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  • When you hear the word symmetry,


  • maybe you picture a simple geometric shape

    幾何学図形を 思い浮かべるかもね

  • like a square or a triangle,


  • or the complex pattern on a butterfly's wings.

    それか蝶のはねの模様が 頭に浮かぶかも

  • If you are artistically inclined,


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

    モーツァルトの協奏曲の 微妙なリズムとか

  • or the effortless poise of a prima ballerina.

    プリマバレリーナのポーズを 思い浮かべるかも

  • When used in every day life,


  • the word symmetry represents vague notions of


  • beauty, harmony and balance.

    美、調和、バランスのような あいまいな概念を示している

  • In math and science, symmetry has a different,

    けれど数学と科学では それとはまた違う

  • and very specific, meaning.


  • In this technical sense,


  • a symmetry is the property of an object.

    対称性とは 対象が持っている性質だ

  • Pretty much any type of object can have symmetry,


  • from tangible things like butterflies,

    蝶のようにはっきりした 形があるものや

  • to abstract entities like geometric shapes.


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

    じゃあ対象が対称性を持つって どういうことなんだろう

  • Here's the definition:


  • a symmetry is a transformation that leaves that object unchanged.

    対称性とは 対象を変えない変換のこと

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

    ちょっと抽象的だから かみくだいてみよう

  • It will help to look at a particular example,


  • like this equilateral triangle.

    こういうのを見るときに 対称性が役に立つ

  • If we rotate our triangle through 120 degrees,


  • around an access through its center,

    真ん中を通る 軸を中心にして

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

    すると最初と全く同じ 三角形になる

  • In this case, the object is the triangle,

    このとき 三角形が さっき言った対象で

  • and the transformation that leaves the object unchanged


  • is rotation through 120 degrees.


  • So we can say an equilateral triangle is symmetric

    つまり正三角形は 対称性を持つと言える

  • with respect to rotations of 120 degrees around its center.

    中心軸を基準に 120度回転させたときにね

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


  • the rotated triangle would look different to the original.


  • In other words, an equilateral triangle is not symmetric


  • with respect to rotations of 90 degrees around its center.

    中心軸を基準に 90度回転させたときはね

  • But why do mathematicians and scientists care about symmetries?

    でもどうして数学者や科学者は 対称性に興味を持つんだろう

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

    それは 数学や科学で 対称性はとても重要だからだ

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

    一つ例を見てみよう 生物学における対称性だ

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

    もっと身近に対称性がある と気づいているかもしれないね

  • we haven't mentioned yet:


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

    人間の体における 左右の対称性だ

  • The transformation that gives this symmetry is reflection

    ここで対称性を得る変換は 鏡映といい

  • by an imaginary mirror that slices vertically through the body.

    体を垂直に通る 鏡をイメージするんだ

  • Biologists call this bilateral symmetry.

    生物学者はこれを 左右対称と呼ぶ

  • As with all symmetries found in living things,

    全ての生物にみられる 対称性と同様に

  • it's only approximate,


  • but still a striking feature of the human body.

    けれどこれは人間の体の 際立った特徴だ

  • We humans aren't the only bilaterally symmetric organisms.

    人間だけが左右対称な生物 というわけではない

  • Many other animals, foxes, sharks, beetles,

    他の多くの動物 キツネ、サメ、甲虫

  • that butterfly we mentioned earlier,


  • have this kind of symmetry,

    人間のような対称性を 持っている

  • as do some plants like orchid flowers.

    ランのような 花だってそうだ

  • Other organisms have different symmetries,

    また他の生物は 異なる対称性を持つ

  • ones that only become apparent


  • when you rotate the organism around its center point.

    中心点を基準に 回転させてみたときだ

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

    さっきみた正三角形の 回転対称性のようなものだね

  • But when it occurs in animals,

    ただ回転対称性が 動物にみられるとき

  • this kind of symmetry is known as radial symmetry.


  • For instance, some sea urchins and starfish


  • have pentaradial or five-fold symmetry,


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

    中心を基準に72度回転したとき 対称になるんだ

  • This symmetry also appears in plants,


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

    りんごを水平に切ってみると わかるだろう

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

    90度回転させると対称な クラゲがいるし

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

    イソギンチャクはどう回してみても 必ず対称だ

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

    一方でサンゴは 全く対称性を持たない

  • They are completely asymmetric.


  • But why do organisms exhibit these different symmetries?

    でもなぜ生物はこのような 異なる対称性を持つのだろう

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

    体の対称性を見ることで その動物の生活がわかるだろうか

  • Let's look at one particular group:

    一つのグループを例に 見てみよう

  • bilaterally symmetric animals.


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

    今ここにいるのは キツネ、甲虫、サメ、蝶

  • and, of course, humans.


  • The thing that unites bilaterally symmetric animals


  • is that their bodies are designed around movement.

    動きやすさを基準に 体が作られていることだ

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


  • it helps to have a front end

    体の前側が決まっているのは 便利だ

  • where you can group your sensory organs--

    そこに感覚器官を 集結させればいい

  • your eyes, ears and nose.


  • It helps to have your mouth there too


  • since you're more likely to run into food

    食べ物を見つけるのは 体の前側だし

  • or enemies from this end.


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


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

    動物の体の前面についているけど これを何と呼ぶか知っているね

  • It's called a head.


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

    頭を持つことによって 左右対称性を持つようになる

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

    それに加えて 魚なら流線型のひれ

  • aerodynamic wings if you're a bird,


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

    きつねなら走りやすい脚 なんかがあると役立つ

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

    しかしこれは進化と何の 関係があるのだろう

  • Turns out, biologists can use these various body symmetries

    どうやら生物学者は これらの対称性を使って

  • to figure out which animals are related to which.

    動物同士の関係を 見つけ出せるようだ

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

    例えばヒトデとウニは 五放射対称だと言ったけど

  • But really what we should have said was


  • adult starfish and sea urchins.

    大人になったヒトデとウニが 五放射対称なんだ

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

    幼生期では 人間のように左右対称なんだ

  • For biologists, this is strong evidence

    生物学者にとってこれは 有力な証拠になる

  • that we're more closely related to starfish

    人間がヒトデと 生物学的に近いという証拠だ

  • than we are, to say, corals,

    たとえばサンゴ あるいは―

  • or other animals that don't exhibit bilateral symmetry

    発達段階で 左右対称を持たない他の動物と

  • at any stage in their development.


  • One of the most fascinating and important problems in biology

    生物学で最も素晴らしく 重要な問題は

  • is reconstructing the tree of life,

    生物の系図を 構築しなおすことだ

  • discovering when and how the different branches diverged.

    いつどうやって枝分かれしたのかを 見つけ出すことだ

  • Thinking about something as simple as body symmetry

    体の対称性という 単純なことを考えることは

  • can help us dig far into our evolutionary past

    私たちが進化してきた 過程を探求し

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

    私たち人類がどこから来たかを 理解する助けとなる

When you hear the word symmetry,



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