Chimp

Dx and Dp are the uncertainties in position and momentum, represented as probabiliuty distributions; h is Planck's constant and C is another constant related to the Planck scale.

There is a minimum size that can be probed in string theory. An absolute limit to the precision that any object can be located in space. Ergo, according to M-theory, space cannot be continuous; an infinite amount of information cannot be packed into a finite volume of space.

According to conventional theories, the surface area of the horizon surrounding a black hole, measures its entropy, where entropy is defined as a measure of the number of internal states that the black hole can be in without looking different to an outside observer, who must measure only mass, rotation, and charge. Another theory states that the maximum entropy of any closed region of space can never exceed one quarter of the area of the circumscribing surface, with the entropy being the measure of the total information contained by the system.

S' = S_m + A/4

So the "black hole" theorists came to realize that the information associated with all phenomena in the three dimensional world, can be stored on a two dimensional boundary, analogous to the storing of a holographic image.


I have followed everything you have written in this thread.

The set of all dogs is itself "not" a dog. It is not a member of itself. Sets that are not members of themselves leads to a contradiction in the construction of a universal set. The "set of all sets" cannot exist under these limiting conditions.

Another definition of "Algorithm" for ...you:

http://education.yahoo.com/reference.../a0197800.html

2^x = x is a recursion

2^x = x

then

2^[2^x] = x

2^[2^[2^x]] = x

2^[2^[2^[2^x]]] = x

etc.

DNA is also defined as an algorithm. A finite set? of instructions, a step by step problem solving procedure.

The information contained in DNA can construct a carbon based life form.

So the "DNA" contains the life form analogously to the way a blueprint contains a house.

The life form contains the DNA in the topological sense, while the DNA contains the life form in the "abstract" sense.

The Universal Algorithm contains the Universe in the abstract sense, while the Universe contains the algorithm in the topological sense.

[<-[->[U]<-]->]

The universal set.

The abstract contains the concrete and the concrete contains the abstract.

Mike Rosoft

The set of all dogs is itself "not" a dog. It is not a member of itself. Sets that are not members of themselves leads to a contradiction in the construction of a universal set. The "set of all sets" cannot exist under these limiting conditions.

I explicitly stated that the set of all sets would have to be a member of itself. This is not a problem.

The problem is that if the set of all sets exists, its subset - a set of all sets x for which "x is not an element of x" is true - exists as well. But such a set cannot exist for reasons which I have already stated. Hence, the set of all sets cannot exist.

In other words: the requirement that a set cannot be an element of itself is not necessary to prove that there is no set of all sets. Its existence is precluded by the axiom of separation (also called subset axiom).

You like to quote from Wikipedia. Here is the overview of set theory axioms.


Mike Rosoft

Goliath

Uncertainties in position and momentum of what?!

How do you "probe a size"?

You lose again: you are deviating from the mathematical to the scientific. Your argument is not a mathematical argument.

Incorrect, as you cannot construct a universal set!

Again: If A is any set, then THERE CANNOT BE AN ONTO FUNCTION from A to 2^A.

LISTEN!!!

Sets are not algorithms, whence this is an irrelevant tangent.

Here you are treating x as a variable, NOT as a set. Whence your argument FAILS yet again!

Nonsensical, as you HAVE NOT:

1. Defined a topology on life (nor explained why life is a set).

2. Defined a topology on DNA.

You have STILL NOT DEFINED WHAT YOU MEAN BY THIS, whence you LOSE AGAIN.

Sincerely,

Goliath

Chimp

A simple[trivial?] postulate that gives a "Universal Set" and resolves the "set of all sets" paradox[in the geometric sense]:

A circle of radius R, is isomorphic to a circle of radius 1/R.

[1/R]<--->[R]

For any arbitrarily large circle of radius R, there is an exact correspondence with a circle of radius 1/R, such, that the product

R*[1/R] = 1