Deeper than primes

[doronshadmi]

Infinite sets don't exist in your universe, doron, remember? There can be no set of the integers (which necessarily would be all of them), there can be no set of the reals, there can be no infinite sets of any kind.

They exist as incomplete collections (1+1+1+... form).

 

[sympathic]

sympathic,

thanks!

 

[doronshadmi]

All of Doron's answers to this question so far have led me to conclude that the achievements or practical applications of OM (except for the conventional strictly quantitative aspects of number) are non-local in nature, qualitative and inspirational.

Not correct. OM exposes the qualitative atomic aspects that enable Quantity, which is not less than the linkage between Non-locality and Locality.

Though, I seem to remember Doron saying that a positive contribution was liberation from the evils of mathematics as it has developed since Euclid strayed from the path.

Since a fundamental concept like Number is the result of Memory\Object Linkage, then Math is not totally disjoint from the one that develops and uses it.

By developing this linkage, Math becomes a tool that enables to define the bridge between Ethic AND Logic under a one comprehensive framework, which is based on better understanding of Evolutionary Ethics Model (http://www.scribd.com/doc/16547236/EEM) that stands at the basis of Complexity’s understanding.

Another answer he has given is that you, yourself are an example of ./__ Interaction. An amazing achievement!

Only if this notion is understood by many parsons.

(Bottom line: what we're asking of him is some "local only," "deductive," profane expectation that doesn't pertain to OM.
Or the question we are asking is incoprehensible to him.)

OM’s answers are incomprehensible to "local only" AND/OR "deductive only" reasoning.

 

[The Man]

The "sum" of an infinite collection.

Perhaps in your imagination, but the reference to Cantor says nothing about geometric series, an infinite collection or a sum, it simply expresses Poincaré’s distain for Cantor's theory of transfinite numbers.

In a diverges series each size is bigger than any arbitrary previous size.

In a converges series each size is smaller than any arbitrary previous size.

Again.

http://en.wikipedia.org/wiki/Geometric_series

The behavior of the terms depends on the common ratio r:
If r is between minus 1 and plus 1 the terms of the series become smaller and smaller, approaching zero in the limit. The series converges to a sum, as in the case above, where r is a half, and the series has the sum one.

If r is greater than one or less than minus one the terms of the series become larger and larger. The sum of the terms also gets larger and larger, and the series has no sum. (The series diverges.)

If r is equal to one, all of the terms of the series are the same. The series diverges.

If r is minus one the terms take two values alternately (e.g. 2, -2, 2, -2, 2,... ). The sum of the terms oscillates between two values (e.g. 2, 0, 2, 0, 2,... ). This is a different type of divergence and again the series has no sum.

In case you have missed it again

If r is equal to one, all of the terms of the series are the same. The series diverges.

Your “1+1+1+…” “general form” is specifically and only a divergent form of series.

1+1+1+… is the general form of both cases, and it has no sum, if we deal with infinitely many sizes (diverges or converges, it does not matter).

If by “sizes” you mean the terms in the series, then your “1+1+1+…” “general form” does not “deal with infinitely many sizes” since every term in that series is the same.

Again “1+1+1+…” is not any form (general or otherwise) of a convergent series, it is specifically divergent and that fact does specifically matter to anyone except apparently just you. Your continued, deliberate and self-serving ignorance of that fact clearly demonstrates the inherent, deliberate and self-serving dishonesty of your own ethics that you would simply like to impose upon others.

 

[Apathia]

OM’s answers are incomprehensible to "local only" AND/OR "deductive only" reasoning.

I don't think you understand this question people are asking you when they ask for a demonstration of how OM generates practical scientific or ethical content. Or when they ask "How does it work?"

They ask what does OM give us that traditional math can't?
You answer:

OM exposes the qualitative atomic aspects that enable Quantity, which is not less than the linkage between Non-locality and Locality.

They ask: And what does that do?

You answer:

By developing this linkage, Math becomes a tool that enables to define the bridge between Ethic AND Logic under a one comprehensive framework, which is based on better understanding of Evolutionary Ethics Model (http://www.scribd.com/doc/16547236/EEM) that stands at the basis of Complexity’s understanding.

They ask: Could you maybe show how that development proceeds to a practical application?"

And you just return to saying it reveals the atomic linkage.

then Math is not totally disjoint from the one that develops and uses it.

There's that ongoing debate over whether human discover or create mathematics.
It's a both to me. And already i don't find even traditional mathematics disjoint from Humanity.
It's not a matter of a Creation/Discovery Linkage, but that creation is discovery and discovery is creation. They interpenitrate in our participation as integral organisms in reality.
(That's the Way I tend to go.)


Does awareness of non-locality encourage ethical behavior?
Sure!
It does that in the context of many different philosophical and religious traditions, or just on its on in the case of non-religious people who transcend their prejudices.
But you have a specific Way of your own: the Way of the Atomic Linkage.
You state that your Way is the superior one.

That requires you to demonstrate its superiority.

Many Ways require practice to understand, especially when they offer something beyond ordinary comprehension.

So, I reword the question:

How does one practice OM?

 

[doronshadmi]

If by “sizes” you mean the terms in the series, then your “1+1+1+…” “general form” does not “deal with infinitely many sizes” since every term in that series is the same.

Only to an ignorant like you that does not understand that any infinite collection of sizes or not, is incomplete, because infinite collection is not necessarily closed under any class.

For example: 1+1+… is smaller than 1+1+1+… by 1 and both of them a infinite and incomplete.

1+1+1/2+1+… is smaller than 1+1+1+1+… by 1/2 and both of them are infinite and incomplete.

1+1+0.111…[base 2]+1+… is smaller than 1+1+1+1+… by 0.000…1[base 2] and both of them are infinite and incomplete.

Etc, etc. ... ad infinituum …


So there are infinitely many incomplete sizes, whether you interpret them by cardinality or by long addition of absolute sizes, where each one of them is > 0.

Your understanding of infinite collections is trivial and naïve.

Again, if infinitely many positive R members + infinitely many negative R members = 0 it does not mean that any one of these collections is complete. It simply means that these collections have the same incomplete size, where sum 0 is a direct result of the symmetry between opposite and (in this case) incomplete sizes.

The Man, your naïve approach of infinite collections does not let you to understand that (1/2+1/4+1/8+…) - (1/2+1/4+1/8+…) = 0 ( again, 0 is a direct result of the symmetry between opposite and (in this case) incomplete sizes) even if 1/2+1/4+1/8+… < 1 (because the sum of 1/2+1/4+1/8+… is based on asymmetry).

By dealing (in the absolute values sense) with asymmetrical cases like infinite diverges series (where each size is bigger than any arbitrary previous size) or infinite converges series (where each size is smaller than any arbitrary previous size) there is no doubt that these series are both incomplete AND have no sum, whether Cardinality or long addition is used here.

You still do not get that Wikipedia (and in this case http://en.wikipedia.org/wiki/Geometric_series) is nothing but a documentation of already agreed knowledge about any discussed subject.

 

[doronshadmi]

How does one practice OM?

By facing Complexity, which is naturally unexpected and can't be captured by any method that is not direct perception.

 

[Apathia]

By facing Complexity, which is naturally unexpected and can't be captured by any method that is not direct perception.

By facing Complexity, which is naturally unexpected and can't be captured by any method that is not direct perception.

That answer has much merit by me.
And it touches the place in which you and I agree.
The place to begin is in the complex of direct perception which is non-linear and pre-logical.

Seventeenth Century Japanese Zen Master Bankei called it "The Unborn."
In Japanese Esoteric Buddhism it's called the "Cosmic Womb."
It's also called "The Faith Mind."

Now I realize you include in "Direct Perception" the special construct of your two interacting limbs. This is very absent from the Buddhist Way, and may have more in common with Taoist teaching about Yin and Yang.
However, I get the message, OM has no applicable construct or method to be used in multiple situations (except where number is restricted to mere quantity/quantity.). It simply asks one to be aware in each unique circumstance. Seeing things in their own light, we are then able to bring in the appropriate tools.

In that sense of "OM" I set aside some time early each morning to sit in focused awareness and openness.

Pardon me then while I pursue that. Since no matter, that is the essential.

Now, what the mathematicians want of you, that is a different matter.
I leave that to be fought out between you and them.

 

[jsfisher]

They exist as incomplete collections (1+1+1+... form).

Nonsense. Sets are not of the form of some vague summation. Sets are, well, sets. Collections of distinct objects. Stop trying to obfuscate things with ridiculous asides.

Either you accept that there are infinite sets, like the set of the integers for example, or you don't. And if you don't, then your set theory doesn't include the Axiom of Infinity.

So, which is it?

 

[The Man]

Only to an ignorant like you that does not understand that any infinite collection of sizes or not, is incomplete, because infinite collection is not necessarily closed under any class.

Nope the only ignorance remains yours in not understanding that you assumption are simply your assumptions.

For example: 1+1+… is smaller than 1+1+1+… by 1 and both of them a infinite and incomplete.

1+1+1/2+1+… is smaller than 1+1+1+1+… by 1/2 and both of them are infinite and incomplete.

1+1+0.111…[base 2]+1+… is smaller than 1+1+1+1+… by 0.000…1[base 2] and both of them are infinite and incomplete.

Etc, etc. ... ad infinituum …

So there are infinitely many incomplete sizes, whether you interpret them by cardinality or by long addition of absolute sizes, where each one of them is > 0.

Your understanding of infinite collections is trivial and naïve.

I noted your use of “size” to specifically refer to the terms in the series in your previous post, but surmised that you might change that reference to the sum of the series when questioned. Which is why I specifically said “If by “sizes” you mean the terms in the series”, but you simply choose to ignore that.

Again, if infinitely many positive R members + infinitely many negative R members = 0 it does not mean that any one of these collections is complete. It simply means that these collections have the same incomplete size, where sum 0 is a direct result of the symmetry between opposite and (in this case) incomplete sizes.

The Man, your naïve approach of infinite collections does not let you to understand that (1/2+1/4+1/8+…) - (1/2+1/4+1/8+…) = 0 ( again, 0 is a direct result of the symmetry between opposite and (in this case) incomplete sizes) even if 1/2+1/4+1/8+… < 1 (because the sum of 1/2+1/4+1/8+… is based on asymmetry).

What? That “(1/2+1/4+1/8+…) - (1/2+1/4+1/8+…) = 0” is a key element of the proof that such a convergent series has a sum. Try reading the article again.

By dealing (in the absolute values sense) with asymmetrical cases like infinite diverges series (where each size is bigger than any arbitrary previous size) or infinite converges series (where each size is smaller than any arbitrary previous size)

Now your specifically using “size” to refer to the terms of the sires again, well at least your ignorance extends even to yourself, I’ll give you that much.

there is no doubt that these series are both incomplete AND have no sum, whether Cardinality or long addition is used here.

Again an assumption you base on you deliberately confusing a divergent series with a convergent one.

You still do not get that Wikipedia (and in this case http://en.wikipedia.org/wiki/Geometric_series) is nothing but a documentation of already agreed knowledge about any discussed subject.

Again try reading Wikipedia sometime you will find sometimes part of the “discussed subject” are the disagreements about that subject. (but I guess you just choose to ignore that as well)

 

[doronshadmi]

And if you don't, then your set theory doesn't include the Axiom of Infinity.
So, which is it?

By the axiom of infinity if n is a member of N then n+1 is a member of N, and as a result N is inherently an incomplete collection of distinct things.

 

[doronshadmi]

Again try reading Wikipedia sometime you will find sometimes part of the “discussed subject” are the disagreements about that subject. (but I guess you just choose to ignore that as well)

No The Man, by using old knowledge that is found in Wkipedia on this interesting subject, you simply block your mind to novel notions of the discussed subject.

In order to see how your mind is blocked to novel notions, let us use again Koch fractal.

We start by a 1-dim element that has a triangle shape of length 1 with 3 equal angles.

Now we bend in the outside direction each side of the triangle in its 1/3 middle length, by keeping that same proportion of the initial triangle.
As a result, the length 1 of the 1-dim element is not changed, but the closest circumference, which is around the bended 1-dim, becomes smaller.

Infinitely many bended level, do to change the fact that the 1-dim has length 1, or is other words, the shrinked circumference can’t be a point, because if it become a point, we get finitely many bended levels.

If we insist that the circumference is a point (gets to the limit point in the middle of the area that is closed by the bended 1-dim element) and the bended 1-dim is still found, the we actually say that 1=0.

The only solution that keeps length 1 of the bended 1-dim element, and also deals with infinitely many bended level, is the solution where the circumference around the bended 1-dim element of length 1, can’t reach the limit where the circumference is actually a point.

By using this novel notion if the infinite, we understand better, why, for example, the mass of a shrinked star increases but is will not become a point, even it is compressed by infinitely many scale levels.

I do not think that this novel view is achieved if we insist to keep the old notions of Lmit AND infinite and complete collection of bended levels.

 

[zooterkin]

We start by a 1-dim element that has a triangle shape of length 1 with 3 equal angles.

Excuse me?

 

[sympathic]

No The Man, by using old knowledge that is found in Wkipedia on this interesting subject, you simply block your mind to novel notions of the discussed subject.

In order to see how your mind is blocked to novel notions, let us use again Koch fractal.

We start by a 1-dim element that has a triangle shape of length 1 with 3 equal angles.

Now we bend in the outside direction each side of the triangle in its 1/3 middle length, by keeping that same proportion of the initial triangle.
As a result, the length 1 of the 1-dim element is not changed, but the closest circumference, which is around the bended 1-dim, becomes smaller.

Infinitely many bended level, do to change the fact that the 1-dim has length 1, or is other words, the shrinked circumference can’t be a point, because if it become a point, we get finitely many bended levels.

If we insist that the circumference is a point (gets to the limit point in the middle of the area that is closed by the bended 1-dim element) and the bended 1-dim is still found, the we actually say that 1=0.

The only solution that keeps length 1 of the bended 1-dim element, and also deals with infinitely many bended level, is the solution where the circumference around the bended 1-dim element of length 1, can’t reach the limit where the circumference is actually a point.

By using this novel notion if the infinite, we understand better, why, for example, the mass of a shrinked star increases but is will not become a point, even it is compressed by infinitely many scale levels.

I do not think that this novel view is achieved if we insist to keep the old notions of Lmit AND infinite and complete collection of bended levels.

In "Standard English" the inflected form of "bend" is "bent"

 

[doronshadmi]

Excuse me?

 

[zooterkin]

[qimg]http://www.indstate.edu/cirt/ittrain/resources/tutorials/instructional/hotpotatoes/shape-triangle.gif[/qimg]

I am aware of what a triangle looks like, thank you. Please explain how that is one-dimensional.

 

[doronshadmi]

This is a corrected version of post (http://www.internationalskeptics.com/forums/showpost.php?p=5694975&postcount=8932)

Again try reading Wikipedia sometime you will find sometimes part of the “discussed subject” are the disagreements about that subject. (but I guess you just choose to ignore that as well)

No The Man, by using the old knowledge that is found in Wkipedia on this interesting subject, you simply block your mind to novel notions of the discussed subject.

In order to see how your mind is blocked to novel notions, let us use again Koch’s fractal.

We start by a 1-dim element that has a triangle shape of length 1 with 3 equal angles.

Now we bend in the outside direction each side of the triangle in its 1/3 middle length, by keeping the same proportion of the initial triangle.

As a result, length 1 of the 1-dim element is not changed, but the closest circumference, which is around that bended 1-dim, becomes smaller.

Infinitely many bended levels do to change the fact that the 1-dim has length 1, or in other words, the shrinked circumference can’t be a point, because if it becomes a point, we have lost our 1-dim element of length 1.

If we insist that the circumference is a point (which is the limit point in the middle of the area that is closed by the bended 1-dim element) and the bended 1-dim is still found, then we actually say that 1=0.

The only solution that keeps length 1 of the bended 1-dim element, and also deals with infinitely many bended levels, is the solution where the circumference around the bended 1-dim element of length 1, can’t reach the limit , which is actually an 0-dim.

By using this novel notion of the infinite collection, we understand better why, for example, the mass of a shrinked star increases, but it does not become a point even if it is compressed by infinitely many scale levels.

I do not think that this novel view is achieved if we insist to keep the old notions of Limit AND infinite (and complete) collection of bended levels.

 

[doronshadmi]

I am aware of what a triangle looks like, thank you. Please explain how that is one-dimensional.

Follow the line.

 

[doronshadmi]

Now, what the mathematicians want of you, that is a different matter.

There is no different matter. Mathematicians and Mathematics are aspects of the same realm, known by direct perception.

 

[zooterkin]

Follow the line.

You mean the three lines which make up the triangle, in two dimensions?