When I took a creative writing class at UCSD many years ago, one fellow student made a claim that the behavior of a certain character was unbelievable because that's not how girls think. Someone else suggested that whatever you think are the limits of human behavior, there's almost always someone that has gone beyond that limit. The more I read, the more I recognize how individual we all are. Among the myriad skills that a person can have, there are combinations of skill, and there are tendencies to use certain skills in certain situations. Given these variables, there is a tremendous number of possible ways for a person to be.

For example, how much of a positive attitude do you have? How curious are you being? Are you a good listener? Do you teach well? How patient are you with children? With adults? How viciously would you fight if someone were pulling your hair? Of course, the answers to these questions change over time.

Each of us has an idea of the range of different ways people can be. In mathematical terms, let's think of each person's "way of being" at this instant as a point in a box. Take three measures of behavior or personality, like...
  1. How likely it is that your behavior toward others will produce an outcome favorable to yourself.
  2. How much of a daylog you will read when it starts meandering into math.
  3. What is the relative importance of ideas you get from other noders compared with those you get from friends and coworkers?
These measurements are not well enough defined to actualize, but if we pretend that we filled in enough detail, we can imagine that we could start collecting measurements under highly controlled circumstances. We would get three numbers for each of us. If we use those three numbers as spatial coordinates, we would expect to see similar people represent points that are near each other. If we take the measurements periodically, we'd expect to see that the points for each of us move around, delineating a volume, like a balloon with a funny shape. Suppose we were able to collect these measurements for everyone and we looked at how the balloons intersect with each other and who has large balloons and whose balloons extend out toward the edge of the box.

Manic-depressives would likely have large balloons, whereas conservative old ladies would probably have small ones. But if we wait long enough and allow our subjects to get themselves into extreme situations, we might see people take remarkable excursions outside of the balloons in which we usually find them. Perhaps you are now wondering, what is the point of all this silly mapping of mathematics to human behavior?

I think if you pick interesting measurements and you think about the kinds of people that would occupy balloons that are small or large or squished up against the side of the box, you can get a good feel for all the different kinds of people there are, and how amazing we are. It's a fun thing for a geek like me to think about, but I have drawn a helpful conslusion from it as well: The kind of realizations that change our lives for the better often come from being very near to the edge of our balloons. Explore your limits, and help others explore theirs. Also, consider the likelihood that the balloons of people you know may be much larger that you think. Coming up with interesting measurements of behavior or personality can make these mathematical musings very enlightening.