If the smallest community has historically consisted of between 12 and 36 members, is there a limit to the maximum size of a community?

One factor that might limit the maximum size is possible awareness by each member of the community of every other member of the community. Awareness depends on two variables: speed of communication and speed of information processing by each individual. The minimum speed of communication would be one message in a useful interval of time, and the message would need to be comprehensible. The maximum number of people that could be sensed by a member, subject to these constraints, would therefore be the maximum population of the community.

For a useful interval, one year seems like a reasonable guess. Natural processes and activities that humans have mostly relied on for survival tend to cycle over this period. For example, the seasons affect agriculture, and businesses key their activities on transactions that occur over the course of a fiscal year. One year is also the amount of time a human could travel a distance equal to the world’s circumference at speeds attainable on foot.

We know from psychology that people can comprehend between four and seven things per second. If those “things” were pieces of information representing other people, then a person could be aware of no more than seven people per second (the "awareness rate"). Over the course of a year, the maximum number of people in a community is therefore seven times the number of seconds that an average member can receive a message, and the average is 5.5.

If a person is aware of 5.5 groups (of 5.5 people) per second for one hour per day, then over the course of a year the person will be aware of a maximum of about 40 million people (a "super-group"). This represents the size of the person's community, which could grow to nearly one billion people (at 24 hours per day).

The minimum useful size for a group can be estimated in one of two ways.

The first assumes that a person is aware of one person per hour; over the course of a day this amounts to 24 people, which is close to the observed average for similar modern populations.

Another approach is to assume that a super-group has a population equal to the minimum group size raised to the 5.5 power (the small group is one member of a larger group consisting of the same number of members as people in a small group; this larger group is one member of another larger group with the same number of members, and so on, repeated 5.5 times); this also results in a small group size of approximately 24 individuals.

The following table summarizes estimates that include population ("Pop.") and consumption per capita ("CPC") using the combined population model and laws of consumption with the initial amount of resources that may have existed in 0 A.D. (in 2008, there is likely only 63% remaining). Life expectancy ("Lifespan") is given in years and generations ("L/gen"), where 1 generation = 21 years. Depletion time ("DepTime") is the time that the resources would be consumed if the population stayed constant, given in years and generations ("Dtg").

Note that as hours and population grow by a factor of 10, per capita consumption is also ten time larger, lifespan doubles, and depletion time decreases by 99 percent.

See also: Detailed Calculations (worksheet)

© Copyright 2008 Bradley Jarvis. All rights reserved.