The Big X - Numberphile
Summary
TLDRIn this engaging video script, the presenter explores 'The Ground of Arts,' a pioneering arithmetic book by Robert Record, published in 1542. It aimed to bring England's arithmetic skills in line with the rest of Europe by introducing the Indo-Arabic numeral system, including the revolutionary concept of 'cipher' or zero. The script also delves into the historical significance of the cipher, its impact on arithmetic, and its playful references in Shakespeare's works. The presenter speculates on the origin of the multiplication symbol and its possible connection to Record's times table technique, offering a unique perspective on the evolution of mathematical symbols.
Takeaways
- đ 'The Ground of Arts' is a significant historical arithmetic book written by Robert Record in 1542, aimed at the general public in English to explain arithmetic concepts.
- đ The book was a response to England's lag in arithmetic knowledge compared to the rest of Europe, particularly due to the country's break from the Catholic Church and the Renaissance's influence.
- đą It introduced the Indo-Arabic numeral system to the English public, including the concept of place value and the revolutionary 'cipher' or zero, which simplified arithmetic significantly.
- đČ Robert Record made learning arithmetic more approachable by incorporating verses and a friendly tone, demystifying the subject for the general populace.
- đ The term 'cipher' for zero was not universally used; it was a term that emerged later, and at the time, people referred to it as 'nothing' or 'nil'.
- đ€ The script ponders the origin of the multiplication symbol, suggesting it might have been inspired by the 'X' shape of the times table technique introduced in 'The Ground of Arts'.
- đš Shakespeare, who was part of the first generation to learn this new arithmetic, made references to it in his plays, indicating the impact of the cipher and arithmetic on culture.
- 𧩠The script highlights the ingenuity of the times table technique for tricky multiplications, such as 8 * 7, and demonstrates how it works with an algebraic explanation.
- đ It also discusses the practical application of arithmetic in the book, including long multiplication and word problems that reflect the everyday life of the Elizabethan era.
- đ€ The video script speculates on the influence of 'The Ground of Arts' on the development of mathematical symbols and the cultural significance of arithmetic during the English Renaissance.
- đ The script encourages viewers interested in the intersection of mathematics and culture to explore further resources, such as Rob's book on numbers and the Objectivity channel.
Q & A
What is the book 'The Ground of Arts' about?
-'The Ground of Arts' is an arithmetic book first written in 1542 by Robert Record. It was the first book aimed at the general public in England to explain how to do arithmetic using the new Indo-Arabic numeral system.
Why was 'The Ground of Arts' significant in England during its time?
-The book was significant because it helped England catch up with the rest of Europe in arithmetic, which was important since England had fallen behind due to the Reformation and the break from the Catholic Church.
What numeral system does 'The Ground of Arts' introduce?
-The book introduces the new Indo-Arabic numeral system, which included the use of zero, referred to as 'cipher' in the book.
How does Robert Record explain the concept of zero in his book?
-Robert Record refers to zero as 'cipher,' a term derived from Arabic. He explains that this symbol, despite representing nothing, is crucial in making numbers large and revolutionizing arithmetic.
What multiplication technique does Robert Record introduce in 'The Ground of Arts'?
-Record introduces a technique for doing times tables, which involves drawing diagonals and using number bonds to make multiplication easier. This method was particularly useful for multiplying single-digit numbers.
Does Robert Record's multiplication technique work for numbers outside the range of 6 to 9?
-Yes, the technique works for numbers outside the range of 6 to 9, though it may seem unnecessarily complex for such cases. The algebra behind the method shows that it is valid for any numbers.
How were long multiplication problems addressed in 'The Ground of Arts'?
-The book includes practical word problems that require long multiplication. Record demonstrates how to solve these problems without the modern multiplication symbol, which had not been invented yet.
Who is credited with inventing the multiplication symbol, and how might Robert Record's work have influenced this?
-William Oughtred is credited with inventing the multiplication symbol around 1630. It's suggested that he may have been inspired by Record's technique of drawing diagonals, which resembles an 'X'.
How does Shakespeare reference arithmetic in his plays, and what might this indicate?
-Shakespeare refers to arithmetic in his plays, such as 'Romeo and Juliet' and 'Henry V'. This indicates that he was likely familiar with arithmetic concepts from 'The Ground of Arts', which was published shortly before his time.
What is a notable mathematical reference in Shakespeare's 'Henry V'?
-In 'Henry V', the chorus refers to himself as a 'crooked figure a one' and the other actors as 'ciphers'. This reflects the arithmetic concept introduced by Record that small symbols, like zero, can significantly expand numbers.
Why is the term 'cipher' significant in the context of Robert Record's work and Shakespeare's plays?
-The term 'cipher' is significant because it represents the concept of zero, which was a new and revolutionary idea in arithmetic. Shakespeare's references to 'cipher' in his plays suggest that he found this concept intriguing and important.
Outlines
đ Introduction to 'The Ground of Arts' Arithmetic Book
The video script introduces 'The Ground of Arts,' an arithmetic book written by Robert Record in 1542. It was the first of its kind to explain arithmetic to the general English-speaking public. The book played a role in helping England catch up with other parts of Europe that were already adept at arithmetic. England had been somewhat behind due to its break from the Catholic Church and the Renaissance's delayed impact. The script highlights the book's unique approach, including the use of verses to make learning fun and the introduction of the Indo-Arabic numeral system, which was revolutionary at the time, especially the concept of 'zero' or 'cipher,' which was a new and somewhat mystical concept in mathematics.
đą The Innovation of the Indo-Arabic Numeral System
This paragraph delves into the specifics of the Indo-Arabic numeral system introduced in 'The Ground of Arts.' It discusses the significance of the cipher (zero) and its representation, which was a major innovation in arithmetic. The script also explains Robert Record's method for teaching multiplication, particularly for numbers 6 through 9, using a clever technique involving diagonal lines and simple arithmetic. The method is demonstrated through the multiplication of 8 by 7 and then 8 by 9, showing how this system simplifies the process. The script also touches on the broader implications of the cipher's introduction, noting that it allowed for more efficient arithmetic without the need for complex Roman numerals.
đ The Influence of Arithmetic on Shakespeare and the Multiplication Symbol
The final paragraph explores the impact of 'The Ground of Arts' and the new arithmetic concepts on English literature and society, particularly on William Shakespeare. It suggests that the book may have influenced Shakespeare's use of arithmetic in his plays, such as the reference to 'the book of arithmetic' in 'Romeo and Juliet.' The script also speculates on the origin of the multiplication symbol, proposing that it might have been inspired by Record's times table technique. The paragraph discusses the broader cultural significance of the cipher and arithmetic during Shakespeare's time, indicating that these mathematical concepts were not only educational but also found their way into the creative arts and everyday language.
Mindmap
Keywords
đĄThe Ground of Arts
đĄArithmetic
đĄIndo-Arabic numeral system
đĄPlace value
đĄCipher
đĄTimes tables
đĄLong multiplication
đĄMultiplication symbol
đĄShakespeare
đĄRenaissance
đĄRobert Recorde
Highlights
The Ground of Arts is a math book written in 1542 by Robert Record, aimed at the general public to explain arithmetic in English.
The book was written to help England catch up with the rest of the world in arithmetic, as England was behind due to breaking away from the Catholic Church and missing the Renaissance.
Robert Record made math fun by adding little verse bits to make the book engaging.
The book introduces the new Indo-Arabic numeral system, showing place value and the concept of zero.
The word for zero at the time was 'cipher', derived from the French word 'chiffre' which means a digit.
Record's book includes a method for doing times tables using a unique technique involving diagonal lines and number bonds.
This method works by finding the number bonds to 10, multiplying these numbers, and then using diagonals to simplify the calculation.
The method is demonstrated with examples like 8 x 7 and 8 x 9, and an algebraic explanation of why it works is provided.
The technique even works with numbers outside the 6 to 9 range, as demonstrated with the example 5 x 13.
Robert Record's book also teaches long multiplication through practical word problems, such as calculating the total number of lambs owned by 264 men.
At the time of the book's writing, there was no multiplication symbol, which was later introduced by William Oughtred around 1630.
It's speculated that the multiplication symbol may have been inspired by Record's technique of drawing diagonals.
Shakespeare, who lived around the same time as the book's publication, made several references to arithmetic and the concept of zero in his plays.
In Romeo and Juliet, a character refers to fighting by the book of arithmetic, which might be a nod to Record's book.
In Henry V, Shakespeare uses the concept of cipher to explain how a small number of actors can represent a large army.
The transcript suggests that Shakespeare was excited by the new arithmetic concepts, using them as sophisticated references in his works.
Transcripts
so this is a book called The Ground of
arts and it's actually a math book and
more specifically it's an arithmetic
book it's a book first written in 1542
by Robert record and it's the first book
aimed at the general public to explain
in English how to do arithmetic so we
can catch up in England with the rest of
the world who always already pretty good
at doing arithmetic was England behind
the curve was it behind the curve yeah
because of breaking away from the
Catholic Church and all that it was like
we were behind the Renaissance that
happened in like Italy and was working
its way through Europe so this is just
before the English Renaissance and it's
quite a fun book he he adds little verse
bits in here and there just to make it
fun you know Matt is fun it's not too
scary and so on ground of Arts is a
strange name for a maths book but uh
Arts and Sciences and maths obviously
the same thing to him let's turn to an
important page because what he is
introducing people to
is the new indo-arabic numeral system
that had had come in as he got a little
table here so uh he's showing place
value so we've got uh nine units nine
tens hundreds whatever he's just written
the nine all the way across uh and says
this is nine which is a word that they
would have known eights can be placed in
any place value up to millions and tens
of millions 7 6 5 4 3 2 uh 1 and then
here is the big innovation this circle
what we now called zero do you know what
that word is going to be underneath
underneath here it's not zero because
that's a French word that appeared in
like 1650 in in England really any
guess no idea Rob okay be n or nil or
something no yes yeah that would be I
would I would have guessed yeah like
null or something yeah yeah good guess
but wrong sorry about that because when
it says cth uh which is thought for the
word Cipher this is the cipher we think
these days of ciphers as like code and
mysticism and so on and I think there's
an element of this was a mystical symbol
because it was like it means nothing and
yet it can make numbers big as well so
it is the cipher and we still have the
French word shifa which is uh means a
digit and this is the digit the most
important one because it's what
revolutionized arithmetic um it meant
you could add things up uh without
having to have lots of different symbols
like the Romans did so here we are but
he's spelling it out literally was
everyone in England calling it C or is
that just something that this author has
opted for cuz he had nothing else uh
well everyone was calling it Cipher not
the cipher not CF but no that was it
there was no other word for it other
than nothing nil shakespare refers to
the O which is the shape of it but
that's just him being sort of figurative
no it it was the cipher there was no
zero in the late 1500s here is something
else that Robert record is introducing
people to which is how to do your time
tables especially those tricky ones like
8 * 7 so here you can see the eight and
the Seven first of all you draw this
these two diagonal lines to sort of join
the corners then for each of the numbers
so eight and two you you you basically
find the number bond of that so what's
the number you have to add to eight to
make 10 and it's two okay seven plus
what is 10 three so that's where the
three comes from so that's stage two of
this technique next in your head or
using your fingers not using this method
you multiply the two numbers in the
right hand column so 2 * 3 is six so six
is entered there and then finally you
pick a diagonal and it doesn't matter
which diagonal let's take the bottom
left to top right s and two take that
number from this one 7 takeway two is
five so 8 * 7 is
56 I mean what could be simpler than
that um do you want to try it for
another uh uh another thing we can we
can uh we can we can do it and then I
can show you how it works as well all
right let's do it do you want to give me
a nice safe times table to do uh did you
say do you want single that were single
digits and yeah let's do ones in the
range six to n because that's what
Robert record intended this for um oh
okay so could I do uh 8 * 9 okay let's
do 8 * 9
so8 * 9 let's just draw those diagonals
in like that lovely and then eight plus
two there very very nice yeah excellent
now we multiply these two numbers
together let's draw a line underneath
two ones are two and pick a diagonal do
you have a preference for diagonal do
you like this one I like the one you
used yeah that one okay so nine takeway
two is 7 72 how wonderfully elegant is
that but of course I'm sure everyone on
number file is asking why does it work
and uh it's rather a nice little algebra
exercise actually so we're multiplying
together two numbers let's call them
for sake of Simplicity A and B let's
draw the diagonals so this is 10 minus
a and this is 10 - B let's draw the line
underneath we next multiply these two
numbers together so it's 10 - A * 10 - B
ooh ouch okay so that is 100 minus 10 a
- 10
B plus a there we go so that's that's
the units column and then the 10's
column is this take away this so it's
B minus 10 -
A Time 10 because these are the 10 so
it's 10 times
B which is equal
to 10
B plus 10 a because the negative cancel
out minus
100 okay so that is what a * B is is
this horrible lot well if we add this
lot together the hundreds cancel out the
10 A's cancel out the 10 BS cancel out
and all you're left with is a which is
what we're looking for a * B is equal to
a * B so that's why it works ingenious
the question you and everyone watching
is asking is can we break this by making
numbers not in the range 6 to 9 okay so
let's see if it still works so do you
want to give me two other numbers
outside that range to multiply together
we'll see if I can get this right let's
do uh 5 * 13 5 * 13 okay let's let's see
how it works under this stress test so 5
* 13 okay so 5 plus 5 that's that's easy
enough makes 10 13 +us 3 makes 10 okay
so in the units column we've got
-5 and then let's pick a diagonal let's
go this one it's pretty change 5 takeway
minus three is eight now Robert record
and the uh English folk of the time
would not have been into uh subtracting
negatives it wasn't part of their
general math vocabulary but anyway we've
got 80 take away 15 because this 8
represents 80 and 80 take away 15
is equal
to 65 which I believe is what 5 * 13 is
so it works it works for any numbers
just you got to ask why would anyone
want to do that that's just just your
time tables what about big long
multiplication people didn't know about
it they need to learn about long
multiplication and there's word problems
through this book and there's one where
it's uh there are 264 men who have 29
Lambs each how many lambs are there in
total one of those entirely practical
everyday Elizabeth life problems to work
out just as an opportunity to do some
long multiplication and uh here we've
got it 264 * 29 for some reason record
has little lines through it's like you
cross out each of the numbers maybe to
check you've done them all but anyway
just as we do today 49's a 36 carry the
three except I don't see any three being
carried so you're keeping it in your
head uh and do it all that so 9 * it is
2376 then 20 * it is 528 no no there's
no Cipher has been put there but you
don't need it it's just nice practice
and we get
7,656 as the answer now I said a
Cipher's missing there's something else
that's missing there as well which is
there is no multiplication symbol for
the simple reason when he wrote this
book it hadn't been invented yet all
these symbols didn't just appear out of
nowhere they had to be invented and the
multiplication symbol is always credited
to a an English guy called William out R
Who sometime around 1630 just used it
for the first time but as far as I know
no one has ever said where he got the
idea for it he just kind of came up with
it well I think it seems to me pretty
clear everybody would have had and known
about Robert record's book and they'd be
very familiar with that little trick for
doing your times tables well there's a
there's a very obvious big X happening
there why not represent multiplication
by having a miniature version of Robert
records times tables technique and use
that as a multiplication symbol so like
is it are you suggesting that that
little diagram there on page 71 of This
Book Is the is the birth of the
multiplication symbol or I I have I've
not had anyone challenge me on this um
and perhaps it's been known by people
for years and just no one's made it made
it popular until number file did but uh
you know perhaps every day we're all
just reminding ourselves of that quirky
Little Tim table technique of Robert
record so that's not like it's not like
that's not like the official story on
Wikipedia as to where the the symbol
came from not not yet it isn't no but
it's just a matter you know anyone can
change Wikipedia um but um but no I I
had genuinely not seen any source of it
and and it could and it could not be as
well it could not be as well and and or
indeed it could be on Wikipedia um but
um no it was just in reading through
this book and and discovering there was
no symbol it and and using this this big
X method lots of times it just seemed so
obvious that uh and it probably when you
first saw it you probably thought is
that is that a multiplication symbol so
it it it does kind of jump out of the
page so I mentioned earlier the the
cipher and I think this was a new idea
the cipher and uh Shakespeare I think
was excited by this first of all this is
his vintage is it this is his vintage
this is basically it came out it was
first published about 20 years before
Shakespeare was born so um hence his dad
would only ever if he used Roman
numerals cuz this didn't catch on very
much so Shakespeare was actually the
first generation really who' have been
learning this kind of arithmetic um he
refers to arithmetic quite a bit in his
plays and in Romeo and Juliet there's a
fight between mausio and tibol where
mikio says TI you fight by the book of
arithmetic well which book of arithmetic
is it well I think it could well be this
one um and we saw earlier about this new
symbol the the cipher that can make
numbers big well in the opening scene of
Henry V which is the Battle of ainor and
the actors are playing this massive Army
but there's only let's say seven of them
the the character comes on stage he's
called the chorus and he says to the
audience you can have to use your
imagination guys because uh there's not
many of us and we're representing a
massive Army but that's okay if you look
at me as being a crooked figure a one
and you'll see elsewhere in in records
one was very much a crooked figure in
1599 when that play was first performed
um so I'm the one and if you treat the
other actors as ciphers and there're six
of them that makes a million so that
Shakespeare playfully using this notion
of you can expand numbers really big
with small number of
symbols if if one didn't know about this
the the the use of Cipher cph is
zero that like that would just make no
sense to to to Modern viewers that line
in sh must just be completely bizarre I
think it's not actually even doesn't
even get used in the Henry VI movie I
looked for it perhaps that's the reason
because people and I wonder whether I
mean it's quite a sophisticated
reference even then frankly and Sh does
this a few times with Cipher uh which
convinces me he thought it was a really
cool idea that was sweeping through
England that these simple symbols can do
so much for you and and uh in one case
in King Leah he talks about uh
I think he might use Cipher or or or
refers to the symbol AS basically saying
you know without a figure in front of
you you're nothing you're like a you're
like a a 10 without the one in other
words you are zero if this crossover
between mathematics and shakespear is
your kind of thing you really need to
check out Rob's new book much ad do
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he was not just a words guy he was also
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you love pouring over these ancient
documents and old objects and you like
that sciency mathy bent as well you
really might like my channel objectivity
have you ever watched these videos
possibly a lock of Z mutants here I'll
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one of the most juicy r that has ever
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