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!