Part 1: Chapter 1
Genes as parameters
A Hilbert Space can be defined such that its dimensions (parameters) are genes. These dimensions could include every possible gene from every gene pool on the planet.
In this space there would be a genetic description of every creature in existence - each at a position where the lines of their genes intersect. For example, a worm would be at the place where a worm's gene lines crossed. A fruit fly would be at the position where a fruit fly's gene lines crossed. A human would be at a place where a human's gene lines crossed.
You can imagine moving around in this space and coming across all kinds of creatures, not only those that exist today, but creatures that are now extinct and even creatures that will exist in the future as a result of the evolutionary process. You will also come across every kind of hybrid. It is this ability of Hilbert space to include every possibility - past present and future - that makes it such a valuable conceptual model.
Note: Evolutionary progress can be visualized as an organism moving through this space - moving progessively to new positions where it acquires an improved genetic make-up. Nature has provided organisms with an appropriate strategy to be able to navigate through this space in a positive direction.
The full scope of the variety that can be described in a genetic Hilbert space can be visualized more clearly by limiting the Hilbert Space to the dimensions of the genes from a single gene pool - say that of the human gene pool. This space would describe all possible human genetic variation. It would describe tall people, short people, superior athletes, superior brains - in fact any variation of humans you can think of including those with genetic defects.
The obvious limitation of this conceptual model is that the number of viable gene combinations present in this space will be infinitesimally small compared to the total number of possible gene combinations . Trying to find an optimum gene combination in this space would be like trying to find a grain of sand with of a particular intricate shape in the Sahara desert.
As impossible at it seems, Nature has found a way to navigate around this genetic space to produce viable creatures. It is by understanding this strategy that can lead to an explanation as to how the human brain is able to locate items in memory and process these through the selection and coordination of appropriate neural functions.