WEBVTT

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How many times can you
fold a piece of paper?

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Assume that one had a piece
of paper that was very fine,

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like the kind they typically
use to print the Bible.

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In reality, it seems like a piece of silk.

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To qualify these ideas,

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let's say you have a paper

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that's one-thousandth
of a centimeter in thickness.

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That is 10 to the power
of minus three centimeters,

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which equals .001 centimeters.

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Let's also assume that you have
a big piece of paper,

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like a page out of the newspaper.

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Now we begin to fold it in half.

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

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And another question:

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If you could fold the paper over and over,
as many times as you wish,

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say 30 times,

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what would you imagine
the thickness of the paper would be then?

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Before you move on,

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I encourage you to actually think
about a possible answer to this question.

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OK.

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After we have folded the paper once,

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it is now two thousandths
of a centimeter in thickness.

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If we fold it in half once again,

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the paper will become
four thousandths of a centimeter.

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

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And if we continue to fold
it again and again,

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always in half, we would confront
the following situation

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after 10 folds.

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Two to the power of 10,

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meaning that you multiply
two by itself 10 times,

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is one thousand and
24 thousandths of a centimeter,

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which is a little bit over one centimeter.

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Assume we continue folding
the paper in half.

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What will happen then?

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If we fold it 17 times,

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we'll get a thickness
of two to the power of 17,

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which is 131 centimeters,

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and that equals just over four feet.

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If we were able to fold it 25 times,

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then we would get two to the power of 25,

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which is 33,554 centimeters,

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just over 1,100 feet.

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

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

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Folding a paper in half, even a paper
as fine as that of the Bible,

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25 times would give us a paper
almost a quarter of a mile.

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What do we learn?

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This type of growth
is called exponential growth,

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and as you see, just by folding a paper

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we can go very far, but very fast too.

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Summarizing, if we fold a paper 25 times,

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the thickness is almost
a quarter of a mile.

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30 times, the thickness reaches 6.5 miles,

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which is about the average
height that planes fly.

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40 times, the thickness
is nearly 7,000 miles,

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or the average GPS satellite's orbit.

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48 times, the thickness
is way over one million miles.

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Now, if you think that the distance
between the Earth and the Moon

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is less than 250,000 miles,

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then starting with a piece of Bible paper

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and folding it 45 times,
we get to the Moon.

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And if we double it one more time,

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we get back to Earth.