③ Enchanting Numbers▪On computers’ invention as mechanical calculators A History of Science

Computing began long before the twentieth century. Mechanical calculators ran on cogs, wheels, and steam engines.

How would you like a job as a computer? Not a programmer, not even a mathematician. A computer. Someone who makes calculations. By hand. All day, every day.

I guess that doesn’t sound appealing. Until well into the previous century, however, those jobs did exist. And so did the word computer. It referred to these people, who worked patiently in the back-office of every factory, bank, and government department. There they calculated everything, from mortgages to railroad bridges to government budgets.

In the decades after the Second World War, they were quickly being superseded, first by mechanical calculators and later by electronic computers. To us in the twenty-first century, the idea that those jobs ever existed seems utterly ridiculous. But it took centuries of increasingly complex inventions and visionary realizations before manual computing was finally a thing of the past.

Hello and welcome to A History of Science: Episode 3: Enchanting Numbers.

Introduction

Until the invention of the modern electronic computer in the 1940s, calculating had always been hard manual labor. In the sixteenth century already, Tycho Brahe, the astronomer who was renowned for the accuracy of his data, complained about it in the preface to one of his books. He strikingly reminded his readers that if they got tired of the many calculations in his writing, they’d better take pity on the author, who had had to do them all three times over.

The burden of calculating could be reduced somewhat using an abacus, but it remained tiring and mind-numbing work. During the Enlightenment, when the whole world was increasingly being interpreted in terms of math, the first attempts at mechanizing math itself were made. These early mechanical calculators marked the beginning of the long journey that culminated in the invention of the computer.

In this episode, we will explore the inventors of the mechanical computer. It is a story of men and women who lived centuries apart but were all ahead of their time. And who, in contrast to our heroes of our previous episodes, all applied science that was actually correct.

Blaise Pascal and the Pascaline

Let’s start off with a little thought experiment. Imagine a clock. But instead of twelve numbers, this one has ten. It starts at zero and counts up all the way to nine. And instead of just two arms, this clock has ten: one for each number. All arms move on the same wheel, so if one moves, they all move. And finally, the arms are all black, except for the one pointing to zero: that one is bright red. Congratulations, you have just invented a calculator.

Don’t see it yet? Let’s try a sum: three plus four. Imagine moving the red arm from the zero to the three. Now move the black arm that happens to point to the zero to the four. The red arm now points to seven: three plus four.

What I have just described is the Pascaline, the first ever mechanical calculator. It was invented in 1642 by the Frenchman Blaise Pascal. Pascal was something of a child prodigy, who would go on to become an influential mathematician and philosopher in his own time. When he was nineteen, however, he saw his father struggling with tax collection, and decided to invent a machine to help him with additions and subtractions.

Pascal’s machine was more advanced than the one you just imagined, even though the basic principles were the same. As you may have noticed, the clock-like calculator we discussed only works for sums under ten. Above that, you need some sort of mechanism to increment one digit at every ‘hour’ to a similar clock representing the tens. That way, a sum that passes nine will move on to zero on the same clock, but will add one digit to another clock on its left. Pascal designed an elegant lever for that operation,