05.5 Trade-offs in Abstraction
5.5 Trade-offs in Abstraction Abstraction makes mathematics powerful, but it is never free. Each level of abstraction preserves some information and suppresses other information. The benefit is generality. The cost is distance from concrete examples. At a concrete level, everything is visible. We can compute, test, and inspect. The object is close to intuition. But concrete reasoning often fails to scale. A calculation may explain one case without explaining the...