In Our Time - Alan Turing

Episode Date: October 15, 2020

Melvyn Bragg and guests discuss Alan Turing (1912-1954) whose 1936 paper On Computable Numbers effectively founded computer science. Immediately recognised by his peers, his wider reputation has grown as our reliance on computers has grown. He was a leading figure at Bletchley Park in the Second World War, using his ideas for cracking enemy codes, work said to have shortened the war by two years and saved millions of lives. That vital work was still secret when Turing was convicted in 1952 for having a sexual relationship with another man for which he was given oestrogen for a year, or chemically castrated. Turing was to kill himself two years later. The immensity of his contribution to computing was recognised in the 1960s by the creation of the Turing Award, known as the Nobel of computer science, and he is to be the new face on the £50 note.WithLeslie Ann Goldberg Professor of Computer Science and Fellow of St Edmund Hall, University of OxfordSimon Schaffer Professor of the History of Science at the University of Cambridge and Fellow of Darwin CollegeAnd Andrew Hodges Biographer of Turing and Emeritus Fellow of Wadham College, OxfordProducer: Simon Tillotson

BBC Sounds, music, radio, podcasts. Thanks for downloading this episode of In Our Time. There's a reading list to go with it on our website, and you can get news about our programs if you follow us on Twitter at BBC In Our Time. I hope you enjoy the programs. Hello, at the age of 24, Ian Shuring founded computer science. He didn't know that, nor did the wider public, yet his reputation has grown as our reliance on computers has grown.

He was also openly gay and made no secret of his science. sex life in a world where that was a crime. His real secret was his vital contribution to the Bletchley Park Code Crackers, who it said shortened World War II by two years and saved millions of lives. The enormity of Turing contribution to society stands in shameful contrast to the injustice he and many other gay men faced. He was sentenced to be chemically castrated and age 41 he killed himself. Next year he used to be the face on the new 50-pound note. We'll need to discuss Alan Turing's ideas in life are Leslie Anne Goldberg, Professor of Computer Science and Fellow of St. Edmunds

Hall University of Oxford. Simon Schaffer, Professor of the History of Science at the University of Cambridge and Fellow of Darwin College, and Andrew Hodges, biographer of Turing, an Emeritus Fellow at Wardham College, Oxford. Each of them in their eerie somewhere in the UK. First of all, Andrew Hodges. Can you tell us about Turing's early life

and his relationship with his family? Well, Alan Turing's early life was the story of the British Empire around the First World War. He was born in London in 1912, but his parents were mostly away governing India until he was 14 or so. And there was a relentless, unforgiving programme of fostering prep school and the all-important public school education. Everything revolved around giving him an upper-middle-class identity. But Alan Turing took rather little notice of all of this. what you can see from his letters home and so on is his interest in nature and science from an early age, quite self-aware as well.

He's not good at exams at all, and he nearly failed the equivalent of the GCSEs. Ah, but when he's 16, his grandfather gave him a copy of Einstein's semi-popular exposition of relativity theory, and his notes on that were absolutely outstanding. I mean, they're quite extraordinary. you can see there was something really there, which no one around him, except perhaps his grandfather, actually grasped. You've skidded through his early days,

but he scarcely saw his parents for the first 12 years of his life and so on, then sent off to a public school in those days. Well, pretty rough place to go to. Did that, of course, it did have an effect on him. What sort of effect do you think it had? Oh, well, he said, of course, the one thing about a public school education is that after, as you know,

that nothing can ever be so bad, again. But I think what's more interesting is that he did escape that being trapped in that kind of social environment. And it is in a very, rather extraordinary way. There was another boy, Christopher Morecambe, at Sherbourne School, where he was, also very, very keen on science, but much more successfully, practically so. And is he who brought Alan Turing into communication and a, you know, a more practical way of doing things. And this meant so much more because this is when Alan Tearing fell in love. I mean, totally unrequited. It was just worship almost from afar with a very limited contact. And then this other boy, Christopher Morecambe, died just after

winning a place at Cambridge. Now, Alan Tearing was very open about his grief and he set himself to do what the other boy would have done. I mean, all very emotional. And he did indeed make good by winning a scholarship to King's College, Cambridge, where he went in October 1931 to read mathematics. Thanks, Leslie Ann Goldberg. This was a particularly exciting time to be a mathematician, as I understand it. Can you tell us why? Yeah, so the 1920s and 30s were really, there was a lot going on in mathematics. So in 1920, Hilbert announced his big program, and what he really wanted to do was to set up a logical foundation for mathematics. So his idea was that he was that he was that, that if you carefully chose the axioms,

then maybe everything else would just be provable from the axioms in a really formal way. So he'd put that idea forward. An axiom here is a statement taken to be true, so more reasoning can be done. In 1931, which I noticed we've just heard as the same year that Turing under Cambridge, we had Gerdl's incompleteness theorem.

So the first incompleteness theorem said, essentially, that Hilbert's program was impossible, in the sense that if you had axioms that were consistent, so that no statement could be proved both true and false, then there would have to be true statements that can't be proved. And then at the time that Turing entered the field, roughly 1936, he had an open problem, which had been posed by Hilbert and Ackerman in 1928, called the Enshrigings Problem or Decision Problem.

And what that's about is that Hilbert thought that there was an algorithm or a kind of mechanical recipe for solving procedure, such that if you proposed a mathematical statement or a formula, that this algorithm would determine whether it could be proved from the axioms. So he thought that there must be such an algorithm, and he'd asked for the algorithm. This was the open problem that Turing solved, and this was the setting in which he began his work in this area.

Was it unusual for somebody that young to pick up that particular idea. You've talked about Hilbert, who was a great man of his time. Others were around. There was a big buzz, if I use that word, about mathematics at the time. Turing was certainly exceptional, but there were other people working on similar topics. And in fact, Turing's solution to the problem was pretty much simultaneous with church. So both of them solved the problem in 1936.

And what they actually showed was that Hilbert was actually wrong. So instead of finding the algorithm that Hilbert had asked for, they actually just prove that no such algorithm exists. It's simply impossible. Simon. Simon Schaffer. There was exactly as Leslie has just said, a small group of expert mathematicians, logicians, philosophers of mathematics who were working on very similar problems.

What I think was remarkable, perhaps most remarkable, about Turing's approach in the 1936 paper is something that would characterize a vast amount of his work, which was to take the problem literally, in a certain sense, to deflate a lot of the grandiose claims that were being made about the logical and philosophical problems

associated with the foundations of mathematics. So one of his Cambridge teachers, very important man called Max Newman, had formulated the problem as the possibility of finding a mechanical process for deciding whether a proposition or its opposite was formally provable. And what Turing did magnificently, so it seems to us now, was to take the phrase mechanical process absolutely literally. In other words, let's see if we can define a machine and define the way that machine works.

so that what that machine is doing is mathematics. And the key word in what Turing was then going to do was, of course, the word computer. In 1936, a computer was a human being. It was a human being doing sums. And what Turing shows brilliantly in the paper is that whatever a human computer can do, a machine can do. And not only that, but, and Leslie and Andrew will want to say much more about this,

there can be what we now call a general purpose machine, a universal machine, which can do not only what any human computer can do, but what any other computing machine can do. that opened up a vast landscape for thinking about what computers do in general and, at least as interestingly, thinking about what machines are doing when they're calculating. Leslie, Turing's paper in 1936 was crowded with new ideas, this young man. Turing actually ended up laying the whole foundations for computer science. The whole foundations, that's a big claim.

The first thing is if you're going to talk about whether or not there's an effective algorithm, you better decide what that even means. Turing had a different definition of effective computation. So he introduced the notion of a Turing machine. It actually is so simple you can reason about it, but it captures what we can compute on the computers that we have now. So it actually gives us a mechanism to actually understand what it is that our computers can do. once he defined the Turing machine,

then he showed that there's actually no algorithm for solving this decision problem. So that was demonstrating provable limits of computability. He also developed the tools that we still use today to study the limits of computation and to study how hard computational problems are. So that's something called reducibility. Sam, that's an immense amount,

even in summary, to be there in the more. paper. We'll move on in a moment, but just to stay with you for a second, Simon. His ideas might be seeming, seem very abstract to people listening to this programme, but he grounded them in concrete practical work, didn't he? He was very fond of working with engineers. He was clearly exceptionally competent. Before the war, both in Britain and in his brief period before the United States, he'd been working very practically on building machines, on constructing machines that could do various computational tasks, ranging from calculating the values of a function that would unlock the problem of how many prime numbers there are, all the way to

really early work, this is in the late 1930s before the war, on cryptography and coding about which we'll hear much more in a moment. Can I turn to you again, Andrew Hodges. He sometimes represented Turing as a permanent outsider. Well, that's a very interesting question, outsider versus insider. And certainly within the narrow business of getting into mathematical logic, he absolutely came in as an outsider. I mean, no one had heard of him before.

He didn't write any precursor papers. He didn't correspond with the big names. He just produced his paper in 1936, and everyone would. gasped and at it, basically. In a way, it's ridiculous to call him an outsider when he's upper-middle-class character from a respectable background. But it's true that he didn't act like a big shot.

And I think you may be hinting at him being an outsider as a gay man, although he was far more open than most. But another factory you should bear in mind here is that King's College where he was and became a fellow in 1935 was the most sort of gay, friendly location in the English-speaking world, you could imagine, run by John Maynard-Kenz and a whole

coterie of people. And Turing had the benefit of being an insider to this. He wasn't a belonging. He had a teddy bear like the Bricehead revisited, aesthetic set of the Twenties. But he went in for rowing and running. You couldn't characterize him. And it was the same in maths. He was on track for a very perfectly good lectureship. and later a chair in pure mathematics by 1939, which we're thinking about. But as Simon's been saying, he was an outsider in having such an extraordinarily wide range. Thank you. Leslie Goldberg, can we talk about Turing's universal machine, which he thought was his greatest discovery invention?

When Turing was doing his work, as Simon has already told us, he needed to have a model of computation, what computers at the time were human, but what would it be a machine for doing computation? And the Turing machine, which he came up with, looks a little bit like a toy model of computation. It's kind of so simplistic you would never really build such a thing. But actually, it turns out that it captures what all of our real computers can do. So, you know, with the simplistic model, it actually captures what can be computed. Imagine that you have a tape, and it extends infinitely in both directions,

and it's divided into little squares. It had a tapehead, and what the tapehead could do is it could read or write a symbol onto each square of this tape. When the computation starts, the tapehead is somewhere and the input is just on the tape. And as computation goes on, the machine is always in one of some small number of states. If a state is accepting, it means the computation is over. Otherwise, the roles of computation are extremely simple. at any one time the machine is in some state it can see what's under the tapehead

it just writes a new symbol under the tapehead moves the tapehead to the left or the right or stay still and move to a new state so the remarkable thing is you can actually translate any computer program to that and in fact there's something we have in computer science called the church touring thesis

we believe that a touring machine not only does it capture all of the machines we have now, but we also believe it will actually capture machines we haven't thought of yet. What a universal machine is, it's a Turing machine, its input is just a description of some other Turing machine, along with the input to that. In this way, the universal machine can do what any Turing machine can do. So instead of every time you want to do a different task,

you have to build a different computer to do that, now you have one Turing machine, and it can do the job of any other. Thank you. Simon, can you, I was Turing ahead of others of his time? The question of how far ahead Turing was was a very tortured question actually at the time. Turing's paper of 1936 was completed during the period and immediately after the completion of a paper, we now treat as equivalent. A paper by someone Leslie just mentioned,

Alonzo Church, who was a mathematician at Princeton University, and who had demonstrated essentially the same result as Turing using a complementary but different method. Max Newman, one of Turing's patrons in Cambridge, broke the bad news that Turing to a certain extent had been anticipated, and therefore, it seems to me, brilliantly, suggested that Turing should go to Princeton to study with church. Newman's view in a letter to church was that Turing's treatment was different from church, which is absolutely true, and the difference, crucially, was that what Turing had done

was to describe a kind of machine, what Turing himself called the A machine, the automatic machine, which could just grind out computable sequences. It was Church, who in reading and reviewing Turing's great paper, invented the phrase Turing machine, which is, of course, an enormous compliment. Andrew Hodges, can I turn to you?

The war is about it's coming on, and Turing went to. Bletchley and was given a role and strongly welcomed as part of the British code breaking centre. What did he do? Sir Simons mentioned Turing had already developed a cipher scheme with an electromechanical implementation while away at Princeton. And Germany was what he had in his mind when he was doing it. He could have stayed in the United States in 1938 with a postdoc, as we'd now call it,

but he turned that down and returns to Cambridge in 38 and essentially volunteers. for government service at that point. Now, he was pushing it an open door for two reasons. GCCS were already recruiting science people, science mathematics people, whom they had not had before. And also, Turing was so well connected with Maynard Keynes and other King's fellows who were themselves very closely connected with the cipher establishment.

But, of course, he wasn't just any Cambridge mathematician. He was the first in, it was important thing, that he was the first such person to play a role. but he wasn't the typical one because he had this very concrete engineering sort of impulse. And that turned out to be exactly what was needed when the Poles, the Polish mathematicians in Warsaw, revealed the vital enigma information to the British in July 1939, absolutely crucial date. And Turing took off from that. And his first thing, very, very quick, based and inspired by what the polls had done,

was this basic algorithm for mass systematic breaking of the now famous enigma ciphers and implemented an especially engineered electromagnetic machine called the bomb. So that was his first great contribution and very striking how fast it was. This was being built at Letchworth in Hertfordshire in October 1939 and the first version of it was working in March 1940. subsequently improved. Turing didn't have all the ideas. And it's that pouncing on the

first ideas that were striking them about the whole crypto war and grip that the whole establishment had and taking up Turing's ideas was absolutely vital at that point. Is there a real link, Simon, between Turing's work at Letchley Park and the emergency

of computers as we know them now? Absolutely. I think that's very important. The connection is maybe not quite as direct as one might think. The bombs that the code-breaking machinery with which Turing was working in which he helped design and direct were, after all, not universal Turing machines. They were vast versions of the machine the Germans were using to encode naval messages at the famous Enigma device. And so they precisely were not the kind of general purpose device,

which Turing was so brilliantly urging. On the other hand, key insights such as the insight that mechanical computers, and then electronic computers could use numbers to represent something other than quantities, that they were symbol manipulators, the idea that this would effectively mechanise and automate and represent the labour of literally thousands of human computers and assistance. Remember how large the working staff at Bletchley Park was,

10,000 or more people working on this system. That was an image and model of the kind of power that an electronic, programmable, internally stored, modifiable computer run by electronics could do. And perhaps most importantly, as Andrew has pointed out, the way in which Turing's combination of a penetrating insight into what electronics and digital electronics especially could do with the idea of what programs could do, especially if the machine could modify its own programs, all of that was being developed at Bletchley Park.

Can I come back to you for a moment, Andrew? Did Curing's interest in artificial intelligence flow naturally out of the work he was doing, if I can use of the natural in commuters, or did he suddenly switch and become interested in this? Oh, I think it's the other way around. His interest in the nature of the mind went back much further, at least to Christopher Morecambe's death when he was writing about this as a major scientist.

scientific problem. And his 1936 analysis of what a Turing machine would be, why this was the right definition of what we'd now call an algorithm, that analysis involves a philosophical discussion of what a human mind is doing in following a procedure. And that's the most audacious part of his paper that it goes into the realms of psychology and philosophy in this analysis to show that this is the most general possible way that you could ever describe something it would want to call a definite procedure. Now, I think the war does come into it because I think he was naturally very impressed

by the power of algorithms to outdo human work and not just in the bomb machine, but in the statistical programs that he developed using techniques actually, which are now used in artificial intelligence, Bayesian analysis. They might be carried out by people, but they are essentially algorithms.

And they outdid what he, human intuition and guessing would do. I think he was very struck by that as well as the thing that Simons mentioned that it's talking about symbol manipulation, not just about doing fast arithmetic. All of that goes into his computer design of 1945-46. And in that prospectus, which he drew up immediately after the war, which had detailed electronics, more important is it had a great prospectus for the uses of the machine, which include check. playing as a model for artificial intelligence, along with many software ideas, which are well ahead of anyone else. And those, you can see that right at the start. In fact, a key expression

that he used was electronic brain. He quite shamelessly talked about computers, as they were becoming to be known, as electronic brains at a time. And all the respectable people in science, they said, oh, no, he mustn't call them brains and nothing like brains at all. They're just doing fast calculations and so forth. No, he actually, he used the expression. and he said his interest in developing technology was precisely to find out what their scope was, what the competition with human brain, what human thinking was all about

by doing experimenting with electronic computers. Leslie Goldberg, does this take us to the Turing test, and what is it? The Turing test is something that Turing introduced in a 1950 paper called Computing Machinery and Intelligence. In this paper, he was trying to address the question, can machines think? And it's hard to decide what this question really even means because it's really difficult to define.

What does it mean for a machine to think? And so, in his words, what he said he would do would replace the question by another, which is closely related to it, and is expressed in relatively unambiguous words. And the question that he replaced it with was whether machines could do what we, as thinking entities can do.

So really, the question was, can a computer imitate what a human does when a human thinks? So the Turing test is a sort of a parlor game where there's a human interrogator and has a written conversation with both a human and a computer and has to determine which one is the computer.

Actually predicted that by the year 2000, that relatively small computers, ones with about 100 megabytes of storage, would actually be able to fool 30% of human judges in a five-minute test. Now, that hasn't come to pass. I think the important part of the test is this idea that imitating what humans can do might be more important than determining what it means to think. I should note that mainstream AI is not mostly concerned

with trying to write programs that pass the Turing test. That's not really the goal. It's more relevant for the philosophy of AI. But there are developments in AI that come closer to passing the Turing test. So some of the programs that have been introduced for language generation. But I think nobody would really say that this test has been passed. I think it's worth mentioning that when Turing first presented what he called the imitation game in late 19th, The way he set it up has led to an enormous debate and a great deal of confusion because the way he defines the imitation game is that there are three players.

Player A, who is a man pretending to be a woman. And player B, who is a woman. And player C, who can't see them, but can communicate with them, who is the judge. and then he says, all right, take A away and replace him with a machine. So in the first version of the imitation game, the Turing test, the computer, the machine is given the job of pretending to be a man, pretending to be a woman. And that has led to a great deal of debate about what else might be said to be going on in Turing. Ring's original formulation of the imitation game. What I think is even more striking about the imitation game,

exactly as Leslie says, I don't think AI research now, even if it is interested in mutant algorithms, it's not that interested in designing machines that can win an imitation game. What is interesting about what Turing did with this set of arguments, this absolutely extraordinary paper was to treat intelligence as performance. If you can perform in a certain way, then you are intelligent. And I think that's an absolutely fascinating, admittedly highly behaviourist version of trying to define what it is to be intelligent and how anyone would know that an interlocutor is in is intelligent or not. And goodness,

knows that over the past six months, we've all had to play various versions of the imitation game. Was that the spell the end of his great number of inventions or contributions, or did he go on to further things before we come to his death? Well, there's the work that he did in early 1952 on the chemical basis of morphogenesis. By this period, he was working at Manchester University on really, major innovations in computer design and the philosophy of computation, as well as this, I think, completely remarkable work on how in living systems shape and pattern can emerge from chemical reactions, catalysts, inhibitors, and so on alone. Goodness only knows what we would have

learnt had he not so catastrophically and tragically died in the summer of 1954. Andrew, you've studied his life and knowing enormous amount about him. What was his mood at the time? And was he going onward and upward, thinking, there's more here, there's more here, I can keep digging away at the face of this? Well, as Simon's indicated, his work on mathematical biology, which he suddenly started and seems out of the blue. It seems it's hard to know how he got going on it,

but he worked from 1950 onwards. And was, incidentally, one of the first scientific, pure scientific programs to use a computer as part of the experimental method. It involved differential equations you couldn't actually solve analytically, and he used them for numerical calculations. So it was a very, I was a major scientific program, and by 1954, he was beginning to build up a research,

group. If he'd gone on, you could see him as the, he got scruffer and scruffy as he went on, so he would have been a T-shirts and jeans professor and science guru of the 1960s, absolutely. But that wasn't to be, he suddenly died in 1954. It wasn't to do with his work. He had all sorts of other things going on. He was very interested in getting, he's thinking about quantum mechanics again, for instance, something which he'd neglected somewhat since his early days and thinking about the relationship with computation, it seems very likely to me. I mean, a number of different areas. That wasn't the thing.

It was his life as a gay man that was the problem. And the thing was he had been arrested in 1952. He had left that protective bubble of King's College, Cambridge. He'd never really clung to it for protection as other gay men might have done. He quite liked the urban adventure. and there was a pick-up spot right next to Manchester University. His chat-up line was, I work on the electronic brain. It led to a pretty unfortunate affair with a young man

who visited him at his home in Wilmslow, and the affair came to light, an absolute classic 1950s manner through petty crime and the difference in class. That was the thing that the police spotted immediately. He was arrested actually on the first day of Her Majesty Queen Elizabeth's reign, and the trial the following month meant that, well, by that time, it wasn't just the classic case,

it was a very particular case of him and him as the absolutely top person in the British scientific cryptology business, a very, very unfortunate business for everyone in the secret world, I should imagine. His case was acknowledged, and so he was given the modern scientific treatment of chemical castration, effectively, injection of estrogen, which went on for a year after that point. And that meant he didn't go to prison and didn't indeed lose his job. I mean, he carried on at Manchester

and using the computer just the same. So it was a big surprise when he did suddenly die of cyanide poisoning in June 1954. The other side, I think, is that... When you say it was a surprise, can you not see a direct connection with what had happened to him

and his suicide. I think you're quite right. There was a need of connection, but I'm emphasising that it was over two years after the trial. You see, and people sometimes think, oh, he was knocked out by the horror and the shame of it and so forth. That's not how it seemed at the time. He was someone who seemed to fight back.

But one way he was trying to find a way out of it, well, it was by going abroad, which wasn't really the solution. But he was also going in for Jungian therapist. He made great efforts after the trial to find a sympathetic psychoanalyst, and that is to say someone who would entirely accept him being gay. But I think it's very clear from remarks that he made to his friends that he rather hoped that by this, some sort of bisexuality could emerge,

and as he said, he really wanted a long-term relationship, not one-off things. He rather hoped, I think, that some sort of bisexuality could emerge, and as he said, he really wanted a long-term relationship, not one-off things. I think that some sort of feeling could come through. He tried that in 1941 and he hadn't worked. Maybe he thought he could have another go at this. Well, I think that was completely hopeless. I think that was just not in him to find such an attraction. There was no real woman that he was attracted to or anything like that.

He just said he'd had dreams which made him think he was changing. My feeling is that this was what really gnawed away at him, that he felt completely trapped in terms of, of having a decent life as a human being, and they had a very lonely life many ways as well, in which he could not discuss with any of his friends, after all, none of them had the faintest idea why he was so important

that he had this enormous iceberg under the surface of all this knowledge of top Anglo-American security business. It was quite extraordinary life. Thanks, Andrew. Perhaps you could hear more about this in the extra discussion which makes up the podcast. Leslie Ann Goldberg, do you think he was prepared to go on and do more work at that stage in his life? I think it's undoubtedly true that he would have.

I mean, in every stage of his life, he made completely remarkable contribution. So it's hard to imagine that if he'd lived longer, that he wouldn't have had lots more work from him. Actually, even now, it's still true that in computer science, his ideas are still being used. all the time in the solution to problems. So there's a whole field within computer science where the goal is to understand the inherent difficulty of problems and to kind of map the boundary between problems that are tractable that we can solve and ones that are intractable

that are inherently difficult. And the main tool we have for studying them is the notion of reduction, which goes back to Turing. And that's really the main method that we use for solving them. So I'm sure that he himself would have contributed lots of ideas and results if he'd live longer. Simon, what would you say his legacy is? I think his legacy is immense for just the reasons Leslie has given, for example, that there are really major intellectual, philosophical and, of course,

deeply practical projects that use Turing's resources, his arguments and his techniques in an everyday manner. I mean, as I said earlier, it seems to me always that one of the distinguishing features of his work is the literalism and the deflationary quality of it. This is someone who, in the very first

and one of the most important reports ever written about computers, his 1945-46 report on the automatic computing engine, wrote an account of how it is that we need to deal with computers in general and how literal-minded computers are. Unless you say exactly what you mean, Turing argued, you'll get trouble, right?

So that's an argument against the idea of a mutant algorithm and it's an argument in favor of, this I think is very striking legacy of Turing, it's an argument in favor of welcoming computers into our society. Right. One of his most important arguments, an argument we're still exploring, is that computers have to be in contact with humans

so that computers can adapt to us. that seems to me to be an immensely important argument whose implications we still haven't exhausted. Well, I think we've talked a little about the 1950 paper, including the Turing test. It actually had much more than the Turing test. It's a whole thing about the foundation of computing and also practical suggestions about the development of AI research.

But not striking, you just look at page. I mean, it's just full of life. It's full of human life. I mean, he wanted to say, I know what it is to be human. I mean, it just stands out from all the other articles in the philosophical journal because it's just full of jokes and funny references. And it has race and sex class.

I mean, everything's in it, really. And that's because he had this view of what real intelligence would mean, and he wants to pit it in a way that makes sense to people. Again, it's a jury, if you like, who decides what intelligence is and not a white-coated expert. That's part of his life as well. So I think those things have made his writing, really, they have lasted for that reason. People are often drawn again and again to the slight, I mean, it's funny and it's slightly camp and it's full of stuff.

And people are drawn back to it again and again. And incidentally, he did give talks on the radio and he gave very interesting talk, follow up to this 1950 paper. And unfortunately, no recording of it was made and we haven't got it. So we have to imagine it, but I think he'd been very delighted to know that we were using computers to put our voices on the radio now in his memory. And we're towards the end now, Simon Schaffer. One of the driving principles here was a project to articulate and then defend and understand a better model of intelligence

than the ones that his culture was providing him with. And that went back a very long way. I mean, what I know about Turing, I've mainly learned from Andrew. But we go all the way back to public school to Sherbourne, where he'd been told by the headmaster, who was in Oxford Classics Don, that if Turing wanted to stay in Sherbourne, and be educated, he had to give up science.

I can't remember the line. It's something like, if he is to be a scientific specialist, he is wasting his time at public school. That's perfectly true, of course. Right, which is true. And in order to articulate a better, more humane, and I think more rounded and encompassing model of what it is to be intelligent,

perhaps what it is to be scientific as well, that's a driving principle in a lot of what Turing does, and why he does it so wittily, right? material which has now been made familiar because of declassifying what up till recently had been secret messages like the dispatches Turing sent home from his US mission during the Second World War are often hilarious. These are technical briefs to secret service and technical officers written from New York and Washington, D.C. And they mix up fantastically astute remarks about technology culture in the US with quite waspish and very amusing comments on many of the people that he's meeting, including people at prestigious institutions like Bell Labs, for example, where he's really quite bitchy, but in a very funny way.

So I think there is an admirable politics of, intelligence going on, and we probably need that right now. Thank you. Finally, Leslie, have we missed anything out? Actually, you mentioned the upcoming banknote commemorating Turing, and I just wanted to mention another kind of a commemoration. Within computer science, the equivalent of what people would call the so-called Nobel Prize of Computer Science is actually the Turing Award,

So that's the biggest prize anybody could ever win for academic work in computer science. And this was started actually only 12 years. The first Turing Award was given out in 1966, so just 12 years after Turing's death and just wanted to mention that somehow he's still really the central figure in the field. Well, thank you.

Thanks to Leslie Goldberg, Simon Schaffer and Andrew Hodges. Next week, it's The Lust of the Habsburgs. Empress Maria Theresa, who reigned for 40 years. Thanks for listening. And the In Our Time podcast gets some extra time now with a few minutes of bonus material from Melvin and his guests. Now, when you ask about his mood, I mean, there are many, many different strands. In one way, he was very defiant. He was always very open about what had happened. And real resistance. So in summer 1952, he went off to Norway because he'd somehow got wind of the very early Scandinavian gay rights. movement, which had social functions in Norway.

But this, you see, led to trouble with his security status. You must remember that he had access to everything that was going on, the UK, and the United States' crypto business during the war, and had done post-war work for GCHQ as well. That was extremely secret. All this meant that personal questions already very hurtful were enormously amplified by being turned into questions. of state security.

But he wasn't knocked out by that. He continued very lively in interaction with his friends as well as in his maths work. Anyway, his death, he was found dead in bed. He did it on the end of the Whitson Bank Holiday of 1954. The inquest was rushed through, rather, and the verdict was suicide. Some people think it could have been an accidental ingestion,

but I'm quite sure that's because Turing carefully set it up as a chemical accident to allow people, his mother in particular, to believe that this was the case. And she did more or less believe this. And there was a sort of Agatha Christie element to this, which I think he probably quite liked. This chemical plan of his went back before the war. I mean, because he'd been very depressed, I think, about being gay back in 19, in the 30s. And his first boyfriend, James Atkins, told me of this plan. He also, you can see, made a very individual and elaborate will. He started making preparations for this immediately after the trial in 1952.

It was very, well, by the standards at the time, very shocking will in which he favoured his supportive friends above his family. It was a very individual document. And that again showed that he was, I think he was prepared for death. He didn't know when it might come or if it necessarily would come. But he had made all the preparations for. it and then something over that weekend made him do it on the impulse i think maybe he'd got through that weekend things that might have looked cheerier the next day i i who can tell

no one can ever tell and no one can give us definite proof about his state of mind but i think i've indicated the various different strands of defiance but a resignation and of persistence and yet a willingness to, well, to resign. He resigned. As I heard, he left every group that he really might have belonged to and including, unfortunately, the human race. Leslie. One of the things that I would have really liked to do

would be actually to give Turing's proof that there's no algorithm for something called the halting problem. I had a go at the halting problem, but why do you have a go at the halting problem? Okay. You're much more likely to get much, much further than I did in much less time. Turing actually proved that there was no algorithm for the incitence problem. What he actually did is he studied a different problem called the halting problem.

And what the halting problem is, is the input's just a Turing machine and an input, and the problem is just to determine whether or not that Turing machine would halt with that input. And he proved that there's no algorithm for that, which implied using a reduction, that there's no algorithm for the incitence problem. problem. But I just wanted to tell you the actual proof that there's no algorithm for the halting problem because it's remarkably simple and cute. So everything we need for it, we've actually already had in this program. So we've had a universal machine. And I just don't need to tell you one more fact, but it's kind of a natural fact. So because a Turing machine can be described by a sequence of

zeros and ones, it makes sense to talk about the first Turing machine, the second Turing machine, the third Turing machine. And we could put the Turing machines in a list like that, and all of them are accounted for that way. Okay, so that's all you need. I can now give you the proof, and it uses an idea that goes all the way back to Aristotle, called proof by contradiction.

And proof by contradiction works as follows. If you want to prove that something is true, what you do is you assume that it's false, you work out the consequences, until you arrive at something that's just wrong. And when you get there, you know that your assumption was false, so the thing you wanted to prove is really true. Okay, so here's a proof that there's no algorithm for the halting problem, and here's how it goes. Let's pretend that there was.

Pretend that there was an algorithm for the halting problem. Okay, so just pretend we have it. And now what we're going to do is we're going to build a contradiction. And this is Turing's idea. Okay, so what does he do? He builds a Turing machine that cannot exist. Okay, I'm going to call it Turing Machine O for opposite. So what does this opposite machine do?

Well, it takes the input on the tape. If the input is one, then what does it do? It just uses the halting program to check whether the first Turing machine halts on the first input. If it does, it goes into an infinite loop. If not, it halts. So it just does the opposite. If the input is two, it checks what the second Turing Machine. would do on the second input, it does the opposite, and so on.

So this is our Turing machine, the Turing machine opposite. Now, it can't be the first Turing machine because it does the opposite on input one. It can't be the second Turing machine because it does the opposite on input two, and so on. Turns out it can't be any Turing machine in our list of the first, second, third, fourth, Turing machines. So we've got a contradiction. That contradiction means the original assumption must have been wrong that we were able. to check halting.

So for mathematicians, there's echoes of canter and girdle, but that's the whole proof. And it's an incredibly clever way, especially just out of the blue for proving that the algorithm couldn't exist. Oh, I loved that. Well, that was downside clearer than I read it. Thank you very much for clearing that up.

Andrew, finally, do you think that had his ideas, had he been more recognised for what he'd done earlier on, that would emboldened him and sort of strengthen his position in society to go out and keep going and build a team around him, as you suggested he might be doing. Well, he was building a team in the mathematical biology, that's what I was specifically referring to, and that was the first sort of modern research group you can see starting,

but didn't get very far. And he would have, that's what I imagine would have taken off in the 1960s if he'd lived. He wasn't unrecognised. I mean, he was elected an FRS in 1951 for the 1936 work. He'd been on the, you know, it was on the radio, and he was, especially at the beginning of the computer business in 1946, he was mentioned quite a bit.

But he didn't, you see, he didn't work for himself very much. He didn't do all the things you'd need to do to make a real impression and impress people. There are lots, there are a lot of things he could have done in writing or organizing conferences to make his vision of computing and computing science and the importance of software and other things he understood better than other people, he didn't really make the most of the opportunities that he had because he just wasn't like that. He just liked doing his own thing.

I'll just tell a story which relates to what Simon said about the United States. One of the big questions is really who invented the computer. Was it during, or was it John von Neumann? in America, possibly, and almost certainly probably helped by knowledge of the universal machine idea, but coming out with a definite plan before, just six months before, Turing did. It's a very, very difficult question in history of science, and there's very little to go on about exactly what people thought and what they intended and so on. But Turing never got involved into an argument about I was first or anything like that. He did say,

very clearly in 1947 that all the computers being built were implementations of the universal machine idea. But he didn't make a great deal of that. He didn't pick an argument. And he said that very deliberately after coming back and seeing the American development. So he knew what he was saying. But he didn't make a great thing of it. Where he did, the only time I know he made a definitive statement about his place in the origin of the computer was when he was a great marathon and long distance run. and after a race on Boxing Day in 1946, he was interviewed by the sports reporter of the evening news.

And the reporter asked him, because he'd been in the newspapers, is it true that you started this thing, the ACE, the automatic computing engine? He said, well, and the reporter, he says, well, he said, he said the Americans had done quite a lot of the donkey work. And that's kind of comment. using that typical English phrase, where I think summed up the way that he was prepared

to just let that pass, really. And so he didn't make a great deal of his being in on the seminal moment of 20th century technology, which was the development of the electronic implementation of the universal machine. But there we are. I did loads of other things as well. If he'd lived, he would have done, I'm sure, many other things as well.

in our time with Melvin Bragg is produced by Simon Tillotson Before you go I'm Miles the producer of a brand new podcast for Radio 4 called Tricky This is how it works Four people from across the UK Meet up and without a presenter breathing down their necks Talk about issues they really care about

Sex work is quite complicated for a lot of people And it's okay to be against it but not to shame someone because of their professional. Across the series, we'll hear anger, shock and even the odd laugh. Another thing that really gets to me is when people say, I know what we need to do. I know what black people. Shut up.

You don't, like, that's the thing, that's not how it works. Nobody knows if you knew you would have done it. Discover more conversations like this by searching Tricky on BBC Sounds.