-------- Original Message --------
To George Shimanovich:
I was wondering whether you meant "increase their entropy"
rather than "decrease". But your original word makes sense
too: VN's works resist simplification by critics who try to
impose their own ideas of order (even at Key West--and
there's not only Stevens but Frost again).
To Jansy Mello:
I was struck by your mention of Moebius strips and your
thoughts on "manifold" in the same post, since in
math, a Moebius strip is an example of a "manifold".
(If you make it out of ideal paper, anyway.)
To Sergei Soloviev:
I don't think there's a problem with EPR correlations.
They reduce the number of possible states, reducing
the entropy, but such effects are well understood.
Nor do I think there's a probloem with unknown substructures.
In quantum mechanics, calculations of entropy include only
the degrees of freedom whose minimum energies can be
reached frequently at the temperature of interest. See
for example
<http://en.wikipedia.org/wiki/Specific_heat#Theoretical_models>.
At low temperatures--even at room temperature, to a great
extent--the energies available aren't enough to excite
electrons in molecules, so these degrees of freedom are
"frozen out" and unimportant to the entropy. The nuclear
degrees of freedom are "frozen out" till you reach vastly
higher temperatures: those of nuclear weapons (except in
certain special situations, such as nuclear reactors). The
quark degrees of freedom are frozen out till you reach
temperatures of billions of kelvins, as at the particle
accelerator RHIC. Any smaller structures would require
even higher energies, which is why they're still unknown
even to high-energy particle physics, and we don't have
to worry about them.
Implicit in the above is the well-known fact that in quantum
mechanics, smaller size means higher energy. So something
I said to James Studdard was wrong, namely that there's
no reason for the Planck time to be the shortest time
any more than for the Planck mass to be the smallest
mass, which it isn't. That's backwards: if the Planck
time is the shortest time, then one might think the
Planck mass is the /biggest/ mass (of an elementary
particle?), which is reasonable.
I've learned more since then about statements that the
Planck time and length are the smallest possible. Not
to get into details, but I don't think that means that
space and time are divided into discrete bits, as in
television. Nevertheless I apologize for my incorrect
correction.
Jerry Friedman
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