Each of these dimensions tells us something about how the social units that are parts of a society relate to each other and to units outside the society. We might think of the basic social units --individual people -- as social atoms which combine in a variety of specific ways into compound social units -- households, families, kin-groups, villages, districts, regions, etc. Societies are just collection of such units that interact strongly with each other and weakly (if at all) with other units. Just how one makes this notion of interactiont more precise will be dealt with below.
Social units “do things” like produce maize, consume pottery, go to war, etc.. We might think of the things that social units might do as comprising a set of activities. All the things that social units might do (within the bounds of available technology) are on this list. But, any given social unit need only do a few things on the list.
With this picture, we can understand the social systems vocabulary in the following way.
At least two interesting types of complexity may be distinguished horizontal complexity and vertical complexity. To make this distinction, we need to talk about a part of relation among social units.
Clearly, from the above examples, some social units are part of other social units. Note that some social units, a household, might be a part of other social units, a clan and a village. But, the clan and village need not stand in the part ofpart of relation is a partial ordering of the set of social units comprising a society.
Using the part of relation one can define levels of social units. Roughly, two social units are at the same level if all the “chains “ of the part of relation connecting them with atomic units are the same length. The idea is that villages will turn out to be social units of the same level (level two) because households are part of and individual people (social atoms) are part of households. We can then group all the social units at the same level with a given unit into a level. And, in fact, the set of levels will divides up the set of social units into mutually exclusive and jointly exhaustive sets. (This is because, assuming we take care in defining it, the same level relation will be what the mathematicians call an ‘equivalence relation’.) Now horizontal complexity is a measure of the extent to which social units in the same level engage in different activities. For example, assuming that there is township-level of social unit just above the village-level. Villages are part of townships (as here conceived). A situation in which all townships (located in a central town) had markets and temples would exhibit less horizontal complexity than a situation in which some towns had only markets , others had only temples and still other had both markets and temples.
Similarly, vertical complexity is a measure of the extent to which social units at different levels engage in different activities. For example, a situation in which both townships and villages had temples would exhibit less vertical complexity than a situation in which villages lacked temples, but townships had them.
The concept of horizontal complexity may be used to capture at least part of the concepts of social structure and social status in the social institutional vocabulary. At least part of what is involve in difference in social status among households, families and kin-groups is simply that they do different
Most (quite possibly all) interesting way that social units can interact involve moving something from one unit to another. Among the things that might flow from one social unit to another constituting an interesting interaction are:
It is not implausible to think that every interesting thing that moves among social units can be reduced to an energy equivalent. Maize can be converted into food calories; people can be persuaded to convert food energy into work in maize fields (or simply eaten straightway); pieces of obsidian embody the energy expended to produce and transport them. A view of this sort has been elaborated in some detail in Adams, ‘75 and ‘81,
Reducing all interesting interactions to information flow requires us to agree that the only interesting thing about societies is how the activities of one social unit influence the activities of another. More explicitly, one might think of social units having strategies of the form:
Do activity A when U1 does A1, U2 does A2....Un does An.Thus the flow information of the sort needed to trigger such strategies would be important to understanding influence among social units. It’s not too far fetched to think that this information is sometimes (frequently, always ?) embodied in the flow of physical objects like baskets of maize.
A little reflection here suggest that one might even be able to arrive at a quantitative concept of interaction in terms of strategies alone, without utilizing the concept of information at all. All we need to look at is how many activities of a unit are influenced/determined by the activities of another unit.
