“It's all right,” Alice said. “I'm Alice Neville. We met at the zoo— oh, it feels like years ago. I was with Gertrude Hardy.”
Memory, then, a reawakening that was visible in Mrs. Chase's eyes. But a good memory?
“Of course,” she said, smiling. “How lovely to see you.”
And she reached out her hand, and took Alice's arm, and mysteriously, thrillingly, kissed her on the cheek.
14
New Lecture Hall, Harvard University
BY THE END of 1916, we had the partitions formula. Here is what it looked like:
where
the sum being over p's that are positive integers less than and prime to q, v is of the order of √n and ωp, q is a certain 24q-th root of unity and
Today whenever I write out the formula, I think: what an extraordinary creature! It is like one of those circus bears trained to balance a motor car on its nose, or some such thing. There is dazzle in its every baroque convolution; yet the dazzle belies the laborious process by which we got to it: a process, sometimes, of trial and error, as if we were standing in a room the walls of which were lined with thousands upon thousands of light switches, and we had to try each one with the goal of eventually arriving at a very particular degree of brightness. One switch would bring us close—and then we would try another and the light would be blinding, or the room would go dark. Still, over weeks, we got closer, and then, almost without noticing, one day we had the light almost right.
Now I must address, once again, the mystic faction that accepts, without a hint of incredulity, Ramanujan's claim that his mathematics came to him in dreams, or that formulae were inscribed upon his tongue by a deity. I am sure that he believed this to be the case, just as I am sure that, on occasion, he did haul up from the depths of his imagination treasure chests from which glittering jewels gleamed forth, while the rest of us were chiseling away in the diamond mines with our pickaxes. And yet, the ability to voyage on a regular basis (as poor Moore could not) into regions of the mind from which most of us are barred does not necessarily require the intervention of a goddess. On the contrary, all of us experience, on occasion, such “miracles.”
Let me give an example. All of you who know him would agree that no mathematician is less “mystic” than Littlewood. Yet even Little-wood described to me once an occasion on which, while working on the M1 (1 — c)M2 problem for real trigonometrical polynomials, his “pencil wrote down” a random formula that turned out to be the key to the proof. According to Littlewood, this episode was “almost unattended by consciousness”—a claim which, had psychoanalysis been in vogue during the war, would have been of considerable interest to its adherents. In those years it would have been of interest only to adherents of the Ouija board. And that is just my point. Were I to announce, today, that a goddess was writing formulae on my tongue, you would show me the way to the asylum. But Ramanujan was Indian, and so he was labeled a “visionary.” Yet what this label neglects is the price he paid for his vision, and how hard he had to work to attain it.
While it is true, for instance, that the formula sprang from one of the conjectures that he had brought with him from India, it must be borne in mind that the journey from that initial conjecture to the final product was laborious and long. It was a process of refinement, and while it is fair to say that, had I not brought to the table certain technical know-how that I possessed and that he did not, we couldn't have got there, let me emphasize that my contribution was not merely technical. I contributed my own share of vision.
I remember it was Christmas when we finished. I was at Cranleigh, at the house in which I had grown up, the house my mother shared with my sister, and to which I returned on holidays. My mother, at this point, had been dying for several years. Every few months, it seemed, she would come close to death, she would see the angels beckoning her, and then, at the eleventh hour, something would pull her back from the brink, and before we knew it she would be out of bed, making tea and proposing a game of Vint. To this game—does anyone now remember it?—she was devoted. It was Russian in origin, a variant on Contract Bridge. (I'm told “Vint” means “screw” in Russian.) That Christmas we played it for hours every day, with our neighbor and Mother's friend, Mrs. Chern, making up the fourth. Mrs. Chern cheated, I think. I wonder if Mother noticed.
I may have already mentioned that she possessed a certain degree of mathematical talent—a talent, I am sorry to say, that in her later years she applied exclusively to the playing of Vint, which at least has the advantage of being a harmless pastime, in contrast to the occult evils in which Ramanujan's mother indulged. And Mother, to her credit, was a very good Vint player. Almost as good as I was. That year I had the idea to write a book on how to win at Vint, and make enough money from it that I could give up teaching. My goal, I told Russell, was to score a million points, so that later, when people asked me what I'd done in the Great War, I could say that I'd become head of the Vint League and given the world at large the benefit of my expertise. But I never wrote the book, just as I never wrote the murder mystery about the Riemann hypothesis, and now, when people ask me what I did during the Great War, I tell them, “I took care of Ramanujan.” Perhaps, in my dotage, I shall write both.
But I am straying. To get back to partitions: that Christmas, Ramanujan sent me a postcard from Trinity, providing the last piece in the puzzle and asking me to write up the final proofs. By then MacMahon, who was really the dearest of creatures, had provided him with the typewritten copy of values he had come up with for p(n) up to n = 200, and Ramanujan had made his comparisons. The formula was not precise. Instead it gave an answer that was correct only when rounded to the nearest integer. Yet the difference was extraordinarily small. In the case of n = 100, for instance, our formula gave a value for p(n) of 190569291.996, whereas the actual value was 190569292. A difference, to be precise, of .004.
Ramanujan was thrilled with the results. He called them “remarkable,” which was unusually expressive, coming from him. It was exciting enough news that I mentioned it to Mother, to whom I rarely spoke about my work, but as the question had no bearing on Vint, she responded only with an air of contrived vagueness, saying something along the lines of “How nice” before drifting back to the card table.
You see, she was really sharp as a tack. Vagueness was a convenience for her, to which she resorted when a subject bored her. Her illness let her get away with all sorts of things she could never have got away with had she been well. And in the meantime my poor sister danced attendance on her, indulging her every fancy and never managing to distinguish between the real complaints and those that were purely fictitious. Poor Gertrude. In this regard she was far more credulous than I was.
Was the Russell business in full swing then? I think so. But no: most of the action—his arrest, the court case, his dismissal from Trinity— must have happened in the late summer and early autumn, because I remember light coming over my shoulder as I read one of his letters while drinking tea; at Christmas it would have been dark already at teatime, a darkness which the wartime prohibition on streetlights only deepened. The habit of memory (my memory, at least) is to organize by category, not date. It's as if some immemorial secretary has plucked events out of their natural sequence and then filed them away under such headings as “Ramanujan,” “The War,” “The Russell Affair,” so that now, in order to see clearly the chronology, I have first to dig out from each file the pertinent details of a moment and then place them alongside the details of another moment, dug out of another file. Nor, once I've completed this elaborate reconstruction, am I quite convinced of its veracity.
By the way, this is an episode of which, if you Harvard men have heard of it at all, you have probably heard only because it touches lightly on the history of your own illustrious university. For in 1916 not only was Russell dismissed by Trinity, he was refused a passport by the Foreign Office, and this meant that he could not take up a position he had been offered at Harvard. All of which suited his i
ntentions perfectly.
I shall try to be as brief as possible. Russell was not, as is commonly believed, dismissed by Trinity after he was sent to prison. In fact, by the time he was sent to prison, two years had passed since his dismissal. This second arrest resulted from an article he wrote for the Tribunal that was adjudged likely to muck up relations between England and the United States; my own personal belief is that he wrote the article in order to be sent to prison, and thereby prove once and for all his willingness to endure sufferings, if not equal to, then at least approaching those of the men at the front. For it was difficult, in his position, to escape being labeled a shirker, and prison would show the manliness of his opposition.
But this is jumping ahead. In 1916 I don't believe prison was as yet on Russell's mind. What he had done was acknowledge, in a letter to the Times, authorship of a leaflet issued by the No Conscription Fellowship. The leaflet contained language the government considered inflammatory and possibly illegal, and so when Russell announced that he had written it, the Crown had no choice but to prosecute. The exact charge was that in the leaflet Russell had made statements “likely to prejudice the recruiting and discipline of His Majesty's forces.” This was just what he wanted, for now he could use the trial as a soapbox for his pacifism. By getting himself prosecuted and, if possible, convicted, he hoped both to draw attention to the injustices being suffered by the conscientious objectors and to obtain a larger audience for his tirades.
The trouble was, his tirades could go over the heads of their intended audience. At the trial, he was in every way the logician, dismantling the prosecution's case as if it were a piece of specious mathematical reasoning. For instance, in addressing the principal charge against him—that the leaflet prejudiced recruiting—he noted that, at the time that the leaflet was issued, single men were already subject to conscription, while married men were not. Therefore the only deleterious influence that the leaflet might have would be on married men who were considering voluntary enlistment and were therefore, ex hypothesi (Russell actually used this phrase), not conscientious objectors. The leaflet, Russell summed up, merely informed such men that, if they chose to “pose” as conscientious objectors, they would be liable to two years' hard labor. “I do not consider that knowledge of this fact,” he said, “is likely to induce such a man to pretend that he is a conscientious objector when he is not”: an argument that, while it might dazzle a Trinity undergraduate, was only likely to antagonize a Lord Mayor.
And antagonize the Lord Mayor it did. Indeed, I would say that the strategy backfired completely, with the result that Russell was found guilty and fined £100, which he refused to pay. And the irony is, he could easily have got off. The Crown's case against him was incredibly weak. Now I suspect that in fact his game was far more subtle than any of us guessed; that, having recognized the weakness of the case, he had deliberately chosen to employ an approach that would annoy the Lord Mayor and insure his conviction. Now, because he refused to pay the fine, all the goods in his rooms at Trinity would go on the auction block. The newspapers would report the auction, and he would look every inch the martyr.
On the other hand, I very much doubt that he expected the Trinity Council actually to dismiss him. I certainly didn't expect it. After all, it is one thing to refuse a pacifist group permission to meet on the college grounds; it is another to rescind the fellowship of a man as eminent, respected, and famous as Bertrand Russell. And though the college bylaws gave the Council the right to dismiss any fellow convicted of a crime, it did not oblige them to do so. There was a choice to be made, and in making it, the Council revealed itself to be despotic and cowardly, undermining—perhaps permanently—the very foundations of intellectual freedom on which the college was built, and drawing ire from both inside and outside Cambridge.
Yet it was worse than that. Of the eleven members of the Council who voted against Russell, five were Apostles—McTaggart and Jackson among them. That ghastly shit McTaggart, I still believe, should have been cursed and roby-ized for what he did, for roby had merely decided that the society was not worth his time, while McTaggart turned against a brother who had once regarded him as a mentor. That year, every time I saw McTaggart creeping along a wall, or riding by on his decrepit tricycle, I would walk the other way, for fear that, should we encounter each other, I might lose my temper and kick him. Finally I understood why, in his school days, other boys had found kicking him such an irresistible temptation.
Of course, if Russell was shaken, he seemed to get over it quickly enough. Indeed, within a few days, he was telling me that the dismissal was the best thing that could have happened to him because, as he put it, it “decided the issue.” Now he would be free of Trinity once and for all, and could travel around the country offering “intellectual food” to working men, miners and the like. Whether he really believed this or had merely struck a bargain with his pride I cannot say. But he did go off, to Wales and other places, and give lectures. Nor did he appear, when on occasion I saw him in London, to miss Trinity in the slightest. I cannot blame him. I loathed Trinity myself.
Yes, I loathed Trinity. I say this today without regret or embarrassment, even though, in the interval, I have left for Oxford and returned again. In dismissing Russell, we all agreed, the Council had at last gone too far. And yet we were divided as to how we should respond, some (myself included) feeling that militant action was called for, others believing that we should lie low until the war was over. And in the end, we compromised. Instead of a strongly worded statement published in the Cambridge Magazine, we settled for a weakly worded petition circulated only within the college:
The undersigned Fellows of the College, while not proposing to take any action in the matter during the war, desire to place on the record that they are not satisfied with the action of the College Council in depriving Mr. Russell of his Lectureship.
What astounds me, in retrospect, is that even with this diluted language we collected only twenty-two signatures. It was mostly the enlisted fellows, the ones whose signatures would have carried the most weight, who refused to sign. Nor did Russell make the job any easier for us when he wrote to the Trinity porter and asked that his name be struck from the college books. That such a gesture should be considered provocative may strike you as puzzling, but in the Trinity of those years, any action that could be interpreted as expressing contempt for tradition was taken very seriously indeed. Because of it, we very nearly gave up on the whole effort, reasoning that if Russell had no desire to be helped, we ought not to risk our futures to help him. For he was having a fine old time right then, drinking beer with his new Welsh miner mates and sleeping with three women at once, though how they could withstand his breath I cannot imagine.
What did Ramanujan make of it all? Was he even aware that it was happening? I wish I knew. I wish I had asked him. But I didn't.
No doubt the most absurd moment in the affair, and the one in which Russell took the greatest satisfaction, was the auctioning off of his goods. This was necessitated, you will recall, by his refusal to pay the fine. Yet from the beginning he maintained an underhanded control of the proceedings. Remember, he had two domiciles. In addition to his rooms at Trinity, he kept a flat in London. Somehow he had managed to persuade the court to leave the London flat alone, and impound only what was at Trinity. I suspect that, from his vantage point, auctioning off the stuff at Trinity would be doubly beneficial: not only would the spectacle of the auction secure his public reputation, it would relieve him of the necessity of returning to Trinity to clear out his rooms, which he would be vacating anyway. Now his Welsh lecture tour need not be interrupted. And of course—at least this is what he said at first—he didn't really care about any of the stuff at Trinity. The truth was, it didn't have much value. Under ordinary circumstances it would never have fetched the £110 (a £100 fine plus £10 in costs) that Russell was required to pay if he was to avoid prison. For it was hideous stuff, chosen deliberately, or so Norton and I believed, to sug
gest the sort of studied indifference to environment that Russell considered befitting an intellectual.
Now, when I look over the advertisement for the sale (the immemorial secretary has kindly preserved it), I am really quite astonished at its brutality. The auctioneers, Messrs. Catling and Son, were experts at the use of a certain kind of language the sole intention of which is to whet the appetites of antique dealers and predatory collectors. For you must understand, most of the stuff was tasteless and worthless, which was why it made Norton and me laugh to see a particularly ugly little table described as a “Coromandel Wood Tea Caddy, mounted with 10 plated medallions,” or Russell's battered desk transformed into a “Walnut Kneehole Writing Table,” or the stained rugs described as “Superior Turkey Carpets.” Indeed, of all Russell's furniture, only one piece—a six-legged Chippendale sofa—was any good, and this, in the end, I bought myself.
Any mirth that this advertisement might have aroused, however, ceased with the first paragraph. For immediately after listing “upwards of 100 ozs. of plate, Plated Articles, Gentleman's Gold Watch and
Chain,” Messrs. Catling and Son skipped a line and announced—the text here is centered and in capital letters—the pièce de résistance: “COLUMBIA UNIVERSITY BUTLER GOLD MEDAL, awarded to Bertrand Russell, 1915.” And then the books: Royal Society Proceedings and Transactions, London Mathematical Society Proceedings; the complete works of Blake, Bentham, Hobbes; Baldwin's Dictionary of Philosophy and Psychology; Cambridge Modern History. To sell a man's medal! And his books! Even Russell must have felt enough of a spasm at the prospect of these losses to reconsider his desire to see everything sold off, for a few days before the auction took place he was writing that, though he did not mind giving up the philosophy and mathematics books, he should not like to lose the literature books. And then—a further refinement—while it was true that he did not mind giving up the philosophy and mathematics books, he did think that he should like to keep the complete sets of the great philosophers, as these had belonged to his father. And then there was the tea table for which he seemed to feel a disproportionate attachment. But the medal could go. It would make good copy, this emblem of his fame overseas melted down and put on the market as raw gold. He could not resist that.
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