Friday, July 25, 2008

The Metaphor of Mean-Variance

Sitting on the beach with a friend, we discussed the eternal topic of how much beauty one should look for. It is known that for the same "price" you will get either more beautiful and less smart and vice versa. Those with beauty and wits, will look for a higher quality lad than you.

Friend says that everyone looks for different kinds of beauty.
But there is a common element!

There is no contradiction. If you ask different people to rate beauty, you will find some correlation between them.
Common element + individual/deviant element.

Mean-variance is very relevant to every knowledge. All we know is partial, and depends on conditions (the correlation between the beauty in my eyes an African man is lower than between me and other Israelis, I guess. But there also there is a strong correlation! again. three quantities: common to all, more common for Israelis alone, and variable). It can go on...

Intuition can be true. However, without thinking it out, we suspect it a little. Its reliability is probabilistic (any knowledge is probabilistic. Anyone not understanding it should see a doctor). On average ("mean") it has certain chance to be right, but a good probability to be a mistake = unknown

Many controversies come about because of not understanding. Evidence to an effect does not say it is exclusive, and the same for counter examples. Many counter examples disprove just the generality of the rule, there may still be a partial generality (sometimes a generality is dependent on various conditions and other problems. Long story).

The mind does not like half truths, continuous gradients of stuff, etc.
Baumeister (the cultural animal) explains: Most decisions and actions in life are discreet. You either order the cake or not. tell the joke or.... tell first three words and see reactions.... (this is the continuous way, but most do not use it). Our mind May have a adapted to this reality.
Simplification of information is another reason. I surmise that both explanations are right.

PS. To make Nassim Taleb happy, I state that variance can be a crazy distribution/fractal/unknown/jumpy or whatever. In another sense, the idea of mean and variance above, reflects the idea of commonalities between things, while there are differences and possibly big ones. Sorry reader. It is not me complicating matters. It is reality that is opaque making our minds dizzy.

No comments: