RE: Turing vs math

From: <hal.domain.name.hidden>
Date: Thu, 21 Oct 1999 09:18:47 -0700

Why can't the simplest possible program be taken as computing a universe
which includes us? We tend to say "it computes all universes" as though
it computes more than one. Then it is fair to object that the program
is too simple, because it computes more than one universe.

But this is a semantic objection based on the definition of a universe.
How do we know how many universes a given program computes? Is there
an objective, well defined measure? That seems necessary in order to
rule out a trivial counting or dovetailing program as one which creates
our observable universe and our minds as a subset of its output.

Wei Dai proposed a solution to this, which was to say that it is not
enough to compute a universe that matches what I see; it must compute
a universe which includes my mind. And then, he proposes that the
probability measure should not be calculated as just the size of the
universe program, but rather as the size of the program that computes
the universe PLUS the size of the program that localizes (finds, locates)
my mind within that universe.

This provides an objective measure of the degree of
overkill/redundancy/extra-universes produced by the universe simulation.
Something objective like this seems necessary to reject the notion that
we live in a universe produced by a trivial program.

Hal Finney

juergen.domain.name.hidden (Juergen Schmidhuber) writes:
> Ah! The point is: the information content of a particular universe U is
> the length of the shortest algorithm that computes U AND NOTHING ELSE.
> But the shortest algorithm for everything computes all the other universes
> too. Hence it does not convey the information about U by itself!
>
> Everything conveys much less info than most particular computable
> objects. More is less. But to calculate the probability of a particular
> universe you need to look at its particular algorithms, of course, not
> at the collective probability of all universes.
Received on Thu Oct 21 1999 - 09:23:10 PDT