I guess the pertinent question is whether this stimulates your intellectual curiosity because you find it to be an interesting question, or at least because it raises interesting questions, or whether it stimulates your curiosity because you think it's exceedingly important and making this change will have big consequences.
I think the dismissive types see people obsessing over it as the latter, and this is, at least in my opinion, way more than is called for. There's nothing wrong with considering the consequences of such a change just for some mathematical fun. (After all, who here hasn't drawn out a complete system of units based on furlongs, fortnights, etc. as the fundamental units, rather than mks or cgs? What's that? None of you? Oh....) But the original manifesto seems to be overstating its case severely in terms of the consequences of such a change, and I think that's what others are reacting to.
Ignoring the boring costs of switching the installed base of mathematicians, software, etc. from one constant to the other, the benefit of a switch seems to be that certain things become easier and other certain things become harder. At best, there's a small net gain. Hardly seems worth the discussion when considered in that light.
If you're considering it as an interesting exercise to extract meaning from equations, well, go for it! But that seems to fit more under the banner of "What would happen if we switched this?" rather than "It would provide enormous benefit if everybody switched this!" as the original manifesto seemed to be saying.
I won't belabor the point any further than this, but the argument really is that it would provide enormous benefit. It's not just a "what would happen?", and it's not that τ "extracts" meaning from equations. It makes the intrinsic meanings of equations drastically more clear. For instance, what does sin(x) mean? What does Euler's equation mean? They're both eminently simple concepts, but they remain obscured by π.
It's exactly like refactoring code: sure, it does the same thing, but now it's more compact, more concise, more clear, more elegant; the parts of the system all fit together better, and people coming onto the project will be able to learn it faster. If you don't care about those things, then you won't refactor your code, or see the point of τ.
>They're both eminently simple concepts, but they remain obscured by π.
They are equally obscured by tau, or whatever other arc-length you might choose! The meaning does not depend on the definition of a circle but on the properties of the exponential function:
> The meaning does not depend on the definition of a circle but on the properties of the exponential function
Actually, you can go backwards and say that its circular properties define the exponential function. Euler's formula describes the rotation of the unit vector through the imaginary plane.
> As for sin(x)...specific values of arc length do not enter the definition
It's not about the definition, it's about the meaning. Sin(x) is the height of the circle at x radians. And it's super awesome with tau: one tau is full circle, and one period.
>And it's super awesome with tau: one tau is full circle, and one period.
Well, if you've already made the jump to understanding negative heights as going below the real line. This is a topic for an introductory course in geometry? When I learned about sine and cosine, it was first defined in terms of SOHCAHTOA!
I think the dismissive types see people obsessing over it as the latter, and this is, at least in my opinion, way more than is called for. There's nothing wrong with considering the consequences of such a change just for some mathematical fun. (After all, who here hasn't drawn out a complete system of units based on furlongs, fortnights, etc. as the fundamental units, rather than mks or cgs? What's that? None of you? Oh....) But the original manifesto seems to be overstating its case severely in terms of the consequences of such a change, and I think that's what others are reacting to.
Ignoring the boring costs of switching the installed base of mathematicians, software, etc. from one constant to the other, the benefit of a switch seems to be that certain things become easier and other certain things become harder. At best, there's a small net gain. Hardly seems worth the discussion when considered in that light.
If you're considering it as an interesting exercise to extract meaning from equations, well, go for it! But that seems to fit more under the banner of "What would happen if we switched this?" rather than "It would provide enormous benefit if everybody switched this!" as the original manifesto seemed to be saying.