## Wednesday, September 24, 2008

### Super-groups

In Maximum Community Size, I derived the largest size of a population of people who can consider themselves part of a community. I later defined a “world” as a collection of people who can usefully interact with each other (such as moving themselves or resources) over a year. These ideas led to my discovery of the first law of consumption; which, combined with the other two laws, can now be used to better describe such communities.

While a few people in any population will be able to process information at the maximum seven units per second, most people will process information close to the average of 5.5 units per second. At this rate, if another person represented a unit of information, someone could be aware of over 7 million people per year if attention was paid for just one hour per day; and being aware for every hour of every day would result in awareness of 17 million people.

When dealing with large numbers of things, most of us tend to group them. If instead of paying attention to people, we were only aware of groups (again, as units of information) and an average of 5.5 people constituted one group, then someone could be aware of more than 7 million groups over a year at one hour per day. Such a “super-group” would represent a total population of nearly 40 million people. Each additional hour per day devoted to this activity would add another super-group to the total population that the person was tracking as part of the “community.” If every hour of every day was spent, the maximum community size would be 954 million (or almost one billion) people.

Keeping in mind that this discussion is based entirely on theoretical possibilities in order to explore limits, let’s now see what the laws of consumption have to say about all of this.

It is reasonable to assume, based on historical data, that per capita consumption was fairly constant until the world’s population exceeded 300 million people; a single isolated super-group could therefore expect to live to the minimum life expectancy of 40 years. A population size of 300 million corresponds to between 7 and 8 super-groups, corresponding to (potentially) as many hours spent by each member with the others; this is interestingly close to one-third of a day, or a modern “work day.” If an average person needs 8 hours for sleep and 8 hours for personal activity (with limited exposure to others), 8 hours for social interaction may represent a natural limit to sustainable world population size – 318 million people. Indeed, if the population remained constant at this value, then the amount of total resources I’ve estimated for 0 A.D. would have lasted roughly 48,000 years if it was totally non-renewable.

In a world of fixed resources, the first and third laws of consumption strongly suggest that humanity has traded species longevity and time spent not dealing with other people for population size and longer individual life expectancy. In 1829, the world’s population exceeded a full day of (24) super-groups; at that time, I project that life expectancy was 61 years and there were 1,760 years of resources remaining if the population had not grown. There are now nearly 174 super-groups with a life expectancy of 69 years and 68 years of resources; the United States, by contrast, harbors more than 7 of those super-groups which are living much better than the average by effectively taking more resources from others.