On 5/21/2012 12:51 AM, Bruno Marchal wrote:

On 21 May 2012, at 07:31, meekerdb wrote:

On 5/20/2012 8:15 PM, Stephen P. King wrote:



Yes. Are those entities that exist from the beginning (which is what ontological primitivity implies...) or are they aspects of the unfolding reality?

I think they are concepts we made up. But you're the one claiming the universe (actually I think you mean the multiverse) is not computable and you think this is contrary to Bruno. But Bruno's UD isn't a Turing machine and what it produces is not computable, if I understand him correctly.


?

The UD is a Turing machine. I gave the algorithm in LISP (and from this you can compile it into a Turing machine).

What it does is computable, in the 3-views, but not in the 1-view (which 'contains' consciousness and matter).

A simple pseudo code is

begin
For i, j, k, non negative integers
Compute phi_i(j) up to k steps
end

The relation 'phi_i(j) = r' is purely arithmetical.

The UD is just a cousin of the universal machine, forced to generate all what it can do. It has to dovetail for not being stuck in some infinite computations (which we cannot prevent in advance).

The existence of UMs and UDs are theorem of elementary arithmetic.

The UD gives the only one known effective notion of "everything".

Ok, I stand corrected.

Then what is the relation to the problem Stephen poses. Can the UD compute the topology of all possible 4-manifolds - it seems it can since they correspond to Turing machine computations. So does Markov's theorem just correspond to the fact that there is no general algortihm to determine whether to Turing machines compute the same function?

Brent

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