[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:07.99,0:00:11.29,Default,,0000,0000,0000,,These are the first five elements\Nof a number sequence.
Dialogue: 0,0:00:11.29,0:00:13.03,Default,,0000,0000,0000,,Can you figure out what comes next?
Dialogue: 0,0:00:13.03,0:00:14.96,Default,,0000,0000,0000,,Pause here if you want \Nto figure it out for yourself.
Dialogue: 0,0:00:14.96,0:00:16.03,Default,,0000,0000,0000,,Answer in: 3
Dialogue: 0,0:00:16.03,0:00:16.82,Default,,0000,0000,0000,,Answer in: 2
Dialogue: 0,0:00:16.82,0:00:17.73,Default,,0000,0000,0000,,Answer in: 1
Dialogue: 0,0:00:17.73,0:00:19.36,Default,,0000,0000,0000,,There is a pattern here,
Dialogue: 0,0:00:19.36,0:00:22.05,Default,,0000,0000,0000,,but it may not be the kind\Nof pattern you think it is.
Dialogue: 0,0:00:22.05,0:00:26.17,Default,,0000,0000,0000,,Look at the sequence again\Nand try reading it aloud.
Dialogue: 0,0:00:26.17,0:00:29.25,Default,,0000,0000,0000,,Now, look at the next number\Nin the sequence.
Dialogue: 0,0:00:29.25,0:00:31.88,Default,,0000,0000,0000,,3, 1, 2, 2, 1, 1.
Dialogue: 0,0:00:31.88,0:00:37.43,Default,,0000,0000,0000,,Pause again if you'd like to think\Nabout it some more.
Dialogue: 0,0:00:37.43,0:00:38.39,Default,,0000,0000,0000,,Answer in: 3
Dialogue: 0,0:00:38.39,0:00:39.29,Default,,0000,0000,0000,,Answer in: 2
Dialogue: 0,0:00:39.29,0:00:40.45,Default,,0000,0000,0000,,Answer in: 1
Dialogue: 0,0:00:40.45,0:00:43.88,Default,,0000,0000,0000,,This is what's known as\Na look and say sequence.
Dialogue: 0,0:00:43.88,0:00:45.57,Default,,0000,0000,0000,,Unlike many number sequences,
Dialogue: 0,0:00:45.57,0:00:49.45,Default,,0000,0000,0000,,this relies not on some mathematical\Nproperty of the numbers themselves,
Dialogue: 0,0:00:49.45,0:00:51.47,Default,,0000,0000,0000,,but on their notation.
Dialogue: 0,0:00:51.47,0:00:54.31,Default,,0000,0000,0000,,Start with the left-most digit\Nof the initial number.
Dialogue: 0,0:00:54.31,0:00:58.69,Default,,0000,0000,0000,,Now, read out how many times \Nit repeats in succession
Dialogue: 0,0:00:58.69,0:01:01.60,Default,,0000,0000,0000,,followed by the name of the digit itself.
Dialogue: 0,0:01:01.60,0:01:06.89,Default,,0000,0000,0000,,Then move on to the next distinct digit\Nand repeat until you reach the end.
Dialogue: 0,0:01:06.89,0:01:10.10,Default,,0000,0000,0000,,So the number 1 is read as "one one"
Dialogue: 0,0:01:10.10,0:01:13.59,Default,,0000,0000,0000,,written down the same way \Nwe write eleven.
Dialogue: 0,0:01:13.59,0:01:17.60,Default,,0000,0000,0000,,Of course, as part of this sequence,\Nit's not actually the number eleven,
Dialogue: 0,0:01:17.60,0:01:19.15,Default,,0000,0000,0000,,but 2 ones,
Dialogue: 0,0:01:19.15,0:01:21.80,Default,,0000,0000,0000,,which we then write as 2 1.
Dialogue: 0,0:01:21.80,0:01:25.41,Default,,0000,0000,0000,,That number is then read out\Nas 1 2 1 1,
Dialogue: 0,0:01:25.41,0:01:31.98,Default,,0000,0000,0000,,which written out we'd read as\None one, one two, two ones, and so on.
Dialogue: 0,0:01:31.98,0:01:37.76,Default,,0000,0000,0000,,These kinds of sequences were first\Nanalyzed by mathematician John Conway,
Dialogue: 0,0:01:37.76,0:01:40.74,Default,,0000,0000,0000,,who noted they have \Nsome interesting properties.
Dialogue: 0,0:01:40.74,0:01:46.12,Default,,0000,0000,0000,,For instance, starting with the number 22,\Nyields an infinite loop of two twos.
Dialogue: 0,0:01:46.12,0:01:48.39,Default,,0000,0000,0000,,But when seeded with any other number,
Dialogue: 0,0:01:48.39,0:01:51.66,Default,,0000,0000,0000,,the sequence grows in some\Nvery specific ways.
Dialogue: 0,0:01:51.66,0:01:54.90,Default,,0000,0000,0000,,Notice that although the number\Nof digits keeps increasing,
Dialogue: 0,0:01:54.90,0:01:58.88,Default,,0000,0000,0000,,the increase doesn't seem\Nto be either linear or random.
Dialogue: 0,0:01:58.88,0:02:04.17,Default,,0000,0000,0000,,In fact, if you extend the sequence\Ninfinitely, a pattern emerges.
Dialogue: 0,0:02:04.17,0:02:07.57,Default,,0000,0000,0000,,The ratio between the amount of digits\Nin two consecutive terms
Dialogue: 0,0:02:07.57,0:02:13.10,Default,,0000,0000,0000,,gradually converges to a single number\Nknown as Conway's Constant.
Dialogue: 0,0:02:13.10,0:02:16.02,Default,,0000,0000,0000,,This is equal to a little over 1.3,
Dialogue: 0,0:02:16.02,0:02:19.94,Default,,0000,0000,0000,,meaning that the amount of digits\Nincreases by about 30%
Dialogue: 0,0:02:19.94,0:02:22.94,Default,,0000,0000,0000,,with every step in the sequence.
Dialogue: 0,0:02:22.94,0:02:25.72,Default,,0000,0000,0000,,What about the numbers themselves?
Dialogue: 0,0:02:25.72,0:02:27.100,Default,,0000,0000,0000,,That gets even more interesting.
Dialogue: 0,0:02:27.100,0:02:30.30,Default,,0000,0000,0000,,Except for the repeating sequence of 22,
Dialogue: 0,0:02:30.30,0:02:36.11,Default,,0000,0000,0000,,every possible sequence eventually breaks\Ndown into distinct strings of digits.
Dialogue: 0,0:02:36.11,0:02:38.39,Default,,0000,0000,0000,,No matter what order these strings\Nshow up in,
Dialogue: 0,0:02:38.39,0:02:43.66,Default,,0000,0000,0000,,each appears unbroken in its entirety\Nevery time it occurs.
Dialogue: 0,0:02:43.66,0:02:46.57,Default,,0000,0000,0000,,Conway identified 92 of these elements,
Dialogue: 0,0:02:46.57,0:02:50.29,Default,,0000,0000,0000,,all composed only of digits 1, 2, and 3,
Dialogue: 0,0:02:50.29,0:02:52.24,Default,,0000,0000,0000,,as well as two additional elements
Dialogue: 0,0:02:52.24,0:02:56.97,Default,,0000,0000,0000,,whose variations\Ncan end with any digit of 4 or greater.
Dialogue: 0,0:02:56.97,0:02:59.45,Default,,0000,0000,0000,,No matter what number the sequence\Nis seeded with,
Dialogue: 0,0:02:59.45,0:03:02.84,Default,,0000,0000,0000,,eventually, it'll just consist\Nof these combinations,
Dialogue: 0,0:03:02.84,0:03:08.54,Default,,0000,0000,0000,,with digits 4 or higher only appearing\Nat the end of the two extra elements,
Dialogue: 0,0:03:08.54,0:03:10.97,Default,,0000,0000,0000,,if at all.
Dialogue: 0,0:03:10.97,0:03:12.84,Default,,0000,0000,0000,,Beyond being a neat puzzle,
Dialogue: 0,0:03:12.84,0:03:16.66,Default,,0000,0000,0000,,the look and say sequence\Nhas some practical applications.
Dialogue: 0,0:03:16.66,0:03:18.76,Default,,0000,0000,0000,,For example, run-length encoding,
Dialogue: 0,0:03:18.76,0:03:23.11,Default,,0000,0000,0000,,a data compression that was once used for\Ntelevision signals and digital graphics,
Dialogue: 0,0:03:23.11,0:03:25.65,Default,,0000,0000,0000,,is based on a similar concept.
Dialogue: 0,0:03:25.65,0:03:28.59,Default,,0000,0000,0000,,The amount of times a data value repeats\Nwithin the code
Dialogue: 0,0:03:28.59,0:03:31.59,Default,,0000,0000,0000,,is recorded as a data value itself.
Dialogue: 0,0:03:31.59,0:03:36.03,Default,,0000,0000,0000,,Sequences like this are a good example\Nof how numbers and other symbols
Dialogue: 0,0:03:36.03,0:03:38.70,Default,,0000,0000,0000,,can convey meaning on multiple levels.