We all have things that we want for ourselves: traits, skills, experiences — just look at 43things.com — and yet most of us fall short of these goals. Why? Thinking about this today, I discovered that the reason I’m not doing certain things I’d like to do — buy property, get regular exercise, learn a new programming language, etc. — is due to my being stuck in certain local extrema — I’m living in a cheap place that is good enough and close to BART, my bike is in Santa Barbara and I walk a bit every day, and I’ve gotten really good at Ruby.

To envision what I’m talking about, think about a surface with some hills and valleys. Then imagine dropping a ball on that surface. If you do it enough, it’ll settle in different spots. These spots are called minima, and the lowest one is the absolute minimum. All others are local minima. To envision local and absolute maxima, imagine Mount Everest (the absolute maximum) and all the other mountains surrounding it (local maxima).

The trick is determining whether these things are local or absolute extrema. Whether buying or renting is the absolute extremum is yet to be determined, but my semi-unhealthy state vs. regular exercise is more clear. If you think about the example with the ball, it won’t move out of its spot without some sort of disturbance, and even so small disturbances won’t do it. You really need to shake things up to get it out of its current position. Interestingly, this is the same method used by simulated annealing to solve constraint-satisfaction problems.

So what lessons can we take from the world of math into the world of the real? If we’re to take it literally, it tells us that we need to devise ways to knock ourselves out of local minima, try new ones, and go back if the new situation is much worse than the old. This threshold of tolerance for worse situations should decrease as time goes on, and so we should be led to expect that, by using this approach, we’ll spend a fair amount of time trying to find the absolute minimum. Keep in mind that, like with math, simulated annealing isn’t guaranteed to find the absolute minimum.

The other approach is to use logic to try to solve the problem. This approach is often used with things that are expensive (either money, time, or both) to try, and so do not lend themselves to simulated annealing. An example might be the process of buying a car. As much as we might like to, we can’t just buy a car, try it out for a while, then return if if it’s not as good as our old one.

What other things keep you from becoming the person you’d like to be?