Placeholder Image

字幕表 動画を再生する

  • 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--

STEVE MOULD: I'm Steve Mould.

字幕と単語

ワンタップで英和辞典検索 単語をクリックすると、意味が表示されます

B2 中上級

タウvsパイのスマックダウン - Numberphile (Tau vs Pi Smackdown - Numberphile)

  • 20 1
    liuyangism に公開 2021 年 01 月 14 日
動画の中の単語