Deeper than primes

[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 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.

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]

 

[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.