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.

Jump to achieve/change

Our options are limited. We try to choose the best one (assume).

But we can create new interesting options.
For me, driving involves so much effort, that having a car is useless. But if I engage in driving for a long time, driving will become automatic. Then having a car may improve my life.

There are endless ways we can have better options by engaging a certain amount of negative/effortful experience.
Those endless possibilities do not occur naturally. They occur only when you forget everything you know about your own

life and experience. Questioning even the smallest basic assumption about how you feel, function, mind working, wants, etc.
Beware, that even with much effort, you will see only a minority of hidden options in your life. The scope of potential

possibilities is never seen fully.


1) Over optimism. We expect life to get better after the change becoming natural. We are usually overestimating the

expected improvement. We may not learn the skill/get used to the situation. The very usefulness of the learned stuff can be illusory. Adaptation, that is human's tendency to get used to everything, cancels out various supposedly improvements of life.

2) Gamble. Skewed bets (like lottery, but with maybe positive expectation). Sometimes, the cost is relatively low, but the possible progress is enormous. No big loss if useless. But the change in life can be forever. Other changes to life are long investment, but small improvement for a little while only.
Life is short!

A change starts negatively, where we lose immediately from it. The trick is that sometimes, the later value is large. The farther the positive value, the larger the effort invested, the less worth it seems to be.

Hidden options are endless. It is a complex territory, sometimes worth the trouble.

Saturday, July 12, 2008

Darwin's Epistemological insight: Unreliability of probabilities.

What are the probabilities of our existence?

OK. There could have been many "existence" so the question should be asked "what is the probability of an existence that is 'interesting'" or something like that.

Technically, we cannot calculate, because we have no knowledge about the variety of processes that could have happen.
But we may try intuitively, with some understanding of the space of possibilities, to gauge. Where are the odds going to land?

In short, I see that it feels that the probability is very low. Not 1 / 1 ^ infinite zeros. But rather 1 / 1 ^ very many zeros.

Darwin killed 99.9999% of the improbability of existence.

But I believe, that while we may (and have to) intuit about these probabilities, we should learn from this experience is how far our estimates can be from the ultimate numbers.

Before Darwin, if asked what are the odds for this world, reply would be infinitely low. Because the probabilities for all these species and their complexity and efficiency is so impossible.

One good algorithm of Darwin (gradual process of evolutionary selection) dumped the probabilities infinitely. They still seem low, but in relation to the odds we had before Darwin, the odds are infinitely more probable.

Statistically, Darwin taught us how a not thought of process can change dramatically our subjective probability assessments.

We Know that our estimates are terribly unreliable. That is, after Darwin

Epistemologically, that is Darwin's most important lesson!