# Re: The limit of all computations

On 5/20/2012 3:06 PM, meekerdb wrote:
On 5/20/2012 9:27 AM, Stephen P. King wrote:
On 5/20/2012 6:06 AM, Quentin Anciaux wrote:

In Bruno's theory, the physical world is not computed by an algorithm, the physical world is the limit of all computations going throught your current state... what is computable is your current state, an infinity of computations goes through it. So I don't see the problem here, the UD is not an algorithm which computes the physical world 4D or whatever.

Quentin

Hi Quentin,

Maybe you can answer some questions. These might be badly composed so feel free to "fix" them. ;-)

1) If my "current state" is equivalent to a 4-manifold and the "next" state is also, what is connecting the two? Markov's proof tells us that it is not a algorithm. So what is it?

I don't think Markov's theorem tells you that. It says there can be no algorithm that will determine the homomorphy of any two arbitrary compact 4-manifolds. But there is nothing that says the next state can be any arbitrary 4-manifold. In most theories it is an evolution of the Cauchy data on the present manifold, where 'present' is defined by some time slice.

Dear Quentin,

"there can be no algorithm that will determine the homomorphy of any two arbitrary compact 4-manifolds" Exactly. The physical theories that are used today and accepted as fact define our objective universe as a "compact 3,1-manifold"(up to isomorphisms), this includes "time" as a dimension. There is only a technical difference between a 3,1-manifold and a 4-manifold.

My point is that for there to exist an a priori given string of numbers that is equivalent our universe there must exist a computation of the homomorphies between all possible 4-manifolds. Markov theorem tells us that no such homomorphy exists, therefore our universe cannot be considered to be the result of a computation in the Turing universal sense. It is well known that the act of defining an exact "time slice" is a computationally intractable problem, the Cauchy surface problem <http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&sqi=2&ved=0CE8QFjAB&url=http%3A%2F%2Fwww.tapir.caltech.edu%2F%7Elindblom%2FPublications%2F10_CommMathPhys.61.87.pdf&ei=G1O5T9y1NYG69QT036GoCg&usg=AFQjCNGQxEJa9DEFbyKnXiub-nS7zvPksw&sig2=9za6duwSbfQp-yZ_Cj6vzA>. Physicists use approximations and cheats to get around this intractability.

2) Is there another equivalent set of words for "the physical world is the limit of all computations going through your current state"?

3) Is there at least one physical system running the computations? Is the "physical universe" a purely subjective appearance/experience for each conscious entity? What is it that shifts from one state to the next?

Well that's a crucial question. Bruno assumes that truth implies existence.

I agree with that claim. An entity must exist for there to be a true representation of it.

So if 1+1=2 is true that implies that 1, +, =, and 2 exist.

No, existence does not determine or define properties, it is the mere necessary possibility of such. Just because some unstated sentence may be true and its referents might exist does nothing to the determination of the properties of said sentence or its referents. Properties are determined by physical acts of measurement and by nothing else, therefore the meaning of the sentence "1+1=2" is indefinite in the absence of a physical means to evaluate the sentence.

I think this is a doubtful proposition; particularly when talking about infinities. Even if every number has a successor is true, what existence is implied? Just the non-existence of a number with no successor.

4) What is the cardinality of "all computations"?

Aleph1.

Is the content of Alph_1 sufficient to represent all knowledge?

5) Is the totality of what exists static and timeless and are all of the subsets of that totality static and timeless as well?

6) Does all "succession of events" emerge only from the well ordering of Natural numbers?

Do you understand these questions?

--
Onward!

Stephen

"Nature, to be commanded, must be obeyed."
~ Francis Bacon

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