Part 1: Chapter 1
Functions in Hilbert space
The dimensions of a Hilbert Space can also be functions. This can be visualized by again using the credit card example. This, as we have seen, provides a number space that contains 1,200,000,000 different numbers.
A dimension of this Hilbert space can be added that will create another set of numbers that are the sum of the digits of every number in the space. Similarly, a dimension can be added that creates a set of numbers that are the multiplication of the digits of every number in the space.
Once you get the idea, you can see how all kinds of functions can be added, as new dimensions, to create new sets of numbers. In this way, the Hilbert space can be as complicated or as simple as you care to design it.
If we now apply this conceptual model to represent the genes in a biological cell, we can visualize a Hilbert space as consisting of a space that contains every possible variation of a biological cell - in terms of which genes are turned on and which genes are turned off.
In among the countless billions of possible combinations, there will be a cell that is a bone cell, a muscle cell, a neuron, etc. In this space there will be cells that provide every kind of cell that is present in the human body.
Now think of functions that add new sets of cell combinations, where the performance of each gene in the cells is modified (i.e., increased or decreased in activity). You'll then have a Hilbert space that contains all the components of the dynamic system that make up a living human being.
Of course, the number of locations in this space is beyond comprehension. Clearly, no computer could ever be designed to sort through these countless combinations to select those that make up a human being. But, this is what Nature has managed to do - using a fairly simple strategy.