From: J. Andrew Rogers (andrew@ceruleansystems.com)
Date: Fri May 28 2004 - 01:17:56 MDT
On May 27, 2004, at 8:19 PM, Marc Geddes wrote:
> --- Ben Goertzel <ben@goertzel.org> wrote: >
>> Or else you allow Boolean logic at the quantum
>> level, and then
>> Kolmogorov axioms break, yielding Youssef's quantum
>> probability theory
>> (in which probabilities are complex numbers rather
>> than real numbers).
>
> Precisely so! Boolean logic holds, Kolmogorov's
> axioms break.
The digression into quantum logic and related bits set off some red
flags in my mind, and after going back and reading some of the
literature, it *really* started to set off some flags. The
mathematical models seem vaguely consistent in isolation, but they do
not appear to be completely consistent as a body nor with the evidence
available for practical matters. This isn't a direct criticism of the
above quoted material or what anyone wrote per se, but something
doesn't hold up. There is some type of mismatched assumptions in the
interaction of all the pieces. It looks like a variant of a mistake
I've actually seen before in literature.
1.) QM models generally assert non-determinism inappropriately. They
assume literal mathematical non-determinism, but generally make no
distinction for systems that are not measurably deterministic but which
are nonetheless fundamentally deterministic. Expressions of both cases
will look empirically identical but the mathematical consequences of
which model you assume are qualitatively different. There is no
justification for assuming non-determinism over non-measurable
determinism in practice.
2.) The physics do not seem to imply mathematical non-determinism,
just a system which is not measurably deterministic. Hell, the
mathematics of QM in question have finite descriptions, which means
"deterministic" in a normal Kolmogorov sense (it is worth noting that a
number of other people have raised this particular objection in
literature).
The basic problem that I see is that no distinction is made in the math
between non-deterministic systems and systems which are not measurably
deterministic in some finite context. And that an assumption of
non-determinism is used for some of the physics appears incorrect prima
facie from an information theoretic standpoint. One could throw in a
bunch of stuff about Fisher information etc, but i think the real
problem lies in the assumption I already mentioned. So from this
standpoint, the standard deterministic model would still seem to apply.
I've noticed that very few papers actually deal with the measurability
of determinism in their models, which is closely related to predictive
limits (how I became acquainted with the concept a number of years
ago). It is nonetheless a very important concept to keep straight when
talking about computation on finite state machinery because the
consequences are broad and subtle.
So in short, I'm not buying the non-deterministic quantum escape hatch
unless someone can make a convincing argument that we are not looking
at a non-measurable deterministic (there has got to be a better term
for this -- it doesn't have a namespace in math AFAIK) phenomenon,
because there is not insignificant evidence that the latter is the
actual case. I call it an "escape hatch" because using an assumption
of non-determinism automagically solves nasty problems without much
additional thought. In other words, it is probably popular because it
is theoretically convenient and most folks are not terribly familiar
with predictive limits/measurability of determinism math.
This is probably a bad time to be dropping a hairy theory grenade since
I'll be traveling for a few days, but there it is. I'm calling
shenanigans. I'll add that fine models for consciousness, qualia, etc
can be elegantly derived from the deterministic system, even if it
doesn't allow you to conveniently bury the subtleties in
non-determinism.
j. andrew rogers
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