Modelling Combinator Mathematicians as a Genetic Algorithm Deme Network

This experiment started as a model of a community of mathematicians, each one posting his recently discovered results to colleagues.

The simulation was implemented as a deme-based genetic algorithm, and consisted of an NxN grid with a mathematician at each node. Each mathematician maintained his own personal library of Combinator definitions (a particular type of mathematical function).

As the simulation proceeded, each mathematician would spend some of his time experimenting with creating new combinators, made from combinations of combinator that were already in his library (just S and K to start with); and some of his time sending combinator definitions, from his library, to a chosen colleague.

Each mathematician's experiments consisted of generating a compound combinator expression at random, and testing the resultant expression to see what it did when applied to an indefinitely long string of arguments. If the result was a messy expression, with combinators mixed up with arguments, the experiment was discarded; if, though, the result was an expression involving just the arguments, the new combinator was given an arbitrary, but unique name, and added to his library.

The aim of the simulation was to observe the way in which knowledge was acquired within the community, and to measure the rate at which structure built up spontaneously. On the other hand, the names for the new combinators were allocated automatically by the simulator, and did not form part of the investigation.

Interestingly, Steels of the Sony Computer Science Laboratory in Paris has investigated a complementary idea: modelling the way that new words are invented and adopted in a community (New Scientist, 15-Oct-2005, p16). In effect, his model concentrates on the adoption of the names, while the concepts to which they are applied are not part of the study. It would be interesting, perhaps, to consider how the two projects might be combined – though, it should be noted that he has already investigated such combinations in the real world (NS, 30-Mar-2002, p24).