Calculating machines, computing and the digital world

Six women pose together in an office, some of them seated at work tables. — NASA human computers, photographed in January 1959. NASA, Public domain, source

Before it was a machine, a computer was a person.

In English, the word computer referred to an occupation: someone whose job was to calculate, all day long, by hand. It was most often a woman.

Making a machine calculate

A calculating machine relies first of all on toothed wheels. A wheel advances one notch per unit; when it has made a full turn, it pushes its neighbour forward one notch. Carrying becomes mechanical.

The principle is easy to describe and hard to achieve. The whole difficulty lies precisely in the carry: at the moment when nine becomes ten, the neighbouring wheel must be pushed without jamming the machine.

In 1623, in Germany, Wilhelm Schickard described such a machine in two letters to the astronomer Kepler. It added, subtracted and helped with multiplication. But the copy ordered from a craftsman burned half-finished the following year, Schickard gave up, and he never spoke of it again. We know his calculating clock from these letters and from sketches found in 1935. Reconstructed, it works, but its carry remains fragile: a carry that runs through all the digits risks damaging the wheels.¹

Twenty years later, in 1642, Blaise Pascal solved the carry problem and had about fifty machines built.²

So who invented the calculating machine? The question is wrongly framed. One had the idea and never made the object work; the other made the object work. Two different achievements, by two different people.

Telling the machine what to do

A machine that calculates is of little use if it has to be told what to do all over again each time. A second invention is needed, and it comes from elsewhere: from music, then from weaving.

In Lyon, around 1725, Basile Bouchon was a silk weaver. He knew the pinned cylinders that make musical automata play: the pins are the melody, the cylinder is merely a machine. He transferred the idea to the loom and controlled the threads with a strip of paper pierced with holes.³

Three years later, in 1728, Falcon’s loom replaced the strip with punched cards tied together in an endless chain. It was the first machine in the world, of any kind, to be controlled by punched cards. Jacques de Vaucanson then tried to automate the whole process. In 1804, Joseph-Marie Jacquard took up the three inventions, combined them, and at last produced a system that worked in real factories.⁴

The pattern is no longer in the weaver’s head or in the machine: it is on a separate medium, which can be changed. This is exactly the idea of the program.

In England, Charles Babbage seized on it. From 1837, he designed a mechanical machine that would calculate whatever it was asked, controlled by cards borrowed from the Jacquard loom. He never completed it.

In 1843, Ada Lovelace translated an article on this machine and added notes three times longer than the text. Historians disagree about what exactly she invented in them, and about what came from Babbage. But all agree on one point, and it is the most astonishing: she was the first to write that such a machine would not be limited to numbers. Since instructions can be coded on cards, it could be made to manipulate symbols — and, she wrote, to compose music.⁵

One hundred and eighteen years after Bouchon, the idea had returned to its starting point.

Counting a country

Punched cards then left the workshop for the administration.

In the United States, the 1880 census took eight to nine years to tabulate. With a growing population, the 1890 census risked not being finished before the next one was due. The Census Office held a competition in 1888: the contestants received the same files from St. Louis, and were timed.

The first two took one hundred and forty-four hours and one hundred hours to capture the data, then forty-five and fifty-five hours to sort it. Herman Hollerith captured the data in seventy-two and a half hours — and sorted it in five and a half hours.⁶

A story found everywhere must be corrected here: the 1890 census was not done in six weeks. Six weeks corresponds to the raw count of the population, and that count did not use the cards. The full tabulation took much longer: its results were published only a year and a half earlier than those of 1880 — and it cost almost twice as much. At the time, some wondered whether the machine was really worth its price.⁷

The company founded by Hollerith would later become IBM.

These machines were used everywhere, and for everything: counting inhabitants, managing payrolls, keeping inventories. In France, during the Occupation, the statistical services had them. But what states did with their counts did not depend on them: the lists that mattered, at that time, were kept by hand. This story is told in Entry 9.6.

The human computers

For a long time, truly lengthy calculations were done by people.

During the Second World War, the American army needed firing tables: for each gun angle, each wind, each distance, where the shell would land. That meant thousands of equations. A single one could take more than forty hours of work.

This work was entrusted to women. Such calculation was then considered too tedious for engineers. There were more than eighty of them at the University of Pennsylvania, and their job was called computer.

When an electronic machine was built to do this work faster, someone was needed to program it. Six of them were chosen: Kathleen McNulty, Frances Bilas, Betty Snyder, Marlyn Wescoff, Ruth Lichterman and Jean Jennings.⁸

No one could teach them: this job did not yet exist. They were handed a pile of wiring diagrams and told, in essence: understand how the machine works, then work out how to program it.

They succeeded. On 15 February 1946, the machine was presented to the press. The demonstration chosen was a trajectory calculation, developed by Jean Jennings and Betty Snyder.

Erased, then rediscovered

What followed is instructive.

The articles published about this demonstration spoke of the engineers who had built the machine. They did not mention the six programmers. In the evening, a dinner was held to celebrate the success. They were not invited.

The most troubling thing is that the archival photographs do show them. They are there, in front of the machine, in the pictures. It was the captions and the articles that made them disappear.⁹

It was not until the 1990s that women historians took an interest in these photographs and asked the question: who are these women? From then on, their work was recognised.

A source can remain in plain sight for fifty years and say nothing, as long as no one asks the right question.

How a machine calculates

Everything that follows rests on a disconcertingly simple idea: a machine can do only one thing: distinguish between two states. A switch open or closed, a current flowing or not. These two states are written 0 and 1, and they are called bits.¹⁰

With bits, numbers can be written — this is the binary system, which counts in powers of two instead of ten. Eight bits are enough to write all the numbers from 0 to 255. Since numbers can be written, anything can be written: all it takes is to decide that a number represents a letter, the colour of a pixel, a moment of sound. A text, an image and a piece of music are, inside a machine, exactly the same thing — sequences of bits, distinguished only by the rule used to read them back.

A calculating machine has three parts.

The processor executes operations, one by one, but at a rate of several billion per second. It can only do additions and comparisons; everything else is built from them.
The memory stores the data and instructions in use. A distinction is made between memory that is erased when the power is switched off and memory that persists.
Inputs and outputs — keyboard, screen, sensor, loudspeaker — provide the link with the world.

A program, or software, is the list of instructions that the processor must execute. The algorithm, for its part, is the method itself, independent of the machine: a cooking recipe is an algorithm, and it stays the same whatever the stove.

None of this presupposes intelligence. A machine applies rules without understanding them, very fast and without making mistakes. It is this speed, and not any kind of understanding, that produces the results.

Ada Lovelace’s sentence, and the reply it received

Someone had already set this idea down in 1843 — the very person discussed at the beginning of this page.

In her notes, after imagining that a machine could manipulate symbols and compose music, Ada Lovelace sets a limit:

The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform.¹¹

The position is remarkable. The woman who saw furthest into what a machine might do is also the one who set the clearest boundary on what it would not do.

Yet the story does not end there. More than a century later, in 1950, a mathematician took up this sentence, named it “Lady Lovelace’s Objection”, and challenged it.¹²

His argument is subtle. He shifts the question: instead of asking whether a machine can originate, let us ask whether it can take us by surprise. And he observes that the objection rests on a false idea — the assumption that as soon as a fact is presented to a mind, all its consequences spring into the mind simultaneously with it.¹³

It is not true, he says, and it is even an error to which mathematicians are particularly prone.

This debate is still open. It has lasted for nearly two centuries, between two people who never met, and it concerns exactly the question that everyone asks when faced with the machines of their own time.

Smaller and smaller

What followed technically can be summed up in one word: miniaturisation. It can be told in three dates.

On 16 December 1947, in an American laboratory, John Bardeen and Walter Brattain placed two tiny gold contacts on a small slab of germanium, and obtained a device that amplified an electrical signal. This was the transistor. It replaced the vacuum tube: smaller and sturdier, it gave off almost no heat. A colleague came up with its name. With their team leader, William Shockley, the two men would receive the Nobel Prize nine years later.¹⁴

In 1958, then in 1959, two engineers who did not work together and did not know each other had the same idea: instead of making components one by one and connecting them by hand, etch them all together on a single wafer. Jack Kilby made the first, Robert Noyce the version that would lend itself to mass production. This is the integrated circuit.

In 1971, finally, Intel’s first microprocessor appeared, the 4004: a chip of twelve square millimetres, the size of a fingernail, which brought together everything needed to calculate — about two thousand three hundred transistors.¹⁵

It was not invented for a computer. It was a Japanese calculator company, Busicom, that ordered and paid for it, and one of its four designers, Masatoshi Shima, was that company’s engineer.

It is said everywhere that this chip was “as powerful as the ENIAC”. Caution is called for: this phrase comes from the manufacturer’s advertisement, in 1971, and has been copied ever since. The two machines are not so easily compared. What can safely be stated concerns the two objects: on one side a room of one hundred and sixty-seven square metres and thirty tonnes of equipment, on the other an object that fits on a fingertip.

In the 2020s, a chip contains several billion of them. It is this shrinking, more than any other new idea, that has put a computer in every pocket.

What it really weighs

It is often said that the digital world is “immaterial”. This is false, and it is worth knowing.

A phone contains dozens of different metals, extracted from real mines, by real people, sometimes in very harsh conditions. The services used every day run in buildings full of machines that must be powered and cooled continuously: data centres. In 2024, they consumed about one and a half per cent of the world’s electricity, and their consumption could more than double by 2030.¹⁶

The following must be added, or the figure will mislead. Over the same period, it is electric cars, factories and air conditioning that will drive most of the increase in global electricity consumption — not data centres.

Discarded devices, for their part, become waste. Sixty-two million tonnes in 2022. It is known that about twenty-two per cent is officially collected and recycled; for the rest, no one really knows, because a great deal of recovery takes place without being recorded anywhere.¹⁷

The cloud has an address, an electricity bill and a skip.

Two inventions, not one

What is needed	What it is for	Where it comes from
A mechanism that calculates	carrying out the operations	toothed-wheel machines, then electronics
A medium for instructions	saying what to do, and being able to change it	punched strips and cards, from musical automata and then from weaving
People who know how to use it	translating a problem into a sequence of operations	the occupation of computer

Note 1

On September 20, 1623, Schickard wrote to Kepler saying (in translation): […] These two letters, both of which were found in Kepler's papers […] it certainly works well on the reproductions constructed by von Freytag Loringhoff. […] This operation would require enough force that it might well do damage to the gears on the units digit.

Lee, J. A. N., “Wilhelm Schickard”, Computer Pioneers, IEEE Computer Society, 1995, mis à jour en 2013

I had placed an order with a local man, Johan Pfister, for the construction of a machine for you; but when half finished, this machine, together with some other things of mine, especially several metal plates, fell victim to a fire which broke out unseen during the night three days ago. […] Sketches of the calculator have been preserved in the manuscripts left by Schickard and Kepler. These however, were not rediscovered until 1935 when they were found during research into Kepler's life.

O’Connor, John J. and Robertson, Edmund F., “Wilhelm Schickard”, MacTutor History of Mathematics, University of St Andrews