大自然似乎有着无数的图案来打扮自己 无论是牛的斑点
Nature exhibits a seemingly endless array of patterns – from the cow’s spots to
热带鱼的条纹 还是猎豹的斑点条纹 但艾伦图灵
the surgeonfish’s stripes to the cheetah’s spots and stripes – but Alan Turing (the
发明电脑的神人 认为这些图案可能实际上没有那么不同
guy who invented computers) thought those patterns might not actually be all that different.
为了诠释他的看法 他提出了一系列简单的 可以衍生各类图案
To show what he meant, he came up with a simple set of mathematical rules that could give
的数学定理
rise to all manner of patterns.
这一定理表述如下 理论上 每个存在的生物体内都有两种
The rules go something like this: Inside each theoretical organism, there are
不同的 被称为激活剂和抑活剂的物质
two substances called an activator and an inhibitor.
激活剂促进这两种物质释放 而抑活剂使这两种物质的释放减缓
The activator stimulates production of both substances, while the inhibitor slows production down.
换句话说 这就好比捕食者和被捕食者的关系一样 兔子（激活剂）越多
In other words, it’s kind of like a predator-prey relationship: the more activator bunnies there
出生的小兔子越多 但越多的兔子 同时也意味着狐狸（抑活剂）
are, the more new bunnies they make, but a bigger bunny population also means more food
有了更多的食物 这也就意味着会有更多狐狸 最终导致兔子变少
for the inhibitor foxes, which means more foxes, which leads to fewer bunnies, which
而导致狐狸变少 尽管图灵定律这么说 随着捕食者
leads to fewer foxes.Except the Turing’s rules say that, as the populations of predator
和猎物增多 他们的占领区域不断扩大 只是狐狸占地更大
and prey increase, their ranges expand – only the foxes need more room, so their range expands
所以他们的占领速度更快
faster than the bunnies’ range.
用不了多久 狐狸占满了周围的空间 使得中间的兔子
Soon, the foxes dominate the surrounding areas, leaving the bunnies in the middle to keep
继续衍生
multiplying.
最终形成了周围包裹了一圈抑活剂的激活剂 并且一旦
So what we end up with is a pool of activator surrounded by a moat of inhibitor . And wherever
激活剂多于抑活剂 就会引起一些变化 比如
the activator is more abundant than the inhibitor, it triggers some kind of change – like the
在这种情况下 色素的增多便生成了一个斑点
production of pigment – which, in this case, gives rise to a spot of color.
图灵理论的妙处在于 通过改变变量 比如激活剂和抑活剂的传播速度
The beauty of Turing’s theory is that, by adjusting the variables, like the spreading
或是系统总的空间 你可以得到所有
rate of the activator and inhibitor, or the total area of the system, you can get all
种类的图案
kinds of patterns.
举个例子 如果一开始有些地方激活剂多一点点
For example, if you start out with slightly more activator than inhibitor in a bunch of
最后就会形成一些点状图案
spots, you might end up with…well, a bunch of spots.
或者 当整个系统只是一条窄带 像蛇或尾巴
Or, if the system is just a narrow little strip – like a snake or a tail – you might
最终则会形成条纹
end up with stripes.
而当激活剂扩散更快时 可能激活剂就冲破抑活剂的包围
Or, if the activator spreads a little faster, it might leak out and join up with other patches
造成点连成线 形成迷宫一样的花纹
of escaping activator, creating a labyrinth pattern.
还有 图灵理论也能模拟奶牛斑点
What’s more, Turing’s rules could be used to simulate patterns that closely mimic the
鱼的纹理 长颈鹿的马赛克图案
splotches on cows, the stripes on fish, the mosaic patterns on giraffes, and even the
甚至还有水螅触角
tentacles on hydras.
但实际上 图灵“纸上谈兵”的数学理论无法证明大自然的确
But the fact that his mathematical rules worked on paper didn’t prove that nature followed
这样运转
them.
几十年后的现在 科学家仍试图弄清
And now, several decades later, scientists are still trying to figure out whether some
自然形成的图案和结构是否由激活剂和抑活剂产生
of the patterns and structures in nature arise from real-life activators and inhibitors.
一方面 有人发现了一些非图灵规则的图案 比如
On the one hand, we’ve found some patterns that happen in a very un-Turing way, like
还在发育中的果蝇的分段 实际上的决定因素是
the segments in a developing fruit fly, which come predetermined by the fly’s genetic
基因蓝图
blueprint..
但另一方面 我们也喜大普奔地发现了图灵系统
But on the other hand, we’ve also come across some tantalizingly Turing-like systems; in
拿发育中的小鼠举个例子 ＂音猬因子＂蛋白抑制另一种激活剂蛋白
developing mice, for example, a protein called “sonic hedgehog” inhibits another, activator
此蛋白名字就不那么令人生“猬”了 它在胚胎时期使小鼠上颚产生
protein with a less awesome name, producing stripey ridges on the roof of the embryo’s
条状皱纹
mouth.
在小鼠的块状肢末端 有三种不同的蛋白协同激活 抑制组织的生长
And in its nubby limb ends, three different proteins activate and inhibit tissue growth
以产生条状的附属体 也就是脚趾
to generate the stripe-like appendages known as digits.
但不管图灵的理论能把我们所见的真实世界解释的有多完美或不完美
But regardless of how perfectly or imperfectly Turing’s theory describes what we see in
它最酷的地方在于激励着生物学家们在生物身上
the real world, the coolest thing about it may be that it inspired biologists to go looking
寻找图灵的理念的证据
for evidence of Turing’s ideas in living creatures.
可以说 观察是图灵理论的来源 而图灵的理论启发科学家们观察 从而使我们
So observations inspired a theory that inspired observations that are bringing us a little
进一步理解 猎豹的斑点和条纹是怎么样形成的
closer to understanding how the cheetah got its spots – and its stripes.
视频由Audible赞助 你可以在Audibl上找到最全的有声书
This video was supported by Audible, where you can find the largest selection of audiobooks
包括很赞的The Information 作者是James Gleick
available anywhere, including “The Information,” an awesome book by science writer James Gleick
此书讲述了像图灵这样的杰出人物是怎样帮助探索
that explores how luminaries like Alan Turing have helped us figure out what information
信息 的含义 和我们怎样创造 传输 存储信息
even is, and how we can go about creating, transmitting, and storing it.
想下载这本书以及其他你想看的书或者想表示你对
To download The Information or another book of your choice, and show your support for
分钟地球的支持 可以去 www.audible.com/minuteearth
MinuteEarth, go to www.audible.com/minuteearth.
噢 话说 我们之前发起了调查问卷想知道你吃完芦笋后
Oh – AND, a while ago we put out a survey to find out about your personal experiences
再上厕所的体验 结果我们得到了很多很好的回应
with asparagus pee, and we got tons of great responses.
点开下面描述区的链接就可以查看结果喽！
Check out the link in the description below for the results!