re:Re: "Everything" need a little more than 0 information

[Marchal Bruno]

Russell Standish wrote:

>Hal Finney wrote:
>> 
>> That would be true IF you include descriptions that are infinitely long.
>> Then the set of all descriptions would be of cardinality c.  If your
>> definition of a description implies that each one must be finite, then the
>> set of all of them would have cardinality aleph-zero.
>> 
>> What Russell wrote was that the set of all descriptions could be computed
>> in c time on an ordinary Universal Turing Machine.  My question is, does
>> it make sense to speak of a machine computing for c steps; it seems like
>> asking for the "c"th integer.
>
>The descriptions in the Schmidhuber ensemble are infinite in length.


The computations are infinite, but descriptions are supposed to be finite.

>
>At this stage, I see no problem in talking about machines computing c
>steps, but obviously others (such as Schmidguber) I know would
>disagree.


And me too, here. c type of infinities appears only from first person
point of views which relies on all infinite digital conputations.


> Its like asking for the "c"th real number, rather than the
>"c"th integer, if you like.
>
>I'm not sure what the connection is with this non-standard model of
>computation and others such as Malament-Hogarth machines (sp?)


Ah. Yes, what you say make sense with non-standard notion of machines.
(Well beyond comp I think).

Bruno

re:Re: "Everything" need a little more than 0 information

[Marchal Bruno]

Jesse Mazer wrote

> [snip]
> ...
>Doesn't the UDA argument in some sense depend on the 
>idea of computing "in the limit" too?

Yes. This follows from the "invariance lemma", i.e. from
the fact that the first persons cannot be aware of delays
of "reconstitution" in UD* (the complete work of the UD).

The domain of uncertainty can be defined by the collection
of all maximal consistent extensions of our actual state/history.
Those maximal extensions are not r.e. (not recursively
enumerable, not algorithmically generable, not computable
in some sense), but are r.e. in the limit, on which our
average experiences will proceed (and this is enough
for the working of the UDA).

(An interesting paper from recursion theory which is relevant
for *further* studies is the technical but readable
paper by Posner 1980. 
Readable by beginners in Recursion Theory I mean.

POSNER D.B. 1980, A Survey of non r.e. degrees ? O', in F.R.
Drake and S.S. Wainer (eds), Recursion Theory: its generalisation
and applications, Cambridge University Press.)

I think that Schmidhuber has *different* motivations for the
limit computable functions. There are also important in the
field of inductive inference theory.

Bruno