It seems like a question with an obvious answer.

聞くまでもない質問に 思えるかもしれません

After all, most of us have ten fingers, or to be more precise, eight fingers and two thumbs.

大抵の人の指は10本厳密に言えば 親指２本と残り８本あります

This gives us a total of ten digits on our two hands, which we use to count to ten.

つまり  数を表すものが 両手で合計10ありそれで10まで数えることができます

It's no coincidence that the ten symbols we use in our modern numbering system are called digits as well.

近代の数体系で使う10の数字を 英語で「指」（digit）とも呼ぶのは偶然ではないのです

But that's not the only way to count.

でも数え方はそれだけではありません

In some places, it's customary to go up to twelve on just one hand.

地域によっては片手で12まで 数える慣習もあります

How?

やり方はというと

Well, each finger is divided into three sections, and we have a natural pointer to indicate each one, the thumb.

指にはどれも節が３つあって親指はその場所を指すのに ぴったりなので

That gives us an easy way to count to twelve on one hand.

片手で12まで数えるのは 簡単です

And if we want to count higher, we can use the digits on our other hand to keep track of each time we get to twelve, up to five groups of twelve, or 60.

もっと大きな数を数えたければ12に届くたび もう片方の指で記録すれば 12×5で60までいけます

Better yet, let's use the sections on the second hand to count twelve groups of twelve, up to 144.

いっそ もう片方の手の節も使えば12×12で144までいけます

That's a pretty big improvement, but we can go higher by finding more countable parts on each hand.

だいぶ上限が上がりましたが数えるための印を増やせば もっと数えられます

For example, each finger has three sections and three creases for a total of six things to count.

たとえば指１本につき 節３つ 皺３つで数える印は計６つ

Now we're up to 24 on each hand, and using our other hand to mark groups of 24 gets us all the way to 576.

片手につき24箇所までいきますもう片方の手を記録用に24回使うと 上限は576まで上がります

Can we go any higher?

もっと数えられるでしょうか

It looks like we've reached the limit of how many different finger parts we can count with any precision.

指の印を細かく分けて 正確に数える方法はそろそろ限界のようです

So let's think of something different.

他のやり方を検討しましょう

One of our greatest mathematical inventions is the system of positional notation, where the placement of symbols allows for different magnitudes of value, as in the number 999.

数学史上 最大の発明に位取り記数法があります 数字が置かれる位によって その値が変わるわけです 999という数字では

Even though the same symbol is used three times, each position indicates a different order of magnitude.

同じ数字が３回使われていますが数字のある位で 表される桁が異なります

So we can use positional value on our fingers to beat our previous record.

同様に指に位をつけることで これまでの上限を突破できます

Let's forget about finger sections for a moment and look at the simplest case of having just two options per finger, up and down.

指の印の件はいったん無しにして指は大まかに２つのポジションがとれますね 立てると 曲げる

This won't allow us to represent powers of ten, but it's perfect for the counting system that uses powers of two, otherwise known as binary.

10のべき乗を表すことはできませんが２のべき乗を使う 計算システムには最適です いわゆる二進法です

In binary, each position has double the value of the previous one, so we can assign our fingers values of one, two, four, eight, all the way up to 512.

二進法では隣の位に移るたび 値が倍化します指に １ ２ ４ ８ 値をふっていくと 512までいけます

And any positive integer, up to a certain limit, can be expressed as a sum of these numbers.

一定までの正の整数ならこれらの数字の計によって表せます

For example, the number seven is 4+2+1.

たとえば７は４+２+１なので

so we can represent it by having just these three fingers raised.

これらの３本の指を立てて表します

Meanwhile, 250 is 128+64+32+16+8+2.

250は128+64+32+16+8+2となります

How high can we go now?

どこまで いけるでしょう？

That would be the number with all ten fingers raised, or 1,023.

10本の指を全部立てた数 1023になります

Is it possible to go even higher?

まだ いけるでしょうか

It depends on how dexterous you feel.

あとは あなたの器用さ次第です

If you can bend each finger just halfway, that gives us three different states - down, half bent, and raised.

半分曲げができるなら 指のポジションは３つになります曲げ 半分曲げ 立てる

Now, we can count using a base-three positional system, up to 59,048.

この３ポジションを使えば 数えられる上限は59048までいきます

And if you can bend your fingers into four different states or more, you can get even higher.

指の曲げ方が４つ以上できたらもっと数えられます

That limit is up to you, and your own flexibility and ingenuity.

上限はあなたの柔軟性と創意工夫次第です

Even with our fingers in just two possible states, we're already working pretty efficiently.

指の立て方が２通りだけでも充分役に立ちます

In fact, our computers are based on the same principle.

実際 コンピュータは これと同じ原理で動いています

Each microchip consists of tiny electrical switches that can be either on or off, meaning that base-two is the default way they represent numbers.

マイクロチップは 小さな電気スイッチの集まりでそのスイッチが それぞれ オン、オフするのです 二進法は数字を表す既定の方法なのです

And just as we can use this system to count past 1,000 using only our fingers, computers can perform billions of operations just by counting off 1's and 0's.

このシステムによって指だけで 1000以上の数が数えられるようにコンピュータでの膨大な処理を 可能にしているのも １と０の積み重ねなのです