have, I think, captured the principles of their operation sufficiently for clear understanding.)

Originally Posted by rcronk

A funny result of the above definitions is that 1,2,3,4,5,6,7,8,9,10 is a random list because each item appears statistically the same number of times.

No, sorry, this is wrong. That list would be a legitimate single occurrence of output from a random process, but for the process to be adjudged random, it would have to occur on average no more than one time in ten billion (the number of permutations of ten numbers taken ten at a time). The other nine billion, nine hundred and ninety-nine million, nine hundred and ninety-nine thousand, nine hundred and ninety-nine times, on average, it would have to be different. (I am of course using American numbering- the British use "billion" to denote a million million, not a thousand million.) It might still be within the expected deviation if you saw it a few times- but the more times you see it, the less likely it is that the process is random, and that probability declines abruptly after just a few repetitions within a trial of ten billion.

Originally Posted by rcronk

Most people seem to think that random means mixed up or shuffled in such a way that it seems arbitrary. The number PI is actually statistically random as all numbers appear in it statistically the same number of times for a given set (like the first billion digits, for example).

Well, at least the second part is true. I hesitate to agree with statements about what "most people think."

Originally Posted by rcronk

I think this all might have something to do with "free will" if you mean that free will is a decision that a person makes that's not based on anything but what the person "wants" to do at that moment - coming from somewhere within them that isn't deterministic or dependent upon anything else. It would seem that people's decisions are in fact affected by their experiences up to that point, but who knows if there's something inside a person that affects that decision that doesn't have anything to do with their experiences up to that point.

I tend toward the view that we cannot show that we do not have free will, and therefore the question is meaningless. It is also true that we are constrained by physical law; for example, due to the symmetry of physics over rotations, it is unlikely in the extreme that any of us will ever turn a corner and "turn into" a penguin. Do we therefore lack "free will?" Obviously, this example cannot answer the given question; my contention is, there is no example that can answer it. Certainly we lack free will in many situations; however, it appears that we have free will in many others. But now we're straying into philosophy on the Science forum.

Originally Posted by rcronk

This is also something I've been struggling with lately and I'm not sure where to take the logic of it from here. The paradox I'm faced with is that I believe in an omniscient God but I also believe in free will, or the ability for me to do whatever I want to do. I don't believe in predetermination (that I'm following a predetermined script) but I do believe that God knows what's going to happen with my choices in the future.

If you're going there, perhaps you should consider whether it is possible for God to both be omniscient and have free will. I think the answer is an obvious "no," and offer this as some inducement to think outside the box you are currently inhabiting, in my view; you are of course free to ignore my advice.

Originally Posted by rcronk

Any ideas people here have would be very helpful to me. Thanks.

Perhaps my meager ideas may help you; perhaps they are useless. Either way, you are welcome to them.

[Schneibster]

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.

[rcronk]

Excellent comments everyone. Thanks! I'm going to go do some more research on the topics brought up here.

[fls]

Originally Posted by Schneibster

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.

How do we know this (other than by reference to basic principles)?

And is there a discussion somewhere as to the extent that single quantum events influence outcomes in everyday life, as in speculative essays or articles from someone who is knowledgeable in the field? (Much as I appreciate your essays, they must take considerable effort on your part and I don't wish to put you out - I'm willing to do my own legwork if you can point me in a particular direction).

Linda

[Rolfe]

Originally Posted by rcronk

The paradox I'm faced with is that I believe in an omniscient God but I also believe in free will, or the ability for me to do whatever I want to do. I don't believe in predetermination (that I'm following a predetermined script) but I do believe that God knows what's going to happen with my choices in the future.

Any ideas people here have would be very helpful to me. And please don't bash me for believing in God, I'm really just looking for some more ideas about how to resolve this apparent paradox and get a little closer to the truth of reality. Thanks.

Have you considered the aspect that you are living in a linear, two-dimensional time stream (or at least it appears to you that you are), but God is not confined to that time stream?

Rolfe.

[Ivor the Engineer]

Originally Posted by Schneibster

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.

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.

According to the outcome of experiments, there really is randomness in the non-quantum world, and it springs from:

Yes, again, according to the outcome of experiments.

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.

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.

How does the Many Worlds interpretation of QM affect the randomness?

ETA: And Bell Test loopholes?

[Harpoon]

Originally Posted by Schneibster

...It is a common misconception that "random" means "equal probability of all outcomes;" actually, it does not. They might have unequal probabilities, as any gambler can tell you, but still be random.

That misconception may result from statistics. In order to conduct a scientific, random survey of a group or community, each member must have an equal opportunity to be included in the survey. Random is not at all haphazard.

[andyandy]

ok, how does infinity effect considerations of randomness?

If we accept that by random we mean that which can not be predicted from the preceeding event, then situations can be constructed through infinity to remove randomness from a probalistic framework....

Working within an infinite set encompassing all that which can occur and will occur, if we have an event A then regardless of the probability we assign to it for its occurance, as long as it is greater than zero, the fact that it belongs to our set means that it occurs with 100% certainty an infinite number of times - all probabilities, whether 0.01 or 0.9999 are subsumed into 1, and all occur with the same infinite frequency....

...and then we're no longer dealing with that which is random, but that which is determined and independent of probability.

[rcronk]

Originally Posted by Rolfe

Have you considered the aspect that you are living in a linear, two-dimensional time stream (or at least it appears to you that you are), but God is not confined to that time stream?

Rolfe.

Yes - as I thought about this discussion, the time issue came to mind. In many places it says that everything is an eternal present to him and that time as we know it doesn't exist. There are many references to infinite and eternal things and that God exists in that context where we are in a different context of finite time and beginnings and endings, etc. I'm still churning it around in my head and I'm looking to read up on the topics brought up here too. Thanks.

[Folly]

Originally Posted by andyandy

ok, how does infinity effect considerations of randomness?

Poorly?

Quote:

If we accept that by random we mean that which can not be predicted from the preceeding event, then situations can be constructed through infinity to remove randomness from a probalistic framework....

Working within an infinite set encompassing all that which can occur and will occur, if we have an event A then regardless of the probability we assign to it for its occurance, as long as it is greater than zero, the fact that it belongs to our set means that it occurs with 100% certainty an infinite number of times - all probabilities, whether 0.01 or 0.9999 are subsumed into 1, and all occur with the same infinite frequency....

...and then we're no longer dealing with that which is random, but that which is determined and independent of probability.

With infinite samples, you can have things occurring which have zero probability. Random samples from distributions over intervals of real numbers are all zero probability events. Even worse in the latter case, I strongly believe (but can't remember for sure) that the reasoning of "infinite samples -> surety of outcome" breaks down.

So I think instead you're stuck saying "if I make a set of all things that will occurr, anything that will occurr is in the set with probability 1" which is not so interesting.

[andyandy]

Originally Posted by Folly

With infinite samples, you can have things occurring which have zero probability. Random samples from distributions over intervals of real numbers are all zero probability events. Even worse in the latter case, I strongly believe (but can't remember for sure) that the reasoning of "infinite samples -> surety of outcome" breaks down.

So I think instead you're stuck saying "if I make a set of all things that will occurr, anything that will occurr is in the set with probability 1" which is not so interesting.

Ah, true, with a random sample from the real numbers (say), the probability of any particular choice is

well that buggers things up even more

I've seen the infinity of samples, surety of outcome espoused in certain physical interpretations of cosmology - many worlds, bubble universes....but whether or not the interpretation is mathematically valid, I don't know....it seems pretty counter-intuitive in some respects - I started a short thread on this not too long back....this was my op, based on an argument in Chown's The Never Ending Days of being Dead -

first we take the premise of a bubble universe [BU] which is formed as a result of utterly random quantum contortions in the primoridal vacuum - which means that everything within the observable universe is ultimately the result of random processes that occured in the first split second of the universe's existence. So what is true of our observable universe must be true of all other regions the size of the observable universe in our BU. This means that all possible arrangements of protons in an area the size of our observable universe will occur in other regions of the BU. The way in which protons can be arranged within the observable universe is finite, and so because the BU is infinite it follows that every possible arrangement must occur somewhere - indeed every possible arrangement must occur an infinite number of times in an infinite number of places

it starts by asserting that the number of protons which could fit in the observable universe is about 10^118

and that in each one of these 10^118 locations can either have a proton or no proton, and as such if there are n possible locations for protons, and so there are 2n different universes possible. In our universe where n=10^118 then there are 2^(10^118) possible ways to arrange the protons which is approx equal to 10^(10^118)

Applying this method to finding the distance one would have to travel to find an exact replica of oneself, the figure of 10^28 is used for the number of particles in one's body, which means there are 10^(10^28) possible arrangements of the protons within the body, and therefore this means that one's nearest double is just approximately 10^(10^28) metres away.

The chapter concludes that the existence of your double is extremely difficult to take, but an unavoidable consequence of the standard theory of the universe incorporating both QM and inflation - so if it is not true, then either QM or inflation is incorrect.

otherwise Elvis lives.

http://forums.randi.org/archive/index.php/t-83314.html

[andyandy]

double post double post double post

[Rolfe]

Originally Posted by rcronk

Yes - as I thought about this discussion, the time issue came to mind. In many places it says that everything is an eternal present to him and that time as we know it doesn't exist. There are many references to infinite and eternal things and that God exists in that context where we are in a different context of finite time and beginnings and endings, etc. I'm still churning it around in my head and I'm looking to read up on the topics brought up here too. Thanks.

C. S. Lewis has some musings on this, though I don't think they're especially profound. I suppose you could say that while you had free will to chose to type that post or not, now we all know you typed it and the deed is done, does that mean you didn't have free will at all?

Lewis talks about an author writing a book and going off and thinking about things then returning, while only seconds may have passed in the time scale of the narrative. I'm not sure that's terribly helpful though, because the characters in a novel don't have free will as I'd understand it.

I'm not sure that "eternal present" is a very good analogy either, because the whole concept of "present" is so tied up to the linear time stream we experience. Being "outside" of time as we know it, as we are "outside" the page of the book we are reading or writing might be a better analogy.

Rolfe.

[steenkh]

Originally Posted by Rolfe

Have you considered the aspect that you are living in a linear, two-dimensional time stream (or at least it appears to you that you are), but God is not confined to that time stream?

But in this case, you are effectively trying to find an explanation for something for which there is no evidence, or God is magic, and anything goes - including a number of paradoxes.

[andyandy]

Originally Posted by Rolfe

Have you considered the aspect that you are living in a linear, two-dimensional time stream (or at least it appears to you that you are), but God is not confined to that time stream?

Rolfe.

Wouldn't our time stream be one dimensional - ie backwards or forwards along a line?

Not that this affects the consideration at all....

[rcronk]

rolfe - thanks for the thoughts - do you have a link or reference for C.S. Lewis' thoughts you referred to?

P.S. I saw elvis at 7-11 last week. ;-)

[Folly]

Originally Posted by andyandy

first we take the premise of a bubble universe [BU] which is formed as a result of utterly random quantum contortions in the primoridal vacuum - which means that everything within the observable universe is ultimately the result of random processes that occured in the first split second of the universe's existence. So what is true of our observable universe must be true of all other regions the size of the observable universe in our BU. This means that all possible arrangements of protons in an area the size of our observable universe will occur in other regions of the BU. The way in which protons can be arranged within the observable universe is finite, and so because the BU is infinite it follows that every possible arrangement must occur somewhere - indeed every possible arrangement must occur an infinite number of times in an infinite number of places

it starts by asserting that the number of protons which could fit in the observable universe is about 10^118

and that in each one of these 10^118 locations can either have a proton or no proton, and as such if there are n possible locations for protons, and so there are 2n different universes possible. In our universe where n=10^118 then there are 2^(10^118) possible ways to arrange the protons which is approx equal to 10^(10^118)

I totally agree that follows from the assumptions, and it's an interesting idea.

I don't know about the assumptions, though. My physics stops at classical mechanics augmented by what I've picked up here, but what about non-exclusionary particles? (fermions? or was it bosons... bah - so much for me having learned anything...) Is space-time position actually quantised? If not, if I have an empty space, neighbouring protons could be anywhere in a small real interval of positions and the whole thing is sunk.

[Blu]

This thread seems to have leaned on the side of probability rather than what I was expecting to read, i.e. randomness.

What is meant by randomness? Well... there are numerous ways in which people generate "random" numbers, for example, but why can they be called random?

If you take random to mean that you cannot determine the outcome of an event based on previous knowledge, then randomness does exist and is truly random.

Although I can throw dice 1000 times, there may be statistical probabilities that determine the chance of certain numbers coming out so many times each, but that's begger all to do with randomness. Let's keep a clear distinction between the two. Just because I throw a certain combination of numbers on my dice in one throw does not give me any indication of what any subsequent throw is going to be, therefore it's random.

Shemp,

Quote:

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?

You would have to have a computer that knows every variable in the Universe as everything could, potentially at a quantum level, effect everything else. The only thing powerful enough to know all that is the Universe itself. In which case the randomness is an integral part of the very computer universe that is trying to detect it.

Quote:

2. Similarly, is there really randomness in the quantum world?

Quantum is "theory". Of course randomness can be incorporated into quantum theory, although it does depend on what quantum model you wish to use.

Quote:

3. If the answers to questions 1 and 2 are different, where can we draw the line separating the two?

Randomness exists in both, no difference, no need for drawing lines (unless you want to draw some pretty pictures of course. )

Quote:

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

Free will is a whole philosophical topic on it's own, however, assuming randomness exists, then there is room for free will to exist.

In answer to Ivor the Engineer...

Quote:

How does the Many Worlds interpretation of QM affect the randomness?

Each distinct event splits the world (universe) into all possible outcomes. The randomness comes in whichever of those worlds you see your existence in.

[Schneibster]

Originally Posted by fls

How do we know this (other than by reference to basic principles)?

I assume by "this," you mean my assertion that quantum phenomena are truly random. If I am wrong, please disabuse me of the notion.

We know because we have proven fairly conclusively that characteristics that are uncertain are not merely unmeasurable, but do not have a value. Since such characteristics are omnipresent, that is, some characteristics are rendered uncertain at every quantum interaction, we can be sure that their values after that interaction will be a probability function in every such case; if they actually had values, this probability distribution would be altered by them. The fact that we can measure that it is not is the proof of the randomness of quantum phenomena.

Now, I don't know if that's a basic principle or not. But it's empirically determined data, so I'm not sure it matters.

Originally Posted by fls

And is there a discussion somewhere as to the extent that single quantum events influence outcomes in everyday life, as in speculative essays or articles from someone who is knowledgeable in the field? (Much as I appreciate your essays, they must take considerable effort on your part and I don't wish to put you out - I'm willing to do my own legwork if you can point me in a particular direction).

Linda

I don't have anything like that to hand. Let me know if you can't find anything, but I suspect a quick google will get you where you're going. Thanks for your consideration; keep in mind, though, that I do it because I like to.

Considering this, I'm not sure I properly answered your question. So assuming that was wrong, and "this" means my assertion that individual quantum events can influence macroscopic reality, I'll point to the fact that a scintillation counter is, at simplest, a screen that emits a photon every time an electron hits it. The photons can be seen by the human eye, individually. Quantum events therefore individually are capable of generating macroscopically observable phenomena.

But this is a trivial example, and one might dismiss Schroedinger's Cat as a fanciful one.

Do the search I have suggested and come back if you don't get anything; I'll assume you're looking for a credible instance in which classical motion is affected by individual quantum events, and I'll go hunt one up for you.

[Rolfe]

Originally Posted by rcronk

rolfe - thanks for the thoughts - do you have a link or reference for C.S. Lewis' thoughts you referred to?

P.S. I saw elvis at 7-11 last week. ;-)

Unfortunately I've recently moved house and I've no idea which of the distressingly large number of boxes the "L" books are in. (That and the one about the Lockerbie bombing I referenced in the CT forum, can't even remember the name of the author of that one....)

I'll see if a quick glance in a few boxes reveals anything.

Rolfe.

[Rolfe]

Originally Posted by andyandy

Wouldn't our time stream be one dimensional - ie backwards or forwards along a line?

Not that this affects the consideration at all....

I stand corrected, you're right.

Rolfe.

[Rolfe]

Originally Posted by steenkh

But in this case, you are effectively trying to find an explanation for something for which there is no evidence, or God is magic, and anything goes - including a number of paradoxes.

Rcronk is starting from that premise. I see no objection to continuing the discussion assuming the premise, for the sake of the discussion.

Rolfe.

[fls]

Originally Posted by Schneibster

I assume by "this," you mean my assertion that quantum phenomena are truly random. If I am wrong, please disabuse me of the notion.

Sorry, I meant a single quantum event influencing the outcome of a die roll; perhaps some relevant (i.e. relevant to classical motion, not dice specifically) empirically determined data.

Quote:

Do the search I have suggested and come back if you don't get anything; I'll assume you're looking for a credible instance in which classical motion is affected by individual quantum events, and I'll go hunt one up for you.

Yes, that is what I'm looking for. I'm having trouble finding something that specific (that's not related to consciousness).

Thank you.

Linda

[Soapy Sam]

I think the multiple universes of this thread nicely illustrate the differences in meaning of words like "random" when used in (any of several) scientific contexts as opposed to general daily usage. Miscommunication can arise from this phenomenon and I feel it needs a name if it does not have one already. I propose "definistrition" , since at least one definition must be thrown out of the window for the duration of the discussion;- or we end up arguing about "inorganic" potatoes again.

Unpredictability seems to me largely an issue of time. Before I flip a coin, even given exact data on air resistance, humidity, windspeed, thumb stickiness, coin weight, local gravity etc, all I can predict is that it will be heads, tails, passing seagull or some other edge / lost variant. This is true even without introducing the quantum acausality Schneibster describes. We just couldn't do the maths fast enough, even if the results were inherently predictable, the start values had clearly defined values, or if there were no macroscopic results of quantum events.

After the spinning coin stops moving, predictability is either 0 again, or 1, depending how we define "predictability".
But about 1/100,000th of a second before the coin stops moving, predictability is around 0.999..., which as we are all very tired of hearing, equals 1.
And there is a gradually lesser spectrum of predictability ranging backward in time, all the way to the original, pre toss value of zero.
At which point do we call a halt? Off track betting is usually not permitted after the race starts. Bookies do not believe in randomness.

As for free will, I have never believed in it. Whether this is because I chose not to do so, or because I never believed in it, I cannot say.

[Schneibster]

Originally Posted by Ivor the Engineer

How does the Many Worlds interpretation of QM affect the randomness?

Which World do we wind up in? The answer looks pretty random to me.

Originally Posted by Ivor the Engineer

ETA: And Bell Test loopholes?

Technically, there aren't any loopholes in Bell's Theorem; either locality is true, or local realism is true. There are various loopholes in the actual tests done. I would not state definitively at this time that all these loopholes are closed in a single experiment; it appears to be the considered opinion of most physicists that closing various loopholes in different experiments is sufficient to decide the matter, and actually that it was really decided by Aspect, and I have to say that I agree. There are bigger and better fish to fry.

[SirPhilip]

What about black holes, damnit.

[Schneibster]

Originally Posted by fls

Sorry, I meant a single quantum event influencing the outcome of a die roll; perhaps some relevant (i.e. relevant to classical motion, not dice specifically) empirically determined data.

Yes, that is what I'm looking for. I'm having trouble finding something that specific (that's not related to consciousness).

Thank you.

Linda

OK, here you go:

http://findarticles.com/p/articles/m...138/ai_8986262

This discusses how, in classically chaotic situations like rolling dice, the uncertainty of the underlying quantum description of the system increases to permit the chaotic behavior.

[blobru]

I agree with those who say dice tosses (and coin flips) are unpredictable, but does that make them perfectly random? (To return to Shemp's original question: "How random is 'random'?")

If it were possible say to exactly repeat all the influences on a given dice toss -- the position of the thrower's hand, how he holds the dice, the impetus he gives to the dice, various environmental factors -- and then repeat that same dice toss over and over -- I don't think you'd get perfect randomness, but rather a skewed version of the two dice probability curve.

It seems too that dice should be much more unpredictable in such a scenario than coins, given their different geometry. Coins have two faces and one edge. Dice have six faces, twelve edges, and eight corners. How the object will react after a 'face' collision with whatever surface you're using should be much easier to predict than an 'edge' collision (teetering between two faces), and a 'corner' collision (between three faces) should be hardest of all.

A coin moreover, if you catch it in your palm so it doesn't bounce and then repeat the motions, unless it lands almost upright on its edge, should be very predictable. At the other extreme, the outcome for a coin tipped upright and spun on a table should be almost impossible to predict, even after several ideal repetitions. And here, unlike the coin flip example where the probability slides from 0 to 1 the closer the coin comes to rest, the probability seems to stay at 0 until the spinning coin wobbles, and then shift instantly to 1.

Interesting to note that philosophers who believe in determinism prefer billiards to dice in their examples. Billiard balls of course have no edges, and always collide face to face (much easier to predict). Not sure though how 'predictable' pool breaks are: my experience playing was that hitting a rack in almost the same spot with almost the same force could produce wildly different outcomes!

[shemp]

Originally Posted by blobru

I agree with those who say dice tosses (and coin flips) are unpredictable, but does that make them perfectly random? (To return to Shemp's original question: "How random is 'random'?")

If it were possible say to exactly repeat all the influences on a given dice toss -- the position of the thrower's hand, how he holds the dice, the impetus he gives to the dice, various environmental factors -- and then repeat that same dice toss over and over -- I don't think you'd get perfect randomness, but rather a skewed version of the two dice probability curve.

It seems too that dice should be much more unpredictable in such a scenario than coins, given their different geometry. Coins have two faces and one edge. Dice have six faces, twelve edges, and eight corners. How the object will react after a 'face' collision with whatever surface you're using should be much easier to predict than an 'edge' collision (teetering between two faces), and a 'corner' collision (between three faces) should be hardest of all.

A coin moreover, if you catch it in your palm so it doesn't bounce and then repeat the motions, unless it lands almost upright on its edge, should be very predictable. At the other extreme, the outcome for a coin tipped upright and spun on a table should be almost impossible to predict, even after several ideal repetitions. And here, unlike the coin flip example where the probability slides from 0 to 1 the closer the coin comes to rest, the probability seems to stay at 0 until the spinning coin wobbles, and then shift instantly to 1.

Interesting to note that philosophers who believe in determinism prefer billiards to dice in their examples. Billiard balls of course have no edges, and always collide face to face (much easier to predict). Not sure though how 'predictable' pool breaks are: my experience playing was that hitting a rack in almost the same spot with almost the same force could produce wildly different outcomes!

As a thought exercise, let's say that we build a machine that throws dice onto a table; the dice are perfectly cubic and uniformly balanced; they are always in the exact same position before the throw; that the machine always throws them in the same direction with the same force; that the table is perfectly flat and hard; that this takes place in a vacuum; in short, at scales larger than the molecular level, EVERY condition is exactly the same EVERY time. Therefore, if there is any variance in the results, it should be due to quantum fluctuation. How much variance can we expect in the results compared to the normal probabilities we see in a typical craps game?

[andyandy]

Originally Posted by shemp

As a thought exercise, let's say that we build a machine that throws dice onto a table; the dice are perfectly cubic and uniformly balanced; they are always in the exact same position before the throw; that the machine always throws them in the same direction with the same force; that the table is perfectly flat and hard; that this takes place in a vacuum; in short, at scales larger than the molecular level, EVERY condition is exactly the same EVERY time. Therefore, if there is any variance in the results, it should be due to quantum fluctuation. How much variance can we expect in the results compared to the normal probabilities we see in a typical craps game?

they should in that case always land on exactly the same number. With a coin toss you should also be able to achieve 100% predictability through controlling the height, force, number of rotations - it's easy enough with a couple of minutes practice to skew it 60-40 without the use of any machine....
could a 3 [moving] ball collision be predicted if we knew everything about the system - or is there an inherent randomness? I'd tend towards it being wholly determinable, but i'm not sure

[cyborg]

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?

From the computing perspective the Kolmogorov Complexity is probably most relevant.

For any finite sequence we can define a machine and a language to construct it. A language is any finite set of symbols. A machine can output language symbols. We can define the machine in terms of those language symbols to form a program for outputting the symbols. Now we can measure the complexity of a sequence as the smallest set of symbols from our language that describes both the machine and its output.

Now our machine can also define infinite sequences if it is able perform recursion in the language. We can now define a random sequence as any infinite sequence which cannot be constructed by any finite machine. That is to say the Kolmogorov Complexity is infinite.

Computing equivalence can tell us what machines are equivalent. Every algorithm we have thus been able to think of can be described by a well known class of machines - the Turing Machine equivalence.

Are there infinite sequences for which there is a finite machine that is not equivalent to a Turing Machine that can describe them?

If so does every infinite sequence have a finite machine that can construct it?
If not then everything is deterministic - we could always build a machine that could describe even the behaviour of QM precisely.

If not we might then consider if we can have more powerful computation with random behaviour in the machine. Here we need to have some notion about the meaning of the output sequence in order to have any notion about computational power. We can now construct a class of sequences that have equivalent meaning. We can reduce our random set by excluding those sequences which have an equivalent sequence that can be described by a machine without random behaviour. We have not computed any more meaning therefore the power of the computation is the same.

So what we want to know is if there are infinite sequences for which no meaning can be constructed for finitely. These would be truly random in the fullest sense of the word; in that there is absolutely no purpose behind it at all. If we could prove otherwise then there would be no randomness at all.

Quote:

4. Is the question of the existence of “free will” related to these questions, or not? Can free will exist without randomness?

Humans can be described in terms of the machine/language defined above - as humans are finite we can construct some machine with some associated meaning that can completely describe a human's life. Now in order for free-will to be term with a meaning beyond that the already defined for our machines it would have to be a mechanism that provides more computing power than we already have. If it didn't then either free-will is randomness or free-will is deterministic - the later is clearly not acceptable for the 'free' concept and the former for the 'will' concept.

As such free-will would have to describe some meaningful sequence that does not have some equivalent sequence describable by a machine using randomness and determinism to formulate its output.

[Soapy Sam]

Shemp, if we are going to control all possible variables so far as nature will permit, it would surely be simpler to paint a six on every side of the die, or to build a machine that simply laid it down with the six uppermost, even if quantum fluctuation somehow tried to turn it into a four.

The point is that usually, most of those variables are not controlled. That's where the genuine unpredictability comes from. I agree this is not the same thing as randomness by some definition, but for practical purposes it may as well be.
The quantum issue is rather different, but I suspect there's a limit to it's importance too, in that no matter how acausal or odd a quantum event, the macroscopic universe only seems to permit certain outcomes.
No matter how the quantum event is amplified, the answer may be constrained to be 0 or 1, but never "Penguin", so there's a discarding of acausal randomness at some point- which may indeed be at a molecular scale size wise and somewhere else timewise.

I really think this is a debate about definitions.

[Schneibster]

Originally Posted by andyandy

they should in that case always land on exactly the same number. With a coin toss you should also be able to achieve 100% predictability through controlling the height, force, number of rotations - it's easy enough with a couple of minutes practice to skew it 60-40 without the use of any machine....

I suspect that you'd find you could skew the odds, probably quite far, but not reproduce the same number (or heads, for example) on every throw.

Originally Posted by andyandy

could a 3 [moving] ball collision be predicted if we knew everything about the system - or is there an inherent randomness? I'd tend towards it being wholly determinable, but i'm not sure

You're forgetting: the three-body problem has no tractable solution.

[Schneibster]

You do realize, cyborg, that the Kolmogorov complexity of a string is not computable, right? A function that could compute Kolmogorov complexity would be the Turing equivalent of the halting function- one that can compute whether another function yields a terminating or non-terminating result. This is a relatively well-known result based on the same characteristic of computation that Godel's theorem rests upon.

Your statement therefore boils down to whether it is possible to define a finite machine that can produce an infinite string that is not describable in shorter terms (for example, an infinite string of the character "3" endlessly repeated obviously has a low Kolmogorov complexity).

This is Turing equivalent to the halting program. Which means...

<gives everyone a moment to think about it>

We can never know by computation whether randomness exists or not.

This sentence is false.

ETA: Just so everyone's clear, the fact that Turing was able to prove that we cannot construct a general algorithm that can tell whether another algorithm will halt or not means that we cannot use finite computation (that is, computation in which each step takes a finite amount of time) to determine that a program will produce infinite output; in other words, to find out in a finite period if a computer program can generate infinite Kolmogorov complexity, we would have to use the Turing halting program, which we already have proven cannot exist. It is therefore obvious that the shortest way to find out is to run the program and examine its output to see if it's infinite; which, equally obviously, being a finite computation, takes an infinite amount of time.