[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.43,0:00:01.85,Default,,0000,0000,0000,,What I want to do\Nin this video is
Dialogue: 0,0:00:01.85,0:00:04.69,Default,,0000,0000,0000,,think about the\Norigins of algebra.
Dialogue: 0,0:00:04.69,0:00:08.39,Default,,0000,0000,0000,,The origins of\Nalgebra, and the word,
Dialogue: 0,0:00:08.39,0:00:10.64,Default,,0000,0000,0000,,especially in association\Nwith the ideas
Dialogue: 0,0:00:10.64,0:00:15.62,Default,,0000,0000,0000,,that algebra now represents,\Ncomes from this book,
Dialogue: 0,0:00:15.62,0:00:17.95,Default,,0000,0000,0000,,or actually this is a page\Nof the book right over there.
Dialogue: 0,0:00:17.95,0:00:20.43,Default,,0000,0000,0000,,The English translation\Nfor the title of this book
Dialogue: 0,0:00:20.43,0:00:23.05,Default,,0000,0000,0000,,is the "Compendious\NBook on Calculation
Dialogue: 0,0:00:23.05,0:00:25.28,Default,,0000,0000,0000,,by Completion and Balancing."
Dialogue: 0,0:00:25.28,0:00:29.12,Default,,0000,0000,0000,,And it was written by a\NPersian mathematician who
Dialogue: 0,0:00:29.12,0:00:32.05,Default,,0000,0000,0000,,lived in Baghdad\Nin, I believe, it
Dialogue: 0,0:00:32.05,0:00:33.51,Default,,0000,0000,0000,,was in the eighth\Nor ninth century.
Dialogue: 0,0:00:33.51,0:00:37.74,Default,,0000,0000,0000,,I believe it was actually 820\NAD when he wrote this book.
Dialogue: 0,0:00:37.74,0:00:38.62,Default,,0000,0000,0000,,AD.
Dialogue: 0,0:00:38.62,0:00:42.73,Default,,0000,0000,0000,,And algebra is the Arabic word,\Nthat here is the actual title
Dialogue: 0,0:00:42.73,0:00:45.07,Default,,0000,0000,0000,,that he gave to it, which\Nis the Arabic title.
Dialogue: 0,0:00:45.07,0:00:47.46,Default,,0000,0000,0000,,Algebra means restoration\Nor completion.
Dialogue: 0,0:00:50.60,0:00:55.11,Default,,0000,0000,0000,,Restoration or completion.
Dialogue: 0,0:00:55.11,0:00:58.38,Default,,0000,0000,0000,,And he associated it in his book\Nwith a very specific operation,
Dialogue: 0,0:00:58.38,0:01:01.49,Default,,0000,0000,0000,,really taking something\Nfrom one side of an equation
Dialogue: 0,0:01:01.49,0:01:03.66,Default,,0000,0000,0000,,to another side of an equation.
Dialogue: 0,0:01:03.66,0:01:05.45,Default,,0000,0000,0000,,But we can actually\Nsee it right over here,
Dialogue: 0,0:01:05.45,0:01:07.08,Default,,0000,0000,0000,,and I don't know\NArabic, but I actually
Dialogue: 0,0:01:07.08,0:01:08.55,Default,,0000,0000,0000,,do know some\Nlanguages that seems
Dialogue: 0,0:01:08.55,0:01:10.33,Default,,0000,0000,0000,,to have borrowed a\Nlittle bit from Arabic,
Dialogue: 0,0:01:10.33,0:01:12.31,Default,,0000,0000,0000,,or maybe it went the\Nother way around.
Dialogue: 0,0:01:12.31,0:01:15.77,Default,,0000,0000,0000,,But this says Al-kitab,\Nand I know just enough
Dialogue: 0,0:01:15.77,0:01:18.35,Default,,0000,0000,0000,,Urdu and Hindi to understand\Na good India movie,
Dialogue: 0,0:01:18.35,0:01:20.17,Default,,0000,0000,0000,,but Al-kitab, kitab means book.
Dialogue: 0,0:01:20.17,0:01:22.55,Default,,0000,0000,0000,,So this part is book.
Dialogue: 0,0:01:22.55,0:01:23.17,Default,,0000,0000,0000,,Book.
Dialogue: 0,0:01:23.17,0:01:26.82,Default,,0000,0000,0000,,Al-mukhtasar, well, I think\Nthat means compendious,
Dialogue: 0,0:01:26.82,0:01:28.69,Default,,0000,0000,0000,,because I don't know\Nthe word for compendious
Dialogue: 0,0:01:28.69,0:01:29.93,Default,,0000,0000,0000,,and that seems like that.
Dialogue: 0,0:01:29.93,0:01:33.17,Default,,0000,0000,0000,,Fihisab, hisab means\Ncalculation in Hindi or Urdu,
Dialogue: 0,0:01:33.17,0:01:35.21,Default,,0000,0000,0000,,so this is calculation.
Dialogue: 0,0:01:35.21,0:01:36.30,Default,,0000,0000,0000,,Calculation.
Dialogue: 0,0:01:36.30,0:01:38.50,Default,,0000,0000,0000,,Al-gabr, this is the root.
Dialogue: 0,0:01:38.50,0:01:41.11,Default,,0000,0000,0000,,This is the famous algebra,\Nthis is where it shows up.
Dialogue: 0,0:01:41.11,0:01:45.52,Default,,0000,0000,0000,,So this is for completion, you\Ncould view that as completion.
Dialogue: 0,0:01:45.52,0:01:46.45,Default,,0000,0000,0000,,Completion.
Dialogue: 0,0:01:46.45,0:01:52.05,Default,,0000,0000,0000,,And then wa'l-muqabala, and that\Nmeans essentially balancing.
Dialogue: 0,0:01:52.05,0:01:52.66,Default,,0000,0000,0000,,Balancing.
Dialogue: 0,0:01:52.66,0:01:55.30,Default,,0000,0000,0000,,Completion and balancing.
Dialogue: 0,0:01:55.30,0:01:56.68,Default,,0000,0000,0000,,So if we wanted\Nto translate it--
Dialogue: 0,0:01:56.68,0:01:58.89,Default,,0000,0000,0000,,I know this isn't a video\Non translating Arabic,
Dialogue: 0,0:01:58.89,0:02:04.10,Default,,0000,0000,0000,,but the book, I guess\Nthis is saying compendious
Dialogue: 0,0:02:04.10,0:02:10.72,Default,,0000,0000,0000,,on calculation by\Ncompletion and balancing
Dialogue: 0,0:02:10.72,0:02:12.58,Default,,0000,0000,0000,,is the rough translation\Nright over there.
Dialogue: 0,0:02:12.58,0:02:15.47,Default,,0000,0000,0000,,But that is the source\Nof the word algebra,
Dialogue: 0,0:02:15.47,0:02:17.94,Default,,0000,0000,0000,,and this is a very, very,\Nvery important book.
Dialogue: 0,0:02:17.94,0:02:20.70,Default,,0000,0000,0000,,Not just because it was the\Nfirst use of the word algebra,
Dialogue: 0,0:02:20.70,0:02:24.72,Default,,0000,0000,0000,,but many people viewed\Nthis book as the first time
Dialogue: 0,0:02:24.72,0:02:29.80,Default,,0000,0000,0000,,that algebra took a\Nlot of its modern--
Dialogue: 0,0:02:29.80,0:02:31.94,Default,,0000,0000,0000,,took on many of\Nits modern ideas.
Dialogue: 0,0:02:31.94,0:02:34.24,Default,,0000,0000,0000,,Ideas of balancing an equation.
Dialogue: 0,0:02:34.24,0:02:36.32,Default,,0000,0000,0000,,The abstract problem\Nitself, not trying
Dialogue: 0,0:02:36.32,0:02:38.54,Default,,0000,0000,0000,,to do one off problems\Nhere or there.
Dialogue: 0,0:02:38.54,0:02:42.16,Default,,0000,0000,0000,,But al-Khwarizmi was\Nnot the first person,
Dialogue: 0,0:02:42.16,0:02:44.64,Default,,0000,0000,0000,,and just to get an idea of\Nwhere all this is happening.
Dialogue: 0,0:02:44.64,0:02:47.12,Default,,0000,0000,0000,,So he was hanging\Nout in Baghdad,
Dialogue: 0,0:02:47.12,0:02:48.58,Default,,0000,0000,0000,,and this part of\Nthe world shows up
Dialogue: 0,0:02:48.58,0:02:50.13,Default,,0000,0000,0000,,a lot in the history of algebra.
Dialogue: 0,0:02:50.13,0:02:51.65,Default,,0000,0000,0000,,But he was hanging\Nout right there
Dialogue: 0,0:02:51.65,0:02:54.05,Default,,0000,0000,0000,,in around the eighth\Nor ninth century.
Dialogue: 0,0:02:54.05,0:02:56.15,Default,,0000,0000,0000,,So let me draw a\Ntime line here, just
Dialogue: 0,0:02:56.15,0:02:58.23,Default,,0000,0000,0000,,so we can appreciate everything.
Dialogue: 0,0:02:58.23,0:03:03.59,Default,,0000,0000,0000,,So that is timeline,\Nand then whether or not
Dialogue: 0,0:03:03.59,0:03:06.71,Default,,0000,0000,0000,,you are religious, most\Nof our modern dates
Dialogue: 0,0:03:06.71,0:03:11.72,Default,,0000,0000,0000,,are dependent on the birth of\NJesus, so that is right there.
Dialogue: 0,0:03:11.72,0:03:13.90,Default,,0000,0000,0000,,Maybe I'll put a cross\Nover there to signify that.
Dialogue: 0,0:03:13.90,0:03:15.28,Default,,0000,0000,0000,,When we want to\Nbe non-religious,
Dialogue: 0,0:03:15.28,0:03:17.11,Default,,0000,0000,0000,,we say the common era.
Dialogue: 0,0:03:17.11,0:03:19.75,Default,,0000,0000,0000,,Before the common era, when\Nwe want to be religious
Dialogue: 0,0:03:19.75,0:03:22.53,Default,,0000,0000,0000,,we say AD, which means\Nin the year of our lord.
Dialogue: 0,0:03:22.53,0:03:25.12,Default,,0000,0000,0000,,I don't know the Latin,\NAnno Domini, I believe,
Dialogue: 0,0:03:25.12,0:03:26.22,Default,,0000,0000,0000,,year of our lord.
Dialogue: 0,0:03:26.22,0:03:28.97,Default,,0000,0000,0000,,And then when we want--\Nin the religious context,
Dialogue: 0,0:03:28.97,0:03:32.18,Default,,0000,0000,0000,,instead of saying before common\Nera, we say before Christ, BC.
Dialogue: 0,0:03:32.18,0:03:36.79,Default,,0000,0000,0000,,But either way, so this\Nis 1000 in the common era.
Dialogue: 0,0:03:36.79,0:03:39.66,Default,,0000,0000,0000,,This is 2000 in the common era.
Dialogue: 0,0:03:39.66,0:03:41.53,Default,,0000,0000,0000,,And obviously, we are\Nsitting-- at least when
Dialogue: 0,0:03:41.53,0:03:44.40,Default,,0000,0000,0000,,I'm making this video, I'm\Nsitting right about there.
Dialogue: 0,0:03:44.40,0:03:48.56,Default,,0000,0000,0000,,And then this is 1000\Nbefore the common era,
Dialogue: 0,0:03:48.56,0:03:52.21,Default,,0000,0000,0000,,and this is 2000\Nbefore the common era.
Dialogue: 0,0:03:52.21,0:03:54.56,Default,,0000,0000,0000,,So the first traces--\Nand I'm skipping out,
Dialogue: 0,0:03:54.56,0:03:56.19,Default,,0000,0000,0000,,and really, it's just\Nwhat we can find.
Dialogue: 0,0:03:56.19,0:03:57.42,Default,,0000,0000,0000,,I'm sure if we were\Nable to dig more,
Dialogue: 0,0:03:57.42,0:03:59.04,Default,,0000,0000,0000,,we might be able to\Nfind other evidence
Dialogue: 0,0:03:59.04,0:04:02.08,Default,,0000,0000,0000,,of different civilizations\Nand different people stumbling
Dialogue: 0,0:04:02.08,0:04:04.72,Default,,0000,0000,0000,,on many of the ideas in algebra.
Dialogue: 0,0:04:04.72,0:04:07.43,Default,,0000,0000,0000,,But our first records of\Npeople really exploring
Dialogue: 0,0:04:07.43,0:04:09.69,Default,,0000,0000,0000,,the ideas that are\Nhit upon in algebra
Dialogue: 0,0:04:09.69,0:04:13.59,Default,,0000,0000,0000,,come from ancient\NBabylon around 2000 years
Dialogue: 0,0:04:13.59,0:04:16.16,Default,,0000,0000,0000,,before the common\Nera, before Christ.
Dialogue: 0,0:04:16.16,0:04:22.56,Default,,0000,0000,0000,,So right around there\Nthere are stone tablets
Dialogue: 0,0:04:22.56,0:04:24.27,Default,,0000,0000,0000,,where it looks like\Npeople were exploring
Dialogue: 0,0:04:24.27,0:04:26.08,Default,,0000,0000,0000,,some of the fundamental\Nideas of algebra.
Dialogue: 0,0:04:26.08,0:04:27.88,Default,,0000,0000,0000,,They weren't using\Nthe same symbols.
Dialogue: 0,0:04:27.88,0:04:30.78,Default,,0000,0000,0000,,They weren't using the same ways\Nof representing the numbers,
Dialogue: 0,0:04:30.78,0:04:33.09,Default,,0000,0000,0000,,but it was algebra that\Nthey were working on.
Dialogue: 0,0:04:33.09,0:04:35.43,Default,,0000,0000,0000,,And that was, once again,\Nin this part of the world.
Dialogue: 0,0:04:35.43,0:04:38.76,Default,,0000,0000,0000,,Babylon was right about there.
Dialogue: 0,0:04:38.76,0:04:42.72,Default,,0000,0000,0000,,And Babylon, it's kind of\Nkept the tradition of Sumeria.
Dialogue: 0,0:04:42.72,0:04:44.92,Default,,0000,0000,0000,,This whole region was\Ncalled Mesopotamia,
Dialogue: 0,0:04:44.92,0:04:47.29,Default,,0000,0000,0000,,Greek for between two rivers.
Dialogue: 0,0:04:47.29,0:04:49.23,Default,,0000,0000,0000,,But that's the first\Ntraces of people
Dialogue: 0,0:04:49.23,0:04:51.27,Default,,0000,0000,0000,,that we know of that\Nwhere people were starting
Dialogue: 0,0:04:51.27,0:04:54.55,Default,,0000,0000,0000,,to do what we would\Ncall real, real algebra.
Dialogue: 0,0:04:54.55,0:04:55.89,Default,,0000,0000,0000,,And then you fast forward.
Dialogue: 0,0:04:55.89,0:04:57.60,Default,,0000,0000,0000,,And I'm sure we're\Nmissing-- and I'm sure
Dialogue: 0,0:04:57.60,0:05:01.96,Default,,0000,0000,0000,,even our historians don't know\Nall of the different instances
Dialogue: 0,0:05:01.96,0:05:08.30,Default,,0000,0000,0000,,of people using algebra, but the\Nmajor contributions to algebra,
Dialogue: 0,0:05:08.30,0:05:11.45,Default,,0000,0000,0000,,we saw it here in\NBabylon 2000 years ago.
Dialogue: 0,0:05:11.45,0:05:13.99,Default,,0000,0000,0000,,And then if we fast\Nforward to about 200 to 300
Dialogue: 0,0:05:13.99,0:05:17.31,Default,,0000,0000,0000,,AD, so right over there,\Nyou have a Greek gentleman
Dialogue: 0,0:05:17.31,0:05:18.87,Default,,0000,0000,0000,,who lived in Alexandria.
Dialogue: 0,0:05:18.87,0:05:21.02,Default,,0000,0000,0000,,So this is Greece\Nright over here,
Dialogue: 0,0:05:21.02,0:05:23.21,Default,,0000,0000,0000,,but he lived in Alexandria,\Nwhich at the time
Dialogue: 0,0:05:23.21,0:05:25.24,Default,,0000,0000,0000,,was part of the Roman Empire.
Dialogue: 0,0:05:25.24,0:05:27.89,Default,,0000,0000,0000,,So Alexandria is\Nright over here,
Dialogue: 0,0:05:27.89,0:05:30.63,Default,,0000,0000,0000,,and he was a gentleman by\Nthe name of Diophantus,
Dialogue: 0,0:05:30.63,0:05:31.89,Default,,0000,0000,0000,,or Diophantus.
Dialogue: 0,0:05:31.89,0:05:36.30,Default,,0000,0000,0000,,I don't know how to\Npronounce it, Diophantus.
Dialogue: 0,0:05:36.30,0:05:38.55,Default,,0000,0000,0000,,And he is sometimes\Ncredited with being
Dialogue: 0,0:05:38.55,0:05:41.33,Default,,0000,0000,0000,,the father of algebra,\Nand it's debatable
Dialogue: 0,0:05:41.33,0:05:44.20,Default,,0000,0000,0000,,whether it's Diophantus\Nor al-Khwarizmi.
Dialogue: 0,0:05:44.20,0:05:45.77,Default,,0000,0000,0000,,al-Khwarizmi, who\Nkind of started
Dialogue: 0,0:05:45.77,0:05:48.32,Default,,0000,0000,0000,,using these terms of\Nbalancing equations
Dialogue: 0,0:05:48.32,0:05:50.05,Default,,0000,0000,0000,,and talking about\Nmath in a purer way,
Dialogue: 0,0:05:50.05,0:05:53.37,Default,,0000,0000,0000,,while Diophantus was more\Nfocused on particular problems.
Dialogue: 0,0:05:53.37,0:05:55.84,Default,,0000,0000,0000,,And both of them were\Nkind of beat to the punch
Dialogue: 0,0:05:55.84,0:05:57.78,Default,,0000,0000,0000,,by the Babylonians,\Nalthough they all
Dialogue: 0,0:05:57.78,0:05:59.17,Default,,0000,0000,0000,,did contribute in their own way.
Dialogue: 0,0:05:59.17,0:06:00.14,Default,,0000,0000,0000,,It's not like they\Nwere just copying
Dialogue: 0,0:06:00.14,0:06:01.37,Default,,0000,0000,0000,,what the Babylonians did.
Dialogue: 0,0:06:01.37,0:06:03.23,Default,,0000,0000,0000,,They had their own\Nunique contributions
Dialogue: 0,0:06:03.23,0:06:06.36,Default,,0000,0000,0000,,to what we now consider algebra.
Dialogue: 0,0:06:06.36,0:06:08.17,Default,,0000,0000,0000,,But many, especially\NWestern historians,
Dialogue: 0,0:06:08.17,0:06:11.48,Default,,0000,0000,0000,,associate Diophantus as\Nthe father of algebra.
Dialogue: 0,0:06:11.48,0:06:13.58,Default,,0000,0000,0000,,And now, al-Khwarizmi\Nis sometimes
Dialogue: 0,0:06:13.58,0:06:16.39,Default,,0000,0000,0000,,what other people would argue\Nas the father of algebra,
Dialogue: 0,0:06:16.39,0:06:18.29,Default,,0000,0000,0000,,so he made significant\Ncontributions.
Dialogue: 0,0:06:18.29,0:06:22.20,Default,,0000,0000,0000,,And if you go to 600 AD-- so\Nif you go to about 600 AD,
Dialogue: 0,0:06:22.20,0:06:26.14,Default,,0000,0000,0000,,another famous mathematician\Nin the history of algebra
Dialogue: 0,0:06:26.14,0:06:29.20,Default,,0000,0000,0000,,was Brahmagupta, in India.
Dialogue: 0,0:06:29.20,0:06:32.58,Default,,0000,0000,0000,,Brahmagupta, in India.
Dialogue: 0,0:06:32.58,0:06:34.18,Default,,0000,0000,0000,,So obviously, and\Nactually, I don't
Dialogue: 0,0:06:34.18,0:06:35.49,Default,,0000,0000,0000,,know where in India he lived.
Dialogue: 0,0:06:35.49,0:06:37.90,Default,,0000,0000,0000,,I should look that\Nup, but roughly
Dialogue: 0,0:06:37.90,0:06:39.44,Default,,0000,0000,0000,,in that part of the world.
Dialogue: 0,0:06:39.44,0:06:41.66,Default,,0000,0000,0000,,And he also made\Nsignificant contributions.
Dialogue: 0,0:06:44.29,0:06:45.79,Default,,0000,0000,0000,,And then you have\Nal-Khwarizmi, who
Dialogue: 0,0:06:45.79,0:06:50.53,Default,,0000,0000,0000,,shows up right\Nthere, al-Khwarizmi.
Dialogue: 0,0:06:50.53,0:06:53.56,Default,,0000,0000,0000,,And he is the gentleman\Nthat definitely
Dialogue: 0,0:06:53.56,0:06:56.81,Default,,0000,0000,0000,,we credit with the name\Nalgebra, comes from Arabic
Dialogue: 0,0:06:56.81,0:07:00.08,Default,,0000,0000,0000,,for restoration, and some\Npeople also consider him to be,
Dialogue: 0,0:07:00.08,0:07:02.17,Default,,0000,0000,0000,,if not the father of\Nalgebra, although some people
Dialogue: 0,0:07:02.17,0:07:05.37,Default,,0000,0000,0000,,say he is the father, he is\None of the fathers of algebra
Dialogue: 0,0:07:05.37,0:07:08.34,Default,,0000,0000,0000,,because he really started\Nto think about algebra
Dialogue: 0,0:07:08.34,0:07:11.41,Default,,0000,0000,0000,,in the abstract sense, devoid\Nof some specific problems
Dialogue: 0,0:07:11.41,0:07:13.44,Default,,0000,0000,0000,,and a lot of the way\Na modern mathematician
Dialogue: 0,0:07:13.44,0:07:17.11,Default,,0000,0000,0000,,would start to think\Nabout the field.