Two of Barcelona's architectural masterpieces are as different as different could be. The Church of the Holy Family, designed by Antoni Gaudí (1852–1926), is only a few miles from the German Pavilion, built by Mies van der Rohe (1886–1969). Gaudí's church is flamboyant, complex, and irregular. Mies's pavilion is tranquil, simple, and rectilinear. Mies, the apostle of minimalist architecture, used the slogan “less is more” to express what he was after. Gaudí never said “more is more,” but his buildings suggest that this is what he had in mind.

One reaction to the contrast between Mies and Gaudí is to choose sides based on a conviction concerning what all art should be like. If all art should be simple or if all art should be complex, the choice is clear. I reject both of these monistic norms; I am a pluralist about artistic simplicity and complexity because I see value in both. True, there may be extremes that are beyond the pale. We are alienated by art that is far too complex and bored by art that is far too simple, but between those two extremes there is a vast space of possibilities. Different artists at different times and places have had different goals. Artists are not in the business of trying to discover the uniquely correct degree of complexity that all artworks should have. There is no such timeless ideal.

Science is different, at least according to many scientists. Einstein (1933) spoke for many when he said that “it can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” This influential point of view holds that the search for simple theories is not optional; rather, it is a requirement of the scientific enterprise. When theories get too complex, scientists reach for Ockham's razor, the principle of parsimony, to do the trimming. This principle says that a theory that postulates fewer entities, processes, or causes is better than a theory that postulates more, so long as the simpler theory is compatible with what we observe. This formulation of the principle is preliminary; it will be fine-tuned in what follows.