Scale

In characterising the three basic eigenmodes, an important factor was the size of the community. I argued, for instance, that a small group of hunter-gatherers could not support the social complexity of a large city.

However, it can be difficult to define the size of the community.

• Although the San split into groups of about a dozen adults most of the time, they come together in bands of fifty or more for festivals or rabbit drives.
• A city like New York not only belongs to a larger nation, but need not have clear-cut boundaries and includes people who commute in and out during the day.

The important issue is people's ability to interact. The point about the city is that people come into contact with perhaps thousands of people over the course of a year, so that they can access all sorts of specialist services and find enough customers for their own specialist skills.

This is captured by the concept of scale:

The scale of a society is the number of distinct persons with whom a member of that society interacts in a given time.

The advantage of this definition is that we do not need to worry about how to draw the boundaries of the society.

Some theories (e.g. A W Johnson and T Earle The evolution of human societies) talk in terms of population density. However, it is not just the number of people per square mile that is important, but their ability to interact with each other, and this can be affected by transport and communications improvements, which bring people into contact without them necessarily living closer together physically.

The scale concept properly captures the importance of the community's size and density along with people's ability to move and communicate.

Emil Durkheim called this dynamic density.

'Interaction' should be interpreted in a very general sense. It does not just mean interaction with people we know.

• A fleeting encounter with someone serving in a shop is an interaction.
• Someone reading a plumber's advertisement in the yellow pages can be an interaction, since there is a flow of information from the plumber to the reader.

A society's scale is the key to its eigenmode (figures in brackets below represent scale in terms of the number of distinct persons encountered per year).

• Low scale (10s of persons) -> family mode
• Medium scale (100s of persons) -> village mode
• High scale (1000s of persons) -> city mode

Although scale is closely connected with eigenmode, it would be wrong to say the society's scale causes its eigenmode. Scale is an aspect of the eigenmode. We should not think of it as coming first, even though we might want to. It is not productive to think in terms of cause-and-effect but instead we should think in terms of interdependency.

With the definition of scale given above, the comparison between two societies depends on the timescale used.

• If we take scale as the number of distinct persons encountered per day, then it might be around 10 for both a hunter-gatherer and a New Yorker, but if we take scale as the number of distinct persons encountered per year, then it might still be around 10 for the hunter-gatherer but in the 1000s or even more for the New Yorker. In other words, if we use a day as the time interval, the scales of the two societies seem similar, but if we use a year they seem very different.

Although we could adopt say a year, which gives a reasonably realistic result, as the standard time span, it would be preferable to have a measure of scale that does not depend on time span.

Let Z_ij(t) be the amount of time that the i^th member of the society spends interacting with the j^th member of the society during a period of time of length t. Define z_ij by

z_ij represents the proportion of time, taken over the long term, for which this member of the society interacts with the j^th other member. The society's scale from the perspective of this member is then given by

The society's overall scale, S, is the mean of the scales from the perspective of each member. If N is the number of persons in the society:

With this measure, some possible scale calculations are as follows (these are simplified illustrations and are not meant to be fully realistic):

Family of 10 persons; people divide their time equally between the other members.	Scale = 1
Village of 1000 persons; people spend much time within a close family group of 10 members and encounter other members of the village one tenth as often.	Scale = 2.9
City of 100,000 persons; people spend much time within a close family group of 10 members, encounter a wider circle of 1000 colleagues one tenth as often, and encounter the remaining citizens one thousandth as often.	Scale = 4.2

Calculations in the above table use base-10 logarithms. This is not important; using other bases will change the absolute but not the relative values.