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#27443 - 08/04/08 10:33 PM About the philosophy of the negation of the axiom
Adib Ben Jebara Offline
Member

Registered: 07/02/08
Posts: 36
About the philosophy of the negation of the axiom of choice

I refer to set theory with urelements ZFU as in "The axiom of choice",
Thomas Jech, North Holland 1973.
Let us assume the negation of the axiom of choice and that
space of particles is U of ZFU.
Let U1xU2X....XUiX...... be the void set with Ui a set of
locations.

We can see the Existence and the Non Existence linked, contradicting
the Existence of Parmenides and the Becoming of Heraclites.
We can see the Infinite and the Void tied up in an unexpected way.
We can see that Non Existence is closer to the Infinite than to the
finite.

We can see that we can apprehend space with mathematics in a way that we
cannot apprehend with direct experimentation.
We can see that space is not so much fundamental data, contradicting Kant.
It is to the philosophy of Plato and of Albert Lautman that we refer.

As the Big Crunch and the Big Bang are explained by the use of the negation of
the axiom of choice upon space, we can see the existence of a cyclical
phenomenon.

In the future, ZFU should be considered the foundations of mathematics.
Historically it was an attempt to show that the negation of the axiom of
choice is consistent with the other axioms.
So, we see how the progress of science induces a change in the status of a
theory.

That physical space is infinite (with a quantity of matter finite) puts us in
the border Between mathematics and physics.
We can see the usefulness of interdisciplinary research.

Giordano Bruno was sentenced to death by fire on 1600 in Italy for saying
that the Universe is infinite.
Nowadays, people still find it hard to think of an infinite physical space.

Adib Ben Jebara
http://www.freewebs.com/adibbenjebara

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#27449 - 08/05/08 02:16 AM Re: About the philosophy of the negation of the axiom [Re: Adib Ben Jebara]
Zephir Offline
Superstar

Registered: 07/01/08
Posts: 498
Originally Posted By: Adib Ben Jebara
We can see the usefulness of interdisciplinary research.
Yep, You can consider my note here.
Originally Posted By: Adib Ben Jebara
..that physical space is infinite (with a quantity of matter finite) puts us in the border between mathematics and physics..
While I can agree with many points of your posts, I'm still missing more detailed explanation of many of your implications, which makes your ideas difficult to follow. How the claim "border between mathematics and physics" follows from the fact, "physical space is infinite", for example? By my opinion, such border follows from fact, math cannot derive the existence of time concept, for example.

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#27455 - 08/05/08 06:12 AM Re: About the philosophy of the negation of the axiom [Re: Zephir]
Adib Ben Jebara Offline
Member

Registered: 07/02/08
Posts: 36
You wrote "I can agree with many points of your posts" and I
thank you because I feel depressed with people not interested in my ideas.
If there are much mathematics in physics, then one might think
that he is in the border between physics and mathematics.
It is very difficult for me to think of time not using mathematics.
Adib Ben Jebara.

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#27458 - 08/05/08 11:06 AM Re: About the philosophy of the negation of the axiom [Re: Adib Ben Jebara]
Zephir Offline
Superstar

Registered: 07/01/08
Posts: 498
Originally Posted By: Adib Ben Jebara
...it is very difficult for me to think of time not using mathematics...
You cannot understand the time concept by using of mathematics only, just because of "border between physics and math". The math is the tool of (exact) description of reality, not the understanding. Understanding is the phase transition based on intuition, i.e. parallel, fuzzy approach of neural net.

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#27468 - 08/05/08 10:00 PM Re: About the philosophy of the negation of the axiom [Re: Zephir]
Anonymous
Unregistered


I rely on mathematical intuition.
I think physics is going towards mathematics applied to physics, for instance there is not much physical intuition in quantum mechanics.
My research is mathematics applied to physics.
You wrote that in case of space and time not being continuous
particles would be teleporting themselves all the time. That
is interesting. Can you add something of the kind ?
Adib Ben Jebara.

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#27475 - 08/06/08 09:36 AM Re: About the philosophy of the negation of the axiom [Re: Anonymous]
Zephir Offline
Superstar

Registered: 07/01/08
Posts: 498
Originally Posted By: Anonymous
I rely on mathematical intuition.
Some people prefer to think in formal way, while some others have nonformal feeling of the subject. It's important to understand, both approaches aren't competitive, but mutually inclusive. The AWT makes the understanding of the duality of intuitive (parellelistic) and logical (consecutive) thinking simple by using of the foam model.

Such foam is formed by density fluctuations of another particles, i.e. by the field of parallel interactions. The fluctuations are observable, so they can be described in terms of causal math. Note that the energy/information spreading occurs along surfaces of density fluctuations in transversal waves - it means, it's consecutive by the same way, like the logical thinking and derivation of math formulas. The foam membranes are direct analogy of strings and branes of M-theory.

Consecutive approach works well, until the foam will not become too dense, so that many concurrence approaches exist here, which makes the concurrent math models poorly conditioned. For example, the string theory has fragmented into many branches and it suffers by lack of testable predictions, following from landscape of 10E+500 possible solutions of the vacuum.

At this moment, the intuitive, nonformal approach in thinking becomes more successful, because it enables us to reveal a fundamentally new connections, which are enabling to decrease the number of possible solutions. We shouldn't forget, the math models is deterministic "WYPIWYG" approach ("what you put in is what you get") by its true nature - so we cannot reveal more fundamental insights, then those, which were used for its derivation.

The alternation of formal and nonformal approach in evolution of human understanding corresponds the evolution of nested Aether foam with space/time scale, where the causal (foamy) phase alternates the less causal (particle based) phase, similar to gas.

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#27476 - 08/06/08 10:10 AM Re: About the philosophy of the negation of the axiom [Re: Anonymous]
Zephir Offline
Superstar

Registered: 07/01/08
Posts: 498
Originally Posted By: Ben Jebara.
...in case of space and time not being continuous particles would be teleporting themselves all the time..
The causality requires, the particles cannot propagate at distance through "nothing". Instead of this, they're undulating through space like less or more dense clusters of Aether foam - pretty like the flocks of foam along water surface.



This model requires, every bubble of foam remains filled by smaller bubbles, recursively. While the nested level has no apparent limitations, from distant perspective the interior of foam bubbles is formed by remote generation of another bubbles.
Originally Posted By: Ben Jebara.
...we can apprehend space with mathematics in a way that we cannot apprehend with direct experimentation..
Question is, what the "direct experimentation" is. Most of physical experiments are indirect, i.e. by interpretation based. We never saw the electron, photon, atom nuclei - they're all the result of indirect observations.

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