Re: Flying rabbits and dragons

From: Alastair Malcolm <amalcolm.domain.name.hidden>
Date: Mon, 18 Oct 1999 20:34:38 +0100

----- Original Message -----
From: Jacques M. Mallah <jqm1584.domain.name.hidden>
[AM:]
> > Here the measure is initially based on the symbols comprising the formal
> > systems which include the mathematical structures specifying universes
> > (as in Tegmark's paper).
> > The starting point is all possible symbol strings containing all
> > possible symbols. Now, bearing in mind that any symbol can have any
> > interpretation, we can start to select those strings which contain
> > symbols that can be interpreted in their entirety as well-formed
> > formulae (wff's). Of these we can select those which comprise mutually
> > consistent axioms (both directly, and after taking into account derived
> > theorems via standard rules of inference), connected by an 'AND' (that
> > is, a string of the form 'Axiom1 AND Axiom2 AND ...'). We can also
> > strike out any cases of duplicate axioms.
>
> The above I have a problem with. I do not see how the above is
> supposed to be defined.

Depends on how you define 'define' I suppose - I thought that I had just
defined it! But seriously, my aim was to formalise my ideas sufficiently to
rebut one of the main criticisms of all-possible-universes hypotheses,
namely that there would appear to be far more lawless paths for our universe
to take than that (or those if QM is included) prescribed by the known
physical laws.

> > Now, as an extreme approximation (all that is necessary here), we can
> > say that our TOE requires n axioms, the dragon universe 2n axioms. In
> > comparing all possible theories containing a finite number of axioms,
> > then it is reasonable to suppose that occurences of TOE's will vastly
> > outnumber dragon universe theories, once functionless axioms are taken
> > into consideration: consider all strings up to m axioms in length, for
> > large finite m; there will be n more surplus axioms for the TOE than for
> > the dragon universe theory (m-n as opposed to m-2n), and so bearing in
> > mind that each axiom can contain an infinite variety and number of
> > different symbols, and that each axiom (functionless or not,
> > participating in the specification of another universe or not),
> > contributes to the measure, then there will be far more combinations of
m
> > axioms that include our TOE than is the case for dragon universe
> > theories, with the result that we are far more likely to be in a simpler
> > (TOE-based) universe - dragon universes are not more probable.
>
> Again, this is clearly the same argument that I made, and that Wei
> Dai made for a different reason, that the set of all Turing programs
> should lead to the appearance of simple physical laws. It helps to have,
> as in the Turing case, an 'end of program' symbol; the rest of the string
> after this is functionless.

The scheme I have described is different in that it does not necessitate
TM's - all the computational-based
explanations for simple physical laws that I have seen have tended to rely
on the specific mechanism of a sequential TM processor ('program stop'
codes, loop-backs and so on). As you stated in our last discussion (11/7),
only *some* mathematical structures are TM's, and one would need first to
show that TM's were the most prolific way of generating universes out of all
possible such structures before any of these ideas could be given good
credance. (From what you have said before it doesn't seem to me that you
hold that *only* TM's are suited to generating consciousnesses - but no
doubt you will tell me if I am wrong in this surmisal.) All this however is
not to say that TM's may not provide a useful analytical tool in this area.

> I think you misspoke about 'axioms containing
> symbols' above.

'axioms *representable* by symbols' would certainly read better, if that is
your criticism.


Thanks for your comments

Alastair
Received on Mon Oct 18 1999 - 13:02:03 PDT