## Kurt Godel and John Holland

The first clue came from the work of Kurt Godel, a Czech mathematician who in 1930 described how statements and rules could be represented by numbers. Together with the rules of logic, Godel showed how it was possible to represent any complex, rule based processing system solely by numbers. It was this work that had inspired Alan Turing to build the Turing machine: the basic mechanism underlying the design of all modern day computers.

Godel's work also described how tangible as well as intangible entities could be represented as numbers, allowing any kind of tangible or intangible system to be modeled in mathematical form. The inference to me was that this could also include neural mechanisms and the esoteric and intangible phenomena we describe as emotions.

The second clue came from the work of John Holland, a computer scientist, who in the 1980's discovered the mathematical mechanism that causes biological organisms to evolve. He called his mathematical device a genetic algorithm. The essence of this deceptively simple mathematical mechanism is that it provides a fast way of optimizing any system comprised of a large number of dependent variables: a task impossibly difficult for conventional mathematics.

Unbelievably, the principle of genetic algorithms is that you start off by making wild guesses at what the variables of a system should be and then breed different versions of the system to see which work best. At regular intervals (generations) the systems that work best are selected to "breed", whereby new systems are created using various mixes of the variable values.

It is similar to the way biological organisms evolve: survival of the fittest and the fittest get to pass their genes into the next generation. In the case of John Holland's genetic algorithms it is numbers that survive to reproduce, but, thanks to Godel's theories, these numbers can represent any kind of entity both tangible and intangible from physical assemblies to rules and statements.

There is no question that this technique is effective because variations of genetic algorithms are now used extensively in the design of all manner of complex systems.