Today, mathematics fails to tell us what's inside Virginia. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.
I've just seen the movie, The New World. It was wonderful by many measures, but with a curious wrinkle: Most of it takes place during seven years from the arrival of the Jamestown settlers to John Rolfe's return to England with his wife Rebecca, once nicknamed Pocahontas. The camera draws our eyes again and again to the texture of the Virginia tidewater area. (It'll be a crime if it doesn't win the Oscar for cinematography.)
The mathematics enters as we realize that we're seeing only the edge of a continent. The lowering forests vanish into the distance and what lies beyond this edge is dark and unknowable.
Now, imagine that we cut a slab of copper into the shape of Virginia. Let's insulate the top and bottom of the slab, as well as the edges, and let's hold the edges at different temperatures -- one temperature on the seashore, another on the border with North Carolina and so forth. Mathematics will then allow us to determine the temperature anywhere inside our slab of Virginia. When we know the edges, we know the interior. There's more: change the temperature along the border with North Carolina and we can predict the temperature in Richmond or in Lynchburg at any time in the future.
But Virginia's no slab of copper. The math for calculating its interior, or its future, is far more complex and virtually powerless to extract information from what we know about the edges. A tiny change on the edge of the land, or the present edge of the future, gives infinitely different results in time or in space.
All that ran in my mind during the movie. Pocahontas' intervention in John Smith's execution, and her aid to the starving colonists, were small events on the edge of the vast forest reaching westward, or on that edge of time. Yet that tiny stitch in history's tapestry formed a historical watershed.
The movie brilliantly captures that mathematical fact. It does so by narrowing its lens and showing us the texture of the edge -- the smallness of events along the edge. We see the distant horizontal landscapes in all their changing colors. But those views express unknowability, while close-ups of leaves and rills, bark and dirt, cry out to us to see the intimate scale of reality.
Pocahontas herself is only a teenager, driven by a cat's curiosity, mixed loyalties, and a yearning to do the right thing. When Rolfe asks her to marry, she looks at him searchingly, then finally asks, "Are you kind?" That should be a poignant reminder to us, as we babble incessantly about the quality of "leadership".
History is far less shaped by leaders than by modest acts in the common place. That becomes quite clear if we choose to master the mathematics of non-linear differential equations. But now an eerie and complex movie says the same thing in another language entirely. It reminds us that the future is shaped in the delicate intimacy of small events, out on the very edges of time and of space.
I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.
For more on the movie, including reviews and much background, check the In-ternational Movie Data Base: https://www.imdb.com/title/tt0402399/
Without using the term here, I've referred to the much talked-about Butterfly Effect. See, e.g., Episode 652. For more on calculating the steady or transient temperature in a slab, see, e.g., A Heat Transfer Textbook., Chapters 4 and 5.
Contemporary print of Pocahontas/Rebecca made during her two years in England before her death in 1616.
The Edge of Land (photo by JHL)