Strategies in Hilbert space

You can always be sure that you have a winning system if it is used in biological systems. After all, nature has had three or four billion years start on us. This system of objects randomly spreading around is the way our complement of genes have sorted themselves out. These are the dimensions of our human form and as this arrangement has moved around in Hilbert space they have been progressively selected as our organisms move closer and closer towards some perfect optimisation for survival and reproduction.

We don't need to go into the intricacies of molecular biology to appreciate how nature performs its optimisation tricks, all we need be aware of is that it has managed to optimise these genes and our human form without the need for any forward planning. It manages to do this blindly, just by selecting for best results.

Instead of an observer, nature simply uses a rule to decide which of its marbles is nearest to the hole. That rules is: "Those organisms that manage to reproduce are counted as being nearest to the hole". In this way, organisms and the genes that describe them, move progressively towards a state optimal for reproduction.

This then is the key to controlling the direction of a bottom up design process. Trial and error and selecting for the best that perform optimally according to any given rule or rules. In the case of organic evolution, the fundamental rule is simply to survive, but, this rule can easily be qualified to control the direction of the evolutionary process. This is readily apparent when we observe the human qualifications imposed on this rule when we breed domestic pets, farm animals, agricultural products etc.

Humans impose conditional rules on the reproduction to steer evolutionary progress along lines convenient for human purposes. This is why we have cute and friendly dogs that evolved from fierce wolves; it's why we have cows with huge malformed udders; it's why we have fields of uniformly sized corn with gigantic seeds. Humans have just added an extra rule to the selection processes that changes the positions of animals or plants in Hilbert space.

All this would be of only academic interest if it wasn't for the extensive flexibility of Hilbert space to be able to work with abstract dimensions. For example, a strategy can be thought of as a set of rules: rules we can define and put into a list. These can be regarded as the dimensions of a strategy.

If a strategy is placed into Hilbert space we can think of the rules changing as the strategy is moved around in Hilbert space. Or, conversely, by changing the rules we can change the position of the strategy in Hilbert space and because the rules are changing, the strategy works more or less efficiently according to where it is in Hilbert space.

As is done with domesticated pets, farm animals and agricultural product, we can move the strategy around in Hilbert space by means of an evolutionary process that selects appropriate rules according to the qualifications placed upon the conditions of reproduction. This is elegantly demonstrated in the CD-ROM "How God Makes God" by giving software objects behaviors that are activated by simulated emotions.

The objects are placed into an artificial competitive environment where only particular behaviors will be successful. By arranging these objects to breed and selecting for the objects that are most successful in the competitions the simulated emotions gradually evolve to cause the objects to act optimally for success in the competitive environment.

This in itself is remarkable, but, even more remarkable was the fact that acting in groups the individual objects evolved emotions that caused them to behave in ways that were less than optimal for the individual but more appropriate for the success of a group as. In other words, altruistic behavior emerged out of the blind evolution of objects competing with each other in a competitive environment. Emotions evolved that maintained the efficiency of a group, rather than individual competitive performance.