# RE: Renormalization

From: Niclas Thisell <niclas.domain.name.hidden>
Date: Thu, 6 Jan 2000 14:31:42 +0100

Marchal wrote
> I was just showing I don't even need to invoque cut-off. K could be
> compressible of course (my aim, a little like yours was showing Hal is
> "bias" against large programs).

I think the difference (and confusion on my part) arises from the fact
that you are not using the measure suggested by Schmidhuber. Instead you
are looking at all infinite computations and 'peek' into the state of
the machine. And I agree this will probably give an additional shift
towards 'large' numbers and concepts involving limits towards infinity,
like the reals. And perhaps it's not a bad idea. It is, after all, a
larger set than the set of turing machines that come to a halt - i.e.
all halting turing-machines can be implemented by your set by simply
adding an 'infinite loop' at the end, so to say.

So, how is that measure defined? One shot at a semi-formal definition
would perhaps be something like this;
O(p,i)=The i:th string the program p chooses to expose.
I~(O)=An interpretation of O.
I(p)=lim( I~(O(p,i)), i->inf )
M(IŽ,N)=(number of programs p of length N whose I(p)=IŽ ) / 3^N
M(IŽ)=lim( M(IŽ,N), N->inf )
Or do you have a better suggestion? (Note that this definition gets rid
of 'internal' UD:s since they don't have an interpretation in the limit)

>(BTW do you believe that
> Planck constant is compressible ?).

Uhh... It's not dimensionless, is it? So, um... I think it's 1 :-).

> Now, personaly, I will never presume a linear differential
> equation: that
> is really what I try to derive from more reasonable
> hypothesis like comp.

Well, that was a mistake on my part that I tried to correct in a
followup; I didn't actually mean 'linear differential equation'.
But I did make an assumption. And I frequently do just to see what
happens, even though I don't even believe these assumptions to be true.

> Arithmetical truth, as the 'Schmidhuber plenitude' is not enough as an
> explanation. The explanation will come with the adequacy between the
> different type of discourse possible by the 'average'
> Self-Referentially
> Correct Universal Turing machine and our own experience.
> I propose and illustrate ways for making this mathematicaly precise in
> http://iridia.ulb.ac.be/~marchal.

Unfortunately I don't understand a word of french :-(.

>
> You can see in the archive that although I agree with
> Schmidhuber's (and
> even has invoked it by myself) computationalist plenitude, I disagree
> a lot with Schmidhuber conclusion in his paper.

Oh, I too disagree with a number of things. The explanation, or even
description, of Everett's relative state interpretation comes to mind.
And, btw, I can't really say that I agree with the computationalist
plenitude either - I'm merely toying with the idea. (If someone pressed
me, I would admit that I think that our universe can probably be
simulated by a turing-machine and that consciousness could arise, but
I'm not sure we can make any/correct predictions)

<snip>
> >NT: Whereas these infinite computations more or less assert an
> >absolute time.
<snip>
> Third person physical time and first person subjective time
> are internal
> modalities (infered by machines entangled with deep
> computations, ...).
> They have nothing to do with the 'time step' of the DU. In my
> 'ultimate

Heh, no, I didn't think so. And I feel that I somewhat unjustly accused
you. Perhaps I should have accused Schmidhuber instead, whose first
assumption of his paper is "Each universe evolves on a discrete time
scale". I also feel that the concept of MWI splitting promotes this
picture (and should therefore be banned :-).
Personally, I could just as well look at the universe as 'evolving in
the x-direction'. Or, simply, looking at e.g. the Maxwell equation, that
the program has a 4-dimensional array that is successively expanded and
refined to reach an infinite extent and infinite resolution in the
limit.

Best regards,
Niclas
Received on Thu Jan 06 2000 - 05:33:49 PST

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