[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:14.34,0:00:17.08,Default,,0000,0000,0000,,How many times can you\Nfold a piece of paper?
Dialogue: 0,0:00:17.10,0:00:20.60,Default,,0000,0000,0000,,Assume that one had a piece\Nof paper that was very fine,
Dialogue: 0,0:00:20.62,0:00:23.48,Default,,0000,0000,0000,,like the kind they typically\Nuse to print the Bible.
Dialogue: 0,0:00:24.100,0:00:28.33,Default,,0000,0000,0000,,In reality, it seems like a piece of silk.
Dialogue: 0,0:00:28.36,0:00:29.98,Default,,0000,0000,0000,,To qualify these ideas,
Dialogue: 0,0:00:30.00,0:00:31.44,Default,,0000,0000,0000,,let's say you have a paper
Dialogue: 0,0:00:31.47,0:00:34.55,Default,,0000,0000,0000,,that's one-thousandth\Nof a centimeter in thickness.
Dialogue: 0,0:00:35.46,0:00:38.89,Default,,0000,0000,0000,,That is 10 to the power\Nof minus three centimeters,
Dialogue: 0,0:00:38.91,0:00:42.22,Default,,0000,0000,0000,,which equals .001 centimeters.
Dialogue: 0,0:00:43.45,0:00:46.36,Default,,0000,0000,0000,,Let's also assume that you have\Na big piece of paper,
Dialogue: 0,0:00:46.39,0:00:47.98,Default,,0000,0000,0000,,like a page out of the newspaper.
Dialogue: 0,0:00:48.94,0:00:51.68,Default,,0000,0000,0000,,Now we begin to fold it in half.
Dialogue: 0,0:00:52.51,0:00:55.18,Default,,0000,0000,0000,,How many times do you think\Nit could be folded like that?
Dialogue: 0,0:00:55.98,0:00:57.08,Default,,0000,0000,0000,,And another question:
Dialogue: 0,0:00:57.89,0:01:01.80,Default,,0000,0000,0000,,If you could fold the paper over and over,\Nas many times as you wish,
Dialogue: 0,0:01:01.84,0:01:03.12,Default,,0000,0000,0000,,say 30 times,
Dialogue: 0,0:01:03.14,0:01:06.16,Default,,0000,0000,0000,,what would you imagine\Nthe thickness of the paper would be then?
Dialogue: 0,0:01:07.16,0:01:08.73,Default,,0000,0000,0000,,Before you move on,
Dialogue: 0,0:01:08.75,0:01:12.98,Default,,0000,0000,0000,,I encourage you to actually think\Nabout a possible answer to this question.
Dialogue: 0,0:01:14.03,0:01:15.06,Default,,0000,0000,0000,,OK.
Dialogue: 0,0:01:15.09,0:01:17.15,Default,,0000,0000,0000,,After we have folded the paper once,
Dialogue: 0,0:01:17.17,0:01:20.50,Default,,0000,0000,0000,,it is now two thousandths\Nof a centimeter in thickness.
Dialogue: 0,0:01:21.42,0:01:23.84,Default,,0000,0000,0000,,If we fold it in half once again,
Dialogue: 0,0:01:23.86,0:01:26.98,Default,,0000,0000,0000,,the paper will become\Nfour thousandths of a centimeter.
Dialogue: 0,0:01:27.82,0:01:31.17,Default,,0000,0000,0000,,With every fold we make,\Nthe paper doubles in thickness.
Dialogue: 0,0:01:32.36,0:01:35.06,Default,,0000,0000,0000,,And if we continue to fold\Nit again and again,
Dialogue: 0,0:01:35.09,0:01:38.84,Default,,0000,0000,0000,,always in half, we would confront\Nthe following situation
Dialogue: 0,0:01:38.86,0:01:39.98,Default,,0000,0000,0000,,after 10 folds.
Dialogue: 0,0:01:40.84,0:01:42.83,Default,,0000,0000,0000,,Two to the power of 10,
Dialogue: 0,0:01:42.85,0:01:46.42,Default,,0000,0000,0000,,meaning that you multiply\Ntwo by itself 10 times,
Dialogue: 0,0:01:46.44,0:01:50.97,Default,,0000,0000,0000,,is one thousand and\N24 thousandths of a centimeter,
Dialogue: 0,0:01:50.99,0:01:54.07,Default,,0000,0000,0000,,which is a little bit over one centimeter.
Dialogue: 0,0:01:54.09,0:01:56.25,Default,,0000,0000,0000,,Assume we continue folding\Nthe paper in half.
Dialogue: 0,0:01:57.25,0:01:58.98,Default,,0000,0000,0000,,What will happen then?
Dialogue: 0,0:01:59.00,0:02:00.98,Default,,0000,0000,0000,,If we fold it 17 times,
Dialogue: 0,0:02:01.00,0:02:03.98,Default,,0000,0000,0000,,we'll get a thickness\Nof two to the power of 17,
Dialogue: 0,0:02:04.00,0:02:07.72,Default,,0000,0000,0000,,which is 131 centimeters,
Dialogue: 0,0:02:07.74,0:02:09.67,Default,,0000,0000,0000,,and that equals just over four feet.
Dialogue: 0,0:02:10.75,0:02:12.98,Default,,0000,0000,0000,,If we were able to fold it 25 times,
Dialogue: 0,0:02:13.00,0:02:15.98,Default,,0000,0000,0000,,then we would get two to the power of 25,
Dialogue: 0,0:02:16.00,0:02:21.26,Default,,0000,0000,0000,,which is 33,554 centimeters,
Dialogue: 0,0:02:21.29,0:02:23.12,Default,,0000,0000,0000,,just over 1,100 feet.
Dialogue: 0,0:02:24.28,0:02:27.98,Default,,0000,0000,0000,,That would make it almost\Nas tall as the Empire State Building.
Dialogue: 0,0:02:29.36,0:02:31.98,Default,,0000,0000,0000,,It's worthwhile to stop here\Nand reflect for a moment.
Dialogue: 0,0:02:32.96,0:02:37.55,Default,,0000,0000,0000,,Folding a paper in half, even a paper\Nas fine as that of the Bible,
Dialogue: 0,0:02:37.57,0:02:41.98,Default,,0000,0000,0000,,25 times would give us a paper\Nalmost a quarter of a mile.
Dialogue: 0,0:02:42.00,0:02:43.02,Default,,0000,0000,0000,,What do we learn?
Dialogue: 0,0:02:43.87,0:02:47.63,Default,,0000,0000,0000,,This type of growth\Nis called exponential growth,
Dialogue: 0,0:02:47.66,0:02:49.98,Default,,0000,0000,0000,,and as you see, just by folding a paper
Dialogue: 0,0:02:50.00,0:02:53.16,Default,,0000,0000,0000,,we can go very far, but very fast too.
Dialogue: 0,0:02:54.35,0:02:58.71,Default,,0000,0000,0000,,Summarizing, if we fold a paper 25 times,
Dialogue: 0,0:02:58.73,0:03:00.98,Default,,0000,0000,0000,,the thickness is almost\Na quarter of a mile.
Dialogue: 0,0:03:02.15,0:03:06.19,Default,,0000,0000,0000,,30 times, the thickness reaches 6.5 miles,
Dialogue: 0,0:03:06.21,0:03:08.92,Default,,0000,0000,0000,,which is about the average\Nheight that planes fly.
Dialogue: 0,0:03:08.94,0:03:12.98,Default,,0000,0000,0000,,40 times, the thickness\Nis nearly 7,000 miles,
Dialogue: 0,0:03:13.00,0:03:15.85,Default,,0000,0000,0000,,or the average GPS satellite's orbit.
Dialogue: 0,0:03:15.88,0:03:19.43,Default,,0000,0000,0000,,48 times, the thickness\Nis way over one million miles.
Dialogue: 0,0:03:20.53,0:03:24.23,Default,,0000,0000,0000,,Now, if you think that the distance\Nbetween the Earth and the Moon
Dialogue: 0,0:03:24.25,0:03:27.04,Default,,0000,0000,0000,,is less than 250,000 miles,
Dialogue: 0,0:03:27.06,0:03:29.47,Default,,0000,0000,0000,,then starting with a piece of Bible paper
Dialogue: 0,0:03:29.50,0:03:32.98,Default,,0000,0000,0000,,and folding it 45 times,\Nwe get to the Moon.
Dialogue: 0,0:03:34.11,0:03:36.70,Default,,0000,0000,0000,,And if we double it one more time,
Dialogue: 0,0:03:36.72,0:03:38.00,Default,,0000,0000,0000,,we get back to Earth.