Re: on formally describable universes and measures

From: Marchal <marchal.domain.name.hidden>
Date: Sat Jan 20 06:36:41 2001

Juergen wrote

>The infinite computational histories are countable. The continuum is not.
>
>The concepts of dovetailing and continuum are incompatible.


But you can write a program which dovetails on the reals !
I have already explain in the list why there is no contradiction
with cantor diagonal proof of the non enumerability of the real.
It is no more astonishing than the existence of a short program
which generate all the finite string, including those which
are very long and chaitin incompressible. The trick is to generate
them *all*.


>There is no program generating the uncountable set of all reals.

There is no program generating a *list* of all the reals.

>There only is a program generating countably many prefixes of reals.

Yes, but the dovetailer generates, for each real, all its
bigger and bigger prefixes, and that is called traditionnaly,
generating the real. And the dovetailer do that for each real,
and so generates all the uncountably many reals.

>How to distinguish those from the countably many prefixes of the
>countable rational numbers?


Locally you cannot. Globally the topology is quite different.
The invariance lemma (see my last short paper on consciousness) entails
that if I am a machine the probabilities are defined globally.

Bruno
Received on Sat Jan 20 2001 - 06:36:41 PST