What More Could Alan Turing Have Accomplished?

Many of you have probably heard the name of Alan Turing, but most of those probably don’t appreciate the extent of his contributions. To say that he invented the modern world is an overstatement, but he did dream up the computers we see around us today, and helped win World War II in the process. But the story of Alan Turing is as much about exclusion and defeat as it is of genius.

This is not a happy story. Our modern world tends to fetishize oddball geniuses and celebrate those with great accomplishments: Thomas Edison, the Wright brothers, Albert Einstein, and Steve Jobs, to name a few.

But what about those who were just too odd for our popular consciousness? Consider Nikola Tesla or Howard Hughes, who remain controversial despite massive contributions to science and technology.

Alan Turing is perhaps the ultimate example of our ability to cast off even the most productive members of society if they don’t fit within our social norms. Although it is no surprise that conservative British society did not accept this self-described “homosexual mathematician”, one can ask whether modern America would be any more forgiving.

Alan Turing’s Contributions and Death

Not everyone is familiar with Alan Turing, so let’s start with his accomplishments. Over the course of a short four-decade life, Turing made numerous major developments in mathematics and science:

1. Turing independently proved the Central Limit Theorem, which explains the popular “bell curve” of distributed samples. This impressed Kings College enough to make him a fellow at the age of 22.
2. In answering the Entscheidungsproblem, one of the great questions of mathematical logic, Turing’s metaphoric “machine” became the foundational concept of modern computers.
3. Turing analyzed the German Enigma encryption machine during World War II, discovering many weaknesses and developing a machine and process to read their naval codes for much of the war.
4. In a short liaison at Bell Labs in New York, Turing contributed to the development of voice encryption, invented his own such device, and assisted Claude Shannon in devising practical digital audio sampling, the technology behind CDs and MP3s.
5. Turing envisioned the first programmable general-purpose computer, designing an “Automatic Computing Engine” and creating some of the first “programs” and programming languages.
6. Asked to differentiate between machine and human intelligence, Turing created a pragmatic test which remains relevant today (and retains his name).
7. Turing developed the biological field of morphogenesis, explaining the development of complex organisms and patterns based on the mathematics of waves.

In his short life, Alan Turing made some of the most significant contributions to mathematics and technology of the 20th century. His repeated breaking of the Enigma ciphers during World War II saved countless lives, and perhaps even turned the tide of war in favor of America and Britain since it allowed supplies to reach the island nation. And he was celebrated as a central figure behind the development of digital computers in the 1950s.

But none of this could save Alan Turing. In an era when homosexuality was a crime, Turing was open about his sexual orientation. After a break-in at his home, Turing explained that he was sexually involved with one of the young men responsible. He was imprisoned and convicted and given the option of chemical “treatment”. After a year of hormone injections and a further year of declining interest in life, Turing poisoned himself by lacing his regular evening apple with cyanide. It was 1954, and he was just 41.

A Solitary Genius

Alan Turing’s genius was not unlike that found in many others before and after. He was a solitary thinker, whose key distinction lay in his ability to see the world plainly, rather than through a filter of conventional science or society. Each of his great contributions were made at a time in his life when he was allowed to exercise this ability for abstract thought.

As a child, Turing taught himself to read and then began an investigation of chemistry and mathematics quite apart from his middling performance at school. He seemed entirely unaware of society, refining iodine from seaweed while on vacation in France, and cycling alone 60 miles across an unfamiliar Britain to reach school during a railroad strike.

“All that I can claim is that my deliberate policy of leaving him largely to his own devices and standing by to assist when necessary, allowed his natural mathematical genius to progress uninhibited.” – D. B. Eperson, Alan Turing’s mathematics teacher at Sherborne School

But Alan Turing flourished once he reached King’s College in Cambridge. Stewarded at the time by John Maynard Keynes, a genius of an entirely different sort, King’s was a universe away from respectable and restrictive British society. Turing continued mainly to work in isolation, but no demands were placed on him to conform or succeed.

With carte blanche to think as he wished, Turing tore into cutting-edge mathematics in ways that were unthinkable to the mainstream. His proof of the Central Limit Theorem and concept of Computable Numbers were unorthodox in the extreme, and this made it difficult for him to be accepted even in his own field.

“[Turing] was no world-standard mathematician, and it was often more amazing to the professional mathematician what he did not know, than what he did.” – Biographer Andrew Hodges, writing in Alan Turing: The Enigma

But the Turing Machine would gradually emerge as the correct model for everything we today call a computer: A general-purpose machine that mingles both program and data and can perform any computable task. It is difficult now to think of a computer in any other way, but no one since Charles Babbage had redirected information technology to such a great degree.

“We do not need to have an infinity of different machines doing different jobs. A single one will suffice. The engineering problem of producing various machines for various jobs is replaced by the office work of ‘programming’ the universal machine to do these jobs.” – Alan Turing

Turing separated the values being calculated from the symbols used, breaking all of mathematics into a series of binary operations on an infinite “tape”. A decade later, he performed a similar leap, conforming his thinking to the mechanical needs of his ACE computer: Base 32 numbers written as 5-bit “characters” backwards upon an actual tape. He became so used to this strange system that he once unconsciously wrote backwards base 32 characters on a chalk board while giving a seminar on computing!

Alan Turing enjoyed a similar sort of autonomy while working in the Government Code and Cypher School at Bletchley Park during World War II. Although Polish and British Intelligence had repeatedly cracked Enigma codes before Turing’s involvement, they relied on weaknesses in the operational practice of the Germans. Turing devised procedures to break the code itself, including a method of prioritization based on probability.

The Germans understood that a brute-force attack on their codes was possible, but were confident that it was impractical since it would take decades of calculation to discover a single day’s settings. Turing was able to exploit fundamental mathematical weaknesses in the Enigma machine and direct the work of his mechanical “Bombe” devices to test the keys most likely to be correct. This same process later helped break the completely different mechanical “Fish” encryption used by German High Command.

You may also enjoy reading this piece on My Visit to Bletchley Park

Conformity and Death

Turing’s life was unique, both in positive and negative ways. The absence of his parents in British India set him apart in boarding schools. His placement in the freedom of King’s College allowed his independent development to continue, and his usefulness during the war protected him from social pressures. But once this protection was removed, Turing’s creativity was stifled and he was unable to continue his life.

If freedom allows genius to flourish, conformity is the enemy. Once the codebreaking operations at Bletchley Park became successful without Turing’s involvement, he no longer had a focus for his mind or an environment in which to exercise it.

After the war, Alan Turing’s life wandered and declined. He continued to be productive, creating the ACE computer and contributing to the science of morphogenesis, but his eccentricities were catching up to him. The last half-decade of his life, spent at the University in Manchester, was depressingly lonely. Despite support from lingering friendships, Turing knew he could never return to greatness.

His position at Manchester was greatly diminished, a situation to which Turing probably gave no thought whatsoever. But his ideas were ignored as well, with the Pilot ACE a shadow of his concept and the eventual Manchester Computer substantially diverging from his vision. Although today’s computers are certainly Turing Machines, their complexity and special-purpose circuits do not truly reflect his philosophy.

And so, entrapped by the friend of a boy with whom he had become casually intimate, Alan Turing found the full force of British society against him. None of Turing’s honors or associates could or would protect him from the police and magistrates. He was convicted of “gross indecency” and imprisoned.

“Turing believes machines think,
Turing lies with men,
Therefore machines do not think”
– Alan Turing’s sardonic commentary after his arrest

Homosexuality was an increasingly intolerable offense at the time, with special concern about blackmail and “corruption of youth”. Although Himmler’s policy of sending homosexuals to concentration camps in Nazi Germany had given the advantage to the American and British intelligence, Britain was not much more tolerant. On learning of the prosecution of a similar case, King George V was quoted as saying “I thought men like that shot themselves.”

Although the courts allowed him probation, he was forced to endure hormone injections to stop his “tendencies”. This treatment was thought more humane than “mechanical castration”, which was then practiced, and more effective than psychotherapy. Note that castration was a common “treatment” for homosexuality at the time, legal in 11 American States and with 50,000 cases on record there.

“I am both bound over for a year and obliged to take this organo-therapy for the same period. It is supposed to reduce sexual urge whilst it goes on, but one is supposed to return to normal when it is over. I hope they’re right. The psychiatrists seemed to think it useless to try and do any psychotherapy.” – Alan Turing, in a letter to King’s College mathematician Philip Hall

The conviction cost him his security clearance and thus any opportunity to work in the field of cryptography. It also made him unwelcome in the United States, though Turing exercised a newfound interest in traveling to gay-friendly European destinations. But the situation on the whole proved intolerable. On June 7, 1954, he mimicked both Socrates and Snow White by consuming an poisoned apple.

How Could This Have Happened?

That Alan Turing was given three decades of acceptance is remarkable. He personified the extreme non-conformity of thought sometimes required for genius, something that likely would have been stamped out by most social systems much earlier in life. Perhaps a more-notable element of Turing’s life was not his genius but the fact that he was able to flourish at all, even just for a few decades.

We are often told that we should celebrate diversity, or accept the inherent worth and dignity of all people. But do we really do this? And what to these words really mean? True difference cannot be restricted, even for a short while. Genius is a feeble sprout that is too often pinched out of existence before it can grow. Can any human society truly foster diversity?

I am reminded of another mathematician of the 20th century. Srinivasa Ramanujan was born to a poor Brahmin family in Madras, India, yet taught himself advanced mathematics. Discovered in his 20s, he was brought to Trinity College, Cambridge, but died of infection at just 32. Like Turing, the miracle is that Ramanujan was able to flourish and gain notice for his remarkable skills.

The story of Alan Turing is not one of a reclusive homosexual mathematician, but of society’s tendency alternately to enable and crush genius based on our own prejudices. He succeeded in many ways, and his contributions have endured. But what could he have accomplished? And what of the other Alan Turings who vanished before they could be heard from?

Remember the Apple Computer ads urging everyone to “Think Different”? Thinking different is both a blessing and a curse, as we now see. It can lead to fresh insight and social exclusion. Yes thinking different is essential for the development of society, not just technology. And it is supposed to be what the modern world is all about.

The question for us all is how to foster and support such extreme eccentricity so that we may all benefit. Simplistic affirmations are not enough. Perhaps it is inevitable that society forces conformity even if genius is lost. If this is truly the case, the story of Alan Turing is perhaps not so sad. Perhaps we should celebrate that we know of him at all.