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There's a cute story in Surely You're Joking, Mr. Feynman where a man with an abacus challenges him to an arithmetic contest: http://www.ee.ryerson.ca/~elf/abac

• scarmig 10y ago
  He's a bit too pleased with himself at the end there: they simply are using different algorithms, and those naturally have different performance properties for different inputs. Feynman is relying on a prepopulated lookup table and some heuristics, while the abacus guy is relying on whichever algorithm is best suited for calculating cube roots on an abacus. Though, I admit, I'd probably be pleased as a peach too.
  • yosefk 10y ago
    Feynman uses a much larger set of algorithms though, and can come up with new ones. The guy with the abacus seems like he didn't know why his algorithms worked, he just executed them.
• _yosefk 10y ago
  And in this story he claims that abacus use is mechanical and rids you of having to "know" numbers or approximate methods or understanding anything about the computation and why answers come out as they do. You're just executing steps and the more complex the computation, the more steps you do with no understanding whatsoever. So the opposite thesis from TFA.
  • sn9 10y ago
    It's not really an opposing thesis. The moral of the story is that his opponent became married to the use of the abacus and convinced of its superiority and that led to an overreliance on it and inflexible thinking. The thesis of the TFA is that the abacus can be a great tool for teaching arithmetic and number sense. It doesn't argue that it's the only thing you'll ever need and you should use other tools.