Deeper than primes

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The Man said:
Doron’s new debating tactic seems to be “I’m rubber, you're glue, whatever you say bounces off of me and sticks to you”. Must be something else he got from those kindergarten kids who gave him his ‘notions’.


We are still waiting for your relevant response to this request Doron.
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The Man, as a :boxedin: thinker you have a lot to learn from those kindergarten kids.
 
doronshadmi said:
Because any language (formal or not) is first of all based on notions, where notations are nothing but tools for notions' representations.

At the moment that some language plays with the tools (the notations) and ignores the notions, it gets off stage.
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Nice attempt to side-step things. All that mathy stuff must be just plan wrong, because Doron's got notions.

No, formal languages are used exactly because the precisely and concisely express concepts. Your lack of understanding of those concepts doesn't invalidate their formal expression.

No, jsfisher you totally failed to show interval ordering, because you can't show that the concept of order between intervals is disconnected form their content.
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I never tried to.

The reason is very simple, no interval exists independently of its contents, but the elements that are used as interval contents, do not need the interval for their existence.
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So?

There is here an hierarchy of dependency that cannot be ignored, and you and your community of expertise ignore it with your notationless game with fancy notations.
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Well, then, why don't you take your hierarchy to its end-point? The reals, after all, are built on the notions of the rationals, and the rationals are built from the integers, and the integers are built from fundamental set theory.

By the logic you express, above, we should be reducing everything to set theoretic terms, right?

Jsfisher nothing is original in your illusionary game with fancy notations , as clearly exposed in the following posts:

http://www.internationalskeptics.com/forums/showpost.php?p=4792733&postcount=3587

http://www.internationalskeptics.com/forums/showpost.php?p=4792779&postcount=3588

http://www.internationalskeptics.com/forums/showpost.php?p=4792867&postcount=3590
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Ok, lets consider just one of these for now. For the middle you you responded:

doronshadmi said:
C has no elements so A<C<B expression = A<B expression.

A<B expression totally depends on the comparison between the elements of A (called x) and the elements of B (called y).
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You incorrectly alleged C has no elements. Support your bogus statement.
 
jsfisher said:
He sort of does. He seems to be able to read the simpler predicates that have been posted. Where he completely falls down is any form of synthesis of information.

In this whole interval successor discussion, he's finally accepted that intervals can have an order relation imposed on them. The only way he did that, though, was to translate it to the common order relation for numbers. The rest of us understand interval ordering to be based on numeric ordering; Doron has converted into numeric ordering.

That leaves him lost when faced with the concept of immediate successor; he hasn't synthesized the idea of interval ordering having its own existence, so he can't cope with immediate successors of intervals.

So, even when faced with a Mathematically precise definition for successor and for immediate successor, he cannot bridge from one to the other, even though he may understand the two separately.

You may have noticed, too, he's copy/pasted much of my Latex ad nauseum, but he is yet to post anything original. (Well, anything more intelligible than underscores with dots on them with no explanation of meaning.) I do not believe he can. Until I see evidence to the contrary, I will remain convinced Doron cannot express a complete thought with any rigor, either as a first-order predicate or even in reasonably plain English.
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You are absolutely right. Doron can not express Mathematical ideas in any reasonable way. This is because he simply does not understand the basic concepts. He never will either, because he has a fundamental problem in his learning abilities: he is incapable of accepting things as true although he does not fully understand them. His assumption is that if he does not understand something it must be wrong. When I first took set theory or calculus I did not understand things to their full extent right from the beginning - I guess I am not the only one. But unlike Doron, I moved on and later gained that understanding as I gathered more knowledge and experience. Later on these things I did not understand became trivial. Doron will not go through this process, which is how learning works with most people due to his stubbornness and arrogance. I presume this is a personality issue, and all our efforts to educate him in Math are in vain.
 
jsfisher said:
Well, then, why don't you take your hierarchy to its end-point? The reals, after all, are built on the notions of the rationals, and the rationals are built from the integers, and the integers are built from fundamental set theory
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This "hierarchy" is the "mother of all nonsense" of Standard Math.

According to Standard Math, there is one and only one set of elements, called real numbers, along the real-line, and there are two basic approaches about them.

One approach is to filter the location of these elements, according to some principle, and the other approach is to avoid any filter of the location.

We can use Ford Circle ( http://en.wikipedia.org/wiki/Ford_circle ) in order to rigorously demonstrate it:

FordC.jpg


The whole numbers are the result of a filter that ignores the existence of elements between some two given locations.

The rational numbers are the result of a filter that ignores the existence of elements that are not based on tangent circles, between some two given locations.

The irrational numbers are the result of any location between some two given locations.
 
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sympathic said:
But unlike Doron, I moved on and later gained that understanding as I gathered more knowledge and experience. Later on these things I did not understand became trivial.
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No, later you where forced by the power of the community of the current mathematical scholars to follow the paradigm of that community, otherwise you will not get any degree from that community.

For degree, you must agree, sympathic.
 
doronshadmi said:
No, later you where forced by the power of the community of the current mathematical scholars to follow the paradigm of that community, otherwise you will not get any degree from that community.

For degree, you must agree, sympathic.
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Continue to fool yourself - it's your life. Just don't bother anyone else with your nonsense.
 
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doronshadmi said:
By OM, the base\value form is a kosher number exactly as 1 is a kosher number.
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doronshadmi said:
"kosher" = "valid"
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So after 10 days you define kosher. Your quote still doesn't make sense.
"By OM, the base\value form is a kosher valid number exactly as 1 is a kosher valid number."

Please define "valid number".
 
Let us take this insightful part from cut-the-knot (http://www.cut-the-knot.org/proofs/fords.shtml ):

"Still Mathematics went its own way and nowadays Algebra and Geometry are considered completely independent sciences. But links between the two pop up now and then and many are quite unexpected in their simplicity. [Conway and Guy, p. 153]"

These "unexpected" links are a direct result of the illusionary dichotomy between Algebra and Geometry that began only in the sixteenth century.

OM rigorously repairs this illusion exactly by using methods that are based on abstraction of visual methods, that enable to get things at once (in parallel) in addition to the standard step-by-step serilal thinking style (which is the only thinking style of the current community of mathematicians, which by mistake believe that any research that is not based on a step-by-step serial thinking, is not a mathematical reseach).
 
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Little 10 Toes said:
So after 10 days you define kosher. Your quote still doesn't make sense.
"By OM, the base\value form is a kosher valid number exactly as 1 is a kosher valid number."

Please define "valid number".
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Little 10, you waste your time on energy on nonsense. I am not with you in this dance.
 
doronshadmi said:
The Man, as a :boxedin: thinker you have a lot to learn from those kindergarten kids.
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No, I actually learned in kindergarten and have continued to learn since then. Since you have chosen to go back to the beginning in your education, we are still waiting for you to catch up.
 
doronshadmi said:
Let us take this insightful part from cut-the-knot (http://www.cut-the-knot.org/proofs/fords.shtml ):

"Still Mathematics went its own way and nowadays Algebra and Geometry are considered completely independent sciences. But links between the two pop up now and then and many are quite unexpected in their simplicity. [Conway and Guy, p. 153]"

These "unexpected" links are a direct result of the illusionary dichotomy between Algebra and Geometry that began only in the sixteenth century.
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Such a short quotation and you still managed to misunderstand and misrepresent it.
 
The Man said:
No, I actually learned in kindergarten and have continued to learn since then. Since you have chosen to go back to the beginning in your education, we are still waiting for you to catch up.
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There is nothing to catch up in your case, because you are still in your head\hammer age.
 
doronshadmi said:
There is nothing to catch up in your case, because you are still in your head\hammer age.
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So you proceeded through some “head\hammer age” ? If you recall it was an ‘interaction’ I specifically recommended not being attempted. If your subsequent mental, learning and reasoning abilities are the result of you indeed passing through an ‘age’ of such ‘interactions’, then the reasons for my not recommending it become quite apparent.
 
jsfisher said:
Such a short quotation and you still managed to misunderstand and misrepresent it.
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This is another example of how jsfisher gets things only by a step-by-step reasoning.

By ignoring the content of http://www.internationalskeptics.com/forums/showpost.php?p=4805793&postcount=3651 he thinks that it is a reply to http://www.internationalskeptics.com/forums/showpost.php?p=4805764&postcount=3650 just because it technically follows it.

( the answer to http://www.internationalskeptics.com/forums/showpost.php?p=4805764&postcount=3650 is http://www.internationalskeptics.com/forums/showpost.php?p=4805795&postcount=3652 ).
 
doronshadmi said:
This is another example of how jsfisher gets things only by a step-by-step reasoning.
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Well, whatever style of thinking you are using, you need to rethink it. It continues to get you to incorrect results.

By ignoring the content of http://www.internationalskeptics.com/forums/showpost.php?p=4805793&postcount=3651 he thinks that it is a reply to http://www.internationalskeptics.com/forums/showpost.php?p=4805764&postcount=3650 just because it technically follows it.
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Here's a good example of how your thinking has let you down. I didn't ignore the content of your post. Quite the opposite. Upon rereading you may notice my post was specifically criticizing your misinterpretation of the simple two-sentence quotation you took from the Cut the Knot website. Not only did you mis-attribute the quote to Conway and Guy, you completely misunderstood what the actual author was suggesting was unexpected.

This is no surprise to anyone here, though.
 
jsfisher said:
you completely misunderstood what the actual author was suggesting was unexpected.
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What is this strange use with the words "was" (you use it twice one after the other)?

Do you mean
jsfisher said:
you completely misunderstood what the actual author was suggesting , was unexpected.
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?

Do you claim that nowadays Algebra and Geometry are not considered completely independent sciences by your community?

Also you ignore http://www.internationalskeptics.com/forums/showpost.php?p=4805347&postcount=3645 .
 
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Little 10 Toes said:
1) Someone said something and you say Conway and Guy said it.
2) The original author suggested something was unexpected and you misunderstood what was unexpected.
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1) My mistake, but it does not change my argument that the cut-the-knot author (2) clearly uses the word 'unexpected' (unexpected simple links between Algerbre and Geomety, like Ford Circles) exactly because according to jsfisher's community Algerbre and Geomety are nowadays consider as completely independent sciences.
 
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doronshadmi said:
1) My mistake, but it does not change my argument that the cut-the-knot author (2) clearly uses the word 'unexpected' (unexpected simple links between Algerbre and Geomety, like Ford Circles) exactly because according to jsfisher's community Algerbre and Geomety are nowadays consider as completely independent sciences.
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"...and many are quite unexpected in their simplicity" - their simplicity is unexpected, not the links themselves.
 
sympathic said:
"...and many are quite unexpected in their simplicity" - their simplicity is unexpected, not the links themselves.
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Their simplicity is unexpected, exactly becaue the current community of mathematicians claims that Algebra and Geomtry are independent of each other (this nonsense point of view began only in the sixteenth century).
 
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doronshadmi said:
Their simplicity is unexpected, exactly becaue the current community of mathematicians claims that Algebra and Geomtry are independent of each other (this nonsense point of view began only in the sixteenth century).
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This is not what makes their simplicity unexpected judging both from the structure of the sentence, and from the description of these links that follows.
 
doronshadmi said:
Their simplicity is unexpected, exactly becaue the current community of mathematicians claims that Algebra and Geomtry are independent of each other (this nonsense point of view began only in the sixteenth century).
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Be careful with all that backpedaling. You'll hurt yourself if the chain derails.
 
sympathic said:
This is not what makes their simplicity unexpected judging both from the structure of the sentence, and from the description of these links that follows.
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Hare it is again:
cut-the-knot said:
"Still Mathematics went its own way and nowadays Algebra and Geometry are considered completely independent sciences."
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Fact 1: Nowadays Algebra and Geometry are considered completely independent sciences.

cut-the-knot said:
"But links between the two pop up now and then and many are quite unexpected in their simplicity."
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Fact 2: If Algebra and Geometry are considered completely independent sciences, then it is unexpected to define simple links between them.
 
doronshadmi said:
Hare it is again:
cut-the-knot said:
"Still Mathematics went its own way and nowadays Algebra and Geometry are considered completely independent sciences."
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Fact 1: Nowadays Algebra and Geometry are considered completely independent sciences.
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I suspect Alexander Bogomolny was being a bit more figurative than you would understand, but ok.

cut-the-knot said:
"But links between the two pop up now and then and many are quite unexpected in their simplicity."
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Fact 2: If Algebra and Geometry are considered completely independent sciences, then it is unexpected to define simple links between them.
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No. You jumped the gap from what Bogomolny actually wrote and what you want to be true.
 
doronshadmi said:
Hare it is again:


Fact 1: Nowadays Algebra and Geometry are considered completely independent sciences.



Fact 2: If Algebra and Geometry are considered completely independent sciences, then it is unexpected to define simple links between them.
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This is a perfect example of you giving your own interpretations for things, and then building mountains of baseless claims from these false interpretations.
 
Alexander Bogomolny (http://genealogy.math.ndsu.nodak.edu/id.php?id=81954) wrote in http://www.cut-the-knot.org/proofs/fords.shtml:

Alexander Bogomolny said:
For the Ancients who did not possess a proper symbolism for either specific (arithmetic) or generic (algebra) numbers, calculations were carried out in a geometric framework. A product of two numbers was represented by the area of a rectangle whose sides were given by the two numbers.
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This is an historical fact about making calculations by using geometric framework.

Alexander Bogomolny said:
Algebra and arithmetic were finally separated from Geometry with the systematic introduction of algebraic notations that began only in the sixteenth century. In the seventeenth century, Rene Descartes (1596-1650) invented Analytic Geometry and claimed that any geometric problem can be solved algebraically. (Which is only true in principle because reduction of a geometric problem often leads to algebraic equations that we only know to solve approximately.)
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We can learn that Geometry and Algebra are not fully translated to each other's framework, but instead of try to get the deeper and more profound links between the two frameworks, in order to unify Mathematics under a one comprehensive framework that clearly demonstrates the common source to both Algebra and Geometry, the community of Mathematicians took exactly the opposite idiotic way and as a result
Alexander Bogomolny said:
nowadays Algebra and Geometry are considered completely independent sciences. But links between the two pop up now and then and many are quite unexpected in their simplicity.
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Now this community of mathematicians that took the wrong path for the mathematical science development, uses stupid phrases like "unexpected in their simplicity" about the simple links between Algebra and Geometry, exactly because they are missing the simple common ground of both Algebra and Geometry, and as a result of this dichotomist approach, the common ground randomally and unexpectedly "pops up" (Alexander Bogomolny usues "pop up" exactly because he belongs to a community that does not research and develop systematically the common ground of the mathematical science, and prefers to tear it apart to, so called, "independent sciences")

Jhsisher, you are not aware of my criticism about your community, where Alexander Bogomolny and you are members of it.
 
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