Samantha has an interesting post. It reminds me of Gilda Radner:

“Some stories don’t have a clear beginning, middle, and end. Life is about not knowing, having to change, taking the moment and making the best of it, without knowing what’s going to happen next. Delicious Ambiguity.”

Gilda must be thinking about the relative importance of human actions and sheer luck in life. She argues that we cannot completely control our future,  but we can partially influence it by taking proper action now.

Now let’s try to make her idea more precise.

In current period t, I have a reward f_t(a_t, X_t) of happiness. a_t is the action I take in period t, X_t is a random element that summarize the external, environmental impact on me, say luck; X_t follows probability distribution F_t(X_t|h_t), where h_t=\{(a_s, X_s)\}_{s=0}^t is the history of actions I’ve taken and external factors till now. Hence, the future may not be completely chaos: although I cannot know future X_s precisely, by taking actions a_t now, I can influence how future will unfold via F_t(X_t|a_t, X_t).

Suppose I am a rational hedonist,  in a disciplined pursuit of happiness. In the current moment t, I take the best action a_t^* to maximize the expected, accumulative happiness from current time t till the end of my life T (a random variable), given the history h_t. Let V_t(X_t) = \sum_{s=t}^T f_t(a_s^*, X_s) be the best accumulative happiness in expectation from now onward.

In this model, luck is captured by random variable X_t. My karma h_t will influence how future state X_t plays out by partially controlling F_t(X_t|h_t), which is influenced by relative important of action a_t and luck X_t. Given current history h_t, I make the best decision a_t^*, without knowing X_{t+1}, X_{t+2}, ... precisely (although I may know the distribution F_s):

\displaystyle\Large \max_{a_t} f_t(a_t, X_t) + \mathbb{E}[ V_{t+1}(X_{t+1})|a_t].

That is,
“taking the moment and making the best of it, without knowing what’s going to happen next.”

Solving this model requires backward induction. The irony is:

“Life can only be understood backwards; but it must be lived forward.”


[Atlanta, June, 2006]