On 20 Mar -1, Marchal wrote:
> OK. Suppose now:
> 1) That there is a real concrete universe (this seems to be obvious
> for a lot of people, but I intend to show that it is ultimately false
> or redundant in some way when we accept COMP and a minimal
> amount of arithmetical realism).
> 2) That a concrete UD is beeing completely executed in the universe.
> I recall that UD is a program which generates all programs and which
> dovetails on all their executions. By "completely executed" I mean the
> program really never stops. The UD get all accessible computationnal
> states.
Do you recall the conversation I had with Wei Dai? I think you
are talking about some of the same issues as we did. A 'UD' is not the
simplest possibility. Just assume all computations are executed in
parrallel.
> This is what I call the "extravagant hypothesis" HE, because the
> complete execution of the UD need an ever expansing cosmos with
> an ever generating energy.
No. It requires an infinite set of states, like a Turing machine
has. And the concept of energy does not apply unless you define it. I
assume you don't mean to imply that it's in our type of universe.
> Now, whatever computationnal states I am in at this very instant, the UD
> will generate it virtually, and it will generate also all possible
> computationnal continuation for that state. I mean that the UD
> will "reconstitute my-present-self" infinitely often in all possible
> virtual environment.
>
> So if I make a simple physical experiment, then, even if I believe our
> "universe" obeys deterministic physical laws, I cannot use these laws
> to make a prediction, I must take into account all "reconstitutions of my
> my-present-self".
> If the physical experiment is the "killing myself experiment", then I do
> no more assurance that I will succed. (for exemple).
In other words, you'd have to use probabilitic predictions, unless
it happens that the probability is almost 1.
> To sum up, because you agree with a) and b) above, I think you will agree
> with:
>
> COMP + HE entails [physics must be derivable from some kind of
> conditionnal measure put on the set of computationnal continuation]
>
> We do have strong evidence that there are "physical laws", so now either
> COMP is false, or HE is false or [physics IS derivable from some kind of
> conditionnal measure put on the set of computationnal continuation]. Do
> you agree ?
> (Note also that we cannot define the measure with the number of
> implementations because there is an infinity of such implementations: we
> really need a measure on the infinite set of computationnal
> continuations).
There's nothing wrong with having an infinity of implementations.
It just means you have to take a limit of a finite system as it goes to
infinity in the proper evenhanded way to get the ratios correct.
I'm not sure what you mean by computational continuations. I
thought we had agreed that the basic unit which has consciousness is the
one step computation. Those are what we need to count, and at a given
brain size there are a finite number of possibilities.
In any case there will be an infinite number of copies of
everything; for example infinitely many of the computations will call up
their own UD subroutine for an infinite detour. You'd better get used to
counting infinities. And any self respecting physicist, upon seeing an
infinity, says 'Ha! I eat you guys for lunch!' (Yes, they cause bad
indigestion if not renormalizible!)
> If you agree so far, the only thing which I still need to show is that the
> extravagant hypothesis can be eliminated. In that case if you keep
> believing in COMP, you will believe that [physics MUST be derivable from
> some kind of
> conditionnal measure put on the set of computationnal histories]. Here is
> where I am trying to go: if COMP is true, physical laws emerge
> necessarily on computations and information processing.
Wait a minute. Besides my above objections, you seem to be
missing a major point in my discussion with Wei. As you should recall, we
were talking about my similar hypothesis in which all computations are
implemented in parrallel. The nontrivial question is what would such a
universe look like to the typical observer. The obvious hypothesis is
that it would look like what we see. This is a question, not an answer.
Answer it quantitatively and it's one of the greatest discoveries ever;
speculate without proof and it's just another philosophical curiousity.
It's a form of the 'everything hypothesis'. Personally I think
the analog sector also needs to be included somehow. But it's much harder
to deal with that quantitatively as we don't even have an obvious measure
on that set, except for special cases such as quantum Turing machines.
As for the distiction between physics and math, that is not very
clear in the everything hypothesis.
- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)
Graduate Student / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://pages.nyu.edu/~jqm1584/
Received on Wed Apr 21 1999 - 11:19:10 PDT