Radiolaria: validating the Turing theory

In his 1952 paper ‘The chemical basis of morphogenesis’ Turing postulated his now famous Morphogenesis Equation. He claimed that his theory would explain why plants and animals took the shapes they did. When I joined him, Turing suggested that I might solve his equation in three dimensions, a new problem. After many manipulations using rather sophisticated mathematics and one of the first factory-produced computers in the UK, I derived a series of solutions to Turing’s equation. I showed that these solutions explained the shapes of specimens of the marine creatures known as Radiolaria, and that they corresponded very closely to the actual spiny shapes of real radiolarians. My work provided further evidence for Turing’s theory of morphogenesis, and in particular for his belief that the external shapes exhibited by Radiolaria can be explained by his reaction–diffusion mechanism. While working in the Computing Machine Laboratory at the University of Manchester in the early 1950s, Alan Turing reignited the interests he had had in both botany and biology from his early youth. During his school-days he was more interested in the structure of the flowers on the school sports field than in the games played there (see Fig. 1.3). It is known that during the Second World War he discussed the problem of phyllotaxis (the arrangement of leaves and florets in plants), and then at Manchester he had some conversations with Claude Wardlaw, the Professor of Botany in the University. Turing was keen to take forward the work that D’Arcy Thompson had published in On Growth and Form in 1917. In his now-famous paper of 1952 Turing solved his own ‘Equation of Morphogenesis’ in two dimensions, and demonstrated a solution that could explain the ‘dappling’—the black-and-white patterns—on cows. The next step was for me to solve Turing’s equation in three dimensions. The two-dimensional case concerns only surface features of organisms, such as dappling, spots, and stripes, whereas the three-dimensional version concerns the overall shape of an organism. In 1953 I joined Turing as a research student in the University of Manchester, and he set me the task of solving his equation in three dimensions. A remarkable journey of collaboration began. Turing chatted to me in a very friendly fashion.

The Turing test—from every angle

Can machines think? Turing’s famous test is one way of determining the answer. On the sixtieth anniversary of his death, the University of Reading announced that a ‘historic milestone in artificial intelligence’ had been reached at the Royal Society: a computer program had passed the ‘iconic’ Turing test. According to an organizer, this was ‘one of the most exciting’ advances in human understanding. In a frenzy of worldwide publicity, the news was described as a ‘breakthrough’ showing that ‘robot overlords creep closer to assuming control’ of human beings. Yet after only a single day it was claimed that ‘almost everything about the story is bogus’: it was ‘nonsense, complete nonsense’ to say that the Turing test had been passed. The program concerned ‘actually got an F’ on the test. The backlash spread to the test itself; critics said that the ‘whole concept of the Turing Test is kind of a joke . . . a needless distraction’. So, what is the Turing test—and why does it matter? In 1948, in a report entitled ‘Intelligent machinery’, Turing described a ‘little experiment’ that, he said, was ‘a rather idealized form of an experiment I have actually done’. It involved three subjects, all chess players. Player A plays chess as he/she normally would, while player B is proxy for a computer program, following a written set of rules and working out what to do using pencil and paper—this ‘paper machine’ was the only sort of programmable computer freely available in 1948 (see Ch. 31). Both of these players are hidden from the third player, C. Turing said, ‘Two rooms are used with some arrangement for communicating moves, and a game is played between C and either A or the paper machine’. How did the experiment fare? According to Turing, ‘C may find it quite difficult to tell which he is playing’. This is the first version of what has come to be known as ‘Turing’s imitation game’ or the ‘Turing test’.

Turing, Lovelace, and Babbage

The principles on which all modern computing machines are based were enunciated more than a hundred years ago by a Cambridge mathematician named Charles Babbage.’ So declared Vivian Bowden—in charge of sales of the Ferranti Mark I computer— in 1953.1 This chapter is about historical origins. It identifies core ideas in Turing’s work on computing, embodied in the realisation of the modern computer. These ideas are traced back to their emergence in the 19th century where they are explicit in the work of Babbage and Ada Lovelace. Mechanical process, algorithms, computation as systematic method, and the relationship between halting and solvability are part of an unexpected congruence between the pre-history of electronic computing and the modern age. The chapter concludes with a consideration of whether Turing was aware of these origins and, if so, the extent—if any—to which he may have been influenced by them. Computing is widely seen as a gift of the modern age. The huge growth in computing coincided with, and was fuelled by, developments in electronics, a phenomenon decidedly of our own times. Alan Turing’s earliest work on automatic computation coincided with the dawn of the electronic age, the late 1930s, and his name is an inseparable part of the narrative of the pioneering era of automatic computing that unfolded. Identifying computing with the electronic age has had the effect of eradicating pre-history. It is as though the modern era with its rampant achievements stands alone and separate from the computational devices and aids that pre-date it. In the 18th century lex continui in natura proclaimed that nature had no discontinuities, and we tend to view historical causation in the same way. Discontinuities in history are uncomfortable: they offend against gradualism, or at least against the idea of the irreducible interconnectedness of events. The central assertion of this chapter is that core ideas evidenced in modern computing, ideas with which Turing is closely associated, emerged explicitly in the 19th century, a hundred years earlier than is commonly credited.

ACE

In October 1945 Alan Turing was recruited by the National Physical Laboratory to lead computer development. His design for a computer, the Automatic Computing Engine (ACE), was idiosyncratic but highly effective. The small-scale Pilot ACE, completed in 1950, was the fastest medium-sized computer of its era. By the time that the full-sized ACE was operational in 1958, however, technological advance had rendered it obsolescent. Although the wartime Bletchley Park operation saw the development of the electromechanical codebreaking bombe (specified by Turing) and the electronic Colossus (to which Turing was a bystander), these inventions had no direct impact on the invention of the electronic storedprogram computer, which originated in the United States. The stored-program computer was described in the classic ‘First draft of a report on the EDVAC’, written by John von Neumann on behalf of the computer group at the Moore School of Electrical Engineering, University of Pennsylvania, in June 1945. The report was the outcome of a series of discussions commencing in the summer of 1944 between von Neumann and the inventors of the ENIAC computer—John Presper Eckert, John W. Mauchly, and others. ENIAC was an electronic computer designed primarily for ballistics calculations: in practice, the machine was limited to the integration of ordinary differential equations and it had several other design shortcomings, including a vast number of electronic tubes (18,000) and a tiny memory of just twenty numbers. It was also very time-consuming to program. The EDVAC design grew out of an attempt to remedy these shortcomings. The most novel concept in the EDVAC, which gave it the description ‘stored program’, was the decision to store both instructions and numbers in the same memory. It is worth noting that during 1936 Turing became a research student of Alonzo Church at Princeton University. Turing came to know von Neumann, who was a founding professor of the Institute for Advanced Study (IAS) in Princeton and was fully aware of Turing’s 1936 paper ‘On computable numbers’. Indeed, von Neumann was sufficiently impressed with it that he invited Turing to become his research assistant at the IAS, but Turing decided to return to England and subsequently spent the war years at Bletchley Park.

Breaking machines with a pencil

Dilly Knox, the renowned First World War codebreaker, was the first to investigate the workings of the Enigma machine after it came on the market in 1925, and he developed hand methods for breaking Enigma. What he called ‘serendipity’ was truly a mixture of careful observation and inspired guesswork. This chapter describes the importance of the pre-war introduction to Enigma that Turing received from Knox. Turing worked with Knox during the pre-war months, and when war was declared he joined Knox’s Enigma Research Section at Bletchley Park. Once a stately home, Bletchley Park had become the war station of the Secret Intelligence Service (SIS), of which the Government Code and Cypher School (GC&CS) was part. Its head, Admiral Sir Hugh Sinclair, was responsible for both espionage (Humint) and the new signals intelligence (Sigint), but the latter soon became his priority. Winston Churchill was the first minister to realize the intelligence potential of breaking the enemy’s codes, and in November 1914 he had set up ‘Room 40’ right beside his Admiralty premises. By Bletchley Park’s standards, Room 40 was a small-scale codebreaking unit focusing mainly on naval and diplomatic messages. When France and Germany also set up cryptographic bureaux they staffed them with servicemen, but Churchill insisted on recruiting scholars with minds of their own—the so-called ‘professor types’. It was an excellent decision. Under the influence of Sir Alfred Ewing, an expert in wireless telegraphy and professor of engineering at Cambridge University, Ewing’s own college, King’s, became a happy hunting ground for ‘professor types’ during both world wars—including Dillwyn (Dilly) Knox (Fig. 11.1) in the first and Alan Turing in the second. Until the time of Turing’s arrival, mostly classicists and linguists were recruited. Knox himself had an international reputation for unravelling charred fragments of Greek papyri. Shortly after Enigma first came on the market in 1925, offering security to banks and businesses for their telegrams and cables, the GC&CS obtained two of the new machines, and some time later Knox studied one of these closely.

Meeting a genius

I had the good fortune to work closely with Alan Turing and to know him well for the last 12 years of his short life. It is a rare experience to meet an authentic genius. Those of us privileged to inhabit the world of scholarship are familiar with the intellectual stimulation furnished by talented colleagues. We can admire the ideas they share with us and are usually able to understand their source; we may even often believe that we ourselves could have created such concepts and originated such thoughts. However, the experience of sharing the intellectual life of a genius is entirely different; one realizes that one is in the presence of an intelligence, a sensitivity of such profundity and originality that one is filled with wonder and excitement. Alan Turing was such a genius, and those, like myself, who had the astonishing and unexpected opportunity created by the strange exigencies of the Second World War to be able to count Turing as colleague and friend will never forget that experience, nor can we ever lose its immense benefit to us. Before the war, in 1935–36, Turing had done fundamental work in mathematical logic and had invented a concept that has come to be known as the ‘universal Turing machine’ (see Chapter 6). His purpose was to make precise the notion of a computable mathematical function, but he had in fact provided a blueprint for the most basic principles of computer design and for the foundations of computer science. I joined the distinguished team of mathematicians and first-class chess players working on the Enigma code in January 1942. Alan Turing was the acknowledged leading light of that team. However, I must emphasize that we were a team—this was no one-man show! Indeed, Turing’s contribution was somewhat different from that of the rest of the team, being more concerned with improving our methods, especially the machines we used to help us, and less concerned with our daily output of deciphered messages. It was due to the efforts of Turing and the entire team that Churchill was able to describe our work as ‘my secret weapon’.

The man with the terrible trousers

My uncle, Alan Turing, was not a well-dressed man. It is a tribute to those who employed him that he was able to flourish in environments that ignored his refusal to comply with social norms as much as he disregarded mindless social conventions. Social conventions, however, became an increasingly powerful influence over his life. Here I retell the story from the family perspective. There is an old photograph in the family album that shows Alan in his last years at Sherborne (Fig. 2.1). It was taken in June 1930—a few months after his friend Christopher Morcom’s death—and Alan looks relaxed and happy. But his trousers are a complete disgrace. It is not clear who took the picture, but the timing suggests that it was done at Commemoration, the annual festival at Sherborne to which parents and dignitaries are invited, and where boys, particularly senior boys, should be smartly turned-out. Ordinarily, Alan’s mother (my grandmother) would have intervened and spruced him up. But given that Alan was, like other boarding-school boys, responsible for his own clothes, she probably had no control over him any more, if indeed she ever had done. My grandmother had had little direct control over Alan during his formative years. My grandfather was serving the Empire in India, and she, as a good memsahib, was expected to be with him to run his household. (From the distance of a century or so, this seems a waste of talent, for my grandmother had a formidable intellect as well as many other gifts, and in a later age would probably have become a scientist of distinction.) So Alan was deposited in England with foster parents in St Leonards-on-Sea, and at nine years of age was sent off to a prep school called Hazelhurst, near Frant in Sussex. School seems to have been a reasonably good experience for him—at least in his first term. There was the incident of the geography test. At that time my father, being four years older than Alan, was in the top form while Alan was in the bottom one. The whole school was made to do a geography test. Turing 1 (my father) got 59 marks and Turing 2 (Alan) got 77; my father considered this a thoroughly bad show.

Turing and the paranormal

Of the nine arguments against the validity of the imitation game that Alan Turing anticipated and refuted in advance in his ‘Computing machinery and intelligence’, the most peculiar is probably the last, ‘The argument from extra-sensory perception’. So out of step is this argument with the rest of the paper that most writers on Turing (myself included) have tended to ignore it or gloss over it, while some editions omit it altogether.1 An investigation into the research into parapsychology that had been done in the years leading up to Turing’s breakthrough paper, however, provides some context for the argument’s inclusion, as well as some surprising insights into Turing’s mind. Argument 9 (of the nine arguments against the validity of the imitation game) begins with a statement that to many of us today will seem remarkable. Turing writes:… I assume that the reader is familiar with the idea of extra-sensory perception and the meaning of the four items of it, viz. telepathy, clairvoyance, precognition, and psycho-kinesis. These disturbing phenomena seem to deny all our usual scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming…. To what ‘statistical evidence’ is Turing referring? In all likelihood it is the results of some experiments carried out in the early 1940s by S. G. Soal (1899–1975), a lecturer in mathematics at Queen Mary College, University of London, and a member of the London-based Society for Psychical Research (SPR). To give some background, the SPR had been founded in 1882 by Henry Sidgwick, Edmund Gurney, and F. W. H. Myers—all graduates of Trinity College, Cambridge—for the express purpose of investigating ‘that large body of debatable phenomena designated by such terms as mesmeric, psychical and spiritualistic . . . in the same spirit of exact and unimpassioned enquiry which has enabled science to solve so many problems, once no less obscure nor less hotly debated’. Although the membership of the SPR included numerous academics and scientists—most notably William James, Sir William Crookes, and Lord Rayleigh, a Nobel laureate in physics—it had no academic affiliation. Indeed, in the view of their detractors, the ‘psychists’, as they were known, occupied the same fringe as the mediums and mind-readers whose claims it sought to verify—or disclaim.

Connectionism: computing with neurons

Modern ‘connectionists’ are exploring the idea of using artificial neurons (artificial brain cells) to compute. Many see connectionist research as the route not only to artificial intelligence (AI) but also to achieving a deep understanding of how the human brain works. It is less well known than it should be that Turing was the first pioneer of connectionism. Digital computers are superb number crunchers. Ask them to predict a rocket’s trajectory or calculate the financial figures for a large multinational corporation and they can churn out the answers in seconds. But seemingly simple actions that people routinely perform, such as recognizing a face or reading handwriting, have been devilishly tricky to program. Perhaps the networks of neurons that make up a brain have a natural facility for these and other tasks that standard computers simply lack (Fig. 29.1). Scientists have therefore been investigating computers modelled more closely on the biological brain. Connectionism is the science of computing with networks of artificial neurons. Currently researchers usually simulate the neurons and their interconnections within an ordinary digital computer, just as engineers create virtual models of aircraft wings and skyscrapers. A training algorithm that runs on the computer adjusts the connections between the neurons, honing the network into a special-purpose machine dedicated to performing some particular function, such as forecasting international currency markets. In a famous demonstration of the potential of connectionism in the 1980s, James McClelland and David Rumelhart trained a network of 920 neurons to form the past tenses of English verbs. Verbs such as ‘come’, ‘look’, and ‘sleep’ were presented (suitably encoded) to the layer of input neurons. The automatic training system noted the difference between the actual response at the output neurons and the desired response (such as ‘came’) and then mechanically adjusted the connections throughout the network in such a way as to give the network a slight push in the direction of the correct response. About 400 different verbs were presented to the network one by one, and after each presentation the network’s connections were adjusted. By repeating this whole procedure approximately 200 times, the connections were honed to meet the needs of all the verbs in the training set. The network’s training was now complete, and without further intervention it could form the past tenses of all the verbs in the training set.

Turing’s Zeitgeist

This chapter reviews the history of Alan Turing’s design proposal for an Automatic Computing Engine (ACE) and how he came to write it in 1945, and takes a fresh look at the numerous formative ideas it included. All of these ideas resurfaced in the young computing industry over the following fifteen years. We cannot tell to what extent Turing’s unpublished foresights were passed on to other pioneers, or to what extent they were rediscovered independently as their time came. In any case, they all became part of the Zeitgeist of the computing industry. At some universities, such as ours in New Zealand, the main computer in 1975 was a Burroughs B6700, a ‘stack’ machine. In this kind of machine, data, including items such as the return address for a subroutine, are stored on top of one another so that the last one in becomes the first one out. In effect, each new item on the stack ‘buries’ the previous one. Apart from the old English Electric KDF9, and the recently introduced Digital Equipment Corporation PDP-11, stack machines were unusual. Where had this idea come from? It just seemed to be part of computing’s Zeitgeist, the intellectual climate of the discipline, and it remains so to this day. Computer history was largely American in the 1970s—the computer was called the von Neumann machine and everybody knew about the early American machines such as ENIAC and EDVAC. Early British computers were viewed as a footnote; the fact that the first stored program in history ran in Manchester was largely overlooked, which is probably why the word ‘program’ is usually spelt in the American way. There was a tendency to assume that all the main ideas in computing, such as the idea of a stack, had originated in the United States. At that time, Alan Turing was known as a theoretician and for his work on artificial intelligence. The world didn’t know that he was a cryptanalyst, didn’t know that he tinkered with electronics, didn’t know that he designed a computer, and didn’t know that he was gay. He was hardly mentioned in the history of practical computing.