Alan Turing's Most Underrated Discovery Was Also Among His Greatest

One of Turing’s most fascinating intellectual achievements is his research into the mathematics governing patterns in the natural world.

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Nov 28 2014, 7:35pm

Alan Turing in 1927. Image: The Turing Archive

The Imitation Game, a biopic about mathematician Alan Turing, finally came out in theatres in the US today (the UK got it two weeks earlier, the lucky ducks). The film is part of a welcome revival of interest in Turing, whose life story is equal parts inspiring and demoralizing.

He was the father of computer science and artificial intelligence, a world-class marathon runner, and the cryptographer that broke the Nazi Enigma code, contributing hugely to the Allied victory in WWII. That is one stacked resume.

Trailer for The Imitation Game. Credit: YouTube/Weinstein Company

But Turing was also gay in a homophobic world. In 1952, the British government convicted him of indecency over his homosexuality, publicly shaming him and sentencing him to be chemically castrated with estrogen treatments. He became impotent, lost his treasured physical fitness, and resorted to suicide two years later on June 7, 1954, about two weeks shy of his 42nd birthday.

The Imitation Game is mainly focused on Turing's cryptography efforts at Bletchley Park, although apparently it gets into many other parts of his life, including the maddeningly stupid conviction that ultimately ended it. But the film is unlikely to cover one of Turing's most fascinating intellectual achievements, often overlooked in summaries of his life: his research into the mathematics governing patterns in the natural world.

In short: Turing literally figured out how the leopard got its spots. It was the last significant work he ever completed, culminating in the publication of a paper called, "The Chemical Basis of Morphogenesis" in 1952. He worked on his morphogenic theories only sporadically after that, and it's difficult not to wonder if his research inspired him to reflect on his own chemically-altered biology.

Regardless of his personal connection to the subject, one thing is clear: Turing identified the basic reaction-diffusion equations behind natural pattern formations, like the spiral of a seashell and the stripes of a tiger. He proposed that these patterns are formed by the interaction between two chemicals, or "morphogens" as he called them: an activator and an inhibitor.

The activator encourages the expression of a certain feature, like the darkness of a leopard spot, while the inhibitor deactivates the expression. The two morphogens diffuse into a biological system at different rates, and the result is a macro pattern built from local chemical interactions. If you're having trouble picturing this dynamic, take a virtual scroll through artist Jonathan McCabe's portfolio of Turing patterns, which is packed with stunning representations of Turing's equations at work.

"into the colorflow." Credit: Jonathan McCabe, used with permission of the artist

Turing's morphogenesis theory was finally empirically validated in spring of this year, 60 years after his death. His visionary anticipation of these algorithms makes him a good candidate for the world's first biohacker—not in the traditional sense of integrating technology into the body, but in his reimagining of biological patterns as dynamic computer algorithms. Some have even argued that his work in this field makes him the first chaos theorist as well, because he showed how simple states can complexify into larger systems on with non-uniform properties.

It makes sense that his scientific swan song is overshadowed by the many other triumphs he racked up during his lifetime. After all, when stacked against decrypting Enigma and conceiving AI, you can see why morphogenesis often slips through the cracks of Turing's biography.

If anything, the fact that his ideas were so plentiful that they have to compete with each other is further testament to his multidimensional genius, and the need to learn both from his tragic fate and his insane productivity. As Turing himself said in 1950, "we can only see a short distance ahead, but we can see plenty there that needs to be done."