2010/03/31

Known unknowns and unknown unknowns



A lot of people made fun of poor Donald Rumsfeld for his infamous quote..

"Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns -- the ones we don't know we don't know."

But actually, he had a very good point. There are things that have uncertainty but we know the shape of the uncertainty. For example, I don't know who will the lottery tomorrow, but we do know the probability of any one person winning, or the distribution of winning amounts. And by the way from that we do know that playing the lottery is one of the dumbest activities known to man, though it is a kind of stupidity that we can harness for good perhaps... but I digress. My point is the outcome of the lottery is a known unknown. Which is different type of ignorance than say, not knowing if God exists. There you don't even have a probability space to support a distribution. Once someone asked to me: What's the probability that God exists? Obviously it was a rhetorical question, and it assumed the answer is "very low" (the question came from an atheist). But then I was like: it could be 0.01% or 99.99% or anything. If you have to choose, it might as well be 42.