Trilobites: How the Father of Computer Science Decoded Nature’s Mysterious Patterns

Many have heard of Alan Turing, the mathematician and logician who invented modern computing in 1935. They know Turing, the cryptologist who cracked the Nazi Enigma code, helped win World War II. And they remember Turing as a martyr for gay rights who, after being prosecuted and sentenced to chemical castration, committed suicide by eating an apple laced with cyanide in 1954.

But few have heard of Turing, the naturalist who explained patterns in nature with math. Nearly half a century after publishing his final paper in 1952, chemists and biological mathematicians came to appreciate the power of his late work to explain problems they were solving, like how zebrafish get their stripes or cheetahs get spots. And even now, scientists are finding new insights from Turing’s legacy.

Most recently, in a paper published Thursday in Science, chemical engineers in China used pattern generation described by Turing to explain a more efficient process for water desalination, which is increasingly being used to provide freshwater for drinking and irrigation in arid places.

Turing’s 1952 paper did not explicitly address the filtering of saltwater through membranes to produce freshwater. Instead, he used chemistry to explain how undifferentiated balls of cells generated form in organisms.

It’s unclear why this interested the early computer scientist, but Turing had told a friend that he wanted to defeat Argument From Design, the idea that for complex patterns to exist in nature, something supernatural, like God, had to create them.

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A keen natural observer since childhood, Turing noticed that many plants contained clues that math might be involved. Some plant traits emerged as Fibonacci numbers. These were part of a series: Each number equals the sum of the two preceding numbers. Daisies, for example, had 34, 55 or 89 petals.

“He certainly was no militant atheist,” said Jonathan Swinton, a computational biologist and visiting professor at the University of Oxford who has researched Turing’s later work and life. “He just thought mathematics was very powerful, and you could use it to explain lots and lots of things — and you should try.”

And try, Turing did.

“He came up with a mathematical representation that allows form to emerge from blankness,” said Dr. Swinton.

In Turing’s model, two chemicals he called morphogens interacted on a blank arena. “Suppose you’ve got two of these, and one will make the skin of an animal go black and the skin of the animal go white,” explained Dr. Swinton. “If you just mix these things in an arena, what you get is a gray animal.”

But if something caused one chemical to diffuse, or spread, faster than the other, then each chemical could concentrate in evenly spaced localized spots, together forming black and white spots or stripes.

This is known as a “Turing instability,” and, the Chinese researchers who published the new paper determined that it could explain the way shapes emerged in salt-filtering membranes.

By creating three-dimensional Turing patterns like bubbles and tubes in membranes, the researchers increased their permeability, creating filters that could better separate salt from water than traditional ones.

“We can use one membrane to finish the work of two or three,” said Zhe Tan, a graduate student at Zheijang University in China and first author of the paper, which means less energy and lower cost if used for large-scale desalination operations in the future.

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Beyond his final publication, Turing’s notes revealed the complicated ideas he was wrestling to explain.

“The 1952 paper that everybody knows is not the end of the story,” said Jonathan Dawes, a mathematician at the University of Bath who has also been trying to make sense of Turing’s later work. “It doesn’t show the full depth of his thinking.”

Turing appeared to be looking for a general mechanism for the creation of form — like how thought or consciousness spontaneously emerges or how sunflowers neatly pack their seeds together. But Turing would die before completing and publishing his final musings.

“What I hope we appreciate more because of him, is to value diversity and individual creativity in our science base,” Dr. Dawes said. “We need people who we allow to be driven by their curiosity, and we also need people who will take those basic science ideas and turn them into useful technology.”


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Side Effects: Sifrhippus, the First Horse, Got Even Tinier as the Planet Heated Up

Scientists have known that many mammals appear to have shrunk during the warming period, and the phenomenon fits well with what is known as Bergmann’s rule, which says, roughly, that mammals of a given genus or species are smaller in hotter climates.

Although the rule refers to differences in location, it seemed also to apply to changes over time. But fine enough detail was lacking until now.

In Science, Ross Secord, of the University of Nebraska-Lincoln; Jonathan Bloch, of the Florida Museum of Natural History at the University of Florida in Gainesville; and a team of other researchers report on the collection and analysis of Sifrhippus fossils from the Bighorn Basin.

They report that the little horse got 30 percent smaller over the first 130,000 years, and then — as always seems to happen with weight loss — shot back up and got 75 percent bigger over the next 45,000 years.

The fossils indicate that at its smallest Sifrhippus weighed about eight and a half pounds, and at its largest about 15 pounds.

Using fine-grained detail on both climate and body size, the researchers concluded that the change in size was, as suspected, driven primarily by the warming trend.

“It seems to be natural selection,” said Dr. Secord. He said animals evolved to be smaller during warming because smaller animals did better in that environment, perhaps because the smaller an animal is, the easier it is to shed excess heat.

Paul L. Koch, head of the department of earth and planetary sciences at the University of California, Santa Cruz, and a specialist in reconstructing ecosystems and climates from many millions of years ago, said, “The paper lets us see the effect of warming on mammals where the climate change is really large.”

Dr. Koch, who was not involved in the study, said he thought that the question of whether natural selection was the cause of the changes was still open, and that the disruption of ecosystems during the warming period might have led smaller animals to migrate to new locations.

The current warming period is occurring on a scale of hundreds of years, not thousands, and scientists can only speculate on whether modern mammals will shrink.

“It’s difficult to say that mammals are going to respond in the same way now,“ Dr. Secord said. “If I had to guess,” he said, he thinks some will get smaller. And, he said, some studies have shown some birds to be getting smaller in response to warming.

If warming continues at the highest rate projected, he said, there’s another question: “Can mammals keep up?” 

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