[light3]

Of course if you're doing it by trial and error on paper it is pointless tedium. But I'm sure that the point of doing these exercises were not bore you to death, but to really make you understand arithmetic so you can do most given problems faster. If all you knew was how to multiply and divide numbers by hand, that problem would take you hours to solve!

A great example is the section 'lucky numbers' in Feynman's book:

http://lib.ru/ANEKDOTY/FEINMAN/feinman_engl.txt

[jedbrown]

> that problem would take you hours to solve

I don't know, two Newton iterations are enough:

  *GHCi> let croot f x = x - (x^3 - f) / (3*x^2) in take 5 . iterate (croot 0.0093) $ 0.2
  [0.2,0.21083333333333332,0.2102957483409451,0.2102943717551532,0.21029437174614204]

Guessing 0.2 as a starting point is obvious enough because 0.2^3 = 0.008.

[derleth]

True enough, except it's also along the lines of memorizing the works of Cicero or knowing all of the books of the Bible off by heart: It's useful at developing a skill that the correct tools render obsolete (cheap books in the case of the memory feats, computers in the case of the arithmetical ones). Similarly, knowing Latin and Greek had a purely practical motive as well back then: It marked you as a member of the social elite, defined as people who had enough leisure to study objectively useless things such as Latin and Greek. Memorizing paradigms wasn't something a farmer's son could be expected to do, after all.

I suppose my point, which I expressed poorly, is that it can be interesting to examine how technology impacts coursework.