The science of symmetry - Colm Kelleher

翻译人员: Alex Wang 校对人员: Qingqing Mao

When you hear the word symmetry,

当你听到“对称”这个词时，

maybe you picture a simple geometric shape

你的脑海里大概会出现一个简单的几何图形，

like a square or a triangle,

比如一个正方形或三角形，

or the complex pattern on a butterfly's wings.

或者是更复杂一点的图案，诸如蝴蝶翅膀。

If you are artistically inclined,

如果你是一个富有艺术感的人，

you might think of the subtle modulations of a Mozart concerto,

你可能会想到莫扎特协奏曲中微小的转调，

or the effortless poise of a prima ballerina.

或者芭蕾舞首席女演员毫不费力的舞姿。

When used in every day life,

在日常生活中，

the word symmetry represents vague notions of

对称这个词含糊地代表了

beauty, harmony and balance.

唯美，和谐以及平衡的观念。

In math and science, symmetry has a different,

在数学和科学中，对称有着不同，

and very specific, meaning.

而且非常特殊的定义。

In this technical sense,

从技术角度而言，

a symmetry is the property of an object.

对称是物体的一种特性。

Pretty much any type of object can have symmetry,

基本上所有物体都有对称性，

from tangible things like butterflies,

从有形的物体比如蝴蝶，

to abstract entities like geometric shapes.

到抽象物体如几何图形。

So, what does it mean for an object to be symmetric?

那么，一个物体有“对称性”是什么意思呢？

Here's the definition:

定义如下：

a symmetry is a transformation that leaves that object unchanged.

对称是使物体维持原样的一种变换。

Okay, that sounds a bit abstract, so let's unpack it.

嗯，听起来有点抽象，让我们来具体解释一下。

It will help to look at a particular example,

举个等边三角形的例子

like this equilateral triangle.

会有助于我们理解。

If we rotate our triangle through 120 degrees,

如果我们把这个三角形以中心为轴

around an access through its center,

旋转120度，

we end up with a triangle that's identical to the original.

我们会得到一个完全一样的三角形。

In this case, the object is the triangle,

在本例中，物体是三角形，

and the transformation that leaves the object unchanged

而使物体维持原样的变换

is rotation through 120 degrees.

是旋转120度。

So we can say an equilateral triangle is symmetric

所以我们可以说，等边三角形以中心为轴的120度旋转

with respect to rotations of 120 degrees around its center.

是有对称性的。

If we rotated the triangle by, say, 90 degrees instead,

如果我们把这个三角形旋转90度，

the rotated triangle would look different to the original.

这个三角形和原来那个就不同了。

In other words, an equilateral triangle is not symmetric

换句话来说，等边三角形以中心为轴的90度旋转

with respect to rotations of 90 degrees around its center.

是没有对称性的。

But why do mathematicians and scientists care about symmetries?

但是数学家和科学家们为什么要在意对称呢？

Turns out, they're essential in many fields of math and science.

答案是，对称在数学及科学的很多领域中至关重要。

Let's take a close look at one example: symmetry in biology.

让我们举一个例子来说明：生物学中的对称。

You might have noticed that there's a very familiar kind of symmetry

你可能会注意到，我们还没有提及

we haven't mentioned yet:

一类很常见的对称：

the symmetry of the right and left sides of the human body.

人体左右两侧的对称。

The transformation that gives this symmetry is reflection

这个对称所对应的变换是反射，

by an imaginary mirror that slices vertically through the body.

我们可以想象一面镜子把人体从中间竖直分开。

Biologists call this bilateral symmetry.

生物学家们把这叫做“两侧对称”。

As with all symmetries found in living things,

如同所有可以在生物体上找到的对称，

it's only approximate,

这只是一种近似的对称，

but still a striking feature of the human body.

但这依旧是人体的一个显著特征。

We humans aren't the only bilaterally symmetric organisms.

我们人类并不是唯一一种两侧对称的生物。

Many other animals, foxes, sharks, beetles,

还有很多动物也是，比如狐狸，鲨鱼，甲壳虫，

that butterfly we mentioned earlier,

还有我们之前提到的蝴蝶等，

have this kind of symmetry,

都有这种对称性，

as do some plants like orchid flowers.

一些植物比如兰花，也是如此。

Other organisms have different symmetries,

其他生物体有不同的对称性，

ones that only become apparent

有一些对称只有你在把它

when you rotate the organism around its center point.

绕中心点旋转时才看得出来。

It's a lot like the rotational symmetry of the triangle we watched earlier.

这和我们之前看到的三角形的旋转对称非常相似。

But when it occurs in animals,

不过当这种对称出现在动物身上时，

this kind of symmetry is known as radial symmetry.

我们称它为“辐射对称”。

For instance, some sea urchins and starfish

例如，某些海胆还有海星

have pentaradial or five-fold symmetry,

呈五辐射对称，或五次对称。

that is, symmetry with respect to rotations of 72 degrees around their center.

意思是，这些生物以中心为轴进行72度旋转是有对称性的。

This symmetry also appears in plants,

植物中也会出现这种对称，

as you can see for yourself by slicing through an apple horizontally.

你去把一个苹果从水平方向切开就会发现了。

Some jellyfish are symmetric with respect to rotations of 90 degrees,

有些水母是关于90度旋转对称的，

while sea anemones are symmetric when you rotate them at any angle.

而海葵则是对于任意角度都是旋转对称的。

Some corals, on the other hand, have no symmetry at all.

另一方面，某些珊瑚不具有任何对称性。

They are completely asymmetric.

它们完全不对称。

But why do organisms exhibit these different symmetries?

但是为什么生物体会呈现这些不同的对称呢？

Does body symmetry tell us anything about an animal's lifestyle?

物种身体的对称性是否向我们揭示了动物的生活习性？

Let's look at one particular group:

让我们来重点观察一个群体：

bilaterally symmetric animals.

两侧对称的动物。

In this camp, we have foxes, beetles, sharks, butterflies,

在这个分组里，我们有狐狸，甲壳虫，鲨鱼，蝴蝶，

and, of course, humans.

当然，还有人类。

The thing that unites bilaterally symmetric animals

这类两侧对称的生物的特点是

is that their bodies are designed around movement.

它们的身体构造是建立在运动的基础上的。

If you want to pick one direction and move that way,

如果你想朝某个方向移动，

it helps to have a front end

有一个集中了各种感官的前端

where you can group your sensory organs--

是很有帮助的

——包括了你的眼睛，耳朵和鼻子。

your eyes, ears and nose.

It helps to have your mouth there too

把嘴放在前端也很有用，

since you're more likely to run into food

因为这个前端既会的得到食物，

or enemies from this end.

也有可能遭遇敌人。

You're probably familiar with a name for a group of organs,

你应该对一个带有包括嘴在内的一堆器官，

plus a mouth, mounted on the front of an animal's body.

伫立在动物身体最前端的东西很熟悉。

It's called a head.

这个东西叫做——头。

Having a head leads naturally to the development of bilateral symmetry.

有一个头的生物会很自然地进化成两侧对称体。

And it also helps you build streamlined fins if you're a fish,

如果你是一条鱼，这也会帮助你长出流线型的鳍，

aerodynamic wings if you're a bird,

如果你是一只鸟，那就会长出符合空气动力学的翅膀，

or well coordinated legs for running if you're a fox.

或者如果你是狐狸，那你就会有非常协调的腿。

But, what does this all have to do with evolution?

但是这些和物种进化又有什么关系呢？

Turns out, biologists can use these various body symmetries

答案是，生物学家们可以用这些身体对称性

to figure out which animals are related to which.

来判断物种间的联系。

For instance, we saw that starfish and sea urchins have five-fold symmetry.

比如，我们知道海胆和海星都具有五次对称。

But really what we should have said was

但我们要注意的是

adult starfish and sea urchins.

只有成年海星和海胆才这样。

In their larval stage, they're bilateral, just like us humans.

在它们幼年时期，它们就像我们人类一样是两侧对称的。

For biologists, this is strong evidence

对于生物学家来说，这是一个有力的证据，

that we're more closely related to starfish

这表明，

than we are, to say, corals,

相比于珊瑚

或者其他在任何生长阶段都不具备两侧对称的生物而言，

or other animals that don't exhibit bilateral symmetry

at any stage in their development.

我们人类与海星的关系要近得多。

One of the most fascinating and important problems in biology

生物学中有一个迷人且又重要的任务就是

is reconstructing the tree of life,

重建“生命之树”，

discovering when and how the different branches diverged.

找出物种进化中各分支形成的时间与方式。

Thinking about something as simple as body symmetry

研究身体对称性这种简单的东西

can help us dig far into our evolutionary past

可以帮助我们深入发掘我们的进化历程，

and understand where we, as a species, have come from.

从而了解我们，作为一个物种，是从何而来的。