About

took notes while he swept the skies for mysterious objects, one day sweeping up the new planet Uranus. Using my father’s old Olivetti typewriter, I made up a book and kept adding to it. I would pore over the ghostly pictures of spiral galaxies taken in all-night exposures from Mount Wilson during the blackout years of the war. I memorized long passages about the sky: “There are countless millions of far-distant, superheated, self-luminous gaseous bodies called stars, each one in itself a sun.” I put that from the Almanac in my book. I drew pictures of astronomers, comets, galaxies, and observatories in my book. It was to be an illustrated history of astronomy. I took my book to class as part of a project. I read constantly. I spent Saturday mornings looking for a place to hide from my father because he always wanted me to work in the yard. He would find me buried in a chair, and I’d have to put aside my reading and dutifully pull weeds or rake. Before each birthday, he offered to drive me to any observatory of my choice in the Southwest. Over the years, we visited Mount Wilson and Mount Palomar observatories and even the great meteor crater in Arizona. He enjoyed the trips as much as I did. I was magnetically drawn to Palomar which in those days was still fairly new. Its gleaming dome was architecturally stunning. How thrilling that people would build such fabulous structures just to see stars and galaxies! What was cool to me was obviously also important. In my middle years we moved to Florida. We were lucky enough to have a house on the ocean in Atlantic Beach. The skies were dark and rich with stars. As my family was getting ready for bed, I’d set up my telescope out on the lawn by the ocean. That’s where I learned about the sky.  I still get excited when I see Hercules rising in the east in Spring. Those were also the years of my astronomy club and of building rockets. (We all had read and absorbed Rockets, Missiles, and Space Travel by Willy Ley who wrote vividly about the origins of the German rocket program. Hell, if the Germans could experiment with rocket engines in their kitchens and garages, we could too.)  And it was around that time I realized how mathematics could let me participate, in a way, in the things of the earth and sky. With pencil and paper and the help of some books I could compute times and distances of objects that exhibited wildly different, almost inconceivable measures: the orbital periods of satellites, the returns of comets, the distances to stars. It was as if I was floating above time and space, somehow ‘managing’ it by calculating about it on paper. Later when I got my degree in mathematics, engineers were using slide rules. Now with computers anyone can noodle around with newly discovered comets, moons, dwarf planets and the like. And best of all, we can simulate astronomical phenomena in most any era and recreate historical problems. I especially like to probe the past's nagging issues that kept natural philosophers awake at night, to better understand history. I use mathematics to try to ‘get into their heads' and follow their logic. After all, mathematics – particularly geometry – is a shared language with the past. Euclid was born when Aristotle died, and his Elements has been in student classrooms for two thousand years. Which fact alone is worth a pause to reflect upon. Actually, when I think about it, all of my readings and interests in astronomy, physics and mathematics – even from my earliest years – have always come alive to me most vibrantly in the context of their history. Some textbooks seem to hand us science on a platter, problems all neatly solved. History lets us learn why the movements of the natural world seemed so intractably difficult to understand. Every moment of my teaching has been historically informed (as you can see throughout Newton’s Gravity.) You can’t really understand anything, I say, unless you understand its historical context. History, indeed, is full of surprises, unknown nuggets waiting to be discovered. It helps us connect, in a human way, with the process of science.