JAMES GRIME: 0. That's our friend. Yes. To a mathematician
this is a number. But it wasn't always obvious. ROGER BOWLEY: Math existed to do
financial transactions, to sell sheep, to buy copper
things, whatever. And you would use coins. And there would be values
to the coins. So you would say this
costs 5 pounds 20 shillings, or whatever. You don't do any trading
with the number 0. I've got no sheep here. Oh, I'm gonna buy no sheep,
I'll give you no pounds. It doesn't make any sense. So there was no need
for shopkeepers to invent the number 0. JAMES GRIME: They had
the idea of 5 cows. But the idea of 5,
not so much. The idea of 5-ness they didn't
quite understand. So a number like 0, which
is the absence of-- well, whatever, cows,
whatever it was-- made no sense to them. I'm going ask Brady
a question. See if I can catch him out. Brady, is 0 an even number? BRADY HARAN: I think
the answer is no. But it feels like it is
because it is round. JAMES GRIME: So this
is an interesting-- OK, let me ask another
question. Is 16 an even number? BRADY HARAN: Yes. JAMES GRIME: Yes. So people have studied this. People have a delayed
reaction. People are not sure whether
0 is an even number. Now I can tell you that 0, categorically, is an even number. It will follow every definition
of an even number. ROGER BOWLEY: So there was an
Indian called Brahmagupta who invented the idea of nothing not
being nothing but existing as an abstract quantity
in the mathematics. Well, then it goes
to North Africa. And there's a guy called
Al Qasimi. And he writes a book about the
art of Hindu mathematics and reckoning by Hindu
mathematics. And that spreads through North
Africa to Spain and so forth. And it becomes, they think,
Arabic numbers. So you have all the
numbers plus 0. That was fine. Until 1200 when Leonardo of
Pisa, also known as Fibonacci, translates this book. It's a wonderful idea. But this is in the period
of the Crusades. So people think these are Arabic
numbers, not Hindu numbers because it's come
from North Africa. So the Catholic church objects
to this because there are Crusades going on and this
is the work of the enemy. So in Florence, for example,
they banned the use of this Arabic number 0. And it was thought to be
the work of the devil. BRADY HARAN: Because my
definition of an even number is something that can
be divided by 2. JAMES GRIME: So Brady's just
told me an even number is a number that can be
divided by 2. Well, 0 can be divided by 2. 0 divided by 2 is 0. In fact, in that sense, it
is the most even number. In ancient times they had this
idea of things being singly even or doubly even. So 12 would be doubly even
because you can divide by 2 and then 2 again. Well, by that sense, 0 can be
divided by 2 and 2 and 2 and 2-- it is the most
even number. The correct definition of
an even number is it's a multiple of 2. Something times 2. Something times 2. Well, it is. There's no problem with that. It's 0 times 2. Great. Brady said it had to
be divisible by 2. Well, that works. 0 divide by 2 is 0. OK, so it fits between
two odd numbers. That might be a definition
for even. Let's do that. There's 0. And over here that's 1. Over here that's minus 1. And then you get 2 over
here, minus 2. Perfectly fits. There are some rules
for numbers. Some arithmetic rules. Two even numbers, if you add two
even numbers together, you get an even number. Well, that works. 0 plus 4 is 4, an even
number again. That's what we want. We're saying 0 is even. It follows every definition. In fact, if it wasn't even, then
it would break our rules of arithmetic, which would
be a disaster. It is true to say that 0 is
neither positive or negative. It sits here between the
positive numbers and the negative numbers. So it is neither positive
or negative. ROGER BOWLEY: The discovery of
0 was the most important advance in mathematics of all,
because it made mathematics capable of being understood
by everybody. Everybody could do
this mathematics. JAMES GRIME: The Babylonians,
the Greeks, they had the idea of a space. So there was a difference
between 26, 2 and 6, and 206, 2-0-6. They had a space there. They didn't use the symbol
0, but they had a space. It was more like a
punctuation mark. So the Babylonians would
understand the difference between 26 and 206. But instead of using the symbol
for 0, they would just have a space. However, if they wanted
to write 260, 260 was written like this. And to us, that looks like 26. To them and in context,
that would make sense. But they didn't have this
idea of 0 by itself. In the 9th century, the
first instance-- or the first recorded
instance of 0-- was found. It was actually found by a
gardener keeping track of the number of flowers that his
garden would produce. And he used the number 50 as
we would recognize it. 5, 0. After that point, they started
to experiment with 0. What could it do? If you add 0, it makes
no difference. If you times by 0, you get 0. Dividing by 0-- that caused them some problems
as it still does today. ROGER BOWLEY: In this sense,
the mathematical sense, the number 0 does not
mean nothing. It means a quantity which you
can manipulate in the mathematics. And so it's better to call
it 0 rather than nothing. Nothing is when you're
counting. There's nothing there. 0 is the abstract mathematical
quantity. CGP GREY: I'm CGP Grey and
my favorite number is 0. I like 0 because it's not
an obvious number. You can have counting systems
where there's one thing, two things, three things,
four things. But mathematics existed for a
long time without having a 0 as part of it. So it's a number, but
it also isn't anything in and of itself.
