Happy Tau Day

by huguesdk • 10 years ago

142 120 10 years ago

thecopy• 10 years ago

The 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.

adwf2• 10 years ago

To 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 ;)

jeffwass9• 10 years ago

So 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.

aaron695• 10 years ago

Like how we should stick with GMT?

csydas_work• 10 years ago

While 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• 10 years ago

"Because that's the way we've always done is" is never a valid argument.

kintamanimatt• 10 years ago

I"m not entirely sure that's the argument being made.

dri_ft• 10 years ago

Often it is. It's a perfectly good answer to, for example, "why do we drive on the side of the road that we do?"

peterbonney• 10 years ago

Of course it's a valid argument - you have to consider the costs and benefits of switching whenever you propose a change in a broadly accepted convention.

For example, one could make an argument that oral and written communication in the United States would be more efficient if everyone was forced to communicate in Klingon. But the switching cost would be so astronomically high that any possible gains pale in comparison.

(I'm not saying the pi/tau cost/benefit is comparable to English/Klingon, I'm just pointing out that "that's the way we've always done it" is in fact a perfectly legitimate argument. The onus is on the person proposing a change to show that the change is worth it.)

phkahler• 10 years ago

> "Because that's the way we've always done is" is never a valid argument.

But it is. For the pi/tau thing, it's better if the whole world uses one set of formulas. For the guy who pointed to which side of the road we drive on, it's best if we all agree to drive on the same side. And for units, it's best if we all agree to measure things using the same units - otherwise probes crash into mars and such. All of those are arbitrary decisions and we're better of just sticking with them - except the units one, by using SI units a lot of formulas simplify and arbitrary constants go away. I'm not so sure tau/pi have a similar advantage. If you do change, you'll put the world in a weird transition phase until the change is widespread and that causes problems until it's resolve. Also, with mathematics you have existing and historical papers that use pi, so what to do about those? The legacy of pi would be around a long long time.

denzil_correa• 10 years 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• 10 years ago

Wow, they've really redesigned that site's look. Not sure I like it... the figures especially look bad.

rplst8• 10 years ago

I 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• 10 years ago

Multiply the current dates by 2 and to a very near approximation (~1% off) that's what you get :P

singularity2001• 10 years ago

As today tauday is tuesday,

the Angle programming language now knows tau:

⦠ assert tau / 2 = pi

True

https://github.com/pannous/angle

libeclipse• 10 years ago

It'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.

jobigoud3• 10 years ago

That'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• 10 years ago

Let 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?

gravypod4• 10 years ago

This 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.

jeffwass9• 10 years ago

I honestly can't tell if you're being sarcastic or not.

camiller• 10 years ago

The only thing useful about it is you have an excuse to eat two pies....

Bromskloss7• 10 years ago

I use 1.07 pi; it should be the same, as it is only a matter of convention.

nabla9• 10 years ago

While 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.

contravariant• 10 years ago

Treating 2π as a single entity is probably the best option for now. Not sure if formulas like 1/2 (2π) r^2 will ever catch on, but in more complicated formulas it's probably better to not simplify things like (2π)^4 / 6 to 2^3 π^4 / 3.

sevenless3• 10 years ago

The idea of 2π as symbolic entity in its own right, should be easier to accept than τ.

Introduce a single symbol that joins 2 and π, a bit like the Jupiter symbol (http://unicode-table.com/en/2643/), and pronounced 'two-pi'. Like τ it also starts with a T, for turn.

That would be totally backward compatible in reading, writing and speech.

ejlo• 10 years ago

Mathematically, tau is clearly superior, since it represents a full circle. The question is whether the gain is big enough compared to the trouble of introducing a new constant. It's not like pi is going to disappear any time soon.

jobigoud3• 10 years 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.

jeffwass9• 10 years ago

It 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>

BenFrantzDale• 10 years ago

My favorite example of why τ is the true circle constant is actually the equation A = 1/2 τ r^2. It fits the usual quadratic form and shows how circumference and area relate: c = dA/dr = τ r and so A = ∫ c dr = ∫ τ r dr = 1/2 τ r^2. At first glance those 1/2s seem superfluous and like it would be nicer to just have a 2 in the other terms, but the 1/2 shows that differentiation and integration with respect to r are happening, where the "1/2" and the "^2" anhialate each other on differentiation and then re-form on integration.

agumonkey3• 10 years ago

Reminds me of Taylor series. The factorial terms eluded me for so long until I realized it was a cancelling factor for accumulated derivation of polynomials. Now there's this link in my mind between powers / derivation / factorials.

devishard4• 10 years ago

Okay, 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.

formula12• 10 years ago

I 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.

devishard4• 10 years ago

Arguments 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.

EugeneOZ• 10 years ago

"6/28 in the American calendar system"

it's enough to ignore this day by all people except Americans, so don't worry about others :)

panglott• 10 years ago

billions worldwide speak languages that are inefficient and ambiguous

All humans speak languages that are inefficient and ambiguous. Thank goodness!

devishard4• 10 years ago

No, not all humans speak. That's why I said what I said.

It's splitting hairs, of course. :)

wtbob2• 10 years ago

millions of Americans use imperial measurements

There are two types of countries: those using 'metric' units, and those who have been to the Moon.

There's absolutely nothing fundamentally wrong with standard units (indeed, they are better for concrete manipulation). One can do science and engineering just as well with grains as with grams, with cups as with litres, with inches as with centimetres. They could do with a bit more regularisation (e.g. to make a fluid ounce a cube exactly 1, 1¼, sqrt(2) or 2 inches — each has advantages — and adjust the ounce accordingly), but they're each completely acceptable for their purpose.

The advantage of the standard units is that they are easy to physically convert: cutting a yard into feet or a foot into inches is each (⅓ in one case; ⅓, ½, ½ in the other); dividing a gallon into cups is easy (½ × 4); dividing a pound into ounces is easy (½ x 4).

The number of times a person converts between barleycorns and parsecs in a lifetime is approximately zero, while the number of times he takes one physical quantity of a unit and breaks it into smaller quantities is pretty common; optimising for the former is IMHO kinda foolish.

jimktrains2• 10 years ago

There are two types of countries: those using 'metric' units, and those who have been to the Moon.

What about Liberia and Myanmar?

devishard4• 10 years ago

This would be entirely missing the point of my argument.

sevenless3• 10 years ago

I hope you realized NASA using imperial caused the loss of a Mars rover.

hexane360• 10 years ago

But I think the standard unit system is one of many reasons engineers rely on formulas for 100% of their calculations. When you have that many conversion factors just to get between energy, force, distance, power, etc., you lose out on the universality of physics. At that point you find someone who has already done all the unit conversions and isolated it in a nice factor out front.

Also, IMO stuff in decimal is almost always easier to compare than fractional. When someone asks me for a size up from an 8mm wrench, I know to grab the 9mm. When someone asks me for a size up from 5/16", it'll take me a bit to get to 11/32".

Angostura• 10 years ago

Pi is better because 'a slice of pie' links nicely to radius and makes it easy for kids to remember. QED.

nenreme• 10 years ago

But pi links to diameter, not radius.

jonsen• 10 years ago

A slice has two sides. 2*r = d.

chronial• 10 years ago

But pi isn't a slice of pie – it's half a pie, right?

lgas• 10 years ago

But half a pie is a slice of pie, right?

ubertaco• 10 years ago

Exactly. 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• 10 years ago

I 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• 10 years ago

If 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.

Bromskloss7• 10 years ago

I 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• 10 years ago

Mathematics has no shortage of bikesheds.

jeffwass9• 10 years ago

Let's assume the bikesheds are spherical, with radius r. They'll have surface area 4pi*r^2 and, oh never mind...

jessriedel2• 10 years ago

You'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• 10 years ago

Yeah, 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.

m000z0rz• 10 years ago

Really? This seems very similar to problems with variable naming and magic numbers, which are far from bike shedding.

stonogo• 10 years ago

No, they aren't.

JadeNB3• 10 years ago

If mathematics has a bikeshed, this is it.

In my experience, few professional mathematicians care about this. The question that Bromskloss (https://news.ycombinator.com/item?id=11993750) mentions, of whether or not 0 is a natural number, is likely to incur a far more passionate response. (At the risk of downvotes: it is.)

Bromskloss7• 10 years ago

In therms of practical consequences such as making mathematical expressions look different, it seems to me that 0 vs. 1 makes a smaller difference than does τ vs. π, because many statements about the set ℕ of natural numbers make no mention of what its first element is anyway. Often you can drag along any of the two definitions of ℕ through the argument, without changing it's conclusions. For example, if f:ℕ→ℝ (and ε∈ℝ, N∈ℕ, n∈ℕ), the limit L∈ℝ is given by (∀ε>0)(∃N)(∀n≥N)(|f(n)-L|<ε), regardless of whether one takes ℕ={0,1,2,…} or ℕ={1,2,3,…}.

tempodox• 10 years ago

I find your interpretation rather benign. Saying, “pi is wrong, tau is right” is the equivalent of mathematical bigotry to me.

mithaler• 10 years ago

I have to disagree.

I'm a programmer, but I'm not good at math. I know this. And yet, the Tau Day Manifesto explained the geometry of the circle to me more clearly and understandably than any of the math classes I've ever taken. And it's not just because it's a well-written work; the concept is genuinely simpler to understand.

Pi really is a pedagogical disaster, and tau really does help.

MrManatee2• 10 years ago

I 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.

jeffwass9• 10 years ago

Your 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.

tgb• 10 years ago

Surely the Cauchy distribution you're replying to doesn't have any steradians going on, right? It's a 1D distribution and the gun described would point towards a random point on a circle, not on a sphere.

MrManatee2• 10 years ago

As you already realized, my example was supposed to be in 2D, but I forgot to mention it. Sorry about that.

But your point about steradians is still spot on. If I had been talking about the 3D case, there would have been a 1/(2pi) factor in the front of the pdf. Using tau would not have helped anyone realize that this particular 2pi is most naturally thought of as 1/2 of the full 4pi steradians. Using tau is not a substitute for careful thinking.

And I am not even actually advocating switching to tau; I am not sure if it is worth the effort. But I still think that tau is a good way of conveying the idea that the current definition of pi as basically a historical accident. This can be enlightening even if one doesn't start using tau. As a more extreme example, I think it is useful to recognize that the decimal base (as opposed to binary, hex, etc.) is a historical accident, but I wouldn't advocate changing it.

Confusion• 10 years ago

  One argument in favor of tau is that in many formulas pi 
  often has the multiplier 2 in front of it.

And an argument in favor of pi is that many formulas do not have that any multiplier in front it. So this cannot be resolved without quantitative evidence of the number of formulas using either one, including their frequency of use.

Of course you can construct infinitely many formulas, but most of those are used a vanishingly small number of times. The question is what common formulas use pi or tau. How often would people actually have to write, read or say a factor?

kazinator7• 10 years ago

In any formula where the 2 in 2π has been canceled by some irrelevant 2, the cancellation is not really an advantage; it obscures semantics.

Also, when counting formulas don't forget to expand "angular frequency" ω to the 2πf it denotes.

jordigh• 10 years ago

On to more important matters, Gamma function or Pi function?

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• 10 years ago

Using tau would uglify euler's equation, wouldn't it?

kqr• 10 years ago

You be the judge of that. Compare

    e^(iπ) = -1

    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.

kej3• 10 years ago

Writing 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.

Steuard2• 10 years ago

e^(i tau) - 1 = 0

Seems pretty comparable to me: this one elegantly demonstrates the full periodicity of complex exponentials, while the original elegantly demonstrates how complex exponentials can produce pure negative numbers.

lazyant• 10 years ago

I'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• 10 years ago

It's probably closer to 98% and 2% of the time for serious math, engineering, and physics.

NaNDude• 10 years ago

i 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!).

kazinator7• 10 years ago

Angular frequency (ω = 2πf) is related to this:

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.

Bromskloss7• 10 years ago

This 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• 10 years ago

OT, 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/

thanatropism3• 10 years ago

What's a nice infinite series summing to tau that isn't merely 2S(n) where S(n) sums to pi?

thanatropism3• 10 years ago

Ha. I've said a lot of continental-philosophy stuff that gets downvoted by the techie culture, but this is amazing.

Bromskloss7• 10 years ago

Just checking: Do you mean that your comment amounts to continental philosophy?

andrewla• 10 years ago

The 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• 10 years ago

I'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

karmakaze• 10 years ago

This simultaneously illustrates how e^(180') is halfway round a unit. Tau (literally/numerically?) > Pi

Happy Tau Day

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