the chaos theory
In: Physics
There are a billion random things that exist in any “system” that we don’t account for or assume will happen in a standard or non change inducing way.
Chaos theory exists to demonstrate the magnitude of assumptions we take for granted in any given moment
Chaos does not mean unpredictability in itself. Instead it describes systems which are very sensitive to even the tiniest changes. So if you make any alteration, however inconsequential and minor it may look, it can and often will lead to vastly different outcomes.
The standard example is that of a butterfly whose wing flap might cause a hurricane 17 years later. But it might at the same time have avoided two worse hurricanes 14 and 35 years after, as well as an asteroid impact in the year 8215. Weather and gravity are notoriously chaotic.
The problem is that even smaller changes might have even larger effects, and that we simply cannot know all the data to infinite precision. That together with limited computational prowess is why weather forecasts are not perfect. To stay somewhat on track they have to update their data as often as possible, and acquire as much as feasible as well. For the sheer amount of even most basic data, I like to point to [this website](https://earth.nullschool.net/)
Some things, you can see how they are now and guess pretty well how they’ll be in the near future. Change how they are by a little, and you’ll change what happens by a little.
Other things, change how they are by a little, and you’ll change what happens by a lot. Or maybe a little. Hard to say. CHAOS!!!
The study of *dynamical systems* is, loosely speaking, the mathematical study of things that interact and change over time. These include things like pendulums, planets, animal populations, as well as many other mathematical models.
Chaos theory deals with the study of how such dynamical systems can be sensitive to their initial conditions, among other (less well-known) characteristics of chaos like repelling periodic orbits and mixing within the state space. How a system evolves over time can be fixed (it is deterministic with a specified formula and there is no randomness), but if we even very slightly change our starting position, the outcome after a while can be drastically different. We want to examine when systems become chaotic (in terms of model parameters), “how chaotic” they are, if spontaneous order can arise, among other things.
You can look up videos of a *double pendulum*, which is one of the most well-known chaotic systems. And you would have heard of the *butterfly effect*, which is a metaphor of the sensitivity to initial conditions.
The simplest example I can think of is a double pendulum. The motion is deemed chaotic because it is super hard if not impossible to get it to move the exact same way twice. Even digital models are hard to do this with because the tiniest of differences in initial setup of the arm positions result in different behavior when it moves.
Chaos theory is essentially the study of such systems.
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