# Re: hypotheses of everything; measure

From: Wei Dai <weidai.domain.name.hidden>
Date: Wed, 18 Nov 1998 16:51:41 -0800

On Wed, Nov 18, 1998 at 06:15:06PM -0500, Jacques M. Mallah wrote:
> Perhaps, but if so that's just an example of the point that I
> made, that even if all possibilities exist there are still free parameters
> in specifying how to count them up in order to make predictions. So it's
> really not a problem with the idea I described, which is a simple (thus
> interesting) choice for the free parameters, but rather it's a problem for
> the more ambitious goal of having no information, which I currently doubt
> could be achieved.

I think having free parameters is ok, as long as the free parameters don't
really matter (i.e. the predictions don't change very much when you vary
the free parameters). For example, suppose binary strings can be
self-aware, and consider the hypothesis that the only objects in the
universe are finite binary strings, and the measure of string x is Q_U(x),
where Q_U is the universal prior:

Q_U(x)=\sum_{U(p)=x}2^-l(p)

and U is a universal prefix machine.

U is a free parameter here, but if you change U to U', the measure of x
changes by at most a multiplicative factor that depends on U and U', but
not on x.

I wonder if there is an (abstract) computer that is universal in speed.
That is, is there one that is as fast as any other computer up to a
constant multiplicative factor?

> Thanks for posting the archive. I looked at it and noticed that
> Max Tegmark has never posted to this list. Do you know why not? Does he