Re: The White Rabbit Conjecture

From: Marchal <>
Date: Mon Mar 22 02:56:35 1999

Jacques Baihache write:
>It seems to me that we cannot derive only OUR physics from classical
>computation theory because we can also derive other physics of other
>universes; we can derive only the part of our physics which says that our
>universe is regular, in the sense I explained in
> :
>"The informations that we perceive are not random, they contain

It is indeed consistent with comp. that the multi-verse-phenomenology
extends itself in a multi-multi-verse-phenomenology, with a somewhat
weaker "accessibility" relation among clusters of "many-worlds".
Note that there is no universe at all, and that "universes", with comp
are only kind of projections made by collection of self-referentially
correct machines sharing deep algorithmic information trough a common
[defined by a quotient by some indistinguishibility equivalence relation,
(itself linked to the comp substitution level)] computationnal history.

Comp makes possible to derive the necessary part of (all) physics, which
happen to include the many-world phenomenology, indeterminism... Unless
the substitution level is very low, there is no hope to derive from comp
something like the existence of the sun and the moon around the earth. In
that sense we cannot derive OUR physical reality.
Nevertheless, I tend to believe that it should be possible to derive also
some qualitative aspects of classical mechanics under the form of some
variationnal principles.

Your remark reminds me the following statement by Raymond Smullyan (at
the page 47 of Forever Undecided):

"The physical sciences are interested in the state of affairs that holds
for the ACTUAL world, whereas pure mathematics and logic study ALL
possible state of affairs". [emphasis by Raymond].

I am astonished to find such a statement in a book which bear on modal
logic and self-reference because the very concept of "ACTUAL" can be
considered as a typical (indexical) concept definissable with
Indeed with comp any world and any time is considered as actual by the
self-referential machines which belong to them. The non-triviality of the
self-referential machines (as Smullyan illustrates so well) help to
isolate the non-empty common part of all possible physics or "actualness".

BTW, another idea of you seems to be consistent, and perhaps necessary
 with comp (I need more thinking), is the fact that there could be an
infinity of levels of physical-explanation.
This is provable (from Godel-Blum's speed-up phenomenon) if we take the
(not really occamist ?) notion of "more-efficacious theory", which is a
theory with shorter proof for all theorems (except a finite number of

>This outside world is not directly
>accessible but only through this information exchange.

Exactly, with or without the (new?) comp conception of "outside world".

>- Consider a given program P.
>- Chose randomly a program P' (for example generate a random string,
> analyze
>it, if it is not a syntaxically correct program generate another one)
>- Consider the probability f(P) that the output of P is included in the
>output of P' (i.e. the proportion of programs P' in the Universal
> Dovetailer
>whose output contains the output of P).
>- The conjecture says that f(P) is greater for small programs P than for
> big
>Small programs appear often as parts of other programs in the Universal
>Dovetailer, so their output are often produced by other programs.
>But there could be big programs whose output appears often in the Universal
>Dovetailer, for example a program with a big piece of code which is never
>So instead of considering the size of P, we could consider size'(P) =
>smallest n such that n = size(P'') and P'' produces the same output as P.
>The conjecture says that f(P) is greater for small size'(P) than for big
>size'(P), i.e. the repartition of programs looks like :
> f(P) ^
> |
> 1 |
> |**
> often | **
> | ***
> | *****
> | *******
> rarely | *******
> | ********
> 0 +---------------------->
> small big size'(P)
>Exercise :
>- Formulate precisely the conjecture;
>- Prove it.

That seems interesting. You should perhaps also take into account the
fact that there are programs which will "naturally" dovetail on the real
oracles. This entails kind of multiplicative noise. In our multi-verse
that could be represented by (sort of bohmian) initial position of

>I don't believe in COMP because I don't believe that consciousness
>supervenes on a finite program, because consciousness is the perception of
>an outside by an inside, but this inside must also be perceived by an
> inside
>of this inside, and so on ad infinitum,

It is hard to attribute consciousness to a finite thing, but, at least
for me, it is equally hard to attribute consciousness to infinite things.
Remember also that with comp consciousness is ultimately linked to
infinite collection of computationnal (including counterfactuals)
histories. This, in some (still vague) sense, makes a link between
consciousness and infinities.

(I add also that most infinite regression in computer science are handled
with the first, or better the second, recursion theorem).

>I don't believe in COMP because ...

Remember I propose thought experiments showing intuitively that if comp
is true then comp is, in a variety of sense, unbelievable. (And latter I
propose a relation with godelian sentences).

I don't know if COMP is true (of course). I don't even known if I hope or
fear it to be true. However I aknowledge easily that I am quite
fascinated by the ontological and epistemological consequences of it.

Actually, the question is not "is comp true ?". May be the real questions
looks much more like "would you accept your son to marry a
computationnalist woman?... or your daughter a computationnalist man ?,
or ...?

The beauty of comp, at least according to my taste (for sure), is that it
gives a complete justification why, if comp is true, it cannot be
anything but a matter of personal opinion.

Of course there is something diabolical here (to speak like Raymond
Smullyan). For it shows comp having some self-fulfilling meaning for
consistent reasonners.

Am I a computationnalist ? I prefer to remain silent (here).

May be I have a common point with Jacques M. Mallah, I feel myself much
more like an advocate ... of any (hopefully consistent) sets of possible
computationnalist beliefs.
Perhaps a real modern computationnalist (or mechanist) hero is Thomas
Donaldson, a US mathematician with a brain tumor who has been under trial
for having ask physician to cryogenise his still-living brain.



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Received on Mon Mar 22 1999 - 02:56:35 PST

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