Part 1: Chapter 1
People as parameters
A space with infinite dimensions or parameters is far too complex to be imagined and does not provide a useful conceptual framework. But, a Hilbert space can be defined in terms of any set of dimensions or parameters you care to choose. For example, there is no reason why you cannot have a Hilbert space where the dimensions are people.
Consider a Hilbert space where the dimensions are every person on this planet. Think of the different ways these dimension lines can intersect. Somewhere in this space there will be a place where every person who lives in London will be listed. Another place would list everyone who lives in New York. There would be a place that lists every one of your friends. There would be a place that listed everyone who works for Microsoft, there would be a place that listed the top fifty poker players; a place that listed the fifty best computer programmers; etc. Every possible grouping you can think of will be listed at some location in this space.
Note: A 'list' will appear at the location in the people space where the dimension lines - representing each person in the list - intersect.
This theoretical people space will also contain listings of combinations of people who are grouped according to intangible concepts. For instance, the space would separate out groups of people according to how effectively they could collaborate together. It would have lists of people who would make a perfect team to carry out a particular task or complete a particular project. It would contain a list of people who would make the perfect friends for you to be associated with.
This space would also match together individuals. Somewhere is this space would be your ideal business partner. Somewhere else would be your perfect marriage partner. If you knew how to navigate this space, you might be able to find them.
Finding a particular individual match in a Hilbert space that includes everybody on the planet would, quite obviously, be an unrealistic proposition. However, additional dimensions (parameters) can be added to a Hilbert Space, to limit the search space to include only practical possibilities. For example, adding the dimension of "locality" could restrict the possible solutions to only those people who live or work in your local environment. Or, by adding the dimension of "Internet connected" would restrict the people in the search space to only those connected to the Internet.
A good example of a Hilbert Space is the three billion Web pages indexed by the search engine Google. This is an information space where the dimensions are key words or phrases.