You come to me and say:

sine!cosine!tangent!arctangent!atan2!

I say:

Those words are meaningless. You're fired.

Math language in general is really terrible about this; it forces the student to learn meaningless foreign names for concepts that, to mathemeticians, have become intuitive.

Which raises the question, what would you call those functions?

sine could be:

math.RightTriangle.height_of_opposite_side(angle)

or

math.UnitCircle.position_from_angle(angle).y

...I got nothing.

Isn't that what new words are for? You have some complicated concept ("the ratio of the length of the opposite side to the length of the hypotenuse") that you want to be able to refer to more easily, and so you invent a single word ("sine") to refer to it.

ReplyDeleteMightn't you complain just as legitimately that, say, "up" is an arbitrary and meaningless foreign name for "the direction that is pointed against the pull of gravity"?

Yes. At some point concepts warrant their own words. The trigonometric functions probably do indeed qualify. But if we were writing trigonometry from scratch, today, we would totally use long stupid descriptive names. ;-)

ReplyDeleteHonestly the base functions of sine and cosine get used so much in so many different contexts, they would almost certainly get a name.

ReplyDeleteThese days, it seems it would most likely end up with the usual "arbitrary greek letter" a la gamma function and phi function, or named after some mathematician a la Euler's function, Bessel functions, or Legendre functions. Don't overlook the possibility it would be

both, like the Dirac delta, Kronecker delta, or Riemann zeta.When you think that it could be, say, "the Perelman tau function", "sine" and "cosine" are pretty good.

I agree with sam. At least they are unique identifiers and not overloading some single-letter greek or latin letter. And at least every math, science, and engineering discipline uses the same convention. As a piece of satire, the article works, and your logic is sound but ... Leaving succinct notation alone... for the win!

ReplyDeleteAlright, I'm retroactively applying the 'satire' tag to this post. It's totally a satire on how computer programmers get twisted into knots trying to name things well. ;-)

ReplyDeleteI'm not advocating renaming the trigonometric functions. Just sayin', is all.