Scientific Understanding of Consciousness
Consciousness as an Emergent Property of Thalamocortical Activity

Recursive and Combinatorial Operations



Nature 460, 190-196 (9 July 2009)

Marc D. Hauser

Departments of Psychology, Human Evolutionary Biology, and Organismic & Evolutionary Biology, Harvard University, Cambridge, Massachusetts 02138, USA.

Recursive and Combinatorial Operations

Recursive and combinatorial operations provide the only known mechanisms for generating an almost limitless variety of meaningful expressions, whether mathematical, linguistic, musical or moral. Recursion is an iterative operation, in which a rule is called up repeatedly to create new expressions, be they embedded phrases within a sentence, new musical scores with repeating themes, or tools within tools. Each expression has a unique interpretation or function depending on the arrangement of the elements. By contrast, combinatorial operations allow discrete elements to be unified and ordered, thus creating new ideas, which could be expressed as novel words or novel musical forms.

Recursive and combinatorial operations are ubiquitous in human mental life, operating in language, music, morality, technology and mathematics. A simple example, in the case of language, is creating a list, which has the recursive rule AND X+, where X is the name of a person. Thus, one list could be Sally AND Bill AND Sam AND Jane, and so on. This example, which every child immediately understands, illustrates the almost limitless capacity of humans to create linguistic expressions (that is, the property of discrete infinity), as well as the fact that the child's starting state is not blank but prepared with a competence that readily and implicitly understands recursive operations. In the example above, there is simply no experience that informs the child about the iterative and limitless power of list building.



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