Goliath

Chimp,

This looks more like an argument based on scientific evidence rather than a mathematical argument. If you want to give an argument that's the logical equivalent of "oooh, look how complicated everything is, therefore god exists!" then that's fine...it's based only on evidence and thusly fails as a proof for the existence of a god.

Sincerely,

Goliath

Chimp

It is interesting that a "physicist" is also an expert at mathematics:

http://www-groups.dcs.st-and.ac.uk/~...ns/Witten.html

A scientific proof can also be a mathematical proof...

Goliath

As usual, you don't understand. You are using an argument that (as I understand it...although I am an amateur physicist at best) is based on certain scientific theories. Since these theories have not been proven mathematically, your argument is not entirely a mathematical argument, whence it fails as a proof of the existence of a god.

Of course, mathematics can be used in physics. But I doubt you're going to see a mathematical proof that solipsism is false (for example)*

Sincerely,

Goliath

* - Yes, I know what solipsism is. If you have to go to your little encyclopedia to look it up, then fine, but please stop wasting bandwidth by posting the definition to every word that I understand but that you don't.

Chimp

On one level of stratification, two photons are separate. On another level, of stratification, the photons have zero separation.

Instantaneous communication between two objects, separated by a distance interval, is equivalent to zero separation[zero boundary] between the two objects.

According to the book "Gravitation", chapter 15, geometry of spacetime gives instructions to matter telling matter to follow the straightest path, which is a geodesic. Matter in turn, tells spacetime geometry how to curve in such a way, as to guarantee the conservation of momentum and energy. The Einstein tensor[geometric feature-description] is also conserved in this relationship between matter and the spacetime geometry. Eli Cartan's "boundary of a boundary equals zero."

A point can be defined as an "infinitesimal". The Topological spaces are defined as being diffeomorphism invariant. Intersecting cotangent bundles[manifolds] are the set of all possible configurations of a system, i.e. they describe the phase space of the system.

Waves are then abstract distributions and particles are convergent "concrete" localizations.

Quantum mechanics leads us to the realization that all matter-energy can be explained in terms of "waves". In a confined region(i.e. a closed universe or a black hole) the waves exists as STANDING WAVES In a closed system, the entropy never decreases.

The analogy with black holes is an interesting one but if there is nothing outside the universe, then it cannot be radiating energy outside itself as black holes are explained to be. So the amount of information i.e. "quantum states" in the universe is increasing. We see it as entropy, but to an information processor with huge computational capabilities, it is compressible information.

Quantum field theory calculations where imaginary time is periodic, with period 1/T are equivalent to statistical mechanics calculations where the temperature is T. The periodic waveforms that are opposed yet "in phase" would be at standing wave resonance, giving the action.

Periodicity is a symmetry. Rotate into the complex plane and we have
real numbers on the horizonal axis and imaginary numbers on the
vertical axis. So a periodic function could exist with periodicity
along both the imaginary AND the real axis. Such functions would have
amazing symmetries. Functions that remain unchanged, when the complex
variable "z" is changed.

f(z)---->f(az+b/cz+d)

Where the elements a,b,c,d, are arranged as a matrix, forming an
algebraic group. An infinite number of possible variations that
commute with each other as the function f, is invariant under group
transformations. These functions are known as "automorphic forms".

Mike Rosoft

Chimp,

you can try to define the "set of all sets" via recursion. But what you define cannot exist in the set theory because it is a self-contradictory.

In plain language:

If the set of all sets exists, a set of all sets that do not have itself as a element exists. [a consequence of a set theory axiom]

Such a set (U') cannot exist, because neither "U' is an element of U'" nor "U' is not an element of U'" can be true, both would contradict the definition of U'.

Understood?


Mike Rosoft

Goliath

Chimp,

Instead of addressing my previous post, you decided to spew out seemingly irrelevant garbage. How much of your last post do you actually understand?

Since you still aren't putting forth a coherent argument, are you ready to concede?

Sincerely,

Goliath

Chimp

Certain types of sets do not contain themselves as elements. for example the set of all dogs is itself "not" a dog, and it does not contain itself as an element.

The "set of all sets" and "the set of all things that are not dogs" contain themselves as elements.

The set S whose elements x, are sets that are not elements of themselves, leads one to the question, is S and element of S?

This leads to a paradox where S is an element of itself and S is not an element of itself.

The set S, whose elements x, are sets that are not elements of themselves cannot exist.


On the other hand, a "power set" is the set of all subsets of a given set, containing the empty set and the original set.

If a set has "x" elements, its power set, P[x], is 2^x

The largest possible set is the set that is its own power set:

2^x = x

P[x] = x

The "universal set" is the set that is its own power set ...not the set of barbers who shave those and only those men who do not shave themselves.

Algorithms are interpretable, finitely representable sets of instructions, capable of dealing with contingencies and accomplishing tasks which have recognizable end-states, for all inputs.

So the "Universal Set" is the Universal Algorithm.

An algorithm contains the information regarding the topological/geometrical constructions of spacetime and mass-energy. Likewise, the spacetime and mass-energy topologically contains the abstract set of instructions, the "string bits".

I admire your "consistency" Goliath. :banghead:

Is this a debate or something?

Goliath

LISTEN! There is NO SUCH THING as the set of all sets! The set of all sets is NOT a set! Why do you refuse to comprehend this?

Yes, you have hit upon Russel's paradox.

No. LISTEN (for a change)! If X is any set, then there can NEVER be an onto function from X to 2^X. This is a result that has been known since Cantor.

If it is, you've lost since the beginning.

Sincerely,

Goliath

Chimp

If the physical "universe" is the set of all that exists, then it is the largest possible set. Why the hell do you refuse to comprehend this?

:boohoo:

Goliath

It isn't (for example, non-physical mathematical objects are not in the universe), whence you are wrong yet again.


Sincerely,

Goliath