The science of symmetry - Colm Kelleher

譯者: Wei-Jung Liu 審譯者: Qingqing Mao

When you hear the word symmetry,

當你聽到對稱這個詞時，

maybe you picture a simple geometric shape

浮現在腦海裡的 或許是一個簡單的幾何圖形

like a square or a triangle,

像是正方形或是三角形，

or the complex pattern on a butterfly's wings.

又或是像蝴蝶翅膀上較複雜的圖案。

If you are artistically inclined,

若是站在藝術的觀點來看，

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

浮現在你腦海裡的可能是 莫札特協奏曲中的微妙的轉調，

or the effortless poise of a prima ballerina.

或者是首席女舞者不費力的舞姿。

When used in every day life,

當應用在每天的生活中，

the word symmetry represents vague notions of

對稱這個字眼代表了對美，和諧及平衡

beauty, harmony and balance.

模糊的詮釋。

In math and science, symmetry has a different,

而在數學與科學領域，對稱有了個不一樣

and very specific, meaning.

且非常具體的意義。

In this technical sense,

從技術角度來說，

a symmetry is the property of an object.

對稱是物體的一種性質。

Pretty much any type of object can have symmetry,

幾乎任何物體都有對稱性，

from tangible things like butterflies,

從有形的東西例如蝴蝶，

to abstract entities like geometric shapes.

到抽象的東西例如幾何圖形。

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

那麼，到底物體的對稱性是什麼意思呢？

Here's the definition:

定義如下:

a symmetry is a transformation that leaves that object unchanged.

對稱是使物體維持原樣的一種變換。

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

是的，這聽起來非常抽象， 讓我們一一解釋它。

It will help to look at a particular example,

讓我們來看個例子吧， 這會幫助我們理解它，

like this equilateral triangle.

像這個等邊三角形。

If we rotate our triangle through 120 degrees,

如果我們試著轉動這個三角形120度，

around an access through its center,

保持著中心不變，

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

我們會得到一個與原本看起來 一模一樣的三角形。

In this case, the object is the triangle,

在這個案例中，三角形就是那個物體，

and the transformation that leaves the object unchanged

而使物體維持原樣的變換，

is rotation through 120 degrees.

就是轉動了120度。

So we can say an equilateral triangle is symmetric

所以我們可以說等邊三角形具有

with respect to rotations of 120 degrees around its center.

繞中心點旋轉120度的對稱性。

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

如果我們旋轉三角形90度，

the rotated triangle would look different to the original.

旋轉後的三角形看起來 跟原本的就不一樣了。

In other words, an equilateral triangle is not symmetric

也就是說，一個等邊三角形不具有

with respect to rotations of 90 degrees around its center.

繞中心點旋轉90度的對稱性。

But why do mathematicians and scientists care about symmetries?

但是為何數學家跟科學家 這麼在意對稱呢？

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

這麼說吧，它們在數學及科學的 很多領域中至關重要。

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

讓我們舉另一個例子吧： 生物學中的對稱。

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

你可能已經注意到了 一個看起來很熟悉的對稱

we haven't mentioned yet:

但是我們還沒提到——

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

人體左側及右側的對稱性。

The transformation that gives this symmetry is reflection

這一對稱所對應的變換是反射，

by an imaginary mirror that slices vertically through the body.

想象有一面鏡子垂直得 將身體分成兩半。

Biologists call this bilateral symmetry.

生物學家把這叫做雙邊對稱。

As with all symmetries found in living things,

就如同在所有生物身上可以找到的對稱，

it's only approximate,

這只是一種近似的對稱，

but still a striking feature of the human body.

但這依舊是人體的一個顯著特徵。

We humans aren't the only bilaterally symmetric organisms.

事實上不是只有我們人類 才是雙邊對稱的有機體。

Many other animals, foxes, sharks, beetles,

很多其他的動物例如狐狸，鯊魚，甲蟲，

that butterfly we mentioned earlier,

還有我們先前提到的蝴蝶，

have this kind of symmetry,

都有這種對稱性，

as do some plants like orchid flowers.

還有些植物像是蘭花。

Other organisms have different symmetries,

其他有機體有不一樣的對稱性，

ones that only become apparent

有些有機體只有在以他的中心點轉動後

when you rotate the organism around its center point.

才會變得明顯。

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

就像我們剛剛看到的 旋轉對稱的三角形那樣。

But when it occurs in animals,

但是，當它在動物身上發生時，

this kind of symmetry is known as radial symmetry.

這種對稱性叫做放射對稱。

For instance, some sea urchins and starfish

舉個例子，有些海膽與海星

have pentaradial or five-fold symmetry,

有五放射對稱或五倍對稱，

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

也就是說，對中心點轉動72度 會看到一樣的形狀。

This symmetry also appears in plants,

這樣的對稱也同時出現在植物身上，

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

就像你橫切蘋果時看到的那樣。

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

有些水母的對稱是轉動90度後形狀一樣，

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

又或是有些海葵的對稱性是 轉動任何角度牠們的形狀都一樣。

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

而一些珊瑚，可以說是毫無對稱可言的。

They are completely asymmetric.

牠們完全是不對稱的。

But why do organisms exhibit these different symmetries?

但為何有機體會出現這些不一樣的對稱呢?

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

身體的對稱性是否也在告訴我們 動物們的生活方式？

Let's look at one particular group:

讓我們針對特定的群體來看看：

bilaterally symmetric animals.

雙邊對稱的動物。

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

在這個群體裡，我們有 狐狸，甲蟲，鯊魚，蝴蝶，

and, of course, humans.

當然還有人類。

The thing that unites bilaterally symmetric animals

對雙邊對稱的動物來說很重要的一件事

is that their bodies are designed around movement.

就是牠們身體的設計是因為動作的需要。

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

如果你選定一個方向前進，

it helps to have a front end

那麼有一個

集中各種感官的前端是有好處的——

where you can group your sensory organs--

your eyes, ears and nose.

你的眼睛，耳朵跟鼻子。

It helps to have your mouth there too

把嘴巴放到前端也有好處，

since you're more likely to run into food

因為在這個前端你更有可能撞到食物

or enemies from this end.

或是敵人。

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

你應該很熟悉這個 帶有一堆器官和一張嘴，

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

長在動物身體前端的東西。

It's called a head.

這個叫做頭。

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

有頭的生物會自然地發展出雙邊對稱。

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

它也有助於形成魚類流線型的鰭，

aerodynamic wings if you're a bird,

鳥類符合空氣動力學的翅膀，

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

或者是狐狸奔跑時有協調性的腳。

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

但是，這些跟演化有什麼關係呢?

Turns out, biologists can use these various body symmetries

有的，生物學家透過各種身體的對稱性

to figure out which animals are related to which.

可以知道物種間的關聯。

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

就像我們看到的海星與海膽有五倍對稱。

But really what we should have said was

但確切來說指的是

adult starfish and sea urchins.

成年的海星和海膽。

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

在他們的幼體階段， 是雙邊對稱的，就跟人類一樣。

For biologists, this is strong evidence

對生物學家來說這是一個有力的證據，

that we're more closely related to starfish

也就是說我們跟海星的關係

than we are, to say, corals,

要比珊瑚

or other animals that don't exhibit bilateral symmetry

或其他那些在任何生長階段 都不具備雙邊對稱的動物

at any stage in their development.

都更為緊密。

One of the most fascinating and important problems in biology

生物學中有一個非常引人入勝且重要的問題

is reconstructing the tree of life,

就是重建生命之樹，

discovering when and how the different branches diverged.

尋找不同的分支是在何時以及如何分化的。

Thinking about something as simple as body symmetry

思考身體的對稱性這種簡單的問題

can help us dig far into our evolutionary past

可以幫助我們深入發掘過去的演化歷程，

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

並且了解我們作為一個物種是從哪裡來的。