Christopher Maloney wrote:
> Jerry Clark wrote:
> >
> > Christopher Maloney wrote:
> >
> > > we can only, each of us, deduce things from the SSA from a first
> > > person perspective. We can't take anyone's word for what they've
> > > deduced from the SSA. So we shouldn't, for example, take the word
> > > of a scientist who's just performed the QS experiment and survived
> > > despite thousand-to-one odds, that QS really works. *He* would have
> > > a strong reason for believing it, but I would have no additional
> > > incentive to believe it.
> > >
> >
> > But if deductions from the SSA can only be made from a first person perspective
> > then that makes all deductions from the SSA completely bankrupt because all the
> > deductions I've seen made from the SSA are very *general* statements (e.g.
> > your one about Life universes not subjectively existing). You can't say that
> > deductions are
> > subjective unless what they are *about* is also subjective. Or do you believe that
> > there is no fact of the matter about whether the probability of finding oneself in
> > a Life universe is 0? Is there one probability as far as Chris Maloney is concerned
> > and another as far as, say, Al Gore is concerned? Hmmm.
>
> The above makes no sense. Yes, I believe in objective facts. And I also
> believe that it is possible for me to make some deductions about those
> objective facts by using a first-person reasoning from the SSA. My
> deductions would only be probabalistic, of course. That is, they'd only
> have a certain probability of being true. But then again, any deductions
> I make from empirical evidence is probabalistic.
>
I see your point. Your post has cleared up my understanding of these Bayesian
arguments a great deal, and you are right: knowing that 'one' is in one sort
of universe *does* have a significant distorting effect on one's estimate of the
number of those universes, as you claim. I see red at words like transfinite in
these arguments, but actually, one the dust has settled and the transfinite numbers
have been replaced by v. large numbers the argument still works.
The only distribution of P(R) which gives an estimate of E [ P(R | 1 blue) ] near
to 1/2 (which is E [ P(R)] if we assume a priori equal probability of being in a "Life"
or an "Our" world) , in fact, is one heavily weighted towards the middle of [0,1], and
I can't think of any reason to prefer such a weighting (though I wish I could).
Thanks for the patient explanation.
> There were two quite good posts on this topic recently by Jacques Mallah:
> http://www.escribe.com/science/theory/m1192.html, and
> http://www.escribe.com/science/theory/m1194.html. The difficulty arises
> in the confusion between a priori and a posteriori probabilities. For
> example, I know that my license plate number is AFT-058. It's not now
> valid for me to compute the odds of the car in my driveway having the
> license plate AFT-058 as 1/(26^3 10^3).
>
> Likewise, it should not be surprising to me that I'm an American, even
> though Americans only make up 1/20 the population of the world.
>
> So this just shows that any conclusions to be derived from the SSA must
> have a suitable prior. In my example above, the prior was the assumption
> that the any *ratio* of green/blue SAS's was equally likely. Fine. Now
> if I were a blue SAS, I would have a sample set of one, from which I could
> compute a probability distribution on ratios of colors.
>
> Let R be the ratio of blue to green SAS's, R = b/g. I want to compute
> the probability distribution as a function of R on the domain [0,1]:
>
I'm assuming you mean 'R = b/(b+g)'...
>
> P(R) P(1 blue | R)
> P(R | 1 blue) = ----------------------
> P(1 blue)
>
> Now, P(R) is the prior, and I said above that the assumption is that
> this is constant over [0,1], and P(1 blue) = 50%, so P(R)/P(1 blue) is
> a constant, and is just a normalizing factor.
>
> Clearly, P(1 blue | R) = R. Therefore, with the normalizing condition
> that the integral of P from 0 to 1 = 1, we get
>
> P(R | 1 blue) = 2R
>
> Which has an expection value for R of 2/3. That is, given a sample of
> one blue SAS, and the prior mentioned above, I would compute that the
> probablity of any SAS being blue is 2/3.
>
> >
> > >
> > > So if the set of life-SAS's is not isomorphic to the set of (3+1
> > > dim. pseudo-Riemannian manifold quantum field)-SAS's, then we'd
> > > have no a priori reason to assume that the measures of these sets
> > > are the same. If the measures are different, then one is larger
> > > than the other. My money will be on our set having the larger
> > > measure. If the measures
> > > are transfinite but of different orders, then I conclude that the
> > > probability of finding oneself to be a life-SAS is zero.
>
> I stand by this. Note that I explicitly give a new prior: *if* the
> measures of each set are of different orders of transfinite numbers.
> Using blue and green again, that would mean that either R=0 or R=1.
>
> We still have the ratio of prior probabilities, P(R)/P(1 blue), is a
> constant. But now P(1 blue|R=0) = 0, and P(1 blue|R=1) = 1. The
> normalization integral becomes a sum, and we get, simply,
>
> P(R=0 | 1 blue) = 0
> P(R=1 | 1 blue) = 1
>
> Which is pretty easy to interpret.
Jerry
Received on Fri Dec 10 1999 - 03:44:42 PST