4 ms·

Wow this is hilarious. Truly a "manifesto" to set a constant for 2pi. It definitely has a great point, and I totally agree that it's a better constant than pi,

Wow this is hilarious. Truly a "manifesto" to set a constant for 2pi. It definitely has a great point, and I totally agree that it's a better constant than pi, but it's not the worst historical accident of mathematics. The thing is, tau is really my go-to variable when I need a 2nd constant to compare with t. It is already used as a time constant, a dummy integration variable that substitutes for t... The manifesto has a pre-made counter-argument to this... But I'm not sure it's convincing. The thing is that we like to say some variation of e^(-tau) a lot, and we also like to say e^(2 pi i) a lot. And often we combine these (rotation and exponential decay), and we get e^(-tau+2pi i). And this would ruin tau notation! It would be e^(-tau'+tau i)...

samatman 13y ago
May I recommend ת ? Tau notation is pretty excellent stuff. There's even a gloss: ת in mainstream Kabbalah corresponds to Saturn, the god of time. Electrical engineers need i for something else, incidentally, and use j for imaginary numbers. Mathematical notation is intentionally flexible.
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mhartl 13y ago
I really like using tau as a time constant, too, and I'm sorry to lose it when there are pi's in the picture. It's tough picking good notation, though, and unfortunately no choice is conflict-free. Before writing The Tau Manifesto, I tried several other candidates before settling on tau. After using it for a while, tau started to "feel right" in ways that other choices didn't. Then, as noted in the manifesto, I found out that I wasn't alone: Since the original launch of The Tau Manifesto, I have learned that Peter Harremoës independently proposed using τ to “π Is Wrong!” author Bob Palais in 2010, John Fisher proposed τ in a Usenet post in 2004, and Joseph Lindenberg anticipated both the argument and the symbol more than twenty years before!
- thetwiceler 13y ago
  Yeah, I've literally never seen lower-case pi used as a variable (thank goodness!). tau is a good choice because it looks like pi, and is possible for normal people to write (I would have had a fit if it were lowercase xi!). I like the explanation page for why tau a lot, and I think that page is much more important than actually using tau in real mathematical works. It's a great explanation of how 2*pi is the more natural quantity, and how it comes into play in the different functions. But it's just much easier to deal with factors of 2 than it is to explain alternate notation. In fact, I think a lot of making mathematical works easy to understand is using commonly accepted notation...
- Radix_ 13y ago
  Why didn't you make the circle constant a circle in your manifesto? I'm not sure but it seems the function composition symbol could be safely reused without confusion or perhaps a larger circle with a drawn radius. Wouldn't a circle have avoided some of the Tau criticisms?
  - sesqu 13y ago
    The major problem is that a circle is too ambiguous a symbol; you'd need to add a notch or line or something to make it clear that you're referencing a constant. And when you do that, it becomes harder to write. I always favored a variation on ◷, something like ◯̶ or ◯̵ or ○̵. Unfortunately, combined glyphs are representationally very unstable.
jessriedel 13y ago
Yea, the thing about a circle constant (whether pi or tau) is that it's so ubiquitous you can't use the symbol for anything else. It's pretty rare to use lower case pi for anything in physics and math, and most of the exceptions including something like boldface or a vector hat to distinguish it. There are no available symbols. The only option is to introduce a new one, like ת suggested by samatman, or possibly by using a weird typeface (like \mathfrak in LaTeX). Incidentally, my friend has pointed out to me that sigma is a much better choice than tau if we're going with existing symbols. Who cares about tau sounding like a "t" for "turn", when sigma actually looks like someone trying to measure the circumference of a circle with the radius of the circle: σ.
- anigbrowl 13y ago
  There are no available symbols. Why not just start in on Chinese characters? There's plenty of those and I'm sure Chinese mathematicians could suggest some likely candidates based on their long mathematical traditions. http://en.wikipedia.org/wiki/Chinese_mathematics http://en.wikipedia.org/wiki/Chinese_mathematics
- manicbovine 13y ago
  \pi is very frequently used to denote a projection or some other mapping.
- mhartl 13y ago
  σ has potential, but there's a pretty bad conflict with standard deviation. The circle constant shows up an awful lot in statistics. Who cares about tau sounding like a "t" for "turn" Pi comes from perimeter, phi comes from Phidias, etc. There's a long tradition of naming constants using a linguistic root (typically Greek). To my knowledge, there's no precedent for using a symbol based on its visual appearance to a geometric object. (Of course, you could always break with tradition.)
  - sesqu 13y ago
    To be completely fair, π turns up occasionally in statistics too, as a symbol for probability.
jessriedel 13y ago
What's the worse historical accident of mathematics?
- thetwiceler 13y ago
  The use of infinitesimals in calculus! Things like integrating against "dx" or taking a derivative of a function "df/dx" make calculus seem like something it's not. Worse, it really introduces a whole new language whose rules for manipulation are unclear. Like if we have a function f(x,y), we often write the "total" derivative of f as df = (df/dx) dx + (df/dy) dy And the rules for manipulating a differential like this are quite strange (e.g., dx on top cannot cancel the dx on bottom). There's a language of differential forms that makes this notation a bit more rigorous, but I still think the notation is very misleading and confusing, especially for those who begin to learn calculus.
  - kryten 13y ago
    This. Notation in formal mathematics is just totally awful. You pick on a great example as well there.
  - currymesurprise 13y ago
    To be fair to mathematics, in your example the proper notation is df = (del f/del x) dx + (del f/del y) dy, which does not suggest the possibility of cancelation.
mtdewcmu 13y ago
If it succeeds, it's worthy of the Ig Nobel Prize.

samatman 13y ago

May I recommend ת ? Tau notation is pretty excellent stuff. There's even a gloss: ת in mainstream Kabbalah corresponds to Saturn, the god of time. Electrical engineers need i for something else, incidentally, and use j for imaginary numbers. Mathematical notation is intentionally flexible.

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mhartl 13y ago

I really like using tau as a time constant, too, and I'm sorry to lose it when there are pi's in the picture. It's tough picking good notation, though, and unfortunately no choice is conflict-free. Before writing The Tau Manifesto, I tried several other candidates before settling on tau. After using it for a while, tau started to "feel right" in ways that other choices didn't. Then, as noted in the manifesto, I found out that I wasn't alone: Since the original launch of The Tau Manifesto, I have learned that Peter Harremoës independently proposed using τ to “π Is Wrong!” author Bob Palais in 2010, John Fisher proposed τ in a Usenet post in 2004, and Joseph Lindenberg anticipated both the argument and the symbol more than twenty years before!

thetwiceler 13y ago
Yeah, I've literally never seen lower-case pi used as a variable (thank goodness!). tau is a good choice because it looks like pi, and is possible for normal people to write (I would have had a fit if it were lowercase xi!). I like the explanation page for why tau a lot, and I think that page is much more important than actually using tau in real mathematical works. It's a great explanation of how 2*pi is the more natural quantity, and how it comes into play in the different functions. But it's just much easier to deal with factors of 2 than it is to explain alternate notation. In fact, I think a lot of making mathematical works easy to understand is using commonly accepted notation...
Radix_ 13y ago
Why didn't you make the circle constant a circle in your manifesto? I'm not sure but it seems the function composition symbol could be safely reused without confusion or perhaps a larger circle with a drawn radius. Wouldn't a circle have avoided some of the Tau criticisms?
- sesqu 13y ago
  The major problem is that a circle is too ambiguous a symbol; you'd need to add a notch or line or something to make it clear that you're referencing a constant. And when you do that, it becomes harder to write. I always favored a variation on ◷, something like ◯̶ or ◯̵ or ○̵. Unfortunately, combined glyphs are representationally very unstable.

jessriedel 13y ago

Yea, the thing about a circle constant (whether pi or tau) is that it's so ubiquitous you can't use the symbol for anything else. It's pretty rare to use lower case pi for anything in physics and math, and most of the exceptions including something like boldface or a vector hat to distinguish it. There are no available symbols. The only option is to introduce a new one, like ת suggested by samatman, or possibly by using a weird typeface (like \mathfrak in LaTeX). Incidentally, my friend has pointed out to me that sigma is a much better choice than tau if we're going with existing symbols. Who cares about tau sounding like a "t" for "turn", when sigma actually looks like someone trying to measure the circumference of a circle with the radius of the circle: σ.

anigbrowl 13y ago
There are no available symbols. Why not just start in on Chinese characters? There's plenty of those and I'm sure Chinese mathematicians could suggest some likely candidates based on their long mathematical traditions. http://en.wikipedia.org/wiki/Chinese_mathematics http://en.wikipedia.org/wiki/Chinese_mathematics
manicbovine 13y ago
\pi is very frequently used to denote a projection or some other mapping.
mhartl 13y ago
σ has potential, but there's a pretty bad conflict with standard deviation. The circle constant shows up an awful lot in statistics. Who cares about tau sounding like a "t" for "turn" Pi comes from perimeter, phi comes from Phidias, etc. There's a long tradition of naming constants using a linguistic root (typically Greek). To my knowledge, there's no precedent for using a symbol based on its visual appearance to a geometric object. (Of course, you could always break with tradition.)
- sesqu 13y ago
  To be completely fair, π turns up occasionally in statistics too, as a symbol for probability.

jessriedel 13y ago

What's the worse historical accident of mathematics?

thetwiceler 13y ago
The use of infinitesimals in calculus! Things like integrating against "dx" or taking a derivative of a function "df/dx" make calculus seem like something it's not. Worse, it really introduces a whole new language whose rules for manipulation are unclear. Like if we have a function f(x,y), we often write the "total" derivative of f as df = (df/dx) dx + (df/dy) dy And the rules for manipulating a differential like this are quite strange (e.g., dx on top cannot cancel the dx on bottom). There's a language of differential forms that makes this notation a bit more rigorous, but I still think the notation is very misleading and confusing, especially for those who begin to learn calculus.
- kryten 13y ago
  This. Notation in formal mathematics is just totally awful. You pick on a great example as well there.
- currymesurprise 13y ago
  To be fair to mathematics, in your example the proper notation is df = (del f/del x) dx + (del f/del y) dy, which does not suggest the possibility of cancelation.

mtdewcmu 13y ago

If it succeeds, it's worthy of the Ig Nobel Prize.