Re: Turing vs math

From: Marchal <marchal.domain.name.hidden>
Date: Thu Nov 4 05:16:51 1999

Juergen wrote:

>Bruno, why are we discussing this? Sure, in finite time you can compute
>all initial segments of size n. In countable time you can compute one
>real, or a countable number of reals. But each of your steps needs more
>than twice the time required by the previous step. Therefore you need
>more than countable time to compute all reals.

Just to fix things, let us say that a computer computes a real
number in case it outputs a sequence of better and better
rational approximations of that real, and let us say the
computer quasi-computes a real if it generates a set of distinct
rational approximations among which there is a sequence converging
to that real.
In these terms, what I say is that the UD quasi-computes any
real number.
Now, why are we discussing this?
Because we are searching the domain of the computational
indeterminism (just look at my recent posts to Nick
and Jacques).
When we are duplicated, there is a 1-person indeterminism and
the way we quantify that indeterminism doesn't depend on the
delays between similar reconstitutions. That is why, from a first
person point of view the fact that each step needs more than
twice the time required by the previous step changes nothing.
The UD duplicates us an infinite countable number of time,
and the measure we are searching must be defined on all the
infinite computational histories going through our actual state.
A priori, for isolating the measure, we must take into account
the reals which are quasi-computed by the UD, even, if, being a
machine prevent us to distinguish for sure between a random oracle
and a machine which is just more complex than ourself.

Bruno
Received on Thu Nov 04 1999 - 05:16:51 PST