The psychologist David Marr argued that every information processing system should be studied at three distinct levels: the fundamental properties of the problem it’s solving; the algorithms and representations used to solve it; and how they are physically implemented. For example, addition can be defined by a set of axioms irrespective of how it’s carried out; numbers can be expressed in different ways (e.g., Roman and Arabic) and added using different algorithms; and these can be implemented using an abacus, a pocket calculator, or even, very inefficiently, in your head. Learning is a prime
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