## Tuesday, April 24, 2007

### Theoretical Stress

In a simulated population of 1,000 people whose “comfort zones” are distributed randomly between values of 1 and 5, starting from “positions” also randomly distributed in that range, each member will experience a “stress” defined as the distance between where they are and where they want to be (their comfort zone). This stress will motivate them to move closer to their comfort zones, but they will be restricted by two variables: “power” or the fraction of the distance they can practically cover in their lifetimes; and “intelligence,” their perceptions of the directions and distances to their targets. Power and intelligence determine the distances (and directions) that people travel.

In this theoretical model, each member of the population has a random value of power and intelligence that lies between specified minimum and maximum values. By varying the ranges of power and intelligence, we can see what effect they have on the distribution of stress throughout the population at the end of an interval of time (the lifetime of a person).

For the full range of power and intelligence (zero to one for power, and minus one to positive one for intelligence), the average final stress is 1.3 and the standard deviation (a measure of the width of the “bell curve”) is 1.0. There is 47 percent of the population within 1.0 unit of the average, and 53 percent of the population with stress from 1.0 to 4.0. For no range of power or intelligence (both equal zero), the average stress is still about 1.3, the standard deviation is 0.9, and the fraction of stressed people (those with stress of at least 1.0) increases to 56 percent.

Restricting intelligence to positive values, from zero to one (people work toward reaching their comfort zones, instead of moving away from them) reduces the average stress of the population from 1.3 to 1.0; and reduces the fraction of stressed people from 53 to 42 percent. If, after this, the minimum power is adjusted upward, the average stress decreases linearly with power to a value of two-thirds (about 0.7) at total power (power equals one). Note that varying power in this way is mathematically equivalent to keeping the range of power between zero and one, and varying the minimum intelligence.

If, as it appears, the violent crime rate is proportional to the fraction of stressed people (divide the number of such people in a population of 100,000 by the number of years in a lifetime, currently about 77), then this theoretical exercise implies that to reduce crime we should decrease the overall stress on the population by increasing people’s abilities and training them to perceive the world accurately.