[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:15.46,0:00:16.86,Default,,0000,0000,0000,,(Spanish) Buenas noches.
Dialogue: 0,0:00:17.57,0:00:19.95,Default,,0000,0000,0000,,Welcome to math class!
Dialogue: 0,0:00:19.95,0:00:24.44,Default,,0000,0000,0000,,The coming 9,000 seconds you'll be mine.
Dialogue: 0,0:00:24.44,0:00:25.43,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:00:25.43,0:00:26.100,Default,,0000,0000,0000,,OK, that was a joke.
Dialogue: 0,0:00:26.100,0:00:29.57,Default,,0000,0000,0000,,But raise your hand\Nif you love mathematics.
Dialogue: 0,0:00:30.54,0:00:33.16,Default,,0000,0000,0000,,Oh, that's a lot. Mmm. (Laughter)
Dialogue: 0,0:00:33.91,0:00:36.62,Default,,0000,0000,0000,,Mmm, that will be a tough one. (Laughter)
Dialogue: 0,0:00:39.89,0:00:46.67,Default,,0000,0000,0000,,Let's take you back \Nto 2600 B.C. to Mesopotamia.
Dialogue: 0,0:00:47.92,0:00:49.79,Default,,0000,0000,0000,,The Babylonians were not only good,
Dialogue: 0,0:00:49.79,0:00:53.60,Default,,0000,0000,0000,,were not only producing\None of the first literary works,
Dialogue: 0,0:00:53.60,0:00:55.19,Default,,0000,0000,0000,,The epic of Gilgamesh,
Dialogue: 0,0:00:55.19,0:00:57.65,Default,,0000,0000,0000,,they were actually\Nquite good at mathematics.
Dialogue: 0,0:00:59.10,0:01:02.71,Default,,0000,0000,0000,,The epic of Gilgamesh was written\Nin cuneiform on clay tablets,
Dialogue: 0,0:01:04.23,0:01:06.90,Default,,0000,0000,0000,,but they were good\Nat mathematics, as I said,
Dialogue: 0,0:01:06.90,0:01:10.92,Default,,0000,0000,0000,,because they already knew\Nthe Pythagorean theorem,
Dialogue: 0,0:01:10.92,0:01:12.88,Default,,0000,0000,0000,,and that is quite remarkable,
Dialogue: 0,0:01:12.88,0:01:15.73,Default,,0000,0000,0000,,because Pythagoras wasn't even born yet.
Dialogue: 0,0:01:15.73,0:01:17.16,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:01:17.89,0:01:21.32,Default,,0000,0000,0000,,They also could handle\Nquadratic equations,
Dialogue: 0,0:01:21.32,0:01:22.41,Default,,0000,0000,0000,,they could solve them,
Dialogue: 0,0:01:22.41,0:01:25.88,Default,,0000,0000,0000,,they had a general formula\Nfor quadratic equations.
Dialogue: 0,0:01:25.88,0:01:29.20,Default,,0000,0000,0000,,They could even handle\Nsome cubic equations.
Dialogue: 0,0:01:30.58,0:01:35.74,Default,,0000,0000,0000,,Now, when you solve any equations,\Nyou often get negative solutions,
Dialogue: 0,0:01:35.74,0:01:39.84,Default,,0000,0000,0000,,and negative numbers are not that easy.
Dialogue: 0,0:01:39.84,0:01:41.56,Default,,0000,0000,0000,,Let me give an example.
Dialogue: 0,0:01:42.29,0:01:46.92,Default,,0000,0000,0000,,If I have two tennis balls\Nand if I have to give away three,
Dialogue: 0,0:01:46.92,0:01:51.69,Default,,0000,0000,0000,,then I give away one, two...
Dialogue: 0,0:01:51.69,0:01:53.10,Default,,0000,0000,0000,,and then what?
Dialogue: 0,0:01:54.65,0:01:58.95,Default,,0000,0000,0000,,Well, let's create an imaginary ball,\N- this is an imaginary ball -
Dialogue: 0,0:01:58.95,0:02:02.59,Default,,0000,0000,0000,,and I give it away,\Nso what do I have left?
Dialogue: 0,0:02:03.86,0:02:06.03,Default,,0000,0000,0000,,Minus one imaginary ball.
Dialogue: 0,0:02:06.03,0:02:07.49,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:02:08.63,0:02:10.58,Default,,0000,0000,0000,,Well, the Greek mathematicians
Dialogue: 0,0:02:10.58,0:02:14.17,Default,,0000,0000,0000,,were working with length,\Nand area, and volume,
Dialogue: 0,0:02:14.17,0:02:18.85,Default,,0000,0000,0000,,so they didn't need negative numbers,\Nthey only kept the positive ones.
Dialogue: 0,0:02:18.85,0:02:22.52,Default,,0000,0000,0000,,What they did was\Neliminating the negative numbers.
Dialogue: 0,0:02:23.12,0:02:26.36,Default,,0000,0000,0000,,Now, that's a great way\Nto deal with problems, isn't it?
Dialogue: 0,0:02:26.36,0:02:30.02,Default,,0000,0000,0000,,Think about the amount of money\Nin your bank account
Dialogue: 0,0:02:30.02,0:02:32.44,Default,,0000,0000,0000,,if we could only...
Dialogue: 0,0:02:32.44,0:02:36.11,Default,,0000,0000,0000,,eliminate the negative numbers,\Nthat would be great.
Dialogue: 0,0:02:36.71,0:02:37.66,Default,,0000,0000,0000,,Yes.
Dialogue: 0,0:02:39.90,0:02:44.72,Default,,0000,0000,0000,,Negative numbers only began to appear\Nin Europe in the 15th century.
Dialogue: 0,0:02:45.58,0:02:49.62,Default,,0000,0000,0000,,And that was because scholars\Nwere translating and studying
Dialogue: 0,0:02:49.62,0:02:51.87,Default,,0000,0000,0000,,Islamic and Byzantine sources.
Dialogue: 0,0:02:52.39,0:02:57.29,Default,,0000,0000,0000,,Even the great Euler, the genius Euler,\Nwho invented the number e
Dialogue: 0,0:02:57.29,0:02:58.89,Default,,0000,0000,0000,,and much, much more,
Dialogue: 0,0:02:58.89,0:03:03.20,Default,,0000,0000,0000,,didn't quite understand\Nnegative numbers as we do today.
Dialogue: 0,0:03:05.57,0:03:10.21,Default,,0000,0000,0000,,Finally, there was a guy John Wallis,\Nan English mathematician,
Dialogue: 0,0:03:10.21,0:03:11.96,Default,,0000,0000,0000,,and he had a great idea.
Dialogue: 0,0:03:12.50,0:03:17.28,Default,,0000,0000,0000,,What he did was extending\Nthe number line to the left.
Dialogue: 0,0:03:19.25,0:03:20.90,Default,,0000,0000,0000,,Just as simple.
Dialogue: 0,0:03:20.90,0:03:23.89,Default,,0000,0000,0000,,Then it became quite clear\Nwhat a negative number was,
Dialogue: 0,0:03:23.89,0:03:27.28,Default,,0000,0000,0000,,because if you have two\Nand you subtract three,
Dialogue: 0,0:03:28.29,0:03:30.29,Default,,0000,0000,0000,,you end up in minus one.
Dialogue: 0,0:03:31.10,0:03:32.77,Default,,0000,0000,0000,,So that was quite clear.
Dialogue: 0,0:03:32.77,0:03:35.44,Default,,0000,0000,0000,,But what about complex numbers?
Dialogue: 0,0:03:35.44,0:03:39.19,Default,,0000,0000,0000,,Well, there was a Greek mathematician,\NHeron of Alexandria,
Dialogue: 0,0:03:39.19,0:03:40.74,Default,,0000,0000,0000,,and he had a great idea
Dialogue: 0,0:03:40.74,0:03:46.80,Default,,0000,0000,0000,,because in his work, the number,\Nthe square root of minus 63 appeared,
Dialogue: 0,0:03:46.80,0:03:51.48,Default,,0000,0000,0000,,and what he did was replacing it\Nby the square root of 63.
Dialogue: 0,0:03:52.01,0:03:56.11,Default,,0000,0000,0000,,So, he replaced a minus by a plus.\NNow that's even better, right?
Dialogue: 0,0:03:56.11,0:03:58.86,Default,,0000,0000,0000,,Think about the amount of money\Nin your bank account now,
Dialogue: 0,0:03:58.86,0:04:01.96,Default,,0000,0000,0000,,if we could only replace\Na minus by a plus; well, that's great!
Dialogue: 0,0:04:03.40,0:04:06.34,Default,,0000,0000,0000,,Yes, the Greeks were\Nvery inventive with numbers.
Dialogue: 0,0:04:07.11,0:04:10.23,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:04:10.23,0:04:11.41,Default,,0000,0000,0000,,They still are.
Dialogue: 0,0:04:11.41,0:04:13.58,Default,,0000,0000,0000,,(Applause)
Dialogue: 0,0:04:13.59,0:04:16.24,Default,,0000,0000,0000,,Maybe, maybe, maybe...
Dialogue: 0,0:04:16.24,0:04:20.62,Default,,0000,0000,0000,,Maybe, I don't know, maybe, that's part\Nof their current financial problem,
Dialogue: 0,0:04:20.62,0:04:22.27,Default,,0000,0000,0000,,I don't know.
Dialogue: 0,0:04:24.94,0:04:27.73,Default,,0000,0000,0000,,But if we continue the story\Nabout complex numbers,
Dialogue: 0,0:04:27.73,0:04:31.64,Default,,0000,0000,0000,,we have to time-travel to Bologna,\NRenaissance Italy, 16th century.
Dialogue: 0,0:04:31.64,0:04:34.87,Default,,0000,0000,0000,,There was a guy named Tartaglia,
Dialogue: 0,0:04:34.87,0:04:37.82,Default,,0000,0000,0000,,and he won a mathematical competition.
Dialogue: 0,0:04:39.26,0:04:42.85,Default,,0000,0000,0000,,He wrote about the solution\Nof a cubic equation,
Dialogue: 0,0:04:42.85,0:04:44.11,Default,,0000,0000,0000,,and that was really great
Dialogue: 0,0:04:44.11,0:04:48.65,Default,,0000,0000,0000,,because other mathematicians at that time\Nthought it was impossible,
Dialogue: 0,0:04:48.65,0:04:53.49,Default,,0000,0000,0000,,because it required an understanding\Nof the square root of a negative number.
Dialogue: 0,0:04:54.81,0:04:58.71,Default,,0000,0000,0000,,He even encoded his solution\Nin a form of a poem,
Dialogue: 0,0:04:59.90,0:05:04.17,Default,,0000,0000,0000,,and my Italian is not good,\Nbut let me try the first two sentences.
Dialogue: 0,0:05:04.99,0:05:06.82,Default,,0000,0000,0000,,It goes something like this:
Dialogue: 0,0:05:06.82,0:05:10.08,Default,,0000,0000,0000,,(Italian) "Quando chel cubo\Ncon le cose appresso,
Dialogue: 0,0:05:10.08,0:05:13.40,Default,,0000,0000,0000,,se agguaglia à qualche numero discreto."
Dialogue: 0,0:05:14.34,0:05:16.64,Default,,0000,0000,0000,,It was a long poem,
Dialogue: 0,0:05:16.64,0:05:19.13,Default,,0000,0000,0000,,and he made this in order to prevent
Dialogue: 0,0:05:19.13,0:05:22.60,Default,,0000,0000,0000,,that other mathematicians\Ncould steal his solution.
Dialogue: 0,0:05:23.73,0:05:29.51,Default,,0000,0000,0000,,But unfortunately, it was leaked\Nto the other guy, Cardano,
Dialogue: 0,0:05:29.51,0:05:35.08,Default,,0000,0000,0000,,and he published this proof\Nin his book "Ars magna" in 1545.
Dialogue: 0,0:05:35.64,0:05:37.71,Default,,0000,0000,0000,,But he'd promised not to do so.
Dialogue: 0,0:05:39.59,0:05:42.97,Default,,0000,0000,0000,,Tartaglia was mentioned in the book,\Nhe was acknowledged in the book,
Dialogue: 0,0:05:42.97,0:05:44.85,Default,,0000,0000,0000,,but he didn't agree, so...
Dialogue: 0,0:05:46.24,0:05:49.92,Default,,0000,0000,0000,,Tartaglia engaged Cardano\Nin a decade-long fight
Dialogue: 0,0:05:49.92,0:05:52.02,Default,,0000,0000,0000,,over the publication,
Dialogue: 0,0:05:52.02,0:05:54.84,Default,,0000,0000,0000,,and the real problem was\Nthat this Cardano guy
Dialogue: 0,0:05:54.84,0:05:58.45,Default,,0000,0000,0000,,didn't even understand\Nwhat he had written down in the book,
Dialogue: 0,0:05:58.45,0:06:02.23,Default,,0000,0000,0000,,because he called these imaginary\Nnumbers 'mental tortures.'
Dialogue: 0,0:06:04.98,0:06:09.60,Default,,0000,0000,0000,,Later on, there was another guy,\NBombelli, who is below,
Dialogue: 0,0:06:09.60,0:06:11.31,Default,,0000,0000,0000,,and he was the first one
Dialogue: 0,0:06:11.31,0:06:14.34,Default,,0000,0000,0000,,who really understood something\Nabout complex numbers.
Dialogue: 0,0:06:14.34,0:06:17.01,Default,,0000,0000,0000,,He could make the link\Nbetween the real numbers,
Dialogue: 0,0:06:17.01,0:06:19.14,Default,,0000,0000,0000,,- the normal numbers, 1, 2, 3, 4, -
Dialogue: 0,0:06:19.14,0:06:21.27,Default,,0000,0000,0000,,and the complex, imaginary numbers.
Dialogue: 0,0:06:21.27,0:06:23.00,Default,,0000,0000,0000,,So he was the first one.
Dialogue: 0,0:06:24.00,0:06:28.00,Default,,0000,0000,0000,,He introduced the symbol i\Nthat we are using today,
Dialogue: 0,0:06:28.00,0:06:31.07,Default,,0000,0000,0000,,and he made also\Nsome rules for calculating.
Dialogue: 0,0:06:31.74,0:06:34.70,Default,,0000,0000,0000,,In the 17th and 18th century,
Dialogue: 0,0:06:34.70,0:06:39.24,Default,,0000,0000,0000,,there were a lot of mathematicians\Nworking with the complex numbers,
Dialogue: 0,0:06:39.24,0:06:42.06,Default,,0000,0000,0000,,but nobody really understood\Nwhat was going on.
Dialogue: 0,0:06:42.82,0:06:45.47,Default,,0000,0000,0000,,And then, another guy came,
Dialogue: 0,0:06:45.47,0:06:49.88,Default,,0000,0000,0000,,and he made a geometrical interpretation\Nof this complex number.
Dialogue: 0,0:06:49.88,0:06:54.01,Default,,0000,0000,0000,,I will spare you the details,\N- that's homework -
Dialogue: 0,0:06:54.01,0:06:55.71,Default,,0000,0000,0000,,so I will spare you the details,
Dialogue: 0,0:06:55.71,0:07:00.42,Default,,0000,0000,0000,,you figure out yourself when you come home\Ntonight or tomorrow, I don't care.
Dialogue: 0,0:07:00.42,0:07:01.49,Default,,0000,0000,0000,,(Laughter)
Dialogue: 0,0:07:02.24,0:07:08.11,Default,,0000,0000,0000,,What he did was, he gave\Na geometrical interpretation,
Dialogue: 0,0:07:08.11,0:07:13.77,Default,,0000,0000,0000,,and he didn't create this imaginary ball,\Nno, he created an imaginary axis,
Dialogue: 0,0:07:13.77,0:07:18.74,Default,,0000,0000,0000,,so this vertical axis\Nthat is the imaginary axis.
Dialogue: 0,0:07:21.76,0:07:23.78,Default,,0000,0000,0000,,And then it became\Nquite clear what it was.
Dialogue: 0,0:07:23.78,0:07:29.48,Default,,0000,0000,0000,,A complex number was\Na 2-dimensional number: a plus i b.
Dialogue: 0,0:07:30.23,0:07:32.43,Default,,0000,0000,0000,,Then, everybody understood\Nwhat was going on.
Dialogue: 0,0:07:32.43,0:07:34.27,Default,,0000,0000,0000,,By analogy, it can be said
Dialogue: 0,0:07:34.27,0:07:38.54,Default,,0000,0000,0000,,that complex numbers were\Nnot only complex, but also absurd,
Dialogue: 0,0:07:38.54,0:07:41.56,Default,,0000,0000,0000,,until someone gave\Na geometrical interpretation.
Dialogue: 0,0:07:43.84,0:07:47.26,Default,,0000,0000,0000,,Now, I'm a math teacher and an author,
Dialogue: 0,0:07:47.26,0:07:52.11,Default,,0000,0000,0000,,and that may sound like a rare\Nor strange combination, but it isn't.
Dialogue: 0,0:07:52.11,0:07:55.41,Default,,0000,0000,0000,,I like to read stories,\Nand I like to write stories,
Dialogue: 0,0:07:55.41,0:07:59.71,Default,,0000,0000,0000,,I like doing math,\NI like to imagine the imaginary.
Dialogue: 0,0:08:01.29,0:08:03.56,Default,,0000,0000,0000,,A few years ago,
Dialogue: 0,0:08:03.56,0:08:07.91,Default,,0000,0000,0000,,I read this proof,\Nthis beautiful poem, isn't it?
Dialogue: 0,0:08:07.91,0:08:11.06,Default,,0000,0000,0000,,If you read it aloud,\Nyou can really hear the rhythm,
Dialogue: 0,0:08:11.06,0:08:12.04,Default,,0000,0000,0000,,and I know for sure
Dialogue: 0,0:08:12.04,0:08:15.72,Default,,0000,0000,0000,,that the author thought\Nlong and hard about the structure.
Dialogue: 0,0:08:15.72,0:08:21.21,Default,,0000,0000,0000,,And every word, and every sign\Nis written down with the highest care.
Dialogue: 0,0:08:22.53,0:08:26.53,Default,,0000,0000,0000,,It is taken from "Principia Mathematica",\Nbeginning of the 20th century.
Dialogue: 0,0:08:26.53,0:08:29.34,Default,,0000,0000,0000,,It's written by Alfred North Whitehead\Nand Bertrand Russell
Dialogue: 0,0:08:29.34,0:08:31.93,Default,,0000,0000,0000,,who also won\Nthe Nobel Prize in Literature.
Dialogue: 0,0:08:33.25,0:08:36.76,Default,,0000,0000,0000,,It took them over 360 pages
Dialogue: 0,0:08:36.76,0:08:40.92,Default,,0000,0000,0000,,in order to prove\Nthat one plus one equals two.
Dialogue: 0,0:08:42.89,0:08:45.19,Default,,0000,0000,0000,,So that's not so easy.
Dialogue: 0,0:08:46.38,0:08:49.76,Default,,0000,0000,0000,,Now, mathematics and literature\Nhave something in common.
Dialogue: 0,0:08:49.76,0:08:54.63,Default,,0000,0000,0000,,They've been a part of our human culture\Nfor thousands of years.
Dialogue: 0,0:08:54.63,0:08:57.68,Default,,0000,0000,0000,,They are more interrelated\Nthan you might think,
Dialogue: 0,0:08:57.68,0:09:01.33,Default,,0000,0000,0000,,and I think mathematics can learn\Nsomething from literature.
Dialogue: 0,0:09:02.22,0:09:05.85,Default,,0000,0000,0000,,Instead of giving you\Nthe definition of a complex number
Dialogue: 0,0:09:05.85,0:09:08.34,Default,,0000,0000,0000,,and giving some rules for calculating,
Dialogue: 0,0:09:08.34,0:09:10.46,Default,,0000,0000,0000,,I told you a story.
Dialogue: 0,0:09:13.05,0:09:18.31,Default,,0000,0000,0000,,In my talk, I made the case for telling\Nstories in mathematical education
Dialogue: 0,0:09:18.31,0:09:21.11,Default,,0000,0000,0000,,instead of endless algebra exercises.
Dialogue: 0,0:09:22.02,0:09:23.78,Default,,0000,0000,0000,,Without stories,
Dialogue: 0,0:09:23.78,0:09:26.60,Default,,0000,0000,0000,,mathematics become maybe boring,
Dialogue: 0,0:09:26.60,0:09:28.91,Default,,0000,0000,0000,,and without stories,
Dialogue: 0,0:09:28.91,0:09:33.11,Default,,0000,0000,0000,,some important aspects of mathematics\Nare left out of the curriculum.
Dialogue: 0,0:09:33.11,0:09:37.58,Default,,0000,0000,0000,,Think about the history of mathematics,\Nthink about the philosophy of mathematics,
Dialogue: 0,0:09:37.58,0:09:40.78,Default,,0000,0000,0000,,and think about the applications\Nof mathematics.
Dialogue: 0,0:09:42.40,0:09:46.38,Default,,0000,0000,0000,,I've seen too many students\Nthat don't follow mathematics
Dialogue: 0,0:09:46.38,0:09:49.10,Default,,0000,0000,0000,,because of the way we teach the subject.
Dialogue: 0,0:09:49.91,0:09:51.75,Default,,0000,0000,0000,,And this, ladies and gentlemen,
Dialogue: 0,0:09:51.75,0:09:55.18,Default,,0000,0000,0000,,can only be improved by telling stories.
Dialogue: 0,0:09:55.18,0:09:56.29,Default,,0000,0000,0000,,Thank you.
Dialogue: 0,0:09:56.29,0:09:57.74,Default,,0000,0000,0000,,(Applause)