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Happy Tau Day
- thecopy 10y agoThe choice between Pi vs. Tau is completely arbitrary and should be based on minimizing the friction of use. Everyone knows Pi, few knows about Tau. I see no point in spending any more energy than that on this kind of nonsense decisions.
- adwf 10y agoTo use your own argument, 2*pi is far, far more common to encounter in physics/maths ie. real world examples, therefore minimizing friction would be using Tau ;)
- jeffwass 10y agoSo to save confusion over a mere factor of two, you're proposing devoting an entire new Greek letter to just double a constant, and requiring students to understand pi anyway to make sense of hundreds of years of mathematical and scientific corpus? It's just like that xkcd comic about introducing a new standard and now having N+1 standards. Except in this case the new standard offers only a factor of two.
- deleted 10y ago[deleted]
- adwf 10y agoRelax, the whole thing is a joke, including my comment above.
- jeffwass 10y agoHa, yeah I know. On rereading my comment, it does come across as somewhat defensive but I definitely wasn't meaning it to be that way. Actually I was smiling as I wrote it. See my other comments on this thread about sigma, for instance.
- FeepingCreature 10y agoIt's not about the factor, it's about making the connection to the circle obvious.
- e12e 10y agoLook, it's more about saying that the area of a right triangle is naturally represented (and explained) as half that of a rectangle sharing the height and width - but being divided in two equal halves by the hypotenuse. You can argue that you're so used to right triangles that it's the square and the rectangle that should be considered special, and "twice the area" - but I don't think that makes much sense. Pi is a useful constant, but it's chief role is in cycles/frequencies and circles. Not half-circles. It is perfectly ok to disagree - but I'm one of those people to find the concepts behind pi start making much more sense when thinking of tau as the constant, and half-tau (pi) as the special case. Maybe it's because I always hate having logic and math concepts waved away as "that's the way it is" when there obviously is some pattern or explanation that's being hidden or lost. I'm no good at rote calculation, and with tau a lot of things that just look odd and "special" unify quite nicely. It may very well be that for higher dimensions than two (or three) tau doesn't make much more sense than pi - but I found the "tau manifesto" examples plenty convincing. It was easier for me to grasp, and I believe it would be a lot easier to teach.
- aaron695 10y agoLike how we should stick with GMT?
- csydas_work 10y agoWhile I appreciate the actual methematical point of the site (and assume there is a small sense of deadpan humor intended), discussions as to which day should be "celebrated" are pointless since the day's importance to the general public has nothing to do with the value of pi or tau, but instead the fact that pi is a homonym of pie and march 14th happens to be the same numerically as the first few digits. As far as I know, that's the extent of the popularity - you can make pies on Pi Day. Again, I'm assuming the Tau day thing is a bit of deadpan, but otherwise it seems to me to be that simple.
- greydius 10y ago"Because that's the way we've always done is" is never a valid argument.
- kintamanimatt 10y agoI"m not entirely sure that's the argument being made.
- bbcbasic 10y agoStraw man city on hn
- dri_ft 10y agoOften it is. It's a perfectly good answer to, for example, "why do we drive on the side of the road that we do?"
- robert_tweed 10y agoI sometimes wonder if handedness or eye dominance have any effect on accident statistics.
- jobigoud 10y agoIf the choice really is arbitrary then yes. If there was a compelling argument to driving one side or the other then it would cease to be a good answer IMHO. https://en.wikipedia.org/wiki/Dagen_H https://en.wikipedia.org/wiki/Dagen_H
- denzil_correa 10y ago> Tau is completely arbitrary and should be based on minimizing the friction of use. Isn't that what the proponents of Tau also argue for?
- juped 10y agoWow, they've really redesigned that site's look. Not sure I like it... the figures especially look bad.
- deleted 10y ago[deleted]
- rplst8 10y agoI just wish instead of celebrating these days on arbitrary month/day combinations, that we'd instead use some physics or math based use of them. Pi day should be when we've gone half way around the Sun and Tau, New Years Day.
- pizza 10y agoMultiply the current dates by 2 and to a very near approximation (~1% off) that's what you get :P
- singularity2001 10y agoAs today tauday is tuesday, the Angle programming language now knows tau: ⦠ assert tau / 2 = pi True https://github.com/pannous/angle https://github.com/pannous/angle
- libeclipse 10y agoIt's just the same useless argument every year. Just use what you want. I've been taught pi since secondary school. I understand it well and can use it effectively. Never have I sat there and thought, "if only there was a shortcut to multiplying this by 2". There's whole sites, videos and movements to get tau popular. I just personally don't understand the point.
- jobigoud 10y agoThat's exactly the issue. You are thinking in terms of pi, so it might be hard to see from a different perspective. It's like using a slightly off abstraction for a concept. At first you have to make a small effort to hold it in your head, then at some point it's committed and you can manipulate the concept directly.
- MichaelBurge 10y agoLet x be a randomly chosen real number in [0,1]. What does it mean to "manipulate x's concept" or "think in terms of x"? Do these phrases attach themselves to the real number, or to the expression language? If the latter, do you say two number-expressions are equivalent if applying some normalization function yields two equal expressions? Do you consider two number-expressions distinct if they evaluate to the same real number, but cannot directly be related to each other? For example, let: S = { (x, e^(ix) + 1) | x in R, x > 0 }, T = { x | (x,y) in S, y = 0 }, c1 = min(T), c2 = 6 * sqrt(sum(n^-2, n > 0)) If my memory's right, c1 and c2 evaluate to the same real number which happens to be equal to Pi. What does it mean to manipulate c1's concept or think in terms of it? Does c1 have the same concept as Pi?
- gravypod 10y agoThis isn't to save time multiplying by two. This is to uniform a hole slew of previously unrelated equations that can now be represented similarly.
- jeffwass 10y agoI honestly can't tell if you're being sarcastic or not.
- nabla9 10y agoWhile choice between tau and pi is arbitrary from mathematical point, things like pedagogy, notational simplicity and aesthetics matter. The reason why I think π is probably better choice is because small multiples of constant are cognitively easier to process than fractions. 2π is easier to write and see as single object than τ/2. All we need to do is to make slight cognitive adjustment and think and teach 2π as a number instead of 2×π.
- jobigoud 10y ago> 2π is easier to write and see as single object than τ/2 The point is that you shouldn't have to write 2π in the first place. So notational simplicity would mandate the use of τ, not π. Noting that you will have to write τ/2 for a half turn is moot, in your case you'll also have to write π/2 for a quarter turn anyway.
- jeffwass 10y agoIt gets worse! When using solid angles over a sphere, you're still going to need to use 2Tau steradians to cover a sphere. This factor of 2 will continue to cause confusion for the Tau fans. Therefore we must also define a new constant Sigma = 4pi so we can cleanly and easily deal with steradians. Anybody up for writing the Sigma Manifesto? </sarcasm>
- agumonkey 10y agoMaybe we could subscript tau with dimension n.
- jerf 10y agoDoes it help the pedagogy and understanding? Does it help form equations that match the form of other equations in some mathematically-meaningful way? Then, yes, I'd support it just fine. So the sarcasm fails. One of the other things I don't see mentioned very often in this discussion is that mathematics evolves. We almost never get it right the first time. The original Maxwell's Equations were 20 equations, rather hairy ones at that, now expressed in 4 with superior notation. Derivative and integral notation did not spring fully-formed from Newton or Leibniz, it has evolved. Matrix notation evolved. Number notation has evolved. The idea that pi itself may have to evolve because it wasn't quite right is perfectly natural and normal. What's bizarre is the idea that it must be held to be perfect, that criticism is all-but-morally wrong, and that anybody even talking about it is crazy. I blame our terrible math system, for teaching people that math consists entirely of edicts handed down from, I presume, aliens, or possibly some form of diety, since apparently it can't be humans as we're not allowed to touch the Holy Notation. But that's not how it works in reality, and there's nothing bizarre about the idea that we might want to change pi; what's bizarre is the idea that such a thing is blasphemy.
- deleted 10y ago[deleted]
- devishard 10y agoOkay, tau is a little better. Meanwhile, millions of lines of code are written in languages with no type system to speak of, millions of Americans use imperial measurements, billions worldwide speak languages that are inefficient and ambiguous, and many many people aren't even educated enough to know about pi or tau. We have much more damaging problems than multiplying by 2. Given the gigantic amount of effort it would take to fix this one, I think that effort could be better spent.
- formula1 10y agoI understand this perspective if arguments were a limited resource and that by not fighting about tau we would win other battles (which is not true). The reality is that there is no such thing as time "better spent" withoit enforcing some sort of oppressive regieme and ways to curb imagination. I believe the tau fight is one of the rare good fights.
- devishard 10y agoArguments are a limited resource. I have 45 minutes on the train and I'm using it to argue about tau, and I don't have the time or energy for more. And when society is divided on a lot of issues, people run into outrage fatigue and become apathetic. And to say that there is no such thing as time better spent unless you enforce an oppressive regime is a perfect solution fallacy. Sure, people will always do inefficient things, but if I could persuade even one person to behave more efficiently, that's a pretty significant gain. I'd also like to note that if you're arguing for tau over the more popular pi based on its efficiency, you probably shouldn't argue against efficency.
- formula1 10y agoOoooo.... I feel your passion! Great points. Internet conversations will only take things so far, after conversation generally action is necessary. Whats nice about hacker news is that with many actions we can take action with functional programming or framework xyz immediately. With something like tau, publicity is its problem. So few people know about it that any sort of exposure benefits it. To say that untyped systems are worse than typed requires minimal exposure, simply more experience to understand why
- Angostura 10y agoPi is better because 'a slice of pie' links nicely to radius and makes it easy for kids to remember. QED.
- nenreme 10y agoBut pi links to diameter, not radius.
- chronial 10y agoBut pi isn't a slice of pie – it's half a pie, right?
- lgas 10y agoBut half a pie is a slice of pie, right?
- ubertaco 10y agoExactly. It's much a "stickier"/"easier" mnemonic to tell a(n English-speaking) grade-school student "the area of a circle is 'pi r squared'" and let them giggle at the incongruity of the fact that no, silly, pie is round! It builds a connection to a thing they already know, and it's "silly"/"absurd" enough to be "sticky" in terms of memorization.
- rectang 10y agoI feel very fortunate that the tau vs. pi argument was around when I went back to study math in earnest. I found tau much more intuitive and it helped me to visualize and learn the material more effectively. I now use tau whenever I can. However, I don't find switching back and forth to accommodate pi loyalists that taxing. You don't really have to choose one exclusively.
- skrebbel 10y agoIf mathematics has a bikeshed, this is it. I enjoy the ridiculousness of it all, but people who consider this anything other than a well-executed joke really should get a hold of themselves.
- Bromskloss 10y agoI find it worthwhile to think about questions like this, whose answers, on some level, do not matter, but, on another level, can be felt to be more or less in line with insights about the underlying structure. Examples of other questions in the same category: - Whether the natural numbers should be defined so as to include zero or not (and, relatedly, whether counting should start on zero or on one). - How to structure a database or a piece of computer code (including the details of how to formulate individual lines of code).
- ska 10y agoMathematics has no shortage of bikesheds.
- jeffwass 10y agoLet's assume the bikesheds are spherical, with radius r. They'll have surface area 4pi*r^2 and, oh never mind...
- jessriedel 10y agoYou're right about the bikeshedness, but that doesn't mean there isn't a clearly better bike shed design. I also find that these sorts of inefficiencies/inelegances compound. One or two are trivial, but when you have 30 of them, suddenly the mental tax becomes noticeable. Furthermore, the cost falls mostly on the students, while the experts have already paid it and don't see the need to worry about it anymore.
- lamontcg 10y agoYeah, but this bikeshed got decided hundreds of years ago. Its only appealing to internet hipsters who want to brag about their organically grown free range tau. Making the next generation of math students use "2 pi" in their formulas is going to be vastly easier than literally rewriting all the books.
- MrManatee 10y agoI have found the idea of tau useful even though I have never used it in writing. One argument in favor of tau is that in many formulas pi often has the multiplier 2 in front of it. If these formulas are written in terms of tau, they may become slightly easier to memorize and manipulate. Perhaps so, but I don't really care about this. It’s not a big difference. Besides, there are also lots of formulas that are easier to memorize and manipulate using pi instead of tau. The probability density function of the standard Cauchy distribution f(x) = 1/pi * 1/(1 + x^2) is one example. However, to get a deep understanding of mathematics, I want to understand the connections between different parts of mathematics. If I see a mathematical formula with the constant pi in it, I ask myself: "How is this connected to circles?" The idea of tau taught me that that 2pi is the natural state of affairs. If I see pi by itself, I need to ask myself: "How is this connected to half-circles? Or has the multiplier 2 been cancelled away?” So, why does the pdf of the standard Cauchy distribution above contain pi instead of 2pi? What is the standard Cauchy distribution anyway? Take a gun that shoots particles in random directions, and place it one unit distance away from an infinitely long wall. Standard Cauchy distribution is where the particles will hit the wall. The particle will only hit the wall if it is shot in a direction towards it. This corresponds to 180 degrees - and there you have it: the connection to half-circles. Of course, you also have to work out the technical details. But on an intuitive level, when I see pi in the pdf of the standard Cauchy distribution I don’t think about how the missing multiplier makes it easier to remember a bunch of symbols; I think of particles hitting a wall.
- jeffwass 10y agoYour Cauchy argument is actually misleading and runs right into my joking example elsewhere in this thread about needing to define a new constant Sigma=4pi to work better with steradians. Pi doesn't always represent only a pure circle. Eg, in solid angles there are 4pi steradians over a sphere. Or 2tau. Or what I define as Sigma. This extra factor of two when using Tau should be just as disconcerting to tau enthusiasts for steradians as pi is for radians. Your example is talking about shooting particles in all directions over 3D space. This calls for a solid angle approach. Which means you should be integrating over steradians just as you'd use radians for an angular system. There are 4pi steradians over a sphere's full solid angle, the wall only covers 2pi steradians. Meanwhile the extra factor of two comes from the integration of decreasing infinitesimal wall cross sections over the azimuthal angle. The fact that it comes out to 1/2 tau is merely happy coincidence. Ie, the geometry introduced an extra factor of two because it's just as easily 1/4 sigma, and for a solid angle system (shooting particles in all directions) you should be using steradians. Hence sigma.
- jordigh 10y agoOn to more important matters, Gamma function or Pi function? 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... Obviously, the Pi function is the right one since Pi(n) = n! for all integers n.
- dajohnson89 10y agoUsing tau would uglify euler's equation, wouldn't it?
- kqr 10y agoYou be the judge of that. Compare e^(iπ) = -1 to e^(iτ) = 1. The whole business of re-writing the identity as e^(iπ) + 1 = 0 is nothing but a hack to get around the weirdness of π as a constant.
- kej 10y agoWriting it equal to 0 isn't a hack, it's a common method of understanding a function. You factor polynomials by setting them equal to 0, for example. In the case of Euler's identity, what we're really asking is "what values of x make e^(ix) + 1 = 0 true?" and the answer is "every multiple of π". Using τ instead hides half of the answers.
- kazinator 10y agoYou mean "every multiple of 2π". The value -1 only comes around once per revolution of the unit circle!
- kazinator 10y agoYou mean "every multiple of 2π, shifted by π". The value -1 only comes around once per revolution of the unit circle! The solutions to e^(ix) + 1 = 0 are { π, 3π, 5π, ... } Whereas the solutions to e^(ix) - 1 = 0 are: { 0, 2π, 4π, 3π, ... } i.e. { 0, τ, 2τ, 3τ, ... } Also, note that when we set a polynomial to zero, the roots appear subtracted on the opposite side from the independent variable: (x - r0)(x - r1)...(x - rn) = 0 In the Tau-oriented Euler formula written homogeneously, there is a vague analogy to this since we're similarly subtracting that 1: e^(ix) - 1 = 0
- kej 10y agoPoor phrasing and math-before-coffee on my part. The point I was going for is that e^(ix) has real values for each multiple of π. That is mathematically interesting, and is obscured if you use τ instead.
- lazyant 10y agoI'd rather multiply by 2 75% of the time than divide by 2 25% of the time (just a wild-ass guess of how often one or the other appear in common equations)
- xigency 10y agoIt's probably closer to 98% and 2% of the time for serious math, engineering, and physics.
- NaNDude 10y agoi totally suck at math, however i think i know what is a circle, i can draw one with a compas. then i think i know what is the diameter of this circle, i can draw it by drawing two more circles and a line with a ruler. because a mathematician told me that the product of this diameter by a number is the circumference of the first circle i believe him, but if another mathematician ask me to draw two more circles and another line to define the same circumference... i will probably believe that the first one suck less than the second one at maths! (sorry for my english!).
- kazinator 10y agoAngular frequency (ω = 2πf) is related to this: https://en.wikipedia.org/wiki/Angular_frequency https://en.wikipedia.org/wiki/Angular_frequency Note how convenient ω is when squared, in the expression of angular acceleration, eliminating a ridiculous 4 factor.
- Bromskloss 10y agoThis ties into "ħ" vs. "h" as well: E = ħω E = hf I don't mean this as an argument for anything; I just felt like mentioning it.
- mkane848 10y agoOT, but Michael Hartl's RoR tutorials are amazing and helped me learn so quickly. Worth checking out[0] if you're looking to learn [0]: https://www.railstutorial.org/ https://www.railstutorial.org/
- thanatropism 10y agoWhat's a nice infinite series summing to tau that isn't merely 2S(n) where S(n) sums to pi?
- thanatropism 10y agoHa. I've said a lot of continental-philosophy stuff that gets downvoted by the techie culture, but this is amazing.
- Bromskloss 10y agoJust checking: Do you mean that your comment amounts to continental philosophy?
- thanatropism 10y agoI'm saying this comment should be far less contentious than my comments that somehow cite Heidegger or Deleuze.
- andrewla 10y agoThe simplest formula that I can think of is pi/4 = tau/8 = atan(1) = 1 - 1/3 + 1/5 - 1/7 + ... 4 vs 8 doesn't seem like a change in the arbitrariness of the constant. The other major simple ones are: pi^2 / 6 = tau^2 / 24 = 1 + 1/(2^2) + 1/(3^2) + 1/(4^2) + ... pi^2 / 12 = tau^2 / 48 = 1 - 1(/2^2) + 1/(3^2) - 1/(4^2) + ... Once again, 6 vs 24 (and 12 vs 48) is an arbitrary difference in arbitrariness. I'm not really aware of any commonly used series expansions that don't involve a constant multiply just to get to pi. On the other hand, I'm not aware of anything super-elegant that yield tau here either, so I think it's a tie at best.
- kerkeslager 10y agoI'm in favor of keeping pi because of one simple equation: e^{i\pi} + 1 = 0 This is, IMHO, the most beautiful equation I've come across. It's concise and it relates all the most basic constants in mathematics. It's also useful, for example, for operating on the logarithm of a negative number: e^{i\pi} + 1 = 0 e^{i\pi} = -1 i\pi = \ln{-1} \ln{x} + i\pi = \ln{x} + \ln{-1} \ln{x} + i\pi = \ln{-x} For more see Euler's Identity[1]. [1] https://en.wikipedia.org/wiki/Euler%27s_identity https://en.wikipedia.org/wiki/Euler%27s_identity
- karmakaze 10y agoThis simultaneously illustrates how e^(180') is halfway round a unit. Tau (literally/numerically?) > Pi