[roumenguha]

To add another point, my A-Level teacher always said anything the calculator can do, you can do, and just as fast.

And then she chose a question from the book, had one of us start typing, and she started at the board solving the same thing.

She finished first. Not by much, and obviously the calculator is the faster choice more often, but she finished first.

[scarmig]

Reminds me of the story of Feynman vs the Abacus. [1]

Though, as a story, the conclusion he draws is pretty self-congratulatory and bothers me a bit. The substrate on which you implement an algorithm like arithmetic doesn't really speak to whether you "know numbers." It's like the high schooler thinking being very good at computing integrals makes you good at math.

[1] http://www.ee.ryerson.ca/~elf/abacus/feynman.html

[posterboy]

Being powerful, ie good in something, is a function of Work over Time, so if you are good without much effort, that implies some sort of talent I think.

[cgoughnour]

Well, she certainly proved that there's at least one problem whose solution she can sometimes produce faster unaided than at least one high school student with a calculator.

[adamnemecek]

> She finished first. Not by much, and obviously the calculator is the faster choice more often, but she finished first.

This is more of an interface problem I believe.

[WorldMaker]

It's a low level magic trick: she chose the problem. Even supposing she didn't have the answer memorized, she knew exactly what to min/max to favor herself in the challenge.

(A real magician would also work to make sure that the kids thought they chose the problem, but the choice had already been primed for them.)

[FeepingCreature]

That says more about the book than about calculators. :)

[mikeash]

That's going to depend heavily on the problem in question. Multiplying large numbers? Probably. Computing the fifth root of pi to eight decimal places? Probably not so much. (Maybe there's some quick way to do that second one mentally, substitute something different if so.)

[HillaryBriss]

sounds like she proved that she could do it just as fast as a calculator. good thing i wasn't in that class. i would have proved her wrong: i couldn't out compute the calculator.

then again, they wouldn't have let me in that class in the first place.

[tree_of_item]

> my A-Level teacher always said anything the calculator can do, you can do, and just as fast.

This is obviously false, and I don't really understand the point of saying this.

Plus, the benefit of using a computer is that computation is effortless, letting you use more of your brainpower on actually interesting problems rather than something that is easily automated.