10 ms·
No, really, pi is wrong: The Tau Manifesto
- mcdaid 15y agoHi posted this earlier, but it didn't get any traction. I guess the people here might be interested. http://www.visnos.com/demos/pi#launch http://www.visnos.com/demos/pi#launch
- tzaman 15y agoSometimes I just feel stupid. Reading this article is one of those times :) Kudos to author though, I think most of mathematicians out there just take math as it is. Lack of entrepreneurial spirit I'd say.
- archgoon 15y ago> I think most of mathematicians out there just take math as it is. Really? People whose job is continually creating new math daily are just taking math as it is?
- serge2k 15y agounless there is a reason not to. math builds on earlir work
- huxley 15y agoSure, creating new stuff doesn't necessarily imply throwing everything out each time you make an addition or change. It would be like a startup guy re-inventing alarm clocks and breakfast every morning, followed by re-inventing showering, shaving, dressing, opening the door, entering the car, starting the car, what lane you drive in, etc. You'd never get to your workplace to do whatever it is that your startup is creating ("We Are Re-inventing Innovation!" -- you might think I'm joking but that's a common tagline even PARC used it). Some stuff you take as it is (a baseline) and you create around it. Maybe tau is something to consider more seriously but pi has done pretty well for itself and many don't consider changing it to be a big priority.
- ianterrell 15y agoEmail me your address for a free* patch if you're the type to wear one. http://www.kickstarter.com/projects/ianterrell/say-no-to-pi http://www.kickstarter.com/projects/ianterrell/say-no-to-pi *Free if I can get it to you with a stamp in the US.
- andylei 15y agohttp://www.thepimanifesto.com/ http://www.thepimanifesto.com/
- ddlatham 15y agoBe sure to check out the rebuttal. http://tauday.com/tau-manifesto#sec:the_pi_manifesto_a_rebuttal http://tauday.com/tau-manifesto#sec:the_pi_manifesto_a_rebut...
- onemoreact 15y agoThat's hardly a meaningful rebuttal. C = 2 * Pi * r = Tau * r A = Pi * r ^2 = Tau / 2 * r PS: When dealing with radians Tau is fine, but I like showing +Pi and -Pi both point away from 0.
- baby 15y ago> I like showing +Pi and -Pi both point away from 0. What would be cool is to see two different points showing what the direction is. c = Pi/2 +c would point upwards, -c would point downwards. 4c is a pizza.
- mhartl 15y agoThe awesome thing is, today he posted his own rebuttal: http://spikedmath.com/fact-005.html http://spikedmath.com/fact-005.html
- Dove 15y ago#define tau 6.2831853 If you haven't gotten around to it, today's a good day.
- hdevalence2 15y agoWouldn't it be better to do #define M_TAU = (2.0*M_PI) instead, so that it's clear that it's a math constant instead of a local variable? Also, I suspect that the math.h pi constant is accurate to more than 8 decimal places, so this way you don't lose precision.
- Dove 15y agoWhatever is appropriate in your context. :) What I really mean is this: use it. If you're a tauist, but tau isn't in your header file / constant library / whatever you use, today might be a good day to put it there.
- bascule 15y agoThe best part of this is the area of a circle, which is the integral with respect to r of rtau, or taur^2/2. Sure, pi*r^2 is nice and easy to remember, but also remember even the mnemonic is wrong... pies are round!
- DrHankPym 15y agoIt's also easier to remember that the area of a unit circle is pi. Also, e ^ (-i * pi) + 1 = 0
- RuggeroAltair 15y agoWhat's the kinetic energy of a unit speed, unit mass? What's the potential energy of a unit distance unit spring constant? What's the energy of a unit mole, unit temperature in Boltzmann units? :-)
- 4ad 15y agoπ is not "wrong", that doesn't make any sense. However, I agree with the author that expressing things by using π is more complicated and not as elegant as expressing things with τ.
- FaceKicker 15y agoFourth paragraph: > It should be obvious that π is not “wrong” in the sense of being factually incorrect; the number π is perfectly well-defined, and it has all the properties normally ascribed to it by mathematicians. When we say that “π is wrong”, we mean that π is a confusing and unnatural choice for the circle constant.
- 4ad 15y agoYes, the article is correct and I agree with it, I just feel the wording is unfortunate.
- breckinloggins 15y agoThe wording is marketing.
- mhartl 15y agoTrue, and it's not even my marketing; it comes from Bob Palais' original article "Pi Is Wrong!".
- nandemo 15y agoI don't give a damn about tau. On the other hand, the way π iｓ rendered on Firefox on Windows is so wrong... it looks just like a small version of Π (capital pi), or the Cyrillic small Pe: http://en.wikipedia.org/wiki/Pe_%28Cyrillic%29 http://en.wikipedia.org/wiki/Pe_%28Cyrillic%29
- gbaygon 15y agoTL; DR: “Let τ=2π” It's a simple substitution, and it should be used "when it's convenient to". I really don't see any innovation in the article as everything in it is directly derived from the above mentioned substitution.
- jessriedel 15y agoUsing τ is better than using π for the same reason (albeit not as strong a reason) that using π is better than using g=17π. It has little to do with convenience, and more to do with conceptual clarity. Actually, the difference between g and π might be less bad, because at least when mysterious factors of 17 appear you would know where they came from. On the other hand, the factor of 2 that rides along when you choose to use π over τ could come be confused with a million other factors of 2.
- sophacles 15y agoIt isn't innovation from a math sense, it's innovation in a pedagogical sense. Once you've internalized pi (and math in general) it is pretty hard to see what is so difficult about it (a well studied issue with expert knowledge and teaching things to novices). However a simplification from the point of view of the novice who doesn't "just get it" is a good thing.
- tokenadult 15y agoHowever a simplification from the point of view of the novice who doesn't "just get it" is a good thing. Questions about mathematics pedagogy are inherently empirical, and should be answered by observation of actual learners. So where is the evidence that learners who don't get how to use π will be better able to learn mathematics if they use τ to tackle the same problems?
- sophacles 15y agoI don't know. Perhaps they are still at the "convince someone to actually try it for an entire n-year math curriculum" stage? It's not like using Tau is something that you can do in class for a week and expect better results. Even if you try the lesser "here's tau, always substitute 2pi with tau" every couple years on a group of students and track them through their math learning, it takes time and a lot of effort to get those numbers. In the mean time, there is lots of anecdotal evidence of people understanding a lot of concepts easier with it, suggesting these studies be done in a scientific way.
- polemic 15y agopi is "wrong" in the same way as imperial measurements are "wrong".
- philwelch 15y agopi is "wrong" in the same way as non-Planck units are "wrong". SI is almost as arbitary as imperial.
- polemic 15y agoAs in - because pi is a unit-less ratio? Plank units are still units (albeit a special case), so I don't agree with your syllogism. However, what I meant was the human processing overhead in converting between units. I mean, pi is correct, for what it is. Tau would simply be easier for humans to use, much like SI units.
- philwelch 15y agoTau is better than pi because a lot of useful expressions have 2pi as a term; SI is better than imperial because we happen to have ten fingers. Tau is a universal simplification like Planck units; SI is merely an anthropocentric simplification.
- Skalman 15y agoI think the greatest advantage of the SI system is that it's exponential. I don't care that much about what base is used, but switching is just confusing (12" = 1', 3' = 1yd).
- angersock 15y agoPi is better then tau because all of our damned engineering formulas have pi. SI is, however, the right answer (though useless without reference tools, whereas imperial isn't).
- polemic 15y agoOk, but "...a lot of useful expressions..." sounds like an anthropocentric argument as well. Anywho, the point stands. They're simplifications for our benefit.
- deleted 15y ago[deleted]
- TeMPOraL 15y agoCome on, stop trolling, Tau Day will be on 28th of June. Live and let others live. Today is Pi day, let people celebrate. ;)
- angersock 15y agoAs a mechanical engineer by training, I will be a sad panda if you use tau for something other than torque. EDIT: And shear stress. Derp. That's why I write software now. :)
- aqme28 15y agoTau is used for tons of other things already. http://en.wikipedia.org/wiki/Tau#Modern_usage http://en.wikipedia.org/wiki/Tau#Modern_usage I wish each letter could have only one use, but sadly that isn't possible (like some notorious equation from my plasma physics days that forced us to use different versions of P and Rho for density, pressure, charge density, and momentum).
- Jach 15y agoI'm more of a fan of having multi-character symbols than to try and pigeonhole every concept into one symbol. Have full or partial names, just like we do in programming. We started down that path with writing things like sin x, cos t, div f, |rad|, etc. We should continue! If people really have problems distinguishing we can go the Perl route and add sigils.
- zokier 15y agoNow that I have been programming for longer than doing maths, I just must wonder why math community seem so entrenched in using single letter variable/function names. How confusing larger source codes would be if programmers did the same.
- angersock 15y agoYou've never looked at academic or numerical code, have you? It's totally fugly. Go skim the first edition of Numerical Recipes in C--it'll give you nightmares.
- angersock 15y agoIf going the Perl route is the way to fix your solution your solution sucks (doesn't matter what it solves). Also, that's why we have subscripts.
- orbitingpluto 15y agoI always enjoy these little diatribes. However tau will never beat out pi because of one very important reason. The chicken scratch that passes for writing these days makes tau unreadable. Tau can be a: r, 7, t, tau, etc... For the sanity of TAs everywhere, please stop this madness.
- Jach 15y agoIt's just a pi with one leg in the middle. It's pretty easy to read. Also engineers (who don't have very good writing) have been using tau for things like a time constant (among other uses) for a long time. The bad handwriting problem is solved very easily, TAs should complain to the professor to make it a requirement that if you guys can't read it, it's wrong. I've had classes like this, I just use LaTeX.
- DrHankPym 15y agoYeah, I remember using Tau mainly for time constants back in school. http://en.wikipedia.org/wiki/Time_constant http://en.wikipedia.org/wiki/Time_constant
- orbitingpluto 15y agoI did a symbolic dynamics course that required the letter xi ad nauseum in lowercase. I still can't write that damn letter.
- woodall 15y agoSo π is a reduced version of τ?
- msluyter 15y agoFor a quick overview of the pedagogical significance of tau, compare figures 6, 7, and 8. I learned figure 6 in high school trig, but by "learn" I mean I basically memorized it without a deep understanding of what was going on. Figures 7 & 8 unveil what I had been missing.
- brudgers 15y agoIs it that time of year again?
- InclinedPlane 15y agoNope, this is about 3 and a half months early.
- angersock 15y agowell played good sir/madam
- bartl 15y agoMarch 14. Yep.
- oflannabhra 15y agoThis argument gets pretty complex, but the thing I like about pi is that it is fundamental. Sure 2 * pi might occur more commonly in important expressions, but 2 * pi is only special because pi is special.
- ianterrell 15y agoIs it circular reasoning to suggest pi is only special because 1/2 tau is special? See what I did there?
- haberman 15y agoI find the argument for tau very convincing. I remember having similar thoughts when I learned about radians and had a hard time understanding why they would define pi to be half of a turn, particularly since the diameter equation was d=2πr. The fact that A=πr² seemed like a counterargument, but the Tau manifesto makes a good case that having 1/2 in this equation helps show its similarity to other physics equations. I think pi's best argument is that the area of the unit circle is pi. I actually find it very enlightening to think of the unit circle as having an area of pi but a turn of tau radians. It makes sense to me to use both pi and tau; whichever makes a particular set of equations more clear. I certainly don't think that pi should be preferred just because it's older, or that pi's prevalence should prevent introduction of a new symbol.
- adambyrtek 15y agoOccam's razor to the rescue. Using two distinct constants which differ only by a factor of two sounds more confusing than choosing either one and sticking to it.
- T-zex 15y agoDiameter is 2*radius, so 2pi as another constant isn't that bad. pi being expressed in terms of diameter and tau in terms of radius.
- scythe 15y agoSee also: h and ħ in physics.
- haberman 15y agoOccam's razor pertains to competing hypotheses that attempt to explain some phenomenon, not the question of which of several equivalent formulations is best. If you argue that there can only be one, I say tau is better. But to me it's less confusing to have both tau and pi, simply because both of these graphics seem very fundamental to me: http://tauday.com/images/figures/tau-angles.png http://tauday.com/images/figures/tau-angles.png http://www.thepimanifesto.com/areas.png http://www.thepimanifesto.com/areas.png
- maaku 15y agopi is “wrong” in the same way that mobile electrons being the carrier of negative charge is “wrong”
- RuggeroAltair 15y agoNope. Although they are both conventions, in the electric charge there is really no natural choice. While mathematicians can argue whether or not a factor of 2 is a natural choice for a convention.
- maaku 15y agoIsn't the “natural” choice to have the direction moving charged particles to be the same as a moving charge? In everyday life it is electrons, not protons that move. When we say "charge is moving from high voltage to low voltage" we are actually saying "electron particles are moving from a position of low voltage to high voltage"--the exact opposite. How is that natural? Even if that weren't the case, it's still a matter of opinion. Minus signs show up in a number of pretty unnatural positions as a result of the negative electric charge. The convention in Physics is that minus signs convey semantic information (reversal in direction, slowing down, etc.). The negative electric charge upsets this convention, resulting in un-semantic minus signs.
- RuggeroAltair 15y agoI use a different definition of natural. The fact that the electrons, negatively charged, were moving wasn't known when they assigned the positive-negative labels. But still, although what you are saying is certainly true in proton/electron systems, it would be completely reversed in antiproton/positron systems, where the charge would be moving together with the particles. Also, don't forget of ions, or particles in space, or in particle physics experiments, where both charges move. The point is that the natural choice that you assign would be natural just because of some contingent conventions, but it's not more natural in terms of some more fundamental/mathematical meaning. While the pi vs. tau is.
- abrahamdemoivre 15y agoGood article, and your arguments are strong. As long as we're being contentious, though, I would like to point out that e is a more interesting number than τ or π. Sure, you can make circles with π (or τ) and do angular calculations galore, but without e you've really got nothing more than that. Rate of growth? Compound interest? Hidden things of the universe? Fuhgedaboutit.
- mhartl 15y agoThe Tau Manifesto author here. Don't yell it too loudly, but I strongly agree: e is by far the most important of these numbers. But e is the natural choice, so I don't have any bone to pick with it. (Bob Palais made an analogy in "Pi Is Wrong!" Suppose e were defined as 1/2.718281828... Then there would be confusing negative signs everywhere. Exponential decay would have a positive exponent, etc. Such is the case with τ and π, with a factor of 2 in place of a factor of -1.)
- bartl 15y agoIn math, you see 2π everywhere, for example in the Fourier Transform. So in that regard it'd make more sense if that was the constant. Visually it looks wrong, pi looks like 2 tau, not the reverse.
- mhartl 15y agoThe revision of The Tau Manifesto that launched today includes a wealth of new material, including a rebuttal of the "Pi Manifesto" (http://tauday.com/tau-manifesto#sec:the_pi_manifesto_a_rebuttal http://tauday.com/tau-manifesto#sec:the_pi_manifesto_a_rebut...) and a new section on the volume of a hypersphere: http://tauday.com/tau-manifesto#sec:volume_of_a_hypersphere http://tauday.com/tau-manifesto#sec:volume_of_a_hypersphere If you thought the original quadratic-form argument for circular area was good, prepare to be blown away by n-dimensional spherical volumes.
- chalst 15y agoNonsense! The Leibniz sequence is the most simple way to describe the equivalence class under multiplication by non-zero rationals of numbers that contains both pi and tau: 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - ... which sums to equivalently pi/4 or tau/8. The fundamental simplicity of the Leibniz sequence makes this value the only natural choice from that equivalence class. Let us call it lambda, for Leibniz. Then the area of the unit circle is 4 lambda, the diameter of the unit circle is 8 lambda, the volume of the unit sphere is 16 lambda, the surface of the unit sphere is 16/3 lambda, etc. Should I start selling the t-shirts?
- RuggeroAltair 15y agoI wouldn't call it nonsense. If the comparisons with the virial theorem and energy isn't enough to consider it at least as a reasonable choice, at least you should consider it as such because John Baez agrees with it. And you don't mess with John Baez ;-)
- chalst 15y agoI'm attempting irony. The tone of the manifesto is a bit breathless, putting up interesting enough considerations in a overwrought manner, with half-hearted efforts made at looking at the issues raised from more than one point of view. Draft one of my lambda manifesto shows that the only consideration of conceivable value, namely ease of defining a transcendental by means of a convergent series, leads to only one possible choice of fundamental trigonometric constant, lambda. Of course to gain widespread acceptance, I will have to cover up having written the indulgently tolerant http://www.advogato.org/person/chalst/diary/275.html http://www.advogato.org/person/chalst/diary/275.html
- RuggeroAltair 15y ago+1 for irony anyways...
- adharmad 15y agoEuler's identity: e ^ (i * pi) = -1 will be uglier: e ^ (i * tau/2) = -1
- ianterrell 15y agoMaybe read the linked page? Maybe see section 2.3?
- pfanner 15y agoThe next 100 years people will ask "what is tau?" and one will say "it's 2pi".
- scythe 15y agoI am a graduate student, first-year, so I have a lot of problem sets to work on. I've been thinking about tau every so often since the last time this was posted here, and so every time I work a problem, I think to myself: would this be clearer if I used tau? And the answer is usually "no". Sometimes 2 is next to pi because of the natural reason appealed to in the tauifesto, and other times it's there for some other reason, other times it isn't there at all; there's usually a huge constant factor out front anyway, and often a single equation goes across the whole sheet of paper, so even making it one character shorter doesn't accomplish much. Not that I haven't learned notation that really helps. Gaussian units and Einstein notation are a godsend. If you could standardize introductory physics courses using these, I think it could help significantly, especially when people struggle to work out the curl of a cross product or some-such strenuous vector calculation. All hail the Levi-Civita tensor! But we haven't even been able to agree on this. Furthermore, as a test grader of nearly-a-year, the work done by undergraduates is nigh-inscrutable in the maximally acceptable way already, and so the tau "rebellion" promoted here would just make my job harder. It's not too much of an issue: only the technically-inclined, who already do pretty clear work, are likely to use it; still, telling people "just start doing your work like this, let them figure it out!" means that I have to know if that scribble is a tau or a T or what-have-you, two hundred times. Pi is a very recognizable character. Plus, tau is the letter I reach for whenever I need to introduce an adjusted time of some sort, such as proper time; it's also the natural temperature in stat mech (though thermodynamic beta is itself more natural and usually better), it's torque, it's a common time constant, &c. People generally avoid pi as a character which does not represent 3.14159, though it is the prime counting function and an adjusted momentum, in which case it usually has a half-arrow, so you can tell what it's doing. We don't avoid tau at all; it's everywhere. So the tau-switch, as notational improvements go -- and math has had many over the years -- seems like a relatively large-pain, small-gain deal. Many things must change, since pi is all over the place, but few are greatly improved. So I don't see much reason to use tau in my work, or for my students to use it in theirs. If it works for you, though, good!
- haberman 15y agoTo me it has almost nothing to do with "making it one character shorter," it's about making it easier to see fundamental relationships intuitively. It's not a notational improvement as much as a model improvement. It's sort of like how angles can be measured using degrees or radians, but the derivative of sine is cosine only when using radians. It's not the notation of radians that is better, it's the model.
- vibrunazo 15y agoThe benefit of the easier formulas tau might provide. Minus. The confusion of having different generation of students being taught differently. Is it worth it? The author tries to dismiss this by saying "it's easy, they'll get it quickly, we don't need to rewrite all textbooks if you can just say 'let tau = 2pi'". But it seems he's rushing in that conclusion. The imagine the confusion between trying to convince students who are used to a whole set of formulas to use new ones will be huge. The confusion caused by different generations trying to communicate seems huge. You might not need to burn old books but you would need to write new ones, which again does sound like a huge endeavor. I'm not even questioning whether he's right about tau formulas being easier. That seems irrelevant to me. Just the problems you're creating with the confusion seems not worth the small benefits. It just doesn't seem the pros outweigh the cons.
- tfm 15y agoAw dang, I missed Pi Day again! Stupid timezone. I guess tau will be getting my support this year ...
- randomibis 15y agoTau in Python: http://bugs.python.org/issue12345 http://bugs.python.org/issue12345 (rejected) Tau in Ruby: http://bugs.ruby-lang.org/issues/4897 http://bugs.ruby-lang.org/issues/4897 (ignored) :(
- verve 15y agoYeah, yeah, and degrees are wrong for expressing angles, and steering wheels are wrong for driving cars. Incidentally, there's already a symbol for \tau: 2\pi. Same number of syllables and characters as 14, so what's the problem?
- verve 15y agoWhy tau, BTW? Why not winnie, after the Wonder Years character portrayed by the eminent mathematician Danica McKellar?
- randomibis 15y agoYour question is answered in the article...
- RockofStrength 15y agoBoth pi and tau form infinite strings of prime numbers with their digits. See if you can get the first twelve!
- mitko 15y agomath background and then studying robotics for a bit, where all we have are models of the reality, I now laugh at such comparisons. Both Tau and Pi are models for mathematics that work- to argue which is true is nonsense. They are both correct but neither is true, or god-chosen. We made them up, folks!