The Tau Manifesto

For the discussion of math. Duh.

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Re: The Tau Manifesto

Postby skeptical scientist » Tue Feb 08, 2011 12:00 am UTC

antonfire wrote:Right there along with temperature being backwards and Lp spaces being backwards. It's one of those things that's too minor to change but still kind of annoying.

Just so that the dual of Lp would be L1-p (for 0<p<1)? Or is there some other reason why this notation is better?

With regards to temperature, I'll point out that differences in temperature come up a fair bit in physics. One example is the differential equation for an object coming to thermal equilibrium with its environment:
dT/dt=-l(T-T0)
(l is some constant measuring how much thermal contact there is between the object and the environment).

If we make the change of variables B=1/T, these differences get troublesome to deal with. For instance, we get the rather ugly differential equation:
dB/dt=l(B-B2/B0)
so I think inverting temperatures would cause more difficulties than they solve. Sure, negative temperatures being hotter than any positive temperature is weird, but really, how often does one encounter, in physics, a negative temperature?
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Re: The Tau Manifesto

Postby gmalivuk » Tue Feb 08, 2011 12:27 am UTC

nwest wrote:But instead we use the radius, so we have to have an ugly 2 next to Pi all the time.
I'd say the 2 next to pi, when it shows up, is far less ugly than the 1/2 you'd have next to tau, in all those other situations where we now just have pi (or an odd multiple thereof).
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Re: The Tau Manifesto

Postby doogly » Tue Feb 08, 2011 5:58 am UTC

It doesn't matter. I am going to set [imath]8\pi G = 1[/imath] anyway.
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Re: The Tau Manifesto

Postby gmalivuk » Tue Feb 08, 2011 4:39 pm UTC

That seems rather less convenient than just setting G=1.
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Re: The Tau Manifesto

Postby antonfire » Wed Feb 09, 2011 5:33 am UTC

Just set 8pi = 1 as well.
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Re: The Tau Manifesto

Postby skeptical scientist » Wed Feb 09, 2011 6:45 am UTC

antonfire wrote:Just set 8pi = 1 as well.

*smacks Anton upside the head*
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Re: The Tau Manifesto

Postby jestingrabbit » Wed Feb 09, 2011 6:48 am UTC

skeptical scientist wrote:
antonfire wrote:Just set 8pi = 1 as well.

*smacks Anton upside the head*

Dude, he's got a hold of a really great idea. I've played around with it a bit and I think I can prove a lot of stuff with this.
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Re: The Tau Manifesto

Postby skeptical scientist » Wed Feb 09, 2011 7:36 am UTC

jestingrabbit wrote:
skeptical scientist wrote:
antonfire wrote:Just set 8pi = 1 as well.

*smacks Anton upside the head*

Dude, he's got a hold of a really great idea. I've played around with it a bit and I think I can prove a lot of stuff with this.

*smacks jestingrabbit upside the head too, for good measure*
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Re: The Tau Manifesto

Postby majikthise » Wed Feb 09, 2011 7:59 am UTC

Hey, don't be pluralist-ist. Inconsistent theories are theories too!
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Re: The Tau Manifesto

Postby skeptical scientist » Wed Feb 09, 2011 9:05 am UTC

Are you itching to get smacked upside the head as well?
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Re: The Tau Manifesto

Postby the tree » Wed Feb 09, 2011 2:09 pm UTC

While we're at it, [imath]8\pi = \frac{\pi}{0}=0.999\dots = i = -i = \aleph_\frac{1}{2}[/imath] as well - it couldn't hurt.

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Re: The Tau Manifesto

Postby undecim » Wed Feb 09, 2011 5:39 pm UTC

So you want me to use (t/2)r^2 for the area of a circle and e^i(t/2) = -1?

I see Pi used more than 2Pi.
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Re: The Tau Manifesto

Postby undecim » Wed Feb 09, 2011 5:41 pm UTC

jestingrabbit wrote:
skeptical scientist wrote:
antonfire wrote:Just set 8pi = 1 as well.

*smacks Anton upside the head*

Dude, he's got a hold of a really great idea. I've played around with it a bit and I think I can prove a lot of stuff with this.


I can prove you can prove a lot of stuff. Anything at all, really, whether it's true or not.
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Re: The Tau Manifesto

Postby skullturf » Wed Feb 09, 2011 7:58 pm UTC

undecim wrote:So you want me to use (t/2)r^2 for the area of a circle and e^i(t/2) = -1?


I can understand your first objection. But I have no aesthetic objection to the second formula you write. Half a turn is multiplication by negative 1!

I agree that practically speaking, we're probably stuck with pi and are never going to change all the textbooks. But I think it could very well be true that in a hypothetical world, where beginning trigonometry students are given descriptions of the "special" angles in terms of tau rather than pi, they might actually find it more intuitive and learn it better!

The angles we call pi/4 and pi/3 would be referred to as tau/8 and tau/6 respectively -- because they're an eighth of a turn and a sixth of a turn. It's like cutting a pizza into eight or six slices.

When students learn that pi/4 is another name for 45 degrees, they might wonder "why is the 4 there?" One answer is "because 180 divided by 4 is 45", and another answer is "because this angle is one-fourth of a semicircle". But why is it a semicircle that's being divided into fourths?

I realize this is just a subjective aesthetic judgement, but to me, a 45 degree angle is "really" an eighth of something, more than it is a quarter of something.

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Re: The Tau Manifesto

Postby doogly » Wed Feb 09, 2011 9:02 pm UTC

But some things only come back to their original position after moving through 4pi; they come back at 2pi with a twist. So clearly 45 degrees is "really" a 16th of something, right?
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Re: The Tau Manifesto

Postby mike-l » Wed Feb 09, 2011 9:23 pm UTC

undecim wrote:So you want me to use (t/2)r^2 for the area of a circle and e^i(t/2) = -1?

Well, I'd write
[math]A = \frac 12 \tau r^2[/math]
much like I write
[math]\int x dx = \frac 12 x^2[/math]
which makes sense to me, because area is an integral over perimeter.

Also I'd write [imath]e^{i\tau} = 1[/imath], much prettier.

doogly wrote:But some things only come back to their original position after moving through 4pi; they come back at 2pi with a twist. So clearly 45 degrees is "really" a 16th of something, right?


You keep [imath]SL_3[/imath] out of this!
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Re: The Tau Manifesto

Postby skullturf » Wed Feb 09, 2011 9:36 pm UTC

mike-l wrote:Well, I'd write
[math]A = \frac 12 \tau r^2[/math]
much like I write
[math]\int x dx = \frac 12 x^2[/math]
which makes sense to me, because area is an integral over perimeter.


Also, formulas for the area of a circular sector "naturally" contain 1/2. For example,

\frac12 r^2 \theta

or maybe

\frac12 r L

where L is the arc length of the sector (and of course r is the radius and \theta is the angle).

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Re: The Tau Manifesto

Postby doogly » Wed Feb 09, 2011 9:51 pm UTC

mike-l wrote:
doogly wrote:But some things only come back to their original position after moving through 4pi; they come back at 2pi with a twist. So clearly 45 degrees is "really" a 16th of something, right?


You keep [imath]SL_3[/imath] out of this!

But fermions!
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Re: The Tau Manifesto

Postby skeptical scientist » Thu Feb 10, 2011 2:00 am UTC

mike-l wrote:...which makes sense to me, because area is an integral over perimeter.

Hey, that's amazing. Now we need only do the same thing for ellipses, and we'll never have to worry about those troublesome elliptic integrals again!
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Re: The Tau Manifesto

Postby antonfire » Thu Feb 10, 2011 4:34 am UTC

doogly wrote:But some things only come back to their original position after moving through 4pi; they come back at 2pi with a twist. So clearly 45 degrees is "really" a 16th of something, right?
In that sense, in two dimensions things don't come back to their original position after any amount of rotation, so pi = infinity.
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Re: The Tau Manifesto

Postby RebeccaRGB » Thu Feb 10, 2011 6:46 am UTC

the tree wrote:While we're at it, [imath]8\pi = \frac{\pi}{0}=0.999\dots = i = -i = \aleph_\frac{1}{2}[/imath] as well - it couldn't hurt.

Which is all equal to nullity!
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Re: The Tau Manifesto

Postby mike-l » Thu Feb 10, 2011 2:02 pm UTC

skeptical scientist wrote:
mike-l wrote:...which makes sense to me, because area is an integral over perimeter.

Hey, that's amazing. Now we need only do the same thing for ellipses, and we'll never have to worry about those troublesome elliptic integrals again!


See, Tau gives closed forms where Pi doesn't!
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Re: The Tau Manifesto

Postby gmalivuk » Thu Feb 10, 2011 2:23 pm UTC

Whoda thunk a simple factor of 2 could be so magical?
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Re: The Tau Manifesto

Postby Jyrki » Thu Feb 10, 2011 5:37 pm UTC

While it has some merits (the post on roots of unity in particular did strike a chord here), this ship has sailed a long time ago. Live with it.

More importantly. Yours truly and many others spent a lot of time memorizing the digits of pi (I was up at 465 at some point). That work is not going to go waste. We OPPOSE!

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Re: The Tau Manifesto

Postby the tree » Fri Feb 11, 2011 3:07 am UTC

doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.

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Re: The Tau Manifesto

Postby Kurushimi » Fri Feb 11, 2011 11:30 am UTC

the tree wrote:
doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.

That doesn't make sense. You mean to tell me if I piled together everything in the universe, it would amount to 1/16th of something? Of what exactly, huh?

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Re: The Tau Manifesto

Postby DavCrav » Fri Feb 11, 2011 11:57 am UTC

Kurushimi wrote:
the tree wrote:
doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.

That doesn't make sense. You mean to tell me if I piled together everything in the universe, it would amount to 1/16th of something? Of what exactly, huh?


Sixteen Universes?

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Re: The Tau Manifesto

Postby Jyrki » Fri Feb 11, 2011 1:05 pm UTC

the tree wrote:
doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.


What if you live in a ring, where 16 does not have a multiplicative inverse?

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Re: The Tau Manifesto

Postby letterX » Fri Feb 11, 2011 5:37 pm UTC

Jyrki wrote:
the tree wrote:
doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.


What if you live in a ring, where 16 does not have a multiplicative inverse?

You can still define 1/16th of something as "something when multiplied by 16 gets you the something". But I feel that's rather spoiling the joke.

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Re: The Tau Manifesto

Postby mike-l » Fri Feb 11, 2011 5:39 pm UTC

Jyrki wrote:
the tree wrote:
doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.


What if you live in a ring, where 16 does not have a multiplicative inverse?


You can still multiply by 16, then x is 1/16th of 16x, even if you can't multiply by 1/16.
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Re: The Tau Manifesto

Postby antonfire » Sat Feb 12, 2011 12:11 am UTC

Jyrki wrote:
the tree wrote:
doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.


What if you live in a ring, where 16 does not have a multiplicative inverse?

It's okay, even though you can't divide by 16, I would say 1 is a sixteenth of 16 in Z/32Z. (And so is 3.)
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Re: The Tau Manifesto

Postby Zach 739085133 » Sat Feb 12, 2011 2:42 am UTC

I'm a supporter of the τ symbol, and the nice thing is we don't have to choose between τ and π. Use whatever is most convenient.

It wasn't that long ago that [imath]\sqrt{-1}[/imath] was a dominant symbol. Wide use of i only came about later. Take a look at some 19th century books at Google Books. This one for example.

One more thing:

[math]\zeta (n) = {{2^{n-1}|B_n|\pi^n}\over{n!}} = {{|B_n|\tau^n}\over{2n!}}\text{ for even } n,\text{ }n \geq 2[/math]
Last edited by Zach 739085133 on Wed Mar 30, 2011 2:43 pm UTC, edited 3 times in total.

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Re: The Tau Manifesto

Postby Tauist » Sat Feb 12, 2011 2:51 am UTC

"While it has some merits (the post on roots of unity in particular did strike a chord here), this ship has sailed a long time ago. Live with it.

More importantly. Yours truly and many others spent a lot of time memorizing the digits of pi (I was up at 465 at some point). That work is not going to go waste. We OPPOSE!"

In the grand scheme of things, you will die soon. Whether future generation memorize pi or tau... well (after memorizing a full 3.1415) i memorized 6.283185307179586476925286766559005768394338798750211641949889184615632812572417987256069650684234135964296173026564613294187689219101164463450718816256862234900568205 (and still growing) during my spare time (starting 3 days ago) and i disagree with τ = 2 pi (doesn't know the alt code for pi)- pi = 1/2τ and so i just set τ=~ 100 digit of τ on my test today (funny watching my teacher see it) :)

*Wants to get a τ Club started at my high school*- so far i have 5 τist followers. Not exactly sure what we would do tho >.<

anyways, "Using π is equivalent having and using a constant for (1/2) gravity, (1/2) kinetic energy, and (1/2) mass. COME ON! Seriously? Would I go around saying I weigh 2(90) Lbs (4.2kg)? No. I would simply state that i weigh 180 Lbs (8.3kg)."
1/2τr^2 FTW :)

Thx for the Tau Manifesto and pi is wrong :0

"(n)=n!2n−1Bn=2n!Bn for even n n2"
u have τ/2 there

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Re: The Tau Manifesto

Postby jestingrabbit » Sat Feb 12, 2011 3:15 am UTC

antonfire wrote:
Jyrki wrote:
the tree wrote:
doogly wrote: So clearly 45 degrees is "really" a 16th of something, right?
Everything is a 16th of something.


What if you live in a ring, where 16 does not have a multiplicative inverse?

It's okay, even though you can't divide by 16, I would say 1 is a sixteenth of 16 in Z/32Z. (And so is 3.)

But not 5?
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Re: The Tau Manifesto

Postby antonfire » Sat Feb 12, 2011 9:14 am UTC

Of course not; obviously 16 times 5 will be bigger than 16 times 3.
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Re: The Tau Manifesto

Postby Zach 739085133 » Mon Mar 14, 2011 9:57 pm UTC

Well, it turns out March 14, 2011 has been a good day for tau. There is coverage at CNN and Vi Hart has debuted an entertaining video with 2879 likes and 61 dislikes at time of writing. Can't wait for June 28.

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Re: The Tau Manifesto

Postby joca63 » Thu Mar 17, 2011 2:01 am UTC

The point of Tau is simply that it is more integrative than Pi. Mathematicians are not going to find and troubles with including an extra /2 and more than they mind the current x2. Tau makes radian measure and trigonometry easier to understand for the beginners. Radians were described to me using the unit circle as: C= 2*Pi*r one rotation is a full 360 degrees so 360=2*pi*r so 180=Pi. this makes sense, until you remember that pi is defined by the ration of a circle's circumference to its diameter, the formula used the radius, and besides degrees are arbitrary anyway. Tau makes it easy to convert to radians: 360=Tau*r so Tau=360, or a full circle. In the end it is not the complicated math that is important, it is that it is easier to teach and learn. Current mathematicians shouldnt have any trouble converting to tau by dividing by two, and most importantly the ease of the Tau notation makes it more likely that a student will eventually become a mathematician

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Re: The Tau Manifesto

Postby BlackSails » Thu Mar 17, 2011 1:10 pm UTC

Yeah, I doubt that there has ever been a student who didnt become a mathematician because of pi.

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Re: The Tau Manifesto

Postby notzeb » Thu Mar 17, 2011 5:52 pm UTC

You know, for some reason I saw the thread title and I was certain it would be about how much muons suck.

Hey, while we're changing mathematical conventions, can we get rid of that annoying off by one problem in the Gamma function by switching to the Pi function? This way Pi still gets some love.
Zµ«V­jÕ«ZµjÖ­Zµ«VµjÕ­ZµkV­ZÕ«VµjÖ­Zµ«V­jÕ«ZµjÖ­ZÕ«VµjÕ­ZµkV­ZÕ«VµjÖ­Zµ«V­jÕ«ZµjÖ­ZÕ«VµjÕ­ZµkV­ZÕ«ZµjÖ­Zµ«V­jÕ«ZµjÖ­ZÕ«VµjÕ­Z

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Re: The Tau Manifesto

Postby dissonant » Fri Mar 18, 2011 5:35 am UTC

Redefining [imath]\pi = 2\pi[/imath] really doesn't do it for me. [I don't buy into this tau (or turn) nonsense!]

Sure, there are aesthetic improvements to some minor mathematical curiousities (Fourier series, Riemann's zeta function, Euler's identity)
But what about Wallis' formula?


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