source file: mills3.txt Date: Fri, 29 Aug 1997 01:55:52 +0200 Subject: Broken Symmetry From: James Kukula 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 SMTPOriginator: tuning@eartha.mills.edu From: PErlich@Acadian-Asset.com Subject: RE: 5-Limit in India? PostedDate: 29-08-97 18:22:16 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 29-08-97 18:22:21-29-08-97 18:22:21,29-08-97 18:22:08-29-08-97 18:22:09 DeliveredDate: 29-08-97 18:22:09 Categories: $Revisions: Received: from ns.ezh.nl by notesrv2.ezh.nl (Lotus SMTP MTA v1.1 (385.6 5-6-1997)) with SMTP id C1256502.0059EE4C; Fri, 29 Aug 1997 18:22:17 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA08741; Fri, 29 Aug 1997 18:22:16 +0200 Date: Fri, 29 Aug 1997 18:22:16 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA08742 Received: (qmail 9497 invoked from network); 29 Aug 1997 16:22:07 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 29 Aug 1997 16:22:07 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu