## Counting the piano tuners – the hard way.

No, Enrico Fermi and his questions weren’t my inspiration for this post – it was Stan Ulam’s quote I read few days ago:

Knowing what is big and what is small is more important than being able to solve partial differential equations.

That is exactly what an engineering student (or an applied mathematics student) needs: sense of reality. One needs to know what parameters of dynamic systems are normal, natural, what is the magnitude of results, what is negligible in calculations. Making fast estimates, estimating the accuracy of such estimates – knowing what accuracy is needed for certain calculations: it saves money, nerves, trees and shows intelligence. One could start with that in a calculus course, where problems concerning integral estimates (using MVT or some known inequalities for instance) could be given. After that – let the student take a course like the one on MIT called Street-fighting matematics. Without that, you can’t expect your students to make an estimate of the number of piano tuners in Chicago – they’ll do a brute-force search through the phonebook.

But hey, no one in charge of making the curricula will ever think of something like this – they managed to squeeze out probability theory, statistics, stochastic processes, numerical methods out of control theory students’ curriculum – enough said.

Still – Mark Twain was right:

Don’t let schooling interfere with your education.