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
