Friday, May 06, 2011

The Law of Parabolic Returns.

There are several intellectual assumptions which I feel are at the root of many of society's maladies. One of the them is what I would call is the misattribution of linearity.

The erroneous logical process runs as follows. Let's say something called X is good, then even more by implication, is better. It's  runs on the assumption that systems are linear and predictable. It's common error that's seen in many facets of life. Take for example vitamins.  Small doses of vitamins are definitely beneficial to individuals who are vitamin deficient, but at ever greater doses, the effects become  negligible and some instances harmful.  Likewise with exercise, many people,  especially sportsmen, are of the the opinion if a little bit of exercise is good for you even more is better and you can never really get too much of it. Public policy makers, who view education in the same light as motherhood, extrapolate its benefits in the same way.

It's a common intellectual pathology and it exists amongst both the left and right to varying degree.

Very few systems of any complexity are linear in their effect. In fact, most systems obey what I call the law of parabolic returns. Here, what happens initially, is there is a bit of a linear effect which after a while peters out and then finally becomes negative. The more you think about complex systems, the more you recognise the effect.

My interest is as to why this phenomenon exists in the fist place. After thinking about it for a while I believe that it is due to three things:

1) Limitations in intelligence. (That is the ability to process information)
2) Limitations in knowledge, which can either be from ignorance or from a lifetime of specialisation.
3) Superficial thinking. (Sentimental thought)
4) Ideological bias. (Thought-filtering)

Understanding multi-parametric systems is hard and therefore, given the relative scarcity of deep and broad thinkers in our community, linear thinking is more likely to be the predominant mode of thought. Hence, in community based decision systems, there will be a deep bias towards linear explanations of complex phenomena. The simple solution is more easily grasped than the complex one, especially when it needs to be explained by the moronic media to the bovine masses.

Ontologically, linear models frequently bear some relation to reality under some conditions, in other words, there usually is a degree of truth to them. This is why some of the claims of Marxists, Libertarians, Keynesian's etc have some validity; they are not outright fantasy. The problem is that their model is only valid under a limited set of conditions.  Conservatives err when they dismiss leftist claims reflexively; sometimes there is a degree of truth to their claims.  In doing so they make themselves look stupid.

The phenomenon of linearity also explains a lot of the idiotic polarisation in our society at the moment.
Take for example, the two extremes: Communists and Libertarians.

Both of them engage in a denial of reality. The communists fail to see that collectivisation has negative consequences just as much as the rabid libertarians can't see that individualisation is just as socially destructive. In many ways they are similar having the same cognitive blinders, just different cognitive models.  As the general levels of intelligence decline and Facebook becomes the information source for the majority of the voting population,  simplistic solutions to complex problems will assume greater political force.

Charles Munger, Warren Buffet's partner, was a meteorologist prior to him becoming a lawyer. Meteorology is hard probably the ultimate multi-parametric discipline He describes the problem of linearity as the problem of "the man with a hammer". To a man with a hammer every problem is a nail. He has written and excellent and easily readable essay on the importance of multi-parametric knowledge: Academic Economics: Strengths and Faults After Considering Interdisciplinary needs. It's well worth a read.


Simon Grey said...

Excellent post, SP. Economists have a phrase for what you're describing here: "diminishing returns."

As for the political polarization, I would simply like to point out that the term "libertarian" covers a wide range of differing political beliefs. Not all libertarians are the same, so lumping them together in one group may not yield a particularly accurate conclusion, but your general point is well-taken.

The Social Pathologist said...

@Simon Grey

Economists have a phrase for what you're describing here: "diminishing returns."

I'm familiar witht he the law of diminishing returns. I had actually edited out a passage on "diminishing returns" from the post.

Perhaps I'm splitting hairs here Simon, but it was my impression that the laws of diminishing returns implied that for a given input, the return would become less and less but not negative.

I'm looking at this from a cognitive perspective, and the reason why I'm a bit particular about this point is because of the "try harder" phenomenon.

Many people, seeing that their policies have not worked, resort to redoubling their efforts to achieve their goal. It never occurs to them that their return on investment, so to speak, can be negative after a while. For such individuals the law of diminishing returns means that they have to "try harder", they still expect positive results with greater effort. The cognitive link between positve result and effort is not broken. In many ways it's the same mental pathology as the assumption of linearity: more effort=more result.

The other example of the law of parabolic returns is the "U" shaped graph. Here return are negative for a while becoming positive after much effort. Say weight training for instance, which initially is painful and tiring for the unconditioned but afterward brings the benefits with increasing effort. Or to paraphrase Chesterton, the Joy of reading Virgil comes after the bore of learning Latin.

I hope I have explained myself clearly.

Country Lawyer said...

I think that the safety net that the government provides may color your perspective on human liberty.

Liberty without consequences is destructive.

Plus prohibitions tend to increase criminal behavior of all sorts (not just the liberty being infringed).

Simon Grey said...

"it was my impression that the laws of diminishing returns implied that for a given input, the return would become less and less but not negative."

I know some economists have made that claim, but the mainstream view is that return can become negative. The professor of my Intro to Econ course made a point of mentioning it, for what it's worth.

Your example reminds me of the time my brother downed eight antihistamines because he thought that if two would help clear up his allergies, eight would banish them forever.

Anonymous said...

It's interesting to note that those with interdisciplinary majors have the highest average GMAT scores. More institutions should require dual curriculum based on liberal arts and science. What do you suggest SP to a combat linear way of thinking?

Also the law of diminishing returns does have a limit.

The common example is a consumer who pays $5 dollars for the first ice cream and then $3 dollars for the next until, he is full and does not want to consumer anymore even if the ice cream is free. At this point he is physically incapable of consuming it.

The Social Pathologist said...

@Country Lawyer.

I think that the safety net that the government provides may color your perspective on human liberty.

It's true that an uncritical safety net divorces action from consequence and as such facilitate socially destructive behaviour, but my criticisms with regard to human liberty stem from dealing with people on a day to day basis. People just seem to have a difficulty of thinking things through.

The Social Pathologist said...


More institutions should require dual curriculum based on liberal arts and science. What do you suggest SP to a combat linear way of thinking?

That's a hard one.

The first big problem is the problem of average human intelligence. Just filling up a man's head with facts from a variety of facts does not mean that he will be able to "connect the dots", so to speak, between them. The ability to integrate data seems to be an innate skill more than a learned one. Though, a education system which strongly emphasises the interconnectedness of things may at least habituate people not to simplify too much.

The other problem is bias and "thought-filtering". Lots of "classically educated" Englishmen just didn't want to see the dangers of Socialism, some the average mechanical engineer from Boise, Idaho had no problem doing.

Still there is much to be recommended to the principal of a generalist education, particularly with regard to the arts graduates. Most of them should at least be partially proficient in the hard sciences before they earned their degree.

The thing about the sciences is that they continually force you to confront reality, your always checking your results against observed results, not fantasy. That's not to say that the hard sciences cant be corrupted, it's just that its much harder to do.

A hard science subject should be part of a "classical education".

Drew said...

Here is another real world example of the negative parabola...

This guy explains the exact same concept, even with same initial linear relationship that causes the poor assumption.