Re: on formally describable universes and measures

From: Marchal <marchal.domain.name.hidden>
Date: Fri Dec 29 03:46:09 2000

At the end of the last post by Juergen Schmidhuber, there is
the following dialog:

Wei Dai:

>>If you don't like the duplicating computer, you would have to choose
>>between a classical TM and a quantum TM. The latter may be able to solve
>>some problems (for example factoring) exponentially faster. Choosing a
>>classical TM would lead to the conclusion that building a practical
>>quantum computer is impossible in our universe, so the choice has real
>>consequences, yet I don't see how you can make it on a priori grounds.

Juergen Schmidhuber:

>None of the quantum effects we observe forces us to give up the simple
>idea that our universe can be simulated on a classic TM, just like
>there is no evidence that forces us to assume the existence of complex
>and incomputable things such as uncountable sets.


Let us suppose there is a universe. Let us suppose also that that
universe can be emulated by a classical TM. Then my mind can be
emulated by a classical TM. (i.e. your hypothesis that there is a
computable universe to which we belongs entails comp). But then my
mind can be (and is) emulated by a vast array of classical TM,
mainly 1) all those
emulating me at some right level L (which exists because at least the
universe is computable) + 2) all those classical TM emulating me at
the levels below, which are necessarily unknown (but are defined
on the whole UD* (the block-universe of comp)).
We must quantify our expectations on all the computations (cf UDA).
This entails a new expectation : that if we look ourselves at the level
below L, we can expect "indeterminism" or "parallel
histories", but also uncomputable phenomena and other glints of
Cantor paradise.

H => comp, (H = "there is a computable universe to which we belongs")

comp => not H,

so H => not H

so not H ! (even without comp !)

(Note that this does not entails that the search of universal prior is
not necessary, but it shows that it is not enough).

Bruno
Received on Fri Dec 29 2000 - 03:46:09 PST