Universal laws for hierarchical systems

Organisms are hierarchically organized, both structurally and behaviorally, where one level is defined to be above another level if the objects from the latter are combined together to make objects of the former level. I say that such a pair of levels is a combinatorial system. To understand organisms will require appreciating the relationships between all pairs of adjacent hierarchical levels in the towers of hierarchical levels found in organisms. In particular, for any pair of adjacent hierarchical levels, a key question is, (1) What rules govern how objects from the lower level (the components) combine to make objects at the higher level (the expressions)? For example, what are the rules dictating how bird syllables are combined to make songs? Or, what are the rules governing how cells combine to instantiate higher level organism functions? Another question is, (2) Are there universal laws governing hierarchical complexity in systems of the same type, in the sense that two combinatorial systems of the same type will share the same rules? For example, if one bird can sing twice as many songs (expressions) as another bird, what can we say, if anything, about how many syllable types (component types) they have? If there are universal laws of hierarchical complexity for bird vocalization—a “universal grammar”—then it may be possible to say something; if there are no universal laws, it may not. A more general kind of question is, (3) What kinds of such “rules of grammar” for combinatorial systems are found in nature, and why do systems have the kinds of rules they have? This latter question is not concerned with the particular details of the pair of levels—e.g., whether it is structural or behavioral—but on the underlying principles governing adjacent hierarchical levels. The main task of this research is to ask and begin to answer these three questions.