> > > >
> > > > An alternative ensemble approach is that of Schmidhuber's[4] -- the
> > > > ``Great Programmer''. This states that all possible programs of a
> > > > universal turing machine have physical existence. Some of these
> > > > programs have will contain self-aware substructures -- these are the
> > > > programs deemed interesting by the anthropic principle. Note that
> > > > there is no need for the UTM to actually exist,
> > >
> > > You don't justify this statement at all.
> >
> > Shouldn't need to - Schmidhuber does it for me.
> >
>
> Beg to differ -- at least you should give a reference. Anyway, I'm just
> giving you my opinions; you asked for constructive criticism. Take what
> you like and leave the rest.
True, your criticism has been very helpful. Nevertheless it is useful
to establish in what way misunderstanding arise in order to circumvent
them, if possible. In the above case there is a reference (ref [4]).
In any case, maybe I should just remove the statement if it is going
to cause problems. The use of the word exist (which has many different
possible meanings, as recent everything list discussion demonstrates)
is deliberately left vague.
>
> > >
> > > > nor is there any need
> > > > to specify which UTM is to be used -- a program that is meaningful on
> > > > UTM1can be executed on UTM2 by prepending it with another program that
> > > > describes UTM1 in terms of UTM2's instructions, then executing the
> > > > individual program. Since the set of all programs (infinite length
> > > > bitstrings) is isomorphic to the set of whole numbers N, an enumeration
> > > > of N is sufficient to generate the ensemble that contains our universe.
> > >
> > > Huh?
> >
> > Isn't this obvious? What part didn't you understand?
>
> Well, I've read it again, several times, and it just doesn't make any
> sense.
>
> "An enumeration of N" - Merriam Webster defines enumeration as "a detailed
> list, an account of a number of things".
>
> I don't see how a list of numbers can generate an ensemble of universes.
>
> Anyway, I think I know what you're *trying* to say, but, again, I was just
> making a criticism -- I think you could be a lot more clear. Take it or
> leave it.
>
I will try. It seems pretty clear to me, unfortunately.
>
> > >
> > > That's confusing, I don't know what you mean. In one phrase you say
> > > "all possible universes", and in the next you say you're not sure that
> > > "this is all there is". What else could there be besides all possible
> > > universes?
> >
> > The Schmidhuber ensemble is some well defined entity. The Tegmark
> > ensemble is less well defined (as Bruno points out endlessly). The "all
> > possible universes" is completely undefined. Schmidhuber and Tegmark
> > have two differing definitions of what AUH means. I remain agnostic
> > as to whether these two different schemes exhaust the possibilties.
>
> Again, I'll stand by my criticism, and you can take it or leave it.
> You could include the above paragraph in your paper to make it more
> clear.
>
Sounds like a good idea.
>
> > >
> > > > Each
> > > > self-consistent mathematical structure (member of the Tegmark
> > > > ensemble) is completely described by a finite set of symbols, and a
> > > > finite set of axioms encoded in those symbols, and a set of rules
> > > > (logic) describing how one mathematical statement may be converted
> > > > into another. These axioms may be encoded as a bitstring, and the
> > > > rules encoded as a program of a UTM that enumerates all possible
> > > > theorems derived from the axioms, so each member of the Tegmark
> > > > ensemble may be mapped onto a Schmidhuber one. The Tegmark ensemble
> > > > must be contained within the Schmidhuber one.
> > >
> > > No, no, no, this is the same error that you've persisted in making
> > > for some time now. Just because two sets have the same number of
> > > members doesn't mean one set is contained within the other set.
> > > Your statement here is just like saying "I count here two apples,
> > > and here three oranges, so each member of the apple ensemble may
> > > be mapped onto the orange one. The apple ensemble must be contained
> > > within the orange one."
> >
> > That is not the argument. The identity relationship I describe is an
> > isomorphism relationship between members of Schmidhuber's ensemble and
> > members of Tegmark's. That is the meaning of a true embedding. Apples
> > and Oranges are clearly not isomorphic (unless you're almost
> > completely blind :).
>
> Yes, and neither is a UTM that generates a set of theorems from axioms
> isomorphic to a universe modelled by the resultant mathematical
> structure. This is now dubbed the Standish Error. If you insist on
> it, then you have a lot more 'splainin to do than you've yet done in
> this paper.
>
>
If this is an error, then it is also an error of Schmidhuber and
Tegmark. All I show is that mathematical structures are isomorphic to
certain sets of bitstrings (equivalence classes under the UTM) in
Schmidhuber's theory. That these entities can then identified with
possible physical universes is something that seems plausible to me,
and is the basis of Tegmark's and Schmidhuber's approaches, however
this is in essence a philosophical issue dating back to the time of
Pythagorus. None of us are likely to resolve this soon, but I think
these approaches shed light on the issue.
Now in this, I take Bruno's criticism (that such RE mathematical
theories miss out on what's important) more seriously, however I'm not
sure I fully understand his criticism. It could be that what I take to be a
Tegmark mathematical structure is slightly different to what Bruno
takes (or for that matter yourself, or Tegmark himself) - I believe
this is worth teasing out to establish if its important or not.
Cheers, and thanks for the criticism!
>
>
> --
> Chris Maloney
> http://www.chrismaloney.com
>
> "Donuts are so sweet and tasty."
> -- Homer Simpson
>
>
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Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 6965
Australia R.Standish.domain.name.hidden
Room 2075, Red Centre
http://parallel.hpc.unsw.edu.au/rks
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Received on Mon Nov 15 1999 - 19:55:26 PST