In real life I think a similar situation holds. First we have to make a distinction between a system having randomness; a completely unpredictable outcome and being chaotic; where the outcome is theoretically predictable but varies significantly with even tiny changes in input.
Yes, thank you for putting it so nicely into words. I was already aware of that distinction.
I’m studying physics right now and trying to organize my thoughts around that. I remember we talked about some mechanical contraption that exhibits non-deterministic (i.e. purely random) behavior due to the equations of motion having non-unique solution. If I remember correctly, it was a kind of “knife standing on its tip right at the edge of a cliff”-edge condition. There’s two solutions to that: It stands still or it falls down. There’s two distinctly different solutions because the equations of motion are non-continuous, i.e. even for the tiniest change in position, the net force changes from 0 to 1g.
Apart from that, there’s some more “pure random” stuff that I’m investigating into right now, like quantum stuff (as you mentioned). But there’s at least one more example that I’d like to think about:
A human/robot cannot fully predict their own future. That is because if they could, they could become aware of it and decidedly act against it. For example, if I predict that I will eat an avocado tomorrow, I might stop myself from doing that. So the prediction becomes wrong. In a certain sense, therefore one cannot predict their own actions. This isn’t due to a lack in accuracy, but it’s fundamentally impossible. I guess. Let me hear your thoughts! Your words are calm and collected; you seem to know stuff.
As I said, it’s an interesting question! I think I’ve found a paper describing something like the scenario you mentioned (Dhar, A. (1993). Nonuniqueness in the solutions of Newton’s equation of motion. American Journal of Physics, 61(1), 58–61. doi:10.1119/1.17411). It’s a apparently shows that for certain conditions (such as the balanced knife you mentioned, or a particle in a field that would accelerate it away from the origin proportionally to it’s distance) Newton’s equations of motion have non-unique solutions, although I confess that the author rather lost me during some of his leaps in mathematics. The discussion section is interesting, a couple of key conclusions stood out to me: ‘In this sense we may say that Newton’s equation has a unique solution even for singular forces like x1/3 but x(0)=0 and derivative(x(0))=0 in such cases do not uniquely specify the initial state.’ and ‘Infinitesimal disturbance in position or velocity will change the state and one of the other solutions will become effective.’
From what I have understood from the paper, the author seems to be mostly pointing out that there are certain conditions under which Newton’s equations do not have a unique solution, but that in reality a deterministic, but chaotic, outcome will occur due to infinitesimal disturbances. Ultimately, no matter how carefully you balance the knife, it’s going to fall over, and the direction it falls will be determined by a multitude of forces rather than pure chance.
@[email protected] has also made a thoughtful reply regarding quantum field theory and it’s implications on determinism, and I need to respond to that too as it’s a fascinating, if baffling, topic.
Your question about predicting your own future is interesting; you’re making the assumption that a prediction must continue to be true after the point at which it is made, but I would suggest that you can resolve the apparent contradiction by considering that any prediction of the future is only true at the instant it is made. After all, if someone else predicted your future, wrote it down, but did not tell you, you would eat the avocado, however seen as you changed the conditions of your future by gaining additional information the result changed. If you predicted your future a second time, directly after having resolved to not eat the avocado, the prediction would have you not eating it.
If we assume the universe is deterministic, and that we have the ability to perfectly replicate it and run that replica forward in time without time passing in our universe it would seem that we could accurately predict the future of our universe just be seeing what happened in the replica. However, that would involve the replica creating it’s own replica as it would evolve in exactly the same way as our universe. That replica would create it’s own replica, and so on. I’m not quite sure of what the implications of that are, and it’s late here, so I’m going to have to call it a night, but if if could be done it would be a clear way to distinguish between a random or non-deterministic universe and a chaotic one. If the predictions sometimes proved incorrect it would suggest true randomness rather than just a chaotic system.
Yes, thank you for putting it so nicely into words. I was already aware of that distinction.
I’m studying physics right now and trying to organize my thoughts around that. I remember we talked about some mechanical contraption that exhibits non-deterministic (i.e. purely random) behavior due to the equations of motion having non-unique solution. If I remember correctly, it was a kind of “knife standing on its tip right at the edge of a cliff”-edge condition. There’s two solutions to that: It stands still or it falls down. There’s two distinctly different solutions because the equations of motion are non-continuous, i.e. even for the tiniest change in position, the net force changes from 0 to 1g.
Apart from that, there’s some more “pure random” stuff that I’m investigating into right now, like quantum stuff (as you mentioned). But there’s at least one more example that I’d like to think about:
A human/robot cannot fully predict their own future. That is because if they could, they could become aware of it and decidedly act against it. For example, if I predict that I will eat an avocado tomorrow, I might stop myself from doing that. So the prediction becomes wrong. In a certain sense, therefore one cannot predict their own actions. This isn’t due to a lack in accuracy, but it’s fundamentally impossible. I guess. Let me hear your thoughts! Your words are calm and collected; you seem to know stuff.
As I said, it’s an interesting question! I think I’ve found a paper describing something like the scenario you mentioned (Dhar, A. (1993). Nonuniqueness in the solutions of Newton’s equation of motion. American Journal of Physics, 61(1), 58–61. doi:10.1119/1.17411). It’s a apparently shows that for certain conditions (such as the balanced knife you mentioned, or a particle in a field that would accelerate it away from the origin proportionally to it’s distance) Newton’s equations of motion have non-unique solutions, although I confess that the author rather lost me during some of his leaps in mathematics. The discussion section is interesting, a couple of key conclusions stood out to me: ‘In this sense we may say that Newton’s equation has a unique solution even for singular forces like x1/3 but x(0)=0 and derivative(x(0))=0 in such cases do not uniquely specify the initial state.’ and ‘Infinitesimal disturbance in position or velocity will change the state and one of the other solutions will become effective.’
From what I have understood from the paper, the author seems to be mostly pointing out that there are certain conditions under which Newton’s equations do not have a unique solution, but that in reality a deterministic, but chaotic, outcome will occur due to infinitesimal disturbances. Ultimately, no matter how carefully you balance the knife, it’s going to fall over, and the direction it falls will be determined by a multitude of forces rather than pure chance.
@[email protected] has also made a thoughtful reply regarding quantum field theory and it’s implications on determinism, and I need to respond to that too as it’s a fascinating, if baffling, topic.
Your question about predicting your own future is interesting; you’re making the assumption that a prediction must continue to be true after the point at which it is made, but I would suggest that you can resolve the apparent contradiction by considering that any prediction of the future is only true at the instant it is made. After all, if someone else predicted your future, wrote it down, but did not tell you, you would eat the avocado, however seen as you changed the conditions of your future by gaining additional information the result changed. If you predicted your future a second time, directly after having resolved to not eat the avocado, the prediction would have you not eating it.
If we assume the universe is deterministic, and that we have the ability to perfectly replicate it and run that replica forward in time without time passing in our universe it would seem that we could accurately predict the future of our universe just be seeing what happened in the replica. However, that would involve the replica creating it’s own replica as it would evolve in exactly the same way as our universe. That replica would create it’s own replica, and so on. I’m not quite sure of what the implications of that are, and it’s late here, so I’m going to have to call it a night, but if if could be done it would be a clear way to distinguish between a random or non-deterministic universe and a chaotic one. If the predictions sometimes proved incorrect it would suggest true randomness rather than just a chaotic system.