>>17Complex numbers are a great example where this doesn't work outside of theoretic examples as the two representations have vastly different strong points. Suddenly changing the performance (or rather, accuracy) characteristics of points to another coordinate system will fuck up everything.
Even though you insist on SICP, you seem to have missed the parts about
EXPERT PROGRAMMERS choosing the abstraction level appropriate for their programs. Changing the fucking coordinate system isn't something that just happens unless you love rounding errors.