Since its arrival, I’ve been unable to put down Steven Strogatz’ newest book which catalogs a friendship through 30 years of letters between he and his high school calculus teacher. But truly, it’s about change:
Calculus is the mathematical study of change. Its essence is best captured by its original name, “fluxions,” coined by its inventor Isaac Newton. The name calls to mind systems that are ever in motion, always unfolding.
Calculus thrives on continuity. At its core is the assumption that things change smoothly, that everything is only infinitesimally different from what it was a moment before. Like a movie, calculus reimagines reality as a series of snapshots, and then recombines them, instant by instant, frame by frame, the succession of imperceptible chances creating an illusion of seamless flow.
Pen pals were worth waiting for. Those decorated envelopes that arrived by post, unpredictably but continuously, held treasures. Illustrations, news, curly cursive. Flourishes and honesty. Pen-pal notes gave everything back if you kept at it. The deal was you must be consistent. Continuity was the only pact, unspoken and unbreakable.
Today, pen pal pacts have moved to email, mostly, but they’re no less binding. Like calculus, these relationships (and by extension systems, people, ideas) are ever in motion, always unfolding, even when they’re silent. Correspondences are likely a series of snapshots that we recombine when inputs change. We receive new information, recombine, and flow it back together. A flow of instants. Continuous and smooth. In motion.