[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:07.04,0:00:10.29,Default,,0000,0000,0000,,In the 16th century, the mathematician\NRobert Recorde
Dialogue: 0,0:00:10.29,0:00:13.04,Default,,0000,0000,0000,,wrote a book called \N"The Whetstone of Witte"
Dialogue: 0,0:00:13.04,0:00:15.97,Default,,0000,0000,0000,,to teach English students algebra.
Dialogue: 0,0:00:15.97,0:00:21.12,Default,,0000,0000,0000,,But he was getting tired of writing\Nthe words "is equal to" over and over.
Dialogue: 0,0:00:21.12,0:00:22.63,Default,,0000,0000,0000,,His solution?
Dialogue: 0,0:00:22.63,0:00:27.24,Default,,0000,0000,0000,,He replaced those words with\Ntwo parallel horizontal line segments
Dialogue: 0,0:00:27.24,0:00:32.26,Default,,0000,0000,0000,,because the way he saw it,\Nno two things can be more equal.
Dialogue: 0,0:00:32.26,0:00:34.95,Default,,0000,0000,0000,,Could he have used four line segments\Ninstead of two?
Dialogue: 0,0:00:34.95,0:00:36.20,Default,,0000,0000,0000,,Of course.
Dialogue: 0,0:00:36.20,0:00:38.29,Default,,0000,0000,0000,,Could he have used vertical line segments?
Dialogue: 0,0:00:38.29,0:00:40.70,Default,,0000,0000,0000,,In fact, some people did.
Dialogue: 0,0:00:40.70,0:00:44.100,Default,,0000,0000,0000,,There's no reason why the equals sign\Nhad to look the way it does today.
Dialogue: 0,0:00:44.100,0:00:48.20,Default,,0000,0000,0000,,At some point, it just caught on,\Nsort of like a meme.
Dialogue: 0,0:00:48.20,0:00:50.73,Default,,0000,0000,0000,,More and more mathematicians\Nbegan to use it,
Dialogue: 0,0:00:50.73,0:00:55.57,Default,,0000,0000,0000,,and eventually, \Nit became a standard symbol for equality.
Dialogue: 0,0:00:55.57,0:00:56.97,Default,,0000,0000,0000,,Math is full of symbols.
Dialogue: 0,0:00:56.97,0:00:57.74,Default,,0000,0000,0000,,Lines,
Dialogue: 0,0:00:57.74,0:00:58.56,Default,,0000,0000,0000,,dots,
Dialogue: 0,0:00:58.56,0:00:59.30,Default,,0000,0000,0000,,arrows,
Dialogue: 0,0:00:59.30,0:01:00.26,Default,,0000,0000,0000,,English letters,
Dialogue: 0,0:01:00.26,0:01:01.21,Default,,0000,0000,0000,,Greek letters,
Dialogue: 0,0:01:01.21,0:01:02.19,Default,,0000,0000,0000,,superscripts,
Dialogue: 0,0:01:02.19,0:01:03.35,Default,,0000,0000,0000,,subscripts.
Dialogue: 0,0:01:03.35,0:01:05.96,Default,,0000,0000,0000,,It can look like an illegible jumble.
Dialogue: 0,0:01:05.96,0:01:09.82,Default,,0000,0000,0000,,It's normal to find this wealth\Nof symbols a little intimidating
Dialogue: 0,0:01:09.82,0:01:13.05,Default,,0000,0000,0000,,and to wonder where they all came from.
Dialogue: 0,0:01:13.05,0:01:16.61,Default,,0000,0000,0000,,Sometimes, as Recorde himself\Nnoted about his equals sign,
Dialogue: 0,0:01:16.61,0:01:21.51,Default,,0000,0000,0000,,there's an apt conformity\Nbetween the symbol and what it represents.
Dialogue: 0,0:01:21.51,0:01:25.20,Default,,0000,0000,0000,,Another example of that \Nis the plus sign for addition,
Dialogue: 0,0:01:25.20,0:01:30.49,Default,,0000,0000,0000,,which originated from a condensing\Nof the Latin word et meaning and.
Dialogue: 0,0:01:30.49,0:01:33.84,Default,,0000,0000,0000,,Sometimes, however, the choice of symbol\Nis more arbitrary,
Dialogue: 0,0:01:33.84,0:01:36.57,Default,,0000,0000,0000,,such as when a mathematician\Nnamed Christian Kramp
Dialogue: 0,0:01:36.57,0:01:40.18,Default,,0000,0000,0000,,introduced the exclamation mark\Nfor factorials
Dialogue: 0,0:01:40.18,0:01:44.68,Default,,0000,0000,0000,,just because he needed a shorthand\Nfor expressions like this.
Dialogue: 0,0:01:44.68,0:01:48.06,Default,,0000,0000,0000,,In fact, all of these symbols \Nwere invented or adopted
Dialogue: 0,0:01:48.06,0:01:51.97,Default,,0000,0000,0000,,by mathematicians who wanted\Nto avoid repeating themselves
Dialogue: 0,0:01:51.97,0:01:57.02,Default,,0000,0000,0000,,or having to use a lot of words\Nto write out mathematical ideas.
Dialogue: 0,0:01:57.02,0:01:59.68,Default,,0000,0000,0000,,Many of the symbols used\Nin mathematics are letters,
Dialogue: 0,0:01:59.68,0:02:03.82,Default,,0000,0000,0000,,usually from the Latin alphabet\Nor Greek.
Dialogue: 0,0:02:03.82,0:02:08.03,Default,,0000,0000,0000,,Characters are often found\Nrepresenting quantities that are unknown,
Dialogue: 0,0:02:08.03,0:02:11.19,Default,,0000,0000,0000,,and the relationships between variables.
Dialogue: 0,0:02:11.19,0:02:15.25,Default,,0000,0000,0000,,They also stand in for specific numbers\Nthat show up frequently
Dialogue: 0,0:02:15.25,0:02:21.02,Default,,0000,0000,0000,,but would be cumbersome or impossible\Nto fully write out in decimal form.
Dialogue: 0,0:02:21.02,0:02:26.35,Default,,0000,0000,0000,,Sets of numbers and whole equations\Ncan be represented with letters, too.
Dialogue: 0,0:02:26.35,0:02:29.49,Default,,0000,0000,0000,,Other symbols are used \Nto represent operations.
Dialogue: 0,0:02:29.49,0:02:32.19,Default,,0000,0000,0000,,Some of these are especially valuable\Nas shorthand
Dialogue: 0,0:02:32.19,0:02:36.88,Default,,0000,0000,0000,,because they condense repeated operations\Ninto a single expression.
Dialogue: 0,0:02:36.88,0:02:41.55,Default,,0000,0000,0000,,The repeated addition of the same number\Nis abbreviated with a multiplication sign
Dialogue: 0,0:02:41.55,0:02:44.48,Default,,0000,0000,0000,,so it doesn't take up more space\Nthan it has to.
Dialogue: 0,0:02:44.48,0:02:47.92,Default,,0000,0000,0000,,A number multiplied by itself\Nis indicated with an exponent
Dialogue: 0,0:02:47.92,0:02:51.21,Default,,0000,0000,0000,,that tells you how many times\Nto repeat the operation.
Dialogue: 0,0:02:51.21,0:02:54.25,Default,,0000,0000,0000,,And a long string of sequential terms\Nadded together
Dialogue: 0,0:02:54.25,0:02:57.21,Default,,0000,0000,0000,,is collapsed into a capital sigma.
Dialogue: 0,0:02:57.21,0:03:01.40,Default,,0000,0000,0000,,These symbols shorten\Nlengthy calculations to smaller terms
Dialogue: 0,0:03:01.40,0:03:05.02,Default,,0000,0000,0000,,that are much easier to manipulate.
Dialogue: 0,0:03:05.02,0:03:07.95,Default,,0000,0000,0000,,Symbols can also provide \Nsuccint instructions
Dialogue: 0,0:03:07.95,0:03:10.64,Default,,0000,0000,0000,,about how to perform calculations.
Dialogue: 0,0:03:10.64,0:03:13.96,Default,,0000,0000,0000,,Consider the following set\Nof operations on a number.
Dialogue: 0,0:03:13.96,0:03:15.92,Default,,0000,0000,0000,,Take some number that you're thinking of,
Dialogue: 0,0:03:15.92,0:03:17.39,Default,,0000,0000,0000,,multiply it by two,
Dialogue: 0,0:03:17.39,0:03:18.96,Default,,0000,0000,0000,,subtract one from the result,
Dialogue: 0,0:03:18.96,0:03:21.40,Default,,0000,0000,0000,,multiply the result of that by itself,
Dialogue: 0,0:03:21.40,0:03:23.24,Default,,0000,0000,0000,,divide the result of that by three,
Dialogue: 0,0:03:23.24,0:03:26.64,Default,,0000,0000,0000,,and then add one to get the final output.
Dialogue: 0,0:03:26.64,0:03:32.19,Default,,0000,0000,0000,,Without our symbols and conventions,\Nwe'd be faced with this block of text.
Dialogue: 0,0:03:32.19,0:03:35.80,Default,,0000,0000,0000,,With them, we have a compact,\Nelegant expression.
Dialogue: 0,0:03:35.80,0:03:37.50,Default,,0000,0000,0000,,Sometimes, as with equals,
Dialogue: 0,0:03:37.50,0:03:40.75,Default,,0000,0000,0000,,these symbols communicate meaning\Nthrough form.
Dialogue: 0,0:03:40.75,0:03:43.61,Default,,0000,0000,0000,,Many, however, are arbitrary.
Dialogue: 0,0:03:43.61,0:03:46.68,Default,,0000,0000,0000,,Understanding them is a matter\Nof memorizing what they mean
Dialogue: 0,0:03:46.68,0:03:52.02,Default,,0000,0000,0000,,and applying them in different contexts\Nuntil they stick, as with any language.
Dialogue: 0,0:03:52.02,0:03:54.62,Default,,0000,0000,0000,,If we were to encounter\Nan alien civilization,
Dialogue: 0,0:03:54.62,0:03:58.76,Default,,0000,0000,0000,,they'd probably have a totally\Ndifferent set of symbols.
Dialogue: 0,0:03:58.76,0:04:04.37,Default,,0000,0000,0000,,But if they think anything like us,\Nthey'd probably have symbols.
Dialogue: 0,0:04:04.37,0:04:08.64,Default,,0000,0000,0000,,And their symbols may even correspond\Ndirectly to ours.
Dialogue: 0,0:04:08.64,0:04:10.77,Default,,0000,0000,0000,,They'd have their own multiplication sign,
Dialogue: 0,0:04:10.77,0:04:12.13,Default,,0000,0000,0000,,symbol for pi,
Dialogue: 0,0:04:12.13,0:04:14.91,Default,,0000,0000,0000,,and, of course, equals.