Friday, August 31, 2007

WWDNGH 3: Crazy mathematics

psychological and personal things are not linear.

Many properties of life related decision do not work in a simple 1+1=2 way.
The principle is - examples below - that values of the same experience vary wildly with time quantity etc. Sometimes, more is actually less. And other strange qualities of real life experiences as opposed to simple calculations.
It follows that it is pretty complicated to get the right calculations as to what, how and how much to pursue things.

No wonder that results are not always optimal.
On the contrary, it is fascinating that we manage our so convoluted life so smoothly.
Nevertheless, one may exopect that some of our "fast and frugal" intuitions that help us manage are not optimal.

Here is a short list:
Concave utilities convex ones. and ......... crazy ones.
Non-monotonic functions (i.e. more is less).
Counter-intuitive logic
fancy complexities
Wubdt curve


Concave utilities are well known to economists. The practical value of the first $1000 in a month is quite higher than the added value one gets from the second $1000 (the difference between earning $1000 and earning $2000).

First $1,000 give you basic food some commute, a cheap dwelling etc.

Second $1,000 will give you more possibilities. Better food, a better sleeping room, etc. But the difference between having theses added conveniencies and not having them, is meaningless compared to the difference between having the minimum $1,000 and having nothing being left to sleep on the street and collecting food from the garbage or othe sophicticated sources.

The generalisation of this idea says that the "utility" of money is concave, meaning that the more money you have the less value yo get form each additional dollar.

A similar idea is covexity. The opposite of oncavity. It means that he second hour of sleep missed is more damaging than the first hour, and the third hour even more.

Concave and convex curves are everywhere. the usefuleness of the second cup of icecream is (usually) less exciting than the first one. The joy from the second hour of a conversation is usually quite less exciting than the first hour. and so on.

Suffering works the same way. After an hour of staying in line you sometimes become quite numb and do not care too much about more waiting. Sometimes it is convex. After three hours in line, the additional fifteen minutes are these that bring you on the verge of being hospirtalized for mental distortions.

Traffic jams, indoctrination sessions with bosses, fatigue from prolonged courtship games, may follow convex feeling. Anger builds up. One can even predict quite accurately at which time forehead veins break up and certain acts being taken.

As a very broad rule of thumb. Positive experiences resemble somehow a concave slope, while negative experiences resemble at times a convex slope.


Non-defined or crazy curves. The example of waiting painlessly for three hours, and than feeling like the world is exmploding unless I am accepted now, illustrates that real life does not neccesarily obey symetric curves. There are crazy jumps, as if the minute no. 187 of waiting in line is the one that causes most of the suffering. In a generalized way one can still say that the expected pain from a minute is averaging somehow. But this is a way round the problem. The fact remins that things do not behave nicely etc. and that values may change quite capriciousely.


non-monotonicity. Monotonicity means that values do not go backward. That you cannot feel worse with too much icecream, or too much mates (sarcastically). It may work with money (?). Even if too mcuh money even if almost useless (the 10th million does not confer much value in real life), it may not make one worse of. But too much eating confers less and less enjoyment until eating becomes painful, stomach gets swollen and sick, not to speak on fat that accumulates on belly/bottoms/thighs.

Recent research shows that having more options may render us worse off (no mistake!). In an experiment, people offered to choose between 6 tastes of jam bought more and enjoyed the taste more than those offered 24 tastes to choose from. The examples of to many girlfreinds would clearly be intuitive. two lovers is where many would agree that more is less.
Ability to choice itself may lower satisfaction. People given the option to return a picture and replace it, felt the picture was less nice. The very option to replace, while technically meaning more, was practically less, in terms of psychological joy.


Counter intuitive logic
The emotinal side of life offers many examples. Eating really tasty icecream on an Italy trip is sure enough to be worthy. But if you remember it and your hometown icecream feels less exciting? is it worthy to lose years of icecream joy for a single cup?
I may give moe examples in a sebsequent post.


Fancy Complexity
A seemingly single decision can account ofr so much things.
How much should I charge for a hour of work? Feels a neat question. An hour = ???
How much will I enjoy this specific task?
How much energy will it take? If I will I afterward be exhausted for five hours, maybe I should charge for five.
What are the expectations of future works from this guy? Maybe this is the ticket for my next job?
Am I getting any experience form it?
Will I get more phone calls from him, making an hour into seven.... and life long commitment?
What are my alternatives for money making?
What is the marginal cost of my time now in emotional terms? is it the first hour of the day, or the 13th after a crazy day, just the hour needed to make me formally sick?

on and on it goes. I may put a real life example in a subsequent post

Point. Calculating and udnerstanding life is less simple because of the huge complexity in real life decisions.


Wundt Curve
Much of our experience goes around our arousal level. When bored it means too less arousal - which hurts. Being too excited is also painful. Our subjective joy if only arousal is the question looks like a one-sided (skewed) curve. Like this:






A classical Wubdt curve (click to enlarge)















The book "The Joyles Economy" (must read) discusses in length how this arousal business affect our life boredom etc.
The interesting property of the curve is that you feel a little better as arousal gets higher, but as ou cross the peak of the graph, your joy declines fast, reaching the suffering area with just a little too much arousal. It has much implications for how to arouse ourselves optimally (do not run too much. Beaware the suffering of an overdose), and explains the puzzlng feeling we have when from sheer joy we feel falling into a deep hole very fast amid a big exciting experience.

More pecularities
Trade-offs
. A most things contain positive and negative sides. Knowing them, calculating them, and comparing them........ Except from the emotional effects the very calculation bear.....

Time mathematics. Difference between our value for different ages, different times in the day, etc. diufferent wakefullnes levels etc.

Strategic effects. Everything we do change our personalities, future preferences etc. etc.

In Summary
This ambigouos and complex nature of experience, explains partly why it is hard to optimize our hedonic experienece as well as other kinds of positive experiences (these maybe even more subtle and complex).

It is not clear for me whether being aware of all this would help people make their life better.

I was tempted to think that the very understanding of these curves, and of all the factors above, would itself help in doing better decisions.
I am very skeptic now.
Not sure that it is feasible to engage in too complex decisions. We are not computers.
It is costly to calculate.
We may calculate mistakenly.
We may concentrate on the math, and forgettnig other, maybe more important factors.

Research by Timothy Wilson and others shows that sometimes, being aware of our decisions and considerations deceases both, Decision quality, and actual satisfaction from the decision.

WEIRD!

9 comments:

i.c. said...

no need to add anything...
are you trying to convince everybody that it's too complicated anyhow?

Yechezkel Zilber said...

I am merely trying to understand the mathematics and dynamics of life calculations.
Complexity etc. is part of why improving life does not work.

In a more general framework, I am first trying to explain why naive optimization do not and will not do.
then, i will try to offer improvements that may not suffer from these problems acutely. Whether theses alternative ideas are fruitful? who knows?

i.c. said...

I'm already curious about your suggestions...

Yechezkel Zilber said...

Started compiling preliminary list. Will post in a day or two

Yechezkel Zilber said...

* Exremely effective actions etc. There maybe several such ides. Exersice (walking or running) improves mood for quite some time afterward, even aftger 24 hours. If ten minutes of exercise makes me better off for a day, it is very profitable. Maybe even pratical to do (??). Meditation also comes to mind, as some reports say that a little meditation a day can improve mood overal, changes the activation level of amygdala etc. See below aobut self-regulation exercises.

* Hidden/inovative options. As in the marketplace, efficiency and rationality are true only for widely known and salient deals. There every optoin is already exhausted. Same for personal decisions. Dating my next co-worker is an option I must have considered, tell me what I do not know. Getting her to introduce me to a freind of her sister is something I may have nto thought about.
Hidden options. Anything that is not open to our default thought may contain very advantagous deals.
Multiple parameter play. The idea of changing a single parameter in life is salient. If you did not do it already you probably think it to be a bad idea. But changing three things at a time? Namely changing your job AND house size AND hours of sleep AND the kind of blogs you are frequenting. Where a single change is unfeasible or not profitable a combination of changes may prove very interesting. Quite fearful to think about. The level of mistakes in such abstract calculations is also higher. But there can be hidden some unseen treasures.

* Changiong hte whole distribution. (similar to above, but a twist). While within a given population we know that little can be done in relation to "explained variance" n the causes of happiness (the things that affect happiness on the explained variance game have small effects, nad most of them are uncontrollable.), we see some strong differences between populations, indicating some strong effects from various causes. If one can artificially change features of his life surroundings etc. in a way theoretically akin to changing his circumstances as iof he relates to a different group. As well as other changes that resemble this idea of moving to another distribution etc. instead of playing the shady rules of given distribution.

* Narrowing the gap between conscious-nonconscious. The difference between consious to nonconscious personality is related negatively to well-being. The bigger the gap the less happy the person is. If one can practically narrow the gap, would it improve happiness?

* self-regulation exercise. In a series of papers Roy Baumeister shows: People higher in self-regulation capacity are happier. Exercise helps to strengthen one's self-regulation capacity. Improving one's self-regulation capacity via exercise leads to improvements in various life domains.
The problem is how one brings himself to do the exercise, because even for donig self0pregulation exercise one need some discipline. The other problem is the eternal problem of bringing one to do any thing "rationaly worthwhile". Anyway, praticing self-regulation thereby improving it feels a fascinating idea.

* Invest in the short term.

Other's ideas:
* Self-deception (/self-help?). Roy Baumesiter. While objective circumstances (e.g. income) correlate very weakly to happiness, perceived circumstances have a strong effect (e.g. satisfaction with income). If ou can just convince yourself that you are better off, you will actually be better off, emotionaly.
The genius insight of Baumeister comes here. Self-help books, even ikf not useful practically, maybe very useful in convincing oneself that he is better off ( or about to become). That way self-help books maybe effective happiness promoters while being a straight joke. Rather, not a joke at all. Books effective in making people thinking they are better, should actually be praised as much as their deluding techniques are better!

* deciding in life based on other's experiences. Or surrogation of decision making. Daniel Gilbert.

i.c. said...

hi:
I almost missed your list - I was expecting a post (not a comment), just by chance I noticed another comment

i.c. said...

...basically I agree with a lot of your list (like obviously: feel your body, be in the moment, use it that you construct your own world)
- but single points are not really a strategy (except if you favor random interventions; which may be quite reasonable??)

cyrille said...

I appreciated this post, in particular because this is courageous to deal this kind of topic where it is so easy to criticize every bit of it.

Also I agree that the world is "not linear" at all, which can make our life difficult, and investigating that is definitly worth doing! Personnally I also look at the world with mathematically curious eyes, and by the way I find myself much happier when I realize why something is strange, as opposed to not knowing...
Cheers,

Yechezkel Zilber said...

Thanks Cyrille

Accepting our ignorance and being curious is the way to know.