BRT has often waxed poetic about phase transitions where two or more conditions give rise to profound changes in a given environment like that of ice covering a pond when the temperature hits 32 degrees because the day before the pond is completely covered, 50% of the pond's surface remains ice free, which mirrors, in statistical fashion, fluctuations in the stock market, interaction of predator/prey populations in a pond or growth patterns of trees in a tropical forest located next to the Amazon. To whit...
Systems of many interacting components — be they species, integers or subatomic particles — kept producing the same statistical curve, which had become known as the Tracy-Widom distribution. This puzzling curve seemed to be the complex cousin of the familiar bell curve, or Gaussian distribution, which represents the natural variation of independent random variables like the heights of students in a classroom or their test scores. Like the Gaussian, the Tracy-Widom distribution exhibits “universality,” a mysterious phenomenon in which diverse microscopic effects give rise to the same collective behavior. “The surprise is it’s as universal as it is,” said Tracy, a professor at the University of California, Davis.
When uncovered, universal laws like the Tracy-Widom distribution enable researchers to accurately model complex systems whose inner workings they know little about, like financial markets, exotic phases of matter or the Internet.
“It’s not obvious that you could have a deep understanding of a very complicated system using a simple model with just a few ingredients,” said Grégory Schehr, a statistical physicist who works with Majumdar at Paris-Sud. “Universality is the reason why theoretical physics is so successful.”
Whereas “uncorrelated” random variables such as test scores splay out into the bell-shaped Gaussian distribution, interacting species, financial stocks and other “correlated” variables give rise to a more complicated statistical curve. Steeper on the left than the right, the curve has a shape that depends on N, the number of variables.
Nature is inherently modular in how she expresses herself to us rubes. Pretty awesome don't you think? :)