Symmetries are transformations that don't transform. A letter like capital "Y" (in most fonts) has a left-right symmetry: exchange the left side with the right and it stays the same. An "E" has a reflection symmetry about a horizontal axis; a "Z" maps back onto itself after a 180 degree rotation about a point in its center.

Broken symmetries are patterns that begin by working but then slip. A pencil balances on its point — but falls upon the slightest disturbance. The electrons in a hot crystal of iron are randomly oriented, with no preferred direction — but cool the metal below its Curie temperature and the electron spins lock with each other and point the same way, giving a strong magnetic field. Make a cylindrical soap film, a tube between two parallel rings — but pull the rings apart and beyond a certain limit the cylinder pinches off and snaps into two separate disks.

More exciting: stand on an empty aluminum soda can. If you're light enough it carries your weight, just as a girder compresses slightly but remains symmetric and supports its burden. But go past its load-bearing capability and the can suddenly buckles. The fourth-order differential equations that govern it develop new solutions that grow exponentially. Ka-pow!

The same thing happens to societies ... and to individuals. We're in a balanced mode, able to handle the usual day-to-day perturbations that come along — and then a little extra stimulus or stress pushes us over the edge of instability. Wisdom consists in recognizing the approach of danger and turning back before we cross the line into catastrophe. After the point of no return, free will goes out the window. (Think teenagers in "love"!) The system evolves to another stable state, regardless of our wishes. Eventually control returns, but often there's no going back to the pre-crisis situation. Stiff systems are particularly vulnerable to such sudden transitions; flexible ones bend before breaking. Rigidity is risky.

Friday, December 10, 1999 at 06:26:27 (EST) = 1999-12-10

TopicScience - TopicPhilosophy

(correlates: InvisibleInstabilities, SicilianDefense, PersonalCosmology, ...)