Excerpt
At the core of areas of study as diverse as cognitive psychology, artificial intelligence, economics, immunogenesis, genetics, and ecology, we encounter nonlinear systems that remain far from equilibrium throughout their history. In each case, the system can function (or continue to exist) only if it makes a continued adaptation to an environment that exhibits perpetual novelty. Traditional mathematics, with its reliance upon linearity, convergence, fixed points, and the like, seems to offer few tools for building a theory here. Yet, without theory, there is less chance of understanding these systems than there would be of understanding physical phenomena without the guidance of theoretical physics. What’s to be done?
Hierarchical Organization and Building Blocks
There are some hints. First, all such systems exhibit a hierarchical organization. In living systems, proteins combine to form organelles, which combine to form cell types, and so on, through organs, organisms, species, and ultimately ecologies. Economies involve individuals, departments, divisions, companies, economic sectors, and so on, until one reaches national, regional, and world economies. A similar story can be told for each of the areas cited.
These structural similarities are more than superficial. A closer look shows that the hierarchies are constructed on a “building block” principle: subsystems at each level of the hierarchy are constructed by combinations of small numbers of subsystems from the next lower level. Because even a small number of building blocks can be combined in a great variety of ways, there is a great space of subsystems to be tried, but the search is biased by the building blocks selected. At each level, there is a continued search for subsystems that will serve as suitable building blocks at the next level.
A still closer look shows that, in all cases, the search for building blocks is carried out by competition in a population of candidates. Moreover, there is a strong relation between the level in the hierarchy and the amount of time it takes for competitions to be resolved—ecologies work on a much longer timescale than proteins, and world economies change much more slowly than the departments in a company. More carefully, if we associate random variables with subsystem ratings (say, fitnesses), then the sampling rate decreases as the level of the subsystem increases. As we will see, this has profound effects upon the way in which the system moves through the space of possibilities.