Thursday, 9 June 2011

Calculus, Hard as a Rock

Calculate / Calculus The origin of both these words is in the Greek word kalyx, for pebble or small stone. The manipulations of small stones on counting boards to do arithmetic operations led to the present mathematical meanings of calculate and calculus. [You can see some beautiful old counting tables at this page from Convergence ] The pebble root is still present in the medical use of the word calculus, a name for an accretion of mineral salts in the body into a small "stone" such as kidney stones. The name for the element calcium comes from the same root. The prefix calci usually relates to calcium or limestone in some way. The furnace used for annealing in the glass making process is called a calcar, and the same word is used for a spur or projection on the heel. Interestingly, the material created in the calcar (glass furnace) is called frit, and is the root of the food product called a fritter; both words coming from the Latin word for fry.
Students who struggled through a first semester calculus course may appreciate the following tale from Steven Krantz's Mathematical Apocrypha
"An American mathematician of some note was returning from a trip abroad and had to go through Customs. The US Customs Officer asked him what he had been doing during his one-week sojourn. The reply was that he had been at a mathematics conference. The Customs Officer then took this man aside and detained him for some time with a great many tedious questions about exactly where he head been and what he had been doing during his travels. The mathematician kept glancing nervously at his watch, worried that he would miss his connecting flight. The Customs Official finally got to a point of asking our friend what he had had for dinner each day. Finally the mathematician threw up his hands and exclaimed, 'Why are you doing this to me?' The Customs Officer smiled and said, 'Ah, Now you know how I felt when I took calculus.'"
The Story reminds me of one of my own trips through customs going into England when I taught there.  While studying my passport (which had entry stamps to England for at least eight consecutive years) he asked what I did.  I told him I was a math teacher and he smiled, "Ahh, then you would know the square root of negative one."   I responded that it was the imaginary constant, i, and waited. He seemed pleased that I knew this and stamped my passport and handed it to me.  After I had it firmly in hand and my briefcase as well, I looked back as I started to move away and replied, "But what's the square root of that?".  His eyes furrowed in concentration but before he could answer (he might have known) or call me back and erase my entry stamp, I exited into the baggage claim area.
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