No. This is nowhere near like the metric vs. english units debate. (If you want to talk about changing units, you should put your weight on that boat instead, as it’s much more of a serious issue.) Pi is already well defined, anyways. It’s defined according to its historical contextual meaning, regarding diameter, for which the factor of 2 does not appear.
Pi is well-defined, yes, and that’s not going to change. But some notation is better than others. It would be better notation if we had a symbol that meant 2pi, and not necessarily any symbol that meant pi, because the number 2pi is just usually more relevant. There’s all sorts of notation we have that is perfectly well-defined, purely mathematical, not dependent on any system of units, but is not optimal for making things intuitive and easy to read, write and generally process. The gamma function is another good example.
I really fail to see why metric vs. english units is much more serious; neither metric nor english units is particularly suggestive of anything these days. Neither is more natural. The quantities being measured with them aren’t going to be nice clean numbers like pi/2, they’re going to be messy no matter what system of units you measure them with.
Yeah. It’s artificially introduced (why the s-1 power?) and is basically just confusing. Gamma function isn’t really something I’ve had reason to use myself, so I’m just going on the fact that I’ve heard lots of people complain about this and never anyone defending it, to conclude that it really is as dumb as it looks.
The t^(s-1) in the gamma function should be thought of as the product of t^s dt/t. This is a standard part of the Mellin transform. The dt/t is invariant under multiplication, which is a sensible thing to ask for since the domain of integration (0,infinity) is preserved by scaling, but not by the translations that preserve dt.
In other words, dt/t = d(log t) and it’s telling you to change variables: the gamma function is the Laplace (or Fourier) transform of exp(-exp(u)).
No. This is nowhere near like the metric vs. english units debate. (If you want to talk about changing units, you should put your weight on that boat instead, as it’s much more of a serious issue.) Pi is already well defined, anyways. It’s defined according to its historical contextual meaning, regarding diameter, for which the factor of 2 does not appear.
Pi is well-defined, yes, and that’s not going to change. But some notation is better than others. It would be better notation if we had a symbol that meant 2pi, and not necessarily any symbol that meant pi, because the number 2pi is just usually more relevant. There’s all sorts of notation we have that is perfectly well-defined, purely mathematical, not dependent on any system of units, but is not optimal for making things intuitive and easy to read, write and generally process. The gamma function is another good example.
I really fail to see why metric vs. english units is much more serious; neither metric nor english units is particularly suggestive of anything these days. Neither is more natural. The quantities being measured with them aren’t going to be nice clean numbers like pi/2, they’re going to be messy no matter what system of units you measure them with.
What about the gamma function is bad? Is it the offset relation to the factorial?
Yeah. It’s artificially introduced (why the s-1 power?) and is basically just confusing. Gamma function isn’t really something I’ve had reason to use myself, so I’m just going on the fact that I’ve heard lots of people complain about this and never anyone defending it, to conclude that it really is as dumb as it looks.
The t^(s-1) in the gamma function should be thought of as the product of t^s dt/t. This is a standard part of the Mellin transform. The dt/t is invariant under multiplication, which is a sensible thing to ask for since the domain of integration (0,infinity) is preserved by scaling, but not by the translations that preserve dt.
In other words, dt/t = d(log t) and it’s telling you to change variables: the gamma function is the Laplace (or Fourier) transform of exp(-exp(u)).