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