Bruno writes

> Le 12-mai-05, à 19:14, Peter D Jones a écrit :
>
> > I don't see why. Surely what is being asserted is that there is a set
> > of physically real universes, and it is a subset of logically
> > possible universes ("Platonia") -- but logically possible universes
> > are not real in any sense, they are just an abstraction.

Well, that is the whole (as yet unproven) claim of those like
Balfour, Schmidhuber, and Marchal, etc.  Namely, that they are
real (see Bruno's nice "sum up" below).

> But logically possible universes are certainly real in one sense: as
> being logically possible. Or as being logically consistent.

Yes indeed. If I have a string that contains (looks entirely arbitrary)

...071CB7150F1B0571C391BF0194C713100F15070C33149054012F0C59202039D10091...

of one's and zeros (in hex notation) and somewhere else an almost
exactly similar string (both either finite, or infinite), then
indeed there *is* an objective relationship between them if they
are sufficiently similar. They are, in fact, related precisely
to the degree that there is such a mapping from one to the other.

Now the more complex the mapping, that is, the more esoteric the
TM that is needed (the greater the Kolmogorov complexity of the
program that relates them), the less that they are *objectively*
related.

And since by hypothesis, all strings "exist" to platonic mathematicians,
all strings exist in Platonia, then any and every relationship that you
care to name exists there also. But one has to keep in mind a sort of
futility that attends such observations; a futility described first by
Borges.

> If they are furthermore enough rich in complexity to have "abstract
> inhabitants", it is reasonable or plausible (at least) that for those
> inhabitants their abstract universe will look as it is real.

This rests on the surprising conclusion that the inhabitants actually
compute later states from earlier ones.  Of course, it can always be
made to *look* as though that is what "happened".  Eternal Truth #6:
seek and ye shall find.

It is precisely this latter "surprising conclusion" that is resisted
by so many (including me).  Just as it would seem that anyone should
resist making conclusions about the relationships between the books
in Borges' Library of Babel.

> And this will make sense if, furthermore again, their relative abstract
> computational continuations have the right measure. And theoretical
> computer science can justify the existence of such relative measure.

We may take the books in the Borges library---admittedly in his
scenario none of which is infinite---and begin willy-nilly assigning
a greater measure to some than to others.  It is extremely tempting
to assign greater measure to short ones. But in the infinite-string
version of Borges' library, Russell Standish (for one) begins by
assigning equal measure to each bit string.

> And, finally, if such mathematical measure leads to the verified
> empirical measure, then, frankly, it seems to me that materialism in
> physics begins to look like ... late vitalism in 19th century biology.

A big "if"!  Indeed, if a single new prediction comes from consideration
of Platonia or of Borges' Library (finite or infinite-string version),
then there will be quite a cause for celebrating.

> To sum up: "real" is just (abstract) consistency as seen from inside.

Great summary. Are all these books in libraries whispering to
each other or not?  They indeed even quote each other verbatim,
and many can be seen to be holding conversations with each other
at arbitrarily high degrees of abstraction and wisdom. But will
anyone a hundred years from now think there is anything substantial
in this perception, or not?

Lee

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