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Deeper than primes

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doronshadmi said:
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).
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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.
 
doronshadmi said:
It is easy to learn by http://www.internationalskeptics.com/forums/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.
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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....
 
TMiguel said:
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.
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1+1=0 in clock arithmetic (mod 2).

The mathematician chooses the initial conditions in order to define some results.
 
jsfisher said:
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....
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Advances that are limited to Asymmetry as a first-order property of the reseached framework.
 
doronshadmi said:
Advances that are limited to Asymmetry as a first-order property of the reseached framework.
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I "obverse" a nonsensical response of a person who writes gibberish.

But more substantively,... how do you address the contradiction raised in post #241?
 
doronshadmi said:
1+1=0 in clock arithmetic (mod 2).
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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.


doronshadmi said:
Advances that are limited to Asymmetry as a first-order property of the reseached framework.
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Well, now that we are in the Philosophy/Religion forum, please feel free to expound upon this sermon topic.
 
drkitten said:
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.
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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.



* :)
 
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jsfisher said:
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]?
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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....
 
drkitten said:
By assuming that C was the integer he was partitioning, hence C=8 in the first instance and C=4 in the second.
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Ah, I see.

Since we both assumed something about what doron meant, it is a safe bet we are both wrong. ;)
 
If you are so certain, here is what you do. Compile it into a text, and submit it to a mathematical journal for peer-review (and get the honour of being called a stupid by a Fields Medal laureate). Far more productive.
 
TMiguel said:
If you are so certain, here is what you do. Compile it into a text, and submit it to a mathematical journal for peer-review (and get the honour of being called a stupid by a Fields Medal laureate). Far more productive.
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He did send once his material to Underwood Dudley (see here) - or at least, he claimed to have done so. No reply :D
 
TMiguel said:
If you are so certain, here is what you do. Compile it into a text, and submit it to a mathematical journal for peer-review (and get the honour of being called a stupid by a Fields Medal laureate). Far more productive.
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The irony --- if indeed irony it be --- is that I've given him much more detailed and polite feedback in this forum than I would be inclined to give him if I received any of his trash via a journal submission.

If he submitted something to any of the journals for which I review, the odds are extremely good that it would be rejected without formal review by the editor-in-chief for failure to conform to any known grammar or syntax. If the editor-in-chief disliked me enough to send the manuscript to me for detailed review, I would return it with a one sentence rejection note.
 
TMiguel said:
LOL! So he really got already called stupid by a professional mathematician.
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Even worse. Prof. Underwood DudleyWP has made it a hobby to collect crank stories. The lack of answer implies that he deems Doron not even interesting as cranks go. :p
 
jsfisher said:
Nope, you are wrong. In "Clock 2" arithmetic, 1+1 is, in fact, [equivalent to] 2. I.e., 1 + 1 = 2 (Clock 2).
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As I said, it depends on the mathematician's decision to interpret a collection of distinct values that is wrapped on itself, by equivalence classes.

I choose to calculate the result, by simply follow the property of "being wrapped on itself".

In that case "Clock 2" with the distinct values 0 and 1, gives the result 0 by the equation 1+1=0.

It is similar to http://www-math.cudenver.edu/~wcherowi/clockar.html except that I choose to start by value 0.

So, as you see, there is no right or wrong in this case, but simply a matter of common agreement about some decision, which is taken by mathematicians.

The real problem starts when agreements are interpreted as absolute truth. In that case there is a very short way from real science to religious dogma.
 
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Universal Reasoning

A foundationalist [1] believes that there are beliefs that do not need any justification by other beliefs. Therefore these beliefs can be used as an objective base ground to justify other beliefs.

An anti-foundationalist [2] believes that there are no beliefs that do not need any justification by other beliefs. Therefore no belief can be used as an objective base ground to justify other beliefs, and beliefs are relative to each other.

Is it possible to define a framework where anti-foundationalist and foundationalist can agree with each other?

For further reading please look at http://www.geocities.com/complementarytheory/UR.pdf .

[1] http://en.wikipedia.org/wiki/Foundationalism

[2] http://en.wikipedia.org/wiki/Anti-foundationalism
 
Clock arithmetic has a specific meaning. The term is not yours to redefine at your convenience.

You asserted that clock was synonymous with modular arithmetic. You were wrong. Live with it. Move on.
 
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