As many of you may recall, my mathematics background is atypical for many math teachers. I do not have a degree in mathematics. Math was a language I needed to know to get a degree in electrical engineering and later, one in business. It had no appeal to me whatsoever beyond offering access to new subject knowledge and associated professions.
Through much of my life, I struggled with math, and still do at times, as well at certain levels of understanding. I did not like math particularly, mostly since I did not have an intuitive sense for it; math was simply a means to an end. While I overcame the difficulties I experienced with math, I still viewed it as a set of tools to use, not as anything to admire.
My perspective changed after I recently entered into a teaching program pursuing a credential in secondary mathematics, and an MA in education. After reading the transcripts from a Learning Company video lecture, From Zero to Infinity: The History of Number, my eyes started to open, my mind started to expand, and my appreciation for mathematics started to take root.
I read about the amazing history of math, its multiethnic origins, and its evolutionary and revolutionary advancement over the past 5,000 plus years. From using stone pebbles to represent quantity as a whole / natural / counting number, to recognizing the existence of “zero” and negative numbers, to identifying irrational numbers to denote “unnatural” dimensions, to defining complex numbers to represent imaginary, “unreal” numbers, and to the many more brilliant discoveries since, the art, and science, of mathematics expanded our ability to make sense of our world.
Unbeknownst to me, until tonight when I watched a NOVA special on PBS, our ability to understand the complexities of life, mathematically, took a herculean leap forward with Benoit Mandelbrot’s pursuit at IBM to find the cause of certain transmission line noise that interfered with sending digital data over long distances at “high speeds,” at the time. In his study of the issue, he recalled the earlier work of Helge von Koch and Georg Cantor, and recognized what he called “self-similarity” in the noise where patterns repeated themselves iteratively as he observed the noise with varying degrees of resolution (e.g., hours, minutes, seconds). Similar work developing methods to measure coastlines more accurately lead him to hypothesize that they were infinitely long, a concept difficult to swallow at the time. Finally, in 1975, he coined the term “fractal” to represent the self-similar property created by iterating a mathematical equation recursively.
With this discovery, and later work by Mandelbrot. fractals emerged as a means to explore our world in ways never imagined. A new mathematical domain, termed “fractal geometry,” enabled scientists, physicians, physicists, mathematicians, and many others to collaborate and to discover details about our world thought impossible. And while I had heard of Mandelbrot Sets many years ago, I neither appreciated their beauty, power, and application, nor understood their mathematical basis or significance.*
Mandelbrot stood on the shoulders of many mathematical giants when he made his discovery. Hopefully, many others will stand on his shoulders, and those of others, as we advance the understanding of our world around us. Advances in medicine, medical treatment, finance, entertainment, and communications owe themselves to fractals. What fabulous new developments are yet to be discovered?
And who will make that discovery? One of the hundreds of millions of today’s students in the world possibly will stand on Mandelbrot and others’ shoulders thanks to teachers. As a math teacher candidate, I am excited about the opportunity to influence a thousand or so students over the next decade or so; I am sure thousands of others feel similarly. PBS’ NOVA program offers lesson plans and activities for teachers to use to share fractals and many other science, technology, engineering, and math (STEM) concepts with students to help.
* I cannot recall when I first heard of Mandelbrot Sets. It could have been in my electrical engineering program, specifically in digital communications or similar coursework such as physics. Sadly, the pointer to that memory address faded a while ago.