Tonight, I went to see the movie "Hidden Figures". The movie is getting lots of good mentions because of its portrayal of the world of "calculators" - the women who would actually make the calculations assigned to them by men engineers in the days before widespread use of computers - and African-American calculators, in particular, at NASA, in the years 1961-63.
The movie was a real feel-good movie: scrappy women fighting against the odds, and winning. Nevertheless, I thought the movie did a real disservice to the world of engineers.
Until the mid-70's, every engineer would have had a slide rule. Calculators would have had mechanical calculators, but they would have had slide rules too. Nevertheless, there wasn't a single slide rule in the entire movie.
In the absence of analytic solutions, calculators would have focused on difficult finite-difference calculations. That's why they had to have mechanical calculators. Nevertheless, there wasn't a single finite-difference equation in the entire movie.
In one scene, the movie edges into non-analytic problems by suggesting the transition from elliptical to parabolic equations had no obvious solution. Good, I thought, here come the finite-difference calculations. To my surprise, the calculator suggests using Euler's Rule (presumably Euler's Formula) to solve an equation. The engineer looks surprised, and complains Euler's Rule is ancient. No engineer would speak like that. Mathematics is eternal - Euler's Rule is as valid today as it ever was, and ever will be.
But as a rule, moviegoers are more-familiar with a world where scrappy women fight against the odds than a world where NASA engineers struggle against non-analytic problems in the early 60's. So, the movie makers choose to mangle that technical world in the interest of enhancing the drama. And it works! I certainly found the movie pleasing. How could it not with the superbly-talented Janelle Monae in the cast? But cry, cry for the lost finite-difference calculations....