9 ms·

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

367 points by mhartl 16y ago

tc 16y ago
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.
- erlanger 16y ago
  > 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.
- pyrtsa 16y ago
  Only there is no year zero, by (that) definition. http://en.wikipedia.org/wiki/0_(year) http://en.wikipedia.org/wiki/0_(year)
  - Semiapies 16y ago
    Nor are BCE and CE all that commonly used.
- amalcon 16y ago
  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.
  - Groxx 16y ago
    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.
    - amalcon 16y ago
      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.
      - samatman 16y ago
        Too much visual similarity to pi is a recipe for many factor-of-two errors.
      - vorg 16y ago
        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.
        Groxx 16y 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‽
- Groxx 16y ago
  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 http://en.wikipedia.org/wiki/Common_Era --- 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().
  - eru 16y ago
    > 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.
  - billybob 16y ago
    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...
- steveklabnik 16y ago
  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.
  - davidcuddeback 16y ago
    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 http://en.wikipedia.org/wiki/Jesus)
    - smallblacksun 16y ago
      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.
  - Naga 16y ago
    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.
    - seasoup 16y ago
      Are you sure that April 20, 2010 isn't 0 BP? :)
    - jcsalterego 16y ago
      Unix epoch had it right. Let's just all count seconds before/after 1 Jan 1970.
- klodolph 16y ago
  AD vs. BC: I prefer using CE with negative numbers, as suggested by ISO 8601. E.g., year -30 CE is year 31 BC.
  - vorg 16y ago
    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)
    - pook 16y ago
      Or we can just adopt the Discordian Calendar and, by increasing confusion, reduce disharmony. http://en.wikipedia.org/wiki/Discordian_calendar http://en.wikipedia.org/wiki/Discordian_calendar Hail Eris!
- mkramlich 16y ago
  speaking for US-ians: would the Texas State School Board actually allow the rest of us to switch from BC/AD to BCE/CE? :)
- stassats 16y ago
  There is no need in "#.".
lutorm 16y ago
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.
- wwortiz 16y ago
  To be fair, even though I disagree with them, they did try to show through their examples why they believed pi to be wrong.
  - Avshalom 16y ago
    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.
    - jerf 16y ago
      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.
mikecane 16y ago
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 16y ago
  > infinite number The term you're looking for is 'irrational.' And tau is also irrational.
  - est 16y ago
    > 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 16y ago
      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 16y ago
        > 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_.CF.80 http://en.wikipedia.org/wiki/Non-integer_representation#Base... http://en.wikipedia.org/wiki/Factorial_number_system http://en.wikipedia.org/wiki/Factorial_number_system
ww520 16y ago
Is this a parody or for real?
- acangiano 16y ago
  It's real (see my blog post about it: http://math-blog.com/2010/06/28/forget-pi-here-comes-tau/ http://math-blog.com/2010/06/28/forget-pi-here-comes-tau/).
  - JadeNB 16y ago
    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 16y ago
      I was actually reporting the equality as expressed by the manifesto. See here: http://tauday.com/#sec:euler_s_formula http://tauday.com/#sec:euler_s_formula
- camiller 16y ago
  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 ....
  - ww520 16y ago
    Is it like converting from Queen's system to metric system in U.S.?
    - techiferous 16y ago
      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.
wwortiz 16y ago
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 16y ago
  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).
  - amalcon 16y ago
jaekwon 16y ago
shut up and happy tau day everyone!
Dirt_McGirt 16y ago
People who suck at satire shouldn't be allowed to title things "A Modest Proposal".
- mhartl 16y ago
  It's not satire, but you're right that using the phrase "A modest proposal" was confusing. I've changed it for clarity.
kinghajj 16y ago
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.
whyenot 16y ago
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.
- nolochemical 16y ago
  Sweet, another nerd holiday I can actually prove with math!!
- techiferous 16y ago
  I love the idea, but I think a better conversion would be 2 pies = 1 taue. :) Twice as much pie on Tau Day! :)
jokermatt999 16y ago
Well, at least this is a lot smarter than the "pi is exactly 3!" movement.
- limist 16y ago
  Or the 22/7 people...
  - martinkallstrom 16y ago
    I'm born on July 22th (22/7). Still like tau better than pi.
- boredguy8 16y ago
  http://www.snopes.com/religion/pi.asp http://www.snopes.com/religion/pi.asp
- pbhjpbhj 16y ago
  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. --- Example references: (short) http://msmvps.com/blogs/coad/archive/2010/05/14/pi-in-the-bible.aspx http://msmvps.com/blogs/coad/archive/2010/05/14/pi-in-the-bi..., (longer) http://www.bibleprobe.com/pi.htm http://www.bibleprobe.com/pi.htm, (several refs) http://www.math.ubc.ca/~israel/bpi/bpi.html http://www.math.ubc.ca/~israel/bpi/bpi.html, (with alternate based on "hands-breadth") http://ldolphin.org/pi/index.html http://ldolphin.org/pi/index.html though I'm not sure on the original source.
rick_2047 16y ago
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
- sophacles 16y ago
  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.
- edanm 16y ago
  "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.
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carterschonwald 16y ago
this was discussed with respect to a different article on the same idea on hn a few days ago. This is not a trolling proposal, and in fact aside from centuries of convention in using pi, it is in fact very well motivated to propose this alternatively. For those without the math background to grasp the examples, the tl;du (to long, didn't understand) is that many classical mathematical objects (the ones that will be seen in any very very advanced hs level or intermediate level college math course ) would become MUCH MUCH more uniform with respect to the values that the coefficients take. Now, ignoring pedagogical considerations, theres no reason for having this tau value, but thats being completely dishonest about how people learn and how the brain best works. Our minds are really really really sophisticated but at times silly pattern recognition engines, and any notation that makes related topics, problems and patterns look more uniform makes it just that much easier to have insight, understanding and improved problem solving skills. the examples to pay attention to if you're rusty beyond the hs level are the ones involving: the notation for radians with tau instead of pi (excellent because every calculation can be thought of as a fraction of the circle), and the extended example at the end involving how using tau rather than pi leads to a natural symmetry with a whole slew of formulae is also quite good. If you don't care about pedagogical simplicity or the overhead of having a needless notational special case, this article is not important to you, but otherwise its a very good idea or at least one worth considering.
JeanPierre 16y ago
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 16y ago
  > 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.
  - nopassrecover 16y ago
    Doubt it, they release annually anyway.
  - blahedo 16y ago
    "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 16y ago
jey 16y ago
Can we fix Gamma(x) to be x! while we're at it?
- bmm6o 16y ago
  http://mathoverflow.net/questions/20960/why-is-the-gamma-function-shifted-from-the-factorial-by-1 http://mathoverflow.net/questions/20960/why-is-the-gamma-fun...
Tichy 16y ago
What a waste of brain cycles
drblast 16y ago
e^(tau*i/2)+1=0 ??? Ewwww, yuck.
- dgritsko 16y ago
  Did you get all the way down to here? http://tauday.com/#sec:euler_s_formula http://tauday.com/#sec:euler_s_formula e^(i*tau) = 1 Much nicer that way.
  - rudd 16y ago
    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.
    - dgritsko 16y ago
      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.
    - pyrtsa 16y ago
      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.
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- gecko 16y ago
  I thought he addressed that in the paper rather well. Did you disagree with that section of the paper, or were you ignoring it?
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boryas 16y ago
As an alternative to tau, I propose the symbol 2*pi.
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joe_the_user 16y ago
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 16y ago
  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 16y ago
    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.
- orangecat 16y ago
  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.
benbeltran 16y ago
Yay for new obscure geek holidays. Now we can act all smug and say: "pi day? no, I celebrate tau day, you ignorant you".
napierzaza 16y ago
This might have kept me in math
edanm 16y ago
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 16y ago
  >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 16y ago
    "the time when" is used here to mean "the period in a person's life" rather than "the period in history".
mjw 16y ago
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.
scelerat 16y ago
Young earth and downplaying evolution is one thing. But this is downright CRAZY!
andrew1 16y ago
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).
zbanks 16y ago
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_significance_of_radians http://en.wikipedia.org/wiki/Trigonometric_functions#The_sig... ) I hate to be a Debbie Downer, but you can't ignore these things.
- jacobolus 16y ago
  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.
mkramlich 16y ago
alternatives since tau is taken: pe, pau, dau, twopi
blahedo 16y ago
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.
nrbafna 16y ago
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 16y ago
  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 16y ago
    That's omega in its minuscule form. I was referring to its majuscule one.
    - tspiteri 16y ago
      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.
FreeRadical 16y ago
I must say, they are some beautiful arguments you have put forward!
elblanco 16y ago
I humbly suggest using the Cedilla instead of Tau to avoid confusion with Tau for torque. http://en.wikipedia.org/wiki/Cedilla http://en.wikipedia.org/wiki/Cedilla
yock 16y ago
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?
masonicb00m 16y ago
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?

367 points by mhartl 16y ago

tc 16y ago

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.

erlanger 16y ago
> 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.
pyrtsa 16y ago
Only there is no year zero, by (that) definition. http://en.wikipedia.org/wiki/0_(year) http://en.wikipedia.org/wiki/0_(year)
- Semiapies 16y ago
  Nor are BCE and CE all that commonly used.
amalcon 16y ago
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.
- Groxx 16y ago
  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.
  - amalcon 16y ago
    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.
    - samatman 16y ago
      Too much visual similarity to pi is a recipe for many factor-of-two errors.
    - vorg 16y ago
      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.
      - Groxx 16y 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‽
Groxx 16y ago
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 http://en.wikipedia.org/wiki/Common_Era --- 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().
- eru 16y ago
  > 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.
- billybob 16y ago
  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...
steveklabnik 16y ago
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.
- davidcuddeback 16y ago
  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 http://en.wikipedia.org/wiki/Jesus)
  - smallblacksun 16y ago
    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.
- Naga 16y ago
  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.
  - seasoup 16y ago
    Are you sure that April 20, 2010 isn't 0 BP? :)
  - jcsalterego 16y ago
    Unix epoch had it right. Let's just all count seconds before/after 1 Jan 1970.
klodolph 16y ago
AD vs. BC: I prefer using CE with negative numbers, as suggested by ISO 8601. E.g., year -30 CE is year 31 BC.
- vorg 16y ago
  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)
  - pook 16y ago
    Or we can just adopt the Discordian Calendar and, by increasing confusion, reduce disharmony. http://en.wikipedia.org/wiki/Discordian_calendar http://en.wikipedia.org/wiki/Discordian_calendar Hail Eris!
mkramlich 16y ago
speaking for US-ians: would the Texas State School Board actually allow the rest of us to switch from BC/AD to BCE/CE? :)
stassats 16y ago
There is no need in "#.".

lutorm 16y ago

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.

wwortiz 16y ago
To be fair, even though I disagree with them, they did try to show through their examples why they believed pi to be wrong.
- Avshalom 16y ago
  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.
  - jerf 16y ago
    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.

mikecane 16y ago

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 16y ago
> infinite number The term you're looking for is 'irrational.' And tau is also irrational.
- est 16y ago
  > 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 16y ago
    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 16y ago
      > 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_.CF.80 http://en.wikipedia.org/wiki/Non-integer_representation#Base... http://en.wikipedia.org/wiki/Factorial_number_system http://en.wikipedia.org/wiki/Factorial_number_system

ww520 16y ago

Is this a parody or for real?

acangiano 16y ago
It's real (see my blog post about it: http://math-blog.com/2010/06/28/forget-pi-here-comes-tau/ http://math-blog.com/2010/06/28/forget-pi-here-comes-tau/).
- JadeNB 16y ago
  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 16y ago
    I was actually reporting the equality as expressed by the manifesto. See here: http://tauday.com/#sec:euler_s_formula http://tauday.com/#sec:euler_s_formula
camiller 16y ago
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 ....
- ww520 16y ago
  Is it like converting from Queen's system to metric system in U.S.?
  - techiferous 16y ago
    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.

wwortiz 16y ago

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 16y ago
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).
- amalcon 16y ago

jaekwon 16y ago

shut up and happy tau day everyone!

Dirt_McGirt 16y ago

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

mhartl 16y ago
It's not satire, but you're right that using the phrase "A modest proposal" was confusing. I've changed it for clarity.

kinghajj 16y ago

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.

whyenot 16y ago

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.

nolochemical 16y ago
Sweet, another nerd holiday I can actually prove with math!!
techiferous 16y ago
I love the idea, but I think a better conversion would be 2 pies = 1 taue. :) Twice as much pie on Tau Day! :)

jokermatt999 16y ago

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

limist 16y ago
Or the 22/7 people...
- martinkallstrom 16y ago
  I'm born on July 22th (22/7). Still like tau better than pi.
boredguy8 16y ago
http://www.snopes.com/religion/pi.asp http://www.snopes.com/religion/pi.asp
pbhjpbhj 16y ago
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. --- Example references: (short) http://msmvps.com/blogs/coad/archive/2010/05/14/pi-in-the-bible.aspx http://msmvps.com/blogs/coad/archive/2010/05/14/pi-in-the-bi..., (longer) http://www.bibleprobe.com/pi.htm http://www.bibleprobe.com/pi.htm, (several refs) http://www.math.ubc.ca/~israel/bpi/bpi.html http://www.math.ubc.ca/~israel/bpi/bpi.html, (with alternate based on "hands-breadth") http://ldolphin.org/pi/index.html http://ldolphin.org/pi/index.html though I'm not sure on the original source.

rick_2047 16y ago

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

sophacles 16y ago
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.
edanm 16y ago
"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.

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carterschonwald 16y ago

this was discussed with respect to a different article on the same idea on hn a few days ago. This is not a trolling proposal, and in fact aside from centuries of convention in using pi, it is in fact very well motivated to propose this alternatively. For those without the math background to grasp the examples, the tl;du (to long, didn't understand) is that many classical mathematical objects (the ones that will be seen in any very very advanced hs level or intermediate level college math course ) would become MUCH MUCH more uniform with respect to the values that the coefficients take. Now, ignoring pedagogical considerations, theres no reason for having this tau value, but thats being completely dishonest about how people learn and how the brain best works. Our minds are really really really sophisticated but at times silly pattern recognition engines, and any notation that makes related topics, problems and patterns look more uniform makes it just that much easier to have insight, understanding and improved problem solving skills. the examples to pay attention to if you're rusty beyond the hs level are the ones involving: the notation for radians with tau instead of pi (excellent because every calculation can be thought of as a fraction of the circle), and the extended example at the end involving how using tau rather than pi leads to a natural symmetry with a whole slew of formulae is also quite good. If you don't care about pedagogical simplicity or the overhead of having a needless notational special case, this article is not important to you, but otherwise its a very good idea or at least one worth considering.

JeanPierre 16y ago

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 16y ago
> 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.
- nopassrecover 16y ago
  Doubt it, they release annually anyway.
- blahedo 16y ago
  "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 16y ago

jey 16y ago

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

bmm6o 16y ago
http://mathoverflow.net/questions/20960/why-is-the-gamma-function-shifted-from-the-factorial-by-1 http://mathoverflow.net/questions/20960/why-is-the-gamma-fun...

Tichy 16y ago

What a waste of brain cycles

drblast 16y ago

e^(tau*i/2)+1=0 ??? Ewwww, yuck.

dgritsko 16y ago
Did you get all the way down to here? http://tauday.com/#sec:euler_s_formula http://tauday.com/#sec:euler_s_formula e^(i*tau) = 1 Much nicer that way.
- rudd 16y ago
  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.
  - dgritsko 16y ago
    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.
  - pyrtsa 16y ago
    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.
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gecko 16y ago
I thought he addressed that in the paper rather well. Did you disagree with that section of the paper, or were you ignoring it?

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boryas 16y ago

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

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joe_the_user 16y ago

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 16y ago
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 16y ago
  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.
orangecat 16y ago
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.

benbeltran 16y ago

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

napierzaza 16y ago

This might have kept me in math

edanm 16y ago

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 16y ago
>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 16y ago
  "the time when" is used here to mean "the period in a person's life" rather than "the period in history".

mjw 16y ago

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.

scelerat 16y ago

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

andrew1 16y ago

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).

zbanks 16y ago

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_significance_of_radians http://en.wikipedia.org/wiki/Trigonometric_functions#The_sig... ) I hate to be a Debbie Downer, but you can't ignore these things.

jacobolus 16y ago
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.

mkramlich 16y ago

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

blahedo 16y ago

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.

nrbafna 16y ago

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 16y ago
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 16y ago
  That's omega in its minuscule form. I was referring to its majuscule one.
  - tspiteri 16y ago
    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.

FreeRadical 16y ago

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

elblanco 16y ago

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

yock 16y ago

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?

masonicb00m 16y ago

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?