Math starts out as a simple tool for kids who are learning those pesky times tables. Then they learn fractions, and that makes sense, because you might need to bake a cake. In high school and college, math becomes a short cut to figuring out more complex problems, like the volume of this squiggle:
At some point concepts become so complicated that only math can be used to explain and understand. This goes beyond ordinary language; it’s more like a language for sophisticated thought. Aristotle had to coin new math in order to explain, explore, and record his ideas. Over time, you learn more math until it finally all comes together when you realize that Fourier transforms are novels, essays, even poetry written in Math, allowing you to comprehend a thing that could never be shared without Math.
Fourier series are used to describe periodic functions, and the Fourier transform allows us to translate non-linear phenomena to analyze there as well. Math, specifically the book of Fourier, enables the analysis of signals in either the time/spatial domain or in the frequency domain. What follows might as well be equivalent to performing mathematics in the 4th dimension to the non-math-speaker. And here I have a confession to make: My knowledge of Fourier analysis is akin to being in Greece and learning how to say, “Where are the bathrooms?” --- only to have the respondent reply in a string of rapid, unintelligible syllables.
But I know what I know, and in a Linear Systems and Analysis class long ago I glimpsed what eternity must feel like; truths so fundamental, windows to new worlds, and the most elegant poetry….that can only be described with Math. Theoretical physicists (Einstein’s colleagues) use math this way, every day. Some engineers do, especially those who design hardware in imaging and radio frequency applications, but also spectroscopists and crystallographers, among others. Computers and computer modeling have replaced most of the math that many engineers use today, but the math is there, under the framework.
The very famous Mother Nature is big on using math in her art. A shell, snowflake, or even a clump of ferns demonstrate fractals, whose elegance is neatly described with math. Math is fundamental to the universe as we know it. The next time you hear a kid say they don’t understand why they need to know all this math, show them an ammonite suture as one example of a fractal and explain that math can be used with a computer to 3D print that clump of ferns over there….and maybe they will pause, not yet with the awe of math that Fourier and the frequency domain bestowed upon me, but at least a shadow of the power of understanding math and a hint of so much more.
Neil Armstrong once said that he thought we would be further along by the year 2000 than we were, yet he also noted that a cell phone is far more powerful than the computers that they used for the Apollo 11 Command Module, the Lunar Module that they used to navigate to the moon, and for operating all of the Apollo 11 control systems. (And they did their own math back then, with little to no computer modeling.) Armed with Math, we can build more than cell phones. Math and Science are already there, we just have to uncover more of them. Engineering, Technology, and yes, Art --- are “what can be.”
Lynnette Reese holds a B.S.E.E from Louisiana State University in Baton Rouge. Lynnette has worked at Mouser Electronics, Texas Instruments, Freescale (now NXP), and Cypress Semiconductor. Lynnette has three kids and occasionally runs benign experiments on them. She is currently saving for the kids’ college and eventual therapy once they find out that cauliflower isn’t a rare albino broccoli (and other white lies.)
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