I ran across a post today on the SquareCircleZ blog, lamenting the effect of some of the poor choices of notation that we use in Mathematics.

It reminded me of the trouble that I have been having saying that cosine is x/r and then making r=1 to get a unit circle. Now x=cosine and we graph the values as y = cos x (what is x!!!).

One of the commenters makes an interesting suggestion about the use of brackets. If we adopted this idea, we could see the difference between 5(x) and f(x).

David Speyer said,

June 17, 2007 at 12:08 pm

By the way, this is Mathematica’s notation. “()” indicates order of operations, “[]” indicates application of functions, “{}” indicates an ordered pair or a list. So

ParametricPlot[{Sin[t], 2*(Cos[t]+1)}]

would plot an ellipse whose x-coordinate is Sin[t] and whose y-coordinate is 2*(Cos[t]+1). (Also, “[[]]” indexes into a vector or array, but pedagogically we want to discourage students from thinking of an array and a function as different objects.)

I find that I have very little trouble making these distinctions, even when I’ve been away from the software for several months, so I think it would be easy for experienced mathematicians to switch to the new notation.