From: J. Andrew Rogers (andrew@ceruleansystems.com)
Date: Fri May 28 2004 - 14:11:55 MDT
Ben wrote:
> As I said, in practice this assumption doesn't seem to make any
> difference. If you assume a weird enough underlying deterministic
> universe (like Bohm's hidden-variables theory) then you can have QM and
> determinism: everyone understands that. But for practical purposes, it
> seems most elegant and convenient to make the assumption of
> nondeterminism, as that makes the math so much simpler and fits the
> observed data conceptually.
Gah, the point was completely missed. Let me elucidate a bit, as I've
actually been thinking about the broader question for some time. There
is a subtle inconsistency in the mathematical assumptions of some
theoretical physics.
There is nothing "simpler" about the non-deterministic model. It is
only nominally simpler if one views the probability model of the output
in isolation. Yes, in that case it is kind of tidy to just declare a
non-deterministic function and walk away. This is the same kind of
fallacy as saying that "God did it" is the simplest explanation for
everything in the physical universe.
Shallow problem:
In the hidden deterministic model, the probability function is
inductive, and is only probabilistic in that there is a predictive limit
because the model is incomplete. It apparently looks identical to your
hypothesized non-deterministic model. However, by definition there is a
simpler deterministic description of the inductive probability model in
the deterministic case which will also therefore be simpler than the
non-deterministic case, since they are indistinguishable from the
standpoint of induction. This also implies that the non-deterministic
function is in fact reducible to a simple deterministic description. We
may not be able to inspect this simple deterministic description, but we
can know that one exists. How is it allowable that a
"non-deterministic" function is mathematically reducible to to a finite
deterministic description in theory?
Deeper problem:
The other point, which is more fundamental, is that a general
discernable distribution in the output of a function implies determinism
ipso facto in normal algorithmic information theory.
This isn't an inconsistency between competing concepts, this represents
some kind of pretty basic inconsistency in the application of the math.
In the non-deterministic models, there is no consistent follow through
with the mathematical consequences of that model selection, and
properties are assumed for the hypothetical non-deterministic function
which are reserved for deterministic functions. If you actually DO
follow through and consistently treat that function as non-deterministic
with all the characteristics implied, the non-deterministic model
clearly collapses as any kind of reasonable description of the physical
universe.
I haven't seen this inconsistency addressed. I've seen some other
people nibble around the edges of this, but I'm wondering if I'm the
first person to frame the problem like this. Given that we are accepting
that the probability functions in physics are real, determinism is the
only consistent model. Otherwise, someone will have to explain this
required notion of a hypothesized non-deterministic function that just
happens to exhibit the algorithmic information theoretic characteristics
reserved for a deterministic one.
j. andrew rogers
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