Re: Renormalization

From: <hal.domain.name.hidden>
Date: Mon, 3 Jan 2000 14:16:34 -0800

Marchal <marchal.domain.name.hidden> writes:
> So I think Thisell is right when he said <<the number of computations in the
> Schmidhuber plenitude using an insanely high number of decimals is a lot
> higher than the ones that use a specific measurable but life-permitting
> precision>>.

This is true as stated, but I claim that the programs which implement the
versions with insanely high decimal places are MUCH LARGER than those which
implement smaller numbers of decimal places. Hence they have much lower
measure and do not make a significant calculation.

The reason, as I said, is that specifying the number of decimal places
takes space, and specifying a very large number takes more space than
specifying a small number. This is a corollary to the well known fact
that most strings are not compressible: most large numbers cannot be
expressed by small programs.

> He is wrong when he suggest this is a trivial matter!
>
> Let us look on what happens precisely with the UD:

The universal dovetailer creates all possible universes, using a very
small program. By itself this does not tell you the relative measure
of the various universes. So this line of argument does not seem to
help in judging whether universes with high precision have lower measure
than universes with low precision. Yes, there are more of the former,
but they are of lower measure.

Hal
Received on Mon Jan 03 2000 - 14:25:27 PST