Saturday, May 24, 2014

That Old Beholding Eye

Earlier this year I bought a couple of "For Dummies" books about some basic math disciplines with hopes of improving my drastically underwhelming understanding of those subjects. Slogging through them has triggered a couple of high school memories (of the actual subject even!) and shown me that one of the reasons I did poorly in these subjects as a youngster was laziness.

My mind has to work hard to follow all of the steps of math and it apparently likes shortcuts and hopping around a lot better than it likes hitting B, C, D, and E when going from A to F. Unfortunately, math is something where shortcuts are themselves quite clearly defined and which require their own special set of steps, meaning that skipping around and cutting corners is not the way to solve equations. In other words, I can probably learn some of this material, but I don't think I have a math mind.

An infographic at the Physics World blog highlights the results of a psychological study of mathematicians in order to try to figure out some of the things that make a math mind tick. They focused on the habit that some scientists have of describing equations as "beautiful," which seems like an odd word to use for an equation. But by doing MRIs of the mathematicians' brains while showing them different equations, they saw electrical activity in the same part of the brain that's active when people see things that are pleasant in appearance.

The qualities of a beautiful equation are actually some of the same qualities that go into making up what most of us think are beautiful -- symmetry, simplicity and significance. The winner of the "mathematical beauty contest" was an equation called "Euler's Identity," which reads like this:

eiπ+ 1 = 0

Although it may not seem simple to those of us for whom the mixture of letters and numbers brought ruin to our dreams of becoming astronauts, the infographic shows how it has those qualities of symmetry, simplicity and significance. Each of the letters, both Latin and Greek, represents a fundamental mathematical constant, meaning that they can't be reduced in form, which are themselves the basis for understanding many other mathematical fields. It's a special case of Euler's formula, which establishes the fundamental relationship between the trigonometric functions (functions of angles) and the complex exponential function (describing how numbers change in relationship to each other in functions).

I'll take the mathematicians' word for this being a beautiful equation -- although I can see how it matches the criteria they set forth, it doesn't strike me as "beautiful" the same way a natural scene or work of art does. Which is why I don't think I have a mathematical mind.

On the other hand, I may be selling myself short, because according to the infographic, the equation by Srinivasa Ramanujan describing the progression of the infinite series 1/π:

is considered very very ugly.

I have a hard time disagreeing.

No comments: