At PARC we had a slogan: "Point of view is worth 80 IQ points." It was based on a
few things from the past like how smart you had to be in Roman times to multiply two
numbers together; only geniuses did it. We haven't gotten any smarter, we've just
changed our representation system. We think better generally by inventing better
representations; that's something that we as computer scientists recognize as one of
the main things that we try to do.
Comments
According to this, multiplication wasn't so bad: http://turner.faculty.swau.edu/mathematics/materialslibrary/...
Actually real Romans did multiplication on an abacus. Reading from Roman numerals to/from an abacus is an incredibly natural operation.
In Europe the disappearance of abacuses was directly tied to the rise of Arabic notation.
Without a table? Just from memory? I think I'd prefer decimal.