Linear and Non-Linear Causality

Sometimes we hear that everything happens for a reason. If something happens for no (apparent) reason, we call it chance. Things that happen for reasons are termed causal. The terms linear and non-linear causality are taken from mathematics, but one or the other applies to every system in the real world. A system, simply, is a group of parts assembled into a coherently functioning whole. The following table gives a breakdown of the two types of causality and where they apply.

  Linear Causality Non-Linear Causality
Applies to: Mechanical systems Complex systems
Characteristics: Whole is sum of parts Whole is more than sum of parts
  Reductionistic Non-reductionistic
  Deterministic Non-deterministic
  Predictable with certainty Only probabilistically predictable

Many (perhaps most) of us operate with a linear worldview that comes from our western scientific culture. Only recently has western science even formulated an approach to non-linear phenomena, though these make up the majority of what we experience. For this reason, most of us need to reassess our linear ways of seeing the world.

Newton’s laws of motion are laws of mechanics that are universally true—they work every time, everywhere. For every action, there will always be an equal and opposite reaction. Let’s say you have a system of a canoe, a pond, a paddle, and you. If you vary the force or direction of your stroke, the path and velocity of the canoe will vary predictably.

Such a system is also reducible. If three components remain constant, but one is changed, the change in the action/reaction will be due to the nature of the change that was made. Substitute a weaker or strong paddler, and the canoe will go slower or faster. Substitute a stick for a paddle and the canoe will hardly move at all. Substitute a rock for the canoe, and good luck! And so forth. Reductionism means that the behavior of the whole can be explained by the qualities and characteristics of the parts. That’s mostly how science works. We explain wholes by studying parts intensively.

But complex systems are non-reductionistic, because the properties of the whole are greater (and different) than the sum of the properties of the parts. If memories were linear phenomena, bits of memory would be stored in this or that neuron. Instead, memories reside in the patterns of interactions amongst neurons (and not necessarily the same neurons), rather than in the neurons per se.

In linear systems, causality is determined. If you apply this amount of force in this direction to an object of this mass, that (and only that) will happen. But, in non-linear systems, behavior is non-deterministic. You have a pretty good idea of what will happen, but then again it may not. When things are deterministic, they are predictable, because they have to happen in a certain way, given the state of the components of the system and the manner of their interaction.

But non-deterministic systems can happen in a number of different ways, and the reasons for this behavior can’t be captured by a reductionistic analysis of the component parts. Therefore the behavior of these systems can only be probabilistically predicted. Consider memory again. Have you ever studied very, very hard for a test and completely blanked when you got there? It’s hard to predict just what you will or won’t remember, or how well. Studying hard generally helps, but sometimes you remember the quirkiest things without even trying . . . and vice versa.

So, the next time somebody says that everything happens for a reason, you can answer, “Yeah, in a mechanical system that follows laws of linear causality.” For the rest of life, things still happen for reasons (usually many more than one), but in a non-linear fashion.

In a linear world, judges could be replaced with sentencing guidelines. A non-linear world is like a courtroom with a judge. The judge’s decision can’t be reduced to an algorithm—each case is different and there are so many factors, often of unknown weight. Experience suggests that, in the more complex (and interesting) world we live in, justice is better served by using judges.

If life were linear, how to live it would be mathematically soluble (at least given enough time, computing power, and knowledge of initial conditions). But it’s mostly not. So it behooves us to become acquainted with the non-linear—but inherently lawful—realities of the world of complex systems.

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