## Sunday, 9 December 2007

### Counting Down

December 9th, and there are only 22 days left in the year, which means 16 more days till Christmas. Lots of people involved with counting involved with this date. This is the day on which statistician Herman Hollerith installs his computing device at the United States War Department. Math and science students of my generation remember him for two other inventions he used to make his computing machine work, punched cards, called Hollerith cards, and the keypunch machine to put holes in them. The company he formed went on to become one of the largest counting compnies in the world, IBM. He got the idea from the mechanical looms of a Frenchman named Jocard.
Speaking of computers and the internet, it was on this day that the NLS, or the "oNLine System", was introduced, It was a revolutionary computer collaboration systemdesigned by Douglas Engelbart and the researchers at the Stanford Research Institute. It was this project that led to the invention of html, and the ubiquitous computer “mouse”.
Of course the statistics which was at the heart of the work done by Hollerith and the big IBM computers were indebted to the work of a great Russian mathematician who died on this day in 1894, Pafnuty Chebyshev (ok, I know there are 20 spellings of the name, sorry if this is not YOUR favorite). The Russian name has been translated as both Chebyshev and Tschebyshev, as well as several other spellings, which can lead to confusion. It is said that Besicovitch used to declare, “We use the letter T for the class of T-polynomials because it is the first letter of Chebyshev”, which he was also known to claim had no letter T. His famous inequality is rememebered, and mis-remembered by each successive year of introductory statistics students. But my favorite is a little ditty I learned in college:
Tchebyshef said it
So I'll say it again
There's always a prime
between N and 2N

From the age of computers, the need for programming and compilers became essential, and so we point out that this was also the day in 1906 that Grace Murray Hopper was born. The lady Admiral is remembered as the creator of Cobol, and even has a cruiser named after her, but the greatest influence she has on modern computing comes from a failure. One of the large Mark I computer/calculator she worked on failed to operate one day, and the cause of the disaster was traced to a dead moth on one of the computer relays. The bug can be seen in the log book where she pasted it in the Smithsonian Museum of American History. It is, so they say, the creation of the term “bug” for a computer malfunction.

Another mathematician born on this day is related to both counting and disasters. William Whiston was a British Mathematician born on this day in 1667. the year after the great fire of London. He was headed for the top, and rubbing elbows with the best for a while. He served as Newton’s deputy at Cambridge, where he was a fellow, and followed Newton in the prestigious Lucasian professorship. He was also one of the earliest proponents of the theory that comets had a periodic behavior, along with Halley.

His contribution to came in the form of a translation of the works of Josephus, the first century Jewish-Roman historian, who survived the Jewish-Roman war perhaps due to his mathematical talents. In his book The Jewish Wars Flavius tells that he was one out of 41 Jewish rebels trapped by the Romans. His companions preferred suicide to escape, so they decided to draw lots to see who would kill whom so that they could avoid both capture and the sin of suicide. The idea that they decided to form a cycle and to kill every third person and to proceed around the circle until no one was left is probably a myth. According to the problem Josephus wasn't excited by the idea of killing himself, so he calculated where he has to stand to survive the vicious circle. The general Josephus problem involves deciding how many people will stand around a circle and how many shall be passed over before the next one is killed and predicting the last to survive. You can find a java applet to “play” at death at that same link.
Comets were also part of the disaster in his life. He had become famous for his studies that stated that the Biblical flood had been caused by a comet, and gave support for other geological impacts of comets on the Earth. Whiston was removed from his position at Cambridge, and denied membership in the Royal Society for his “heretical” views. He took the “wrong” side in the battle between Arianism and the Trinitarian view, but his brilliance still made the public attend to his proclamations. When he predicted the end of the world by a collision with a comet in October 16th of 1736 the Archbishop of Canterbury had to issue a denial to calm the panic.
For those who are wondering, the world did NOT end on that date, at least not according to Wikipedia, and they would know. Not sure what calculations Whiston used to make his prediction, but maybe his computer had a “bug” in it too.