Perhaps the most important message to have emerged from these studies on instabilities is that we do not necessarily have a complete understanding of a system once we know the equations that govern it; what we really want to know are the particular solutions to those equations. The latter need not be obvious from the former. This cannot be emphasized too strongly in any branch of science. The American physicist Freeman Dyson has pointed out that for Albert Einstein and J.Robert Oppenheimer in their later years, 'to discover the right equations was all that mattered.' One might say the same about some physicists working today to develop a 'theory of everything'. But if you take this view, then fluid dynamics was all sewn up once we could write down the Navier-Stokes equation. Yet if we had stopped there, we'd never have guessed at the rich variety of solutions that it held in store even for relatively simple experimental set-ups (take a look again at Fig. 7.38, for instance). Sometimes even knowing the solutions is not enough—: only through experiments can one interpret what they are telling us.

Phillip Ball, The Self Made Tapestry: Pattern Formation in Nature p. 260

Emphasis mine.