'The most common of all follies,' wrote H. L. Mencken, 'is to believe passionately in the palpably not true. It is the chief occupation of mankind.' … - Steven Pinker

The psychologist Dedre Gentner and her collaborators have shown that a focus on relationships is the key to the power of analogy as a tool of reasoning. They note that many scientific theories were first stated as analogies, and often are still best explained that way: gravity is like light, heat is like a fluid, evolution is like selective breeding, the atom is like a solar system, genes are like coded messages. For an analogy to be scientifically useful, though, the correspondences can’t apply to a part of one thing that merely resembles a part of the other. They have to apply to the relationships between the parts, and even better, to the relationships between the relationships, and to the relationships between the relationships between the relationships.

[E]quality is not the empirical claim that all groups of humans are interchangeable; it is the moral principle that individuals should not be judged or constrained by the average properties of their group. … If we recognize this principle, no one has to spin myths about the indistinguishability of the sexes to justify equality.

Suppose the reasoning centers of the brain can get their hands on the mechanisms that plop shapes into the array and that read their locations out of it. Those reasoning demons can exploit the geometry of the array as a surrogate for keeping certain logical constraints in mind. Wealth, like location on a line, is transitive: if A is richer than B, and B is richer than C, then A is richer than C. By using location in an image to symbolize wealth, the thinker takes advantage of the transitivity of location built into the array, and does not have to enter it into a chain of deductive steps. The problem becomes a matter of plop down and look up. It is a fine example of how the form of a mental representation determines what is easy or hard to think.