From: Marc Geddes (marc_geddes@yahoo.co.nz)
Date: Thu Jan 20 2005 - 21:23:30 MST
--- Eliezer Yudkowsky <sentience@pobox.com> wrote:
> What's less commonly appreciated is that reality
> does *not* tell you just
> anything. Reality is *extremely constricted* in
> what it tells you, far
> more constricted than human storytelling. Truth is
> *not* stranger than
> fiction; humans just have a warped idea of what
> constitutes normality. The
> theory of conservation of momentum is not that
> momentum is conserved *most*
> of the time or *nearly all* of the time, it is that
> momentum is conserved
> *every single time*. It isn't a coincidence, we
> hypothesize, that
> conservation of momentum has been observed on every
> occasion thus yet where
> humanity has had opportunity to test it; it's
> because reality obeys this
> *absolute* rule, and this absolute rule has given
> rise to humanity's
> experience so far.
>
> Fallible humans may not dare to assign a probability
> of unity to the
> probability of conservation of momentum. Let us say
> we assign a
> probability of at most 90%, meaning that if we took
> ten contemporary
> physical hypotheses of equal status, we would expect
> at least one to be
> disconfirmed a millennium hence. But the hypothesis
> of conservation of
> momentum is not that momentum is conserved 90% of
> the time or even 99.9999%
> of the time. The hypothesis of conservation of
> momentum is that momentum
> is conserved 100.00000% of the time. We may be
> uncertain, but the
> hypothesis of "conservation of momentum"
> hypothesizes a state of affairs in
> which reality is *not* uncertain; a reality in which
> it is *absolutely
> certain* that momentum will be conserved on each and
> every occasion.
>
Uh...there's a bit of a puzzle here that I ran into
when debating J.C.Wright.
The trouble is that according to Bayes we can't
actually assign a probability of 0 or unity to
anything. And the only natural interpretation of the
probabilities as I understood it is that they were
referring to the frequency of space-time systems in
the multi-verse. For instance a probability of 99%,
meant that in 99 out of 100 alternative space-times
such and such a thing was true.
So are you sure it actually makes sense to assign a
probability of say 99% that something is *absolutely*
true? To say that something is truly 'Universal' is
to say that there is no region of the Tegmark
multiverse where the something is not true. But in
that case, what would the counter-factual mean? How
could the 1% probability of falsehood have any
meaning?
=====
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