**From:** J. Andrew Rogers (*andrew@ceruleansystems.com*)

**Date:** Fri May 28 2004 - 14:11:55 MDT

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Ben wrote:

*> As I said, in practice this assumption doesn't seem to make any
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*> difference. If you assume a weird enough underlying deterministic
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*> universe (like Bohm's hidden-variables theory) then you can have QM and
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*> determinism: everyone understands that. But for practical purposes, it
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*> seems most elegant and convenient to make the assumption of
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*> nondeterminism, as that makes the math so much simpler and fits the
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*> 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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