Re: Combined response Re: Computing Randomness

From: Hal Ruhl <>
Date: Tue, 01 May 2001 21:11:43 -0700

Dear Bruno:

Thank you for your patience and the excellent response.

>You should try to make your model part of established mathematics.
>Not for the glory, but for making it comprehensible.

That is what I am trying to do here, but since I have proven to have too
few current mathematical skills to do so in isolation I deeply appreciate
the help.

> >1a) FAS: A symbol string judge. It can judge all possible symbol strings
> >either "acceptable" or "not acceptable".
> >
> >1b) My FAS contains a single symbol string that is given to be acceptable
> >called its axiom.
>Let us say.

I take it then that the above is ok.

> >1c) The axiom contains all the allowed symbols - the alphabet.
>Why not put the fridge in the bottle of milk?
>Contain in which sense and why ?

Actually that is a very excellent example you came up with.

Take a perfectly insolating closed bottle to define the boundary,


1) add an axiom to the bottle consisting of :

a) milk - the alphabet mostly plus almost no correlation between these
symbols - a nearly uniform distribution of different symbols meaning:
["milk" with some assigned value of each meaningful property],

b) a battery, a thermoelectric chiller, heat sink [more alphabet and
considerable correlation between some alphabet symbols],

2) add some rules of state succession and we have a little universe.

The successive states of this universe are isomorphic to a succession of
finite symbol strings that are judged acceptable by the mathematical [ I
think] FAS we just effectively installed in the bottle.

Change the axiom so that the alphabet contains say tea symbols or apple
juice symbols in place of the milk symbols and we have more little

> >1d) My FAS contains a set of rules for identifying additional acceptable
> >symbol strings with the axiom as the basis.
>If you give us a precise FAS, then give it to us. If you are defining
>a collection of FAS, then give us an example.

I am defining a collection of FAS.

> >1e) My FAS contains the rule that any acceptable string contains the
> >encoded FAS as a prefix.
>It looks like your FAS is a self-delimiting UTM. Is that it?

At this point you are far more able to classify it than I am, but I am not
done yet. Once I get this much to be agreeable I have some modifications
to introduce.

> >I believe my FAS meets the requirements to make it a FAS in the accepted
> >sense.
>Not yet. Have you try to implement your FAS, or its computational part
>in some programming language?

I am reasonably sure that my extensions of your suggestion could be
implemented in a deterministic [single valued machine - no branches in or
out] venue given Toffoli's paper at:

I think my examples are single valued machines - single valued FAS -
leaving out QM etc.

As to the post modification final version of my FAS collection I attempt a
complete elimination of a deterministic venue and do so in a way that I
believe incorporates a part of your UDA plus additional features.

Thank you again.

Received on Tue May 01 2001 - 18:26:06 PDT

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