Subject: BHA: RE: RE: In which kind of world is probability theory useful?
Date: Tue, 31 Aug 1999 11:25:31 -0400


Hans,

This is very interesting, although probably outside both of our main areas
of interest. By allowing quantum mechanics, particularly the Heisenberg
Principle, to include epistemic uncertainty, I was just trying to allow
physics to be fallible (or, in Kuhn's terms, to allow the possibility of a
paradigm shift at some point in the future that would resolve the apparent
impossibility in the HP). Nonetheless, I think you're right, at least as we
understand matter today (which is via quantum mechanics).

BTW, another form of probability that's not quite reducible to other
determinants is the age-old set of urn problems. When the person puts their
hand into the urn they may consciously randomize (e.g., by reaching to a
different part of the urn each time). Probably :) this is more of a
pseudo-random process, but still is consciousness reducible? Other real,
uncertain systems might include those deliberately designed by humans to be
random slot machines, analog simulators, etc. Queues (including traffic,
some labor markets, etc.), of course, are a classic example. In nature,
genetic mutation is another prime example, as is the survival of species and
individuals.

Thanks for the thought-provoking discussion.

Best.
	Marsh

-----Original Message-----
From:	owner-bhaskar-AT-lists.village.virginia.edu
[mailto:owner-bhaskar-AT-lists.village.virginia.edu] On Behalf Of Hans Ehrbar
Sent:	Monday, August 30, 1999 4:22 PM
To:	bhaskar-AT-lists.village.virginia.edu
Cc:	bhaskar-AT-lists.village.virginia.edu
Subject:	BHA: RE: In which kind of world is probability theory useful?


Marsh,

thank you for your additional examples.  I did try to go the
reductionist route: instead of postulating the existence of
irreducibly probabilistic generative mechanisms, I tried to
see how far one gets explaining random outcomes by leakages
from other layers of reality in a stratified world.

You gave convincing examples that this is not always the case:
quantum mechanics is apparently irreducibly probabilistic,
and also thermodynamics cannot be reduced to the mechanics
of lots of molecules, since the laws of mechanics are
reversible in time, but those of thermodynamics are not.

I doubt that quantum mechanics can be seen in part as
epistemic uncertainty.  One such interpretation, according
to which there are "hidden variables" which we don't know
about, can be refuted by the a simple mathematical theorem
which shows that even pure states in quantum mechanics,
which are not mixtures of other states, are subject to
Heisenberg's uncertainty relation, according to which either
location or impulse can be sharp, but not both.

Hans E.



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