The paradox of chaos theory
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Ovid’s chaos
“Before there was earth or sea or the sky that covers everything, Nature appeared the same throughout the whole world: what we call chaos: a raw confused mass, nothing but inert matter, badly combined discordant atoms of things, confused in the one place.”
- Ovid, Metamorphoses
This is a quote by the ancient Roman poet Ovid (43 BCE - 17 CE) from his almost 12,000-line long poem Metamorphoses (a collection of myths and legends that details the history of the world from its origin to the death of Julius Caesar). In this quote, Ovid sets forth that chaos, which is described as a jumbled space of matter and energy, was the first entity to exist. Ovid's conception of chaos is relevant to the colloquial definition of chaos: disorder. However, this definition is diametrically opposed to what mathematicians and scientists perceive as chaos under chaos theory.
Key terms
There's a lot to unpack with chaos theory. First, we need to establish some vocabulary:
System: a group of interrelated features, components, objects, beings, etc.
Initial conditions: the first features or components in a system. If we were to think of a system as a pared-down version of Earth when it was first created, the initial conditions would be molten magma, dust, and gases.
Sensitive dependence: the actions and outcomes of features in a system are affected by the other features in the system. Thus, a change in one feature causes a series of changes in other features. We'll see later on that this is what drives chaos.
Deterministic: outcomes are predictable, not random.
Fractal: a pattern that's self-similar at different scales (e.g. a tree is a fractal since each branch is in the shape of a smaller tree). Fractals are created by repeating a process over and over again.
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What is chaos theory?
Chaos theory boils down to the idea that the smallest change in initial conditions can have a very large, seemingly unpredictable or random impact on the outcome of the system over time.
This is because the features in a system are interrelated and dependent on one another, i.e. they exhibit sensitive dependence—a change in one feature changes the behaviors of the other features. The effect of these changes then gets amplified over time. This is the idea of the commonly cited "butterfly effect" which theorizes that the flapping of a butterfly's wings in one part of the world can cause a hurricane in another part.
We can predict outcomes under chaos theory
While the outcome of a system may seem random, interestingly, chaos theory asserts that it can be predicted because of underlying patterns and connections between the features of the system (even though these patterns are likely difficult to see). And if a system is exactly repeated, we can determine these underlying causal relationships.
So, we can predict the outcome of a system if we know:
The initial conditions
The relationships or patterns amongst features
This is the deterministic element of chaos theory, and why it can raise philosophical questions when applied to life—like whether it's possible to have free will if our thoughts and actions were pre-determined by initial conditions. An example of a perfect chaotic system is a fractal—if we know the initial pattern of a fractal, we can predict its form at different points in time.
The paradox of chaos theory
Thus, in theory, the meaning of chaos here is closer to order and certainty because in a perfect system, we can predict outcomes based on initial conditions. This is the paradox of chaos theory; based on how people commonly denote chaos, we'd expect it to predict disorder and uncertainty, but it predicts the opposite.
However, the idea that chaos allows us to predict outcomes based on initial conditions falls apart in practice. In practice, it's not feasible to accurately predict outcomes because minute or imperceptible errors in measuring initial conditions lead to drastic changes in outcomes.
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Chaos theory falls apart in practice
If we apply chaos theory to life, it seems too difficult to isolate the initial conditions. How can we be sure that A caused B and that B caused X? There are too many different moving variables and factors. But the fact that we can't be certain of the causal relationship amongst factors doesn't mean that the patterns and deterministic elements don't exist. It just means that chaos theory isn't useful when applied to our lives.
Chaos here is an idealistic notion of prediction and certainty, which is only possible under a perfect, controlled system. In an imperfect system, like life, chaos isn't a practical measure.
But just because we can't identify or measure all of the casual connections in life, doesn't mean they don't exist. The universe is governed by laws of physics that underlie and determine all relationships, i.e. if a ball is kicked off of a cliff, it will fall because of gravity. And if we think more deeply about chaos theory, it seems plausible that the slightest changes in initial conditions can have large impacts on life over time.
Small changes in initial conditions can have large impacts
Imagine that a baby was born on September 1st, 2016 at 11:59 PM and that the requirements to join Kindergarten at the local elementary school in 6 years are that you must have been born between September 2nd, 2016 and September 1st, 2017. If the baby was instead born one minute later, he would end up starting Kindergarten an entire year earlier, and would likely go through childhood as less mature than his peers. Or imagine that the baby's mother started smoking while she was pregnant and the baby was born with a birth defect that changes how he interacts with others and views himself.
Accepting that outcomes are affected by slight changes in initial conditions (due to causal relationships we usually can't identify), raises questions about free will. Are our actions and decisions predetermined by our initial conditions?
It's hard to believe that every action we make is predetermined but likely that more outcomes than we realize are somehow and to some extent decided for us at the start.
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