The Tau Manifesto

For the discussion of math. Duh.

Moderators: gmalivuk, Moderators General, Prelates

arbiteroftruth
Posts: 476
Joined: Wed Sep 21, 2011 3:44 am UTC

Re: The Tau Manifesto

Postby arbiteroftruth » Thu Sep 05, 2013 9:07 pm UTC

I think the main point behind tau is that it's worth doing precisely *because* it's irrelevant to real mathematicians. They can handle a variable substitution just fine, but all the anecdotal evidence I've seen indicates that tau is much easier for educational purposes. So if switching to tau helps one group of people, and is irrelevant to the other, the conclusion is to switch.

All the commentary about other places where the circle constant shows up is mainly about showing how those equations are still derived from the basic case of the circle, and in that case the derivation is potentially clarified or easier to follow when the association with the circle uses the more directly associated constant, tau. In particular, a broad range of categories relate back to actual circles in the following way.

The Gaussian integral is evaluated to sqrt(tau/2) by way of evaluating the 2-dimensional integral in polar coordinates, exploiting the function's circular symmetry in 2 dimensions.
From the Gaussian integral, we get all manner of probability applications, the values of the Gamma function at half-integers, and a non-recursive solution to the general problem of hyperspherical volume.
Through the Gamma function we can acquire the functional equation of the Riemann Zeta function.
From the Riemann Zeta function we get applications to number theory.

And so on. The point isn't to find the value that eliminates the most fractions in the most equations. The point is to relate things back to the simplest starting point possible.

Derek
Posts: 2181
Joined: Wed Aug 18, 2010 4:15 am UTC

Re: The Tau Manifesto

Postby Derek » Thu Sep 05, 2013 10:01 pm UTC

Have I posted in this thread before? Not sure. Well, I'm in the Tau camp, for the record.

User avatar
PM 2Ring
Posts: 3713
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

Re: The Tau Manifesto

Postby PM 2Ring » Fri Sep 06, 2013 6:31 am UTC

I may have said this earlier in the thread; I can't be bothered re-reading the old posts. I agree that it's reasonable to claim that tau has various advantages over pi, but are these advantages great enough to warrant changing to tau now, when we've been using pi for so long? As others have said, it boils down to a factor of 2, and if coping with that is too hard then maybe mathematics is not for you. :) OTOH, if multiple trials clearly show the pedagogical advantages of tau over pi, then I'd have no objections to teaching kids tau. After all, the tau proponents don't seem to be pushing for the abolition of pi.

kubit
Posts: 22
Joined: Fri Sep 06, 2013 6:16 pm UTC

Re: The Tau Manifesto

Postby kubit » Fri Sep 06, 2013 6:24 pm UTC

Just to put my two cents worth in... I'm fairly sure mathematics education has far more important problems these days than whether 2pi has its own symbol! Really, even though I agree that there is a point with tau being more intuitive in geometry it seems like major waste of time to argue over it...

User avatar
Cleverbeans
Posts: 1378
Joined: Wed Mar 26, 2008 1:16 pm UTC

Re: The Tau Manifesto

Postby Cleverbeans » Fri Sep 06, 2013 11:33 pm UTC

kubit wrote:it seems like major waste of time to argue over it...


Welcome to the internet. :lol:
"Labor is prior to, and independent of, capital. Capital is only the fruit of labor, and could never have existed if labor had not first existed. Labor is the superior of capital, and deserves much the higher consideration." - Abraham Lincoln

elasto
Posts: 3757
Joined: Mon May 10, 2010 1:53 am UTC

Re: The Tau Manifesto

Postby elasto » Sat Sep 07, 2013 2:21 pm UTC

M= Man looking for an argument
R= Receptionist
Q= Abuser
A= Arguer (John Cleese)
C= Complainer (Eric Idle)
H= Head Hitter

M: Ah. I'd like to have an argument, please.
R: Certainly sir. Have you been here before?
M: No, I haven't, this is my first time.
R: I see. Well, do you want to have just one argument, or were you thinking of taking a course?
M: Well, what is the cost?
R: Well, It's one pound for a five minute argument, but only eight pounds for a course of ten.
M: Well, I think it would be best if I perhaps started off with just the one and then see how it goes.
R: Fine. Well, I'll see who's free at the moment.
Pause
R: Mr. DeBakey's free, but he's a little bit conciliatory.
Ahh yes, Try Mr. Barnard; room 12.
M: Thank you.

(Walks down the hall. Opens door.)

Q: WHAT DO YOU WANT?
M: Well, I was told outside that...
Q: Don't give me that, you snotty-faced heap of parrot droppings!
M: What?
Q: Shut your festering gob, you tit! Your type really makes me puke, you vacuous, coffee-nosed, maloderous, pervert!!!
M: Look, I CAME HERE FOR AN ARGUMENT, I'm not going to just stand...!!
Q: OH, oh I'm sorry, but this is abuse.
M: Oh, I see, well, that explains it.
Q: Ah yes, you want room 12A, Just along the corridor.
M: Oh, Thank you very much. Sorry.
Q: Not at all.
M: Thank You.

(Under his breath) Stupid git!!

(Walk down the corridor)

M: (Knock)
A: Come in.
M: Ah, Is this the right room for an argument?
A: I told you once.
M: No you haven't.
A: Yes I have.
M: When?
A: Just now.
M: No you didn't.
A: Yes I did.
M: You didn't
A: I did!
M: You didn't!
A: I'm telling you I did!
M: You did not!!
A: Oh, I'm sorry, just one moment. Is this a five minute argument or the full half hour?
M: Oh, just the five minutes.
A: Ah, thank you. Anyway, I did.
M: You most certainly did not.
A: Look, let's get this thing clear; I quite definitely told you.
M: No you did not.
A: Yes I did.
M: No you didn't.
A: Yes I did.
M: No you didn't.
A: Yes I did.
M: No you didn't.
A: Yes I did.
M: You didn't.
A: Did.
M: Oh look, this isn't an argument.
A: Yes it is.
M: No it isn't. It's just contradiction.
A: No it isn't.
M: It is!
A: It is not.
M: Look, you just contradicted me.
A: I did not.
M: Oh you did!!
A: No, no, no.
M: You did just then.
A: Nonsense!
M: Oh, this is futile!
A: No it isn't.
M: I came here for a good argument.
A: No you didn't; no, you came here for an argument.
M: An argument isn't just contradiction.
A: It can be.
M: No it can't. An argument is a connected series of statements intended to establish a proposition.
A: No it isn't.
M: Yes it is! It's not just contradiction.
A: Look, if I argue with you, I must take up a contrary position.
M: Yes, but that's not just saying 'No it isn't.'
A: Yes it is!
M: No it isn't!
A: Yes it is!
M: Argument is an intellectual process. Contradiction is just the automatic gainsaying of any statement the other person makes.
(short pause)
A: No it isn't.
M: It is.
A: Not at all.
M: Now look.
A: (Rings bell) Good Morning.
M: What?
A: That's it. Good morning.
M: I was just getting interested.
A: Sorry, the five minutes is up.
M: That was never five minutes!
A: I'm afraid it was.
M: It wasn't.
Pause
A: I'm sorry, but I'm not allowed to argue anymore.
M: What?!
A: If you want me to go on arguing, you'll have to pay for another five minutes.
M: Yes, but that was never five minutes, just now. Oh come on!
A: (Hums)
M: Look, this is ridiculous.
A: I'm sorry, but I'm not allowed to argue unless you've paid!
M: Oh, all right.
(pays money)
A: Thank you.
short pause
M: Well?
A: Well what?
M: That wasn't really five minutes, just now.
A: I told you, I'm not allowed to argue unless you've paid.
M: I just paid!
A: No you didn't.
M: I DID!
A: No you didn't.
M: Look, I don't want to argue about that.
A: Well, you didn't pay.
M: Aha. If I didn't pay, why are you arguing? I Got you!
A: No you haven't.
M: Yes I have. If you're arguing, I must have paid.
A: Not necessarily. I could be arguing in my spare time.
M: Oh I've had enough of this.
A: No you haven't.
M: Oh Shut up.

(Walks down the stairs. Opens door.)

M: I want to complain.
C: You want to complain! Look at these shoes. I've only had them three weeks and the heels are worn right through.
M: No, I want to complain about...
C: If you complain nothing happens, you might as well not bother.
M: Oh!
C: Oh my back hurts, it's not a very fine day and I'm sick and tired of this office.

(Slams door. walks down corridor, opens next door.)

M: Hello, I want to... Ooooh!
H: No, no, no. Hold your head like this, then go Waaah. Try it again.
M: uuuwwhh!!
H: Better, Better, but Waah, Waah! Put your hand there.
M: No.
H: Now..
M: Waaaaah!!!
H: Good, Good! That's it.
M: Stop hitting me!!
H: What?
M: Stop hitting me!!
H: Stop hitting you?
M: Yes!
H: Why did you come in here then?
M: I wanted to complain.
H: Oh no, that's next door. It's being-hit-on-the-head lessons in here.
M: What a stupid concept.


Return to “Mathematics”

Who is online

Users browsing this forum: No registered users and 11 guests