[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:06.65,0:00:10.60,Default,,0000,0000,0000,,How high can you count on your fingers?
Dialogue: 0,0:00:10.60,0:00:13.18,Default,,0000,0000,0000,,It seems like a question \Nwith an obvious answer.
Dialogue: 0,0:00:13.18,0:00:15.79,Default,,0000,0000,0000,,After all, most of us have ten fingers,
Dialogue: 0,0:00:15.79,0:00:17.06,Default,,0000,0000,0000,,or to be more precise,
Dialogue: 0,0:00:17.06,0:00:19.40,Default,,0000,0000,0000,,eight fingers and two thumbs.
Dialogue: 0,0:00:19.40,0:00:22.80,Default,,0000,0000,0000,,This gives us a total of ten digits\Non our two hands,
Dialogue: 0,0:00:22.80,0:00:24.68,Default,,0000,0000,0000,,which we use to count to ten.
Dialogue: 0,0:00:24.68,0:00:28.77,Default,,0000,0000,0000,,It's no coincidence that the ten symbols\Nwe use in our modern numbering system
Dialogue: 0,0:00:28.77,0:00:30.96,Default,,0000,0000,0000,,are called digits as well.
Dialogue: 0,0:00:30.96,0:00:33.13,Default,,0000,0000,0000,,But that's not the only way to count.
Dialogue: 0,0:00:33.13,0:00:38.32,Default,,0000,0000,0000,,In some places, it's customary to\Ngo up to twelve on just one hand.
Dialogue: 0,0:00:38.32,0:00:39.32,Default,,0000,0000,0000,,How?
Dialogue: 0,0:00:39.32,0:00:42.34,Default,,0000,0000,0000,,Well, each finger is divided \Ninto three sections,
Dialogue: 0,0:00:42.34,0:00:46.79,Default,,0000,0000,0000,,and we have a natural pointer\Nto indicate each one, the thumb.
Dialogue: 0,0:00:46.79,0:00:50.81,Default,,0000,0000,0000,,That gives us an easy to way to count\Nto twelve on one hand.
Dialogue: 0,0:00:50.81,0:00:52.34,Default,,0000,0000,0000,,And if we want to count higher,
Dialogue: 0,0:00:52.34,0:00:57.94,Default,,0000,0000,0000,,we can use the digits on our other hand to\Nkeep track of each time we get to twelve,
Dialogue: 0,0:00:57.94,0:01:02.60,Default,,0000,0000,0000,,up to five groups of twelve, or 60.
Dialogue: 0,0:01:02.60,0:01:05.25,Default,,0000,0000,0000,,Better yet, let's use the sections\Non the second hand
Dialogue: 0,0:01:05.25,0:01:10.97,Default,,0000,0000,0000,,to count twelve groups of twelve,\Nup to 144.
Dialogue: 0,0:01:10.97,0:01:12.79,Default,,0000,0000,0000,,That's a pretty big improvement,
Dialogue: 0,0:01:12.79,0:01:17.24,Default,,0000,0000,0000,,but we can go higher by finding more\Ncountable parts on each hand.
Dialogue: 0,0:01:17.24,0:01:21.25,Default,,0000,0000,0000,,For example, each finger \Nhas three sections and three creases
Dialogue: 0,0:01:21.25,0:01:23.66,Default,,0000,0000,0000,,for a total of six things to count.
Dialogue: 0,0:01:23.66,0:01:25.99,Default,,0000,0000,0000,,Now we're up to 24 on each hand,
Dialogue: 0,0:01:25.99,0:01:28.52,Default,,0000,0000,0000,,and using our other hand to mark\Ngroups of 24
Dialogue: 0,0:01:28.52,0:01:31.67,Default,,0000,0000,0000,,gets us all the way to 576.
Dialogue: 0,0:01:31.67,0:01:33.01,Default,,0000,0000,0000,,Can we go any higher?
Dialogue: 0,0:01:33.01,0:01:36.42,Default,,0000,0000,0000,,It looks like we've reached the limit\Nof how many different finger parts
Dialogue: 0,0:01:36.42,0:01:38.76,Default,,0000,0000,0000,,we can count with any precision.
Dialogue: 0,0:01:38.76,0:01:40.62,Default,,0000,0000,0000,,So let's think of something different.
Dialogue: 0,0:01:40.62,0:01:43.32,Default,,0000,0000,0000,,One of our greatest \Nmathematical inventions
Dialogue: 0,0:01:43.32,0:01:46.69,Default,,0000,0000,0000,,is the system of positional notation,
Dialogue: 0,0:01:46.69,0:01:50.85,Default,,0000,0000,0000,,where the placement of symbols allows\Nfor different magnitudes of value,
Dialogue: 0,0:01:50.85,0:01:53.22,Default,,0000,0000,0000,,as in the number 999.
Dialogue: 0,0:01:53.22,0:01:55.73,Default,,0000,0000,0000,,Even though the same symbol is used\Nthree times,
Dialogue: 0,0:01:55.73,0:01:59.85,Default,,0000,0000,0000,,each position indicates a different\Norder of magnitude.
Dialogue: 0,0:01:59.85,0:02:05.54,Default,,0000,0000,0000,,So we can use positional value on\Nour fingers to beat our previous record.
Dialogue: 0,0:02:05.54,0:02:07.85,Default,,0000,0000,0000,,Let's forget about finger sections\Nfor a moment
Dialogue: 0,0:02:07.85,0:02:12.16,Default,,0000,0000,0000,,and look at the simplest case of having\Njust two options per finger,
Dialogue: 0,0:02:12.16,0:02:13.94,Default,,0000,0000,0000,,up and down.
Dialogue: 0,0:02:13.94,0:02:16.33,Default,,0000,0000,0000,,This won't allow us to represent \Npowers of ten,
Dialogue: 0,0:02:16.33,0:02:20.38,Default,,0000,0000,0000,,but it's perfect for the counting system\Nthat uses powers of two,
Dialogue: 0,0:02:20.38,0:02:22.49,Default,,0000,0000,0000,,otherwise known as binary.
Dialogue: 0,0:02:22.49,0:02:26.28,Default,,0000,0000,0000,,In binary, each position has double\Nthe value of the previous one,
Dialogue: 0,0:02:26.28,0:02:29.32,Default,,0000,0000,0000,,so we can assign \Nour fingers values of one,
Dialogue: 0,0:02:29.32,0:02:30.19,Default,,0000,0000,0000,,two,
Dialogue: 0,0:02:30.19,0:02:30.94,Default,,0000,0000,0000,,four,
Dialogue: 0,0:02:30.94,0:02:31.74,Default,,0000,0000,0000,,eight,
Dialogue: 0,0:02:31.74,0:02:34.29,Default,,0000,0000,0000,,all the way up to 512.
Dialogue: 0,0:02:34.29,0:02:36.94,Default,,0000,0000,0000,,And any positive integer,\Nup to a certain limit,
Dialogue: 0,0:02:36.94,0:02:39.98,Default,,0000,0000,0000,,can be expressed \Nas a sum of these numbers.
Dialogue: 0,0:02:39.98,0:02:43.77,Default,,0000,0000,0000,,For example, the number seven\Nis 4+2+1.
Dialogue: 0,0:02:43.77,0:02:47.64,Default,,0000,0000,0000,,so we can represent it by having\Njust these three fingers raised.
Dialogue: 0,0:02:47.64,0:02:56.29,Default,,0000,0000,0000,,Meanwhile, 250 is 128+64+32+16+8+2.
Dialogue: 0,0:02:56.29,0:02:58.26,Default,,0000,0000,0000,,How high an we go now?
Dialogue: 0,0:02:58.26,0:03:03.49,Default,,0000,0000,0000,,That would be the number with all ten\Nfingers raised, or 1,023.
Dialogue: 0,0:03:03.49,0:03:05.63,Default,,0000,0000,0000,,Is it possible to go even higher?
Dialogue: 0,0:03:05.63,0:03:07.73,Default,,0000,0000,0000,,It depends on how dexterous you feel.
Dialogue: 0,0:03:07.73,0:03:12.38,Default,,0000,0000,0000,,If you can bend each finger just halfway,\Nthat gives us three different states -
Dialogue: 0,0:03:12.38,0:03:13.32,Default,,0000,0000,0000,,down,
Dialogue: 0,0:03:13.32,0:03:14.39,Default,,0000,0000,0000,,half bent,
Dialogue: 0,0:03:14.39,0:03:15.76,Default,,0000,0000,0000,,and raised.
Dialogue: 0,0:03:15.76,0:03:19.61,Default,,0000,0000,0000,,Now, we can count using \Na base-three positional system,
Dialogue: 0,0:03:19.61,0:03:24.98,Default,,0000,0000,0000,,up to 59,048.
Dialogue: 0,0:03:24.98,0:03:28.74,Default,,0000,0000,0000,,And if you can bend your fingers\Ninto four different states or more,
Dialogue: 0,0:03:28.74,0:03:30.64,Default,,0000,0000,0000,,you can get even higher.
Dialogue: 0,0:03:30.64,0:03:36.20,Default,,0000,0000,0000,,That limit is up to you,\Nand your own flexibility and ingenuity.
Dialogue: 0,0:03:36.20,0:03:38.80,Default,,0000,0000,0000,,Even with our fingers in just two\Npossible states,
Dialogue: 0,0:03:38.80,0:03:41.30,Default,,0000,0000,0000,,we're already working pretty efficiently.
Dialogue: 0,0:03:41.30,0:03:45.33,Default,,0000,0000,0000,,In fact, our computers are based\Non the same principle.
Dialogue: 0,0:03:45.33,0:03:48.49,Default,,0000,0000,0000,,Each microchip consists of tiny\Nelectrical switches
Dialogue: 0,0:03:48.49,0:03:51.18,Default,,0000,0000,0000,,that can be either on or off,
Dialogue: 0,0:03:51.18,0:03:55.75,Default,,0000,0000,0000,,meaning that base-two is the default way\Nthey represent numbers.
Dialogue: 0,0:03:55.75,0:04:00.19,Default,,0000,0000,0000,,And just as we can use this system to\Ncount passed 1,000 using only our fingers,
Dialogue: 0,0:04:00.19,0:04:03.20,Default,,0000,0000,0000,,computers can perform billions \Nof operations
Dialogue: 0,0:04:03.20,0:04:07.37,Default,,0000,0000,0000,,just by counting off ones and zeroes.