Oddly enough, the smaller the academic arena, the higher the stakes tend to be. In 1936, the discipline of mathematical logic not only had few adherents but was in somewhat bad odor in the larger mathematical community, particularly in America. As Church recalled in an interview with William Aspray conducted in 1984, “there were not many others interested in this field, and it was thought of as not a respectable field, with some justice. There was a lot of nonsense published under this heading.” That few mathematicians would take much interest in something as arcane as the Entscheidungsproblem, however, did not make its resolution any less significant for the two men each of whom saw himself, justly, as the victor in a battle that had been going on for centuries. Moreover, both needed the recognition. In 1936, after all, Church was only thirty-three years old, just nine years older than Turing. He was still an assistant professor and had no other means of support for himself and his family (including his aged father, a retired judge) beyond his Princeton salary. In mathematics, advancement comes about only by way of significant publications, vetted by authorities after careful review. Being able to lay claim to the Entscheidungsproblem by means of “Church’s thesis” mattered as much to Church as being able to do so by means of “Turing’s thesis” meant to Turing.* Yet in the interview with Aspray in 1984, when Church was eighty, he was curiously evasive on the question of how he first heard about Turing and “Computable Numbers.” Indeed, the exchange is as telling for what it leaves out as for what it includes:
Aspray: If you don’t mind, I would like to ask a few more questions about this topic, because it is one of particular interest to me since I wrote my dissertation on Turing. How did you hear about Turing’s work?
Church: Well, Turing heard about mine by seeing the published paper in the American Journal of Mathematics. At the time his own work was substantially ready for publication. It may already have been ready for publication. At any rate he arranged with a British periodical to get it published rapidly, and about six months later his paper appeared. At the same time, I think, Newman in England wrote to me about it.
Aside from errors in chronology, what is striking about this passage is that Church answers the question “How did you hear about Turing’s work?” as if it were the question “How did Turing hear about your work?” For Turing, Church tells Aspray, the news of his own results came “as a great disappointment.” We never learn how Church took the news of Turing’s results.
One point was beyond dispute: although the methods that Church and Turing employed could not have been more different—indeed, it was the uniqueness of Turing’s methods that made his paper so striking—the conclusions they reached were identical. This meant that Turing would have to acknowledge Church before he could publish “Computable Numbers,” and so that August he sketched out, as an appendix to the paper, a proof of equivalency between his notion of computability and Church’s of λ-definability. He then sent the manuscript off. Church appeared willing to have him at Princeton, and on September 23 Turing’s mother saw him off at Southampton, where he boarded the Cunard liner Berengaria, traveling steerage. Among the items that he brought with him were an old violin picked up at the Farringdon Road market in London and an antique sextant. “Of all the ungainly things to hold,” his mother wrote, “commend to me an old-fashioned sextant case. Though some readings were taken, what with the movement of the ship, and a defect in the instrument and Alan’s inexperience, he doubted their accuracy.” Turing headed a letter sent from on board the Berengaria 41° 20′ N. 62° W.
He arrived in New York on September 29. Since the establishment, in 1932, of the Institute for Advanced Study, Princeton had rapidly become the Göttingen of the twentieth century, and though the institute remained a separate entity from the university’s mathematics department, the fact that both were housed at Fine Hall rendered the distinction academic. Turing wrote to his mother,
The mathematics department here comes fully up to expectations. There is a great number of the most distinguished mathematicians here: J. v. Neumann, Weyl, Courant, Hardy, Einstein, Lefschetz, as well as a host of smaller fry. Unfortunately there are not nearly so many logic people here as last year. Church is of course, but Gödel, Kleene, Rosser and Bernays who were here last year have left. I don’t think I mind very much missing any of these except Gödel. Kleene and Rosser are, I imagine, just disciples of Church and have not much to offer that I could not get from Church. Bernays is I think getting rather “vieux jeu” that is the impression I get from his writing, but if I were to meet him I might get a different impression.
Bernays, in fact, had been one of Hilbert’s disciples at Göttingen; as recently as 1930 he had voiced his optimistic faith that a positive solution to the Entscheidungsproblem would eventually be found. As for Hardy, as a fellow Cambridge homosexual, he would have made, one might think, a likely mentor for Turing. Instead, Turing reported, “he was very standoffish or possibly shy. I met him in Maurice Pryce’s* rooms the day I arrived, and he didn’t say a word to me. But he is getting much more friendly now.”
Like most of the graduate students in the mathematics department, Turing spent nearly all his time in Fine Hall, a three-story red-brick building with elaborate casement windows and a slate roof. Notwithstanding its gothic fripperies, Fine Hall had been open only since 1931. The mathematician Oswald Veblen (1880–1960), Church’s mentor and the guiding spirit behind its construction, as well as the nephew of the economist Thorstein Veblen, intended for it to emulate the architecture of Oxford and Cambridge. Although he was from Iowa and of Norwegian descent, Veblen had distinct Anglo-philic tendencies; he had taught at Oxford and was married to Elizabeth Richardson, the sister of the British physicist Owen Willans Richardson. Perhaps for this reason, he conceived of Fine Hall as a sort of Oxbridge college in its own right, albeit one intended exclusively for the use of mathematicians and physicists. Thus, just as at Oxford colleges there were junior common rooms in which the students could mingle with the faculty, and senior common rooms in which the dons could gather alone to drink port, at Fine Hall there was a common room (analogous to the junior common room) open to everybody (it was situated so that one had to pass through it on the way to the library), as well as a room reserved for the exclusive use of the professors on the principle “not always understood by those who try to bring about closer relations between faculty and students that in all forms of social intercourse the provisions for privacy are as important as those for proximity.” In this “professors’ room,” faculty members could chat or read in front of an elaborate wooden fireplace the surround of which was carved with mathematical imagery, including a fly exploring the Moebius strip; over the mantel was inscribed a quotation from Einstein—“Raffiniert ist der Herr Gott, aber boshaft ist er nicht”—which the mathematical physicist H. P. Robertson translated as “God is slick, but he ain’t mean.” Some of the windows were divided into polyhedra, while in others the leaded glass was etched with formulae, including E = mc2.
One of a set of passport photos taken of Alan Turing in the 1930s. (King’s College Library, Cambridge)
As much effort was made to mimic Oxbridge ritual as Oxbridge architecture; thus at the Graduate College, students wore gowns to dinner, while in the Fine Hall common room, tea was served every afternoon at three. And yet in spite of the tea, the common room had a distinctly casual (and distinctly American) tone that was entirely unlike that at King’s College. Graduate students with little money spent nearly all their time there, returning to their furnished rooms only to sleep. There were no tea ladies or waiters; instead, the teas were organized and served by fellowship students, in compensation for the fact that they earned more money and had less work to do. Off the room was a kitchenette with an electric stove and—wonder of wonders—a dishwasher; here there was kept a large quantity of “cookies” (for Turing a foreign term) ordered in bulk from the National Biscuit Company, which would soon become Nabisco. Particularly during the depression, there had to be a quota on the nu
mber of cookies served, in order to discourage hungry graduate students from making a meal of them.
Not surprisingly, few professors actually used the room reserved for their exclusive occupancy. The common room was much more fun. Games were always being played there—go, chess, and kriegspiel (a variety of blindfold chess) as well as games invented on the premises, such as psychology, a card game of which Turing’s friend Shaun Wylie was immensely fond. Wylie, who hailed from Oxford (his father had been a “greats” don), was finishing the last of his three years at Princeton just as Turing was starting the first of what would turn out to be his two. Rather quickly, Wylie drew him into his circle of English and American graduate students, the other members of which included Francis Price, Will Jones, and Bobby Burrell. The group organized treasure hunts, play readings, even an (ad-) hockey team, which played matches against the girls at Miss Fine’s School (Miss Fine was the sister of Dean Fine, for whom Fine Hall was named) and Vassar. But Turing, though he was looked upon with affection, and considered an “honorary member of the clique,” remained a bit aloof. “I suspect that he was glad to be involved,” Wylie later told Frederick Nebeker, “but was certainly at that stage not a leading spirit.”
All told, Princeton proved rather flummoxing for a young middle-class Englishman like Turing. He was puzzled, for example, that none of the graduate students with whom he worked minded “talking shop. It is very different from Cambridge in that way.” American speech habits also took him aback:
These Americans have various peculiarities in conversation which catch the ear somehow. Whenever you thank them for anything, they say “You’re welcome.” I rather liked it at first, thinking I was welcome, but now I find it comes back like a ball thrown against a wall, and become positively apprehensive. Another habit they have is to make the sound described by authors as “Aha.” They use it when they have no suitable reply to a remark, but think that silence could be rude.
The more fluid aspects of American social interaction were particularly disconcerting for a young man raised in a society defined by class distinctions, physical reticence, and rigid notions of propriety. “Though prepared to find democracy in full flower,” Mrs. Turing wrote, “the familiarity of the tradespeople surprised [Turing]; he cited as an extreme case the laundry vanman who, while explaining what he would do in response to some request of Alan’s, put his arm along Alan’s shoulder. ‘It would be just incredible in England.’” Of course, reading between the lines, one wonders if behind Turing’s dismay at the vanman’s “familiarity” there lay a more profound unease: surprise at encountering frank erotic possibility, uncertainty as to how to respond to it, even retrospective disappointment at an opportunity lost.
What news of Mother England he received came through American newspapers. “I am sending you some cuttings about Mrs. Simpson,” he wrote to his mother on November 22, “as representative sample of what we get over here on this subject. I don’t suppose you have ever heard of her, but some days it has been ‘front page stuff’ here.” A little more than a week later he was complaining that he was “horrified at the way people are trying to interfere with the King’s marriage. It may be that the King should not marry Mrs. Simpson, but it is his private concern. I should tolerate no interference by bishops myself and I don’t see that the King need either.”
Strong words, especially to a mother. Yet Turing had reason to identify with the plight of Edward VIII; his love stories, after all, were also of a sort likely to draw disapproval from bishops. The hypocrisy of the Church of England outraged him, as did the apparent effort of the British press to suppress the story. “I believe the government wanted to get rid of him and found Mrs. Simpson a good opportunity,” he wrote. Clearly the idea that political institutions might use a man’s personal life against him neither shocked nor particularly surprised Turing, though it disturbed him, as did what he called the “disgraceful” behavior of the archbishop of Canterbury: “He waited until Edward was safely out of the way and then unloaded a whole lot of quite uncalled-for abuse. He didn’t dare do it whilst Edward was King. Further he had no objections to the King having Mrs. Simpson as a mistress, but marry her, that wouldn’t do at all.”
It was just the sort of sexual hypocrisy that Turing had grown up with, at schools where homosexual behavior was tolerated so long as it was never named, or allowed to evolve into homosexual identity. And how swiftly quiet tolerance turned into brutal suppression, once the lovers decided to go public! The archbishop’s “Don’t ask, don’t tell” policy galled Turing not just on behalf of the king and Mrs. Simpson but because of the implications it held for his own future. Indeed, as late as May of 1939, he was still fretting over the abdication, noting to his mother that he was “glad that the Royal Family are resisting the cabinet in their attempt to keep Edward VIII’s marriage quiet.”
At Princeton, meanwhile, there were parties to go to—the sort at which the fate of Mrs. Simpson might well be the topic of conversation. Although mathematicians don’t usually have a reputation for being party people, the crowd at Fine Hall was famously sociable. In particular, the spirited and glamorous John von Neumann and his second wife, Klara, gave grand parties at their house to which the graduate students were often invited. Hermann Weyl and his wife, Hella, held gatherings at which Turkish coffee was served. By contrast, the occasional dinners that Church hosted with his wife, Mary, were somewhat dreary affairs, at least to judge from what Turing reported to his mother. “Church had me out to dinner the other night,” he wrote to her that October. “Considering that the guests were all university people I found the conversation rather disappointing. They seem, from what I can remember of it, to have discussed nothing but the different states they came from.”
As for Church, if he took any notice at all of Turing, he later forgot it. Many years later, William Aspray asked him to name the graduate students with whom he worked in the thirties. The answer he gave is noteworthy, once again, for the one name it omits: Turing’s. Reminded of Turing by Aspray, Church continued, “Yes, I forgot about him when I was speaking about my own graduate students. Truth is, he was not really mine. He came to Princeton as a grad student and wrote his dissertation there.” When asked to describe Turing’s personality, Church said, “I did not have enough contact with him to know. He had the reputation of being a loner and rather odd.” The same, of course, had often been said of Church himself.
4.
“Computable Numbers” was published by the Proceedings of the London Mathematical Society in January 1937. To Turing’s disappointment, the response was decidedly underwhelming. “I have had two letters asking for reprints,” he wrote to his mother, one from his old Cambridge friend R. B. Braithwaite
and one from a proffessor [sic] in Germany. . . . They seem very much interested in the paper. I think possibly it is making a certain amount of impression. I was disappointed by its reception here. I expected Weyl who had done some work connected quite closely with it some years ago, at least to have made a few remarks.
But Weyl, whose 1918 monograph Das Kontinuum had been a landmark text in classical analysis, said nothing. Neither, apparently, did the dashing and cosmopolitan John von Neumann, like Weyl, a former disciple of the Hilbert program. Von Neumann was in attendance at the 1930 address in Königsberg at which Gödel had announced his incompleteness theorem, and after the talk had approached Gödel asking for details; according to Solomon Feferman, he “was one of the first to appreciate the significance of Gödel’s incompleteness results. In fact, it is reported that he obtained the second incompleteness theorem . . . independently of Gödel, once he had learned of Gödel’s first incompleteness theorem.”
Von Neumann was famous not just for his astounding mathematical aptitude but for the catholicity of his interests—in a discipline notable for its compartmentalization, he was something of a jack-of-all-trades—and when Gödel’s findings were published, he abandoned logic altogether in favor of other fields, once going so far as to claim neve
r to have read another paper in the subject after 1931. Most of his colleagues doubted that this was true; in any case, his apparent allergy to logic may have been behind his failure to respond, either positively or negatively, to “Computable Numbers.”
Ironically, part of the problem was that in 1937 Princeton was such an important center for mathematics and physics. More and more the Institute for Advanced Study was becoming an escape route for European scientists forced to flee their homelands in the wake of Nazism. As a result, the community’s prestige increased in direct proportion to the drain of émigré faculty from such former European powerhouses as Göttingen. Rarely had so many great minds been gathered in a single building. As Joseph Daly explained to Aspray, “You had von Neumann, you had Einstein, you had Veblen, you had Knebelman and T. Y. Thomas and Al Tucker. Everything was going on at once, and the real problem for graduate students was to keep from getting so diverted into 16 different fields that you didn’t get anything done.”
Logicians were already in the minority—a state of affairs that Gödel’s absence and von Neumann’s decampment only worsened. Nor did solving the Entscheidungsproblem look like quite such a big deal when you had Albert Einstein just down the hall. In order to get noticed at Princeton, you had to have done something, but you also had to know how to promote yourself, and in this arena Turing—shy from the outset—was far less adept than his friend Maurice Pryce, of whom he had written to his mother, “Maurice is much more conscious of what are the right things to do to help his career. He makes great social efforts with the mathematical big-wigs.” That Turing had come second in the succession after Church, who was on the Princeton faculty, only added to his difficulty, as did the fact that his paper made for such slow reading. As Newman had pointed out, his isolation, though it lent freshness to his thinking, also made his prose impenetrable. All told, it took time to dig deep enough inside “Computable Numbers” to recognize the startling originality at its heart, and few of his colleagues had the patience.
The Man Who Knew Too Much: Alan Turing and the Invention of the Computer (Great Discoveries) Page 10
