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/abacus/feynman.html
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.
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.