Evolution of the calculator


From Napier’s bones to the Curta calculator, Jason England examines the ingenious, all-but-forgotten inventions that led to the electronic calculator.


Jeffery Phillips

Humans have been using mathematics for so long we can’t be sure what the earliest aids to mental arithmetic were – but the first was probably our fingers, and the second, small piles of stones. Both devices are only useful for small quantities, and in the case of our fingers can only be employed for short periods before sore muscles demand the display be refreshed!

But with the advent of prehistoric agriculture, commerce and astronomy, piles of stones became hopelessly inadequate. A rudimentary version of the abacus, dating to around 2,500 BCE, was developed in Sumeria (now Iraq) and subsequently spread to Europe and the rest of Asia. As the abacus was refined, calculations that had been considered extremely difficult became routine.

For the next 4,500 years, the abacus was humanity’s preeminent counting tool (it is still used in parts of Asia). Then in 1617, Scottish mathematician John Napier published Rabdology (“calculation with rods”), describing a device that came to be known as Napier’s bones. The bones are thin rods, inscribed with multiplication tables. The user calculates his sum by adjusting the rods’ vertical alignment, and then reading off the multiplication totals horizontally. With a few hours of study anyone can use a set to solve large multiplication and division problems. Experts can even use them to extract square roots from fairly large numbers – no easy feat in the early 17th century!

These devices were not calculators – they worked by simplifying the sums a human operator still had to perform mentally. Then in 1642, French polymath Blaise Pascal invented his Pascal calculator, a device truly capable of performing mathematical calculations by means of a clockwork-type mechanism.

The Pascal calculator was ingenious, attempting arithmetic functions previously thought impossible, but they were difficult to produce and only a handful were ever made. Napier’s bones and the abacus remained in accountants’ offices until the mid-19th century, when Thomas de Colmar invented and produced the first mechanical calculator robust enough for everyday use. The invention spawned a proliferation of calculating machines that could add, subtract, multiply and divide large numbers rapidly and accurately. Their biggest disadvantage was their size: they often filled a desktop and weighed 15 kilograms or more.

Enter Curt Herzstark. Born in Vienna in 1902 into a family that produced calculators and other office machines, young Curt demonstrated the devices for prospective buyers. By 1937, Herzstark had begun work on a new calculator that could be held in the hand. A year later, he had a finished design that achieved everything he wanted.

But on March 12, 1938, Herzstark’s plans were interrupted when Adolf Hitler led his army into Austria. For four years the occupying Nazi government forced Herzstark’s factory to build military parts and equipment for the Reich. Then, in 1943, Herzstark was arrested and sent to Buchenwald concentration camp; his knowledge and experience of precision factory manufacturing kept him alive.

Hearing of Herzstark’s plans for a portable calculating machine, the camp commander struck a deal with him: develop the device and if it works it will be presented to the Fuehrer as a gift. (They did not need to tell Herzstark what would happen if it didn’t perform as promised.) For the next two years he worked on the machine in whatever spare time he could find, dredging every design detail from his memory. By 1945, just as he was finalising the new plans, Allied forces freed the Buchenwald prisoners.

The Curta was the best and the last of its kind.

After making it back to Vienna with his drawings in his pocket, Herzstark was able to convince the Prince of Liechtenstein to invest in his Curta calculator. It is a work of staggering ingenuity. The unit sits approximately 10 centimetres high and is only five centimetres in diameter with a cylindrical body and a small crank handle on top. From a distance, it resembles a short, stocky pepper grinder. Yet it contains more than 600 precision parts, allowing the operator to add, subtract, multiply and perform long division with a mere turn of the crank. Advanced users can even calculate natural logs and square roots.

The Curta was eventually produced in two slightly different models. The type-1 can display eight-digit answers and the slightly larger type-2 can display 15-digit answers. That’s remarkable when you consider my iPhone 6 Plus displays 16 digits in its answer field – and that’s in scientific mode!

Some 150,000 Curta calculators were made between 1948 and 1970, production ending with the advent of the electronic calculator. No truly mechanical calculators have been invented since. The Curta was the best and the last of its kind.

The forgotten genius Curt Herzstark died in 1988. According to the display on my perfectly functioning 65-year-old type-1 Curta, he was 86 years old.

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