Story from T.V.Raman
Hi Dick,
Here is a short write-up of something I remember -- edit to taste.
I worked at the MSC in Spring 1990 --- and the experience was
enriching along many dimensions, especially with respect to
understanding how students ended up hitting a stone wall at times
because of how Math notation can confuse while intending to be
intuitive -- here is one such example.
A studious Sophomore walked in saying
"I cant get the right answer on this Calculus problem".
So I observed him perform each step of the calculation, he did it
perfectly until step n-1. Then he simplified E^{-x} to \log(x).
I asked him how he got that and he confidently said "that is the
definition of Log(x)".
I told him it was not, and he confidently pulled out his class-notes
saying Yes it is -- the Professor wrote it on the board.
So I asked him to show me what the Professor had written, and sure
enough his notes read
"If f(x) = e^x, then F^-1(x) == log(x)"
It took me a while to explain the function inverse notation vs
negative exponentiation to him --- but it illustrates how Math
notation while intending to be intuitive and often confuse.
--raman
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Dick Furnas - 2021-05-18