Ergodicity

I have only recently been introduced to the idea of probabilistic thinking, and I like what I see. Probabilistic thinking refers to a way of seeing the world through the lens of statistics and probability theory. My introduction to this has come from Nassim Nicholas Taleb's Fooled by Randomness and Michael Lewis' Moneyball. I suppose the ideas of probabilistic thinking are not new to me. I studied statistics and econometrics while in college, but Taleb and Lewis have made the implications and importance of probabilistic thinking much more clear to me.

What appeals to me about probabilistic thinking is that it devalues actual outcomes in favor of expected outcomes. Actual outcomes are very often deceptive and probabilistic thinking alerts us to this fact and cautions us against drawing conclusions from individual events. It seems like a simple and very obvious insight, but I wonder how many people actually practice probabilistic thinking because it is so inherently abstract.

We are trained to treat results as being important. It doesn't matter if a team has a 0.6 probability of winning a game. What matters is if the team manages to notch a tally in the win column. We are trained to judge things by results rather than by processes. A lot of people and a lot of companies will tell you that they are "results-oriented." But when was the last time that you heard someone tell you that he/she is "process-oriented?" Part of the problem is that processes are much harder to observe.

In a recent job interview, I was asked the question, "What has been one of the biggest decisions you have made in your life? How did you arrive at your decision?" My instinct (and I think the instinct of most people) is to go through an inventory of decisions I've had to make in my life and think about which has been most important, and then to think about the process through which I arrived at the decision.

But you see how that is sequenced? Precedence is given to the decision...you think about the decision first, and then you think about the process. The instinct is to think about our lives as a series of big and small, but all discrete, decisions.

And this, finally, is where my discussion comes to the idea of ergodicity. As I understand from Taleb, ergodicity is the idea that a very long sample path will show its long-term properties. I am sure that there is a more technically and mathematically rigorous definition, but I like the elegance of the idea. Despite short-term volatility, things eventually settle according to their long-term properties. A very Aristotelian idea, I suppose. Like telos.

But if we take ergodicity seriously, then how important are individual decisions at all? How big of a decision was it for me to move to San Francisco as opposed to Philadelphia or New York City? The generator of this decision as well as of past and future decisions remains the same. Eventually, my life will settle into its long-term properties. So the difficult but important thing is to examine those long-term properties.

What started me on this train of thought was a passage from Philip Zimbardo's book, The Time Paradox:

Compared to people from other cultures, Americans today seem more obsessed with personal happiness and have been criticized for having become a feel-good rather than a do-good culture. We are obsessed with looking good, with having a great tan, tight buns, and blemish-free skin. Yet what is important in life is more than skin-deep. It is a spiritual inner happiness that does not diminish over time. (256-257)

Thought about in this way, and viewed through probabilistic thinking, personal happiness over a short time horizon is not all that important. The important question to ask, strangely enough, ought to be: How probabilistically happy are you?

Expected outcome over actual outcome. A long, long time horizon over a short time horizon.