Nonlinearities
Nonlinearities describe relationships where changes in variables do not produce proportional or constant effects, contrasting with the rarity of linearity in real-world phenomena.
THE IDEA
Nonlinearities
The situation can get a little more tragic—the world is more nonlinear than we think, and than scientists would like to think.
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 and a 5 percent increase in obsequiousness on the part of the personal banker.” If you have more money in the bank, you get more interest. Nonlinear relationships can vary; perhaps the best way to describe them is to say that they cannot be expressed verbally in a way that does justice to them. Take 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. Yesterday afternoon I tried to take a fresh look around me to catalog what I could see during my day that was linear. I could not find anything, no more than someone hunting for squares or triangles could find them in the rain forest—or, as we will see in Part Three, any more than someone looking for bell-shape randomness finding it in socioeconomic phenomena.
You play tennis every day with no improvement, then suddenly you start beating the pro.
Your child does not seem to have a learning impediment, but he does not seem to want to speak. The schoolmaster pressures you to start considering “other options,” namely therapy. You argue with her to no avail (she is supposed to be the “expert”). Then, suddenly, the child starts composing elaborate sentences, perhaps a bit too elaborate for his age group. I will repeat that linear progression, a Platonic idea, is not the norm.
When to use it
Skill acquisition: recognizing that performance may plateau before sudden improvement.
Child development: understanding that language or cognitive leaps can occur unexpectedly.
Resource allocation: avoiding overinvestment by recognizing diminishing returns in consumption or effort.
Business growth: preparing for nonlinear growth curves where revenue or adoption may accelerate after a critical threshold.
FROM THEORY TO EVERYDAY LIFE
In practice
Water and Pleasure
If you are in a state of painful thirst, a bottle of water increases your well-being significantly. But if given a cistern of water, your well-being becomes rapidly insensitive to further quantities, and you would prefer the bottle over the cistern, showing that enjoyment declines with additional quantities.
Tennis Improvement
You play tennis every day with no improvement, then suddenly you start beating the pro. With nonlinear progress, a period without visible gains can precede a breakthrough.
Child Language Development
A child who does not seem to want to speak suddenly starts composing elaborate sentences, defying the expectation of linear, gradual progression.
A MOMENT TO REFLECT
Put it to work.
Think of an area in your life where progress seems stagnant yet suddenly jumps. How does the nonlinearity concept explain this?
Why do we often expect linear progress in learning, and how might that expectation be misleading?
Can you identify a situation where increasing a resource (like money or time) leads to diminishing returns or even negative effects?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)