Re: relevant probability distribution

From: Saibal Mitra <smitra.domain.name.hidden>
Date: Wed, 19 Jun 2002 00:41:59 +0200

Russell wrote:

> Saibal Mitra wrote:
> >
> >
> > Russell wrote:
> > >
> > > I take "consciousness" to be that property essential for the operation
> > > of the Anthropic Principle. The universe is the way it is because we
> > > are here observing it as conscious beings.
> > >
> > > The first problem this raises is why does the anthropic principle
> > > work? - one can conceive of being immersed in a virtual reality which
> > > is totally inconsistent with our existence as conscious observers, for
> > > example.
> > >
> > That must be explained by the unlikeliness of such a situation. Why
would
> > anyone simulate me living happily on the surface of Venus? They could
have
> > taken any possible person....
>
> I'm not sure how you could advance that argument. Bostrom's recent paper
> indicates it is rather likely...

Well, Bostrom's argument evaporates when you bring in the SIA.

>
> Nevertheless a clear logical argument in favour of the AP would be
> most welcome.

 I will explain below that the measure of a universe should be the product
of an intrinsic measure and the number of observers. This last factor leads
implies the SIA.


> >
> > > However, let us accept the AP. After all, it has passed observational
> > > test with flying colours. We should also expect that we should be an
> > > example of the most likely form of consciousness.
> > >
> > > The second problem is raises is that if ameobae are conscious, then
> > > why aren't we amoebae? There are many more amoebae on the planet than
> > > there are human beings. I can well accept that dolphins and
> > > chimpanzees (for instance) _could_ be conscious, since there are
> > > vastly greater numbers of humans around today than there are of these
> > > other species, but there is something special that we have that amoeba
> > > (or even ants, lets say) don't have.
> > >
> > > Not sure about ant nests (Hofstadter style). Anyone got a good
> > > estimate of the number of extant ant nests vis a vis human population?
> > >
> >
> > I think that one should first define oneself as a particular program,
and
> > then look at where and how often that program is actually running.
Amoebas
> > are incapable of running me. Maybe artificial intelligent agents pose
more
> > of a problem. Why am I not a robot, that can copy himself as many times
as
> > he pleases?
> >
>
> No the issue concerns any conscious "program", rather than any
> particular one. The fact that there are vastly more amoeba than homo
> sapiens tends to argue against amoebae being consious.

I agree with that.

> > B.t.w. Ken Olum made an interesting remark in his paper in which he
> > advocates the Self Indicating Assumption (SIA) (see arxiv.org). If
> > universes with more observers are more likely than universes with less
> > observers, then why don't we live in a universe in which the number was
> > pre-programmed to be some ridicolously large number, say N =
10^1000000000?
> > (Ken gave a different example). He concludes that apparently such
universes
> > must be unlikelier by a factor of at least N, to compensate for the
factor N
> > coming from the number of observers. This fits in nice with the idea
that
> > more complex programs should have lower measure. You can see that the
> > measure of a program must decrease faster than 2^(-p) where p is the
length
> > of the program.
> >
> > Saibal
> >
> >
>
> I'm not entirely sure where this SIA measure really comes from.

Consider a modification of Bostrom's God's coin toss experiment. Let's
assume that God creates two universes. One with 10 observers and another
with 10^10 observers. Each observer is numbered 1...N, where N is the number
of observers. The intrinsic measure of both Universes is the same. However,
I would say that I am 10^9 times more likely to find myself in the second
universe. If you assume that God chooses his observers perfectly randomly,
then this must be true. If I then look at my number, and find that it is 7,
then both universes are equally likely again. So the flaw in the Doomsday
argument is to say that on the one hand: ''10^10 observers or 10 observers,
it doesn't matter. The two universes are equally likely a priory''. But then
on the other hand when you observe your number: ''I have number 7, so the
second universe is disfavored by a factor 10^9''. This is contradictory.

>From
> the multiverse, we get that each observer moment is weighted by a
> factor that decreases exponentially with time. Hence we can predict by
> the classic SSA argument the we should expect to find ourselves in a
> period of time when the population outweighs previous epochs by at
> least an exponential factor, and that future populations will grow
> slower than exponentially.
>
> However, all this seems irrelevant to the conscious amoeba question.

It is relevant to some other related problems. SSA together with SIA make
your predictions independent of your definition of observer. You can narrow
the definition of observer down to include only you, or expand it so that it
also includes amoebae, It doesn't matter if you want to predict the future.

Saibal
Received on Tue Jun 18 2002 - 16:01:36 PDT