STEVE MOULD: I'm talking about an insect called a cicada.
They're in the news at the moment in America.
They are a small flying insect.
And the reason they're in the news at the moment is because
they spend a huge amount of their lives underground.
And very occasionally, they come out in a big swarm for
the three F's-- feeding, fighting, and mating.
And in America, this particular cicada, it's called
a periodical cicada.
And this one comes out every 17 years.
The reason I want to talk about it is because it
illustrates an interesting way that nature does maths,
because if you want to do maths, if you want to solve a
problem in mathematics, what you do is you start with all
the facts that you already know.
You combine those facts together using mathematical
logic to create some new fact that you didn't know before.
So that's how you would prove something in mathematics, how
you would solve a problem.
This is not what they look like.
But let's have a go.
OK, so there's kind of--
imagine you've got a lovely wing.
There you go.
It's mostly wing.
Big buggly red eyes.
Maybe there's an antenna kind of going on, legs coming out,
something like that.
BRADY HARAN: That's real?
Are you serious?
STEVE MOULD: Yeah.
I mean, look, it's as close as we're going to get.
I know it looks like kind of a weird cow or something.
This illustrates the way that nature does maths.
It's basically, instead of having this logical,
methodical process, you just sort of have a guess.
And you see if your answer's correct.
You test it.
And if it's not correct, then you try a new answer and see
if that gets you any closer, and you keep trying and trying
and trying.
So it's a process of trial and error.
And this is genuinely a way that you can solve problems in
mathematics.
I think that the best example of trial and error that the
world has ever seen is evolution,
sort of natural selection.
So how has this happened with the cicada?
Well, the first thing to know about the cicada is that it
has a really interesting method of protecting itself
against predators.
And that is something called predator satiation, which is
basically where you make yourself so numerous that your
predator is literally full.
It's too full, can't eat anymore.
And that's how you survive.
But you sort of think, well, how can that work?
Surely if you satiate your predator, then your predator
is just going to come back stronger in the next
generation and eat even more of you.
That can only work for the predator if the predator can
make its life cycle the same as yours, so it's
in step with you.
So it's eating when you're out and about doing
your thing as well.
And so the next thing the cicada does is to make its
life cycle really, really long, too
long for the predator.
For some reason, predators can't have this really long
life cycle.
So that's why the cicada has this really long life cycle.
It's to kind of get out of step with the predator.
So let's look at that on the number line.
1, 2, 3, 4--
15, 16, 17.
So let's write those out.
So 0, 1, 2, 3, 4--
15, 16, 17.
So this particular cicada that's in the news comes out
every 17 years.
There's another one that comes out every 13 years.
Is that important?
Could it be some other thing?
So for example, what if the cicada chose a
12-year life cycle?
The predator, that's too long for the predator.
It can't wait 12 years.
But the predator still has a trick.
So maybe the predator has a 6-year life cycle instead.
So the predator comes out after 6 years.
There's a predator comes out there, and
there are no cicadas.
But the next generation of the predator, that's at 12 years.
And suddenly, there are loads of cicadas there.
And so every other generation of the predator is able to
feed on cicadas.
And that gives them advantage, and they will grow, and they
will flourish.
Or if 6 years is too long, how about a 4-year cycle?
So we go 4 years, no cicadas.
8 years, no cicadas.
12 years, cicadas.
If 4 is too long, you could even have a 3-year life cycle.
So the first 3 years, no cicadas.
The second 3 years, no cicadas.
The third 3 years, no cicadas.
The fourth lot of 3 years, that's 12 years, cicadas.
Even 2 years, that will work as well.
So if you're a cicada and you choose a 12-year life cycle,
that's a terrible decision, because 12 has all these
things that you can divide it into.
So 12 is divisible by 6, divisible by 4, divisible by
3, and divisible by 2.
So if you're a cicada, you need to choose a life cycle
which is not divisible by anything.
So Brady, what's a number that's not
divisible by anything?
BRADY HARAN: I'm no expert.
But I would reckon you're heading here
towards prime numbers?
STEVE MOULD: Prime numbers.
Exactly.
So that is why the cicada has chosen a 13-year life cycle
and a 17-year life cycle.
It's the solution to a mathematical problem.
And it's the discovery of prime
numbers by natural selection.
Absolutely amazing.
Yeah.
So a cicada lives for 17 years.
But 16 of those years are spent underground in a sort of
larval state.
And then they come out in a big swarm in the 17th year.
BRADY HARAN: 13 and 17 years seems like a long time.
There are a lot of prime numbers lower than that.
STEVE MOULD: Well, yes, there are.
But I suppose the issue with smaller numbers is that just
maybe the predator could stretch to having a
life cycle that long.
And so they can get into step with it.
The great thing is, by the way, if you've got, say, a
13-year life cycle and your predator has a 4-year life
cycle, how often will the predator and the prey meet?
Well, it's 4 times 13, or 4 times 17.
So you have to multiply the two numbers together, and it
becomes this enormous thing.
And that's the genius.
If there was some common factor to these two, then you
wouldn't have to multiply them together to find
out when they meet.
It would be a much smaller number.
The predator is a wasp.
It's called the cicada-killing wasp.
I don't know where they got that name from, but
those guys are crazy.
Yeah, the wasp is great.
It basically kills the cicada with a sting.
And then it plants an egg inside the cicada's dead body,
which then feeds on it from the inside and then releases a
wasp at the end of this.
Great way to go.
But yeah, I love the idea of satiating your predator.
You really don't want to be in the vanguard of the cicada
group when that's your policy.
You have to go really far down this approximation route
before you get close to the golden ratio, much more so
than pi or whatever.
So the golden ratio is the most irrational number.