Well, I (and Gary, Joel, Arthur, and Alvin) saw Stephen Hawking's lecture
on Monday evening.  I actually learned something cool.  (I also attended
the technical talk on Sunday, but it was all WAY over my head, didn't
learn a damn thing.)  I thought I'd pass it on, for fun.

The lecture was about the "Theory of Everything", aka Grand Unified
Theory (GUT), of which the best candidates thus far are "string"
theories.  These postulate that all the subatomic particles (electrons,
protons, neutrons, quarks, photons, neutrinos... *everything*) are
actually just "strings", and the vibration mode and frequency of
the string determines the type of particle.  That's the layman's
explanation; it's really quite a bit more complicated than that,
but I won't go into it... because I don't know any more!  So there!

One of the problems, however, with current QM and the new string
theories is that they have very bad "infinities" that occur, that
nobody is really sure how to get rid of.  The infinities come from the
energy of the vacuum: QM says that virtual particles appear and
disappear all the time, at all energies.  (Aside: in case you don't
know, a virtual particle is a particle that appears out of nowhere,
stealing energy from the "vacuum".  It's OK that the violation of the
conservation of energy occurs, as long as it's "fixed" with a time dt,
where dE * dt <= h, where h is Planck's constant.  This is just a
formulation of Heisenberg's Uncertainty Principle.  The formulation you
may be more familiar with says that you can't know both the position
and momentum of a particle more accurately than dp * dx = h.) There is
no known limit to how many virtual particles can be created and
destroyed in any volume of space-time, and apparently our best guess at
the energy required to propel this constant maylay of virtual particles
leads to a divergent integral somewhere; it boils down to there's no
known limit to the number of quantum states allowed in a given volume
of space-time.

As you may have heard, within the past few years, partly as a
consequence of continuing exploration of the consequences of Hawking
radiation, people have postulated that black holes have a very specific
entropy, and that the entropy is proportional to the surface area of
the event horizon.  (He talked about "hidden internal quantum states",
the number of them being proportional to exp(A), A=area of event
horizon.)  Until recently, nobody put two and two together.
Somebody (not Hawking) recently realized that (a) it's reasonable to
postulate that BH's pack quantum states as tightly as physically
possible; (b) BH's have finite entropy; and (c) therefore, there is a
finite limit to the number of states that can be contained in a given
volume of space-time.  VOILA!  The divergent integrals now have a
cut-off.  So string theorists are very happy about this and have gone
scurrying off in just the past few weeks to re-analyze string theory.

It's such a simple leap of logic that it's surprising nobody came up
with it sooner.  It's exactly analogous with "Hawking radiation":
recall Hawking put two and two together to postulate that virtual
particle creation causes black holes to evaporate.  (In case you don't
know, the idea is that every once in awhile, a virtual particle pair is
created just outside the event horizon; usually they re-merge and
annihilate, but in some cases, one falls into the hole and the other
escapes ---> voila, energy has been stolen from the BH's gravitational
field.  Very trivial idea, but nobody thought of it until Hawking.)

So, I learned something concrete in the general lecture.  So I'm
happy.