What is the Chaos theory?
In: Planetary Science
Chaos, or randomness, is not a very well understood concept. In the sense that we have not found the beginning of determinism, or Order, and the end of randomness.
Before, we used to believe that randomness was the result of complicated and complex systems. Yet, with modern physics, very complex systems that seemed random before were found to be deterministic.
In the other end, simple systems, which we would believe to be very easy to know the outcome, are seemingly random. Most of the time, the systems simply are very sensitive to starting variables.
Nevertheless, chaos theory studies these systems. They analyse what we call random, and tries to find how deterministic we can make them be.
Think of snowflakes for example. They have unique shapes, and it seems impossible to determine what the shape of a snowflake will be. Yet, could we understand the parameters that affect their shape and be able to reproduce the shape of snowflakes by controlling the initial parameters?
Overall, chaos theory tries to find order and determinism in what is seemingly chaotic and random.
“Tiny changes to the step 1 can end up causing large changes in step 1000”, essentially.
Any time a system can only be *predicted*, and not *known*, little changes now can become big effects later.
Imagine you take a pool table, with all 16 balls scattered at random. You hit the cue ball 10 times, identically. … well, as identically as you can. You think it’s identical.
The cue ball flies off and hits the 2 at an angle, which barely skims by the 4 and hits the 6 which goes 5cm and stops.
The second time, the cue ball hits the two at a *slightly* different angle, so after it hits the 2, it also taps the 14, and thus the 4 gets missed and so the 6 doesn’t move.
Every time you do this, you will end up with a slightly different position. So now, you shoot the cue ball again, but because all the balls were slightly different, the 4 is in a completely different place and you have to aim the cue ball in a different direction.
The third shot in each situation is *completely* different! And that just keeps getting more and more extreme.
So, you can see that the tiniest difference in input at the start completely changes the outcome of the game.
You can do this with many things. Imagine you leave your house a minute earlier than usual, which means you run into your neighbour and get invited to dinner where you meet someone who offers you a new job. Had you left a few minutes later, you might have gone out for drinks with friends instead and stayed in the same job.
There are great examples of this. I think the Beatles can be traced back to one of the members’ parents coincidentally moving to a neighbourhood, allowing the bandmates to meet 20 years later. How many kids wouldn’t have been born 9 months after a Beatles concert?
How many people’s lives were saved when they called in sick on 9/11, or when they missed their train to board the Titanic, or so many other disasters?
That’s the basic nature of it. The tiniest variable that seems to make no difference completely changes the landscape very quickly.
The Simple English Wikipedia answers your question better than anyone else has so far: [https://simple.wikipedia.org/wiki/Chaos_theory](https://simple.wikipedia.org/wiki/Chaos_theory)
Chaos theory is basically the underlying mathematics of how small changes to the beginning of a process can have drastically different outcomes, so that they seem random and unpredictable, yet there is an underlying determinism to the randomness.
A famously ridiculous example is the “butterfly effect” in which a butterfly flapping its wings in Europe can affect the weather weeks later in California. As Terry Pratchett wrote in the first footnote in *Witches Abroad*, scientists ought to be “finding that bloody butterfly whose flapping wings cause all these storms we’ve been having lately and getting it to stop.”
A real-world example that always fascinated me is one you can demonstrate yourself. You can do it with water dripping from a faucet but it works better with water dripping from a small spigot. At a low flow, the water has a steady drip, drip, drip, drip. Increase the flow rate slowly, and then you’ll notice a “bifurcation” where the drips double: drip-drip, drip-drip, drip-drip. Increase the flow rate more, and each double drip bifurcates into four drips, but typically faucets can’t resolve the time interval between drips. The point is, increase it a little bit more and you start getting drips falling out at seemingly random intervals. Here we have chaos, which happens in a range of flow rates. The sequence of random drips at one flow rate is completely different from the sequence at any other flow rates, even one that is nearly the same but not quite.
It seems random, but here’s the kicker. If you can measure all the time intervals between these random drips and plot a graph of one interval versus the last interval, you get a smooth curve. This means that the random drips are being determined by a fairly simply underlying rule. You have just applied chaos theory by finding determinism in randomness. If you care to see the scientific analysis, have a look at this paper: [https://nldlab.gatech.edu/w/images/f/f6/Royer_Caleb_PHYS6268_Royer_FinalPaper.pdf](https://nldlab.gatech.edu/w/images/f/f6/Royer_Caleb_PHYS6268_Royer_FinalPaper.pdf) – particularly the graphs near the end.
Chaos theory basically says that small changes in a system can lead to big differences in outcome. Think of a butterfly flapping its wings in Brazil causing a tornado in Texas. It’s all about the butterfly effect!
When a drop of changes flow because tiny variations, the orientation of the hairs on your hands, the amount of blood distending your vessels, imperfections in the skin… never repeat and vastly affect the outcome.
In most cases, an approximation in the initial conditions lead to an approximation in the final conditions. If I know the speed and direction of a car, I know where it will be in 20 minutes. If I know it’s initial speed and position better, I’ll know it’s position in 20 minutes better.
In chaotic movements, that doesn’t happen. If I know the initial position of a double pendulum, I can’t know how it will look like in 20 seconds, even if I improve my understanding of the initial position.
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