

Happy Tau Day - vColin
http://www.bbc.co.uk/news/science-environment-13906169

======
imurray
"What Tau Sounds Like" <http://www.youtube.com/watch?v=3174T-3-59Q>

(Yes, we know that Tau doesn't _really_ sound like anything, but this was fun
and better than I expected.)

~~~
ignifero
on a related note, tau in greek is pronounced ˈtaff

~~~
mhartl
And pi in Greek is pronounced 'pee'. Still lots of pun potential, but maybe
not the kind you'd want. ;-)

~~~
ignifero
Pi is tough and pees on tau?

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imurray
The earliest example I've seen of 2π is in a 1763 letter from Thomas Bayes
(the paper that appeared in the Royal Society proceedings directly after the
one that's famous). He used _c_ for the circumference of a circle whose radius
is unity.

If you've ever used Stirling's approximation, this is the paper that first
points out that it's a divergent series.

Scan of original (it's also on JSTOR):
<http://www.york.ac.uk/depts/maths/histstat/letter.pdf>

With modern typesetting and an explanation:
<http://www.stat.ucla.edu/history/letter.pdf>

(I don't seriously think we should change from pi to tau.)

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vessenes
The most compelling argument for me in using tau, (and I have started trying
to think in tau when it comes up) is the radians argument: one quarter of a
circle is tau/4, or pi / 8, you pick.

I am certain my kids will have an easier time remembering tau/4, as I do
myself.

The other compelling thing for me came from remembering just how many
integrals from 0 to 2pi I wrote over my freshman complex analysis class. A
lot. Less notation is always nice; having tau represent the entire circle just
makes a lot of sense!

~~~
jcarreiro
> one quarter of a circle is tau/4, or pi / 8

I am not particularly well versed in mathematics but isn't 1/4 of a circle
pi/2 radians?

~~~
vessenes
Ah, you made my point for me!

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ianterrell
Can anyone defend Pi on grounds other than _that's the way it's always been_ ,
or _introducing a new constant is hard_?

~~~
smosher
e^(i * pi * x) for integer x is on the real line.

With 'tau' you only get the positive half (consider the integer values of x;
which are 2, 4, 6 for 'tau'):
<http://www.wolframalpha.com/input/?i=plot+e^%28pi+*+i+*+x%29>

I've dozens of subtle little reasons, but I think that one shows it off best
and is easiest to understand.

I was going to add that zero crossings for sine waves (I am into sound
synthesis) are at integer multiples of pi, but that's just a funny way of
stating the above.

~~~
ianterrell
I keep seeing this in my comments so I might as well respond for posterity,
especially since this is not a sound mathematical argument for pi.

> _zero crossings for sine waves are at integer multiples of pi_

This is actually a strong argument for tau.

The sin wave measures the height of a circle at the angle given in radians.
"Integer multiples of pi" don't immediately show you that there are two very
different zeros: one going up, and one going down. Using tau shows you that
explicitly: on half turns around the circle _sin(tau/2)_ , you're at 0 going
down; on whole turns _sin(tau)_ you're going up. You (literally) "come full
circle" with integer multiples of tau—those 0s are equivalent.

The argument is the same with e^(i * pi * x). See Section 2.3 on tauday.com
and the chart under "Eulerian Identities." Each integer increment corresponds
to a rotation in the complex plane. The reason it's on the real line at 2, 4,
6 is because it takes two rotations to get back to the real line.

At 1 rotation ( _i_ ), you're fully imaginary; at 2, fully real, but negative;
3, fully imaginary again, but negative; 4, you're back where you started, real
and positive.

This is what it would look like with tau, and it's exactly what you expect:
[http://www.wolframalpha.com/input/?i=plot+e^%280.5*pi+*+i+*+...](http://www.wolframalpha.com/input/?i=plot+e^%280.5*pi+*+i+*+theta%29)

Elegance is not just whether something is "pretty," as in, _hey look,
integers!_ It's also whether it has strong meaning.

~~~
smosher
I'm sorry but your comment came off as condescending.

The graph I linked coincides with my needs, it was specially crafted to
demonstrate that, not to show off some silly notion of elegance with no ounce
of application. Sorry for not making that clear.

As for: _Elegance is not just whether something is "pretty," as in, hey look,
integers! It's also whether it has strong meaning._ \-- please try applying
that value to your opinions about giving up pi for tau. I'm not the one guilty
of that kind of thinking, you are.

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speckledjim
"Almost anything you can do in maths with pi you can do with tau anyway,"

WTF is this? I'm eagerly awaiting an explanation of what you can do with X
that you can't do with 2X.

It's a moot anal point. X or 2Y, using one over the other doesn't solve
anything.

~~~
michael_dorfman
It doesn't _solve_ anything, but it makes certain formulae and relationships
more intuitive. Have you read the Tau Manifesto?

~~~
speckledjim
More _intuitive_? If you're phased by the odd 2 or 1/2 here or there in maths,
it's probably not the right discipline for you.

Far more important step for mathematicians would be to switch from base 10 to
something more useful like base 8.

~~~
michael_dorfman
Again, I ask: have you read the Tau Manifesto? If not, I suggest you do that,
as it makes the case there much more clearly than I could here.

The point being: for children learning the basics, the odd 2 or 1/2 here and
there masks the underlying relationships. But don't take my word for it-- read
the manifesto.

~~~
speckledjim
I read it a few years ago. I disagree. It's like saying removing a seldom used
letter from the alphabet would mean kids learn to spell better.

The whole point of learning is to learn to read things and understand them.
That means looking behind 'fluff' like 2, or 1/2, and understanding the
concepts.

------
cuponthefloor
Simple and relevant! <http://www.youtube.com/watch?v=jG7vhMMXagQ>

~~~
J3L2404
I'm sold. Especially on Euler's equation.

------
Confusion
The mathematical world is as full of lonely pi's, as it is of 2*pi's. Now we
need to move to tau/2 and tau, only to get a pi-manifesto in a couple of
decades.

Previous discussions:

<http://news.ycombinator.com/item?id=1468341>

<http://news.ycombinator.com/item?id=2322666>

~~~
Jach
I like the compromise of using Tau and its fractions when it makes sense and
using a single Pi when it's not so intuitively-connected with a circle. e.g.
\int_{-\infty}^{\infty} e^{−x^2} dx = \sqrt{\pi}.

Plus Tau Day's a fun excuse to eat two pies.

~~~
drbaskin
I'm not a big fan of introducing a new constant (though I believe \pi should
have been 2\pi), but I love thinking of the integral you wrote down as
\sqrt{\tau / 2} because then the answer practically tells you how to derive
it!

How to derive the value of the integral: Square the integral to make it an
integral in two variables, introduce polar coordinates, then change variables.

~~~
Jach
Yes, it's one of my favorite proofs. (I think I like it more than Euler's
formula, especially since many calc teachers will look at e^{-x^2} and say
it's un-indefinite-integrable without a second thought at what else it can
do.)

But I'm not quite sure how you seeing it as \sqrt{\tau/2} helps you see the
proof more easily. Because if you see \tau (ignoring the 1/2) you think "It
has to do with circles or polar form." as per my rule of thumb?

~~~
drbaskin
I'm sorry I wasn't more clear, but your interpretation is what I meant. Per
your rule of thumb, seeing \tau should suggest that it has to do with circles
or polar coordinates, and the square root points to how to get the polar
coordinates.

------
ianterrell
I started a Kickstarter to create a social object against Pi!

<http://www.kickstarter.com/projects/ianterrell/say-no-to-pi>

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TheOnly92
If it's not broken, don't fix it. I don't see pi broken as it has been used
for _centuries_. Why should we change it all of a sudden? To signify that
we're into a new era? The Tau era?

~~~
edanm
Why did we move from Roman Numerals or other systems of writing down numbers,
to the current numerals we use today? Simple - they make lots of things
easier.

Now, no one is claiming that Tau vs. Pi is even close to the same level of
importance. But it makes some things just that much easier.

~~~
TheOnly92
Of course, if there's proof that the changes from Pi to Tau will accelerate
technological advancement even by 0.01%, I'll totally support it.

The fact is that making things easier doesn't necessarily mean improvement.

~~~
jerf
"The fact is that making things easier doesn't necessarily mean improvement."

Untrue, and if you're a programmer you ought to know better. Making something
that works the exact same way, only easier, is definitely an improvement. Now
it takes less of your finite mental reserves to accomplish a task, and you can
now go further in the same amount of time. Making something that abstracts
away some things and makes the rest easier is often an improvement, when the
advantage of being easier outweighs the loss of control.

Or are you still programming in raw machine language?

Programmers live in such a rich ecosystem of things that are improvements
merely because they are easier that it is easy to take that process for
granted without understanding it. How many _orders of magnitude_ less
effective would I be in machine language? Certainly more than one, almost
certainly more than two (working on a network + manual memory management =
security fail).

~~~
TheOnly92
Okay, I failed to properly address "improvement". By "improvement" I mean the
time required to develop something new. Of course everything improves, simply
because it's built on top of the base of an older version.

A simple example, it took months to write a simple browser with a little less
features than the browsers available during the Win 9x era. Does it take weeks
now? I doubt so.

Ok, to put it more simply, what I meant was improvement in the time required
not as in the thing that was produced. Uh, get what I mean?

~~~
jerf
"Does it take weeks now? I doubt so."

Ooooo, bad choice of example. It takes a day or so now, since WebKit is
embeddable.

You're trying to separate something that can't be separated. You can't
separate "making things take less time" from "making better things possible",
because the bound in all cases is _time_. If you have to spend less time on X,
then you've got more to spend on Y; if you can't spend less time on X you'll
never reach Y. It's the rare improvement that can _only_ improve quality, but
doesn't in any way permit you to instead trade that for time.

~~~
TheOnly92
WebKit is embeddable, sure, but if you're to write a browser that functions
similarly to today's browser, it still takes months. You're gonna need to do
bookmarks, tabs, history. Things have been made easier, surely but things are
still as complicated as ever.

However this is drawn too far from the topic of Tau, what I'm trying to imply
is that science and maths has work centuries with Pi, we've found many great
theories with it as well. But in the modern era (quantum), Tau seems
irrelevant (okay, I haven't studied too much about quantum, but I've read on
articles and there's no mention on Pi either, correct me if I'm wrong).

What's the use of making things simple at the same time confusing people?
Things have always worked out, and it should continue to work on.

------
SeanLuke
> Not all fans of maths agree, however, and pi's rich history means it will be
> a difficult number to unseat.

This statement is never supported (the fan part). Bad BBC, bad!

------
scythe
The Greek letter tau is already used to refer to the period of an oscillation,
the time constant of a decay interval (these are intimately related), plus
plenty of other stuff. There really aren't any Greek letters left that aren't
used for a million things already. tau-as-time-constant is the standard use
for the thing, and the confusion with torque and natural temperature is bad
enough as it is.

Yes, pi shows up as the prime counting function, but there it's a _function_ ,
which clears up the otherwise ambiguous notation. Furthermore these abuses of
notation are generally considered a bad thing, something we try to avoid.

As for the intuitiveness of such deep results as Stirling's formula and the
even values of the Riemann zeta: this is to concern oneself with the
upholstery on the Space Shuttle.

If you want a new pi symbol, might I suggest the variant pi described here:
<http://en.wikipedia.org/wiki/Pi_%28letter%29> \-- though I'm afraid this is
all a waste of time and energy.

~~~
ignifero
Not to mention the tau neutrino. But the bigger question is why would one want
to do that?

~~~
scythe
It is not an exercise worth ignoring: I had also once thought that pi should
be replaced.

Slightly different motivation, though, as it seemed to me that pi/2 was really
more interesting, and anyway it is really much easier to write multiplication
than fractions when you run into a discrepancy. Here the roots of the sine are
at even multiples and the roots of the cosine are at odd multiples, and e^(i
pi/2) = i is more interesting than the previous incarnations of the Euler
formula.

The thing is that the important parts of these formulae are the way they are
derived and the structure they represent, not their appearance on a sheet of
paper. If you can understand what relates the zeta function at even numbers to
the ratio of a circle's radius and circumference, it really does not matter if
you choose to represent this relation with a drawing of an elephant.

~~~
ignifero
You got a good case with pi/2, it's truly useful, as it represents the angle
between 3d axes, the boundaries of the tangent and inverse trigonometric
functions, the monotonic regions of cosine and sine etc. It will even make
spherical coordinates easier to visualize mentally. (It will also make a two-
digit number, 16, a common resident in lots of formulas). I vouch for it, and
i call for a move to name it, confusingly, pi-bar

~~~
Jach
pi-bar? Nooooo, you'll make the Statistics community members' heads explode!

~~~
ignifero
not a big loss [smirk]

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dkastner
I forgot how awesome geometry was. Anyone know of any courses (online) that
each geometry through functional languages (or maybe even vice-versa)?

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Brashman
Is this going to get posted every year?

~~~
saraid216
Only until we win.

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ignifero
I think humanity has bigger issues than that. When are americans going to
adopt the metric system?

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jerrya
It's Tau Day, Tau Day, Gotta get round on Tau Day

------
dlat
ALSO: HAPPY CAPS LOCK DAY!

<http://capslockday.com/>

