Broken Symmetry

Charles Lucy asks:

> Does anyone have any comments on the concept of "broken symmetry"?

I learned about this when studying phase transitions, e.g. water freezing.
Water is isotropic - has no sense of direction. Ice is crystalline and
thus distinguishes directions by the orientation of neat rows of molecules.

Symmetry breaking also arises in cosmology and particle physics. The
Weinberg-Salam unification of electromagnetic and weak forces somehow deals
with them being like two directions that get sort of arbitrarily
distinguished by a spontaneous symmetry breaking, which the cosmologist tell
us happened as the early universe cooled down, probably in the first few
seconds after the big bang but I really don't know.

My excellent undergrad thermodynamics professor illustrated symmetry breaking
by using an inverted pendulum. Basically, if you balance a pencil on its
tip, at first it looks symmetric, the pencil could fall in any direction with
equal likelihood. But in fact it ends up falling in just one direction. So an
initially symmetric situation ends up being not symmetric at all. That's a
broken symmetry.

I suppose just rolling some dice would be a symmetry breaking operation. All
the sides are equally likely to come up, but then afterwards only one side
actually comes up on each die.

I don't see immediately how one could apply the idea of a broken symmetry to
tuning systems. I can sort of imagine thinking of the seven notes of a scale
as starting off all equally spaced, then somehow the symmetry is broken and
a couple of the intervals get smaller. But that seems pretty nutty.

I've thought for a long time about using statistical methods like simulated
annealing to do algorithmic composition. The total duration of the
composition is divided up into many little time slots - like a crystal is
made up of an array of atoms. What note to put at each time slot? At a high
temperature, the choice of notes is random. As one brings down the
temperature, some sort of orderly pattern emerges. That would be a symmetry
breaking.

I've never actually got around to trying this. I just plain don't know how to
write a program on a PC that will make the PC generate noises. My best
guess is to go through some sort of MIDI file. Back around 1984 good old
basica came with DOS and the play command did what I needed. Now every PC has
a CD player, but things are so complicated, I have no clue how to do the easy
things!

Hope my comments are useful!

Jim



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