The Calculus Diaries - Jennifer Ouellette [44]
One could blame James Clerk Maxwell, the prominent physicist who first formulated the set of equations for electromagnetism that still bear his name, for Heaviside’s sudden shift into the ranks of the chronically unemployed. Heaviside discovered Maxwell’s seminal treatise in 1873 and was so enthralled by the work that he quit his job the following year to study it full-time, moving back into his parents’ home in London. (History has not recorded his parents’ reaction.) Once he’d grasped the essential points, “I set Maxwell aside and followed my own course,” Heaviside later recalled. In the end, he reduced Maxwell’s equations from twenty down to four vector equations and built upon that work to develop vector calculus.
Few objects move in a straight, flat line. We don’t drive down straight roads with no turns or hills, and a roller coaster would be a very dull ride indeed if it only moved in flat, linear motion. Vector calculus lets us solve the same calculus problem in three dimensions: retracing our path by determining our position at each instant over the course of the ride. We describe position in three-dimensional space with three Cartesian coordinates (x, y, and z), so there are now three numbers involved in our calculations. Nothing else has changed from the previous example: Our trajectory is still position as a function of time, and thanks to the data gathered by our accelerometer, we know our acceleration as a function of time. Acceleration builds up to give us our velocity, which in turn builds up to give us our position at any moment. It’s just more complicated because our movement has a constantly changing direction. We must keep track of three directions at once, and each has its separate position, velocity, and acceleration.
Heaviside never gained the recognition he deserved until after his death in 1925; he was justly bitter about this. He became quite eccentric in his later years, spending the last two decades of his life as a virtual recluse in Torquay, near Devon. He suffered bouts of jaundice and the tormenting of neighborhood children, who threw stones at his window and scrawled graffiti on his front gate. Neighbors reported that his home was furnished primarily with huge granite blocks. Otherwise scruffy and unkempt, he took to painting his impeccably manicured fingernails bright pink, and signing letters with the mysterious initials W.O.R.M. after his name—providing ample fodder for future armchair psychoanalysts as to what the letters might have meant to him. Perhaps he would have found comfort in the fact that, over a hundred years later, his method of vector calculus would one day shed light on a budding calculus student’s encounters with the rides at Disneyland.
MAKING A SPLASH
By late afternoon, we have worked our way over to Critter Country, where the skyline is dominated by the soaring peak of Splash Mountain. Splash Mountain is a “log flume” ride. Loggers used to transport logs down mountains to a sawmill by floating them down the river. Eventually someone had the brilliant idea of hollowing out those logs and using them as makeshift boats. The first artificial log-flume ride—called El Aserradero (The Sawmill)—opened in 1963 at the Six Flags theme park in Arlington, Texas. The Disneyland version is a large plaster mountain housing canals (or flumes) filled with water, and artificial hollow logs that can seat up to six people. The flow of water along the flumes propels the log boats forward, with a little help from mechanical chains and pulleys to hoist the logs up the hills. Just as with a roller coaster, good old-fashioned gravity does the rest.
Nothing says Disney like plaster facades and cheesy animatronics.