Today I want to talk to you about the
Inca
and their amazing system of numbers.
The largest civilisation in the Americas
before the arrival of the Europeans. They
peaked about the 16th century
where the area covered by the Inca Empire
started in Colombia in the north, went
all the way down to sort of bits of
Chile via Peru, Ecuador and Bolivia, all
in the Andes so that's about several
thousand miles but
about 12 million people? So the Incas are
really interesting
because of the, we call them bronze age
civilisations,
they were the only one that didn't have
certain important things which
the other bronze age civilisations did.
They didn't have a wheel,
and you can maybe explain that because
you know it's the Andes,
wheels aren't going to help you get up
a mountain. They also
didn't have a writing system, but what
they did have
was this amazing system for recording
numbers
and they did this using knots on string.
The system is called khipu or quipu - sometimes it's
q-u-i-p-u
sometimes it's k-h-i-p-u; um
I guess it's a it's a Quechua word.
Quechua which, incidentally,
is the indigenous American language
still spoken by the largest number of
people. There's about- I think about 10
million people
speakers of Quechua and that was the
language of the Incan Empire. Anyway,
I have a quipu here; this quipu is a replica
of one that is in the American museum of
natural history
in New York. And quipus are bunches of
strings - they've got knots on -
but there is some kind of method to them.
Often they were coloured strings,
obviously this is um some kind of
coloured line so not this type of string; but
they all had a primary cord, so that's
the yellow one. So that's the cord
that doesn't have any knots on it but
all the other ones hang off it. It's like a
massive kind of janitor's key ring.
Often there were hundreds of strings,
here I've only got five other strings;
and you've got these red ones are the strings
with the knots on and the green one
is a certain string that links
this set of four. So you see the green
one links the set of four and the green one
also has some knots on. And what I would
like to do today
is to explain to you how this works,
but by replicating the original
decipherment
of quipu. So it was in the 16th century that
the um Incas were conquered by the
Spanish and then
knowledge, amongst Europeans, of how
quipus worked was completely lost.
And it was only rediscovered in 1912
because a maths teacher, a guy called
Leslie Leland Locke -
fantastically alliterative name. Leslie
Leland Locke, maths teacher from Brooklyn,
went to his local museum, the American
museum of natural history; saw
this very quipu and worked out from the knots
what it meant and how it worked. And so
why don't we go through
what he would have done. The first thing
is, let's look
at each bit of string. So when you look
at the string
you see that it seems to be
that there are three positions and in
each different position -
here, here and here - there are
certain knots.
So what I'm going to do, I'm just going
to write that out. I'm going to say
string 1: we're gonna have position one,
position two,
position three. So this is the first one;
so in position one we've got 1,
position two
we've got 3, in position three we've
got 4.
So already
we get some kind of sense of what this
might be, because
all the numbers are quite low - actually
not going above 6, which is kind of
interesting. So that might be the first
clue that something is going on here. And now
let's just put a line here and let's do
the green string. So this is the green string,
this is the string that links them all
together,
so string five I guess - 1, 2, 3, 4
5, 6, 7, 8 actually so that's
8 first.
Then there's a quite a big gap so that's
zero.
1, 2, 3, 4, 5 - and that's 5.
So Brady, or maybe anyone watching this,
already you've got this can you begin to see
what the knots might be recording? And
what the relation might be
between these four strings, the four red ones,
and the green one that links them
together? It's actually very simple
but if you didn't know it it's almost
impossible,
or it's very very difficult, to try and
find out. That's the intellectual efforts
required to decipher something, because
you're not entirely sure what you're
looking for.
But I've made it in fact incredibly
simple, because if you actually look here,
let's add these ones up. 4, 6,
5 is 15, so
5 carry 1. 3, 6,
5, 5 is 19; with that 1 carry is
20 - put 2 there. 1,
4, 5, 6, 7, 8 - 8. So
Leslie Leland Locke
realised that the answer was staring him
in the face, it was nothing more
complicated; that
each string represents a single
number, a single three digit number. So
the one that has
1 in position one, 3 in position
two and 4 in position three
is actually 134 because position one is
the hundreds position, two
is the tens and position three is the units.
The Incas, you know, they had this massive Empire,
10-12 million people. They had
bureaucracy,
bureaucracy requires numbers and
statistics.
So in a sense the quipus, which were used
for
um census information, for
measurements, for money - um
essentially was the gel that glued this entire
Empire
together. And what you would have- if you
needed to record a number you put this
three-digit number, or
it could be longer if you needed more digits,
on each string. And if you wanted to add
them up; to save adding them up
you would join them with another string
and that would be the sum.
So this is incredibly efficient and in
fact what they've done is they've kind of
invented the decimal system without
realising it.
What they hadn't done- there wasn't a
zero knot so you had to realise there's
a space there, so that could be
quite confusing. But they know- they knew
other things. So actually
here I've done them all with the same
knot, that's because I'm not very good at
doing knots;
the way the Incans did is that the last
knots were always slightly different,
there were slightly longer knots.
And that's because a slightly longer
knot was always units
so, just say you had a piece of string
that was- became detached or something;
you could look at it and you think okay
I know exactly the way this is gonna go, I know
to read it this goes units, tens, hundreds;
and so on. - (Brady: This doesn't seem like it)
(would have been the hardest thing to)
(figure out like, how could this be a)
(mystery for so long?)
Well it was figured out in 1912 so
the whole studying these civilisations
was not very developed. Also people were
probably interested in other things
about
that society, and there weren't that many
quipus that you could go and have a look at.
Some of the quipus had hundreds of
strings. If you're going to be kind of
pulling them apart it's quite hard to
know where to look; but also
why would you even think that it was
arithmetic and numbers?
Even to think that - it's much easier once
you know that.
It could be it could have been
anything else, you could have thought, oh
this is something that's going from 1
to the 3 to the 4; it's getting
bigger. There are lots of other patterns
that you can see.
(Brady: It could have been jewellery or headwear)
(or something.) - Yeah, well I think people knew
that from studying it, and obviously when
they were
conquered in the 16th century they
didn't all die out,
they kept on using it, bits and bobs, and
also there were Spanish historians that
came over and wrote about it and said, oh
it's well known that they had a
sort of counting number system which was
based on these um
strings and knots. But yeah, the proper
decipherment was only made in 1912.
There are about a thousand quipus
around in museums and a lot is still not
known about them. It could be the case
that some of them the knots actually
represent phonetic elements.
So one of the great mysteries that
people who look at-
Incaologists looking at today is, was
the quipu more than just the Incas
counting system
but also some interesting new type of
writing system?
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[Music]
(Brady: Alex this was so fascinating, where could)
(I read about this?)
If you want to know more about that, in
my new book called the Language Lovers
Puzzle Book
I have a whole section on the quipu and
on about the decipherment of it.
In fact the book has lots of-
you think it's just going to be about
language but it's also about scientific
language and mathematical notation
and so you're going to learn about the
history of mathematical notation also in
this book.
(Brady: I can't wait! I can't wait!)
[Laughter]
Christmas that's like- what a great
Christmas present, eh? - Yeah, especially in
lockdown yeah.