“[M]athematical ideas originate in empirics, although the genealogy is sometimes long and obscure. But, once they are so conceived, the subject begins to live a peculiar life of its own and is better compared to a creative one, governed by almost entirely aesthetic considerations, than to anything else, and, in particular, to an empirical science. There is, however, a further point which, I believe, needs stressing. As a mathematical discipline travels far from its empirical source, or still more, if it is a second and third generation only indirectly inspired by ideas coming from ‘reality’, it is beset with very grave dangers. It becomes more and more purely aestheticising, more and more purely l’art pour l’art. This need not be bad, if the field is surrounded by correlated subjects, which still have closer empirical connections, or if the discipline is under the influence of men with an exceptionally well-developed taste. But there is a grave danger that the subject will develop along the line of least resistance, that the stream, so far from its source, will separate into a multitude of insignificant branches, and that the discipline will become a disorganised mass of details and complexities. In other words, at a great distance from its empirical source, or after much ‘abstract’ inbreeding, a mathematical subject is in danger of degeneration.”
Part 1 and Part 2
Friedrich Hayek, the Austrian economist who received the 1947 Nobel Memorial Prize in Economics, pointed out that in the physical sciences we know the macroscopic through concrete experience and proceed from to the microscopic by abstraction. [...] In economics, Hayek argued, the order of abstraction should be reversed: we know the individual agents and players from concrete personal experience, and the macroscopic "economy" is the abstraction. If the correct way to proceed is from the concrete to abstract, he argued, in economics we should begin with agents and proceed to economies and markets rather than vice versa.
- It accurately predicts outcomes given input data
- It emits a model that is inspectable and can inform the building of better 'toy models' of the system under study.