On Fri, Jul 15, 2005 at 11:29:01PM -0700, "Hal Finney" wrote:
> Another problem is that the UDist is not unique.  Every Universal Turing
> Machine (UTM) produced a different UDist.  The one thing you can say is
> that the various flavors of UDist do agree with each other up to some
> constant that is independent of the object whose measure being calculated.
> That's a good sign, but I am worried that it is not enough.

I raise this particular problem in my "Why Occam's Razor" paper, and
the solution to it turned out to be remarkably simple: The reference
UTM (or more generally, reference interpreter) is simply that of the
observer, so the universal distribution is relativised to the
observer. The observer itself, I suppose is simply selected from a
uniform distribution over all observers (which can by hypothesis be
taken to be a subset of all UTMs, if one wishes).

> Another problem is that the MWI does not seem to fit too well into
> this model.  Basically, the universe described by the MWI is too big.
> It's vastly bigger than the classical universe.


> (This objection was also pointed out originally by Wei Dai.)

This, I think, is more of a problem for the ASSA than the RSSA. The
RSSA basically describes a version of Darwinian evolution, and creates
the needed complexity. This is kind of glossed over in my paper - I'm
trying to expand on this notion in my book.


> So these are the major problems that I know of with the concept of basing
> measure for all objects on the UDist, which then leads to Schmidhuber's
> multiverse.  In exchange for these though we do get some interesting
> predictions and explanations, which I have largely posted before, but
> here are a few of them repeated:
> 1. The physical laws of our universe should be expressible as a relatively
> simple computer program, and likewise with the initial conditions.

Yes - the standard Occam's razor theorem.

> 2. The universe should not be much bigger than it needs to be in order
> to allow human beings to exist.

It is not obvious what this statement means. Sometimes it is simpler
to be profligate :)

> 3. There should be no substantially simpler computer program that can
> produce observers nearly as easily as our universe does.


> 4. There should not be vastly greater numbers of aliens in the universe
> than humans.

Yes. This is also standard DA.

> 5. There should not be vastly more human beings (or anything we would
> consider observers) in the entire future of the universe than are
> alive today.

Also standard DA.

> 6. There should not be vastly more conscious animals in the world than
> humans.

Yes - this is my ant argument, although the exact formulation takes
some care, and requires some additional information.

> 7. If it ever becomes possible to miniaturize and/or greatly speed-up the
> human mind, we should be surprised to find ourselves as such a person
> (unless that number of such minds is greatly increased to compensate
> for these factors).

I'm not entirely sure what you're getting at here, but it sounds like
an ASSA-only type of prediction.

> 8. We will almost never find ourselves experiencing human observer-moments
> that have much lower measure than typical ones (such as being a one million
> year old cave man).

This is definitely an ASSA-only prediction - Jacques Mallah's argument
in fact.

> I see these as very powerful predictions for such a simple model, and

True, but take care of additional assumptions creeping in.

> my hope is that the problems with the UDist will be able to be cleared
> up with continual improvements in our understanding of the nature of
> computation.
> Hal Finney

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A/Prof Russell Standish                  Phone 8308 3119 (mobile)
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