Working with Alan Turing* Peter Hilton

We are here to honor the outs tanding playwright Hugh Whitemore, and to express to him our apprecia- tion of the service he has done to the cause of dissemi- nating an awareness of the importance of mathematics through his celebrated play Breaking the Code. There can be no doubt that the award he is about to receive is richly deserved, as you will have the opportunity to judge for yourselves when Mr. Whitemore reads ex- cerpts from his play to you.

The play was inspired by the life and work of the great British logician and mathematician Alan Turing (1912-1954) - -a life unusua l ly rich in drama and tragedy. I had the good fortune to work closely with Turing and to know him well for the last 12 years of his short life, and thus I am happy to be given this opportunity, within the context of celebrating Mr. Whitemore's award, to reminisce on my association with Turing and to pay tribute to his memory.

However, I will be rather selective in my recollec- tions and reflections for a number of reasons. First, there exists a very comprehensive biography of Alan Turing by the logician Andrew Hodges [3] and it would be gratuitous for me to supply details already carefully assembled and lucidly described in that ex- cellent book. In fact, Whitemore describes his play as based on Hodges 's book, though I would claim that it is more accurately described as being inspired by it, since Whitemore's is a brilliant work of imaginative fiction; the book and the play fulfill extremely different functions. Second, I have already written briefly of my association with Turing in Part I of the centenary volume of the American Mathematical Society [2], and, while it would be futile to seek to avoid any overlap with that article, I feel that only very major aspects of Turing's character, genius and achievement should be repeated here if treated in [2]. After all, my purpose in [2] was rather different; it was much broader, and Turing featured in those reminiscences because he was an important mathematician who flourished earlier in this century and whom I was for- tunate enough to know.

* Text of a talk delivered on the occasion of the presentation of an award to Mr. Hugh Whitemore, at the winter meeting of the AMS- MAA in Louisville (Kentucky) in January, 1990, for communicating, through his play Breaking the Code, the importance of mathematics to contemporary society.

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Third, I am unfor tunate ly obliged to be reticent about the details of the work we did at Bletchley Park in breaking the h igh-grade German ciphers. For reasons best known-- indeed , almost certainly, exclu- sively k n o w n - - t o themselves, the bureaucrats in Washington and Whitehall steadfastly refuse to de- classify such details. It is, to me, inconceivable that such information could be valuable to a potential enemy today, when the methods of encryption and decoding must be utterly different from those of 50 years ago. Does the State Department envisage Col- onel Gaddaf i gloating over a descr ipt ion of our methods of long ago and concluding that, armed with this knowledge, it is now safe to attack the United States? However that may be, I would not wish to risk deportation from the United States and arrest on re- turning to the United Kingdom, and I must therefore forbear to share with you a fascinating story (as much as I dare tell is to be found in [2]).

I joined the distinguished team of mathematicians and first-class chess players working on the Enigma

code on 12 January 1942--and Alan Turing was the acknowledged leading light of that team. However, I must emphasize that we were a team-- th is 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 mes- sages. This brings me to an important point inevitably g lossed over in W h i t e m o r e ' s play. The phrase "breaking the code," in popular parlance, refers to the analysis of the system whereby the message (= signal = informat ion) is encoded . This is the natural meaning- -as , for example, in the reference to the work of Crick and Watson in "breaking the genetic code" by analyzing DNA. However, cryptanalysts, especially under wartime conditions, have another t a s k - - t h a t of " read ing" the encoded messages so promptly, so rapidly that the intelligence content of those messages could be exploited to advantage. Of course, this second aspect of code-breaking would be impossible without the first (this is not quite t rue- - i t is sometimes possible to decode messages without fully understanding the method of encipherment); but it is clear that the first would have had no impact on winning the war without the second. To Turing, very largely, we owe success in the first, primary aspect of code-breaking, together with an entire approach to the problem of cryptanalysis which was revolutionary and decisive; but it is to the t eam- -and scarcely at all to Tur ing- - tha t we owe our success in providing our war machine with information about enemy disposi- tions, plans, tactics, and strategy on a scale and with a regularity never before achieved. It is due to the ef- forts of Turing and the entire team that Churchill was able to describe our work as "my secret weapon." Turing could never have said, as Derek Jacobi, the actor who so dramatically played the role of Turing in the play, said, "I broke the German code." Neither his modesty nor his honesty would have permitted such grandiosity. But, in the play, there are but three crypt- a n a l y s t s - - a n ancient has-been, a y o u n g w o m a n emotionally involved with Turing, and Turing him- self. In fact, our team contained no has-beens, no pas- sengers at all, and only one w o m a n - - w h o scarcely fitted the description of "Pat Green" in the play; but it did contain some wonderful people, mathematicians and others, whose contributions were enormous.

It is also necessary to point out that the two aspects of code-breaking referred to above continued to be, both of them, of vital importance throughout the war. For the Germans very frequently changed their enci- phering procedures. Such changes might be relatively minor - - fo r example, changing the wheel patterns first monthly, then weekly, then d a i l y - - b u t they might be fundamental. Thus the Germans introduced a totally new mach ine - - the Geheimschreiber, as we

called i t - - fo r transmitting their highest-grade ciphers in 1943, so that a wholly new system had to be ana- lyzed before we could again start providing regular decryptions to military intelligence. Thus Turing's role remained decis ive--but he was not alone in playing that role. However, he was perhaps alone in under- standing that the machine he was designing to help us to read messages encoded by the Geheimschreiber was destined, under his guidance, to be the forerunner of the electronic computer.

Let me now narrow the focus and describe the sort of man Alan Turing was. First, however, let me estab- lish my credentials for offering such a description. I was fortunate to establish an easy, informal relation- ship with Turing virtually from the day of my arrival at Bletchley Park (this probably had something to do with my helping him to solve a chess problem which was intriguing him on my first day on the job); and to maintain that relationship thereafter. I left Bletchley Park in the summer of 1945, shortly after the end of the European war; after a year at the Post Office Engi- neering Research Station I was demobilized and went back to Oxford University to work on my doctorate u n d e r the supe rv i s ion of my good fr iend f rom Bletchley days, the great topologist Henry Whitehead. In 1948 I took up my first academic appointment, at Manchester University, where the head of department was Max Newman, another great topologist and one who had played a decisive role as head of the key sec- tion at Bletchley Park responsible for breaking the Geheimschreiber code. Max had done me the honor of appoint ing me as Assistant Lecturer; he had also b rough t off the t r e m e n d o u s coup of luring Alan Turing away from the National Physical Laboratory to become Reader in Mathematics--with special respon- sibility for designing a computer to be built by Fer- ranti. Thus my relationship with Turing was restored and I can recall vividly the hours he spent explaining to me how the computer functioned and how to use it. I left Manchester for Cambridge in 1952, but I re- mained in touch with Alan Turing until his death.

Alan Turing was obviously a genius, but he was an approachable, friendly genius. He was always willing to take time and trouble to explain his ideas; but he was no narrow specialist, so that his versatile thought ranged over a vast area of the exact sciences; indeed, at the time of his death his dominant interest was in morphogenesis. He had a very lively imagination and a strong sense of h u m o r - - h e was a fundamentally se- rious person but never unduly austere.

If I were to attempt to characterize the nature of his genius, I would say it lay in his capacity for thought of great originality, so often going back to first principles for his inspiration. This is not the place for a careful evaluation of his work, but even the most superficial examination of his oeuvre shows how often he took up a new topic--his publications range very widely in-

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