Hello.
>From: Brent Meeker <meekerdb.domain.name.hidden>
>I haven't finished Nick Bostrom's thesis - as you say it's rather long; but
>where I went to school the rule of thumb was a thesis had to be over a 100
>pages.
A ridiculous rule.
>In reading your response to Nick I was inspired to go to your web site. The
>argument there for selection of the physical constants of nature is
>fallacious:
No.
>Consider three candidates:
>1. that mathematical consistency of a theory of quantum gravity uniquely
>determines the parameters;
>2. that there are infinitely many 'universes' with a uniform distribution
>in the space of the parameters;
>3. that there are infinitely many 'universes'; with a nonuniform
>distribution determined by natural selection that maximizes the number of
>black holes, with each black hole giving rise to another universe which has
>parameters only slightly different from the parent 'universe'.
> Assume that we take the prior distribution to give equal weight to each
>of these three proposals.
> The first one is a bit tricky, because it is not really one model, but
>is an infinite collection of models each of which gives rise to a different
>set of parameters. Only for one in 10^230 of these models has a
>nonnegligable p(o|i), so #1 should be rejected out of hand.
> (If we were to insist that it is only the one model which gives the
>observed values of the parameters that we are interested in, we would
>certainly not be justified in giving that model an equal a priori weight
>with the other two models, since we have no theoretical reason to justify
>that those particular values would be the correct ones. Remember, the
>prior distribution is not supposed to reflect observed data; the role of
>that comes in the conditional probabilities.)
>The hypothesis of candidate #1 is that there are NOT many possible values
>for the physical constants. The number 10^230 comes from considering the
>parameter space of the standard model of elementary particles. But the
>standard model does not even include gravity. Candidate #1 hypothesizes
>that the theory of quantum gravity will be found to have few (or even zero)
>parameters and the parameters will be restricted by the theory to have a
>small range. Hence p(o|1)=1; just like 2 and 3.
Wrong. You are missing the point. Right now, we do not have such a
model. Suppose there is only one physical constant, p, where 0<p<1, and
that we observe the value x for p. What is the prior Bayesian probability
that, if mathematical consistency were to determine p, it would predict the
value x? Note, this is a prior probability with respect to the observation
(o) that we see x. We are not allowed to use the additional information
that we do happen to see the value x to deterimine this prior probability.
So the best we can do is to assume a uniform probability distribution on
(0,1) for the value that would be predicted. Thus if only the values
x-r<p<x-r would support life, model 1 is disadvantaged by a factor 2r
compared to model 2.
Of course, if we already had a theory of quantum gravity, and if the
math calculation already yielded the prediction that p=x, then p(o|1) (if
you like, p(x|1)) would be 1 - based on that math, not on the fact that we
do see x.
>I also read your essay on the interpretation of QM. I was disappointed
>that you did not even mention the consistent histories and decoherence
>interpretations, which seem more parsimonious than either the many worlds
>or hidden variable theories.
I do mention consistent histories briefly on my historical
interpretations page. As for decoherence, that is a common feature of all
interpretations because it's just part of QM, not an interpretation. As for
more parsimonious, you are wrong. The MWI just states (regarding physics)
that the wavefunction evolves normally and doesn't collapse. There is no
simpler interpretation possible in principle. Of course to get predictions
from any mathematical model, even classical mechanics (if you don't cheat by
leaving out the observers from the math), you need a theory of mind such as
computationalism.
>vr, Brent Meeker
What's vr?
- - - - - - -
Jacques Mallah (jackmallah.domain.name.hidden)
Physicist / Many Worlder / Devil's Advocate
"I know what no one else knows" - 'Runaway Train', Soul Asylum
My URL:
http://hammer.prohosting.com/~mathmind/
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Received on Wed Jun 28 2000 - 15:23:23 PDT