For the last year or so I've been watching a bunch of YouTube clips in a series called Begin Japanology, which is an NHK series about Japanese culture and society. I've just been watching a fascinating one about the Japanese abacus, aka the soroban:
The whole thing is worthwhile (it's less than a half hour), but here are some segments to pay attention to:
- How it works: c. 6:15-8:53: the sensorimotor basics. If you want to think about the "extended" mind, you have to start here.
- Mental calculation: c. 12:35-13:23: people can do sorobon calculations without actually having a sorobon. They do the calculations mentally, though they may move their fingers over an imaginary sorobon.
- Divination: 16:23-17:00: In the old days math was used more for divination than for solving practical problems.
And of course there's the usual stuff about how very fast experts are, beating ordinary electromechanical and electronic calculators.