In Our Time Read online

  Gauss also, almost as a game, invented the first telegraph with Weber, though again he did not pursue this. They strung a wire from Gauss’s observatory to Weber’s lab and found a way to send pulses of electricity down it and then detect these at the other end. They developed their own version of Morse code, sending messages such as ‘one of the research assistants is coming over to your lab’.

  Wilhelm Eduard Weber.

  NICK EVANS: Of course, once they’d done it they thought it was for other people to take it on. It didn’t really progress from there. Apparently the wire got hit by lightning eventually and that was the end of it. But they’d understood everything that was needed to do it.

  MELVYN BRAGG: Colva, you wanted to come in.

  COLVA RONEY-DOUGAL: They did briefly have grand plans that you could send messages around Germany using the train lines, the rails that the trains would run on. And, sadly, I think that Gauss was not the best at communicating with business people, so that never quite came to light.

  One of the consequences of Gauss’s work was that the centre of mathematical activity in Europe shifted from France to Germany. In France, Marcus du Sautoy said, the approach was utilitarian and intended to serve the state, which had a rather dismissive attitude to maths for its own sake. Coincidentally, Wilhelm von Humboldt was defining the education system in Germany and made sure that pure knowledge should be valued there. Gauss made tiny Göttingen the hub of mathematics and it remained that way until Hitler kicked out all the Jewish mathematicians.

  Gauss’s legacy was extraordinary.

  NICK EVANS: He’s had a huge impact on all bits of science. His work on electricity and magnetism eventually led to the discovery of Maxwell’s equations and radio, which I think we all agree is very important. But all of modern-day electronics and the lighting in your houses goes back to those equations. His work on error analysis is basically what defines sciences these days, the careful study of data and its application to theories. And then his work on non-Euclidian geometry, which did feed in through his students, led eventually to General Relativity, Einstein’s theory of gravity. And, at the moment, we’re seeing black holes colliding with gravitational wave detectors, all of which goes back to that work.

  COLVA RONEY-DOUGAL: He founded my own discipline, namely group theory, with his study of modular arithmetic. He founded modern number theory, he founded the study of complex numbers. He made the shape of twentieth-century mathematics what it is now.

  In the studio afterwards, there was some talk of whether quadratic reciprocity should have been mentioned. As an example, Colva Roney-Dougal explained that 2 is not a square if we consider it in the ordinary whole numbers, but, if we consider it on the seven clock, then 32 is 9 and 9 becomes the same as 2 and suddenly 3 squares to 2 and so suddenly now 2 is a square … And then there was the matter of pension schemes.

  NICK EVANS: At the end of his life, his university’s widow scheme was going bust and he came in and did a probabilistic analysis of how likely people were to die and therefore how you should run the fund, which basically underlies the way people run pension schemes to this day.

  MELVYN BRAGG: And he was this indigent professor who made a fortune on the stock market.

  COLVA RONEY-DOUGAL: The students at Göttingen used to call him ‘the newspaper eater’ because he would come in every morning and work his way through all the newspapers, seeing what stocks were up and down, and invested accordingly.

  Finally, was he really the greatest mathematician, as we had suggested at the beginning? Yes, said Colva Roney-Dougal, who was prepared to consider Archimedes and Newton also, and yes, said Marcus du Sautoy, who was not and, as for Einstein, whom Nick Evans suggested, well, we heard he could not have done anything without Gauss.

  ADA LOVELACE

  Deep in the bowels of the Pentagon is a network of computers. They control the US military, the most powerful army on the planet and they are, in turn, controlled by a programming language called Ada. It is named after Ada Lovelace, the (allegedly hard-drinking) nineteenth-century mathematician and daughter of Lord Byron. She became the Countess of Lovelace. In her work with Charles Babbage on steam-driven calculating machines, Ada understood, perhaps before anyone else, what a computer might truly be. Ada Lovelace has been called many things – the ‘first computer programmer’, a ‘prophet of the computer age’ – but, most poetically perhaps, by Babbage himself, an ‘enchantress of numbers’.

  With Melvyn to discuss Ada Lovelace and her work were: Doron Swade, computer historian, and former assistant director and head of collections at the Science Museum; John Fuegi, visiting professor in biography at Kingston University; and Patricia Fara, fellow of Clare College, Cambridge.

  There are three principal players in the story of Ada Lovelace – namely, her mother, herself and Charles Babbage – and to understand the significance of Ada Lovelace it helps to understand the role of the other two. Ada Lovelace was born in 1815 to two exceptional parents, Lord Byron and the aristocrat Anne Isabella Milbanke, also known as Annabella. Her parents were only married briefly, Patricia Fara told us, and Ada was only a few weeks old when Byron disappeared and Annabella Milbanke quickly took custody of her. Byron never saw his daughter after that, dying while abroad, athough, in one of his poems, he mentioned her blue eyes.

  PATRICIA FARA: Annabella Milbanke was a very, very courageous woman. She was also a very intelligent woman and she was very interested in mathematics herself. And she was determined to prevent her daughter following in the same footpaths as Byron had done.

  Annabella Milbanke was energetic and phenomenally interested in education and improvements. She had travelled to Switzerland to study the methods of education propounded by Johann Heinrich Pestalozzi and had established a series of schools and supported the establishment of a university in London. She was also part of the antislavery campaign and, at the National Portrait Gallery in London, she can be seen in a group portrait of the campaigners, right there with Wilberforce. She hired a succession of tutors to teach her daughter mathematics and other subjects, working her very hard, and there are messages from Ada Lovelace to her mother along the lines of, ‘I’m sorry I didn’t work hard enough yesterday and I’m really, really going to try hard to do my best tomorrow.’ Ada Lovelace suffered intense headaches when she was quite a little girl and was paralysed for about three years before she was able to start walking and horse-riding again.

  It was unusual for a woman to be so well educated in mathematics at this time, but not unique. Annabella Milbanke had a good education and so did several other women, so it could be an option open to those who had interest and aptitude and, above all, parents who were willing to invest in teaching.

  PATRICIA FARA: There were women who became very, very able in mathematics. There’s the French woman, Émilie du Châtelet. Also, the woman who became Ada Lovelace’s mentor, Mary Somerville, who was a very, very proficient mathematician. There were a few isolated women around who could learn mathematics, but there had to be a special combination of circumstances, and money was definitely one of the things you needed, as well as ability.

  Thanks to her mother’s social circle, as Ada Lovelace grew older, she was able to correspond with some very prestigious friends of the family and she had private tuition, quite often by correspondence, with some very distinguished people, such as the mathematicians William Frend and Augustus De Morgan.

  Intellectually speaking, the most significant relationship in Ada Lovelace’s life would be with the mathematician Charles Babbage. He, as Doron Swade told us, was a colourful, controversial figure best known for inventing computers, and for then failing to build them. His ideas and his prototypes are what inspired Ada Lovelace.

  An important development came in 1821 when Babbage and his friend John Herschel (1792–1871), the astronomer, were checking astronomical tables. In this period, the system for doing this was to hand the same set of calculations to two people, who were called ‘computers’, so that they could wor
k out the answers, and then someone would check that their answers matched. If there were no discrepancies, then those compiling the tables could have confidence in their accuracy. While they were working on these astronomical tables, Babbage became increasingly agitated as the number of discrepancies was very high.

  DORON SWADE: And he clasps his hand to his head and he says, ‘I wish to God these calculations had been executed by steam’ – steam being a metaphor for not only the infallibility of machinery, but for the model of industrial production. And he devoted most of the rest of his life to the development of automatic calculating.

  These calculators were to be vast mechanical machines, the size of steam engines, and Babbage was a pioneer of computing with these methods. His first love was mathematics and he had published about a dozen papers by the time he was thirty. He was also, as Melvyn pointed out, a polymath and a Lucasian professor of mathematics at Cambridge, a post that had been held by Newton. He was prone to letting off his own steam, too, with extraordinary public outbursts, and he was touchy and proud to the point of self-destruction, on matters of principle, as if being right entitled him to be rude.

  DORON SWADE: His diatribes [were] of incontinent savagery against the scientific establishment, particularly the Royal Society. He impugns the personal probity of Sir Humphry Davy, people who lent him great support in his pursuit of government resources to build his engines. He alienated almost everyone whose support he needed.

  Babbage, we heard, was not only a gentleman of science and massively principled, he was hugely charming and a raconteur. His Saturday soirées were where you could find the intellectual glitterati of London. Ada Lovelace was seventeen when she attended one of these momentous soirées at which Babbage inspired her. John Fuegi explained that, at these sorts of gatherings, Babbage would demonstrate his ideas and, at one of them, he displayed a calculating machine called the difference engine, which still exists and is on show at the Science Museum in London. Annabella Milbanke and Ada Lovelace were struck by what they saw.

  JOHN FUEGI: Lady Byron referred to it as a thinking machine and she started to make sketches of it. And Ada – and I think this is amazing in terms of a seventeen-year-old – she sent around the next week to Babbage and said, ‘Well, I’d like to look at the blueprints of this machine.’ Now how many are going to do this?

  At this point, Charles Babbage was starting to develop his machines and Ada Lovelace’s mind was starting to race, although the two of them would not collaborate immediately. Initially, this prototype for what he called the difference engine was exciting for Babbage, and he received government funding to make it. Soon, though, he became fascinated by the next stage of evolution, a machine of another order, which he called the analytical engine, and then, John Fuegi said, he did not really want to build what he had been given the money for. Doron Swade categorised the now less fascinating difference engine as what we would call a calculator, crunching numbers, performing repeated addition, evaluating and tabulating complex mathematical functions called polynomials.

  DORON SWADE: The huge leap from the difference engine to the analytical engine is the leap from something specific that has a fixed set of functions to something that is general purpose. The point about the analytical engine is it is a general-purpose computational engine and embodies, completely startlingly, almost every single significant logical feature of the modern digital computer.

  Although it so far existed only as an idea, the analytical engine was meant to be programmable, and it would automatically execute multiplication, division, subtraction and addition. Babbage, we heard, was led from mechanising arithmetic with his prototype differential engine to the level of a fully fledged digital computation, and that was the significance of the analytical engine.

  Meanwhile, since the soirée, both Annabella Milbanke and Ada Lovelace became very seriously interested in what could be done with machines. They went on a tour of the Midlands to see other machines and find out what they could do.

  JOHN FUEGI: One of the machines that intrigues them is the Jacquard loom; the Jacquard loom constitutes part of the DNA of this project. Here was this person off in France who would program a loom to be able to do these enormously complex pictures. And I think it was something upwards of 30,000 cards that were used to do a portrait.

  MELVYN BRAGG: I’m going to nail this. He’s talking about cards, which he put in the loom, and so it replaced the handmade and closely woven flowers on this cloth and made it much more quickly and in much bigger quantities.

  JOHN FUEGI: Yes, exactly. What is of particular interest in terms of computer history is that it’s essentially an on or off switch, the loom: it either raises or does not raise the thread so that something is going to go through. And it is that central notion that is going to be of tremendous importance then, for the subsequent development within the analytical engine.

  Although the sight of the difference engine had an immediate impact on her, Ada Lovelace was busy on a range of other things for the next ten years. She was educating herself further, she married and had three children and, as Patricia Fara said, she was corresponding with contacts such as William Frend, Augustus De Morgan, Mary Somerville and Charles Babbage himself, all of them helping her learn mathematics. It seems that she was not very good at routine algebraic manipulation of figures and equations, or understanding geometry.

  A model of the analytical engine designed by Charles Babbage.

  PATRICIA FARA: On the other hand, her great skill did lie in having a sort of visionary view of what mathematics could achieve, and I think that’s why she did become so involved in describing the analytical engine, because she understood the concepts and really appreciated the possibilities, the potential, in this machine.

  A set of notes on the analytical engine were to define the reputation of Ada Lovelace and are a significant part of her reputation today, and John Fuegi explained how these emerged. Charles Babbage was getting infuriated in England, so went to speak abroad, reasoning that, if the Italians or Alexander von Humboldt became interested in the analytical engine, then the British government would get behind it. He delivered his presentation about his ideas in Turin and, while the more prominent Italian mathematicians declined the opportunity to write up what they thought of this, significantly there was one person who did take it up. This was Luigi Federico Menabrea, who was obscure at the time but, in the future, would be prime minister of Italy, and he published his report of the analytical engine in a Swiss journal, in French. This was the very point at which Babbage went to Peel, the British prime minister, to ask for funding for his analytical machine, only to be unsuccessful.

  JOHN FUEGI: Lovelace feels that Babbage’s work is so important that there should be something done, and one shouldn’t just leave it at that, with the government having made a horrible mistake. So she does the translation. Ada says, ‘Okay, let’s go for it and we’ll publish it in English so that people can really see it.’

  Ada Lovelace was working with Charles Wheatstone, who was caught up in the idea of this project and had also been working on another calculating machine. Lovelace believed that Menabrea had made a lot of mistakes in his report so she went back to Babbage’s original notes, which were three or four times as long as Menabrea’s article. To Doron Swade, the significance of Babbage’s notes was, primarily, that they were the most comprehensive and insightful account of the thinking of that time about computers. There was then a flurry of exchanges between Babbage and Lovelace in the months before the publication of these notes.

  DORON SWADE: The question is: is there something there that isn’t Babbage’s? Did she see something Babbage did not see? The answer, unquestionably, is yes, and, for all the other reasons that Lovelace has been lionised, the one that is defensible and does hold water is the notion of her as a ‘prophet of the computer age’.

  He added that Lovelace saw that these machines were not bound exclusively by numbers, making the essential transition to a number representing somethi
ng other than quantity. For Babbage, these machines were still about calculation, although he had some inkling that these machines could be used for algebra.

  DORON SWADE: We have Ada, who’s not just suggesting this, but she is thumping the table and saying, ‘This is the fundamental significance of the analytical engine.’ And it’s perfectly clear. And Babbage pays her a tribute, he says: ‘I wish I’d given this further attention to see the great potential of these things. Having read your notes, I now see that I might have done so.’

  Ada Lovelace saw the essential distinction between calculation and computation. In such an analytical engine, numbers could represent something other than quantity, such as notes of music or letters of the alphabet. Ada Lovelace is the one who essentially made the transition from arithmetic to symbolic manipulation, as Doron Swade put it, a machine that can manipulate symbols according to rules, and that is the essential beginning of the concept of a computer.

  PATRICIA FARA: And she also has that marvellously poetic phrase that the machine will weave algebraic patterns like a Jacquard loom weaves flowers. And, I mean, that’s such a perfect description.

  Patricia Fara agreed that what Lovelace did in the notes was very important. She also thought, though, that it was essential to recognise that Lovelace’s visionary ideas were not actually put into practice.

  PATRICIA FARA: Looking back 100–150 years later, we can see that she conceptually grasped the difference between a calculator and what we now call a computer. In a sense, she and Babbage didn’t really have any influence on the course of computing for the next 100 years. So, although it was a marvellous dream, I’m not sure it was a hugely influential one. And, if you’re American, you tell a whole different story of the history of computing that goes through Herman Hollerith and the census at the end of the nineteenth century, and it’s not necessarily traced back to Babbage.