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
Fundamental to it is the idea that for a sufficiently complex system such complete knowledge and prediction is…perhaps the best word is infeasible.
Sure, if you were an omniscient god and could know everything, ignore uncertainty, etc… Maybe you could predict it but we’re not and likely never will be. At the very least we run into the uncertainty principle but there are hordes of things we are nowhere NEAR needing to worry about that on outside of ideal lab conditions.
It would be fair to say that we can grasp and predict the outcomes of MORE complex systems as time goes on, but A) chaos theory is an arguably valid model right up until we meet that point and B) there is a theoretical cap on what we can know.
Chaos theory lives at the margins of what we can sort of predict, but escapes our total comprehension for now. The better we get, the farther out it is pushed.
Chaos theory, or the butterfly effect is an actual mathematical phenomena that is creates a butterfly like pattern called [Lorenz System](https://en.wikipedia.org/wiki/Lorenz_system) where a very, very minute unknown creates a huge effect and its result can be unpredictable. The system, in nature needs absolute perfect knowledge to be able to predict accurately. And considering that we can’t know everything — for instance the minute flapping of a butterfly’s wings not factoring in the calculation, there will always be a degree of uncertainty in the start of the equation, creating the chaos pattern.
You understand it, you just don’t have the final step.
If you had perfect precision data from perfect detail sensors, you could use an infinitely powerful simulation to predict the future. We cannot get any of these things in the real world.
It’s not just “We just lack necessary detail”, but “We can’t actually get enough detail to go past educated guesses and estimates.”
I might get this slightly wrong. It is tempting to conflate complexity with chaos.
Yes, in a very complex system, outcomes will be unpredictable simply because of the amount of factors needed to predict it. This isn’t what chaos theory is about. Rather than complexity, it deals with precision.
We now understand that even fairly simple systems and even in relatively idealized settings (say a computer simulation), there are systems whose outcome over time vary by a lot even with very minute changes in inputs. This is what chaos theory is about. It adds another dimension to unpredictability.
Before chaos theory, there was the idea that given enough input, systems could be predicted long term, ie their outcomes would “converge” and predictions would be reliable and stable. In this situation, giving more precise input would only improve accuracy but not markedly affect the outcome.
An example would be given some speed, we could calculate the arrival time for a certain distance travelled. The more accurate the measure of speed, the greater the precision of the arrival time prediction – but overall we can estimate the error of our prediction based on the uncertainty of the measure of speed. This is broadly not true of chaotic systems.
You understand it, you just don’t have the final step.
If you had perfect precision data from perfect detail sensors, you could use an infinitely powerful simulation to predict the future. We cannot get any of these things in the real world.
It’s not just “We just lack necessary detail”, but “We can’t actually get enough detail to go past educated guesses and estimates.”
Whenever you predict something you first have to measure the initial state. Then you use the model to predict the outcome. However every measurement has only finite precision, which means there is always a margin of error for the initial state and therefore there is a margin of error on the predicted outcome. If small margins of error on the initial state lead to small margins of error on the outcome the system is well behaived and predicting the outcome is possible. Otherwise the system is chaotic and it is impossible to predict the outcome, no matter how precisely measured the initial state was.
In both cases you can actually perfectly predict the outcome if the initial state was perfectly known but perfectly knowing the initial state is simply not possible in practice.
Whenever you predict something you first have to measure the initial state. Then you use the model to predict the outcome. However every measurement has only finite precision, which means there is always a margin of error for the initial state and therefore there is a margin of error on the predicted outcome. If small margins of error on the initial state lead to small margins of error on the outcome the system is well behaived and predicting the outcome is possible. Otherwise the system is chaotic and it is impossible to predict the outcome, no matter how precisely measured the initial state was.
In both cases you can actually perfectly predict the outcome if the initial state was perfectly known but perfectly knowing the initial state is simply not possible in practice.
You understand it, you just don’t have the final step.
If you had perfect precision data from perfect detail sensors, you could use an infinitely powerful simulation to predict the future. We cannot get any of these things in the real world.
It’s not just “We just lack necessary detail”, but “We can’t actually get enough detail to go past educated guesses and estimates.”
I might get this slightly wrong. It is tempting to conflate complexity with chaos.
Yes, in a very complex system, outcomes will be unpredictable simply because of the amount of factors needed to predict it. This isn’t what chaos theory is about. Rather than complexity, it deals with precision.
We now understand that even fairly simple systems and even in relatively idealized settings (say a computer simulation), there are systems whose outcome over time vary by a lot even with very minute changes in inputs. This is what chaos theory is about. It adds another dimension to unpredictability.
Before chaos theory, there was the idea that given enough input, systems could be predicted long term, ie their outcomes would “converge” and predictions would be reliable and stable. In this situation, giving more precise input would only improve accuracy but not markedly affect the outcome.
An example would be given some speed, we could calculate the arrival time for a certain distance travelled. The more accurate the measure of speed, the greater the precision of the arrival time prediction – but overall we can estimate the error of our prediction based on the uncertainty of the measure of speed. This is broadly not true of chaotic systems.
Whenever you predict something you first have to measure the initial state. Then you use the model to predict the outcome. However every measurement has only finite precision, which means there is always a margin of error for the initial state and therefore there is a margin of error on the predicted outcome. If small margins of error on the initial state lead to small margins of error on the outcome the system is well behaived and predicting the outcome is possible. Otherwise the system is chaotic and it is impossible to predict the outcome, no matter how precisely measured the initial state was.
In both cases you can actually perfectly predict the outcome if the initial state was perfectly known but perfectly knowing the initial state is simply not possible in practice.
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