A biological way to think about information, systems, people and collaboration
Copying Nature's strategy
Conventional thinking might see the idea of a Hilbert space that contains every possible grouping of people as amusing, but of little practical value because it doesn't exist in reality. What's the use of knowing all these groups exist in theory if you could never find them in the real world?
But, this situation is no different from the situation faced by all biological systems. They have a Hilbert space where the dimensions are genes. There are hundreds of thousands of different genes, and their Hilbert space will contain every possible combination of these genes so that somewhere in the space there would be a genetic blueprint for every living organism that exists, has existed or will exist in the future.
Try to imagine the impossibly large number of different gene combinations that this space will contain, each having a unique value for the purposes of survival and reproduction. Yet, Nature is able to move around this space to find just the right gene combinations that make up all the different life forms that exist on this planet.
Remember here that biological systems are not designed using planning, logic or calculation. They evolve in a way that is described perfectly by this concept of searching through a space of endless possibilities to find optimum design solutions.
It seems impossible to explain, but John Holland worked out how such a search is conducted when he came up with the concept of the Genetic Algorithm. Biological organisms try out different combinations of genes. The most successful combinations are selected and the genes remixed to create a new set of organisms. This procedure is continuously repeated with the organisms becoming more and more efficient.
There is no reason why we shouldn't use a similar strategy to design information systems and create useful groupings of people for the purpose of collaboration.
Nature's short cut
There is one other important consideration. How quickly can an optimum solution be found?
Genetic Algorithms have proved to be successful but only in situations where there are a limited number of identifiable parameters. What about the situations where the number of parameters is impossibly large, or unknown - such as with a large population of people or a large pool of genes? The search area would be so great that the time needed to find optimum solutions could stretch into infinity.
Nature has solved for this problem by taking advantage of the fact that complex systems settle into a finite number of steady states.
Steady states are where a system keeps acting in the same predictably way and is relatively unaffected by small changes. Most businesses operate in a steady state and only lose this steadiness if there is a substantial change to its organization, its market or the competitive situation. Then it will perform unpredictably, until it adjusts to the new situation and settles down into a new steady state.
Biological species maintain steady states in terms of their physiology. This remains constant as long as there is no evolutionary pressure for change, but if the climate changes or new competition emerges, the stable form will evolve into different stable forms that are more suited for survival in the changed conditions.
Each steady state will have a separate place in a Hilbert space with its own set of parameters that describes it. So, instead of exploring every possible combination of parameters, Nature can cut down the work needed to find optimum solutions by restricting the search to only the parameters that give rise to steady states.
This can be likened to targeted advertising, whereby instead of advertising to everyone in a population, the advertising is concentrated on a small list of people where there is some reason to believe that they would be particularly interested in the product being advertised.
This can be visualized by seeing Hilbert space as a landscape full of pits, where each pit is under a set of parameters that give rise to a system that is operating in a steady state - the depth of the pit indicating how efficiently the system is working in that particular state. You can then think of moving progressively towards the most efficient steady state by jumping into progressively deeper pits.
The strategy then is to create a situation whereby a system can be arranged to jump between these pits (steady states), but always moving to a better steady state - so that its performance constantly improves.
Nature does this by making use of the phenomenon of Stigmergy to cause the "jumps" and Evolution to control the direction of the jumps.