By Phil Nast June 20, 2011 12:33 pm
When I was very young, I owned a book with a cover showing a boy holding a book with a cover showing a boy holding a book with a cover…. I’d try to peer as far as I could down the series of diminishing book covers. Later, when I read The Atom in DC Comics, I’d imagine shrinking along with scientist Ray Palmer to follow the image into the microscopic realm. Though I didn’t have a name for it yet, self-similarity was a concept that fascinated me.
I happened on the concept again in college when I read Russell Hoban’s The Mouse and His Child, a desperately needed escape from 18th century British novels. After being dropped into a pond, the mouse and his son talk with a snapping turtle about recursive infinity, the Droste effect. And I encountered it labeled self-similarity when I read about the Mandelbrot set in James Gleick’s Chaos: Making a New Science.
Note: The Jonathan Coulton song “Mandelbrot Set” includes a word students won’t fail to hear, however, I heard the same word on The Daily Show.
All of these memories came back last week as I watched Hunting the Hidden Dimension, a NOVA program about Benoit Mandelbrot and fractals. (You can watch the program online. The entire program runs 52:59, but if you want to get right to fractals and biology, you can start with section 4 at 34:04.)
Mathematics has revealed a lot of surprising things in nature and in biology. Fractals and self-similarity underlie much in nature, from the branching of trees to our own heart beats. When shown the branching of the respiratory, circulatory, and nervous systems, their relation to the fractal branching of trees seems obvious. Discovering that the beat of a heart is not metronomic but also fractal does not.
Mathematical biology or biomathematics (theoretical biology is a slightly different field) is an exciting field for students to consider if they’re interested in applied math. Steven Strogatz investigates Sync. Flocking birds and schooling fish are examples. Strogatz’s book Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life is a good introduction to Sync written for a general audience.
Mathematical biology is as varied a field as the women and men who pursue it. Christina Cobbold considered a career in art before becoming a mathematician. Her work is more clearly related to the familiar world. She has an extended lecture called Mathematics meets Biology on the Web. John Wesley Cain’s field is cardiac electrophysiology. Much of his investigation is done with interdisciplinary teams. Martin Nowak’s work can be more theoretical and investigates the origins of life, and evolutionary dynamics.
For a math or biology student thinking of an interdisciplinary career, Getting Started in Mathematical Biology might provide an incentive. The author identifies eleven areas of investigation in biology from evolution to neurobiology and behavior almost all of which have been influenced by mathematics.
Math and biology teachers can find downloadable posters illustrating the connections between the disciplines at the American Mathematical Society.
For high school seniors, the Society for Mathematical Biology lists degree programs in mathematical biology.