WIP – tau: add MathConst{:τ}

[StefanKarpinski]

There's an issue with code evaluation order here. Maybe I need a toplevel block or something like that. Anyway, thought I'd throw this out there for comment before spending any more time on it. Do we want τ and tau?

[simonbyrne]

One problem with adding these constants is that they can increase the risk of unexpected behaviour when redefined. I feel that most people expect pi to be 3.14159..., but I often use e and tau as variable names, which increases the risk of shooting myself in the foot. Granted this hasn't caused a problem yet, but it's worth thinking about.

[jiahao]

I’m sorry, but WAT. Are there people seriously using τ out there instead of 2pi??

[ihnorton]

http://www.bbc.co.uk/news/science-environment-13906169

[jiahao]

Far be it from me to be a pi-imperialist (pimperialist?), but I'm really not convinced of the utility of adding tau to Base. This should receive at least as much due consideration as adding a new function to Base; I've seen PRs closed for functions that are more useful than this.

Unless someone can demonstrate that this is actually gaining traction in scientific computing, people who want this should just define it themselves.

[johnmyleswhite]

I agree with Jiahao.

[StefanKarpinski]

Well, that's why it's a pull request and why I didn't spend much time on it :-)

[jiahao]

/me wonders if it’s April 1 in the Nordic calendar...

[ViralBShah]

I have to agree with @jiahao too.

[StefanKarpinski]

I used to be skeptical of the tau thing, but it really does make so much more sense than pi.

[jiahao]

I used to be skeptical of Imperial units, but it really still does not make more sense than metric.

[johnmyleswhite]

I'd love to hear your reasoning sometime, Stefan. I still react to tau as "hipster nonsense".

[StefanKarpinski]

Basically, making the unit number of radians a full circle just makes life easier almost everywhere you look. A half circle is just awkward. For example if you know modpi(x) you know where it falls on a half circle. Great. But which half? If you know mod2pi(x) then you know where it falls on the circle, which is a completely natural thing to want to know. When you write 2π you're essentially saying "two half circles". If we went around saying that in English, we'd sound like jackasses. When you write τ/2 you're saying "half a circle" – which is exactly what it looks like.

[toivoh]

+1 for tau. I've never used it, but it's starting to feel quite compelling.

[JeffBezanson]

I do agree that tau is generally better than pi, but I'm not sure it warrants inclusion in Base. τ is a pretty popular variable name.

[jiahao]

This is the most common argument presented in favor of tau. However, that argument works only in an odd number of dimensions. That pernicious factor of 2 alternates between appearing and disappearing between relations involving circles (spheres, hyperspheres) in odd- and even-dimensions. You can see this most clearly in the formulae for the area and volume for these N-spheres. For any given dimension, the factor of 2 will show up in exactly one formula for either the area or the volume, but not both. Of course, you can hide this with the special functions of your choice, but it doesn’t change the fundamental mathematical reason for the factor of 2 showing up.

[jiahao]

Mathematical bikeshedding aside, there was a suggestion made in #4862 to introduce twoπ as a constant in Base. That would be much less controversial and in line with current common practice.

[jiahao]

It’s also amazing how much virtual ink has been spilled on this: tauday vs pimanifesto

[StefanKarpinski]

So you want to have a MathConst called "twoπ" but you're not interested in τ? Um, what?

[arsatiki]

Hello!

Apologies for messing in this old ticket, but it's dear to my heart. In honor of tomorrow's tau day, I was going to do pretty much this same pull request. I've found tau to be so useful I'm using it exclusively while doing anything trigonometry related. Sadly, redefinition dance is becoming bothersome.

I see that the biggest objection in the previous discussion is conflicting names. Here's a proposal for avoiding that:

• use palaistau as the non-unicode name, analogous to eulergamma
• use (MATHEMATICAL ITALIC SMALL TAU, U+1D70F) as the unicode name

(Addition: the Github comment processing corrupts the italic tau. Sorry about that.)

[pao]

use (MATHEMATICAL ITALIC SMALL TAU, U+1D70F) as the unicode name

This won't help, since it normalizes to GREEK SMALL LETTER TAU (U+03C4):

julia> normalize_string("(that letter github won't print correctly)", :NFKC) "\u3c4" 

[kmsquire]

Hi Antti,

I suggest making a package, which includes the definition of tau and some
example functions of how it's used.

This should satisfy the skeptics (they can ignore the package), and still
let tau be part of Julia (which I support), without conflicting with
anything.

(A general non-Base math constants package would be better, perhaps, but I
don't know what other constants are missing/useful.)

Cheers, Kevin

On Friday, June 27, 2014, Antti Rasinen notifications@github.com wrote:

Hello!

Apologies for messing in this old ticket, but it's dear to my heart. In
honor of tomorrow's tau day, I was going to do pretty much this same pull
request. I've found tau to be so useful I'm using it exclusively while
doing anything trigonometry related. Sadly, redefinition dance is becoming
bothersome.

I see that the biggest objection in the previous discussion is conflicting
names. Here's a proposal for avoiding that:

• use palaistau as the non-unicode name, analogous to eulergamma
• use 𝜏 (MATHEMATICAL ITALIC SMALL TAU, U+1D70F) as the unicode name

—
Reply to this email directly or view it on GitHub
#4864 (comment).

[jiahao]

I'm still unconvinced.

[tkelman]

I use tau often enough as a time constant that this would bug the crap outta me.

[StefanKarpinski]

I think the way to go here is to create a Tau.jl package that defines and exports τ as a MathConst. Then people who want to use τ can just do using Tau and have τ available.

[mgkuhn]

Using MATHEMATICAL ITALIC SMALL TAU (U+1D70F) would be very wrong, because in mathematical notation, italic letters denote variables (see e.g. ISO 80000-1), whereas standard constants should be written in an upright font. And the proposed τ is clearly a constant!

For the same reason, the constants and constant functions π, e, sin, log, etc. are written in upright font. (I know, this practice has sadly eroded somewhat for π and e thanks to TeX, which initially lacked an upright Greek font for π, and generally made typesetting non-italic symbol names rather cumbersome in its math mode.)

Generally, I find the idea of tau far more appealing than 2π, but in mathematics, new notational conventions take about 300 years to catch on. If only Euler had thought of this earlier ...

[waldyrious]

Tau.jl is now available since the merge of JuliaLang/METADATA.jl#1048 :)