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!
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...
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?
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.
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!