STEVE MOULD: I'm Steve Mould.
And I think we should stop using pi and start using tau.
MATT PARKER: And I'm Matt Parker.
And I think Steve said something ridiculous.
I think pi is fantastic.
It's wonderful.
And even if this was an equal race, we would've been using
both of them.
Or even if tau had been established first, I'm still
pretty pro-pi.
STEVE MOULD: Wow, that's quite a claim.
MATT PARKER: Yes, there's [INAUDIBLE].
STEVE MOULD: So let's talk about this.
So pi is the circle constant.
It's the constant that defines a circle.
And the argument is--
MATT PARKER: We're agreed so far.
[RINGING]
STEVE MOULD: Let's think of a reasonable definition of what
a circle is.
The classic is all points equidistant
from a single point.
That distance is the radius.
And if you're ever doing maths using circles, you talk about
the radius.
All your equations about circles talk about the radius.
Unless you're an engineer, you use diameter.
But as a mathematician, you use the radius.
The circle constant should surely be defined in terms of
the radius.
[RINGING]
STEVE MOULD: But it isn't pi--
is the circumference divided by the
diameter, which is crazy.
So the circle constant should be the circumference divided
by the radius.
When you do that, you get 2 times pi.
[RINGING]
STEVE MOULD: And so we're not saying let's redefine pi and
call it 6.28.
But instead--
MATT PARKER: Wow.
STEVE MOULD: --we're saying--
[RINGING]
STEVE MOULD: Shut up.
Instead, we're saying that's going to be confusing, so
let's invent a new constant.
And we'll call it tau.
MATT PARKER: To be honest, one of the points was quite nice,
which is that if you're an engineer, you use pi.
And in fact, historically, we've used pi because when you
measure a circle, the only direct measurement you can
make is of the diameter.
[RINGING]
MATT PARKER: And so that's why historically we've done that.
And to this day in precision engineering we do that.
And yes, you can do some very nice maths with
the radius in a circle.
But the only thing you can directly
measure is the diameter.
So that's why we've used pi.
People say, oh, but we have to put 2 pi into lots of
equations, and then blah, blah, blah.
It's always 2 pi.
Why don't we just use tau instead?
There are as many fantastic equations out there which use
just the single pi.
And there's no reason to bring in 2 pi.
[RINGING]
MATT PARKER: And so I see Steve is holding a pen.
But I have brought my own.
STEVE MOULD: [CHUCKLING].
MATT PARKER: So everyone's classic is the e to the i pi
job, where e to the i pi plus 1 equals 0.
[RINGING]
MATT PARKER: And that is using a solitary pi
out the front there.
And if you want to go wild, things like
the area of a torus--
this is a nice one-- that equals pi squared--
[RINGING]
MATT PARKER: --outside the major radius squared minus the
minor radius squared.
So I'm still doing things in terms of
radiuses or radii or whatever.
But the pi squared-- that's lovely.
What-- you want 4?
I mean, how you are going to--
STEVE MOULD: Yeah, I want--
MATT PARKER: Tau squared on 4?
STEVE MOULD: What-- yeah, absolutely-- tau squared on 4.
And I'll explain why.
And this is important.
OK, let's just say that Matt has cherry-picked a couple of
nice equations there.
Two things I'd say-- let's look at, for example, the area
of a circle.
So we're looking at the area pi r squared.
MATT PARKER: That's just lovely.
Look at that.
[RINGING]
STEVE MOULD: Yeah, OK-- but here's the problem.
Here's the problem.
If we reframe that in tau, that would
be tau by 2 r squared.
And you think, OK, that's less beautiful.
But this tells us something important.
[RINGING]
STEVE MOULD: This tells us something.
This is information that you're obscuring by using pi.
Because you can derive the area--
MATT PARKER: By simplifying your--
[RINGING]
STEVE MOULD: No, listen.
You can derive the area of a circle by integrating.
[RINGING]
STEVE MOULD: So you say, OK, here's our full circle.
Let's look at the area of this little strip where the width
of it is delta r.
And this is r going up.
And so this is full r or whatever.
So you integrate.
The area of this is pi r dr.
MATT PARKER: Tau.
STEVE MOULD: No, but--
sorry, tau, yeah, actually.
[RINGING]
MATT PARKER: See, pi's just easier to use.
STEVE MOULD: Shut up.
And then you end up with 1/2 tau r squared.
[RINGING]
STEVE MOULD: And so that 1/2 tells you something.
It tells you you've done an integration to get there.
[RINGING]
STEVE MOULD: And an equation like this obscures it.
Similarly, with this, if you had tau squared over 4, that
would tell you something.
This equation here-- let's just reframe that.
e to the i tau minus 1 equals 0.
[RINGING]
STEVE MOULD: And the great thing is that is a full
circle, right?
If you want to go through half a circle, then it's e to the i
tau over 2.
If you want to go a quarter of a circle, it's e to
the i tau by 4.
[RINGING]
STEVE MOULD: The pi is confusing.
It's especially confusing for children when
they're learning as well.
A full circle is 2 pi?
OK, so that half a circle is pi.
A quarter of a circle is pi by 2.
So there's always this factor of 2--
[RINGING]
STEVE MOULD: --that you've got to keep in your mind when
you're doing calculations.
And actually, if you're a seasoned mathematician, you're
probably always thinking in terms of 2 pi, anyway.
[RINGING]
STEVE MOULD: And so let's just stop thinking in terms of 2 pi
and start thinking in terms of tau.
MATT PARKER: This is the hypocrisies of tau.
You want halves here.
You don't want halves over there.
[RINGING]
STEVE MOULD: I want halves here because the half tells
you something.
[RINGING]
MATT PARKER: This works out just as nicely.
Because if you want to integrate, and you've got your
2 pi r dr, then you get a wonderful
thing you can simplify.
Because you end up with this-- r squared--
STEVE MOULD: Yeah, so in this particular case--
MATT PARKER: --and you end up with a--
[RINGING]
STEVE MOULD: So in this particular case--
MATT PARKER: --2 pi and the 1/2 simplifies.
[RINGING]
STEVE MOULD: Yeah, yeah.
MATT PARKER: Pi r-- that's just--
there's nowhere else in maths where you say, you know what?
Let's not simplify it.
Let's leave it in a more complicated form because it--
STEVE MOULD: No, but in fact, this is the one case where you
think, actually it's useful to have a 2 there because we can
cancel later.
Most other cases you don't get to do that cancel because
you're not dividing by 2 later on.
[RINGING]
STEVE MOULD: In most cases, you end up with an equation
that's got 2 pi in it.
BRADY HARAN: A lot of smart people, who I know you
respect-- and I know you respect the guy
sitting next to you--
STEVE MOULD: [CHUCKLING].
BRADY HARAN: --make the case--
STEVE MOULD: That's correct.
MATT PARKER: Professionally.
BRADY HARAN: A lot of smart people make the case for tau.
MATT PARKER: Yeah.
BRADY HARAN: How do you explain their reasoning?
How do you--
I mean, you don't think Steve's an idiot.
But he has this feeling about tau that you disagree with.
What's different about his thinking to yours?
MATT PARKER: You know what?
A lot of people do have very good arguments for tau.
And a lot of people have very good arguments for pi.
And there is a wonderful thing--
I don't know.
I think people like the fact that it's different and that
they're going, oh, whoa, whoa, whoa-- everyone
else has got it wrong.
We can change this.
And tau is better.
And oh, people try and do maths and they
think pi's all that.
No, they're wrong.
But I don't think there's any great advantage other than it
can be a bit more exclusive to say, oh, we're all over tau--
[RINGING]
MATT PARKER: --when I think pi works just
as well in all cases.
It's got the--
I know--
historical--
the fact that it's got a bit of heritage doesn't mean we
should keep it around necessarily.
But it's worked for a very long time.
And it's there for very good reasons.
[RINGING]
MATT PARKER: Nothing people have thrown at me in terms of
tau, saying it's better--
you gain as much as you lose from--
[RINGING]
MATT PARKER: --switching from-- both of them have their
disadvantages and their advantages.
[RINGING]
MATT PARKER: I don't think there's enough for an entire
overhaul of the subject because people think, oh,
what, this particular equation looks a bit nicer.
Oh, but we've lost the fact that you get negative numbers
in Euler's identity.
And even your arguments with circles--
this is my clincher.
This is why I genuinely think pi is nicer.
If you've got tau, right?
If you do tau radians--
you do an entire revolution--
you end up right back where you started.
Tau gets you nowhere, right?
[RINGING]
STEVE MOULD: [CHUCKLING].
MATT PARKER: With pi, if you do pi radians, you actually
get somewhere.
And I think if you want a unit to measure things, the unit
shouldn't be the whole thing.
[RINGING]
STEVE MOULD: What?
[LAUGHING].
MATT PARKER: A unit should be a section of it.
And so it's more nuanced.
And for that reason--
STEVE MOULD: Oh, then in that case--
MATT PARKER: I think pi is better.
STEVE MOULD: --divide it by-- you know--360.
[RINGING]
MATT PARKER: Now you've just gone too far.
No one would use that kind of a unit.
BRADY HARAN: Steve--
STEVE MOULD: Yeah.
BRADY HARAN: I've heard you talk a little bit.
And you seem to have an enjoyment of the history of
mathematics.
Maths is beautiful and pure.
But it's also got great stories.
STEVE MOULD: Yeah.
BRADY HARAN: Why are you willing to ditch pi, which is
one of our most important clinged-to, loved stories?
MATT PARKER: Don't overstate my case here, all right?
STEVE MOULD: One word-- progress.
[RINGING]
STEVE MOULD: The historical point is a good one.
[RINGING]
STEVE MOULD: Historically, we used to sacrifice goats.
[RINGING]
STEVE MOULD: And I think we should keep doing that.
No--
so you can't just cling to something because of history.
Having said that, one argument against tau is that pi is very
well established.
And we'll just never replace it.
[RINGING]
STEVE MOULD: The strong argument for me is that tau is
more intuitive.
And so from an educational point of view--
[RINGING]
STEVE MOULD: --in terms of understanding circles and
working with circles, tau makes more sense.
MATT PARKER: Maybe just call it a circle.
BRADY HARAN: OK, Steve--
MATT PARKER: When you're trying to teach kids angles,
and you go, what angle is this?
All of it.
[RINGING]
MATT PARKER: That's just all the way round.
STEVE MOULD: But then you start dealing with radians.
MATT PARKER: And then you get half the circle.
It's called a circle.
BRADY HARAN: Steve, if I made you education minister of the
world tomorrow, what would you do about this situation?
STEVE MOULD: Well, here's the thing.
I think you can actually slowly bring it in.
Because you can use pi and tau at the same time.
[RINGING]
STEVE MOULD: Because wherever you see 2 pi,
you can write tau.
So you don't have to change any--
you don't have to suddenly overhaul textbooks and
redefine pi.
You can bring it in slowly.
And so if I was education minister of the world-- and I
hope to be one day--
you can bring it in very slowly.
BRADY HARAN: Matt, your argument seems to be that the
tau people aren't wrong.
It's just a bit needless.
It's extra work--
MATT PARKER: They're insufficiently right.
[RINGING]
STEVE MOULD: [LAUGHING].
BRADY HARAN: So what's wrong with education minister for
the world there next to you slowly bringing in tau?
MATT PARKER: I have no problem with tau sitting alongside pi.
[RINGING]
MATT PARKER: I have no problem with--
I think it's very important-- you're right-- to teach
radians in terms of it's a whole circle, and we're
splitting it up into smaller amounts, and how it links to
wonderful things like this.
But you never see anyone who's plugging tau in and going, you
know what, this would be useful as well.
They're always like, pi is wrong.
And I'm like, well, pi is not wrong.
STEVE MOULD: Pi is not wrong.
No, I know.
MATT PARKER: It's perfectly serviceable.
It's worked a treat.
And it's a wonderful concept.
And I think genuinely it's got a lot more going for it for
doing maths than tau.
But there's many things where you could say historically--
like, why don't we count in base 12?
That would be nicer.
But we don't.
We count in base 10, which, I admit, I would almost say base
12 has more advantages if we switch to that than if we
switch to tau.
[RINGING]
MATT PARKER: So why are we getting so emotional about our
irrationals when we could be a bit more rational about our
base systems?
BRADY HARAN: I'm stopping the tape before
you both start talking.
MALE SPEAKER: 4.8 kilograms--
MALE SPEAKER: So we define angles counterclockwise--
MALE SPEAKER: --of order--
MALE SPEAKER: --so we go that way rather than that way.
Quite why we do that, I have no idea.
It's convention.
MALE SPEAKER: And similarly, if I went up, say, to the size
of a boulder, so that this was--