THE ARCHITECTURE OF COMPLEXITY

Herbert A. Simon, whose essay on complexity is the most referenced work in Hierarchy Theory, is a psychologist who is most noted for his work on decision theory and on organization theory, Hierarchy Theory, he tells us, is a way of looking at "the complexity of a system without specifying the content of that complexity." In dealing with complex systems he uses the term "hierarchy" in a more general sense than usual. He likens it to a set of special Chinese boxes, The Chinese boxes called "hierarchies" are a variant of that pattern. Opening any given box discloses not just one new box within, but a whole small set of boxes; and opening any of those component boxes discloses a new set in turn. While the ordinary set of Chinese boxes is a sequence, or complete ordering, of the component boxes, a hierarchy is a partial ordering--specifically, a tree, Examples of such hierarchies, he noted, are chemical substances which when analyzed disclose molecules, which dis- close atoms, or living organisms to tissues to organs to cells to macromolecules to organic compounds and thence back to the first hierarchy. Why then, do we find hierarchies so predominant in nature? Simon explained this with a parable of two watch makers. There once was two watchmakers, named Hora and Tempus, who manufactured very fine watches. Both of them were highly regarded, and the phones in their workshops rang frequently. New customers were constantly calling them. Howúever, Hora prospered while Tempus became poorer and poorer and finally lost his shop. What was the reason? The watches the men made consisted of about 1000 parts each. Tempus had so constructed his that if he had one partially assembled and had to put it down-- to answer the phone, say--it immediately fell to pieces and had to be reassembled from the elements. The better the customers liked his watches the more they phoned him and the more difficult it became for him to find enough uninterrupted time to finish a watch, The watches Hora handled were no less complex than those of Tempus, but he had designed them so that he could put together sub-assemblies of about ten elements each. Ten of these subassemblies, again, could be put together into a larger subassembly and a system of ten of the latter constituted the whole watch. Hence, when Hora had to put down a partly assembled watch in order to answer the phone, he lost only a small part of his work, and he assembled his watches in only a fraction of the man-hours it took Tempus. The result is that hierarchies will evolve much more rapidly from elementary constituents than will non-hierarchic systems with the same number of elements. Important to Simon's thesis is the concept he called " near-decomposability ." Put as simply as possible, it is the degree to which the behavior of a system at any one level is free of` the interactions on a lower level and the degree which its interactions are irrelevant to the higher levels of the system, The partial ordering of the hierarchy mentioned before, he explains, is an example of loose vertical coupling. "Loose horizontal coupling" is what Von Bertalanffy calls "equifinality", often called "functional equivalence", or systems that are different but lead to the same result. "The flexibility of coupling among sub-systems can be further enhanced by limiting the variety of different kinds of components that are incorporated in the larger systems". When the numerous component elements (called tokens) all belong to a small number of basic types, we call this set of types an "alphabet". The transactions of an organism with its environment are handled with an alphabet of amino acids. "An organism will have access to a supply of components if it maintains itself in a broth of potential replacement parts. It would be hard-pressed--at least without cannibalism--to find such a broth of appropriate proteins." Finally, he said, "Scientific knowledge is organized in levels, not because reduction in principle is impossible, but because nature is organized in levels, and the pattern at each level is most clearly discerned by abstracting from the details of the levels far below. (The pattern of a half- tone does not become clearer when we magnify it so that the individual spots of ink become visible.) And nature is organized in levels because hierarchic structures--systems of Chinese boxes--provide the most viable form for any system of even moderate complexity."

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