eli5: Doesn’t chaos theory just prove we lack all the small details/data?

Question

I don’t understand this concept of “chaos” in a universe governed by physics.

Just because something is nearly infinitely complicated, doesn’t mean predicting outcomes would be actually impossible. If the universe produces the outcome, doesn’t that mean it’s following a rule set?

Do I fundamentally not understand chaos theory?

In: 4

Answer 1

Chaos is really more of a mathematical concept than a physical one. There are mathematical systems, like the logistic map (take a number between 0 and 1, then multiply it by one minus itself, then multiply by four, and rinse and repeat) for which any difference in the initial state (in this case the initial number chosen between 0 and 1), no matter how small, leads to a big difference in outcomes after long enough. It doesn’t necessarily have much to do with complexity – the logistic map is chaotic but very simple, whereas some very complex systems are not chaotic.

If a real system is accurately modelled by one of those chaotic mathematical systems, then long-term predictions require extremely precise knowledge of the initial state of the system. The further ahead you want to make predictions, the more precise measurements you need. And there is always a limit to how precisely we can measure things. In practice, models that display chaos come up quite a lot, for example in the motion of fluids, or the motion of bodies in the solar system. We can never be sure that these models are perfectly accurate, so in real-world systems you can’t really be sure that it’s fundamentally impossible to make accurate long-term predictions. But there are systems for which those chaotic models do seem to be extremely accurate, so it seems unlikely that anyone will ever find a way of circumventing the chaos.

> If the universe produces the outcome, doesn’t that mean it’s following a rule set?

It’s not enough to know all the rules; you also need to know the previous state of the system. But we don’t know all the rules, and it’s unclear whether we ever will. It’s also not clear whether the rules of the universe are fundamentally deterministic or not. In fact, we can’t really be sure that it does always follow consistent rules. Maybe at some level we’ll eventually find some extremely bizarre process that just doesn’t seem to follow any rules.