Sunday, November 21, 2010

Math--The Ultimate Language

by Richard Crews
"We made a deal with the bank," reads the sign in a diner: "They don't sell chili and we don't cash checks." Likewise the human brain evolved to do a marvelous job finding ripe berries, getting us up a tree when wolves were near, and negotiating the stormy shoals of relationships necessary to pass the family jewels on to the next generation. But it was never called upon to fathom the paradoxes of quantum physics--to envision that the same particle can be at two places at the same time; that two particles, if born together, can communicate instantly although millions of miles apart; or that a sub-atomic entity does not decide whether it is a wave or a particle until it is observed--but its decision is then retroactive; or other quantum weirdnesses like those. Similarly, the human brain enables us run, jump, and hide marvelously well in three dimensions, but is incapable of imagining four or more dimensions--though the physical world, when closely studied, seems to need up to ten or eleven dimensions to come out right.

In addition to developing an operating system that will accommodate such useful apps as berry-hunting, wolf-avoiding, or mate-seducing when a culture sees fit to install them, the human brain has developed considerable flexibility with regard to communications programs. There are (still) over 7,000 distinctly different languages in the world with significantly different grammars, vocabularies, and world views, and any child can learn any one of them--or even several--flawlessly. To be sure, the human brain operating system loses some of its flexibility as it matures: the OS age 5.0.0 cannot install some of the apps it could at version 2.0.0. But it retains considerable plasticity. Even an adult (OS 20.0.0 and beyond) can substantially rewire parts of the brain to accommodate damage.

Moreover the brain, for all its foibles and limitations, has gradually--over the course of centuries--evolved one language that transcends cultural and wiring limitations: the language of mathematics. Mathematics very carefully says, "If A, then B," for example, "if there are bees on the Moon, then they fly in circles." It cautiously and studiously avoids any cultural bias and brain-hardware limitations. And it meticulously steers clear of enforcing--or even implying--any constraints on reality or our freedom to perceive it as we choose. Math does not say, "There are bees on the Moon"--everyone knows there are no bees on the Moon--but it does, through rigorous, logical processes, conclude that "If there were bees on the Moon," then "they would be incapable of flying in straight lines."

The languages of music, visual arts, dance, and poetry can be deeply emotionally moving, but they are fraught with cultural bias and brain-wiring limitations. The language of mathematics is not. The extent to which it is "beautiful" (and it is), the extent to which it inspires "awe" and "reverence" (and it does), is because it proceeds the way porcupines make love--very, very carefully.