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
To get all the data to make a calculation you’d have to consider everything from quantum level. And quantum level is a level at which outcomes exist in a probability.
Take radioactive decay for example. A single atom that is unstable might decay instantly or never. There is absolutely no saying when it will break down. However if you take lots of radioactive material, the decay will be predictable. Consider a crowd of people, one person might never cough, but a in a crowd big enough there will always be some coughing.
So if we consider from this perspective, that this decay does affect the behavior of a bigger system, such as what elements some planet might be composed of. Since radioactive decay releases energy it reduces the mass of that planet. You’d have to consider everything from the level of a single atom decaying. Since fundamentally that atom’s decay can not be predicted, you can never actually be sure of the mass of a planet at any point. You could map it at a single point of time, but further from that point you go in time more your uncertanty grows. Since the mass of the planet affects it’s orbiting behavior, given enough time and radioactive decay, even if you could predict the behavior of that body, you could only predict it’s behavior in that state as it was. Given enough time, these errors in your ability to estimate things will acumulate to a degree where you can’t know anything anymore at a big scale.
Here is a mindfuck for you to think in bed. Since nothing says that an radioactive element has to decayse, there can be a sitaution where for a moment none of the decay. So that would mean that nuclera fission would for that moment just stop. That means that a fluoerescnet dials on your watch with Tritium in them, could just stop glowing for a moment. This obviously will never happen, but universe allows for this to happen. So how can you be sure that this will not happen?
To get all the data to make a calculation you’d have to consider everything from quantum level. And quantum level is a level at which outcomes exist in a probability.
Take radioactive decay for example. A single atom that is unstable might decay instantly or never. There is absolutely no saying when it will break down. However if you take lots of radioactive material, the decay will be predictable. Consider a crowd of people, one person might never cough, but a in a crowd big enough there will always be some coughing.
So if we consider from this perspective, that this decay does affect the behavior of a bigger system, such as what elements some planet might be composed of. Since radioactive decay releases energy it reduces the mass of that planet. You’d have to consider everything from the level of a single atom decaying. Since fundamentally that atom’s decay can not be predicted, you can never actually be sure of the mass of a planet at any point. You could map it at a single point of time, but further from that point you go in time more your uncertanty grows. Since the mass of the planet affects it’s orbiting behavior, given enough time and radioactive decay, even if you could predict the behavior of that body, you could only predict it’s behavior in that state as it was. Given enough time, these errors in your ability to estimate things will acumulate to a degree where you can’t know anything anymore at a big scale.
Here is a mindfuck for you to think in bed. Since nothing says that an radioactive element has to decayse, there can be a sitaution where for a moment none of the decay. So that would mean that nuclera fission would for that moment just stop. That means that a fluoerescnet dials on your watch with Tritium in them, could just stop glowing for a moment. This obviously will never happen, but universe allows for this to happen. So how can you be sure that this will not happen?
To get all the data to make a calculation you’d have to consider everything from quantum level. And quantum level is a level at which outcomes exist in a probability.
Take radioactive decay for example. A single atom that is unstable might decay instantly or never. There is absolutely no saying when it will break down. However if you take lots of radioactive material, the decay will be predictable. Consider a crowd of people, one person might never cough, but a in a crowd big enough there will always be some coughing.
So if we consider from this perspective, that this decay does affect the behavior of a bigger system, such as what elements some planet might be composed of. Since radioactive decay releases energy it reduces the mass of that planet. You’d have to consider everything from the level of a single atom decaying. Since fundamentally that atom’s decay can not be predicted, you can never actually be sure of the mass of a planet at any point. You could map it at a single point of time, but further from that point you go in time more your uncertanty grows. Since the mass of the planet affects it’s orbiting behavior, given enough time and radioactive decay, even if you could predict the behavior of that body, you could only predict it’s behavior in that state as it was. Given enough time, these errors in your ability to estimate things will acumulate to a degree where you can’t know anything anymore at a big scale.
Here is a mindfuck for you to think in bed. Since nothing says that an radioactive element has to decayse, there can be a sitaution where for a moment none of the decay. So that would mean that nuclera fission would for that moment just stop. That means that a fluoerescnet dials on your watch with Tritium in them, could just stop glowing for a moment. This obviously will never happen, but universe allows for this to happen. So how can you be sure that this will not happen?
The nature of complex systems is such that they change themselves over time. the combinatorial complexity of these systems explodes the more you try to take into account this feedback in the system.
If you try to model systems beyond a certain level of complexity you run into a hard limit: it would take more computing power to make a prediction than could exist even if the entire universe itself was made into a computer to perform this computation and was running this computation for billions of years. In order to make it both *feasible* and *viable* to simulate things with computation we need to dramatically reduce the combinatorial complexity of the system.
The nature of complex systems is such that they change themselves over time. the combinatorial complexity of these systems explodes the more you try to take into account this feedback in the system.
If you try to model systems beyond a certain level of complexity you run into a hard limit: it would take more computing power to make a prediction than could exist even if the entire universe itself was made into a computer to perform this computation and was running this computation for billions of years. In order to make it both *feasible* and *viable* to simulate things with computation we need to dramatically reduce the combinatorial complexity of the system.
The nature of complex systems is such that they change themselves over time. the combinatorial complexity of these systems explodes the more you try to take into account this feedback in the system.
If you try to model systems beyond a certain level of complexity you run into a hard limit: it would take more computing power to make a prediction than could exist even if the entire universe itself was made into a computer to perform this computation and was running this computation for billions of years. In order to make it both *feasible* and *viable* to simulate things with computation we need to dramatically reduce the combinatorial complexity of the system.
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.
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.
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.
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.
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