## Saturday, October 20, 2007

### Power and the Peak

In an attempt to equate a typical population of people to an abstract, theoretical population, I endowed the abstract “people” with “intelligence” and “power” as tools for moving from an arbitrary starting position to an arbitrary preferred position (or “comfort zone”) with a range of allowed positions. Combining the possible values of intelligence and power into a single variable called “adjusted power” and recording the distances of the abstract people from their comfort zones over an arbitrary interval of time, I was able to define a mathematical function that related adjusted power to the average distance. I then identified a characteristic of the model population that was equivalent to “happiness” in a real population.

Applying this model to my consumption model, the point at which increasing world consumption corresponds to a peak in population occurs when the adjusted power reaches 50 percent, and the population declines to zero as adjusted power increases to 100 percent.

There are two possible scenarios for 50 percent adjusted power. In the first scenario, half of a population has an accurate sense of the direction they must “travel” to reach their comfort zone from their current “position,” while the other half thinks the direction is opposite from its true direction. In the second scenario, everyone knows the correct direction to go, but the maximum power (fraction of the required distance that can be traveled) is only 25 percent. In the first scenario, increasing adjusted power means making fewer people ignorant of the correct direction; while in the second scenario, it means increasing the average amount of power.