April 28, 2014 • 25 mins
Algebra doesn't have one single origin point -- it developed over time and in multiple places, with many mathematicians contributing. One of those contributors was an 8th-century scholar from Baghdad named Muhammad ibn Musa al-Khwarizmi. Read the show notes here.
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Speaker 1 (00:00):
This episode of Stuff You Missed in History Class is
brought to you by Squarespace, the all in one platform
that makes it fast and easy to create your own
professional website, portfolio, and online store. For a free trial
and ten percent off, visits squarespace dot com, slash history
and enter offer code history at check out. A better
web starts with your website. Welcome to Stuff you Missed
(00:23):
in History Class from how Stuff Works dot com. Hello,
and welcome to the podcast. I'm Holly Fry and I'm
Tracy V. Wilson and Uh. Today's topic was inspired by
an event that I got to go to last week
because I'm super lucky. I got to go see Neil
(00:45):
de grass Tyson speak at Georgia Tech, which was sponsored
I believed, by their physics department. And during his lecture,
which was spectacular, if you ever get a chance to
see him speak, I highly recommend it. Uh, he mentioned
that most people do not realize what an epicenter of
scientific and mathematical grow with medieval Islam was h So
naturally I got all excited about it because it was
(01:05):
fascinating and Neil de Grasse Tyson was saying it, which
automatically puts it above many other things on the interest scale.
So we're going to talk about math today. Do not
become scared or frightened. Like I know Tracy's mentioned before,
arithmetic is not her jam. I'm not particularly good at
it well, And what's funny is arithmetic was really the problem.
Like I loved geometry and I loved doing proofs, but
(01:27):
when it came to like the arithmetic portions of the proofs,
I would get things wrong. Same thing with algebra, Like
my algebra theory would be sound and my arithmetic would
be faulty. Yeah, I think that's pretty common. So we're
gonna talk about math, but really only sort of. There
will be a couple of equations mentioned, but they're super
duper simple and they stand as examples only. You do
(01:49):
not have to solve for X or any other letter
while you're listening. I love math in theory, but like Tracy,
the actual reality of it is not always my strong suit.
So but leave me when I say that the math
that we mentioned is really really basic. And I apologize
to any mathematicians in the crowd that may have been
hoping for more, but that's that's not gonna happen on
this one. So today we are focusing on an Islamic
(02:12):
mathematician named al khara is Me and his contributions to
the development of algebra and mathematics in general with his
ninth ninth century writings. So if you're going to guess
where algebra originated, you might guess ancient Greece or ancient room.
Even though we're talking about an Arabic scholar today, it's
important to remember that algebra does not have just one
(02:34):
single origin point. It developed over time and in multiple places,
with lots of different mathematicians contributing to the overall field
of knowledge. Yeah. I mean, it wasn't like someone woke
up one day and went, I'm inventing algebra. I'm imagining
somebody just sitting bolt up right in their bad No.
It arose out of a need for a way to
calculate certain things. And we'll talk about that more specifically
(02:57):
as we go on. The first traces of the concepts
and fundamental ideas of algebra that we know of are
from ancient Babylon and these fall around about two thousand BC.
And then in the third century, Diaphantus of Alexandria, who
is sometimes called the father of algebra was writing extensively
about algebraic equations and some of the concepts of algebra.
(03:22):
Uh there was also an Indian math scholar named Brahmagupta
who was writing extensively in the six hundreds, and he's
considered a major influence on al qai is Me. Muhammad
ibn Musa al quare is Me was born around seven
eighty and we don't know a lot about his early life,
as is often a case with figures from that long ago.
His exact place of birth is also kind of muddled
(03:44):
by his name because it includes an origin signifier that
it cited differently in various texts. We do know that
he's spent a significant amount of his life in Baghdad,
and he grew up, as we know, to be a
mathematician and an astronomer, and as an adult he worked
at the Dar al Hikma or House of Wisdom, and
the work of the House of Wisdom, which was a
(04:05):
sort of scholarly academy that's sometimes likened to the Library
at Alexandria, focused on the acquisition and translation of text
from throughout the world. The House of Wisdom may have
been established by Kalif Haroun al Rashid, but Kelif al Mamun,
who followed him is often recognized as the man who
really made it into a seat of scholarly discovery. And
(04:28):
before we get into sort of the most famous book
that al quires me worked on, we're going to do
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think domain dot com. Okay, So now we will get
back to the work that is primarily talked about when
people discuss alcoa is Me and his influence on algebra,
and that was called Alcatab al Muktazar fijis Ab Algebar
(05:33):
while Muka or the Compendious Book on Calculation by Completion
and Balancing, and it was written by alcoa is Me
and published through the House of Wisdom, which produced original
works as well as working on all of the translations
we mentioned. The introduction to this book notes that Khalif
al ma Moon and his thirst for scientific knowledge drove
al quare is Me to take on this whole project. Yeah,
(05:54):
that kind of supports the idea that Khalif al Mamon
was really the one that that made the House of
Wisdom flourish. And this book addresses the idea of balancing
and equation across the equal sign in a systematic way
and it features examples of ways that this can be
applied to fiscal transactions. And the book's goal was to provide, quote,
(06:15):
what is easiest and most youthful in arithmetic, such as
men constantly require in cases of inheritance, legacies, partition, lawsuits
and trade and in all their dealings with one another.
Or whether measuring of lands, the digging of canals, geometrical computations,
and other objects of various sorts and kinds are concerned.
The algebar portion of the Arabic title is what gave
(06:38):
algebra it's name. In the Latin translation of the text
several hundred years later in the twelfth century, the actual
translation of the Arabic word algebar is reunion or reunion
of broken parts. Yet also algebra. The word is also
associated with bone setters. Uh so if you ever hear
it used in that terminology, that's why they both share
(06:59):
the same words, and the words jabar andabla signify operations
in this early state algebraic problem solving of quadratic equations.
Jabar names the operation where a numerical value is eliminated
from one side of an equation and incorporated onto the
(07:19):
other side to solve for an unknown So, for example,
if x plus four equals nine, then the act of
subtracting four from both sides to solve for X is
the Jabar step, and muccabla is an operation which cancels
out duplicate elements of an equation to balance it. So again,
for an example, if you start with X minus y
(07:41):
equals twelve minus why y can be eliminated from both
sides of the equation to solve for X equals twelve. Again,
I apologize to the mathematicians in the crowd, because I'm
sure they're like, this is the silliest way to explain this,
but we're giving it very, very simple. In this book Alcorism.
He also establishes that all the problems that talks about
can be reduced down to one of six forms. We
(08:03):
should really note that he's speaking about them in terms
of rhetoric and not as hard equation. Yeah, you don't
actually see a lot of mathematical equations in some of
the translations they come about, but he basically was writing
out like how to divide a thing by another thing?
And it's not numeracle at this point. And the book
is laid out in three separate sections, and the first
(08:26):
section is really the only one that speaks of algebraic concepts,
though again they're not represented with figures, but they're written out.
The second portion of the book, which is headed on
business transactions, includes practical examples of measuring out ownership and proportions,
and also includes guides for measuring out geometrical shapes such
as cones and pyramids for the calculation of volumes and
(08:48):
also for surveying needs. The third section of the book
deals entirely with legacies, in other words, inheritances. Islamic inheritance
law can be extremely complex and it involves value wation
of all the airs proportionate entitlement shares in relation to
one another. So this last section of the book is
composed entirely of example problems about dealing with inheritances. Yeah,
(09:13):
it's I've read a little bit about Islamic inheritance law,
and I'm admittedly coming at it from a completely green perspective.
It is so complex, Uh, the way they sort of
measure out different people's what they're entitled to based on
who else is in the family, the sex of people
(09:33):
in the family. Uh, and it's all, you know, based
in religious texts. So it's something that is very serious,
but it is very hard to figure out. So this
was really hugely helpful. And I have to giggle a
little bit at the fact that most school students today
learning algebra and I did it too, So I apologized
to my many fabulous math teachers. Is that they will
(09:55):
never need this stuff in real life. But the whole
point of al core Me's text is designed entirely to
solve practical, day to day problems that require mathematical computation.
So it just kind of made me laugh that the
origins of algebra are entirely in real life needs, not
in abstract things that you feel like you're learning in school.
(10:17):
I will say I've used algebra in my day to
day life sometimes. Yeah, I use it in my day
to day life in the podcast to calculate how many
more things we have than we did a month ago,
because I am interested in that as trivia. Yeah, But
that was not the only book written by alcoa is Me. No,
(10:39):
there was another mathematical book. Although we don't have the
original text. The earliest example we have is a twelfth
century Latin translation. It boils down to alcoa is Me
concerning the Hindu art of reckoning. Yeah, and the original
title was Algorithm Numero indorham And this work was largely
(10:59):
bay based on the work of an Indian mathematician, Brahmagupta,
who we mentioned earlier, who lived from five to six seventy. Roughly,
there isn't always consensus about the order in which alcoris
Meet wrote his books because the historical record is unclear.
But we do know that the book on Hindu Numerals
came after the compendious book on Calculation by Completion and Balancing,
(11:20):
because it refers to the algebra in that volume. Yeah,
it refers to that earlier book. Uh. And you likely
noticed similarity between the first word of the Latin title
algorithmy and the word algorithm, and that is absolutely no accident.
Algorithm came from the translation of Alcorism's name, so he's
responsible for two pretty big, fundamental important words in mathematics.
(11:43):
This book introduced the Indian numerical system into the Arabic
world and eventually to a greater audience. It features the
numerals one through nine, plus The concept of zero zero
as an idea had been toyed with by a few
different cultures by this time, including the Maya and the Babylonians,
so it's not as though Alcorismy just invented it out
of whole cloth, but his translated texts identifying it in
(12:08):
the Indian mathematical system made their way across Europe in
the twelfth century and helped cement the concept of a
numeral to represent nothing. Yeah, there wasn't always a zero
in competition. And if you're into the cultural identity of
zero in its place in history, which is to me
really fascinating. Uh. There's a great book that I highly
recommend called The Nothing that is a natural history of zero,
(12:29):
and it's written by Robert Kaplan. I didn't really use
it as a source for this, so it's not going
to be in the source notes, but I wanted to
mention it. I think we have how zero works as
an article on how st works also we do. Additionally,
the Indian concept of decimal numbers is discussed in the
book and eventually leads to the idea spreading as the
work is translated and shared. Once again, this is an
(12:51):
idea that had been blossoming in other places, including China. Yeah,
I mean he uh, neither Brahmagupta nor alcorism really the
to recognize that we needed some way to identify smaller
parts of things. But this really kind of gave it
a foothold in mathematical texts. And while we're focusing on
(13:15):
mathematics and how alcors may contributed to that field, we
should also take a quick moment to discuss his work
in geography and astronomy. A writing entitled kitab Surat Alided,
which translates to the image of the Earth, was a
geography book based largely on the work of Ptolemy in
his book Geographia. Algorithm built on what Ptolemy had established
(13:38):
by calculating significantly improved measurements for several parts of the globe,
and the Arabic scholar was also instrumental in creating what
was one of the first world maps. His astronomy work
encompassed calendars, the positions of heavenly bodies, and even eclipse calculations.
He compiled a book of astronomical tables which was translated
into multiple languages, including Chinese. Uh. And before we talk
(14:02):
about sort of how his work spread through Europe, we're
gonna take a quick pause for a moment, So back
to Alcorismy. Yeah, Alcorismi died in eight fifty, so he
never saw the introduction of his work to the European
scholarly community. There's not much in the way of record
of what he died from. He's believed to have died
in Baghdad, where he had been living but that's kind
(14:22):
of all we know. Robert of Chester, who was an
Englishman working in Spain at the time, translated alcorithms algebra
text in the eleven forties, and this translation, with a
very lengthy intro, is on archive dot org and we
will put it in the show notes. It, as well
as Alcorithm's other work, was also translated by Gerard of
Cremona around eleven fifty and Gugliemo de Lunis around twelve fifty.
(14:46):
And once it was translated, Alcorismy's work became a significant
influence on the European development of mathematics, and it was
used as a standard textbook on algebra throughout Europe well
into the sixteenth century. What made the introduction of algebra
inda Europe at this time so significant is that it
moved away from the geometry based mathematics of Greece, and
it also expanded the mathematical landscape significantly, so rational interrrational
(15:10):
numbers were welcome at the algebra table, and that allowed
math to flourish in new ways. Yeah, it kind of
just was a whole new gear of thinking about math
and how numbers could be used. And I feel like
I should mention a thing that I discovered while I
was researching that was unbeknownst to me before we had
gotten into this topic. There are some very vehement folks
(15:32):
in the world with Internet presences who really really want
to discredit Alcorithmy's contributions, and they're coming at it from
an anti Islamic mindset, and they seemed to use the
fact that Alcorismi was building on the work of mathematicians
that came before him as some sort of like gotcha,
like they caught him plagiarizing, And it kind of ignores
(15:54):
the fact that virtually every line of academic research and
discovery builds on what has come before and preceded it,
and also the fact that sometimes certain concepts are developing
independently in multiple places and cultures at one time, or
even at different times, but that aren't communicated. And I
wanted to bring this up as I found it very
troubling and it's really bizarre because some of these are
(16:17):
kind of cloaked in a seeming academia layout, Like I
find these websites that I was like, oh, this is interesting,
and I'm trying to fact check it, and some of
this checks out and then it would suddenly become like
sort of really racist and weird, very like this proves
that nothing good ever came from this part of the world.
And I'm like, whoa, back at the truck, what is
(16:38):
going on here? Well, And I alluded to listener mail
that we get like that sometimes in a recent when
we were discussing, uh, the response to our Crucifixion episode
of episodes back, Um, we will get listener emails from
people sometimes who are wanting us, They like want us
to debunk the contributions of George Washington car of her
(17:00):
because he was really building on the work of people
who came before him. And I'm like, number one, that
sounds extremely racist when you say that. Number Two, all
scientists are building on the work of the people who
came before them. That is how science works. Like there
are extremely few discoveries that come from a bolt from
the blue, and eurica moments are far and few between.
(17:23):
Even when they are Eureka moments, they're Eureka moments, as
the saying goes from on the shoulders of giants, They're
not from nowhere. Yeah. Yeah, it was very I mean
I was actually quite startled at some of it. Um,
because it it really the focus is so laser sharp
that they really wanted to prove that the Arab world
(17:45):
contributed to mathematics. Now, I will say this, there are
debates among modern math historians about how much of al
Korismi's work was original, how much of it was taken
directly from Indian and Greek scholars who proceeded him. But
I feel like that doesn't take away the historical significance
of his works. Whether they were you know, how much
(18:08):
was him building on things and how much of him
was repeating things, These were still really important texts that
spread through Europe and really changed the way people looked
at numbers. So they're significant in that regard, regardless of
whether he was using the work of other people. Let
me also have other historical figures like their their role
in the world of history was archiving and preserving other
(18:29):
language or other discoveries for later generations. Like a lot
of us Alexandria's scholars weren't really putting out new discoveries
of their own. They're notable for having preserved all of
this stuff that has value. Yeah, yeah, it was just
it struck me. It took me by so by surprise
and struck me as so odd and troubling that I
(18:50):
wanted to mention it, particularly of any of our listeners.
I know our listeners, like us, usually like to research
things on their own. And should you run across this,
I want you to be prepared. It is out there
and you will find it accidentally and I be like,
what this took a left turn? H so be smart.
Do you have listener mails? I do. I sort of
have a few different ones. Um that all some. I'm
(19:14):
not reading all of them, but I wanted to discuss
a couple of them because there were several that kind
of popped up that were either short or as something interesting.
And I feel bad because when we only do one
per episode, that's hundreds and hundreds that never get a moment, right. Uh.
First ours from our listener Nancy, who said, I just
listened to the Crucifixion episode in your conversation about mimographing
(19:36):
and that memorable smell, which led me to search the
Internet for more information about this, since the only smell
I remember from my mimograph tests is a paper smell.
And after a little digging, I discovered that the smelling
machine was actually the spirit duplicator a k a. The
Ditto machine, and apparently the mimograph did not produce that smell. Yeah,
I think people are using the words interchangeably. I know,
I am, I do, but it didn't even occur to
(19:58):
me that there's a separation of the two. Well, and
now I wonder which exact machine, whether it was a
colloquial use of memo graph or whether it was an
actual mimi And she also says that she's glad that
as a teacher today we have photocopy here. Well, we
also got somebody on Twitter was like, hey, mimo graph
is still around them, and I said, I said, genuine question,
(20:22):
who is buying memograph nowadays? The tattoo industry, it makes
complete sense because they'll usually do like the someone who
knows more about tattoos will know this better than I.
But they do the like um sort of tests version
that they'll transfer on before they actually ink, and I'm
sure that's part of that. So so cool. And also
(20:43):
thank you for being a teacher, Nancy. That's a thankless
job and it's very hard. And my second one is
also from a teacher that I just wanted to call
out because I love teachers. It's funny because I feel
like talking about math today. Some of uh my favorite
teachers looking back on high school specifically, we're math teachers,
even though I was probably the biggest pain in their
(21:04):
butt because I didn't understand what was going on half
the time. And I think I kept getting put in
classes for advanced mathematics to keep my best friend, who
was a total brainiac happy, and I was like the
struggling monster. I was like the bull in the China
shop of mathematics. I was like, I don't understand any
of this, but I had so many great teachers who
would really take time and and really cared about their
(21:24):
jobs and they were amazing. So thank you all. But
we also got a letter from a teacher named Colleen.
But she has taught high school French for twenty years
and loves her job. Those two things together are like magic.
I think you're a unicorn, Colleen, because twenty years and
still loving your job is cool. And also, yeah, for
teaching French. I probably horrify you many times, um with
(21:46):
my awkward pronunciation, which used to be I think much
better and I have gotten quite rusty. And our third
listener mail is from our listener Bill, and this is
the last one, And he says, one of the episodes
that really inspired you while listening was the two part
Lions of TSAVO podcast. The unfortunate circumstances and often ridiculous
situations that Patterson found himself in while hunting these beasts
(22:09):
led to a one act play, which I've just finished writing.
I went out of my way to see the film
adaptation when was not impressed at the liberties they took
and telling the story. They do, of course, play up
certain things for drama, add in a whole romantical thing
that happens. I know that's not a real word. Um,
And he says, I'm currently looking for smaller venues in
Chicago to workshop the play, but I thought I would
share my story of inspiration and I look forward to
(22:31):
more episodes. Bill. That's so cool. I hope you keep
us updated on how your play goes, because I love it.
I'm thinking about ways you would stage that involving lions,
but then I think it's done indoor running of the bulls. Yes,
And then of course I think of Julie Taymore's designs
(22:53):
for the Lion King, which is a much different and
bigger you know, thing than a one act But I
do hope he keeps us posted and it gets stage
that we'll get pictures or something, because it sounds fabulous.
If you would like to write to us, you can
do so at History Podcast at Discovery dot com. You
can also connect with us on Facebook at Facebook dot
com slash missed in History, on Twitter at missed in
(23:14):
History at missed in History dot tumbler dot com, and
on Pinterest at pinterest dot com slash missed in History.
We are also happily still tagging all of our episodes
on are still fairly newish website, which is missed in
History dot com. As of this episode, we are halfway
through the tag whoo. Tracy is really like the champion
(23:35):
of tag. I do a couple here and there when
they come up, especially when someone emails us and asked
about an episode that that already exists that they haven't
found because we don't have the tags. I'll seek it
out sometimes, But you're the champion of all things. Uh.
And if you would like to learn a little bit
more about what we talked about today, you can go
to how stuff Works dot com and type in the
(23:55):
word math and you will come up with an article
called how math Works, which is written by uh Robert
of stuff to blow your mind, and it is a
very cool article. And if you would like to learn
about math or anything else that your mind can conjure,
because I know not everybody loves the math, you can
do that at how stuff works dot com as well
(24:18):
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This episode of Stuff You Missed in History Class is
brought to you by Squarespace, the all in one platform
that makes it fast and easy to create your own
professional website, portfolio, and online store. For a free trial
and ten percent off, visits squarespace dot com, slash history
and enter offer code history at check out. A better
web starts with your website. Welcome to Stuff you Missed
(00:23):
in History Class from how Stuff Works dot com. Hello,
and welcome to the podcast. I'm Holly Fry and I'm
Tracy V. Wilson and Uh. Today's topic was inspired by
an event that I got to go to last week
because I'm super lucky. I got to go see Neil
(00:45):
de grass Tyson speak at Georgia Tech, which was sponsored
I believed, by their physics department. And during his lecture,
which was spectacular, if you ever get a chance to
see him speak, I highly recommend it. Uh, he mentioned
that most people do not realize what an epicenter of
scientific and mathematical grow with medieval Islam was h So
naturally I got all excited about it because it was
(01:05):
fascinating and Neil de Grasse Tyson was saying it, which
automatically puts it above many other things on the interest scale.
So we're going to talk about math today. Do not
become scared or frightened. Like I know Tracy's mentioned before,
arithmetic is not her jam. I'm not particularly good at
it well, And what's funny is arithmetic was really the problem.
Like I loved geometry and I loved doing proofs, but
(01:27):
when it came to like the arithmetic portions of the proofs,
I would get things wrong. Same thing with algebra, Like
my algebra theory would be sound and my arithmetic would
be faulty. Yeah, I think that's pretty common. So we're
gonna talk about math, but really only sort of. There
will be a couple of equations mentioned, but they're super
duper simple and they stand as examples only. You do
(01:49):
not have to solve for X or any other letter
while you're listening. I love math in theory, but like Tracy,
the actual reality of it is not always my strong suit.
So but leave me when I say that the math
that we mentioned is really really basic. And I apologize
to any mathematicians in the crowd that may have been
hoping for more, but that's that's not gonna happen on
this one. So today we are focusing on an Islamic
(02:12):
mathematician named al khara is Me and his contributions to
the development of algebra and mathematics in general with his
ninth ninth century writings. So if you're going to guess
where algebra originated, you might guess ancient Greece or ancient room.
Even though we're talking about an Arabic scholar today, it's
important to remember that algebra does not have just one
(02:34):
single origin point. It developed over time and in multiple places,
with lots of different mathematicians contributing to the overall field
of knowledge. Yeah. I mean, it wasn't like someone woke
up one day and went, I'm inventing algebra. I'm imagining
somebody just sitting bolt up right in their bad No.
It arose out of a need for a way to
calculate certain things. And we'll talk about that more specifically
(02:57):
as we go on. The first traces of the concepts
and fundamental ideas of algebra that we know of are
from ancient Babylon and these fall around about two thousand BC.
And then in the third century, Diaphantus of Alexandria, who
is sometimes called the father of algebra was writing extensively
about algebraic equations and some of the concepts of algebra.
(03:22):
Uh there was also an Indian math scholar named Brahmagupta
who was writing extensively in the six hundreds, and he's
considered a major influence on al qai is Me. Muhammad
ibn Musa al quare is Me was born around seven
eighty and we don't know a lot about his early life,
as is often a case with figures from that long ago.
His exact place of birth is also kind of muddled
(03:44):
by his name because it includes an origin signifier that
it cited differently in various texts. We do know that
he's spent a significant amount of his life in Baghdad,
and he grew up, as we know, to be a
mathematician and an astronomer, and as an adult he worked
at the Dar al Hikma or House of Wisdom, and
the work of the House of Wisdom, which was a
(04:05):
sort of scholarly academy that's sometimes likened to the Library
at Alexandria, focused on the acquisition and translation of text
from throughout the world. The House of Wisdom may have
been established by Kalif Haroun al Rashid, but Kelif al Mamun,
who followed him is often recognized as the man who
really made it into a seat of scholarly discovery. And
(04:28):
before we get into sort of the most famous book
that al quires me worked on, we're going to do
a quick ad. So when that killer idea hits you
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back to the work that is primarily talked about when
people discuss alcoa is Me and his influence on algebra,
and that was called Alcatab al Muktazar fijis Ab Algebar
(05:33):
while Muka or the Compendious Book on Calculation by Completion
and Balancing, and it was written by alcoa is Me
and published through the House of Wisdom, which produced original
works as well as working on all of the translations
we mentioned. The introduction to this book notes that Khalif
al ma Moon and his thirst for scientific knowledge drove
al quare is Me to take on this whole project. Yeah,
(05:54):
that kind of supports the idea that Khalif al Mamon
was really the one that that made the House of
Wisdom flourish. And this book addresses the idea of balancing
and equation across the equal sign in a systematic way
and it features examples of ways that this can be
applied to fiscal transactions. And the book's goal was to provide, quote,
(06:15):
what is easiest and most youthful in arithmetic, such as
men constantly require in cases of inheritance, legacies, partition, lawsuits
and trade and in all their dealings with one another.
Or whether measuring of lands, the digging of canals, geometrical computations,
and other objects of various sorts and kinds are concerned.
The algebar portion of the Arabic title is what gave
(06:38):
algebra it's name. In the Latin translation of the text
several hundred years later in the twelfth century, the actual
translation of the Arabic word algebar is reunion or reunion
of broken parts. Yet also algebra. The word is also
associated with bone setters. Uh so if you ever hear
it used in that terminology, that's why they both share
(06:59):
the same words, and the words jabar andabla signify operations
in this early state algebraic problem solving of quadratic equations.
Jabar names the operation where a numerical value is eliminated
from one side of an equation and incorporated onto the
(07:19):
other side to solve for an unknown So, for example,
if x plus four equals nine, then the act of
subtracting four from both sides to solve for X is
the Jabar step, and muccabla is an operation which cancels
out duplicate elements of an equation to balance it. So again,
for an example, if you start with X minus y
(07:41):
equals twelve minus why y can be eliminated from both
sides of the equation to solve for X equals twelve. Again,
I apologize to the mathematicians in the crowd, because I'm
sure they're like, this is the silliest way to explain this,
but we're giving it very, very simple. In this book Alcorism.
He also establishes that all the problems that talks about
can be reduced down to one of six forms. We
(08:03):
should really note that he's speaking about them in terms
of rhetoric and not as hard equation. Yeah, you don't
actually see a lot of mathematical equations in some of
the translations they come about, but he basically was writing
out like how to divide a thing by another thing?
And it's not numeracle at this point. And the book
is laid out in three separate sections, and the first
(08:26):
section is really the only one that speaks of algebraic concepts,
though again they're not represented with figures, but they're written out.
The second portion of the book, which is headed on
business transactions, includes practical examples of measuring out ownership and proportions,
and also includes guides for measuring out geometrical shapes such
as cones and pyramids for the calculation of volumes and
(08:48):
also for surveying needs. The third section of the book
deals entirely with legacies, in other words, inheritances. Islamic inheritance
law can be extremely complex and it involves value wation
of all the airs proportionate entitlement shares in relation to
one another. So this last section of the book is
composed entirely of example problems about dealing with inheritances. Yeah,
(09:13):
it's I've read a little bit about Islamic inheritance law,
and I'm admittedly coming at it from a completely green perspective.
It is so complex, Uh, the way they sort of
measure out different people's what they're entitled to based on
who else is in the family, the sex of people
(09:33):
in the family. Uh, and it's all, you know, based
in religious texts. So it's something that is very serious,
but it is very hard to figure out. So this
was really hugely helpful. And I have to giggle a
little bit at the fact that most school students today
learning algebra and I did it too, So I apologized
to my many fabulous math teachers. Is that they will
(09:55):
never need this stuff in real life. But the whole
point of al core Me's text is designed entirely to
solve practical, day to day problems that require mathematical computation.
So it just kind of made me laugh that the
origins of algebra are entirely in real life needs, not
in abstract things that you feel like you're learning in school.
(10:17):
I will say I've used algebra in my day to
day life sometimes. Yeah, I use it in my day
to day life in the podcast to calculate how many
more things we have than we did a month ago,
because I am interested in that as trivia. Yeah, But
that was not the only book written by alcoa is Me. No,
(10:39):
there was another mathematical book. Although we don't have the
original text. The earliest example we have is a twelfth
century Latin translation. It boils down to alcoa is Me
concerning the Hindu art of reckoning. Yeah, and the original
title was Algorithm Numero indorham And this work was largely
(10:59):
bay based on the work of an Indian mathematician, Brahmagupta,
who we mentioned earlier, who lived from five to six seventy. Roughly,
there isn't always consensus about the order in which alcoris
Meet wrote his books because the historical record is unclear.
But we do know that the book on Hindu Numerals
came after the compendious book on Calculation by Completion and Balancing,
(11:20):
because it refers to the algebra in that volume. Yeah,
it refers to that earlier book. Uh. And you likely
noticed similarity between the first word of the Latin title
algorithmy and the word algorithm, and that is absolutely no accident.
Algorithm came from the translation of Alcorism's name, so he's
responsible for two pretty big, fundamental important words in mathematics.
(11:43):
This book introduced the Indian numerical system into the Arabic
world and eventually to a greater audience. It features the
numerals one through nine, plus The concept of zero zero
as an idea had been toyed with by a few
different cultures by this time, including the Maya and the Babylonians,
so it's not as though Alcorismy just invented it out
of whole cloth, but his translated texts identifying it in
(12:08):
the Indian mathematical system made their way across Europe in
the twelfth century and helped cement the concept of a
numeral to represent nothing. Yeah, there wasn't always a zero
in competition. And if you're into the cultural identity of
zero in its place in history, which is to me
really fascinating. Uh. There's a great book that I highly
recommend called The Nothing that is a natural history of zero,
(12:29):
and it's written by Robert Kaplan. I didn't really use
it as a source for this, so it's not going
to be in the source notes, but I wanted to
mention it. I think we have how zero works as
an article on how st works also we do. Additionally,
the Indian concept of decimal numbers is discussed in the
book and eventually leads to the idea spreading as the
work is translated and shared. Once again, this is an
(12:51):
idea that had been blossoming in other places, including China. Yeah,
I mean he uh, neither Brahmagupta nor alcorism really the
to recognize that we needed some way to identify smaller
parts of things. But this really kind of gave it
a foothold in mathematical texts. And while we're focusing on
(13:15):
mathematics and how alcors may contributed to that field, we
should also take a quick moment to discuss his work
in geography and astronomy. A writing entitled kitab Surat Alided,
which translates to the image of the Earth, was a
geography book based largely on the work of Ptolemy in
his book Geographia. Algorithm built on what Ptolemy had established
(13:38):
by calculating significantly improved measurements for several parts of the globe,
and the Arabic scholar was also instrumental in creating what
was one of the first world maps. His astronomy work
encompassed calendars, the positions of heavenly bodies, and even eclipse calculations.
He compiled a book of astronomical tables which was translated
into multiple languages, including Chinese. Uh. And before we talk
(14:02):
about sort of how his work spread through Europe, we're
gonna take a quick pause for a moment, So back
to Alcorismy. Yeah, Alcorismi died in eight fifty, so he
never saw the introduction of his work to the European
scholarly community. There's not much in the way of record
of what he died from. He's believed to have died
in Baghdad, where he had been living but that's kind
(14:22):
of all we know. Robert of Chester, who was an
Englishman working in Spain at the time, translated alcorithms algebra
text in the eleven forties, and this translation, with a
very lengthy intro, is on archive dot org and we
will put it in the show notes. It, as well
as Alcorithm's other work, was also translated by Gerard of
Cremona around eleven fifty and Gugliemo de Lunis around twelve fifty.
(14:46):
And once it was translated, Alcorismy's work became a significant
influence on the European development of mathematics, and it was
used as a standard textbook on algebra throughout Europe well
into the sixteenth century. What made the introduction of algebra
inda Europe at this time so significant is that it
moved away from the geometry based mathematics of Greece, and
it also expanded the mathematical landscape significantly, so rational interrrational
(15:10):
numbers were welcome at the algebra table, and that allowed
math to flourish in new ways. Yeah, it kind of
just was a whole new gear of thinking about math
and how numbers could be used. And I feel like
I should mention a thing that I discovered while I
was researching that was unbeknownst to me before we had
gotten into this topic. There are some very vehement folks
(15:32):
in the world with Internet presences who really really want
to discredit Alcorithmy's contributions, and they're coming at it from
an anti Islamic mindset, and they seemed to use the
fact that Alcorismi was building on the work of mathematicians
that came before him as some sort of like gotcha,
like they caught him plagiarizing, And it kind of ignores
(15:54):
the fact that virtually every line of academic research and
discovery builds on what has come before and preceded it,
and also the fact that sometimes certain concepts are developing
independently in multiple places and cultures at one time, or
even at different times, but that aren't communicated. And I
wanted to bring this up as I found it very
troubling and it's really bizarre because some of these are
(16:17):
kind of cloaked in a seeming academia layout, Like I
find these websites that I was like, oh, this is interesting,
and I'm trying to fact check it, and some of
this checks out and then it would suddenly become like
sort of really racist and weird, very like this proves
that nothing good ever came from this part of the world.
And I'm like, whoa, back at the truck, what is
(16:38):
going on here? Well, And I alluded to listener mail
that we get like that sometimes in a recent when
we were discussing, uh, the response to our Crucifixion episode
of episodes back, Um, we will get listener emails from
people sometimes who are wanting us, They like want us
to debunk the contributions of George Washington car of her
(17:00):
because he was really building on the work of people
who came before him. And I'm like, number one, that
sounds extremely racist when you say that. Number Two, all
scientists are building on the work of the people who
came before them. That is how science works. Like there
are extremely few discoveries that come from a bolt from
the blue, and eurica moments are far and few between.
(17:23):
Even when they are Eureka moments, they're Eureka moments, as
the saying goes from on the shoulders of giants, They're
not from nowhere. Yeah. Yeah, it was very I mean
I was actually quite startled at some of it. Um,
because it it really the focus is so laser sharp
that they really wanted to prove that the Arab world
(17:45):
contributed to mathematics. Now, I will say this, there are
debates among modern math historians about how much of al
Korismi's work was original, how much of it was taken
directly from Indian and Greek scholars who proceeded him. But
I feel like that doesn't take away the historical significance
of his works. Whether they were you know, how much
(18:08):
was him building on things and how much of him
was repeating things, These were still really important texts that
spread through Europe and really changed the way people looked
at numbers. So they're significant in that regard, regardless of
whether he was using the work of other people. Let
me also have other historical figures like their their role
in the world of history was archiving and preserving other
(18:29):
language or other discoveries for later generations. Like a lot
of us Alexandria's scholars weren't really putting out new discoveries
of their own. They're notable for having preserved all of
this stuff that has value. Yeah, yeah, it was just
it struck me. It took me by so by surprise
and struck me as so odd and troubling that I
(18:50):
wanted to mention it, particularly of any of our listeners.
I know our listeners, like us, usually like to research
things on their own. And should you run across this,
I want you to be prepared. It is out there
and you will find it accidentally and I be like,
what this took a left turn? H so be smart.
Do you have listener mails? I do. I sort of
have a few different ones. Um that all some. I'm
(19:14):
not reading all of them, but I wanted to discuss
a couple of them because there were several that kind
of popped up that were either short or as something interesting.
And I feel bad because when we only do one
per episode, that's hundreds and hundreds that never get a moment, right. Uh.
First ours from our listener Nancy, who said, I just
listened to the Crucifixion episode in your conversation about mimographing
(19:36):
and that memorable smell, which led me to search the
Internet for more information about this, since the only smell
I remember from my mimograph tests is a paper smell.
And after a little digging, I discovered that the smelling
machine was actually the spirit duplicator a k a. The
Ditto machine, and apparently the mimograph did not produce that smell. Yeah,
I think people are using the words interchangeably. I know,
I am, I do, but it didn't even occur to
(19:58):
me that there's a separation of the two. Well, and
now I wonder which exact machine, whether it was a
colloquial use of memo graph or whether it was an
actual mimi And she also says that she's glad that
as a teacher today we have photocopy here. Well, we
also got somebody on Twitter was like, hey, mimo graph
is still around them, and I said, I said, genuine question,
(20:22):
who is buying memograph nowadays? The tattoo industry, it makes
complete sense because they'll usually do like the someone who
knows more about tattoos will know this better than I.
But they do the like um sort of tests version
that they'll transfer on before they actually ink, and I'm
sure that's part of that. So so cool. And also
(20:43):
thank you for being a teacher, Nancy. That's a thankless
job and it's very hard. And my second one is
also from a teacher that I just wanted to call
out because I love teachers. It's funny because I feel
like talking about math today. Some of uh my favorite
teachers looking back on high school specifically, we're math teachers,
even though I was probably the biggest pain in their
(21:04):
butt because I didn't understand what was going on half
the time. And I think I kept getting put in
classes for advanced mathematics to keep my best friend, who
was a total brainiac happy, and I was like the
struggling monster. I was like the bull in the China
shop of mathematics. I was like, I don't understand any
of this, but I had so many great teachers who
would really take time and and really cared about their
(21:24):
jobs and they were amazing. So thank you all. But
we also got a letter from a teacher named Colleen.
But she has taught high school French for twenty years
and loves her job. Those two things together are like magic.
I think you're a unicorn, Colleen, because twenty years and
still loving your job is cool. And also, yeah, for
teaching French. I probably horrify you many times, um with
(21:46):
my awkward pronunciation, which used to be I think much
better and I have gotten quite rusty. And our third
listener mail is from our listener Bill, and this is
the last one, And he says, one of the episodes
that really inspired you while listening was the two part
Lions of TSAVO podcast. The unfortunate circumstances and often ridiculous
situations that Patterson found himself in while hunting these beasts
(22:09):
led to a one act play, which I've just finished writing.
I went out of my way to see the film
adaptation when was not impressed at the liberties they took
and telling the story. They do, of course, play up
certain things for drama, add in a whole romantical thing
that happens. I know that's not a real word. Um,
And he says, I'm currently looking for smaller venues in
Chicago to workshop the play, but I thought I would
share my story of inspiration and I look forward to
(22:31):
more episodes. Bill. That's so cool. I hope you keep
us updated on how your play goes, because I love it.
I'm thinking about ways you would stage that involving lions,
but then I think it's done indoor running of the bulls. Yes,
And then of course I think of Julie Taymore's designs
(22:53):
for the Lion King, which is a much different and
bigger you know, thing than a one act But I
do hope he keeps us posted and it gets stage
that we'll get pictures or something, because it sounds fabulous.
If you would like to write to us, you can
do so at History Podcast at Discovery dot com. You
can also connect with us on Facebook at Facebook dot
com slash missed in History, on Twitter at missed in
(23:14):
History at missed in History dot tumbler dot com, and
on Pinterest at pinterest dot com slash missed in History.
We are also happily still tagging all of our episodes
on are still fairly newish website, which is missed in
History dot com. As of this episode, we are halfway
through the tag whoo. Tracy is really like the champion
(23:35):
of tag. I do a couple here and there when
they come up, especially when someone emails us and asked
about an episode that that already exists that they haven't
found because we don't have the tags. I'll seek it
out sometimes, But you're the champion of all things. Uh.
And if you would like to learn a little bit
more about what we talked about today, you can go
to how stuff Works dot com and type in the
(23:55):
word math and you will come up with an article
called how math Works, which is written by uh Robert
of stuff to blow your mind, and it is a
very cool article. And if you would like to learn
about math or anything else that your mind can conjure,
because I know not everybody loves the math, you can
do that at how stuff works dot com as well
(24:18):
for more on this and thousands of other topics because
it how stuff works dot com. Netflix streams TV shows
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