Deeper than primes

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The Man said:
Sorry Manopolus, but still far too much of that “obsolete formal knowledge of this subject”. By Doron’s own assertions “the novel knowledge” of his OM is based specifically upon a kindergarten understanding of math.
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Yeah, well, I guess it's the vocabulary confusing me, more than anything.
 
sympathic said:
how would you know? as I remember the cardinality of the set containing people involved in OM is 1.
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1 is good start ,for example, the axiom of infinity:

n = 1

"If n is a member of OM then n+1 is a member of OM":)

The initial terms can be a stating point for unexpected real complexity.
 
dafydd said:
So the less knowledge you have about a subject,the better you are qualified to speak about it? That says a lot about you.
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If X knowledge blocks the understanding of Y knowledge, then X is not the right way to get Y.
 
The Man said:
None of the circle's length is along its radius, it is all along its circumference. Your “string” has no such restriction and so portions of it can be closer to the center (but not further) than the radius of the circle.
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The Man, you simply cant rid of the use of points (localities) in your analysis.

The circle and the Koch’s fractal are both closed 1-dim elements, with not even a single point along them.

Inside each convergent circle’s length (which is a 1-dim atomic element) there is a Koch’s fractal (which is a 1-dim atomic element) which its length is invariant upon infinitely many convergent levels.

As a result the convergent series of circles is infinite as long as the invariant length within each convergent circle is found, and more precisely, the increased complexity of Koch’s invariant length is found.

If this convergent series of circles’ lengths has the value of the limit (which is zero) Koch’s fractal invariant length and its infinite increased complexity is lost.

Conclusion: Koch’s fractal invariant length and its infinite increased complexity, is found as long as the value of the limit (which is 0) is not reached, and as a result we get a naturally open and incomplete convergent series.

So did you simply miss that fact or are you deliberately ignoring it?

The Man said:
I can put a 500 foot long rope in a barrel with an opening circumference of 2 feet (as long as the barrel is deep enough), so what? Geometry certainly isn’t your forte; you are still having demonstrative problems with the concept of dimensions
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“So what” clearly summarizes your “deep” understanding of this subject.

The Man said:
Again we see that you simply do not understand, how you misinterpret and misrepresent what you call “standard math”.
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Again we see how your standard notion that is based on stretched points as the basis of lines, prevents from you to understand the real complexity, which is the result of Non-locality\Locality Linkage.

The Man said:
Instead you are simply talking about the terms of the series and confusing (again I think deliberately) that with the sum of those terms.
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The terms of the series are exactly the reason of why the given series has no limit and no sum (it is inherently incomplete).

The Man said:
As already pointed out to you by jsfisher, none of those are fractals.
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Simply wrong, and your insistence to claim otherwise does not change the fact that it is a wrong argument of jsfisher, on this subject.

The Man said:
Again as already explained to you before, just because the set of terms in the series may not include its limit as a member of that set does not infer that the set of sums for that series can not include its limit as a member of that set
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As already explained to you before, any infinite collection is inherently incomplete, exactly because it is not limited to any class.

The Man said:
again the fact that an infinite convergent series has a finite sum was proven over 2,300 years ago.
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This “proof” was wrong 2,300 years ago, it is wrong now, and it will stay wrong for the next coming 2,300 years.

In other words, it is a time independent false.
 
jsfisher said:
Too bad that isn't a complete statement of the axiom.
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You are invited to provide the complete statement of the axiom, by using simple English.


jsfisher said:
Openness? You've switched adjectives. Why is that?
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Oppeness and Incompleteness are exactly the same notion about infinite collections, that can't be captured by qany limit or class.


jsfisher said:
All these things you invent but cannot define, explain, characterize, or distinguish. They have no value as a result.
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So you can't grasp a proof withot words (http://en.wikipedia.org/wiki/Proof_without_words) as given in http://www.internationalskeptics.com/forums/showpost.php?p=5696845&postcount=8951 and http://www.internationalskeptics.com/forums/showpost.php?p=5699060&postcount=8955
 
jsfisher said:
I asked before if you could prove that what your crude drawing implies is actually true (i.e. that the circumscribing circles actually nest inside a triangle as show, similar to the lute of Pythagoras.)
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Take a straight 1-dim with length X.

Bend it and get 4 equal sides along it.

Since the length between the opposite edges is changed to the sum of only 3 sides, and since the number of the sides after the first bending is 4 sides, we have to multiply the bended 1-dim element by 1/(the number of the bended sides), in order to get back length X.

As a result the bended 1-dim element has length X, but the length between its opposite edges becomes smaller (it converges).

In general, this convergent series of 1/(the number of the bended sides) is resulted by 1/1+1/4+1/16+1/64+1/256+... , which has no limit exactly because length X is invariant on infinitely many convergent scales of that series.

The proof without words (http://en.wikipedia.org/wiki/Proof_without_words) was drawn by using AutoCad system, and it is accurate (each given bended 1-dim element has the same X length over infinitely many scales):
[qimg]http://farm5.static.flickr.com/4070/4417179545_d4e9c86236_o.jpg[/qimg]

Your inability to realise it by yourself, demonstrates the “usefulness” of your standard formal training, which is immune from novel notions, of this subject.
 
The Man said:
You do understand that your “notion of inherent openness” is closed under an operation of succession on “n”, by your assertion above, don’t you? Please tell us what “n” is missing from your “N” to give it an “incomplete nature”? Still deliberately confusing a list with a set, are you? Again remember, as jsfisher has alluded to several times, if you simply make “incomplete” synonymous with “infinite” then your assertion of an infinite set being “incomplete” is precisely you stating that an infinite set is just infinite (hardly, well, new or novel knowledge).
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Closed under classes, isn't it The Man?
 
The Man said:
Sorry Manopolus, but still far too much of that “obsolete formal knowledge of this subject”. By Doron’s own assertions “the novel knowledge” of his OM is based specifically upon a kindergarten understanding of math.
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Any knowledge (obsolete or novel, it does not matter) uses also "baby staps" in order to help people to grasp it, so?
 
Manopolus said:
I can prove this to be untrue. My formal training in math is limited to nothing beyond college algebra.

And I still have no clue what you are talking about.

I do find it interesting in a bizarre sort of way, however.
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Again, any Any knowledge (obsolete or novel, it does not matter) has to be learned, in order to grasp it.
 
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zooterkin said:
No. The surface of a ball has no bearing on how many dimensions a square has, nor the fact that you need to specify the points at which to apply your 'bends' to your line.
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If one specifies a location along a 1-dim element, it does not make the location a component of the 1-dim element, which stays atomic and non-local by nature.
 
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