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

From: Russell Standish <>
Date: Mon, 2 Dec 2002 17:17:35 +1100 (EST)

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?)


A/Prof Russell Standish Director
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Received on Mon Dec 02 2002 - 01:18:13 PST

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