Please no butterfly analogies.
In: Mathematics
Quantum magic aside, if you have 100% knowledge about state of system, you should be able to predict its future using physics. In practice, you never have 100%, you are limited by the accuracy of measurements you can take. Usually, this is good enough. Approximate information about the system allows us to make approximate predictions. For example, we may be able to predict that a cannonball will fly somewhere between 100-110m. We would know the exact number if we knew how every single air particle it hits on its way is behaving, which we don’t. But on the whole, it’s a useful prediction.
However, if a system is chaotic, predictions based on approximate data will not just be mildly inaccurate, they will be so wildly random they are basically useless. For example, the movement of single grain of sand in a sandstorm. It’s so light and surrounded by so many particles of similar size bumping into it, a tiny variation will send it off on a completely different course. It’s pointless to even try guessing where it ends up.
Some systems fall somewhere in-between: in short term, we can make reasonably good prediction, but the accuracy steeply falls off with longer-term predictions, until the system becomes completely chaotic. Examples of such systems are weather and the movements of celestial objects.
Edit: u/bluebell_sugarslay raises good points in [his comment](https://www.reddit.com/r/explainlikeimfive/comments/mj70p9/eli5_what_is_chaos_theory_and_what_is_it_used_for/gt97r70/?utm_source=reddit&utm_medium=web2x&context=3). I maintain my example is correct, though, if my explanation is a bit lacking. If we were talking about a single grain riding an invisible predetermined roller-coaster, so to speak, the system would indeed not be chaotic despite its complexity. However, the many grains of sand and air molecules themselves in a sandstorm interact with each other constantly, which I believe does make the system chaotic.
Latest Answers