In the section “Numbo: A Study in Cognition and Recognition” the architecture of the program Numbo, designed to solve crypto-like problems, models everyone’s favorite computing device: humans. Numbo has a store of knowledge, pnet of arithmetic facts that function similar to human declarative knowledge. Hoffstadter compares Numbo to its human ideal: combinations are not strongly goal-driven, ideas are often abandoned before fully explored, and the obvious things are noticed immediately. However, Numbo can’t do everything these purposeless, undetermined ideal creatures can: it pays no attention to the order of bricks, has an “impoverished” knowledge base, and doesn’t whine about the problem being too hard.
Numbo is a prime example of Cognitive Science: the creation of a computational model to better understand human reasoning. Even if Numbo does not perform in strictly human way, it still allows us to create models of how a human might approach these problems. Hoffstader reports that many humans aren’t able to describe human ways of solving. Elements of competition, association, all may be present in human mathematical cognition. By programming these we can develop theories about how they work in the brain, and from these theories we can design experiments to test if they are supported in actual human functioning. Unlike other computer models, Numbo doesn’t use a record of objects and does not concentrate on one sub-goal at a time. Numbo is as fluid and chaotic as evolution and from its primordial swamp solutions arise.
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