Assume that one had a piece of paper that was very fine, like the kind they typically use to print the Bible.

聖書に使われているような薄い紙が１枚あったとしましょう

In reality, it seems like a piece of silk.

実際 シルクのように見えます

To qualify these ideas, let's say you have a paper that's one-thousandth of a centimeter in thickness.

計算を進めるため紙の厚さを1000分の1センチとしましょう

That is ten to the power of minus three centimeters, which equals .001 centimeters.

10のマイナス３乗センチつまり0.001cmです

Let's also assume that you have a big piece of paper, like a page out of the newspaper.

またその紙は 新聞紙のように十分に大きいものとしましょう

Now we begin to fold it in half.

これを半分に折っていくと

How many times do you think it could be folded like that?

何回折れると思いますか？

And another question:

もう１つの疑問は

If you could fold a paper over and over, as many times as you wish, say 30 times, what would you imagine the thickness of the paper would be then?

紙を好きなだけ何回でも 折っていけるとしたら例えば30回折ったときに その紙の厚さは どのくらいになるでしょう？

Before you move on, I encourage you to actually think about a possible answer to this question.

先に進む前に答えを自分で考えてみるよう おすすめします

Okay. After we have folded the paper once, it is now two-thousandths of a centimeter in thickness.

ではやってみましょう この紙を１回折ると厚さは1000分の2センチになります

If we fold it in half once again, the paper will become four-thousandths of a centimeter.

もう１度半分に折ると1000分の4センチになります

With every fold we make, the paper doubles in thickness.

１回折るごとに 紙の厚さは２倍になります

And if we continue to fold it again and again, always in half, we would confront the following situation after ten folds.

繰り返し半分に 折り続けていくと10回折った後 どうなっているかというと

Two to the power of ten, meaning that you multiply two by itself ten times, is one thousand and 24 thousandths of a centimeter, which is a little bit over one centimeter.

厚さは２の10乗つまり２を10回 掛け合わせたものですが 1000分の1024センチになります 1センチ強です

Assume we continue folding the paper in half. What would happen then?

さらに紙を半分に 折り続けたとしたらどうなるでしょう？

If we fold it 17 times, we'll get a thickness of two to the power of 17, which is 131 centimeters, and that equals just over four feet.

17回折ったところで厚さは２の17乗 つまり131cmになり ４フィートを越えます

If we were able to fold it 25 times, then we would get two to the power of 25, which is 33,554 centimeters, just over 1,100 feet.

25回折ることができたとしたら２の25乗倍の厚さ つまり33,554cmとなり 1,100フィートを 越えてしまいます

That would make it almost as tall as the Empire State Building.

エンパイアステートビルと ほぼ同じ高さです

It's worthwhile to stop here and reflect for a moment.

ちょっと立ち止まって 振り返ってみましょう

Folding a paper in half, even a paper as fine as that of the Bible, 25 times would give us a paper almost a quarter of a mile.

聖書の紙と同じくらい 薄い紙でも25回折ると 厚さが 約 3分の1 kmにもなります

What do we learn?

何が分かるでしょう？

This type of growth is called exponential growth, and as you see, just by folding a paper we can go very far, but very fast too.

このタイプの増え方を 指数的増加といいご覧の通り 紙を折っていくだけで とても早くとても遠くまで行くのです

Summarizing, if we fold a paper 25 times, the thickness is almost a quarter of a mile.

まとめです 紙を25回折ると厚さは約 3分の1 kmになり

Thirty times, the thickness reaches 6.5 miles, which is about the average height that planes fly.

30回で厚さは10 kmに及び飛行機の平均高度と 同じくらいになります

Forty times, the thickness is nearly 7,000 miles, or the average GPS satellite's orbit.

40回で厚さは ほぼ 11,000 kmGPS衛星軌道までの 平均距離になり

Forty-eight times, the thickness is way over one million miles.

48回だと厚さは 何百万kmにもなります"

Now, if you think that the distance between the Earth and the Moon is less than 250,000 miles, then starting with a piece of Bible paper and folding it 45 times, we get to the Moon.

地球と月の間の距離は38万km程度なので 聖書の紙１枚から始めて 45回折ることで 月まで届きます

And if we double it one more time, we get back to Earth.

さらにもう１回折ると地球に戻ってきます 先生: アドリアン・パエンザ ナレーション: アドリアン・パエンザ アニメーション: TED-Edチーム