Deeper than primes

[doronshadmi]

Notion #1:

If we use partitions in order to define Entropy, then a multiset (a repetition of the same identity) has an entropy that is equivalent to the number of the repetitions that exists within it.

Since a set has no repetitions, it has no entropy.

Let us examine the partitions that exist within any given n > 1

{x} = Full entropy
{x} = Intermediate entropy
{x} = No entropy

2
---
{1,1}


3
---
{1,1,1}
{2,1}


4
---
{1,1,1,1}
{2,1,1}
{2,2}
{3,1}


5
---
{1,1,1,1,1}
{2,1,1,1}
{2,2,1}
{3,1,1}
{3,2}
{4,1}


6
--
{1,1,1,1,1,1}
{2,1,1,1,1}
{2,2,1,1}
{2,2,2}
{3,1,1,1}
{3,2,1}
{3,3}
{4,1,1}
{4,2}
{5,1}


7
---
{1,1,1,1,1,1,1}
{2,1,1,1,1,1}
{2,2,1,1,1}
{2,2,2,1}
{3,1,1,1,1}
{3,2,1,1}
{3,2,2}
{4,1,1,1}
{4,2,1}
{5,1,1}
{5,2}
{6,1}

...

As can be seen, Prime numbers have the least entropy, from this point of view.




Notion #2:

If we understand the Sieve of Eratosthenes ( http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes ) as a whole\part framework, than number 0 is the most dense part of it, and the set of primes is the least dense part of it.

In order to see it, let as represent the Sieve of Eratosthenes by non-finite frequencies notated by half circles, along a non-finite straight-line.

The first frequency is the non-finite collection of half circles that are representing the frequency level 1.

The next frequency is the non-finite collection of half circles that are representing the frequency level 2.

….

The next frequency is the non-finite collection of half circles that are representing the frequency level n.

Etc., … etc. …

Since the non-finite frequencies are synchronized with each other in Zero point, then 0 is the most dense part of the Sieve of Eratosthenes.

The least dense part of the Sieve of Eratosthenes is the set of prime numbers, because each prime number is a synchronization between no more than 3 frequencies, which are level 0, level 1 and the level of the prime itself.

Here is the diagram of the Sieve of Eratosthenes, represented as non-finite levels of synchronized half circles:

http://www.geocities.com/complementarytheory/Tedarim6.jpg

At the left side of this diagram we can see the Zero point, and the first 20 primes are mareked along the 0_level line.

-------------------------------------------------------

The non-local ur-element is the maximum entropy of itself (no differences can be found within it). Also a local ur-element is the maximum entropy of itself (no differences can be found within it).

Maximum entropy exists in both non-locality and locality, but they are opposite by their self nature, so if non-locality and locality are associated, then a non-entropic domain is created.

The history of such a domain is written by symmetry, where at the first stage symmetry is so strong that no outcome of this domain has a unique identity, and all we have is a superposition of identities.

Symmetry is collapsed because the opposite properties of non-locality and locality are expressed more and more until each local ur-element has a unique identity of its own.

This uniqueness, which is anti-entropic by nature, cannot exist without the association between the non-local and the local.

Opposite properties do not contradict each other, if they are based on NXOR connective.

A NXOR connective enables the existence of NXOR\XOR logic (non-locality and locality are associated, and associated realms have more than one entropy level).

A XOR connective does not enable the existence of NXOR\XOR logic (non-locality and locality are isolated, and isolated realms have maximum entropy).

Please read pages 13-14 of my work called Eventors ( http://www.geocities.com/complementarytheory/Eventors.pdf ).

I think that the organic approach (the associations between the non-local and the local) is the accurate way to understand the realm that we are an inseparable part of it.

--------------------------------------------------

Let us re-examine these cases:

Case 1: associated realms have more than one entropy level.

Case 2: isolated realms have maximum entropy.

In case 1 NXOR is associated with XOR and we get an open realm because both NXOR and XOR go beyond their self state of maximum (and opposite state of) entropy.

In case 2 there is no association between NXOR and XOR, and each opposite is closed upon its own maximum entropy, and nothing exists beyond these closed and isolated opposite maximum entropies.

In a complementary realm, each opposite is opened to an "off spring" outcome, which is beyond its own isolated state (an isolated realm has maximum entropy).

About dimensions:

If an organic realm is the result of the associations between the non-local and the local, than our measurement tools must express this association.

For example, let us take the place value method.

If we look at it from both parallel and serial points of view, we get a fractal-like structure, which is a mixed pattern of both parallel and serial parts upon finite/non-finite scales.

Let us examine this structure by using bases 2,3 and 4:

http://www.geocities.com/complementarytheory/234.jpg

The traditional place value system is based only on the serial broken-symmetry building-block, which is used to define non-finite fractals upon non-finite scale levels, where the structure of each fractal is determine by the serial broken-symmetry building-block that is used.

Furthermore, the traditional method ignores the whole/part relations that exists in such fractals and uses single paths along them as measurements tools, for example:
Pi representation in base 10 is a single path along a base 10 fractal, and this single path is notated as 3.141592653589793238462643383279502884197169399375 10 …
where each numeral represents a different scale level along this fractal.

The organic approach changes at least two things here:

1) The fractal-like structure is based on both parallel and serial building-blocks.

2) There can be simultaneously more than a one path , and as a result our measurement tool is not limited to a single path of numerals, but it can be a tree of several paths made of several building-blocks with different symmetrical states, which simultaneously determine the structure of what I call Organic fraction. Here is an example of an organic fraction that is based on different bulging-blocks taken from bases 2,3 and 4:

http://www.geocities.com/complementarytheory/ONNfrac.jpg

So as can be seen, the 4D model is just the standard approach to start with.

In order to deal with Organic fractions, a parallel/serial Turing-like model has to be formulated.

I am in a state of "Michael Faraday"-like* here that seeks for "James Clerk Maxwell"-like** in order to do that.

* http://en.wikipedia.org/wiki/Michael_Faraday
** http://en.wikipedia.org/wiki/James_Clerk_Maxwell

I think that since non-locality is involved here, then any formulation of Organic fractions must be incomplete and therefore open (this is a positive interpretation of Gödel's work).

Please read this message to Prof. Mandelbrot http://www.geocities.com/complementarytheory/2Mandelbrot.pdf .

In my opinion, meaningful frameworks exist as long as there is a difference between X-model and X (which is also a positive interpretation of Gödel's work).

[PixyMisa]

No.

[doronshadmi]

No.

Please explain.

[Alkatran]

I'm going to advise people not to respond to this thread. doronshadmi has a history of being totally incomprehensible and his threads always go for dozens of pages without any progress being made.

Doron, you are misusing common terms.
http://en.wikipedia.org/wiki/Information_entropy
http://en.wikipedia.org/wiki/Multiset

I will not be replying to this thread any more.

[lionking]

Ditto

[nathan]

Notion #1:

If we use partitions in order to define Entropy, then a multiset (a repetition of the same identity) has an entropy that is equivalent to the number of the repetitions that exists within it.

As can be seen, Prime numbers have the least entropy, from this point of view.

Why is this insightful? It just follows from the definition of a prime number and your definition of maximum entropy. Whilst you don't give a rigorous definition of the entropy measure of an integer, it appears that it's related to the number of co-factors of a number. By definition, a prime number only has a single degenerate pair of factors.

Put it another way; you've come to the astounding conclusion that if one selects the numbers that have only 1 and themselves as factors, that they have the fewest factors.

Your notion 2 was impenetrable.

Why are you asking us to read your correspondence to a famous mathematician? Do you want one of us to ask him about it when we meet him next?

[nathan]

I'm going to advise people not to respond to this thread. doronshadmi has a history of being totally incomprehensible and his threads always go for dozens of pages without any progress being made.


I can't help mys.. oo, a shiny thing!

[ddt]

I'm going to advise people not to respond to this thread. doronshadmi has a history of being totally incomprehensible and his threads always go for dozens of pages without any progress being made.

Small correction:
1. doronshadmi has a history of inventing new terms and not defining them;
2. doronshadmi has a history of misrepresenting every field of mathematics he touches upon.

For the rest: seconded.

[doronshadmi]

Put it another way; you've come to the astounding conclusion that if one selects the numbers that have only 1 and themselves as factors, that they have the fewest factors.
I am talking about the general view where:

If we understand the Sieve of Eratosthenes ( http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes ) as a whole\part framework, than number 0 is the most dense part of it, and the set of primes is the least dense part of it.

Also the partition of each n > 1 has an internal degree of entropy, where primes has the least degree of entropy.

By using Symmetry as a first-order property, it is possible to to show how Entropy and Distinction of Ids are related to each other, and open an interesting framework for discoveries.

[TMiguel]

First of all You have to define what you mean by entropy in this mathematical case.
Secondly if you mean by entropy the number of subset in which you can decompose the number in a summatorial series, from which common factors are called to have higher entropy. Then your conclusion is not a bit interesting at all, has you can decompose in such way in an increasing amount of ways has the numbers go bigger. And you cant have primes whit more then one term whit the “highest entropy” (the number 1 by what you are trying to highlight), simply because if you have a set of number “b” in an exclusive cluster, then you would be able to transcribe it into “nb” and therefore not a prime.
Has far as I can tell the rest is just rubbish, a diagram can be a good thing to explain an expression, but whiteout an expression it is completely useless has a final product.

[PixyMisa]

Please explain.
What part of "no" didn't you understand?

[doronshadmi]

First of all You have to define what you mean by entropy in this mathematical case.
Secondly if you mean by entropy the number of subset in which you can decompose the number in a summatorial series, from which common factors are called to have higher entropy. Then your conclusion is not a bit interesting at all, has you can decompose in such way in an increasing amount of ways has the numbers go bigger. And you cant have primes whit more then one term whit the “highest entropy” (the number 1 by what you are trying to highlight), simply because if you have a set of number “b” in an exclusive cluster, then you would be able to transcribe it into “nb” and therefore not a prime.
Has far as I can tell the rest is just rubbish, a diagram can be a good thing to explain an expression, but whiteout an expression it is completely useless has a final product.

Please read again the beginning of my first post:

If we use partitions in order to define Entropy, then a multiset (a repetition of the same identity) has an entropy that is equivalent to the number of the repetitions that exists within it.

Since a set has no repetitions, it has no entropy.

So as you see, I am taking about not less tham Set\Multiset relation based on Symmetry as a first-order property.

[Reality Check]

Is Entropy thermodynamic or information entropy?
What is a partition?
What is the mathematical relationship between "partitions" and entropy?
What is the criteria that separates high, intermediate and low entropy?
What use is this nonsense?

The previous thread started by doronshadmi bogged down in his constant redefining of his terms and the total inconsistency of of his "mathematics".

[Don At Work]

Set\Multiset
local\non-local
sense\nonsense
night\day
habersham\diesel

:bunpan

please spot the pair that is not attributed to doron.

*right, it was night\day

[doronshadmi]

Is Entropy thermodynamic or information entropy?

Both.

[doronshadmi]

What part of "no" didn't you understand?
The part that shows that you understand it, before you conclude "No".

[ddt]

Please read again the beginning of my first post:
Nope, no definition of "entropy". And I predict we won't get one from you either in this thread. Can I now apply for the MDC?


So as you see, I am taking about not less tham Set\Multiset relation based on Symmetry as a first-order property.
Ah, our old tired gibberish\nonsense complementation and Symmetry delusional stuff is back. Nothing really changes.


Is Entropy thermodynamic or information entropy?
What is a partition?
What is the mathematical relationship between "partitions" and entropy?
What is the criteria that separates high, intermediate and low entropy?
What use is this nonsense?
Good questions you'll never get an answer to from doron.


The previous thread started by doronshadmi bogged down in his constant redefining of his terms and the total inconsistency of of his "mathematics".
I never saw an actual rigorous definition of his terms. I did see vague descriptions of them, which indeed were contradictory to each other.

Doron's target audience is, in fact, kindergarten children. Yes, 5-years olds would, according to him, better understand his "mathematical" concepts than adults. Indeed, his own grasp - or at least his presentation thereof - of things like set theory and logic is on level with that of the average 5 years old.

Speaking of which: why don't you search for an internet forum that targets kindergarten children, doron? I guess your buddy Moshe Klein, who is kindergarten teacher, would be able to advise you to find such a forum.

[nathan]

By using Symmetry as a first-order property, it is possible to to show how Entropy and Distinction of Ids are related to each other, and open an interesting framework for discoveries.

Please show an interesting discovery you have made using this framework.

[nathan]

If we understand the Sieve of Eratosthenes ( http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes ) as a whole\part framework, than number 0 is the most dense part of it, and the set of primes is the least dense part of it.

Is this your astounding discovery? That the holes in a sieve are less dense than the bits of the sieve that aren't holes? That some numbers have more factors than others? And in particular primes have the fewest factors, and zero has the most factors?

Well, gosh. Just the breakthrough maths has been waiting for!

[doronshadmi]

Is this your astounding discovery? That the holes in a sieve are less dense than the bits of the sieve that aren't holes? That some numbers have more factors than others? And in particular primes have the fewest factors, and zero has the most factors?

Well, gosh. Just the breakthrough maths has been waiting for!

The keyword in this case is Symmetry.

By using Set\Multiset compelemntation one can systematically research Entropy in terms of both Thermodynamic and Information by a one framework.

Nathen,

You simply cannot get things beyond the Set case, where anything is already clearly identified.

[drkitten]

Notion #1:

If we use partitions in order to define Entropy,

... then we end up with complete gibberish.

Doron, weren't you leaving us because we were too rigid and accurate in our thinking and knew too much mathematics for your tastes?

[doronshadmi]

Please show an interesting discovery you have made using this framework.
This time please read my all of my first post (not part here and part there), and try to get it by using a general viewpoint that enables you to see how it can be used as a common framework to research Entropy in terms of both Thermodynamic and Information by a one framework.

[doronshadmi]

... then we end up with complete gibberish.

Doron, weren't you leaving us because we were too rigid and accurate in our thinking and knew too much mathematics for your tastes?
drkitten,

Nobody forces you to reply here.

[nathan]

By using Set\Multiset compelemntation one can systematically research Entropy in terms of both Thermodynamic and Information by a one framework.

Oh, we're back to complementation I see. Anyway, you've yet to show how your framework leads to new insights in Thermodynamics or Information theory. Care to share one of your results?

[nathan]

This time please read my all of my first post (not part here and part there), and try to get it by using a general viewpoint that enables you to see how it can be used as a common framework to research Entropy in terms of both Thermodynamic and Information by a one framework.

I have read it. It's rubbish. It shows no such thing.

[drkitten]

Nobody forces you to reply here.

Nobody forces you to make drama-queen-like fake exits complaining about the quality of mind here, either. That's the nice thing about this forum.

You're free to post woolly thinking and gibberish.
We're free to ridicule you for it.
You're free to burst into tears and run screaming home to Mummy.
We're free to ignore the histrionics.

... and the only thing that gets hurt is your credibility.

[TMiguel]

Please read again the beginning of my first post:
That is not a definition, nor an expression. Your point was?
(Partition of what? What does it really account for? Which of the sets have more entropy (3,2,1,1,1), (4,3,3,2,2)? how do you really account them?)
I’m guessing you don’t know what math is, much less been able to prove anything.

[nathan]

Nobody forces you to make drama-queen-like fake exits complaining about the quality of mind here, either.

Ahem, *multiple* drama-queen fake exits. He's done it before :)

[doronshadmi]

Nobody forces you to make drama-queen-like fake exits complaining about the quality of mind here, either. That's the nice thing about this forum.


The nice thing about this forum is a fine ability to critique things.

Rudeness or cynicism is not the best way to do it.


More to the point, please show the drama in my first post.

[doronshadmi]

That is not a definition, nor an expression. Your point was?
(Partition of what? What does it really account for? Which of the sets have more entropy (3,2,1,1,1), (4,3,3,2,2)? how do you really account them?)
I’m guessing you don’t know what math is, much less been able to prove anything.


(3,2,1,1,1) or (4,3,3,2,2) are not sets. First you have to know it before you reply.

[Reality Check]

Define entropy.
Define partitions.
What is the criteria that separates high, intermediate and low entropy?
Mathematically prove that primes have minimum entropy according to your definition. This should be easy for a genius like you.

[TMiguel]

(3,2,1,1,1) or (4,3,3,2,2) are not sets. First you have to know it before you reply.
I do know what I'm talking, and you havent yet answered the question.

[69dodge]

Rudeness or cynicism is not the best way to do it.

The best way to deal with trolling is to ignore it.

Unfortunately, that only works if everybody ignores it.

I plan to do my part, anyway.

(Have fun wasting the time of those who don't.)

[doronshadmi]

The best way to deal with trolling is to ignore it.

Unfortunately, that only works if everybody ignores it.

I plan to do my part, anyway.

(Have fun wasting the time of those who don't.)

In my first post I ask each one of you to help me to define notions 1 and 2 mathematically.

What I get instead is a brutal attack, which shows that you misinterpreted post 1.

So, this time please hold your horses and try to get the notions (there is a reason of why I wrote notions and not definitions, which means that I need your help (each one of you) in order to translate them to rigorous mathematical definitions).

Thank you.

[Reality Check]

That is incorrect. Nowhere in the original topic do you ask posters to help to translate your notions to rigorous mathematical definitions.
In order for that you still have to define your notions enough to be understandable, e.g.

Define entropy.
Define partitions.
Tell us what is the criteria that separates high, intermediate and low entropy?
Then someone may do your job for you and may be able to mathematically prove that primes have minimum entropy according to your definition. They may also find that primes have maximum entropy. They may also find that prime do not have any entropy.

The result will have be a conventional mathematical proof and have nothing to do with your non-locality/Organic fractions/NXOR connective/NXOR\XOR logic non-mathematics that we have seen you unable to define in other threads.

[Reality Check]

Let us look at your first example (note that I have replaced the { and } with [ and ] so we are not confused with the standard notation for sets):
How is [1,1] found from the number 2?
How did you determine that [1,1] has a maximum entropy given that entropy is only a "notion" and you have no definition for it?
What is the numeric value that you determined for the entropy of [1,1]?

ETA: Just had a thought: Maybe you mean the definition of partitions in number theory (http://en.wikipedia.org/wiki/Partition_(number_theory))? But these are not sets of numbers but the different ways that a positive integer can be written as the sum of positive integers and includes the actual integer itself, e.g.


The partitions of 4 are listed below:
4
3 + 1
2 + 2
2 + 1 + 1
1 + 1 + 1 + 1

Notice the + signs between the integers.

I do hope that you are not redefining a standard definition in mathematics once again.

[ddt]

In my first post I ask each one of you to help me to define notions 1 and 2 mathematically.
So, we're already at post #34, half a dozen or so people have pointed out your OP lacks definitions, and only now you turn around and say that you ask us to help with those definitions? Who are you kidding?

Could you point out where exactly in the OP you ask our help for those definitions? I see a definite lack of question marks, to begin with, in the OP.

And why can't you provide those definitions yourself? You're such a master at mathematics, aren't you? Hilbert was wrong, Cantor was wrong, several other renowned mathematicians were wrong, and you know everything about Logic, Set Theory, Number Theory, Topology, Calculus, etc.


What I get instead is a brutal attack, which shows that you misinterpreted post 1.
Whining is not very becoming. Nor is disingenuity.


So, this time please hold your horses and try to get the notions (there is a reason of why I wrote notions and not definitions, which means that I need your help (each one of you) in order to translate them to rigorous mathematical definitions).
Explain why you'd need our help. Over 1,300 posts, you have stated to all of us that we don't understand mathematics and you're the only one who does.

What guarantees those who indeed try to help you in this that you don't try to sneak back your own unfounded notions of "locality", "symmetry", and assorted backslash-complementations back into the discussion? In fact, you already did in this thread, which to me signifies this plea for help is dishonest.

Myself, I fondly remember about halfway your previous thread trying to help you define your notion of "locality" when you pretended to honestly accept others' help. Thanks but no thanks.

[TMiguel]

:rolleyes: I wonder why people ignore my questions.

[cwalner]

(3,2,1,1,1) or (4,3,3,2,2) are not sets. First you have to know it before you reply.

Doron,

In your op you actually used slightly different notation you used {3,2,1,1} and {4,3}. In real mathematics we use the '{' and '}' symbols to denote elements of a set. TMiguel accidentaly changed the symbos to '(' and ')' but was responding to your OP which used clearly marked set notation.

So please explain why you are using set notation for something that is not a set? The fact that TMiguel's error of assuming that you were referring to sets was based on your initial error for using standard mathematical set notation makes your response remarkably ignorant in addition to being extremely rude.

How are we supposed to know what you mean when you use incorrect notation to propose your notions?

[TMiguel]

Doron,

In your op you actually used slightly different notation you used {3,2,1,1} and {4,3}. In real mathematics we use the '{' and '}' symbols to denote elements of a set. TMiguel accidentaly changed the symbos to '(' and ')' but was responding to your OP which used clearly marked set notation.

So please explain why you are using set notation for something that is not a set? The fact that TMiguel's error of assuming that you were referring to sets was based on your initial error for using standard mathematical set notation makes your response remarkably ignorant in addition to being extremely rude.

How are we supposed to know what you mean when you use incorrect notation to propose your notions?

I didn’t paid enough attention to notation (I personally tend to ignore them if you understand what it means), it is very common to change notation if you state what it means (in many areas they not only change notation and convention has it is imperative to do so), but your statement is none of the less correct.

However a (sum) partition can also be a set (and in this case is), because he represented has a group of elements independently of what they mean (of course he means to sum the elements of the group in order to reproduce the partitioned number), unless of course I miss interpreted the English word set. A miss interpretation of the question is not however the reason why he didn’t answer my questions, because he did realised what I mean.
He did not answer the question because for him to give an honest answer he is forced to conclude that he missed something very important, and that would simply invalidate what he is doing, in this case he missed a mean of quantification and a definition of order.

[jsfisher]

If we use partitions in order to define Entropy, then a multiset (a repetition of the same identity) has an entropy that is equivalent to the number of the repetitions that exists within it.

Ok, please do so: Define entropy in terms of partitions. We'll wait.

Since a set has no repetitions, it has no entropy.

Minor nit-pick: "Zero" and "no" are not precise synonyms.

...<snip>...
As can be seen, Prime numbers have the least entropy, from this point of view.

Wow! You've only just started this post, and already you are using the term, entropy, differently than first implied. I suppose that is the best thing about never defining anything. You are free to misuse your terms anyway that pleases you.

Here, you began with entropy being a property of a multi-set having something to do with element repetitions; now, it has somehow become a property of numbers (with no hint of how you got there).


By the way: A multi-set is not a repetition of the same identity. Please try to get at least something right.

[RecoveringYuppy]

Pretty picture. I wonder if I can find a spirograph on e-bay.

[doronshadmi]

Let us look at your first example (note that I have replaced the { and } with [ and ] so we are not confused with the standard notation for sets):
How is [1,1] found from the number 2?
How did you determine that [1,1] has a maximum entropy given that entropy is only a "notion" and you have no definition for it?
What is the numeric value that you determined for the entropy of [1,1]?

ETA: Just had a thought: Maybe you mean the definition of partitions in number theory (http://en.wikipedia.org/wiki/Partition_(number_theory))? But these are not sets of numbers but the different ways that a positive integer can be written as the sum of positive integers and includes the actual integer itself, e.g.

Notice the + signs between the integers.

I do hope that you are not redefining a standard definition in mathematics once again.

Actually, there is no problem to use "{" and "}" because I am looking for the relations between sets and multisets as the framework of Entropy's research.

By using Symmetry I find Entropy as a state that is measured by its invariance under exchange, for example:

By using cardinal 4 multisets {1,1,1,1} or {2,2} are invariant under their members' exchange, and in this case we have maximum entropy.

The entropy of {1,1,1,1} is greater than {2,2} because more members are invariant under exchange.

On the contrary {3,1} has no entropy because it is variant (and asymmetric) under exchange.

In my opinion, by using this preliminary idea, we can unify Thermodynamics and Information theory under a one method based on Symmetry as the common measurement tool.

A lot of work has to be done in order to develop this idea, so before any further effort in this direction, I which to know what do you think about this preliminary idea.



Wow! You've only just started this post, and already you are using the term, entropy, differently than first implied. I suppose that is the best thing about never defining anything. You are free to misuse your terms anyway that pleases you.

When we are talking about natural numbers' partition we have to use notations like (1,1,1,1) or (2,2) instead of {1,1,1,1} or {2,2}, but in both cases Symmetry is used as invariance under element's exchange.

[drkitten]

By using Symmetry I find Entropy as a state that is measured by its invariance under exchange, for example:

By using cardinal 4 multisets {1,1,1,1} or {2,2} are invariant under their members' exchange, and in this case we have maximum entropy.

The entropy of {1,1,1,1} is greater than {2,2} because more members are invariant under exchange.

The astonishing thing is that I think this could be worked and formalized into an insightful definition of structural information. Of course, I also suspect that Our Favorite Nutcase has neither the ability nor the interest to actually formalize it, and I suspect that any attempt to so formalize it will meet with her active hostility.

I know that I'm not going to lift a pen to work it out, certainly.


A lot of work has to be done in order to develop this idea, so before any further effort in this direction, I which to know what do you think about this preliminary idea.

I think in your hands it's gibberish.

[nathan]

In my opinion, by using this preliminary idea, we can unify Thermodynamics and information theory under a one method based on Symmetry as the common measurement tool.

A lot of work has to be done in order to develop this idea, so before any further effort in this direction, I which to know what do you think about this preliminary idea.

We[1] think it's so bad it's not even wrong.

[1] and I think I can speak for many people here on this matter.

[doronshadmi]

The astonishing thing is that I think this could be worked and formalized into an insightful definition of structural information.
Go for it. You can do it in another thread; I promise not to interrupt you. I believe that it is a very good exercise for me just to watch of how other people formalizing this preliminary idea.

[drkitten]

Go for it. You can do it in another thread;

I already have done in another thread, and I see no reason to try it again.

Mathematics is not a spectator sport. If you want to learn how to do mathematics, do mathematics -- and then LISTEN to the corrections you get.

I will, however, at least give you one strong hint.

You use the word "entropy" a lot, and you are claiming, for example, that {3,1} < {2,2} < {1,1,1,1}.

Prove it. Define "entropy" (the entropy of a (multi)set S is given by the following expression : [arglebargle]) and show the claim above to be numerically true.

[Reality Check]

Actually, there is no problem to use "{" and "}" because I am looking for the relations between sets and multisets as the framework of Entropy's research.

We will add this to the OT as Notion #3.


By using Symmetry I find Entropy as a state that is measured by its invariance under exchange, for example:

By using cardinal 4 multisets {1,1,1,1} or {2,2} are invariant under their members' exchange, and in this case we have maximum entropy.

The entropy of {1,1,1,1} is greater than {2,2} because more members are invariant under exchange.

On the contrary {3,1} has no entropy because it is variant (and asymmetric) under exchange.

Then we may as well use the words symmetry and asymmetric. It is nothing to do with entropy


In my opinion, by using this preliminary idea, we can unify Thermodynamics and information theory under a one method based on Symmetry as the common measurement tool.

A lot of work has to be done in order to develop this idea, so before any further effort in this direction, I which to know what do you think about this preliminary idea.

No we cannot since thermodynamicis is a lot more than entropy.


That is why I think that they have the minimum Entropy. In this case (

when we are talking about natural numbers' partition we have to use notations like (1,1,1,1) or (2,2) instead of {1,1,1,1} or {2,2}, but in both cases Symmetry is used as invariance under element's exchange).
This is just symmetry again - nothing to do with entropy.

You should really learn what entropy actually is and the thermodynamic and informaional definitions (http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theory). It is not a measure of symmetry.

Theoretical relationship
Despite all that, there is an important difference between the two quantities. The information entropy H can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability pi occurred, out of the space of the events possible). But the thermodynamic entropy S refers to thermodynamic probabilities pi specifically.
Furthermore, the thermodynamic entropy S is dominated by different arrangements of the system, and in particular its energy, that are possible on a molecular scale. In comparison, information entropy of any macroscopic event is so small as to be completely irrelevant.
However, a connection can be made between the two, if the probabilities in question are the thermodynamic probabilities pi: the (reduced) Gibbs entropy σ can then be seen as simply the amount of Shannon information needed to define the detailed microscopic state of the system, given its macroscopic description. Or, in the words of G. N. Lewis writing about chemical entropy in 1930, "Gain in entropy always means loss of information, and nothing more". To be more concrete, in the discrete case using base two logarithms, the reduced Gibbs entropy is equal to the minimum number of yes/no questions that need to be answered in order to fully specify the microstate, given that we know the macrostate.
Furthermore, the prescription to find the equilibrium distributions of statistical mechanics, such as the Boltzmann distribution, by maximising the Gibbs entropy subject to appropriate constraints (the Gibbs algorithm), can now be seen as something not unique to thermodynamics, but as a principle of general relevance in all sorts of statistical inference, if it desired to find a maximally uninformative probability distribution, subject to certain constraints on the behaviour of its averages.

[doronshadmi]

I already have done in another thread, and I see no reason to try it again.

Mathematics is not a spectator sport. If you want to learn how to do mathematics, do mathematics -- and then LISTEN to the corrections you get.

I will, however, at least give you one strong hint.

You use the word "entropy" a lot, and you are claiming, for example, that {3,1} < {2,2} < {1,1,1,1}.

Prove it. Define "entropy" (the entropy of a (multi)set S is given by the following expression : [arglebargle]) and show the claim above to be numerically true.

Let us think about my idea like this:

I have a melody but I don't know how to write the notes for some group of musicians.

I go to some musician how knows how to do it. He will do it if he thinks that this melody has a potential to become a nice piece of music.

If you think that my melody (preliminary idea) can be edited (can be addressed formally) in order to get a nice piece of music (some interesting mathematical work), then please go for it.

[drkitten]

Let us think about my idea like this:

I have a melody but I don't know how to write the notes for some group of musicians.

No, let's not. You don't have a melody. You have a random collection of notes.



If you think the my melody (preliminary idea) can be edited (can be addressed formally) in order to get a nice piece of music (some interesting mathematical work), then please go for it.

No, thanks. As I pointed out, I tried that already in your previous thread, and got roundly abused for my suggestions.

[doronshadmi]

Then we may as well use the words symmetry and asymmetric. It is nothing to do with entropy
This is the whole (new) idea, to get Entropy in terms of Symmetry.

[doronshadmi]

No, let's not. You don't have a melody. You have a random collection of notes.
Maybe.

But you wrote this:


The astonishing thing is that I think this could be worked and formalized into an insightful definition of structural information.
So there is something in your mind, so please go for it.

No, thanks. As I pointed out, I tried that already in your previous thread, and got roundly abused for my suggestions.
Forget about me, open your own thread. I believe that ddt, jsfisher, PixMisa, Nathan and more people that really know Mathematics, will be glad to help you.

[drkitten]

This is the whole (new) idea., to get Entropy in terms of Symmetry.

I told you that you don't have an melody, just a random collection of notes.

This basically proves it. You're trying to "get" an undefined term in terms of another undefined term. Based on this, I think I can "get" Margstrap in term of Bletcherality.

(But it must be important, because I capitalized both Margstrap and Bletcherality, right?)

[doronshadmi]

I told you that you don't have an melody, just a random collection of notes.

This basically proves it. You're trying to "get" an undefined term in terms of another undefined term. Based on this, I think I can "get" Margstrap in term of Bletcherality.

(But it must be important, because I capitalized both Margstrap and Bletcherality, right?)

http://forums.randi.org/showpost.php?p=4088406&postcount=52

[doronshadmi]

By the way: A multi-set is not a repetition of the same identity. Please try to get at least something right.

A=A (self id) , 1=1 (self id)

{A,A,A}, {1,1,1,1}

[drkitten]

Forget about me, open your own thread. I believe that ddt, jsfisher, PixMisa, Nathan and more people that really know Mathematics, will be glad to help you.

I neither need nor want their help; I don't think that the definition you propose will be useful enough to justify spending my effort on it. And I think it will be completely unable to help with your locality/nonlocality theology that you keep trying to push.

I do, however, find it amusing that you finally get one sentence (in what, 1500 posts?) that MIGHT be meaningful, and you refuse to explore the meaning further.

If you think your OP was meaningful, define your terms. Prove me wrong in my belief that you have NOTHING of interest to offer.....

[doronshadmi]

I neither need nor want their help; I don't think that the definition you propose will be useful enough to justify spending my effort on it. And I think it will be completely unable to help with your locality/nonlocality theology that you keep trying to push.

I do, however, find it amusing that you finally get one sentence (in what, 1500 posts?) that MIGHT be meaningful, and you refuse to explore the meaning further.

If you think your OP was meaningful, define your terms. Prove me wrong in my belief that you have NOTHING of interest to offer.....
You wrote "The astonishing thing is that I think this could be worked and formalized into an insightful definition of structural information." at the beginning of http://forums.randi.org/showpost.php?p=4088292&postcount=44 .

Don't you think that it will be a good idea to formalize what you (again, forget about me or my ideas) think as an insightful definition of structural information?

[drkitten]

You wrote "The astonishing thing is that I think this could be worked and formalized into an insightful definition of structural information." at the beginning of http://forums.randi.org/showpost.php?p=4088292&postcount=44 .

Don't you think that it will be a good idea to formalize what you (again, forget about me or my ideas) think as an insightful definition of structural information?

No, I don't, because I think the insights are already available through other channels. (Thank you, Claude Shannon.)

What is astonishing is the fact that you wrote it, since I think it's the first mathematical observation you've made in 1500 posts that might be meaningful.

If you define your terms properly, which you will not.

[Reality Check]

This is the whole (new) idea, to get Entropy in terms of Symmetry.
Then the whole (new) idea is wrong.
Entropy is a continuous numeric value (a real number).
Measures of Symmetry are discrete numeric values (integers) unless you are talking about objects that have infinite symetry, e.g a sphere. This is certainly not the case here. The "partitions" that you talk about do not have infinite symmetry.
Thus Entropy cannot be defined in terms of Symmetry.

[doronshadmi]

No, I don't, because I think the insights are already available through other channels. (Thank you, Claude Shannon.)

What is astonishing is the fact that you wrote it, since I think it's the first mathematical observation you've made in 1500 posts that might be meaningful.

If you define your terms properly, which you will not.

Please show where Shannon defines Symmetry as a common framework for Thermodynamics and Information theory research about Entropy?

Symmetry is defined as invariance under manipulation, where Entropy is the most symmetrical state (no new information can be found under any manipulation, and no work can be done, in terms of thermodynamic equilibrium).

[TMiguel]

Actually, there is no problem to use "{" and "}" because I am looking for the relations between sets and multisets as the framework of Entropy's research.

By using Symmetry I find Entropy as a state that is measured by its invariance under exchange, for example:

By using cardinal 4 multisets {1,1,1,1} or {2,2} are invariant under their members' exchange, and in this case we have maximum entropy.

The entropy of {1,1,1,1} is greater than {2,2} because more members are invariant under exchange.

On the contrary {3,1} has no entropy because it is variant (and asymmetric) under exchange.

In my opinion, by using this preliminary idea, we can unify Thermodynamics and Information theory under a one method based on Symmetry as the common measurement tool.

A lot of work has to be done in order to develop this idea, so before any further effort in this direction, I which to know what do you think about this preliminary idea.




When we are talking about natural numbers' partition we have to use notations like (1,1,1,1) or (2,2) instead of {1,1,1,1} or {2,2}, but in both cases Symmetry is used as invariance under element's exchange.

You still haven’t answered my question.
What does it really account for?
Which of the sets have more entropy {4,2,1,1,1}, {3,2,2,1,1}?
How do you really account them?

[doronshadmi]

Then the whole (new) idea is wrong.
Entropy is a continuous numeric value (a real number).
Measures of Symmetry are discrete numeric values (integers) unless you are talking about objects that have infinite symetry, e.g a sphere. This is certainly not the case here. The "partitions" that you talk about do not have infinite symmetry.
Thus Entropy cannot be defined in terms of Symmetry.

R set is based on distinct values , and so is N set.

I am not talking here about sets, but about the relations between sets and multisets in terms of distinction, measured by symmetry (superposition of identities) and asymmetry (distinct identities).

My first post is just an outline of this idea.

[Reality Check]

Please show where Shannon defines Symmetry as a common framework for Thermodynamics and Information theory research about Entropy?

Symmetry is defined as invariance under manipulation, where Entropy is the most symmetrical state (no new information can be found under any manipulation, and no work can be done, in terms of thermodynamic equilibrium).
Entropy is not the most symmetrical state. The most symmetrical state is the state with the largest number of "invariance under manipulation".
The best that you can say is that there may be a definition of entropy that is a measure of the number of symmetries that an object has. So not all you have to do is provide us with that definition.

Just in case you have not got it yet:
Symmetry is a property of a mathematical object, i.e. when the object undergoes a transformation and that transformation gives you the original object then the object is symmetrical under that operation. It is not a number. It is what happens to the object when transformed.

Entropy is a number.

[Reality Check]

R set is based on distinct values , and so is N set.

I am not talking here about sets, but about the relations between sets and multisets in terms of distinction, measured by symmetry (superposition of identities) and asymmetry (distinct identities).

My first post is just an outline of this idea.
R set is based on distinct continuous values , and N set is based on distinct values.
Symmetry is not a "superposition of identities". It is the result of a transformation of an object. Asymmetry is not "distinct identities". It is a result of a transformation of an object.

[jsfisher]

Wow! You've only just started this post, and already you are using the term, entropy, differently than first implied. I suppose that is the best thing about never defining anything. You are free to misuse your terms anyway that pleases you.

When we are talking about natural numbers' partition we have to use notations like (1,1,1,1) or (2,2) instead of {1,1,1,1} or {2,2}, but in both cases Symmetry is used as invariance under element's exchange.


Two things jump out at me, doron. First, why did you edit my post you quoted? Admittedly, it was a trivial change - an italics tag pair was dropped - but why would you do it?

Second, your response has absolutely nothing to do with my post. My comment is on your inconsistent use of your own terms, and you go off on a tangent about an unnecessary notation shift that you have to use, but didn't.

[jsfisher]

By the way: A multi-set is not a repetition of the same identity. Please try to get at least something right.

A=A (self id) , 1=1 (self id)

{A,A,A}, {1,1,1,1}


I see the independence between quoted post and response continues.

[jsfisher]

By using cardinal 4 multisets {1,1,1,1} or {2,2} are invariant under their members' exchange, and in this case we have maximum entropy.

Are you saying the multi-set {2,2} has cardinality of 4? What did you really mean?

The entropy of {1,1,1,1} is greater than {2,2} because more members are invariant under exchange.

By exchange you mean rearrange the members of the multi-set, right? Since multi-sets, just like sets, are unordered, your statement has no meaning.

On the contrary {3,1} has no entropy because it is variant (and asymmetric) under exchange.

Are you trying to say {3,1} and {1,3} are different multi-sets?

[Reality Check]

Doron: Wikipedia is your friend (since you do not seem to have access to mathematical textbooks): Multiset (http://en.wikipedia.org/wiki/Multiset).

[jsfisher]

Doron: Wikipedia is your friend (since you do not seem to have access to mathematical textbooks): Multiset (http://en.wikipedia.org/wiki/Multiset).

(Emphasis added.)
Don't assume that. Wikipedia is what lead doron to believe a set is the union of its members - a belief rigidly held to this very day.

[TMiguel]

Please show where Shannon defines Symmetry as a common framework for Thermodynamics and Information theory research about Entropy?

Symmetry is defined as invariance under manipulation, where Entropy is the most symmetrical state (no new information can be found under any manipulation, and no work can be done, in terms of thermodynamic equilibrium).
Entropy in thermodynamics and information theory is equal to the number of possible states of a system, nothing to do whit invariance and specially not symmetry.
And you still havn't answered my question!

[doronshadmi]

Are you saying the multi-set {2,2} has cardinality of 4? What did you really mean?
My mistake I mean the sum 4.



By exchange you mean rearrange the members of the multi-set, right? Since multi-sets, just like sets, are unordered, your statement has no meaning.
I am talking about Distinction. A set is asymmetric since each member is distinct. This is not the case in a multiset.


Are you trying to say {3,1} and {1,3} are different multi-sets?

{3,1} is a set. {3,3} is a multiset.

In both cases (set or mutliset) I an talking about thier internal structure, in terms of symmetry)

[drkitten]

Please show where Shannon defines Symmetry as a common framework for Thermodynamics and Information theory research about Entropy?

See? You're doing it again.

I offer some suggestions, and you react with hostility.



Symmetry is defined as invariance under manipulation, where Entropy is the most symmetrical state

Really? To paraphrase you, "please show me where anyone (it doesn't have to be Shannon) has defined entropy as the most symmetrical state"?

I even offered you a chance to be the one who had created that definition, and you couldn't. So again I offer you the chance to define your terms:

Please complete the following phrase: The entropy of a (multi)set S is given by the expression:

(Please bear in mind that, as pointed out, entropy is generally a continuous variable, and multisets are discrete; also bear in mind that to be useful as a definition of "entropy" there should be a set of limiting cases where traditional measures such as H = - sigma (p lg p) and your formulation should get the same answer.)

[drkitten]

{3,1} is a set. {3,3} is a multiset.

All sets are multisets, or more formally, a multiset is a generalization of a set.


In both cases (set or mutliset) I an talking about thier internal structure, in terms of symmetry)

So you're suggesting that the sets {3,1} and {1,3} are distinct?

[ddt]

Actually, there is no problem to use "{" and "}" because I am looking for the relations between sets and multisets as the framework of Entropy's research.
There's no problem in that if your objective is to muddy the waters. Using sets and multisets and denoting both with { } braces makes the whole thing unreadable. But then, this is your standard MO, isn't it?


The entropy of {1,1,1,1} is greater than {2,2} because more members are invariant under exchange.
In your OP, you claimed both multisets had "full entropy". So what is it: are their entropies the same or are they different? Goes to show that you can't keep your story straight within a handful of posts.


When we are talking about natural numbers' partition we have to use notations like (1,1,1,1) or (2,2) instead of {1,1,1,1} or {2,2}, but in both cases Symmetry is used as invariance under element's exchange.
You're back again at your "symmetry" hobbyhorse? Another word in a long line of words you don't understand.


I have a melody but I don't know how to write the notes for some group of musicians.
In addition to drkitten's response: You already have some false notes in there. See above.


I go to some musician how knows how to do it. He will do it if he thinks that this melody has a potential to become a nice piece of music.
But you know it better than the musician, don't you? You've shunned every advice you got in earlier threads. You couldn't even answer a simple question like if you use classical logic or not.


Forget about me, open your own thread. I believe that ddt, jsfisher, PixMisa, Nathan and more people that really know Mathematics, will be glad to help you.
What a silly suggestion. Wasn't your objective with this thread to get the answer to your questions? (whatever they may be). The idea is also that you at least have some understanding of the question you ask in the first place.

At least thanks for the compliment. Does this sentence also imply an admission that you don't know math yourself?

What about, then, actually trying to learn math yourself?

What about a retraction of your earlier statements like "Gödel was wrong", or "Hlibert was wrong"?

What about solemnly promising you stop with your symmetry delusion? Or with your X\Y complementation crap?

[ddt]

(Please bear in mind that, as pointed out, entropy is generally a continuous variable, and multisets are discrete; also bear in mind that to be useful as a definition of "entropy" there should be a set of limiting cases where traditional measures such as H = - sigma (p lg p) and your formulation should get the same answer.)

Well, I'll beat Doron to it, if it must.

View the multiset as a probability distribution. Map, e.g., the multiset [1, 1, 2, 3] to the probability distribution that belongs to drawing from an urn with 4 marbles marked with the numbers 1, 1, 2 and 3 resp. Then apply Shannon's formula.

That gives a result consistent with the OP.

[jsfisher]

My mistake I mean the sum 4.

That clears up one problem. But you still haven't cleared up exactly what you mean by entropy.

Is entropy a measure of some characteristic of a multi-set? Does it have a numeric value? What is it?

I am talking about Distinction. A set is asymmetric since each member is distinct. This is not the case in a multiset.

{3,1} is a set. {3,3} is a multiset.

In both cases (set or mutliset) I an talking about thier internal structure, in terms of symmetry)

As drkitten has also pointed out, {3,1} is also a multi-set. Be that as it may, it seems you are using asymmetric for (multi-)set to mean all members are distinct. Is that what you meant by "I am talking about Distinction"?

If so, what about {1,3,1}: is it symmetric or asymmetric? Is {1,3,1} distinct from {1,1,3} or {3,1,1}?

[drkitten]

Well, I'll beat Doron to it, if it must.

View the multiset as a probability distribution. Map, e.g., the multiset [1, 1, 2, 3] to the probability distribution that belongs to drawing from an urn with 4 marbles marked with the numbers 1, 1, 2 and 3 resp. Then apply Shannon's formula.

That gives a result consistent with the OP.

Well done. Five points to Ravenclaw. (Although I had a different approach in mind in terms of permutation-transformations and topological fixed points, and I haven't taken the time or trouble to verify that it actually produces a useful entropy-like measure.)

Doron, wanna go double or quits on a proof that a "symmetric" multiset maximizes entropy using the definition that ddt has so kindly supplied?

[jsfisher]

That gives a result consistent with the OP.


Not quite. Doron also said this at the tail end of his Notion #1:

As can be seen, Prime numbers have the least entropy, from this point of view.


So, while Claude Shannon would be very proud how you rationalized doron's handwaving with multi-sets in Notion #1, it is still unclear what sort of entropy doron meant for integers.

[doronshadmi]

All sets are multisets, or more formally, a multiset is a generalization of a set.



So you're suggesting that the sets {3,1} and {1,3} are distinct?

No, by set theory {3,1} = {1,3}.

I am talking about the internal structure of distinction, where each member is distinct (order is not important)

This is not the case in a "complete" multiset (fore example: {a,a,a,a,a,...}), where there is no distinction.

By this model (continues or not) a "complete" multiset has maximum entropy and a "complete" set has the minimum entropy.

As much as I know, this is a new idea about entropy.

[arthwollipot]

Two things jump out at me, doron. First, why did you edit my post you quoted? Admittedly, it was a trivial change - an italics tag pair was dropped - but why would you do it?There may be an innocent reason for this. I sometimes copy responses into Notepad for various reasons including instability of my network connection. If I'm copying wysiwyg text (as opposed to marked-up text), then everything is converted to plain text because I'm not copying the tags. Hence, it could be a simple mistake or oversight. Don't attribute to malice what is explainable by the stupid ways computers sometimes work. :)

[Worm]

Uh-oh ... *woop woop* ... *woo-woo alert*

I caught that one ... doronshadmi has started refering to 'complete' sets, this is usually the sign of a massive abyss of incomprehension to come (as if that wasn't already expected....)

[ddt]

Well done. Five points to Ravenclaw. (Although I had a different approach in mind in terms of permutation-transformations and topological fixed points, and I haven't taken the time or trouble to verify that it actually produces a useful entropy-like measure.)
In terms of permutations: I earlier thought of this one: given a multiset of size n, divide the number of different orderings of its elements by the number of permutations you'd have with n different elements (i.e. n!). All multisets which do not have double elements now have a "full entropy " of 1. If you want to achieve that all multisets with only 1 distinct element have the same "no entropy" of 0, subtract 1 from both numerator and denominator.

What properties would in your opinion a useful entropy-like measure have?


Doron, wanna go double or quits on a proof that a "symmetric" multiset maximizes entropy using the definition that ddt has so kindly supplied?


So, while Claude Shannon would be very proud how you rationalized doron's handwaving with multi-sets in Notion #1, it is still unclear what sort of entropy doron meant for integers.

I predict, if you want an answer, that you can wait till the cows come home (or as we say in Dutch, till the calves dance on the ice - and that saying predates AGW :)).

[Reality Check]

No, by set theory {3,1} = {1,3}.

I am talking about the internal structure of distinction, where each member is distinct (order is not important)

This is not the case in a "complete" multiset (fore example: {a,a,a,a,a,...}), where there is no distinction.

By this model (continues or not) a "complete" multiset has maximum entropy and a "complete" set has the minimum entropy.

As much as I know, this is a new idea about entropy.
Your original topic is wrong.

Firstly you list a multiset constructed from the number 5 as {3,1,1}. A multiset is a set so it the order of members is not important. Thus the {3,1,1} multiset is the same as the {1,3,1} multiset. You state that
{3,1,1) has "Intermediate entropy". {1,3,1} would have "Full entropy".
Thus you have a multiset that is defined to have both intermediate and full entropy. So by your own definition your "notion" is contradictory and so wrong.

Secondly it has nothing to do with entropy since you have not even defined what "entropy" in the OT is. Whatever the definition is it has nothing to do with actual entropy which is a number and not a symmetry.

Thirdly you do not seem to know what mathematical symmetry actually is. Symmetry is a property of an object - a object that undergoes a transformation is symmetrical if the transformation returns the same object. An object that undergoes a transformation is asymmetrical if the transformation returns the opposite object. You never define what transformations are being applied to the multisets and so you cannot state what symmetry they have.

Fourthly maybe you assume the transformation of the multiset members is some sort of reordering (e.g. swapping the last and first members). But as stated multisets do not have any order. So you are either wrong again or ignorant of the definition of a multiset.

[jsfisher]

[ot]There may be an innocent reason for this....

Yeah, I knew that. I raised only because doron has in the past made more dramatic alterations to other people's posts. He's even been infracted for the practice.

[doronshadmi]

Your original topic is wrong.

Firstly you list a multiset constructed from the number 5 as {3,1,1}. A multiset is a set so it the order of members is not important. Thus the {3,1,1} multiset is the same as the {1,3,1} multiset. You state that
{3,1,1) has "Intermediate entropy". {1,3,1} would have "Full entropy".
Thus you have a multiset that is defined to have both intermediate and full entropy. So by your own definition your "notion" is contradictory and so wrong.

Secondly it has nothing to do with entropy since you have not even defined what "entropy" in the OT is. Whatever the definition is it has nothing to do with actual entropy which is a number and not a symmetry.

Thirdly you do not seem to know what mathematical symmetry actually is. Symmetry is a property of an object - a object that undergoes a transformation is symmetrical if the transformation returns the same object. An object that undergoes a transformation is asymmetrical if the transformation returns the opposite object. You never define what transformations are being applied to the multisets and so you cannot state what symmetry they have.

Fourthly maybe you assume the transformation of the multiset members is some sort of reordering (e.g. swapping the last and first members). But as stated multisets do not have any order. So you are either wrong again or ignorant of the definition of a multiset.
Again, order is not important here.

R set is based on distinct continuous values , and N set is based on distinct values.
Symmetry is not a "superposition of identities". It is the result of a transformation of an object. Asymmetry is not "distinct identities". It is a result of a transformation of an object.

Distinction is important hare (whether it is continuous or not).

A collection of distinct elements (order is not important) has less entropy than a collection of non-distinct elements.

For example: {a,c,b} = {a,b,c} (because order is not important) has less entropy than {a,b,a} = {a,a,b} (where also here, order is not important).

I am talking here about symmetry that is based on the distinction degree of the reseachad object and not about any transformation that returns to the original state of the researched object.

[arthwollipot]

It's like... passing an accident on the road. You can't help but slow down and look. Even though you know you're contributing to the growing gridlock, you can't look away, just in case someone's bleeding all over the road...

[ddt]

Again, order is not important here.



Distinction is important hare (whether is continuous or not).

A collection of distinct elements (order is nor important) has less entropy than a collection of non-distinct elements.

For example: {a,c,b} = {a,b,c} (because order is not important) has less entropy than {a,b,a} = {a,a,b} (where also here, order is not important).
"Collection" is a synonym for set. You seem to use it above as synonym for multiset - muddying the waters again?

And what have furry, long-eared mammals to do with this? (see line 2). Oh wait:

It's like... passing an accident on the road.

Why did the rabbit cross the road?

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[doronshadmi]

"Collection" is a synonym for set. You seem to use it above as synonym for multiset - muddying the waters again?


A set is a collection of distinct elements where order is not important.

I am talking about a collection that its elements are defined by their distinction of each other (distinction is important).

[ddt]

A set is a collection of distinct elements where order is not important.

I am talking about a collection that its elements are defined by their distinction of each other (distinction is important).

I've never seen the word collection being used in that way. I've only seen it used as either a synonym for "set", or as a synonym for "proper set or class" in Set Theory and Category Theory.

Using "collection" as a synonym for multiset serves only to muddy the waters. Do you do that on purpose? Stick to "multiset" and "set", whichever you mean - those are unambiguous terms. Capice?

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[doronshadmi]

I've never seen the word collection being used in that way.


So now you see it.


Since distinction is important, a collection is a general form of both set and multiset.

In that case, the least Entropy is a collection od distinct elements, where the most is a collection of non-distinct elements.

[drkitten]

A set is a collection of distinct elements where order is not important.


Doron, are you a computer programmer? Are you sure you're not confusing the Java Collections Framework with standard math?

On the other hand, I suppose I should be impressed that you managed to come up with a definition, albeit a backwards one (where you define a term with a known meaning in terms of one with an unknown one).

[jsfisher]

So now you see it.


Since distinction is important, a collection is a general form of both set and multiset.


You missed the original point. You are misusing standard terminology again/still. Multi-set is a perfectly fine standard term that covers exactly what you mean.

{1,3} is a multi-set
{1,1,3} is a multi-set
{1,1,1,1,1,1,1,1,1,1,1} is a multi-set

There is no reason for you to misuse another term for this purpose. And, as with all multi-sets, the elements may not be unique, but they are definitely unordered.

[ddt]

I've never seen the word collection being used in that way.


So now you see it.
... used by someone who is almost invariably wrong when it comes to mathematics. Thanks, that's a great help.


Since distinction is important, a collection is a general form of both set and multiset.
:jaw-dropp

The above is no definition of the word "collection". There is no such general form.

I repeat: do not use the word collection. Use "set" or "multiset", whichever is appropriate.

Capice?

To Add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[doronshadmi]

You missed the original point. You are misusing standard terminology again/still. Multi-set is a perfectly fine standard term that covers exactly what you mean.

{1,3} is a multi-set
{1,1,3} is a multi-set
{1,1,1,1,1,1,1,1,1,1,1} is a multi-set

There is no reason for you to misuse another term for this purpose. And, as with all multi-sets, the elements may not be unique, but they are definitely unordered.
No problem.

{1,3} is a multi-set of distinct elements.

{1,1} is a multi-set of non-distinct elements.

In both cases order is not important.

[ddt]

Doron, are you a computer programmer? Are you sure you're not confusing the Java Collections Framework with standard math?

Doron claims to have been a programmer in the Fortran age. No Java though. In the previous thread, he presented pictures of his "Organic Natural Numbers", which had been generated by a Java program, written by someone else. He failed to come up with the source code.

And off-topic, what did the Java designers think when they didn't include such a framework in Java 1.0? C++ STL had been around for a while by then. At least, with generic types in Java 1.5, they're now also up to par with type safety.

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[doronshadmi]

Since order is not important, then any multiset's elements have to be defined in parallel (not by step-by-step serial research).

It is easier to get it by using a parallel view.

[jsfisher]

No problem.


Great! We have a common term. Now, would you be willing to provide a definition for what you mean by entropy?

Is it a numerical value? How is it calculated? What are the entropies of {} and of {1}?

Is it, instead, a complete (or partial) ordering? Is the entropy of {1,1,1} more or less than the entropy of {1,1}? How does {1,1,1,1,1,1,1,1,1,1,1} compare to {1,8,1}?

[ddt]

In that case, the least Entropy is a collection od distinct elements, where the most is a collection of non-distinct elements.

We're playing the "edit but do not tell so" game again? Don't you ever lose those annoying antics?

Could you rephrase this sentence in an understandable way?

And without the use of the word collection!

[ddt]

{1,3} is a multi-set of distinct elements.

{1,1} is a multi-set of non-distinct elements.
In the name of Thor (*), could we use another notation for multisets? The use of braces might be standard, but it is confusing as hell when we discuss both sets and multisets at the same time - especially with easily-confused and easily-confusing Doron in the discussion.

Someone on page 1 used square brackets [ ] for multisets. I suggest we stick with that.


In both cases order is not important.
You've said that now so many times that I'm inclined to believe you actually got that.

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

ETA: forgot about the damn footnote: (*) it is Thursday, after all. :)

[doronshadmi]

Great! We have a common term. Now, would you be willing to provide a definition for what you mean by entropy?

Is it a numerical value? How is it calculated? What are the entropies of {} and of {1}?

Is it, instead, a complete (or partial) ordering? Is the entropy of {1,1,1} more or less than the entropy of {1,1}? How does {1,1,1,1,1,1,1,1,1,1,1} compare to {1,8,1}?

Each multi-set defines its own entropy according the distinction of its elements and its cardinality (the number of its elements).

{} has the highest entropy because nothing is distinct.

{1} has no entropy because anything is distinct.

{1,2} or {1,3} have no entropy.

{1,1} has an entropy and {1,1,1} has more entropy than {1,1}.

{2,2,2} has the same entropy as {0,0,0} etc...

The the size of difference between the elements is not important.

[ddt]

Since order is not important, then any multiset's elements have to be defined in parallel (not by step-by-step serial research).

It is easier to get it by using a parallel view.

:jaw-dropp :eye-poppi :boggled: :eek: :covereyes

Define the elements of a multiset? What are you smoking?

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[ddt]

Each multi-set defines its own entropy according the distinction of its elements and its cardinality (the number of its elements).
No, the entropy is defined for each multiset. Not the other way round.


{1} has no entropy because anything is distinct.

{1,2} or {1,3} have no entropy

No entropy? So 'entropy' is not defined for each multiset? You certainly mean "entropy zero" or "entropy 0".


{1,1} has an entropy and {1,1,1} has more entropy than {1,1}.

{2,2,2} has the same entropy as {0,0,0} etc...

ETA(2):
In the OP, you say of both [1,1] and [1,1,1] they have "full entropy", suggesting their entropy values are the same.

So, are you absolutely sure now your idea of entropy is as stated above? Do you solemnly vow never to change that opinion again during this thread?


Have you looked at posts #75 and #82?

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[drkitten]

Each multi-set defines its own entropy according the distinction of its elements and its cardinality (the number of its elements).

No, as ddt pointed out, there is one definition for entropy -- entropy is defined for each multi-set.

You still haven't defined it, though. Remember that entropy is a number in both thermodynamics and information theory; it's not sufficient to simply say "x has more entropy than y."


{} has the highest entropy because nothing is distinct.

What does this mean? Does this mean that {} has infinite entropy?


{1} has no entropy because anything is distinct.

Again, as ddt pointed out, every multiset has an entropy. Do you mean {1} has entropy zero (0)?



{1,2} or {1,3} have no entropy.

Ditto.


{1,1} has an entropy and {1,1,1} has more entropy than {1,1}.

Well, of course {1,1} has an entropy. Every multiset has an entropy if any of them do.

But remember, entropy is a number. Consider the following sequence of multisets:
{1},{1,1},{1,1,1},{1,1,1,1},...

Which of those is the first multiset that has entropy >= 1.0? Which is the first one with entropy >= 10.0?

You still haven't defined what the "entropy" is that you're working with, despite two attempts by ddt to offer definitions.

And under the post #75 definition, for example, the sets {1,1} and {1,1,1,1} have identical entropy.

[nathan]

The the size of difference between the elements is not important.

So, it's an ordering. Is it partial or total? Given two multisets A and B, what is the procedure for ordering them by Entropy?

[jsfisher]

Each multi-set defines its own entropy according the distinction of its elements and its cardinality (the number of its elements).

{} has the highest entropy because nothing is distinct.

{1} has no entropy because anything is distinct.

{1,2} or {1,3} have no entropy.

{1,1} has an entropy and {1,1,1} has more entropy than {1,1}.

{2,2,2} has the same entropy as {0,0,0} etc...

The the size of difference between the elements is not important.


You seem to be avoiding cases like {1,3,1}. Why is that?

Does {1,1,1,1,1,1,1,1,1,1,1,1,3} have more or less entropy than {1,1,1,1}?


And how does one determine the entropy of a given multi-set? You need to clarify this.

[ddt]

What does this mean? Does this mean that {} has infinite entropy?

Again, as ddt pointed out, every multiset has an entropy. Do you mean {1} has entropy zero (0)?

Well, of course {1,1} has an entropy. Every multiset has an entropy if any of them do.

But remember, entropy is a number. Consider the following sequence of multisets:
{1},{1,1},{1,1,1},{1,1,1,1},...

You seem to be avoiding cases like {1,3,1}. Why is that?

Does {1,1,1,1,1,1,1,1,1,1,1,1,3} have more or less entropy than {1,1,1,1}?
Please, let's use the [x, y, z] notation. Or something else, but not the same notation as sets. Before you know, Doron uses {} again for sets without saying so and we spend another fruitless 100 or so posts to clarify that.


And under the post #75 definition, for example, the sets {1,1} and {1,1,1,1} have identical entropy.
Indeed. But the one from post #82 (without the -1) gives them different values (1/2 resp. 1/24).

[TMiguel]

Let me give you an example, of what we want.
Consider “F(s)” a function that counts the distinct number of elements whit in a set S.
Ex. “F({1,2,3,4})=4” (4 different entities), “F({1,2,2,4})=3” (because the entity 2 is repeated then it only counts has one)
And in your definition of entropy of a partition “A(n,k)” (partition k of the number n) is equal to “#A(n,k)-F(A(n,k))”.

This is an example of a definition, we now have a way to quantify it, attribute a relation of order, bash it and finally kill it.

If you can’t come up whit something like this, I suggest you stop wasting our time.

[Reality Check]

Doron: When you talk about Symmetry and multisets what are the transformations that you are calling the multisets symmetrical in respect to?
Please give examples, e.g. take {3,1,1} and list the transformations that you used to determine its symmetry.

[doronshadmi]

Let me give you an example, of what we want.
Consider “F(s)” a function that counts the distinct number of elements whit in a set S.
Ex. “F({1,2,3,4})=4” (4 different entities), “F({1,2,2,4})=3” (because the entity 2 is repeated then it only counts has one)
And in your definition of entropy of a partition “A(n,k)” (partition k of the number n) is equal to “#A(n,k)-F(A(n,k))”.

This is an example of a definition, we now have a way to quantify it, attribute a relation of order, bash it and finally kill it.

If you can’t come up whit something like this, I suggest you stop wasting our time.

We have multi-sets and we use Distinction as their first-order property.

It means that if all we care is to define each multi-set by a distinct value, then we are actually closed under the particular case where our researched objects are translated to another multi-set of distinct elements.

In other words non-distinct results are perfectly valid and do not have to be translated to some distinct result, because by this limitation Distinction cannot be considered as a first-order property.

TMiguel uses, for example, this function:

F({1,2,3,4})=4 , F({1,2,2,4})=3 , etc …

By this method he simply wants to reduce multi-sets to their distinct case, but the whole idea here is to save the non-distinct case of 2,2 because Distinction is a first-order property of multi-sets.


Again: {1,1,1} is non-distinct and {1,1,1,1} is more non-distinct if they are compared to each other.

We can get some distinct result of this comparison, which is nothing but some particular case of clearly distinct result.

In other words, if Distinction is a first-order property of the researched framework, then it is not limited to any particular case of Distinction.


If Distinction is a first-order property of our framework, then our framework is not limited to any particular case of it, and each researched case can be both some particular case and general case of the entire framework.

Here is a diagram of Distinction:

http://www.geocities.com/complementarytheory/icmfig4.jpg

As can be seen in this diagram, we are using the particular case of clearly distinct identification as a general viewpoint of the entire system, but any other case which is not a distinct viewpoint, can be used as a general viewpoint of the entire system as well.

[Reality Check]

Multi-sets do not have Distinction as their first-order property. That is not in their definition.
P.S. Please give a list of the second-order properties of multi sets. What about the third-order properties of multi-sets?

Have you thought about the fact that multisets do not have ordered members, have no Symmetry and so they all have minimum Entropy?

[ddt]

We have multi-sets and we use Distinction as their first-order property.

Now stop the crap and keep to the topic. You wanted a definition of entropy. You're not able to come up with one yourself. Other posters have come up with three possible definitions: two from me (posts #75 and #82) and one from TMiguel (post #107).

Now would you show the decency to comment on those?

And stop the crap with your nonsensical beating about the bush. And stop with those silly pictures.

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[doronshadmi]

Multi-sets do not have Distinction as their first-order property. That is not in their definition.
P.S. Please give a list of the second-order properties of multi sets. What about the third-order properties of multi-sets?

Have you thought about the fact that multisets do not have ordered members, have no Symmetry and so they all have minimum Entropy?
Yes they have, for example:

{1,2,3} = {3,2,1} is a multi-set of distinct members (order is not important).

{1,1,2} = {1,2,1} is a multiset of intermediate-distinct members (order is not important).

{1,1,1} = {1,1,1} is a multiset of non-distinct members (order is not important).

[doronshadmi]

Now stop the crap and keep to the topic. You wanted a definition of entropy. You're not able to come up with one yourself. Other posters have come up with three possible definitions: two from me (posts #75 and #82) and one from TMiguel (post #107).

Now would you show the decency to comment on those?

And stop the crap with your nonsensical beating about the bush. And stop with those silly pictures.

#82:

Permutation is not the case since order is not important.

#75:

Probability is not the case since your result is some distinct value (some particular case of Distinction).

[Reality Check]

Yes they have, for example:

{1,2,3} = {3,2,1} is a multi-set of distinct members (order is not important).

{1,1,2} = {1,2,1} is a multiset of intermediate-distinct members (order is not important).

{1,1,1} = {1,1,1} is a multiset of non-distinct members (order is not important).
I am glad you agree - order is not important and so all multisets have the same Symmetry. Thus all multisets have the same Entropy by your very own definition. My guess is this is minimum Entropy.

[doronshadmi]

I am glad you agree - order is not important and so all multisets have the same Symmetry. Thus all multisets have the same Entropy by your very own definition. My guess is this is minimum Entropy.

No.

{a,a,b} has the same entropy as {a,b,a} (order is nor important).

{a,a,b} has the same entropy as {a,c,b} (order is nor important).

{a,b,a} does not have the same entropy as {a,b,c} (and again order is not important but distinction is important, in the case of entropy).

[Reality Check]

No.

{a,a,b} has the same entropy as {a,b,a} (order is nor important).

{a,a,b} has the same entropy as {a,c,b} (order is nor important).

{a,b,a} does not have the same entropy as {a,b,c} (and again order is not important but distinction is important, in the case of entropy).
Distinction is not important in the usual definitions of entropy: Please provide a citation.

Also what is the difference between distinction and order?

ETA: This post imples that you now have a definition for entropy that gives numerical values so that you can state that "{a,b,a} does not have the same entropy as {a,b,c}". Please give that definition.

[ddt]

#82:

Permutation is not the case since order is not important.

#75:

Probability is not the case since your result is some distinct value (some particular case of Distinction).

Epic fail. You obviously didn't understand either of them. I estimate you're the only poster in this thread - I guess all other posters not only understand both of them, but could also explain them.

Go back to start, you don't collect $200.

As for your math: go back to grade 1 and study math from that.

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[ddt]

No.

{a,a,b} has the same entropy as {a,b,a} (order is nor important).

{a,a,b} has the same entropy as {a,c,b} (order is nor important).

{a,b,a} does not have the same entropy as {a,b,c} (and again order is not important but distinction is important, in the case of entropy).

There's a hole in your reasoning here you can drive a truck through.

Order is not important - you keep repeating that - to be more precise: elements of a multiset have no order.

So the entropy of [a,a,b] is the same as that of [a,b,a], since they are the same multiset.

And the entropy of [a,b,c] is the same as that of [a,c,b], since they are the same multiset too.

Do you see the contradiction with what you wrote above?

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[jsfisher]

Yes they have, for example:

{1,2,3} = {3,2,1} is a multi-set of distinct members (order is not important).

{1,1,2} = {1,2,1} is a multiset of intermediate-distinct members (order is not important).

{1,1,1} = {1,1,1} is a multiset of non-distinct members (order is not important).


Please stop saying "order is not important" every time. We are talking about multi-sets, so of course order is not important. There is no reason to belabor the obvious.


Now, and I will adopt ddt's recommendation for multi-set notation, please note that [1] is a multiset of non-distinct members. Every element of [1] is exactly the same as every other member. So, why did you claim [1] had no (presumably meaning 0) entropy?

You have also said [1,1,1] has more entropy than [1,1]. How would you quantify that?

How does [1,1,1,3] compare to [1,1]? Does it have more or less entropy?

Does [1] have more, less, or the same entropy as [1,2,3]?

[ddt]

Distinction is not important in the usual definitions of entropy: Please provide a citation.

Also what is the difference between distinction and order?
I have the impression that "distinction" in Doron-speak here means: a measure of the number of distinct elements in a multiset. At least, with that, doron's posts make a little sense to me. In fact, it's a synonym for his earlier term "entropy". This is SOP for Doron, to introduce multiple words with the same meaning. Or, tomorrow, the intended meaning of either of the words may be different. That's also SOP for Doron.


ETA: This post imples that you now have a definition for entropy that gives numerical values so that you can state that "{a,b,a} does not have the same entropy as {a,b,c}". Please give that definition.
Doron is too little versed in mathematics to even understand the simple possible definitions given by others. Don't hold your breath he can come up with a definition of his own.

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[doronshadmi]

oppsss..

[doronshadmi]

There's a hole in your reasoning here you can drive a truck through.

Order is not important - you keep repeating that - to be more precise: elements of a multiset have no order.

So the entropy of [a,a,b] is the same as that of [a,b,a], since they are the same multiset.

And the entropy of [a,b,c] is the same as that of [a,c,b], since they are the same multiset too.

Do you see the contradiction with what you wrote above?

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

Thank you ddt,

It was a typo.

The right one is :

{a,a,b} has the same entropy as {a,b,a} (order is nor important).

{a,b,c} has the same entropy as {a,c,b} (order is nor important).

{a,b,a} does not have the same entropy as {a,b,c} (and again order is not important but distinction is important, in the case of entropy).

As for Set and Multi-set please look at this ( http://mathworld.wolfram.com/Set.html ):

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset).

[ddt]

Thank you ddt,

It was a typo.
It's more than a typo. You've done this before - frequently. It signifies that either you don't think your posts through before you post, or your grasp of the matter is so low you very easily make such mistakes.

Or a combination of both.



The right one is :

{a,a,b} has the same entropy as {a,b,a} (order is not important).

{a,b,c} has the same entropy as {a,c,b} (order is not important).
That's belabouring the obvious. They're the same multiset!


{a,b,a} does not have the same entropy as {a,b,c} (and again order is not important but distinction is important, in the case of entropy).
And you carefully avoid saying which one is higher.

Drop the "distinction" word. It does not mean what you think it means.

Care to really go into the proposed definitions in posts #75 and #82? If you can't come up with an insightful reaction within 24 hours, it only proves you're out of your league here.

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[ddt]

As for Set and Multi-set please look at this ( http://mathworld.wolfram.com/Set.html ):

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset).

You're "forgetting" again to indicate your edits?

And so what? It only proves my point that the word collection is too vague here to use. It could refer to either a set or a multiset. You've used both in this thread. Sooner or later, you are going to abuse that - you've done that before.

ETA: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[nathan]

Bump


The the size of difference [of the Entropy] between the elements is not important.
So, it's an ordering. Is it partial or total? Given two multisets A and B, what is the procedure for ordering them by Entropy?

Doron, you've had three proposals for an Entropy formula, which you've rejected. You've said the value of the entropy isn't important, and the magnitude of the difference in Entropy between two multisets is not important. That leaves only the sign of the difference, hence it is an ordering.

How about coming up with that ordering? I mean as an algorithm (or set of functions, if you prefer to think of it that way). Do you understand the difference between partial and total ordering?

Do not keep posting examples -- those don't allow one to infer your meaning in a larger set of multisets. Proof of that is trivial, I refer you to the three alternative Entropy formulas that are consistent with all your examples, but you reject.

[nathan]

{a,a,b} has the same entropy as {a,b,a} (order is nor important).

{a,b,c} has the same entropy as {a,c,b} (order is nor important).

That you keep reiterating that order is not important, even though multisets (and sets) are unordered, leads me to suspect you do not know what a multiset (or set) is. So, let's start with some basic questions:

Do you agree or disagree that [a,a,b] and [a,b,a] are the same multiset?

Do you agree or disagree that [a,a,b] and [a,b,a] are different representations of the same multiset?

[TMiguel]

Lets try this one.
Being “A(n,k)” a partition k of a number n
Being F(s) the accounting function for the distinct (none repeated) elements within a multi-set
If F(A(n,k))=1 then the group is said to be un-distinct (in your case max entropy)
Else If #A(n,k)-F(A(n,k)=0 is said to be fully-distinct (in your case no entropy)
Else it is said to be semi-distinct (in your case intermediate entropy)

I really shouldn’t be giving you this apple since you already failed to base your “mathematical construction” without it.

[doronshadmi]

And you carefully avoid saying which one is higher.

As I already said in my first post, {a,b,a} has more entropy than {a,b,c} since {a,b,a} is less distinct.


The order of each multi-set is not important.

Distiction as a first-order property, is important.

[doronshadmi]

Lets try this one.
Being “A(n,k)” a partition k of a number n
Being F(s) the accounting function for the distinct (none repeated) elements within a multi-set
If F(A(n,k))=1 then the group is said to be un-distinct (in your case max entropy)
Else If #A(n,k)-F(A(n,k)=0 is said to be fully-distinct (in your case no entropy)
Else it is said to be semi-distinct (in your case intermediate entropy)

I really shouldn’t be giving you this apple since you already failed to base your “mathematical construction” without it.

You still try to reduce Distinction to the particular case of distinct results.

For example:

a = 0

b = 1

a < c < b

and we get {a,b,c} that is some case with no entropy.

Again Distinction is a first-order property of multi-sets, and as a first-order property it must not be limited to any particular case of Distinction.

{a,b,c} is not the only possible result, if Distinction is a first-order property of what is called multi-set.

[doronshadmi]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.

[TMiguel]

You still try to reduce Distinction to the particular case of distinct results.

For example:

a = 0

b = 1

a < c < b

and we get {a,b,c} that is some case with no entropy.

Again Distinction is a first-order property of multi-sets, and as a first-order property it must not be limited to any particular case of Distinction.

{a,b,c} is not the only possible result, if Distinction is a first-order property of what is called multi-set.

It is how you tell the difference between the things you are trying to discriminate YOU R#%$rd, if you can not tell the difference between what is what, then what is the point of all of this?

A Stupidity certificate coming out, make your test right here: http://nonoba.com/thegamehomepage/the-stupidity-test

[nathan]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.

What is this 'Distinction' property? Can you provide a definition for it?

I see you're avoiding answering my, somewhat fundamental, pair of questions about multisets. Your answers might clarify what you mean.

[jsfisher]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.


So, is this going to be another classic doron thread in which you misuse standard terminology without defining what you actually mean (e.g. entropy), invent new terms without defining what you actually mean (e.g. distinction), attempt to distract us with irrelevant diagrams, invert meaning (each multiset defines its entropy), belabor the trivial (order is unimportant), remain oblivious to contradiction and inconsistencies (entropy of [4] versus [] or [4,4]), ignore questions, and then blame everyone else for not "getting" your idea?

[Reality Check]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.
So long as you cannot define Distinction as multi-set's first-order property, you do not have an idea.

Perhaps you can give us a list of a multi-set's first-order properties?

[Reality Check]

So, is this going to be another classic doron thread in which you misuse standard terminology without defining what you actually mean (e.g. entropy), invent new terms without defining what you actually mean (e.g. distinction), attempt to distract us with irrelevant diagrams, invert meaning (each multiset defines its entropy), belabor the trivial (order is unimportant), remain oblivious to contradiction and inconsistencies (entropy of [4] versus [] or [4,4]), ignore questions, and then blame everyone else for not "getting" your idea?

You missed out that he has yet to define what a "first-order property" of anything is. And that he will blame everyone else for not "getting" his undefined term "first-order property".

[drkitten]

Bump
Doron, you've had three proposals for an Entropy formula, which you've rejected. You've said the value of the entropy isn't important, and the magnitude of the difference in Entropy between two multisets is not important.

I don't think she said that.

I think she said that the magnitude of the difference between two elements is unimportant, as long as they differ. I.e. the quasi-entropy of [2,1,1]* is the same as the quasi-entropy of [5,1,1] or of [Coke, Pepsi, Pepsi] as long as we're dealing with a multiset with one singleton element and one pair.

Similarly, I don't remember her saying that the value of the quasi-entropy isn't important. She's merely demonstrated a complete inability (or more charitably unwillingness) to quantify her notion of quasi-entropy so that we can actually calculate that value.


(*) See, DDT, I'm using your multiset notation. Happy?

[doronshadmi]

It is how you tell the difference between the things you are trying to discriminate YOU R#%$rd, if you can not tell the difference between what is what, then what is the point of all of this?

A Stupidity certificate coming out, make your test right here: http://nonoba.com/thegamehomepage/the-stupidity-test
Distinction is the relation between the certain and the uncertain.

The certain and the uncertain complement each other.

It means that they are not defined in terms of the other.

For example, if the uncertain is darkness, you cannot use light (the certain) in order to research the darkness (the uncertain) because by using light you change the researched subject (darkness, in this case).

The idea is to define the common property that stands at the basis of both darkness and light, and then you are able to get their relations and each one of them without changing them by your research.

By using this knowledge we can develop new methods in order to improve the relations between complement states (any cardinal of complement states can be found, it does not matter) in addition to their property to contradict (prevent) each other.

Multi-set is the result of things that simultaneously complement AND prevent each other, and the best knowledge is based on the non-trivial relation between the certain and the uncertain.

Please look again at ONN5 represented by Penrose tiling:

http://www.geocities.com/complementarytheory/Penrose.jpg

ONN5 is a one thing that simultaneously defined as several states of Distinction.

Please let your mind to get the perception of this distinction.

You can look into each state and directly get how your perception spontaneously defines its distinction (it can clearly be seen if you compare between the first top-left case (that has maximum entropy) and the last bot-right case (that has minimum entropy)).

But please do not forget that this comparison is nothing but the particular case of clear distinction.

The current paradigm of the mathamatical science is limited to clear distinction as its first-order property.

By the the organic paradigm, Distinction is itsef a first-order property of the mathematical science, and it is not limited to any particular case of it.

[drkitten]

Distinction is the relation between the certain and the uncertain.

Well, that's another great doron non-definition.

Distinction (an undefined term) is the relation (a term with a definition, but probably inappropriate here) between the certain (another undefined term) and the uncertain (another undefined term).

Interpret this in light of the assertion that distinction (still undefined) is a first-order property (another undefined term) of a multiset.

[Reality Check]

jsfisher was right: Here are the pretty pictures (irrelevant diagrams), etc. right on schedule!

ETA: And he is back to his non-mathematical organic paradigm.
Plus he thinks mathematics is all about perception (how you see things) not actual mathematics.

It looks like this is another doronshadmi thread heading for the Religion and Philosophy area. One of these days he really should learn the difference between Philosophy and Mathematics.

[jsfisher]

Please look again at ONN5 represented by Penrose tiling:


As will come as no surprise to most, doron has now demonstrated another thing of which he has no understanding, Penrose tiling in this case.

[Worm]

I had high hopes....but, as expected, my head now hurts from trying to unscramble the psuedo-scientific babble that is prevailing.

I should know better, but it's simply too hard to look away.

[doronshadmi]

The aim of the organic paradigm of the mathematical science is to understand what enables to define things, where distinct definitions is only a particular case of Distinction (if Distinction is a first-order property of the mathematical science).

[jsfisher]

The aim of the organic paradigm of the mathematical science is to understand what enables to define things, where distinct definitions is only a particular case of Distinction (if Distinction is a first-order property of the mathematical science).


Doron,
That is not the topic of this thread. If you now drift into your organic non-mathematics non-science, then expect this thread to find its way to the Philosophy forum where you will likely abandon it.

[TMiguel]

Distinction is the relation between the certain and the uncertain.

The certain and the uncertain complement each other.

It means that they are not defined in terms of the other.

For example, if the uncertain is darkness, you cannot use light (the certain) in order to research the darkness (the uncertain) because by using light you change the researched subject (darkness, in this case).

The idea is to define the common property that stands at the basis of both darkness and light, and then you are able to get their relations and each one of them without changing them by your research.

By using this knowledge we can develop new methods in order to improve the relations between complement states (any cardinal of complement states can be found, it does not matter) in addition to their property to contradict (prevent) each other.

Multi-set is the result of things that simultaneously complement AND prevent each other, and the best knowledge is based on the non-trivial relation between the certain and the uncertain.

Please look again at ONN5 represented by Penrose tiling:

http://www.geocities.com/complementarytheory/Penrose.jpg

ONN5 is a one thing that simultaneously defined as several states of Distinction.

Please let your mind to get the perception of this distinction.

You can look into each state and directly get how your perception spontaneously defines its distinction (it can clearly be seen if you compare between the first top-left case (that has maximum entropy) and the last bot-right case (that has minimum entropy)).

But please do not forget that this comparison is nothing but the particular case of clear distinction.

The current paradigm of the mathamatical science is limited to clear distinction as its first-order property.

By the the organic paradigm, Distinction is itsef a first-order property of the mathematical science, and it is not limited to any particular case of it.

Let’s make something clear.

Distinction is the ability to point out the property that makes 2 different elements different.

If there is no distinction (can’t tell no difference) between {1,2,3} and {2,2,2}
Why the heck should you say that {1,2,3} has no entropy and that {2,2,2} has full entropy the same has {3,3}, WHEN YOU CAN’T TELL THE DIFFERENCE?

WHAT MAKES THE DIFFERENCE, AND HOW DO YOU CLASSIFIE THOSE DIFFERENCES!!!!!!

[doronshadmi]

opps..

[doronshadmi]

WHAT MAKES THE DIFFERENCE, AND HOW DO YOU CLASSIFIE THOSE DIFFERENCES!!!!!!

The complementation between the common AND the difference.

No one of them alone is the general state of the mathematical science.

Again, knowing the difference is nothing but some particular case of the mathematical science, where entropy is both inherent state of some multi-set, and a distinct result based on comparing between different multisets (which is the particular case of clear distinction).

[TMiguel]

The complementation between the common AND the different.

No one of them alone is the general state of the mathematical science.

To be able to tell the difference is WHY WE HAVE MATH. To tell what are odds and evens, what properties makes them different, what do they implicate, etc, etc, etc.
To define your terms, IS THE FIRST STEP IN MATH.

And sense you are missing a quite fundamental element, your work is COMPLETELY USELESS.

Get it trough your head.

[drkitten]

The complementation between the common AND the difference.

Three more undefined terms.


Again, knowing the difference is nothing but some particular case of the mathematical science, where entropy is both inherent state of some multi-set, and a distinct result based on comparing between different multisets (which is the particular case of clear distinction).

And three more undefined terms.

If I save up enough of these, can I trade them in for green stamps or something?

[jsfisher]

The complementation between the common AND the difference.

No one of them alone is the general state of the mathematical science.

Again, knowing the difference is nothing but some particular case of the mathematical science, where entropy is both inherent state of some multi-set, and a distinct result based on comparing between different multisets (which is the particular case of clear distinction).


Doron,
Your post is off topic. You should expect many people will be reporting your posts as off-topic to the moderators.

Please return to the topic you, yourself, posed first in this thread. The topic has to do with a mathematical consideration of an Information Theory-like concept of entropy and its relationship to prime numbers.

A very good place to return to the topic at hand would be with the definition for your version of the term entropy. So far, you have presented examples to show it to be a partial ordering. You need to flesh out the rules for that ordering.

[doronshadmi]

To be able to tell the difference is WHY WE HAVE MATH.

Here is some example:

Let us say that we compare things as long as they are between "{" and "}"

{a,a,a} has an entropy because no difference can be found between the members of this multi-set.

{a,b,c} has no entropy because a difference can be found between the members of this multi-set.

{{a,a,a},{a,b,c}} has no entropy because a difference can be found between the members of this multi-set.

So as you see, to know the difference is the particular case of no entropy, where Mathematics is not any of its particular cases.

[drkitten]

Here is some example:

Let us say that we compare things as long as they are between "{" and "}"

{a,a,a} has an entropy because no difference can be found between the members of this multi-set.

{a,b,c} has no entropy because a difference can be found between the members of this multi-set.

You still haven't learned the difference between "no entropy" and "entropy zero," have you, despite many repetitions.

Entropy is a NUMBER, not just a property. (Except possibly in your framework, where it may be a partial ordering, but it's hard to tell because you still haven't given us a definition of entropy in your framework. It may be a partial order, or it may be complete happy horse manure. I'm now taking bets on which.)

[nathan]

I don't think she said that.

I think she said that the magnitude of the difference between two elements is unimportant, as long as they differ. I.e. the quasi-entropy of [2,1,1]* is the same as the quasi-entropy of [5,1,1] or of [Coke, Pepsi, Pepsi] as long as we're dealing with a multiset with one singleton element and one pair.

Similarly, I don't remember her saying that the value of the quasi-entropy isn't important. She's merely demonstrated a complete inability (or more charitably unwillingness) to quantify her notion of quasi-entropy so that we can actually calculate that value.


(*) See, DDT, I'm using your multiset notation. Happy?

Heh, I don't know -- that's why I'm asking Doron. I't's unwise to speculate what Doron means, beyond being confused :)

Btw Doron's a he, not a she, inspite of what one might conclude from the name. (DDT's provided conclusive evidence Doron's some manager at Tahal, some Israeli construction concern.)

[nathan]

As will come as no surprise to most, doron has now demonstrated another thing of which he has no understanding, Penrose tiling in this case.

We bow before your predictive power!

[nathan]

That you keep reiterating that order is not important, even though multisets (and sets) are unordered, leads me to suspect you do not know what a multiset (or set) is. So, let's start with some basic questions:

Do you agree or disagree that [a,a,b] and [a,b,a] are the same multiset?

Do you agree or disagree that [a,a,b] and [a,b,a] are different representations of the same multiset?

You've not responded to these questions. Do you not know what a multiset is?

[ddt]

Here is some example:
You're mostly repeating examples you already gave.

What about commenting with insight on the three entropy functions proposed in this thread?



Let us say that we compare things as long as they are between "{" and "}"
I see another "a set is the union of its members" trainwreck coming on.

Please also use square brackets [ ] for multisets.


{a,a,a} has an entropy because no difference can be found between the members of this multi-set.

{a,b,c} has no entropy because a difference can be found between the members of this multi-set.
Not "no entropy" - entropy 0.


{{a,a,a},{a,b,c}} has no entropy because a difference can be found between the members of this multi-set.
What's different about this than about the multiset [Pepsi, Coke] ? Both multisets have two members that are different. Whether those members are multisets themselves is irrelevant. You want to make matters more complicated when you already have no grasp of what you're dealing with now? Sick.


So as you see, to know the difference is the particular case of no entropy, where Mathematics is not any of its particular cases.
Is that English?

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[jsfisher]

Here is some example:

Let us say that we compare things as long as they are between "{" and "}"

{a,a,a} has an entropy because no difference can be found between the members of this multi-set.

{a,b,c} has no entropy because a difference can be found between the members of this multi-set.

{{a,a,a},{a,b,c}} has no entropy because a difference can be found between the members of this multi-set.

So as you see, to know the difference is the particular case of no entropy, where Mathematics is not any of its particular cases.


Ok, so, according to your (ab-)use of the term entropy, it is a property that a multi-set either has or doesn't have. You continue to skirt examples like [1,1,2], but by your description, above, [1,1,2] has "no entropy" because a difference can be found between the members.

By the way, your description contradicts previous examples. In particular, [1] has "an entropy".

So, where are we? Well, you now have provided some meaning to your non-standard use of the term entropy. Unfortunately, in renders meaningless just about all of your Notion #1.

That doesn't leave you with very much to discuss in this thread.

[ddt]

Distiction as a first-order property, is important.

Refrain from using any more terms you don't understand or define. "Distinction" and "first-order property" are off-limits for you now. Otherwise, you might find a herring head on your pillow. (*)

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

(*) see my custom title.

[ddt]

For example:

a = 0

b = 1

a < c < b

and we get {a,b,c} that is some case with no entropy.
Why do you re-introduce some kind of order? For all we know, there is no ordering on a, b, and c. We only can compare them for (in)equality. This example is totally irrelevant. And, we do get it now.

Where's your definition of entropy? Any of the proposed ones to your liking?

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[ddt]

As long as you ignore Distinction as multi-set's first-order property, you do not get my idea.

What idea? The OP? Despite all help offered we've come no inch closer to anything resembling real math. Why would that be?

Oh yes, you profoundly misunderstood the two proposed definitions in posts #75 and #82. You didn't comment on TMiguel's one. Now, who here doesn't get basic math?

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[TMiguel]

Here is some example:

Let us say that we compare things as long as they are between "{" and "}"
This is not useful at all.


{a,a,a} has an entropy because no difference can be found between the members of this multi-set.
Ok?

{a,b,c} has no entropy because a difference can be found between the members of this multi-set.
What difference? Don’t answer that, because it is obvious to see what it is you failed to mention (which is they have different elements, and not there is a difference), but we are getting somewhere.

So as you see, to know the difference is the particular case of no entropy, where Mathematics is not any of its particular cases.
Evens are different from odds, that has nothing to whit entropy.

Before:

{x} = Full entropy
{x} = Intermediate entropy
{x} = No entropy

You mentioned 3 different states, you only explained (very badly) 2.

Now how do you express that mathematically?
Let me give you a hint:
Lets try this one.
Being “A(n,k)” a partition k of a number n
Being F(s) the accounting function for the distinct (none repeated) elements within a multi-set
If F(A(n,k))=1 then the group is said to be un-distinct (in your case max entropy)
Else If #A(n,k)-F(A(n,k)=0 is said to be fully-distinct (in your case no entropy)
Else it is said to be semi-distinct (in your case intermediate entropy)

[drkitten]

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

Oh, for the love of Freya -- stop bludgeoning Doron with this question. Obviously he/she/it is neither going to justify it or explain it.

[ddt]

(*) See, DDT, I'm using your multiset notation. Happy?
I can't take credit for that; it was RealityCheck in post #36 who proposed that. But good to see it is adopted, it will be helpful later on. When only Doron adopts it too...

Likewise, you should also get credit, by laying the groundwork with your references to Shannon, for "my" entropy definition in post #75.


Btw Doron's a he, not a she, inspite of what one might conclude from the name. (DDT's provided conclusive evidence Doron's some manager at Tahal, some Israeli construction concern.)
Not really conclusive - everyone can lie on the internet, after all. But Doron has mentioned before - on IIDB - that he is a CAD manager at Tahal. Doron has also said he was previously a Fortran programmer. If the level of reasoning Doron here employs is indicative of the general level of the employees at Tahal, I'm not surprised anymore by the enormous water leakages from the Mountain Aquifer that runs through Israel and the West Bank.

But if you want conclusive evidence that Doron works at Tahal, you could just drop a line to the Tahal HR department, not?

[ddt]

http://www.geocities.com/complementarytheory/Penrose.jpg


So how did you make that picture? Did you draw it by hand, or was it generated by a program? Could you provide the source of the program?

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[ddt]

Oh, for the love of Freya -- stop bludgeoning Doron with this question. Obviously he/she/it is neither going to justify it or explain it.

Did I set another trend here with which god to invoke? :). I just ask Doron to retract the statements. That's not too much to ask, methinks. Or should I put it in Latin: "ceterum censeo ..." ? ;)

[doronshadmi]

Ok, so, according to your (ab-)use of the term entropy, it is a property that a multi-set either has or doesn't have. You continue to skirt examples like [1,1,2], but by your description, above, [1,1,2] has "no entropy" because a difference can be found between the members.
No it has a partial entropy.

By the way, your description contradicts previous examples. In particular, [1] has "an entropy".

Worng. Please look again at http://forums.randi.org/showpost.php?p=4090844&postcount=100 .

So, where are we? Well, you now have provided some meaning to your non-standard use of the term entropy. Unfortunately, in renders meaningless just about all of your Notion #1.

That doesn't leave you with very much to discuss in this thread.

You are running too fast and miss what you read.

[doronshadmi]

You didn't comment on TMiguel's one.
http://forums.randi.org/showpost.php?p=4093992&postcount=129

[doronshadmi]

So how did you make that picture? Did you draw it by hand,


Yes I made it by hand.:)

[ddt]

You didn't comment on TMiguel's one.

http://forums.randi.org/showpost.php?p=4093992&postcount=129

But you didn't comment on his original proposal. And the post you referred to shows again miscomprehension. Ah well, nothing really changes.

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[doronshadmi]

Why do you re-introduce some kind of order?

Order is not important here but the difference between b,a and c is important in this example.

[jsfisher]

No it has a partial entropy.

That isn't what you described. If you don't like the conclusion, correct the explanation.

Worng. Please look again at http://forums.randi.org/showpost.php?p=4090844&postcount=100 .

That isn't what you described. If you don't like the conclusion, correct the explanation.

You are running too fast and miss what you read.

Nope. If you don't like the conclusion, correct the explanation.

This should be simple, doron. Just tell us, precisely, what you mean by entropy - no handwaving, no vague descriptions, no selective examples, just the basic concise and precise meaning.

[jsfisher]

So how did you make that picture? Did you draw it by hand, or was it generated by a program? Could you provide the source of the program?

Yes I made it by hand.:)


It doesn't matter. It isn't Penrose tiling as claimed, and it is irrelevant to this thread.

[doronshadmi]

But you didn't comment on his original proposal.
http://forums.randi.org/showpost.php?p=4092043&postcount=109

[doronshadmi]

Let me give you a hint:
Let me give you a hint.

Distinction is a first-order property in this thread.

[ddt]

http://forums.randi.org/showpost.php?p=4092043&postcount=109

Sorry, I stand corrected. It was his original proposal. But you still didn't understand it, did you? As you didn't understand my two proposals. And you still don't understand them, and you'll never understand them as you're never willing to listen to knowledgeable people nor willing to really invest in learning math.

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[ddt]

Let me give you a hint.

Distinction is a first-order property in this thread.

Do you really think, Doron, that shifting from one undefined word to another undefined word is going to endear you with other posters?

Do you really think, Doronl, that not defining your self-invented words is going to bring you one step closer to an actual theory?

Do you really think, Doron, that this behaviour exposes you as anything else than an utter and total crackpot.

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

[ddt]

Order is not important here but the difference between b,a and c is important in this example.

Why then did you introduce an order on a, b, and c, and didn't you just state they were all different?

To add: Doron, what about your statement "Hilbert was wrong". Are you going to retract that or what? Ditto for "Gödel was wrong".

Your question has been stated clearly. To repeat it in every post is uncivil, and a form of flooding. If it's ever going to be answered, it will be, regardless of your attempted harrassment into submission. Please stop this now.

[GreyICE]

Oh my god. My mind is blown. Everything I knew about math was wrong. How can I thank you for showing me the light?

[TMiguel]

I personally give up! There is no other way I can say to him, to what is doing isn't math.

I wonder tough if he ever had any education on the matter, if he has ever demonstrated in his life one of the already proven theorems. If he knows what is a definition, theorem or axiom.

[doronshadmi]

Oh my god. My mind is blown. Everything I knew about math was wrong. How can I thank you for showing me the light?
Not wrong, simply partial.


Light alone or darkness alon are no reseachable, their relation is researchable and it is both prevent AND complement any result.

[doronshadmi]

Why then did you introduce an order on a, b, and c, and didn't you just state they were all different?

Order is a special case of Distinction, exactly as set is a special case of multi-set.

In both cases I look for the general.

[doronshadmi]

The astonishing thing is that I think this could be worked and formalized into an insightful definition of structural information.

In my opinion, this is the right direction to formalize post 1 notions.

Please look at http://en.wikipedia.org/wiki/Structural_information_theory

I claim that Mathematical Science is deeply influenced by how mathematicians think.

If we ignore this influence, we actually ignore an important factor that has an influence on the founded results.

In this thread I wish to show how a partial case of Distinction wrongly became the general viewpoint of the Mathematical Science, and it is all because mathematicians ignore their selves as a factor of their results.

SIT (http://en.wikipedia.org/wiki/Structural_information_theory) if extended, as I suggest, is not limited to visual perception but used to show the influence of the researcher on his results.

In other words, Perception is not less than the relations between internal AND external observations.

[cwalner]

I claim that Mathematical Science is deeply influenced by how mathematicians think.
As somebody who studied mathematics, I can honestly tell you that you have this backwards. Studying mathematics influences how you think, not vice versa.

In other words, Perception is not less than the relations between internal AND external observations.
I other words perception is how our brains process the data they are fed by our sensory organs. Yep, that sound like perception. Thanks for the insight. Now, what does this have to do with your notions in the OP?

[TMiguel]

In my opinion, this is the right direction to formalize post 1 notions. .
No it isn’t.

Please look at http://en.wikipedia.org/wiki/Structural_information_theory

I claim that Mathematical Science is deeply influenced by how mathematicians think.

If we ignore this influence, we actually ignore an important factor that has an influence on the founded results.

In this thread I wish to show how a partial case of Distinction wrongly became the general viewpoint of the Mathematical Science, and it is all because mathematicians ignore their selves as a factor of their results.

SIT (http://en.wikipedia.org/wiki/Structural_information_theory) if extended, as I suggest, is not limited to visual perception but used to show the influence of the researcher on his results.

In other words, Perception is not less than the relations between internal AND external observations.

Absolutely NOT! You couldn’t be more wrong.
First of all it is not mathematical science, it is just mathematics (although you can refer to it has science in the particular case that it is an objective knowledge), but math IS NOT BASED ON THE SCIENTIFICAL METHOD.
Secondly math is based on basic axioms (10 or 12 I don’t remember the actual number of it) whit statements that are easy acceptable like 1 is different from zero and stuff of that sort. Absolutely everything in math comes from implications of those axioms, everything in math is proven logically (and they couldn’t possibly be otherwise).
It does not depend in any way on the perception of the mathematician, nor in any element of the real world for that matter. That is why MATH is the only field of knowledge that man ever possessed that is ABSOLUT, it is more truth then the possibility you actually exist.

You wasted a perfectly good opportunity to shut up.

[doronshadmi]

As somebody who studied mathematics, I can honestly tell you that you have this backwards. Studying mathematics influences how you think, not vice versa.
It works in both directions.

[ddt]

Order is a special case of Distinction, exactly as set is a special case of multi-set.

In both cases I look for the general.

What is "distinction"? Is it what the rest of the (mathematical) world calls "inequality"? If so, please abide by normal nomenclature.

But why did you introduce the special case of an ordering on the elements of the (multi)set? There was no need to do so, it didn't bring anything, and you say yourself above that you want to look at the general case.

Now back to the OP. You wanted a definition for "entropy". That issue is still unresolved. Three definitions were proposed by others (posts # 75, 82, 107). You didn't adequately respond to either of them. Before moving on, pick one or come up with one yourself.

[doronshadmi]

No it isn’t.

Absolutely NOT! You couldn’t be more wrong.
First of all it is not mathematical science, it is just mathematics (although you can refer to it has science in the particular case that it is an objective knowledge)...

Math is called "The queen of Science", "The exact science", where "science" is the art of researching, whether this researching is deductive or inductive.


Secondly math is based on basic axioms (10 or 12 I don’t remember the actual number of it) whit statements that are easy acceptable like 1 is different from zero and stuff of that sort. Absolutely everything in math comes from implications of those axioms, everything in math is proven logically (and they couldn’t possibly be otherwise).

Unless you research what enables easy acceptable like 1 is different from zero.


It does not depend in any way on the perception of the mathematician, nor in any element of the real world for that matter.
Unless Perception is not limited to non-abstract elements (for example: An axiom is an example of an abstract perception).

That is why MATH is the only field of knowledge that man ever possessed that is ABSOLUT, it is more truth then the possibility you actually exist.
I smell some fanatic religious propaganda in the air. Any man's possession is influenced by it, whether it is abstract or not.

You wasted a perfectly good opportunity to shut up.
I observe emotional response here.

[ddt]

In my opinion, this is the right direction to formalize post 1 notions.
What direction? Thus far, you have been waving around, veering off in all sorts of directions, but you haven't addressed any of the insightful posts of others.


I claim that Mathematical Science is deeply influenced by how mathematicians think.
It works in both directions.
No, it isn't and no, it doesn't. How would you know? Have you studied math? No. Nearly every post of yours exhibits a deeply flawed perception of mathematical results, of the mathematical thinking and of mathematical processes. You haven't come up with a single definition of your "notions" in any of your threads, routinely your posts contain grave logical errors, etc.


In this thread I wish to show how a partial case of Distinction wrongly became the general viewpoint of the Mathematical Science, and it is all because mathematicians ignore their selves as a factor of their results.
I have studied mathematics and emphatically say you're wrong. Mathematical results are independent of the (mathematical) researcher. With enough perseverance, I could study Wiles' proof of Fermat's Last Theorem and conclude it is right. In fact, if it were written out in enough detail, anyone who can follow the rules of logic could (with enough perseverance) study that proof and conclude it's right. Going one step further: given a bug-free automated theorem-prover that knows the rules of logic, you could feed the proof to the theorem prover and have it conclude that proof is right. That's the beauty of math, IMHO.

I'm not saying I, or just anybody could think of that same proof. It does take someone like Wiles - with the right specialized knowledge, and the brightness to connect the right dots - to come up with it in the first place.

But the OP doesn't say you want to do what you claimed above. In the OP, you say, a.o., that you are looking for a definition of your notion of "entropy" on multisets. That issue is still unresolved. Three definitions were proposed by others (posts # 75, 82, 107). You didn't adequately respond to either of them. Before moving on, pick one or come up with one yourself.

[ddt]

Light alone or darkness alon are no reseachable, their relation is researchable and it is both prevent AND complement any result.

I see. You don't want to resolve the issues you raised in the OP? You don't want to discuss mathematics, but you want to discuss philosophy?

[doronshadmi]

What is "distinction"? Is it what the rest of the (mathematical) world calls "inequality"?

Distinction is both for inequality and equality, and it is measured by its own symmetrical state.

{a,a,a} is symmetric.

{a,b,a} (order is not important) is less symmetric.

{a,b,c} (order is not important) is asymmetric.

{{a,a,a},{a,b,a},{a,b,c}}(order is not important) is another case of asymmetry.

[ddt]

I wonder tough if he ever had any education on the matter, if he has ever demonstrated in his life one of the already proven theorems. If he knows what is a definition, theorem or axiom.
Everything Doronshadmi has written here shows utter ignorance of what definitions, theorems and axioms actually are and what role they play. He has never provided a definition for any of the terms he invented, and he has never given a correct proof. For laughs, you should look at his rendering of Cantor's diagonal argument in the "Power of X" thread.


I personally give up! There is no other way I can say to him, to what is doing isn't math.
Scores of people have said so and he won't listen. In my first posts in this thread, I have given a summary of his MO in previous threads, things which have been pointed out ad nauseam and they all resurfaced.

There's one sure way he'll stop: when it gets moved to R&P. The other way is to not respond anymore, but thus far there have always been people who did react.

[doronshadmi]

Going one step further: given a bug-free automated theorem-prover that knows the rules of logic, you could feed the proof to the theorem prover and have it conclude that proof is right. That's the beauty of math, IMHO.
A a bug-free automated theorem-prover is your agent.

Ddt, you and your friends here are nothing but a community of people that uses an agreement, which is based on a partial case of Distinction as if it is the only possible case of the entire framework, called Mathematics.

This agreement is 2500 years old, and it is going to be upgraded.

[jsfisher]

Distinction is both for inequality and equality, and it is measured by its own symmetrical state.

{a,a,a} is symmetric.

{a,b,a} (order is not important) is less symmetric.

{a,b,c} (order is not important) is asymmetric.

{{a,a,a},{a,b,a},{a,b,c}}(order is not important) is another case of asymmetry.


You can't define entropy, so at some point you substitute the word distinction. You can't define distinction, so now you substitute the words symmetric and asymmetric. You have already demonstrated your inability to define either of those words*, so where does that leave us?

This is not progress, doron. Are you going to invoke a new term soon to lengthen the chain, or will you be completing the circle?


I also see you are back to the obligatory "order is not important" phrase. Are you likely to forget, otherwise?


*You did make it clear in your world the two words are not antonyms. Curiously, here you are trying to imply they are.

[doronshadmi]

You can't define [I]entropy[/I
No, YOU can't get what's in front of your mind.

[doronshadmi]

No, it isn't and no, it doesn't.
Here you give an example of an opinion that has an influence on the mathematical science.

[ddt]

A a bug-free automated theorem-prover is your agent.
:confused: :confused: :confused:


Ddt, you and your friends here are nothing but a community of people that uses an agreement, which is based on a partial case of Distinction as if it is the only possible case of the entire framework, called Mathematics.

This agreement is 2500 years old, and it is going to be upgraded.

Show me the money! Put up or shut up.

You've written the above in exactly the same way, but with other of your undefined terms. Colour me unimpressed.

Now what about the OP? What about a definition for "entropy" on multisets? What about a real answer to posts # 75, 82, and 107?

[TMiguel]

Lets make an experiment.

Doron, prove whit your mathematical knowledge that cos(u)^2+sin(u)^2=1

Let me give you a cookie:
1. You can use the Pythagoras theorem
2. We allow you only to prove that it is valid for u being a real number whiting [0,pi/2] radians

This is by far the easiest mathematical proof some one can give, even a 9th grader could do it.

Lets see what comes out of it just for laughs.

[jsfisher]

No, YOU can't get what's in front of your mind.


You make up things, you contradict yourself, you provide bogus examples, then you blame me for not getting it.

Why is that?

[doronshadmi]

Lets make an experiment.

Doron, prove whit your mathematical knowledge that cos(u)^2+sin(u)^2=1

Let me give you a cookie:
1. You can use the Pythagoras theorem
2. We allow you only to prove that it is valid for u being a real number whiting [0,pi/2] radians

This is by far the easiest mathematical proof some one can give, even a 9th grader could do it.

Lets see what comes out of it just for laughs.
This thread is about the foundations of the mathematical science, and not about any particular branch of it (Trigonometry, in the case of cos(u)^2+sin(u)^2=1).

In other words, your post is irrelevant, in this case.

I am not talking here about any proof of any kind, but about Distinction as a first-order property of the mathematical science.

Futhermore, I am talking about a research that its aim is to undestand how we are able to get axioms, in the first place.

As we know, axioms are not provable (they are agreed true statements), and I am talking about a pre-axiomatic research.

If you have something to say about Distinction as a first-level property, it would be nice.

You may start by reading SIT http://en.wikipedia.org/wiki/Structural_information_theory .

As for my mathematical knowledge, It is detected only to the foundations of this science.

[doronshadmi]

:confused: :confused: :confused:


:jaw-dropp:jaw-dropp:jaw-dropp

[ddt]

This thread is about the foundations of the mathematical science, and not about any particular branch of it (Trigonometry, in the case of cos(u)^2+sin(u)^2=1).

In other words, your post is irrelevant, in this case.
No. This thread is not at all about foundations of math; it's about, a.o., entropy of multisets, as witnessed in the OP. Your "off topic" reaction is a case of the pot blaming the kettle.

Moreover, by your own reasoning - that this thread is about foundations of math - TMiguel's post is most appropriate. His post is namely not about Trig, but about proof theory, and his case of a Trig theorem is just a particular instance of that.

Your corpus of posts shows such a profound lack of understanding of mathematics, that, IMHO, TMiguel's little test to see if you can write up a proof of such a simple theorem is more than warranted. In fact, I'll give you a little test below.


I am not talking here about any proof of any kind, but about Distinction as a first-order property of the mathematical science.
A nonsensical remark in this context, and then I'm being nice.

My test:

Prove the Theorem of Pythagoras.

Hint: draw a square with side a+b, where a and b are the lengths of the legs of the right triangle.

[doronshadmi]

No. This thread is not at all about foundations of math; it's about, a.o., entropy of multisets, as witnessed in the OP. Your "off topic" reaction is a case of the pot blaming the kettle.

Moreover, by your own reasoning - that this thread is about foundations of math - TMiguel's post is most appropriate. His post is namely not about Trig, but about proof theory, and his case of a Trig theorem is just a particular instance of that.

Your corpus of posts shows such a profound lack of understanding of mathematics, that, IMHO, TMiguel's little test to see if you can write up a proof of such a simple theorem is more than warranted. In fact, I'll give you a little test below.


A nonsensical remark in this context, and then I'm being nice.

My test:

Prove the Theorem of Pythagoras.

Hint: draw a square with side a+b, where a and b are the lengths of the legs of the right triangle.
http://forums.randi.org/showpost.php?p=4098340&postcount=198

[doronshadmi]

TMiguel's post is most appropriate. His post is namely not about Trig, but about proof theory, and his case of a Trig theorem is just a particular instance of that

And I am talking about a research of our abilities to do Math, which is a pre-axiomatic research (its aim is to understand why and how axioms are agreed statements).

Entropy is just some particular case to deal with this subject.

Please read http://en.wikipedia.org/wiki/Structural_information_theory .

[jsfisher]

http://forums.randi.org/showpost.php?p=4098340&postcount=198


Repeating a bogus claim does not make it any less bogus. The topic of this thread is established in Post #1.

[jsfisher]

And I am talking about a research of our abilities to do Math, which is a pre-axiomatic research (its aim is to understand why and how axioms are agreed statements).

Entropy is just some particular case to deal with this subject.

Please read http://en.wikipedia.org/wiki/Structural_information_theory .


Here's an idea: If you want to discuss that sort of thing, why not open a thread on just that topic?

Wacky, I know, but it just might work.

[doronshadmi]

Here's an idea: If you want to discuss that sort of thing, why not open a thread on just that topic?

Wacky, I know, but it just might work.
Because my notions about entropy are deeply related to pre-axiomatic research.

[catbasket]

Because my notions about entropy are deeply related to pre-axiomatic research.

Prove it.

Philosophy is in a different sub-forum.

[nathan]

Doron, why is that that you're unable to answer simple questions about maths? One might reasonably conclude that you are ignorant. Your continued avoidance of answering such questions does nothing to dispel that particular notion.

[GreyICE]

Because my notions about entropy are deeply related to pre-axiomatic research.

Well there's no chance this is a made up concept.

[jsfisher]

Because my notions about entropy are deeply related to pre-axiomatic research.


Your logic is inverted.

You fixed this thread to a narrow topic: Doron's non-standard version of entropy. That's the topic. Live with it. If you want to discuss something much, much broader, start a new thread.

However, since your entropy notions are ill-formed, contradictory, and without merit, a doubt your pre-axiomatic research has much going for it, either.

[doronshadmi]

I other words perception is how our brains process the data they are fed by our sensory organs.
No.

Perception is not less than the relations between internal (abstract) data and external (sensory organs) data.

[doronshadmi]

Prove it.

Philosophy is in a different sub-forum.
Axioms do not need any proof, and I am talking about pre-axiomatic level.

You can easily see that people here are using Philosophy at this fundamental level.

For example:

http://forums.randi.org/showpost.php?p=4097096&postcount=183

http://forums.randi.org/showpost.php?p=4097186&postcount=186

http://forums.randi.org/showpost.php?p=4097210&postcount=187

http://forums.randi.org/showpost.php?p=4097250&postcount=191

As you see, Mathematics is based on agreed beliefs, or in other words, the human factor is an inherent property of this science.

I simply do not ignore it, as ddt and his friends do.

[doronshadmi]

Well there's no chance this is a made up concept.
Like any new fundamental idea.

[ddt]

And I am talking about a research of our abilities to do Math, which is a pre-axiomatic research (its aim is to understand why and how axioms are agreed statements).

Entropy is just some particular case to deal with this subject.

It's clear you won't answer my question, nor TMiguel's question. It's also clear why you won't answer these questions: because you can't. You can't even produce such simple proofs, because your grasp of mathematics is non-existent. (Remember also those simple set theory theorems I asked you to prove in the previous thread?)

I'm out of here, and I'd encourage other members also to refrain from posting. Your nonsensical posts are worse for the sanity than a Call of Cthulhu game. I'll be happy to point out to the moderators that your "pre-axiomatic research" is no mathematics, but philosophy at best.

[doronshadmi]

It's clear you won't answer my question, nor TMiguel's question. It's also clear why you won't answer these questions: because you can't. You can't even produce such simple proofs, because your grasp of mathematics is non-existent. (Remember also those simple set theory theorems I asked you to prove in the previous thread?)

I'm out of here, and I'd encourage other members also to refrain from posting. Your nonsensical posts are worse for the sanity than a Call of Cthulhu game. I'll be happy to point out to the moderators that your "pre-axiomatic research" is no mathematics, but philosophy at best.

http://forums.randi.org/showpost.php?p=4098467&postcount=211

[Reality Check]

Please define Distinction.

[doronshadmi]

Please define Distinction.


Let us research what enables us to define Distinction as an inseparable factor of Math.

For example:

Ddt and some of his friends claim that there is asymmetry of how us as human beings are doing Math.

Math, by the asymmetric viewpoint, changes our understanding but our understanding has no feedback influence on Math.

In other words, Math is an absolute knowledge and we are no more than objective reporters of this knowledge.

By using Distinction as a first-order property of the mathematical science, it is easy to see that this "no feedback influence on Math" is nothing but the particular case of asymmetry that naturally manifests itself as agreed fundamental terms that are based on asymmetry as the general paradigm of the Mathematical science.

If Distinction is used as a first-order property of the mathematical science, then there is also a feedback influence between the mathematical knowledge and the users of this knowledge.

In other words, if Distinction is a first-order property of the mathematical science, then there are particular cases of asymmetry (Math is not influenced by its users) and also there are particular cases that there is symmetry (Math is influenced by its users).

First-order property means that the mathematical science is not limited to any particular case of this property, and this notion holds about Distinction as a first-order property of the mathematical science (if it does not hold, then the mathematical science is nothing but the particular case of asymmetric knowledge. In that case nothing is universal by this science and cannot be considered as an absolute knowledge).

[TMiguel]

This thread is about the foundations of the mathematical science, and not about any particular branch of it
Oh I’m Sorry, I kind of had the feeling that this had something to do about PRIME NUMBERS. Due to the title and then first post. Yeah sorry.

Futhermore, I am talking about a research that its aim is to undestand how we are able to get axioms, in the first place.

As we know, axioms are not provable (they are agreed true statements), and I am talking about a pre-axiomatic research.
You mean like the axioms that we need in the first place to allow you to define what the heck is a number in the first place? Or to define what is an operand? Or what is partitions, Entropy, repetitions, n > 1 (order), Prime, half circles, straight-line, frequency, dense part, non-locality and locality, domain, symmetry, asymmetry, identity, superposition, NXOR\XOR, isolated, dimensions, fractal-like structure, parallel, finite/non-finite, fraction, bases, variant, sum, distinction, complete,
maximum, minimum, continuous, transformation, =, Permutation, multiplicity, cardinal and non-trivial relation?

Sorry I must be totally of here.

[nathan]

It's clear you won't answer my question, nor TMiguel's question. It's also clear why you won't answer these questions: because you can't.

Heck, Doron won't even disprove my theory of his ignorance. It'd be so easy to disprove, were it false.

[doronshadmi]

Oh I’m Sorry, I kind of had the feeling that this had something to do about PRIME NUMBERS.

No, the title is "Deeper than Primes".

http://forums.randi.org/showpost.php?p=4099460&postcount=216

[Reality Check]

Let us research what enables us to define Distinction as an inseparable factor of Math.

For example:

Ddt and some of his friends claim that there is asymmetry of how us as human beings are doing Math.

Math, by the asymmetric viewpoint, changes our understanding but our understanding has no feedback influence on Math.

In other words, Math is an absolute knowledge and we are no more than objective reporters of this knowledge.

By using Distinction as a first-order property of the mathematical science, it is easy to see that this "no feedback influence on Math" is nothing but the particular case of asymmetry that naturally manifests itself as agreed fundamental terms that are based on asymmetry as the general paradigm of the Mathematical science.

If Distinction is used as a first-order property of the mathematical science, then there is also a feedback influence between the mathematical knowledge and the users of this knowledge.

In other words, if Distinction is a first-order property of the mathematical science, then there are particular cases of asymmetry (Math is not influenced by its users) and also there are particular cases that there is symmetry (Math is influenced by its users).

First-order property means that the mathematical science is not limited to any particular case of this property, and this notion holds about Distinction as a first-order property of the mathematical science (if it does not hold, then the mathematical science is nothing but the particular case of asymmetric knowledge. In that case nothing is universal by this science and cannot be considered as an absolute knowledge).

Where in this is Distinction defined? All you say is that you think that it exists due to other undefined terms.

A definition would be: "Given an arbitary multiset this is how you calculate the Distinction of each member". Or maybe the Distinction of the multiset as a whole. Or maybe the Distinction of bits of the multiset.

Otherwise please give the Distinction for every possible multiset. Start with [0], [1], [2], etc. (these are the multisets containing the first partition of every integer - the integer itself which you seem to have ignored in your OP). Then go onto all of the multisets containing the second partition of every integer (all the ways that the integer can be partition into 2 parts). Then go onto all of the multisets containing the third partition of every integer (all the ways that the integer can be partition into 3 parts). Continue until you get the the last possible partition.
This may take you awhile.

[Reality Check]

No, the title is "Deeper than Primes".

http://forums.randi.org/showpost.php?p=4099460&postcount=216
The original topic is about primes (you do remember writing it don't you?)

[doronshadmi]

The original topic is about primes (you do remember writing it don't you?)
I suggest you to read again post 1.

[doronshadmi]

Where in this is Distinction defined? All you say is that you think that it exists due to other undefined terms.

A definition would be: "Given an arbitary multiset this is how you calculate the Distinction of each member".
And the result is again nothing but the particular case of asymmetry (each object's id is clearly distinct, and we again closed under the particular case of asymmetry, as if it is the general property of the researched framework).

[Reality Check]

And the result is again nothing but the particular case of asymmetry (each object's id is clearly distinct, and we again closed under the particular case of asymmetry, as if it is the general property of the researched framework).
So your definition is: If the multiset is asymetrical then it is distinctive (has the property of Distinction). Other wise the multiset does not have Distinction.

Is that correct?

Remember that a multiset does not have any order (you know that is part of the definition of a multiset and have stated it in several posts). So a multiset can be asymmetrical in one representation, the members can be swapped and it will be symmetrical. This is a basic property of multisets. I can even give you your own example:
[a, a, b] is "asymmetrical" (but maybe you have yet again your own definition of asymmetrical). Exactly the same multiset is [a, b, a] and exactly the same multiset is "symmetrical" (but maybe you have yet again your own definition of symmetrical).

[doronshadmi]

Where in this is Distinction defined? All you say is that you think that it exists due to other undefined terms.

A definition would be: "Given an arbitary multiset this is how you calculate the Distinction of each member".
And the result is again nothing but the particular case of asymmetry (each object's id is clearly distinct, and we again closed under the particular case of asymmetry, as if it is the general property of the researched framework).

It is correct and also the particular case where clear distinction is used to distinguish between itself and non-clear distinction.

Another particular case that must not ignored is an unclear distinction that is used to not distinguish between itself and a clear distinction.

In the first particular case, each thing has a clear id.

In the second particular case, there is a superposition of ids.

(The last two cases are also some particular case of clear id, if compared with each other).


Remember that a multiset does not have any order (you know that is part of the definition of a multiset and have stated it in several posts). So a multiset can be asymmetrical in one representation, the members can be swapped and it will be symmetrical. This is a basic property of multisets. I can even give you your own example:
[a, a, b] is "asymmetrical" (but maybe you have yet again your own definition of asymmetrical). Exactly the same multiset is [a, b, a] and exactly the same multiset is "symmetrical" (but maybe you have yet again your own definition of symmetrical).

Again Distinction is not based on any particular order. It means that {a,a,b} and {a,b,a} have the same partial asymmetry (order is not important for Distinction).

[jsfisher]

Let us research what enables us to define Distinction as an inseparable factor of Math.


Let's not.

Let's go back to the opening post and make sense of it. You used several words there in ways that just aren't standard.

In that first post, you told us entropy was a number, but later in the same post you used it as a tri-state property.

In that first post, you told us entropy was a property of multi-sets, but later in the same post you told us it was a property of numbers.

In a later post, you told us [1] had "no entropy", but in another post you indicated it had "full entropy".

Clearly, you have no firm idea what you, yourself, mean by entropy. There is no point, therefore, "research[ing] what enables us to define" anything, since you are incapable of defining anything.

In other words, since nothing enables you to define things; there is nothing to research.

[doronshadmi]

Let's not.

Let's go back to the opening post and make sense of it. You used several words there in ways that just aren't standard.

In that first post, you told us entropy was a number, but later in the same post you used it as a tri-state property.

In that first post, you told us entropy was a property of multi-sets, but later in the same post you told us it was a property of numbers.

In a later post, you told us [1] had "no entropy", but in another post you indicated it had "full entropy".

Clearly, you have no firm idea what you, yourself, mean by entropy. There is no point, therefore, "research what enables us to define" anything, since you are incapable of defining anything.

In other words, since nothing enables you to define things; there is nothing to research.

No.

Entropy and Distinction are in Inverse Proportion. It means that more entropy means less distinction and vice versa. Symmetry is used as the measurement tool of this Inverse Proportion.

The current paradigm of Math is nothing but the particular case of asymmetry (no entropy and clear distinction as the first-order general state of the mathematical science).


In a later post, you told us [1] had "no entropy", but in another post you indicated it had "full entropy".

Let us examine the partitions that exist within any given [i]n > 1

{x} = Full entropy
{x} = Intermediate entropy
{x} = No entropy

x, in this case, is not a singleton but a general way to notate any muti-set of more than one element (as can be found at the beginning of post 1 ( http://forums.randi.org/showpost.php?p=4083359&postcount=1 )).

{1} has no entropy.

[jsfisher]

No.

You say "no" regarding my condemnation of your ability to define anything, but then you provide further proof of my allegation:

Entropy and Distinction are in Inverse Proportion. It means that more entropy means less distinction and vice versa. Symmetry is used as the measurement tool of this Inverse Proportion.

Now, even though entropy, distinction, and symmetry remain doronismsTM (where definitions are unimportant), it is clear you have returned to an "entropy is a number" version. Is this temporary or permanent?

The current paradigm of Math is nothing but the particular case of asymmetry (no entropy and clear distinction as the first-order general state of the mathematical science).

Nonsense.

x, in this case, is not a singleton but a general way to notate any muti-set of more than one element (as can be found at the beginning of post 1 ( http://forums.randi.org/showpost.php?p=4083359&postcount=1 )).

Wrong (and for too many reasons to describe here).

{1} has no entropy.

Yes, you have said that before. You have also indicated it had "full entropy".

Why not just provide a full definition for entropy and resolve all these contradictions and inconsistencies?

[Reality Check]

And the result is again nothing but the particular case of asymmetry (each object's id is clearly distinct, and we again closed under the particular case of asymmetry, as if it is the general property of the researched framework).

It is correct and also the particular case where clear distinction is used to distinguish between itself and non-clear distinction.

Another particular case that must not ignored is an unclear distinction that is used to not distinguish between itself and a clear distinction.

In the first particular case, each thing has a clear id.

In the second particular case, there is a superposition of ids.

(The last two cases are also some particular case of clear id, if compared with each other).

Again where is the definition?
You seem to be saying that there are just 2 distinctions. - one with 'each thing has a clear id" and another with "there is a superposition of ids". So there is just some sort of binbary logic. Nothing to do with Symmetry or Enthropy.


Again Distinction is not based on any particular order. It means that {a,a,b} and {a,b,a} have the same partial asymmetry (order is not important for Distinction).
You do have your own definition of asymmetry that includes "partial asymmetry"! Please provide it.

P.S. Please state the operation under which {a,a,b} and {a,b,a} are partially asymmetry. Is it reflection or rotation or all operations.

[Reality Check]

I see that this thread is now in the appropriate forum - Religion and Philosophy. This is not my area so I will leave it here.

[jsfisher]

I see that this thread is now in the appropriate forum - Religion and Philosophy. This is not my area so I will leave it here.


Doron will abandon it, too.

[ddt]

Heck, Doron won't even disprove my theory of his ignorance. It'd be so easy to disprove, were it false.
1472 posts and waiting for one that shows mathematical insight. Every other post by Doron reinforces my conviction your theory is right.

I see that this thread is now in the appropriate forum - Religion and Philosophy. This is not my area so I will leave it here.

Me too.

[Apathia]

I was tempted to get involved again, seeing the thread has been moved.
I thought I had some inkling of understanding what Doron's Distinction is.
But I see after his responses to other's questions, that I don't really have a clue.

My understanding would come from what I thought I understood about his Organic Numbers. But again, upon closer examination, what I thought doesn't fit what Doron makes of them.

Farewell.

[doronshadmi]

If our framework is limited to clear distinction of the researched subjects, then:

Given some cardinal (notated as C), Entropy (notated as E) is in inverse proportion with Distinction degree (notated as D) where 0 =< D =< 1.

E = C/D and this fromula is the limited case of clear distinction of the reseached subject (where clear distinction is used as the general paradigm of the mathematical science, for the past 2500 years).

[doronshadmi]

If our framework is limited to clear distinction of the researched subjects, then:

Given some cardinal (notated as C), Entropy (notated as E) is in inverse proportion with Distinction degree (notated as D) where 0 =< D =< 1.

E = C/D and this fromula is the limited case of clear distinction of the reseached subject (where clear distinction is used as the general paradigm of the mathematical science, for the past 2500 years).

[Reality Check]

This should go start to the Religion and Philosophy section since it is just his "Deeper than primes" musings again.
It can return here once doron gives the mathematical definitions of:
cardinal
Entropy
Distinction degree

And some idea of what the reseached subject is (set theory, calculus, number theory, topology, something else?) would be nice.

[doronshadmi]

This should go start to the Religion and Philosophy section since it is just his "Deeper than primes" musings again.
It can return here once doron gives the mathematical definitions of:
cardinal
Entropy
Distinction degree

And some idea of what the reseached subject is (set theory, calculus, number theory, topology, something else?) would be nice.

E=C/D where C is any given Cardinal and D is any R member of [0,1].

Please play with it.

[Darat]

Threads merged.

[doronshadmi]

It is easy to learn by http://forums.randi.org/showpost.php?p=4098467&postcount=211 that what is currently known as Mathematics, is nothing but agreed beliefs that are based on asymmetric form of the fundamental terms, as if this asymmetric form is the only possibility of formalization.

The current community of mathematicians is not different from any other religious community that avoids any change of their agreed paradigms.

The current community of mathematicians is doomed to this fanatic attitude, because deduction is a closed method that is not influenced by anything that is not within its borders.

And these borders are a direct result of mathematicians' agreed beliefs.

[TMiguel]

No you are the one perceiving it has a religion. You can't even make sense out of yourself, you never seen how math is made, you never seen a mathematical paper, you never seen how a mathematical theorem is proven.
And if you think that mathematics has anything to do whit belief, Then I dare you to prove me that 1+1 isn’t 2.

[drkitten]

If our framework is limited to clear distinction of the researched subjects, then:

Given some cardinal (notated as C), Entropy (notated as E) is in inverse proportion with Distinction degree (notated as D) where 0 =< D =< 1.

E = C/D and this fromula is the limited case of clear distinction of the reseached subject (where clear distinction is used as the general paradigm of the mathematical science, for the past 2500 years).

Well, at least we now have a formula. Are you willing to stand by this?

My initial observation is that this means that [4,2,2] has exactly twice the entropy of [2,1,1], which violates your statement earlier that size of difference does not matter.

[jsfisher]

It is easy to learn by http://forums.randi.org/showpost.php?p=4098467&postcount=211 that what is currently known as Mathematics, is nothing but agreed beliefs that are based on asymmetric form of the fundamental terms, as if this asymmetric form is the only possibility of formalization.

The current community of mathematicians is not different from any other religious community that avoids any change of their agreed paradigms.

The current community of mathematicians is doomed to this fanatic attitude, because deduction is a closed method that is not influenced by anything that is not within its borders.

And these borders are a direct result of mathematicians' agreed beliefs.


Yeah, what he said. Mathematics is doomed. It can't possibly grow because of all these rigid, limiting beliefs. Geez, we'll never get anything beyond just basic arithmetic because we are so limited. No calculus, no topology, no graph theory, no formal languages, no advances anywhere.

No, wait....

[doronshadmi]

No you are the one perceiving it has a religion. You can't even make sense out of yourself, you never seen how math is made, you never seen a mathematical paper, you never seen how a mathematical theorem is proven.
And if you think that mathematics has anything to do whit belief, Then I dare you to prove me that 1+1 isn’t 2.

1+1=0 in clock arithmetic (mod 2).

The mathematician chooses the initial conditions in order to define some results.

[TMiguel]

1+1=0 in clock arithmetic (mod 2).

The mathematician chooses the initial conditions in order to define some results.

Congratulation you won the idiot award.

[doronshadmi]

Yeah, what he said. Mathematics is doomed. It can't possibly grow because of all these rigid, limiting beliefs. Geez, we'll never get anything beyond just basic arithmetic because we are so limited. No calculus, no topology, no graph theory, no formal languages, no advances anywhere.

No, wait....

Advances that are limited to Asymmetry as a first-order property of the reseached framework.

[doronshadmi]

Congratulation you won the idiot award.
I obverse an emotional response of a fanatic person.

[drkitten]

Advances that are limited to Asymmetry as a first-order property of the reseached framework.

I "obverse" a nonsensical response of a person who writes gibberish.

But more substantively,... how do you address the contradiction raised in post #241?

[jsfisher]

1+1=0 in clock arithmetic (mod 2).

Well, as an unqualified statement, one would normally take "1+1=2" as a proposition in conventional arithmetic. However, since you chose to be "cute", I will point out the inaccuracies in your statement:

Nope, you are wrong. In "Clock 2" arithmetic, 1+1 is, in fact, [equivalent to] 2. I.e., 1 + 1 = 2 (Clock 2).

Nope, your are wrong. Clock arithmetic and modular arithmetic are not exact synonyms.

Nope, you are wrong. Use of the equal sign is incorrect for modular or for clock arithmetic. Both arithmetics deal with equivalent classes and so the equivalence symbol is the correct relational operator.

So, your attempt to be pedantic resulted in not one but three errors from you. Not bad.


Advances that are limited to Asymmetry as a first-order property of the reseached framework.

Well, now that we are in the Philosophy/Religion forum, please feel free to expound upon this sermon topic.

[jsfisher]

My initial observation is that this means that [4,2,2] has exactly twice the entropy of [2,1,1], which violates your statement earlier that size of difference does not matter.

I'm not sure how you came to this observation. C is (presumably) 3 for both multi-sets, and D would seem to relate to the number of distinct multi-set elements. So, wouldn't you expect C/D to be the same for [4,2,2] and [2,1,1]?

On the other hand, since D is confined to the closed interval [0,1] (I now hate ddt's insistence on [.] notation for multi-sets*), then C/D cannot be less than 1 for any non-empty multi-set.

Remember all those multi-sets Doron claimed had "no entropy"? Well, he was wrong.


Still, putting all those discrepancies and contradictions aside, how does any of this nonsense get us to a deeper understanding of anything? So far, Doron has just danced around the obvious with gibberish and hand-waving.



* :)

[drkitten]

I'm not sure how you came to this observation. C is (presumably) 3 for both multi-sets, and D would seem to relate to the number of distinct multi-set elements. So, wouldn't you expect C/D to be the same for [4,2,2] and [2,1,1]?

By assuming that C was the integer he was partitioning, hence C=8 in the first instance and C=4 in the second.

Of course, if Doron would actually define what C was in this context, it would resolve our confusion.

And if I had thirty million dollars and was thirty pounds lighter,.... I mean, as long as I'm wishing for the unattainable....