Mathematics, Beauty, Mystery, Spirit
July 21st, 2011 § Leave a Comment
I had a co-worker, a young engineer, many years ago who designed turbines using a modeling method called finite elements. Computational fluid dynamics is not a field for the mathematically challenged. These mathematical methods would produce models describing pressures, velocities, mass flow, etc. of fluids, in this case air, within the turbine. Those values allow the engineer to ultimately predict how much power could be derived from the turbine. Very utilitarian, just a means to an end, you might say.
Yet on more than one occasion, this engineer would talk at length about the beauty of mathematics. I was reminded of this the other day when I analyzed the recording of the sound of an agricultural aircraft making a seeding run over a field near our house. The recording converted the sound at the microphone into a sequence of numbers representing the pressure fluctuations as a function of time. In my analysis, I load the sound file, the list of numbers, into a computer program called Raven Lite which converts the first list of numbers into an array of other numbers representing the frequencies of the sound as a function of time. The conversion is made mathematically using Fourier methods. The output of the analysis shown in the image above is, in my opinion, visually beautiful. The family of smooth curves, the subtle shadings, and variation in color representing the amplitude of sounds at different times and frequencies combine to elicit an emotional response in me when I look at it. (here is a description of what it means) And beneath the visual surface there is the beauty of the logic, the methods, the rigor, and the universality of mathematics itself.
But still deeper is the mystery of a natural universe that is so ordered that it can be described by mathematics, in fact giving rise to the whole human idea of mathematics in the first place. And the mystery that phenomena as disparate as swinging pendula and electrons coursing through certain electronic circuits can be modeled using the same basic methods…and that those models will work on a planet a million light years away as well as they work right here on earth. In my world view, those mysteries extend deep into the world of the spirit.
My co-worker understood that even though he would not have used those words…
