22 | January | 2016 | A MAN OF ACTION

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]

M	T	W	T	F	S	S
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4	5	6	7	8	9	10
11	12	13	14	15	16	17
18	19	20	21	22	23	24
25	26	27	28	29	30	31

A MAN OF ACTION

Life is either a daring adventure or nothing.

Daily Archives: 01/22/2016

WRITING: CAN WE CONTROL OUR FUTURE?

Day 127, 10pts, 1.22