
No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010) - mhartl
http://tauday.com/
======
tc
Perfect; to my lisp startup file was just added:

    
    
      (defconstant tau #.(* 2 pi))
    

Regarding adoption, I think it's worth pointing out that these sorts of
conventions can and do shift within a generation. I recall quite clearly while
growing up the convention for indicating years < and >= the year one [1] was
B.C. and A.D. It seems like over the past few years we've definitively decided
on B.C.E. and C.E. instead [2].

All it really takes to catch on is adoption by a handful of elementary school
textbooks -- and those publishers have adopter much crazier things in the
past. As the manifesto points out, this is distinctly pedagogically useful, so
it doesn't seem beyond the realm of possibility.

\--

[1] Correction: Julian/Gregorian years begin with 1 A.D. (I still prefer the
AD/BC convention, as the two identifiers have an equal number of characters.)

[2] I'll admit that my perception of prevalence here may be strongly
influenced by the fact that Wikipedia has adopted this convention.

~~~
amalcon
I have no problem with people trying to do this in principle. I really don't
care enough, but other people can.

The symbol "tau", however, is an especially poor choice for a trigonometric
symbol, because it's also used for torque. You won't get many physics teachers
to change over if every time you try to calculate a torque from a force and
radius, you run into a symbol conflict.

~~~
mhartl
This torque issue was really bothering me, and I finally realized why: I was
pretty sure I'd _already_ seen torque represented by a letter other than tau.
Sure enough, I checked my copy of _Introduction to Electrodynamics_ by David
Griffiths, which is a popular (and truly great) intermediate E&M text, and
there it was on p. 162: torque written as N = r X F. The same usage appears in
several other places in that book, and _Introduction to Electrodynamics_ is a
standard text, so I'm confident that other sources use it as well. So we see
that the idea of using a letter other than tau for torque is not some
theoretical possibility—it has already happened, and in a standard textbook to
boot. I've updated the manifesto with a note to this effect at
<http://tauday.com/#sec:four_arguments>.

I realize that this may not convince you, but I urge you to reserve the right
to change your mind about tau. After all, I changed my mind about pi. ;-)

~~~
Kadin
I remember vaguely from my time using Griffiths' book that he uses a lot of
non-standard (or at least not the same as other, more introductory textbooks)
notation. He pretty freely reassigns the symbols used by things that you're
supposed to understand, in order to free them up for other purposes.

Or at least that's my vague recollection. It's been a few years now since I've
cracked open his _Electrodynamics_. It was a pretty decent book though, better
than a lot of textbooks (I kept it and still have my edition around somewhere,
something that I didn't do if I thought a textbook was crummy).

------
edanm
I really hope this convention gains wide adoption. It's pretty obvious to me
that it just makes mathematics make more sense, at exactly the time when it
_needs_ to make more sense (people learning maths in high school).

Until then, here's the trick I'm using: whenever I need to use pi, especially
when it comes to the unit circle and radians, I'm just going to do it in terms
of tau, then convert at the end. I just wish I'd have understood this before I
finished my degree :)

~~~
mitjak
>It's pretty obvious to me that it just makes mathematics make more sense, at
exactly the time when it needs to make more sense (people learning maths in
high school).

People have been studying math at schools for quite a few centuries from what
I recall. There's never a better time in this case.

~~~
nudge
"the time when" is used here to mean "the period in a person's life" rather
than "the period in history".

------
kinghajj
The demonstration of how to derive the circle area formula was the clincher,
especially because of how similar that derivation is to other famous classical
physics formulae. That was the only example I could previously conceive for
why pi was still useful, but now I see that the factor of 1/2 in A = (1/2)τr²
shouldn't be avoided.

------
mjw
This bugged me throughout my maths degree.

In particular complex analysis and Fourier theory would be less of a pain in
the arse without all those factors of two.

Statistics too, heck anything which uses some calculus.

------
andrew1
I don't remember noticing during my (mostly pure) maths degree that most of
the time I was using pi that I was actually using 2 * pi. So there must have
been a lot of problems where I would have been writing tau/2 using the
proposed system, which I find less nice than simply writing pi. If it's a
choice between splitting my writing between [pi and 2 * pi] and [tau and
tau/2] I'd prefer the former, multiplication is nicer to look at than division
(in my opinion).

------
lutorm
Interesting how people equate "I don't like x" with "x is wrong"... If that's
the definition of "wrong" that people use in discussions, I see why science
has such a hard time getting through to the public.

~~~
dieterrams
From the FAQ: "I’m having fun with this, and the tone is occasionally
lighthearted"

The claim that pi is wrong is a claim about pi's inconsistency and
inefficiency as a matter of mathematical language design. These guys aren't
dumb enough to confuse this as a claim about formal correctness. Instead,
they're playfully co-opting the rhetoric of formal correctness.

~~~
lutorm
It's true that they claim in one specific section that it's "lighthearted".
However, that doesn't change the fact that I don't think this is a helpful way
of making the argument. Truth and falseness is already being co-opted enough
that I don't think anything pushing that trend further should be encouraged.
In this case, the "gain" certainly does not outweigh the loss in encouraging
this view of "wrong".

------
boryas
As an alternative to tau, I propose the symbol 2*pi.

------
benbeltran
Yay for new obscure geek holidays. Now we can act all smug and say: "pi day?
no, I celebrate tau day, you ignorant you".

------
blahedo
There's a much simpler way to say this, I think. It is already the case that
we relate everything to the unit radius---hence "radian". (If we tried to
relate everything to the diameter instead, a lot of things would break much
more deeply, starting with the very convenient derivative of sin( _x_ ).)

Given that, ask yourself this: do we want a measure of the semicircle, or of
the circle? The former is \pi. The latter is \tau.

------
joe_the_user
What I would like to see is an informational analysis where you take something
like a thousand common equations and look at how they would be expressed with
pi versus with tau. If you can show they would take significantly fewer bits
of information using tau, then tau would be objectively superior.

~~~
timwiseman
I repectfully think you may be overlooking two things:

1\. While storing fewer bits may be objectively superior in one sense, it is
overlooking the far more significant question of which helps a human
understand and work with the equestions. Math is encoded into the universe,
but our expressions of it exist for our own understanding.

2\. We get a lot of choice in how we encode information, and that choice can
change the number of bits used substantially. For instance:

c = 2 \pi r

c = \pi d

c = \tau r

c = 1/2 \tau d

All say the same thing, but their lengths vary considerably.

~~~
joe_the_user
I'm sure this would overlook many things. It would just supply _one_ objective
measure, not the only thing to consider.

Also, while there are indeed an infinity of representations of a given
expression, there are a finite number of minimal representations, which can be
found by exhaustive search if not some cleverer algorithm.

------
jey
Can we fix Gamma(x) to be x! while we're at it?

~~~
bmm6o
[http://mathoverflow.net/questions/20960/why-is-the-gamma-
fun...](http://mathoverflow.net/questions/20960/why-is-the-gamma-function-
shifted-from-the-factorial-by-1)

------
whyenot
I really like this "modest prpoposal." In its spirit, I suggest that from now
on we refer to 13 pies as a "taue," sort of a bakers' dozen of pies as it
were. Tau Day will be the new Pi day, but students would be inspired to bring
and share many times more delicious home baked goods as before.

~~~
techiferous
I love the idea, but I think a better conversion would be 2 pies = 1 taue. :)
Twice as much pie on Tau Day! :)

------
JeanPierre
Part of me is saying yes, part of me is saying no. Let me elaborate:

It makes all sense that tau _should_ be the number used INSTEAD of pi: It
simplifies things even more. (I hope I'm not the only one tired of writing
2*pi in papers.)

But that doesn't make pi WRONG: It's defined by C/D, and the formulas make
perfectly sense, even though you have to multiply by 2. Besides, it would mean
a total rewrite of a lot of papers, including a lot of mathematical books.

~~~
aspiringsensei
> total rewrite of a lot of papers, including a lot of mathematical books.

Somebody at the textbook publishers is smacking their lips at the prospect of
selling an entirely new edition with an incredibly minor change.

~~~
blahedo
"Incredibly minor": not even close. This is the very worst sort of change to
have to make, because you can't do it automatically, and doing it manually is
fraught with opportunities for bugs.

Not to mention that the natural pedagogical order will change in several cases
that a simple "translation" wouldn't reflect. A lot of CS2 books in Java---
especially two or three years ago---spent a lot of time and trouble showing
how to build a generic linked list using Object, casts and all, and then as a
little addendum, introduced "generics" that let you use a specific type. By
translating the book from old Java to Java 1.5 without rewriting it, they were
losing pedagogical opportunities and introducing confusion. Or the CS2 book in
Java that used .clone() all over the place: wtf, until you realise that it's
been translated from an equivalent C++ book that used copy constructors a lot.
Laaaaame.

So yeah, the publisher that treats this as an "incredibly minor change" is one
whose books you should avoid.

~~~
aspiringsensei
Thanks for you response - I didn't think about that at all. Unfortunately most
textbook purchasers don't have the ability to "avoid" bad texts....

I wonder if there were a way to rewire the textbook market so that teachers
assigned different kinds of things...in other words, so that the teacher
assigned a student to read a credible source of information regarding
geometric identities rather than section 23.6 of a stated text.

Imagine how much more interesting learning would be if students all came to
the classroom having reasoned through the knowledge differently? It would be
really neat to set up a system that was basically a "hacker news" for whatever
piece of information...educators could comment on in-class efficacy & kids
could comment on comprehensiveness.

You'd need to charge for it (Unless you could source the books for free) but
this is interesting conceptually.

------
zbanks
As eloquent as this manifesto is, it fails to actually address some of the
arguments against tau.

In 2.1, it points out that d/dx sin(x) = cos(x) only holds if x is in radians.

 _This is key_

Once you switch to expressing x in diameterians or tau-radians (or whatever
you'll call them), this identity falls apart:

d/dx sin(x) = cos(x) / 2

d^2/dx^2 sin(x) = -sin(x) / 4

...

And so on. The trig functions lose their cyclical nature.

(More explanation on wiki:
[http://en.wikipedia.org/wiki/Trigonometric_functions#The_sig...](http://en.wikipedia.org/wiki/Trigonometric_functions#The_significance_of_radians)
)

I hate to be a Debbie Downer, but you can't ignore these things.

~~~
jacobolus
We went over this a few days ago (also it’s described in the article, in case
you missed it). You are mistaken.

sin(pi) = sin(3.14...) = sin(tau/2)

cos(tau) = cos(6.28...) = cos(2 pi)

etc.

The sin and cos functions are functions of radians, and the arclength of a
radian does not change when you start expressing a circle as 1 tau instead of
2 pi.

------
jokermatt999
Well, at least this is a lot smarter than the "pi is exactly 3!" movement.

~~~
limist
Or the 22/7 people...

~~~
martinkallstrom
I'm born on July 22th (22/7). Still like tau better than pi.

------
nrbafna
How about "omega" as the symbol? 1) It wont bother the physicists as much as
tau. 2) Omega has a circular shape which makes it a 'natural' choice for the
circle constant.

~~~
tspiteri
omega is the symbol of choice for angular frequency, which is very related to
pi, as angular frequency = 2 pi frequency (there is another 2 pi for you right
there).

~~~
nrbafna
That's omega in its minuscule form. I was referring to its majuscule one.

~~~
tspiteri
Oh, I assumed that "omega" is minuscule, and "Omega" would be majuscule, just
like in LaTeX. That's why I started the sentence with a small letter. I missed
your mentioning its circular shape.

------
mikecane
I'm just about a math retard, so 99.9% of that went right by me. My only
question is this. Pi is supposed to be an infinite number: 3.14... So what
would Tau be? Is it also infinite or finite? I didn't see that addressed -- or
I somehow missed it in my concentrated skim. TIA.

~~~
steveklabnik
> infinite number

The term you're looking for is 'irrational.'

And tau is also irrational.

~~~
est
> The term you're looking for is 'irrational.'

I think by infinite he means non-terminating.

Conversely, an irrational number always has a non-terminating non-repeating
decimal representation.

~~~
steveklabnik
You're technically correct, the best kind.

I'd argue, however, that 'irrational' is closer to what he meant, than the
exactness of what he said. Any time you move between a layman's understanding
and a detailed technical one, the abstraction can leak.

I think 'irrational' matches up with intuition better, even if it's described
as 'non-terminating.' People don't talk about 2/3 in the same way they talk
about π.

~~~
est
> I think 'irrational' matches up with intuition better, even if it's
> described as 'non-terminating.'

well, counter example, 1.22333444455555..... is an irrational number, but it's
somehow easy to understand rationally. LOL

Also it's worthy point out decimals are heavily related to positional
notation. Another fun example is we can use base-e number system for maximum
calculation efficiency. Or better, base-tau. So 6.28 in base10 equals 1 in
base-tau numeral system.

see:

[http://en.wikipedia.org/wiki/Non-
integer_representation#Base...](http://en.wikipedia.org/wiki/Non-
integer_representation#Base_.CF.80)

<http://en.wikipedia.org/wiki/Factorial_number_system>

~~~
tspiteri
Rational numbers have more to do with ratios than reason.

------
FreeRadical
I must say, they are some beautiful arguments you have put forward!

------
yock
This is completely logical and sensical and I can see no reason to not adopt
it. Which leaves only one very important question:

What do we eat on Tao Day? May I suggest TAcOs?

------
wwortiz
Tau is an awful symbol in my opinion.

If the people who support double pi as the true symbol they should be writing
papers with a definition of double pi and truly proving to the mathematical
community that pi is the wrong definition. I personally think pi*D is a
perfectly sane way to describe pi and that thinking in 180 degrees is just as
easy as in 360 degrees.

Once the math community is convinced good luck with engineers and physicists
and then the general public.

~~~
ewjordan
_Tau is an awful symbol in my opinion._

Agreed, mainly because it's already used so widely in so many very
standardized ways (including many constants). Of course, most of the Greek
alphabet has been used by convention for one thing or another, and people
would find it all but impossible to change those habits.

 _If the people who support double pi as the true symbol they should be
writing papers with a definition of double pi and truly proving to the
mathematical community that pi is the wrong definition. I personally think pi_
D is a perfectly sane way to describe pi and that thinking in 180 degrees is
just as easy as in 360 degrees.*

I don't think many people would dispute that 2pi is a much more natural
angular constant than pi, the haters are absolutely right, we're stuck with
all sorts of extraneous and unnatural factors that are simple powers of 2
because of that "mistake".

But long standing convention is hard to break. Every formula list in existence
uses pi, as does every textbook, lecture, and problem set. Every formula that
people have memorized is in terms of pi, and that's not something you can
alter by fiat.

I fear that however well-intended, this may be a losing battle. It reminds me
a bit of people complaining about the negative charge on the electron - yeah,
you might be "right", and there are certainly some annoyances that we put up
with as a result of the "mistake", but it's over a hundred years too late for
that to matter, you're never going to get a critical mass of people to change.

Though I will say, at least if a new symbol is used for 2pi, it's _possible_
to get a few people to change over, since using that notation is not mutually
exclusive with using pi (whereas the charge of the electron is a choice that
has to be made, and if you make a different one from your peers, there's going
to be a lot of friction).

~~~
amalcon
_Agreed, mainly because it's already used so widely in so many very
standardized ways (including many constants)._

In particular, note that it's used for torque. The formula for torque from
force and radius involves a cross-product, so you're very likely to need both
the constant conversion factor for radians/cycle and the variable for torque.

------
Dirt_McGirt
People who suck at satire shouldn't be allowed to title things "A Modest
Proposal".

~~~
mhartl
It's not satire, but you're right that using the phrase "A modest proposal"
was confusing. I've changed it for clarity.

------
masonicb00m
i think a good way to spread this idea would be to pick some wikipedia pages
with pi in their equations and add a section demonstrating how the equations
are simpler with tau.

anyone know some good candidate pages?

------
elblanco
I humbly suggest using the Cedilla instead of Tau to avoid confusion with Tau
for torque. <http://en.wikipedia.org/wiki/Cedilla>

------
ww520
Is this a parody or for real?

~~~
acangiano
It's real (see my blog post about it: <http://math-blog.com/2010/06/28/forget-
pi-here-comes-tau/>).

~~~
JadeNB
Note that your equality \\(e^{i\tau} = 1\\) implies only that \\(e^{i\pi} =
\pm1\\), hence is strictly weaker than Euler's equality (which picks a sign).
I think that you might have meant \\(e^{i\tau/2} = -1\\). (Is there a way to
do LaTeX properly here?)

~~~
acangiano
I was actually reporting the equality as expressed by the manifesto. See here:
<http://tauday.com/#sec:euler_s_formula>

------
mkramlich
alternatives since tau is taken: pe, pau, dau, twopi

------
napierzaza
This might have kept me in math

------
rick_2047
I may get down modded for this but I just have to say, this is more like a
religious propaganda than science. Throughout the article they have only
demonstrated how a particular community is more comfortable with using double
pi. I totally believe in what wwortiz said in his/her(sorry cannot open your
website) post. If they like the tau so much they should be writing papers on
its advantage.

I think scientists should be more concerned about finding and confirming
important things than releasing such propaganda.

EDIT: OK I don't usually do this, but I would like anyone who downvotes me to
leave a small note on why this time. Its really important to me

~~~
techiferous
Your comment doesn't fit the article very well which may be why it is being
downvoted.

"this is more like a religious propaganda than science"

First of all, it is about math, not science. And it is not like religious
propaganda, which relies on authority or faith. It clearly and cogently
explains reasons why using tau is better than pi.

"Throughout the article they have only demonstrated how a particular community
is more comfortable with using double pi."

No community was mentioned. Just ideas.

"If they like the tau so much they should be writing papers on its advantage."

The manifesto is exactly that: a "paper" about its advantage.

"I think scientists should be more concerned about finding and confirming
important things than releasing such propaganda."

From the manifesto: "Tau Manifesto author Michael Hartl is an educator and
entrepreneur." He is not a scientist.

So that's probably why people are downvoting you. You probably just skimmed
the article instead of reading it and therefore misunderstood the article.

~~~
waldrews
Hold off on the "he is not a scientist" line... the Caltech Physics Ph.D. (a
theorist, not some namby-pamby experimentalist) does give Michael the street
cred to rant about such things.

Now if only he used his powers for good instead of evil...

~~~
mhartl
I wasn't going to say anything, but I admit that the "he is not a scientist"
line did sting a little. Although it's true that I'm not _currently_ suckling
at the academic teat, I did spend three years at the Harvard-Smithsonian
Center for Astrophysics as an undergrad and eight years at Caltech as a grad
student and postdoc doing research in theoretical astrophysics. I like to
think that gives me some cred as a scientist, and I appreciate your coming to
my defense. :-)

One reason I didn't hold the comment against the parent poster is that
techiferous == Wyatt Greene, and he was by far the single most helpful pre-
launch reviewer of the _Tau Manifesto_. He is clearly on the side of what is
good and sweet and true.

Speaking of good vs. evil, you sound like a supporter of the Jedi. While it is
true that I am a Sith lord, it is my duty to inform you that it is the Jedi,
not the Sith, who are truly evil. How can this be? Suffice to say you've been
exposed to a lot of anti-Sith propaganda. ;-)

------
drblast
e^(tau*i/2)+1=0 ???

Ewwww, yuck.

~~~
dgritsko
Did you get all the way down to here? <http://tauday.com/#sec:euler_s_formula>

    
    
        e^(i*tau) = 1
    

Much nicer that way.

~~~
rudd
I actually disagree that that is nicer. e^(i _pi) = -1, which means you can
square both sides to come to the also factual statement, e^(i_ tau) = 1.
However, if you only knew the latter you'd be wondering whether e^(i*pi) would
be 1 or -1.

~~~
dgritsko
By "much nicer", I was merely attempting to point out that drblast's formula:

    
    
         e^(tau*i/2)+1=0
    

could be stated as:

    
    
         e^(i*tau) = 1
    

As in the article. Whether that's intrinsically "better" than Euler's Identity
is a different question, but not what I was discussing here.

------
jaekwon
shut up and happy tau day everyone!

------
scelerat
Young earth and downplaying evolution is one thing. But this is downright
CRAZY!

------
Tichy
What a waste of brain cycles

