Russell Standish wrote:
>
>
> Now as for the theory's validity or truth - just exactly what do you
> mean by that? This _is_ a trick question, so answer carefully :)
I'll not be drawn into that discussion, Pontius!
> >
> > I disagree with this last sentence, although it is a minor point.
> > I tend to interpret the SAP as being more or less equivalent to
> > the Divine Creator argument (or at least what Tipler calls the
> > "first cause" argument), and therefore in contradiction to any
> > ensemble explanation.
>
> This is curious. I've never heard of the SAP being identified with the
> God hypothesis before. For me, the strength of the AP (shifting now to
> a continuous scale) is related to how much predictive power the AP
> actually has (its surprise factor - as it were). If the universe was
> going to be conducive to intelligent life for other reasons, than all
> the WAP will do is confirm that fact. The stronger the AP, the more
> there will be anomalies (or contingencies) in the universe
> unexplainable by any other means than the AP. The WAP needs no further
> explanation, the SAP does, and traditionally, the two arguments I
> mention are the explanantions given.
Were Barrow and Tipler the first to draw the distinction between these
two? Anyway, I guess you are right. I went back to their book, and
after presenting there definition of the SAP:
The Universe must have those properties which allow life to develop
within it at some stage in its history.
they give three interpretations (without saying that these are
exhaustive):
A. There exists one possible Universe "designed" with the goal of
generating and sustaining "observers".
B. Observers are necessary to bring the Universe into being.
C. An ensemble of other different universes is necessary for the
existence of our Universe.
> > >
> > > 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.
> >
> > > 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.
> >
> > 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.
> >
> > > 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.
--
Chris Maloney
http://www.chrismaloney.com
"Donuts are so sweet and tasty."
-- Homer Simpson
Received on Mon Nov 15 1999 - 19:10:52 PST