How many times can you fold a piece of paper?
一张纸可以对折几次？
Assume that one had a piece of paper that was very fine,
假设有一张很薄很薄的纸
like the kind they typically use to print the Bible.
就像是印圣经的那种纸
In reality, it seems like a piece of silk.
实际上，就像是一根丝那么薄
To qualify these ideas, let's say you have a paper that's one-thousandth of a centimeter in thickness.
为了要把这个想法量化，假设纸的厚度是1/1000厘米
That is 10 to the power of minus three centimeters, which equals .001 centimeters.
也就是10的-3次方厘米，相当于0.001厘米。
Let's also assume that you have a big piece of paper, like a page out of the newspaper.
再假设这张纸够大，像报纸那么大。
Now we begin to fold it in half.
我们开始将它对折。
How many times do you think it could be folded like that?
你觉得我们可以对折几次？
And another question:
另一个问题是：
If you could fold the paper over and over, as many times as you wish, say 30 times,
如果你能将一张纸折叠任意多次，比方说30次
what would you imagine the thickness of the paper would be then?
你想那时纸会有多厚？
Before you move on, I encourage you to actually think about a possible answer to this question.
在开始之前，我鼓励你好好想想这问题可能的答案。
OK. After we have folded the paper once, it is now two thousandths of a centimeter in thickness.
好，在对折一次后，厚度变成2/1000厘米。
If we fold it in half once again, the paper will become four thousandths of a centimeter.
如果再对折一次，这张纸就会变成4/1000厘米。
With every fold we make, the paper doubles in thickness.
每折一次，纸张厚度加倍。
And if we continue to fold it again and again,
如果我们不断对折，
always in half, we would confront the following situation after 10 folds.
十次以后，我们就会见到这种情景。

Two to the power of 10, meaning that you multiply two by itself 10 times,
2的10次方也就是将2自乘10次，
is one thousand and 24 thousandths of a centimeter, which is a little bit over one centimeter.
就是1024/1000厘米，比1厘米多一点
Assume we continue folding the paper in half. What will happen then?
如果我们继续对折。会发生什么事？
If we fold it 17 times, we'll get a thickness of two to the power of 17,
如果对折17次，厚度就是2的17次方，
which is 131 centimeters, and that equals just over four feet.
大约131厘米，超过4英尺。
If we were able to fold it 25 times, then we would get two to the power of 25,
如果我们可以对折25次，就会得到2的25次方，
which is 33,554 centimeters, just over 1,100 feet.
大约33554厘米，超过1100英尺。
That would make it almost as tall as the Empire State Building.
差不多跟帝国大厦一样高。
It's worthwhile to stop here and reflect for a moment.
现在很值得停下来反思一下。
Folding a paper in half, even a paper as fine as that of the Bible,
就算纸张跟圣经一样薄
25 times would give us a paper almost a quarter of a mile.
对折了25次后，厚度会接近1/4英里。
What do we learn?
我们学到什么？
This type of growth is called exponential growth,
这样的成长称作指数型成长
and as you see, just by folding a paper we can go very far, but very fast too.
就如你所看到的，只是把纸对折就会变得很厚，而且变厚得很快。
Summarizing, if we fold a paper 25 times,
总之，如果我们将纸对折25次
the thickness is almost a quarter of a mile.
厚度大约是1/4英里
30 times, the thickness reaches 6.5 miles,
30次的厚度，接近6.5英里，
which is about the average height that planes fly.
大约是飞机的平均飞行高度。
40 times, the thickness is nearly 7,000 miles, or the average GPS satellite's orbit.
40次的厚度，将近7000英里，是GPS卫星轨道平均高度的一半。
48 times, the thickness is way over one million miles.
折48次，厚度就超过一百万英里。
Now, if you think that the distance between the Earth and the Moon is less than 250,000 miles,
你想想，地球到月球的距离还不到25万英里
then starting with a piece of Bible paper and folding it 45 times, we get to the Moon.
用一张圣经纸折45次，我们就可以到达月球。
And if we double it one more time, we get back to Earth.
如果再多折一次，我们就可以回到地球了！