In college, I had eclectic interests. That must be why I went to a liberal arts institution, eh? For some reason, human cognition interested me, though I wasn’t able to articulate it in that way at the time. From time to time, I’d pick up a Psychology Today at the library and thumb through its pages. Once, I ran across an article about mathematics and the mind. As a mathematics major, this article had great appeal to me. The thesis of the article was that mathematical thinking was not entirely natural, that it was learned, sometime with much effort. I remember xeroxing that article and filing it away.
In my first semester as a graduate student at the University of North Carolina (Go Heels!), I was given the responsibility for teaching a course on trigonometry. I was pursuing a Ph.D. to become a college math prof like my heros Paul Humke and Ted Vessey, so I welcomed the teaching assignment. At one point during the course, I remember pulling out the xerox of that article from Psychology Today and sharing it with my students. My point in doing so was to let them know that they should not let their struggles with course materials get them down. Their struggle is natural. Psychologists says so.
My students responded very positively to that. In retrospect, they might have decided to use that article to rationalize their mediocre performance in my course. But I remember them being more engaged in the material. Putting more effort into the course after we talked about that old black-and-white article.
This is what I thought of when I began listening to NYC RadioLab’s recent podcast (a.k.a. essay), Numbers.
The hosts, Robert and Jad (whose aversion to numbers, throughout the show, makes me a bit sad), begin by talking about how people are learning to understand how young children grow into a number sense. What are we born with? (Something, definitely?) What must we learn? (Hint, it begins with the number ‘3’.) How do we learn it? (Hint, it involves a leap of faith by the kid.) The mathematical sense of a young child and the mathematical sense of an older person are very different, they occur in different parts of the brain. Wow! And the show moves on, quickly encountering logarithms, of all things.
The essay moves on through other topics, too. There’s the mind-blowing idea of Beford’s Law, the idea that there are more numbers that begin with low first digits than numbers that begin with high first digits. Sound crazy? Listen to the essay. You’ll also learn from Paul Hoffman, the author of “The Man Who Loved Only Numbers”, about the twentieth century’s most interesting mathematician: Paul Erdos. This part of the story will also give listeners a glimpse into the living, human, and cultural nature of the mathematics profession.
The essay/podcast concludes with a story that builds on the human aspect of mathematics by telling part of the story of the relationship between mathematician Steven Strogatz and his high school mathematics teacher, Don Joffray. That story is told is greater detail, though without the flourishes of RadioLab, by Strogatz in his book, “The Calculus of Friendship.”
RadioLab’s essays are always entertaining and informative. In this mathematical essay, they create an engaging story that relates interesting and provocative factoids from human cognition and mathematical culture. I’m not sure that the program helps people understand how mathematics is connected to other human endeavors (e.g., the other sciences). While Jad’s negative attitude toward mathematics throughout provide something of a foil for co-host Robert, it also seems to pander to America’s culturally endorsed bad attitude toward mathematics. Not helpful, Jad, but maybe you make this essay accessible to lots of people who wouldn’t otherwise be interested in enjoying it.