Linear relationships between things are easy to understand: more of this, leads to more of that.
With linearities, relationships between variables are clear, crisp, and constant, therefore “platonically” easy to grasp in a single sentence, such as “A 10 percent increase in money in the bank corresponds to a 10 percent increase in interest income”. If you have more money in the bank, you get more interest.
But the world is more nonlinear than we think, and than scientists would like to think.
Take, for example, the relationship between pleasure and drinking water. If you are in a state of painful thirst, then a bottle of water increases your well-being significantly. More water means more pleasure. But what if I gave you a cistern of water? Clearly your well-being becomes rapidly insensitive to further quantities. As a matter of fact, if I gave you the choice between a bottle or a cistern you would prefer the bottle—so your enjoyment declines with additional quantities.
These nonlinear relationships are ubiquitous in life. Linear relationships are truly the exception; we only focus on them in classrooms and textbooks because they are easier to understand.
The problem is that in many real world relationships between things, there is a point of too much, where things not only plateau, but actively get worse – once a certain threshold is passed.
You may naively guess a linear relationship among the crime and the severity of penalties. And this is how our judiciary and penalty system is built on. But this is dead wrong.
Inverted U shaped curve, according to Malcolm Gladwell, shows that the real relationship between crime and the severity of imposed penalties looks more like this:
So crime actually starts getting worse again beyond a certain point. Why?
He gives a synergy of reasons:
- Despite obtaining their money illegally, criminals are bread winners too, and putting them in jail means their dependents suffer.
- Children of a jailed parent are 3 times more likely go to jail themselves, and are two times likely to be depressed.
- A stable marriage is one of the best predictors of children in disadvantaged communities living productive lives. Lengthy jail time tends to destroy marriages.
- Freshly released prisoners tend to be worse off after being in prison, and struggle to readjust back into normal community life, often turning back to crime.
Gladwell gives us the threshold point for communities; if more than two percent of a community are jailed, we tend to see crime start getting worse again.
Le’t come back to the example of water: the relationship between pleasure and drinking water.
A linear relationship would lead us to guess that more water means more satisfaction. But it is dead wrong.
Biologic systems have a threshold. At some point more water would mean less satisfaction and at some point zero satisfaction. You will get a U-curve.
But the system is ever more “complex”. At some point the satisfaction would become “negative”: more water shall create “pain”. And, finally, Death.
Even the simple act of brushing teeth – for doing an example familiar to my colleagues – has not linear effects. There is a threshold (that is subjective and difficult to quantify) beyond which brushing become harmful, producing gingival recession, abnormal tooth wear and tooth sensititivity.
Another example, familiar to my colleagues, is the cleaning and shaping in the endodontic procedures. More shaping and cleaning at some point (the threshold) can produce more harm then benefits: it can become iatrogenic, increasing the likelihood of stripping and root fracture.
During this so called “pandemia” of Covid-19, a new experimental procedure has been implemented on large scale: the lockdown.
Lockdown has been introduced on the base of phony linear thinking, that plagues most of the “experts”. This has exposed the world population to “catastrophic” side effects, that have abundantly overcome the alleged benefits on virus spread.