Efficiency is fundamentally at odds with elegance (2013)
Symbolic representation vs floating point as a trade of elegance? The suggestion of maintaining non-numeric representations falls flat very quickly in a number of cases:<p>5th root of a polynomial. There is no closed form solution that could be carried through other computations.<p>Integrals. There is no general method for symbolic integration. A physics simulation cannot maintain closed form solutions and it would not be elegant even if you could.<p>Representations of geometry - as in CAD programs. The intersection of 2 curved surfaces is usually higher order than the surfaces in question and can balloon very quickly.<p>Anything with sampled data - why even bother trying.<p>Sometimes numeric representations are necessary, not just some kind of trade. Unless one thinks the non-existence of some fantasy ideal representation is a kind of tragedy in need of fixing. And that seems to be his point at the end - you&#x27;ll get frustrated very quickly looking for an elegant solution that may not even exist.