Deeper than primes

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jsfisher said:
Again, those are not fractals. The only fractal would be at the limit of the construction, where such a limit to exist. The construction would be far more interesting without the extra constraint on circumference length, though.
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At the limit of the construction we have 0 lengths, or in other words, no construction.

We do not need the circle in order to show how the construction of an invariant length > 0 of a 1-dim element (which is bended over infinity many scales) is found as long as it does not have the value of the limit (which is 0).

In other words, your Limit notion is the exact non-interesting knowledge of the considered infinite complexity.
 
doronshadmi said:
So you don't have any meaninful thing to say about http://www.internationalskeptics.com/forums/showpost.php?p=5696182&postcount=8949 , http://www.internationalskeptics.com/forums/showpost.php?p=5696845&postcount=8951 and http://www.internationalskeptics.com/forums/showpost.php?p=5699060&postcount=8955 .
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By the way - your reading comprehension issues show again. By people who do not know enough math, I was referring to people who did not study math formally. Lucky for me I did.
 
sympathic said:
My obsolete knowledge of this subject has enabled me to successfully obtain a math degree, a decent job and the proper approach to be successful at it.
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Which is irrelevant to the understanding of novel knowledge of this subject.
 
sympathic said:
By the way - your reading comprehension issues show again. By people who do not know enough math, I was referring to people who did not study math formally. Lucky for me I did.
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Sympathic, the main reason behind your inability to get the novel knowledge of this subject, is exactly your obsolete formal knowledge of this subject.

Not lucky for you, in this case.

People who do not know enough obsolete formal knowledge of this subject, have better chances to get the novel knowledge of this subject.
 
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doronshadmi said:
Sympathic, the main reason behind your inability to get the novel knowledge of this subject, is exactly your obsolete formal knowledge of this subject.

Not lucky for you, in this case.
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Man, do you have to hijack everything and twist it back to your endless ramblings? I was making a side comment - leave it alone.
 
doronshadmi said:
Which is irrelevant to the understanding of novel knowledge of this subject.
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Novel!? you just can't help parading yourself can you? writing mountains of word salads based on impressive misunderstandings is hardly something to be content about. Let alone your inability to follow through a single topic, blind stubbornness and inferiority issues.
 
sympathic said:
Novel!?
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Yes, and your formal training can't help you to deal, for example, with http://www.internationalskeptics.com/forums/showpost.php?p=5696845&postcount=8951.

sympathic said:
you just can't help parading yourself can you?
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Since you can't use your formal training in order to get, for example, http://www.internationalskeptics.com/forums/showpost.php?p=5696845&postcount=8951 you choose to deal with the person instead of the subject.

sympathic said:
writing mountains of word salads based on impressive misunderstandings is hardly something to be content about. Let alone your inability to follow through a single topic, blind stubbornness and inferiority issues.
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An excellent self attack. How sad.
 
doronshadmi said:
People who do not know enough obsolete formal knowledge of this subject, have better chances to get the novel knowledge of this subject.
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how would you know? as I remember the cardinality of the set containing people involved in OM is 1.
 
doronshadmi said:
Sympathic, the main reason behind your inability to get the novel knowledge of this subject, is exactly your obsolete formal knowledge of this subject.

Not lucky for you, in this case.

People who do not know enough obsolete formal knowledge of this subject, have better chances to get the novel knowledge of this subject.
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So the less knowledge you have about a subject,the better you are qualified to speak about it? That says a lot about you.
 
doronshadmi said:
EDIT:

Yes it does.

Take a closed and non-searched string, give it a triangle shape with 3 equal angles, and than start to band each given side, according to the shape of Koch’s fractal.

If you do that you will find that the length of the closest circumference of the circle around that bended closed string, becomes smaller if more bended levels are added, yet the length of the bended string is not changed.
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Sure length of the string does not change but the circumference of a circle that inscribes that sting can. You do not mention an inscribing circle before.

Remember a circle is one dimensional because of the consistency of its radius, thus only one ordinate (rotational angle) is need to specify any location along that circumference. 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. It requires at least two coordinates to identify any location along your “string” thus it is two dimensional. That the “string” can have some of its length in a dimension (along the radius of the inscribing circle) that the inscribing circle can not (because it is a circle) should be apparent to almost everyone. So did you simply miss that fact or are you deliberately ignoring it?

doronshadmi said:
You are invited to do this experiment, and realize by yourself that I am right.
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You are invited to be more clear and concise about what you are referring g to, the length of your “string” or the circumference of a circle inscribing your “string”.


doronshadmi said:
This is by the way how, for example, our DNA is packed in a very small space, even if its length is much bigger than the closest circumference of the circle, which is equal to the geodetic line around this space.
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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


doronshadmi said:
Again we see how standard Math does not have the tools to deal with real complexity.
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Again we see that you simply do not understand, how you misinterpret and misrepresent what you call “standard math”.


doronshadmi said:
The Man,

Here are the results of the experiment:

[qimg]http://farm5.static.flickr.com/4070/4417179545_d4e9c86236_o.jpg[/qimg]

Each Koch's fractal has the same length as the triangle above, yet we have an infinite convergent series of circles, where within each one of them there is the invariant length of Koch's fractal, which is > 0.

If this convergent series has the value of the limit point, then the Koch's fractal has 0 length, which is impossible.

Conclusion: Since the length of Koch's fractal > 0 and it is invariant upon infinitely many bended levels, then the convergent series of circles must be incomplete because it can't have the value of the limit, which is 0.
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As already pointed out to you by jsfisher, none of those are fractals. Also as already pointed out to you before a set (even a finite one) need not include its limit as a member. Also you still seem to be confusing the terms of a series (the circumferences of your inscribing circles) with the sum of an addition of those terms (again I think you do this deliberately). Thus once again you simply are not talking about the sum of an infinite convergent series. Instead you are simply talking about the terms of the series and confusing (again I think deliberately) that with the sum of those terms. 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 and again the fact that an infinite convergent series has a finite sum was proven over 2,300 years ago.
 
doronshadmi said:
No jsfisher.

the axiom of infinity is precise and interesting exactly because "if n is a member of N, then n+1 is a member of N"
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Too bad that isn't a complete statement of the axiom.

...rigorously express the notion of inherent openness (and therefore incomplete nature) of any infinite collection.
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Openness? You've switched adjectives. Why is that?

Again, you have a non-interesting notion of infinite collection exactly because your notion is closed under completeness that is based on classes, instead of the real completeness that naturally derived from the non-local and local atomic aspects of any given collection (finite or not).
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All these things you invent but cannot define, explain, characterize, or distinguish. They have no value as a result.
 
doronshadmi said:
Thank you jsfisher for providing once again the needed proof of why your school of thought has the exact properties of a dogmatic sect.

You are doing the job for me, in order to expose your limited notions infront of the public.
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And what proof is that? You wave your hands and say, "See!" and get challenged. Since you cannot support your wild hand-waving, you just blame others.

Can you back-up your statements or not? (The proof is rather trivial. Is it really beyond your capabilities?)

Ahem. Yes they are fractals (from the second form).
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No, sorry. The definition of fractal hasn't changed to accommodate your lack of understanding. None of the generations of Koch's snowflake you provide are fractals.

...gibberish...
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doronshadmi said:
At the limit of the construction we have 0 lengths, or in other words, no construction.
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"Zero" isn't a synonym for "no". Be that as it may, 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.) It's rather trivial to do. Can you do it?

We do not need the circle in order to show how the construction of an invariant length > 0 of a 1-dim element (which is bended over infinity many scales) is found as long as it does not have the value of the limit (which is 0).
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Ok, so why did you include the circle? Just more noise to confuse the issue? That seems to be your hallmark trait. Scramble as much together as possible so you can bounce from the absurd to the inane without missing a beat, and always have enough remaining outlets so gibberish can save you from any criticism.

In other words, your Limit notion is the exact non-interesting knowledge of the considered infinite complexity.
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No, the limit is very interesting. I am very sorry for you that you are unable to appreciate its qualities.
 
doronshadmi said:
People who do not know enough obsolete formal knowledge of this subject, have better chances to get the novel knowledge of this subject.
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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.
 
doronshadmi said:
No jsfisher.

the axiom of infinity is precise and interesting exactly because "if n is a member of N, then n+1 is a member of N" rigorously express the notion of inherent openness (and therefore incomplete nature) of any infinite collection.
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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).
 
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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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.
 
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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