As Hungarian-born mathematician George Pólya put it, “When you have satisfied yourself that the theorem is true, you start proving it.
This is exactly how discovery works, according to David Deutsch, a theoretical physicist at Oxford University. The process starts with a problem, a conflict between two ideas or theories, he says. The first step in solving the problem is to tweak the existing theories so they fit. Failing that, you introduce another theory that resolves the incompatibility.
Assuming you do this successfully, Deutsch says, the outcome is, “You don’t understand the resulting theory. It solves the theoretical problems, but you can’t see what it means
. You don’t understand how that could be a description of the actual world, or what the world would have to be like for that to be true. Then you think of an analogy.
Dangers of metaphors or analogies
In science, metaphor tells you what things are like, not what they are. After analogy, Deutsch says, the final step in the discovery process is “to understand the thing in its own right, not metaphorically. Once you do this, you can dispense with the metaphor and understand the world as it actually is.