圖靈如何用數(shù)學(xué)破譯自然界

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.

很多人都聽(tīng)說(shuō)過(guò)艾倫·圖靈(Alan Turing)，知道他是一位數(shù)學(xué)家和邏輯學(xué)家，在1935年發(fā)明了現(xiàn)代計(jì)算。他們知道圖靈是一位密碼學(xué)家，破譯了納粹的Enigma密碼，幫助同盟國(guó)贏得了第二次世界大戰(zhàn)。他們還知道，圖靈是同性戀權(quán)利的殉難者，在被起訴并被判處化學(xué)閹割后，他于1954年吃了一個(gè)涂有氰化物的蘋(píng)果，自殺身亡。

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 zebra fish get their stripes or cheetahs get spots. And even now, scientists are finding new insights from Turing’s legacy.

但很少有人知道圖靈是一位博物學(xué)家，他用數(shù)學(xué)來(lái)解釋自然界的圖案。在他1952年發(fā)表最后一篇論文后的近半個(gè)世紀(jì)里，化學(xué)家和生物數(shù)學(xué)家們開(kāi)始意識(shí)到，他后期的工作可以用來(lái)解釋他們正在解決的問(wèn)題，例如，斑馬魚(yú)的條紋或獵豹的斑點(diǎn)是如何形成的。甚至到現(xiàn)在，科學(xué)家們還在從圖靈的遺產(chǎn)中找到新的洞見(jiàn)。

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

最近一次，在周四發(fā)表在《科學(xué)》雜志(Science)上的一篇論文中，中國(guó)的化學(xué)工程師利用圖靈描述的斑圖生成理論闡釋了一種更有效的海水淡化處理方法。海水淡化正越來(lái)越多地被用于干旱地區(qū)的飲用水和灌溉用水供給。

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

圖靈那篇1952年的論文沒(méi)有明確提到，可以通過(guò)薄膜過(guò)濾鹽水來(lái)產(chǎn)生淡水。他是用化學(xué)解釋了沒(méi)有明顯差別的細(xì)胞球是如何在生物體中產(chǎn)生形狀的。

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.

尚不清楚這為什么引起了這位早期計(jì)算機(jī)科學(xué)家的興趣，但圖靈曾對(duì)一位朋友說(shuō)他想推翻目的論證，即自然界中存在的復(fù)雜圖案一定是某種超自然的東西創(chuàng)造出來(lái)的，比如上帝。

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.

圖靈從小就是敏銳的自然觀察者，他注意到許多植物包含著可能與數(shù)學(xué)相關(guān)的線索。有些植物的性狀中存在斐波那契數(shù)列。這個(gè)數(shù)列的一個(gè)特征是：每個(gè)數(shù)字等于前面兩個(gè)數(shù)字的和。例如，雛菊有34、55或89個(gè)花瓣。

“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.”

“他當(dāng)然不是一位激進(jìn)的無(wú)神論者，”牛津大學(xué)(University of Oxford)的客座教授、計(jì)算生物學(xué)家喬納森·斯溫頓(Jonathan Swinton)說(shuō)。他研究了圖靈的后期工作和生活。“他只是認(rèn)為數(shù)學(xué)非常強(qiáng)大，你可以用它來(lái)解釋很多東西——你應(yīng)該試一試。”

And try, Turing did.

圖靈的確嘗試了。

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

“他提出了一種數(shù)學(xué)表達(dá)式，可以從無(wú)到有地生成形狀，”斯溫頓說(shuō)。

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.”

在圖靈的模型中，兩種被他稱作成形素(morphogen)的化學(xué)物質(zhì)在一個(gè)空白區(qū)域相互作用。“假設(shè)你有兩種成形素，一種會(huì)讓動(dòng)物的皮膚變黑，另一種會(huì)讓動(dòng)物的皮膚變白，”斯溫頓博士。“如果把它們混合在一起，動(dòng)物的皮膚就會(huì)變成灰色。”

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

但如果某種原因?qū)е乱环N化學(xué)物質(zhì)擴(kuò)散得比另一種快，它們就會(huì)集中在間隔均勻的局部區(qū)域，形成黑色和白色的斑點(diǎn)或條紋。

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.

這被稱作“圖靈不穩(wěn)定性”。發(fā)表這篇新論文的中國(guó)研究人員斷定，它可以解釋鹽過(guò)濾膜中出現(xiàn)的結(jié)構(gòu)。

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

通過(guò)在膜上制造氣泡和管道等三維圖靈結(jié)構(gòu)，研究人員增加了它們的滲透性。這種過(guò)濾器能夠比傳統(tǒng)過(guò)濾器更好地分離鹽和水。

“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.

“我們可以用一張膜完成兩到三張膜的工作，”浙江大學(xué)的研究生譚喆說(shuō)。他是該論文的第一作者。這意味著如果將來(lái)用于大規(guī)模的脫鹽作業(yè)，消耗的能源和成本都會(huì)降低