In theory, there is an infinite number of systems with simple emergent rules that can eventually be taught arithmetic.

> Most things can't be taught to do arithmetic, making this "transformer" thing slightly magical.

Yep, for people who don't have know the fundamentals (i.e. maths). To people who don't know the universal approximation theorem, this may seem like "magic", but it's just as much magic as making a dark room bright by flipping a light switch.