Alex's Adventures in Numberland - Alex Bellos [81]
The oldest item in Peter Hopp’s collection was a wooden slide-rule from the early eighteenth century, used by taxmen for making calculations on alcohol volume. Before meeting Hopp, I had been sceptical as to how interesting slide-rule collecting could be as a pastime. At least stamps and fossils can be pretty! Slide-rules, on the other hand, are proudly functional tools of convenience. Hopp’s antique slide-rule, however, was beautiful, with elegantly crafted numbers on fine wood.
Hopp’s vast collection reflected the small improvements that were made over the centuries. In the nineteenth century new scales were added. Peter Roget – whose compulsive list-making (as a coping mechanism for mental illness) resulted in his timeless, classic, definitive Thesaurus – invented the log-log scale, which enabled calculation of fractions of powers, such as 32.5, and square roots. As manufacturing techniques improved, new devices of increasing ingenuity, precision and splendour were designed. For instance, Thacher’s Calculating Instrument looks like a rolling pin on a metal mount, and Professor Fuller’s Calculator has three concentric, hollow brass cylinders and a mahogany handle. A 41ft-helix spirals around the cylinder, giving an accuracy of five significant figures. The Halden Calculex, on the other hand, looks like a timepiece and is made of glass and chromed steel. Slide-rules, I decided, are indeed objects of surprising appeal.
Professor Fuller’s Calculator.
Among these others, I spotted a contraption on Hopp’s shelf that looked like a pepper-grinder, and enquired what it was. He said it was a Curta. The Curta is a black, palm-sized cylinder with a crank handle on the top, and was a unique invention – the only mechanical pocket calculator ever produced. Demonstrating how it worked, Hopp cranked the handle round for one rotation, which reset the machine to zero. Numbers are input by adjusting knobs positioned on the Curta’s side. Hopp set the numbers to 346 and turned the handle once. He then reset the knobs to 217. When he turned the handle again, the sum of both numbers – 563 – was displayed on the top of the machine. Hopp said that the Curta could also subtract, multiply, divide and perform other mathematical operations. It used to be very popular with sports-car enthusiasts, he added. Navigators were able to calculate driving times by cranking it without taking their eyes off the road for too long. It was easier to read than a slide-rule, and less susceptible to bumps in the road.
Although the Curta is not a slide-rule, its ingeniousness at calculating has endeared it to collectors of mathematical instruments. Immediately upon using it, it was my favourite item in Hopp’s collection. For a start, it was a literal take on number-crunching – in went the numbers, and with a crank of the handle, the result appeared. The notion of grinding out an answer, however, was too crude a way to describe a gadget made up of 600 mechanical parts that moved with the precision of a Swiss watch.
Curta advert from 1971.
Even more intriguing, the Curta has a particularly dramatic history. Its inventor, Curt Herzstark designed the prototype for the device while a prisoner at the Buchenwald concentration camp during the final years of the Second World War. Herzstark, an Austrian whose father was Jewish, was given special dispensation to work on his calculating machine because he was known to the camp authorities