Monday, January 11, 2010

Emergent Properties

Back in 2007, BRT discussed the fantastic theoretical properties of E8, a mathematical object possessing 248 dimensions, the most complex entity ever conceived by man, a construct never thought to exist in nature, but in actuality, it does...

Strange things occurred when the experimenters applied a powerful 5.5-Tesla magnetic field perpendicular to the direction of these electron "magnets". Patterns appeared spontaneously in the electron spins in the chains – in a simplified example with three electrons, the spins could read up-up-down or down-up-down, among other possibilities. Each distinct pattern has a different energy associated with it.

The ratio of these different energy levels showed that the electron spins were ordering themselves according to mathematical relationships in E8 symmetry.

Complex symmetry

Alexander Zamolodchikov, currently at Rutgers University in Piscataway, New Jersey, pointed out in 1989 that the theoretically predicted energies of such systems match expectations from E8 symmetry.

But the underlying reason why is still mysterious. Robert Konik of Brookhaven National Laboratory in Upton, New York, who was not involved in the experiment, says the fact that such a simple system – essentially consisting of one-dimensional chains of magnets – should display such complex symmetry is surprising.

"Just sort of looking at the system, you wouldn't necessarily expect it to occur," he told New Scientist. It is "remarkable" to see this rather exotic piece of mathematics appear in the real world, he adds.

When looking at this emergence of something totally unexpected, one is struck by how common this actually is in nature, particularly when examining chaos and how complexity comes forth from simple actions like the moon orbiting the earth (Strange Attractors/Henon Curve)

or the impact of initial conditions on events like financial markets or changes in the weather. (butterfly effect).

Because of this, it's obvious Black Swans or unexpected events of great impact occur without question, a concept that should be taught to students of all ages to better prepare them to deal with the vagaries of the real world. For proper edification of same, here are a few examples of why black swans rule:

  • 2008 financial crash
  • The Great Depression of 1929
  • 9/11
  • Pearl Harbor
  • Theory of Relativity
  • Penicillin
  • Tsunami of 2004
  • Katrina
  • Bach
  • Alexander the Great
  • Avatar
  • "W"
  • Obama
  • Shakespeare
  • Etc., etc., etc.
"And the beat goes on." - The Whispers
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