No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010) | Hacker News Reader

No, really, pi is wrong: The Tau Manifesto (Tau Day, 2010)

tauday.com

367 pointsmhartl147 comments

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.

> It seems like over the past few years we've definitively decided on B.C.E. and C.E. instead.

I don't think that is the case. Amongst recently published works of history that I have read (1st ed. books), from some very reputable publishers (Cambridge, Oxford, UC, etc), I have only seen BC/AD in use.

Only there is no year zero, by (that) definition. http://en.wikipedia.org/wiki/0_(year)

Nor are BCE and CE all that commonly used.

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.

How many symbols aren't in use, though? If you've got a notably better one, the "manifesto" may consider changing, but they seem (to me) to have pretty good reasons for choosing tau.

I'd ideally prefer to pick one that isn't used in angular things. Because non-English, non-Greek glyphs are somewhat underused for this sort of thing, and because of visual similarity to pi, I'd suggest the hebrew Het or Russian л. However, I really have no problem with continuing to use the multi-glyph symbol 2pi.

Too much visual similarity to pi is a recipe for many factor-of-two errors.

Why a multi-glyph symbol 2π when a single-glyph symbol 2π would be better. By creating a new symbol by joining the bottom-right of the 2 to the topleft of the π, we can make a new one-glyph symbol, perhaps put it next to € in Unicode.

And instead of saying two words "Two Pi", we could say it as one word "Twopi", with stress on the first syllable, much like the word "teenager" used to be spoken and written as two words a century ago.

I like the idea of "Twopi". Looks like it could be pronounced like "Toupee". (yes, it'd be a mispronunciation, but people do that)

Do you also favor the almighty interrobang‽

We pronounce the constant as pee in German anyway. (No confusion with bodily fluids there.)

Or we might as well go with dvapee (Russian), or tsveypee (German (zweipi, written so that you can pronounce it the English way and it'll come out ok)).

We can go for pronouncing the thingy pipi. (Though would lead to confusion with bodily fluids in German.)

You know, I really don't care that much about the 2pi thing, but this is just cool enough that I might be able to get behind it.

My first thought exactly. Mechanical engineers and physicists appreciate where Tau is at the moment. But as someone notes, there is always symbol conflicts.

"at the moment"

very funny ;)

I mention torque in the manifesto, but I wasn't specific enough in this case, and I've added an example addressing this issue at http://tauday.com/#sec:four_arguments. The short version is that when necessary you can easily add a subscript to avoid ambiguity, such as tau_R for rotational torque. (Superscripts work, too. Particle physicists deal with pions, which are represented by the letter pi, but all the symbols have superscripts indicating their electric charge. As a result, no one ever confuses them with the number.)

The thing is, torque is a particularly bad thing to conflict with. While you're not using torque every time you work with pi, you usually end up using pi every time you work with torque.

edit: It's much like using i for both sqrt(-1) and for current. Electrical engineers need to use both of these all the time, so they often use j for sqrt(-1) instead.

Or you could use M for moment and stop using tau for torque. Most mechanical engineers talk about moments with M instead of tau.

The electrical engineering thing demonstrates that you're unlikely to get a particular discipline to change its own notation. It would have made much more sense in retrospect to change current to something other than i, but that's not what happened.

As an electrical engineer (by way of physics and math), I'll use any other damn letter that makes sense for current that you want, and try to sway my fellows too. I just haven't seen a good option yet. What have you got?

"c"... no good, speed of light for one; and also current needs good a good alteration for DC vs AC, "c" and "C" look too similar when written by someone else's hand (and "C" is crap in equations anyway since it can look too much like a "("). Current is a flow, but "f" is well used. Any good suggestions?

Agreed. He mentions overloading the pi symbol for the prime counting function but the difference is that you very rarely encounter pi in the prime counting function.

The parent comment is now obsolete; I came up with something even better: http://news.ycombinator.com/item?id=1470379

I would argue though that the torque example is a particularly problematic symbol conflict as any equations involving torque are by definition going to include many, many references to the circle constant. Yes there are other symbol conflicts in math, but usually they are separated by logical fields (you generally are not doing using e when dealing with the charge of an electron constant (except in the case that you are dealing with magnitude of the electric field as a function of distance) and even when you are, it is hardly a problem because you never use the natural logarithmic constant except as a power function).

I think the appropriate change here though would be to change the symbol for torque to say, 'q' or something. Probably not going to happen, but wouldn't be as much of an issue.

I would suggest a change to uppercase Gamma, which looks like a T, kinda. Also, it has always struck me as a looking kind of like a moment arm.

Something like this is bound to happen if mathematics pedagogy moves to tau as the circle constant, which it should. The math department has no motivation to respect physics convention, and the physics department will just have to get in line, eventually.

Or physicists/engineers will do their own thing, as seen by using j = sqrt(-1).

Also, uppercase gamma is already used, too. http://en.wikipedia.org/wiki/Gamma_function

Granted, but interference with mechanical torque is unlikely.

Greek letters are pretty polysemantic in the context of maths and physics.

These arguments are assuming that tau would be a total replacement for pi in all situations. Why not just keep using pi in situations where you are doing calculations with torque?

The point of tau (or pi) is to do calculations with angles. One of the main uses of angles in physics is calculations having to do with torque. Basically, using pi for calculations that might involve torque is giving away one of the situations where tau would be most useful.

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. ;-)

And there are only so many letters in the alphabet(s). Although I have to admit common usage hasn't really exhausted the hebrew alphabet, yet.

And when the Chinese finally take over, we will have enough short symbols to last us for millenia.

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).

Interesting. N may not be such a great symbol to use for torque, because the equation relating it to force and radius is a cross-product. In that context, N often refers to a "normal" vector. Still, it's apparently in use somewhere, which is interesting.

Except BC/AD -> BCE/CE is a label change, not a numbering change, and it's arguably for largely P.C. reasons; conforming to P.C. is the "in" thing. We in America have also changed from Indians to Native Americans to American Indians to Indigenous Peoples to whatever, and N* to Black to Colored to African American to something supposedly unoffensive while still defining the same group.

http://en.wikipedia.org/wiki/Common_Era

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edit in response to edits: I too agree with preferring BC/AD, they're the same size and look more different. BCE/CE both end in "CE", and the similarities between "B" and "E" don't help :\ And I see BCE more-ish in recent history books, but not much outside there (though there aren't qualifiers for most things I read, it's all too recent).

I'm voting for positive values == CE and negative values == BCE. They're already numbered that way, just adopt the frickin' sign instead of the suffix! Nearly everything becomes easier, left-to-right hints at relative age prior to even seeing the number, and parsing from a computer standpoint is as easy as to_i().

> I'm voting for positive values == CE and negative values == BCE. They're already numbered that way, just adopt the frickin' sign instead of the suffix!

Nope, not really. There's no year 0. Neither A.D. nor B.C.--that's because zero wasn't known to the guys who invented this numbering system, and also because those guys counted years with ordinal numbers (first year, second year, etc) and not with cardinal numbers since Christ.

You see the same confusion over death (Friday) and resurrection (Sunday): Jesus rose on the third day, not after three days. (Since the weekdays are not given in the bible directly, you can also find alternative suggestions for the weekdays.)

Disclaimer: Words like Jesus, Christ, death and resurrection are used purely as labels to describe stuff some people believe in. No judgement implied.

I think it's ridiculous to rename dates just to remove their religious connotations, especially when the reference point is still the (slightly inaccurate) birth of Christ. If someone wanted to start with a new system, where year 0 is the Big Bang, that would be reasonable - it would put all dates on the same time scale instead of having to convert between BC and AD. But if you're going to keep the religious reference point, why pretend it's something else? Prejudice is the only reason that I can see.

Of course, when we revise our estimates of when that happened, it would screw everything up again...

Ugh, I know this is slightly offtopic, but there's nothing more I dislike than B.C.E and C.E. I can understand not trying to promote a Christian-centric worldview, but by only changing the labels, they accomplish nothing. Now, the birth of Christ sets a 'common era,' which arguable makes it _more_ 'offensive' than just acknowledging what happened on that particular day.

The switch to B.C.E. and C.E. is also because the year of Jesus' birth is debated. Some believe he was born in 4 C.E. At least that's what I recall from school many many years ago. Personally, I prefer "B.C." and "A.D." because those two are more different from each other (edit distance of two) than "B.C.E." and "C.E." (edit distance of one, unless you count periods).

Edit: Wikipedia says Jesus was born in 5 B.C. (http://en.wikipedia.org/wiki/Jesus)

While you are correct that most scholars don't believe that Jesus was born in 1 AD, the reason the change was made was to distance scholarship from Christianity.

There is another dating system which aims to get around this, by actually changing the numbers, which is called Before Present (BP). It sets 0 to be January 1, 1950, as an arbitrary date of the present. So, 1500 BP is 450 AD. I see it used most often it dealing with archaeology.

Are you sure that April 20, 2010 isn't 0 BP? :)

Unix epoch had it right. Let's just all count seconds before/after 1 Jan 1970.

A slight complication to this solution is that the length of a year is not exactly divisible to seconds, or even of constant length. So counting seconds is fundamentally different from, though pretty close to, counting years.

Don't forget, though, AD stands for Anno Domini, which means "in the year of our Lord." Which is a little more than just acknowledgement.

The "our" translation is just convention, not actually there in the latin.

Actually, AD is the shortened form for "the year of our Lord". The "Year of our Lord" came first, before the initials.

Why can't we dispense with the annotation completely? BC/BCE counts backwards, so let's just say 1970 or -1970.

edit: posted this before I saw Groxx's reply below

I don't know what you folks are on about. My ddate clearly tells me

<pre>Today is Prickle-Prickle, the 33rd day of Confusion in the YOLD 3176</pre>

AD vs. BC: I prefer using CE with negative numbers, as suggested by ISO 8601. E.g., year -30 CE is year 31 BC.

Too many people would get confused, forgetting to substract 1 from the BC-tagged number, or unsure whether to add or substract 1, or wondering if the other person remembered to subtract 1.

I suggest adding 7000 to all dates, as well as using negatives. So...

2010AD -> 9010

1AD -> 7001

1BC -> 7000

31BC -> 6970

5000BC -> 2001 (except people talk about year ranges, not years, when refering to events that far back, so there'd be no confusion with our current AD references)

Or we can just adopt the Discordian Calendar and, by increasing confusion, reduce disharmony.

http://en.wikipedia.org/wiki/Discordian_calendar

Hail Eris!

speaking for US-ians: would the Texas State School Board actually allow the rest of us to switch from BC/AD to BCE/CE? :)

There is no need in "#.".

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 :)

>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.

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

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.

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.

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).

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.

To be fair, even though I disagree with them, they did try to show through their examples why they believed pi to be wrong.

Pi is defined as C/D, the only way to prove it wrong would be to show that C/D isn't a constant in euclidean geometry, which you can't. What they show examples of is that using pi is ill advised.

You're operating under the wrong definition of "wrong". Axioms and definitions simply exist, but we are not therefore obligated to suspend all judgment on which ones are better for some purpose.

I can reformulate all of physics to accept the Earth as a constant reference frame. It will be isomorphic to current physics based on being set in inertial reference frames, and therefore every bit as "correct" as conventional physics. There will be no place where conventional and Earth-centric physics will disagree about the result of an experiment. However, Earth-centric physics is wrong. It produces terrifically complicated equations for even simplified versions of predicting the orbit of a planet around a distant star. The speed of light is anisotropic. If you really get down to specifying things precisely it has to include rather a lot of kludgy compensations for variations in the Earth's rotation that are nevertheless perfectly definable. It isn't a useful way to approach physics. It is "wrong".

The previous paragraph isn't metaphorical. I am not saying "it is theoretically possible to reformulate all of physics to be Earth centric". I'm saying that one can in fact mechanically translate all physics equations into such a framework, and similar transforms occur all the time (although with better cause). I'm not just being rhetorical, though of course I am, it is also literally true. There is a set of equations that corresponds to the reference frame I am describing.

We select our representations of equations for two major reasons that I can see: One, to minimize the number of symbols necessary to express the concept. "distance = velocity x time" encodes a number of assumptions into it to shorten it, including a wrong idea about reference frames, but we still teach it because it's simpler than the relativistic version (and a hell of a lot simpler than the Earth-centric version!). Second, to enhance the human understanding of the situation being represented by the equation. That's not entirely separate, obviously, but they're not quite the same.

And I would argue tau wins on both fronts, and I for one plan on adopting it in my code. It's better.

No, no, no. Your Earth-centered physics is not wrong. It's perhaps "bad", or "awkward", "clumsy" or "suboptimal", but not wrong. The word wrong should be reserved for factually incorrect statements (unless you are discussing morals), otherwise it's been diluted to meaninglessness.

It's better.

See, you already agree with me. It's not "right", it may be "better" (though I question that fact, too.)

"Wrong" can mean "factually incorrect", but it can also mean "poorly suited." For example, outfits do not have a property of factual correctness, but somebody wearing a tux to a semiformal event would be wearing the wrong thing, as would somebody wearing a speedo.

According to the OED, wrong as an adverb:

5. The fact or position of acting unjustly or indefensibly;

6. Not right or satisfactory in state or order; in unsatisfactory or bad condition; amiss.

7. a. Not adapted, according, or answering to intention, requirement, or purpose; not proper, fitting, or appropriate; unsuitable.

Any and all of which, but particularly #7, apply to the use of the term wrong in the tauday site.

Pi is [not adapted to purpose, not fitting].

See?

Only because you pulled out the OED did I feel it might be acceptable to point out that in the sentence "Pi is wrong", "wrong" is an adjective, not an adverb.

More to the point, in the online OED as I see it, definitions 1 and 2 deal with physical shape, 3 and 4 deal with moral character, and interestingly, my 5) differs from yours, being given as follows :

5. a. Not in conformity with some standard, rule, or principle; deviating from that which is correct or proper; contrary to, at variance with, what one approves or regards as right. b. Not in consonance with facts or truth; incorrect, false, mistaken. c. Of belief, etc.: Partaking of or based on error; erroneous. d. Of a painting: having an erroneous attribution.

Given that it's not until we get to 6 and 7 that we find definitions regarding quality of 'state or order' or 'appropriate' and 'suitable', I think readers are quite justified in finding the OP's use of "wrong" to be at least very freely used -- which was, of course, part of the whole point.

If someone teaches or uses Earth-centric physics, I am perfectly comfortable calling that "wrong". They shouldn't do it. They are at the very least incurring opportunity cost and at worst actively harming the student.

While I sympathize with you in general, I believe you've erred here on two accounts:

1) The author here is being lighthearted; your comment implies instead that he's being a demagogue.

2) This sort of pattern is far more common in "public" discussions such as public policy than in science, so I think you are directing your ire incorrectly.

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.

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".

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

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

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.

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.

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.

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.

Really that reduces to looking at how often pi appears by itself (without being multiplied by a constant) versus how often 2pi appears. If there's a multiple other than 2 it's a wash; "4/3 pi r^3" isn't any better or worse than "2/3 tau r^3". And 2pi shows up all over the place, while the most common occurrence of a single pi is the area of a circle, which the proposal convincingly argues should have a 1/2 factor.

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

http://mathoverflow.net/questions/20960/why-is-the-gamma-fun...

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.

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

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.

> 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.

Doubt it, they release annually anyway.

"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.

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.

> you can't do it automatically

Why not? This seems like precisely the sort of change that you can make manually: Every π becomes (τ/2). Granted, this'll produce some weird formulæ, like `C = 2(τ/2)r`; but fixing those little problems is an excuse for still more editions. :-)

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... )

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

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.

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

Or the 22/7 people...

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

http://www.snopes.com/religion/pi.asp

There are two standard rebuttals.

One is that the thickness of the vessels wall (hands-breadth) is not taken into account in the establishment of 3 as the value being used for pi despite this being mentioned right there in the text, this apparently gives a value of 3.1414 for pi.

The other is that 1 Kings 7:23 reference uses a special rendering of the term line (Hebrew numbers are expressed using letters) such that the ratio of line to ordinary line and the rendering in the text give the actual value as:

3 * 111/106

This gives Pi accurate to 0.00026%.

This all seems quite ex-post-facto but Hebrew has a strong tradition of numerology and this "special" variant of the word line is used only 3 times and always referring to circular objects.

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Example references: (short) http://msmvps.com/blogs/coad/archive/2010/05/14/pi-in-the-bi..., (longer) http://www.bibleprobe.com/pi.htm, (several refs) http://www.math.ubc.ca/~israel/bpi/bpi.html, (with alternate based on "hands-breadth") http://ldolphin.org/pi/index.html though I'm not sure on the original source.

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.

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).

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

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.

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.

> infinite number

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

And tau is also irrational.

> 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.

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.

> 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/Factorial_number_system

Rational numbers have more to do with ratios than reason.

Their tau is just two times pi.

Both Pi and Tau are irrational (what you call "infinite", http://en.wikipedia.org/wiki/Irrational_number) and trascendental (http://en.wikipedia.org/wiki/Transcendental_number). They are also believed to be normal (http://en.wikipedia.org/wiki/Normal_number), but there is no proof of this.

Thanks, everyone for the replies.

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

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?

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.

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 piD 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).

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.

So maybe instead of teaching in terms of the unit circle, we should switch to the unit semi-circle, as that would be 100% as easy to understand?

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

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

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?

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

Is this a parody or for real?

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

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?)

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

I think real. Although I didn't read all of the article I think the main thrust was that since 2pi appears in so many places in math that a constant based on the ratio of circumference to radius rather than diameter would be more appropriate. Realistically I think there are better ways to spend your time but ....

Is it like converting from Queen's system to metric system in U.S.?

Not exactly, since there is only one constant to convert (not many units) and the conversion factor is very straightforward (2 pi = 1 tau instead of 39.37 inches = 1 meter). But yes in that many people would have to change their ways.

Like Jonathan Swift's proposal for ending poverty and hunger in Ireland, I am sure this "modest proposal" is entirely serious.

Though it shares some elements of propagandistic tone, the Tau Manifesto is unlike Swift's proposal in the most important sense, in that it's perfectly serious. Using the phrase "a modest proposal" in this context was a dubious choice (to say the least). I've changed the section name for clarity.

I should have anticipated this confusion, which resulted from my infelicitous use of the phrase "A modest proposal". The Tau Manifesto is meant to be fun, but it's definitely not a parody. For clarity, I've changed the name of the section in question.

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

This might have kept me in math

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

Look at it like a refactoring. Sometimes it is desirable to stop and reorganize a bit. The fact that there is a good reason for using both pi and tau may not be immediately obvious to some people, so they tell us about it. I for example, would never catch on to what tau is, and why it is useful without this. Now that I read it however, I can understand it well. Further, I have gone back and re-examined some things I have been learning lately that contain major sin and cos components. Suddenly they make much more sense to me -- using Tau gives me an intuitive understanding of how cos and sin are related.

To put it another way: If I, and other willing but not genius types, can't understand the results of scientists "finding and confirming important things" why should they do it in the first place? [Edit:] I mean can't understand in a way for use in engineering and other practical ways.

A final note: there is a strong resistance in the math, science, and engineering communities to the idea of "lets look at what we know and reformulate it in a consistent way". They think it is intuitive as it is, even tho there may be ways that people can learn it faster and to as deep of an understanding if a different formulation is used. This results in a lot of stupidity in the world like teaching physics in the order it was discovered, rather than some order building on concepts, or teaching physics by expressing velocity as a fundamental concept instead of as a derivative of something else.

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

The manifesto explains why using tau is better mostly for non-mathematicians. Especially, but not limited to, children learning about radians for the first time. You may disagree, but I think helping explain mathematics better is incredibly important.

Notation is a pretty big deal in Mathematics. As software people we should be able to appreciate how evocative notation can get rid of unnecessary cognitive load when dealing with complexity.

Here is a link that talks about notation in Maths: http://www.cut-the-knot.org/language/index.shtml . Here's another link: http://en.wikipedia.org/wiki/Nabla_symbol . The example from calculus is also pretty famous.

Also, FWIW, I didn't downvote you.

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.

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...

Ah, I didn't catch that. :)

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. ;-)

I've heard it said that a good notation is worth 10 good theorems.

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

Ewwww, yuck.

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

    e^(i*tau) = 1

Much nicer that way.

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

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.

I actually disagree with that logic as well. If you just knew that e^(i * pi) = -1, then how would you know, whether halving that exponent would yield +i or -i?

Considering that, we'd need to state Euler's identity as: e^(i * pi/2) = i, but again we'd know nothing about fractions of that exponent. And there we go!

The point is, Euler's identity is a nice property of the definition of complex numbers, but in itself, not too generic. That's why OP's form, e^(i*tau) = 1, would do just fine.

Edit: fixed asterisks.

I thought he addressed that in the paper rather well. Did you disagree with that section of the paper, or were you ignoring it?

There's a section about that: http://tauday.com/#sec:euler_s_formula

    e^(tau * i) = 1

    e^(pi * i) = -1

Which looks better?

shut up and happy tau day everyone!

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

What a waste of brain cycles

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