I was joking with a colleague today about replacing Mathematica (a symbolic math program) with an abacus, and it started me wondering: how would one go about making a "symbolic abacus"?
Let's just limit it to finding roots of polynomials, for example. Could you make a mechanical device that lets you slide/fold/twist "x^2 = x+a" and then slide/fold/twist to get "x = (+/- sqrt(4a+1) + 1 )/2" ?
(Edit: To emphasize symbolic, not numeric solutions)
