Collapse and Distillation
Things fall apart–but why? And how? Perhaps it is mere anarchy loosed on the world, but Charlie Hadlock has other ideas. In Six Sources of Collapse, published last year by MAA, Hadlock describes a half-dozen mechanisms that lead to collapses that seem abrupt.
He begins with the humble passenger pigeon. Two centuries ago North America was, literally, aswarm with passenger pigeons. In 1813 Aubudon observed a flock that obscured the midday sun and took three days to pass. Alexander Wilson once observed a flock that he estimated contained more than 2 billion individual birds; that is eight times the current estimate for the world’s total rock pigeon population. A single nesting ground near Sparta, Wisconsin, covered 850 square miles and housed an estimated hundred million birds. Flocks were so thick that folks hunted by swinging a stick in the air and picking up what came down.
It seems hard to credit that we hunted such abundance to complete extinction. (The last known passenger pigeon, Martha, died at the Cincinnati Zoo in 1914.) Hadlock explains the mechanism as the blank and pitiless result of evolution–the birds had evolved to live in enormous flocks. Their reproductive success depended on that, and these gigantic flocks were well adapted to a completely forested eastern United States. A flock of half a billion birds could denude and befoul a patch of forest in a few days, then move on to the next patch. Human settlement and forest clearing limited the available resources for this behavior. The combined effect of thinned forest and thinned flock (from a tide of hunting) led to dramatic population collapse.
The passenger pigeon example is less mathematical than many of the other examples in the anecdote-rich book. Hadlock explicates the collapses of empires, bridges, species, markets, and companies. The author has been a business consultant for decades, and that experience is evident in the many business-related cases he recounts.
The six sources of collapse of the title are: low probability events; the behavior of crowds; evolutionary processes; unstable equilibria; the unexpected appearance of nonlinearity; and network phenomena. There are examples aplenty of all of these.
As I read I kept thinking, “Oh, nice example for my ODE course,” and “I need to remember this example in Calc 2.” You will find material to enrich your probability course, your dynamical systems course, your business math course…
By the end, I was thinking it would be fun to teach a first-year seminar on collapse with this as a text. The lack of exercises might make it difficult, but there is so much good stuff here that I’m tempted to try anyway. At the very least, Hadlock enriched and enlivened my long plane ride to the Joint Mathematics Meetings in Baltimore. I recommend you take him along on your next trip; surely some revelation is at hand.
I had two books with me on the flight to Baltimore (I am always prepared for delays). I shoved DistillingIdeas: An Introduction to Mathematical Thinking by Brian Katz and Michael Starbird into my briefcase at least in part because it is small and didn’t take up much room. At the meeting itself, everyone was buzzing about Starbird’s entertaining invited address and, even more, the all-day, all-star invited paper session he organized. Mike and Brian are inspiring advocates for the power of mathematics to free a person’s mind and spur him or her to insight and creativity.
They are also powerful advocates for inquiry-based learning, and this little volume is a set of four inquiry experiences. The topics are graph theory, group theory, number theory, and calculus. Each of these modules is a well-designed series of questions and prompts to lead a student (or class) on a rich mathematical excursion. If you have ever been tempted to experiment with the Moore method, a painless (and potentially life-changing) way to begin would be to embed one of these modules into one of your courses.
Steve Kennedy teaches mathematics at Carleton College in Northfield, Minnesota, and is the senior acquisitions editor for MAA Books. He is eager to talk to you about the book you are writing–email him at email@example.com.