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>How does "hyper-determinism" differ from "determinism"? It's the difference between a trajectory that looks like Brownian motion consisting of a preprogrammed

>How does "hyper-determinism" differ from "determinism"? It's the difference between a trajectory that looks like Brownian motion consisting of a preprogrammed constant function, versus actually being sampled from a Wiener Process. In the former case, if you know the function, you can predict the trajectory with total certainty. In the latter case, if you use the Wiener Process as a model, you can predict the trajectory probabilistically.

jamesrcole 10y ago
I'm not familiar with those concepts (like Wiener Process), but I don't think notions of predictability should be mixed up with notions of determinism. Whether something is predictable or not does not change how deterministic it is.
- eli_gottlieb 10y ago
  I think what I have to say, then, is welcome to quantum mechanics. Or, in fact, welcome to probability theory. Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world. An interesting question is: how could a fully deterministic ontology give rise to beings capable of having probabilistic beliefs? Worse, how can a fully deterministic ontology give rise to truly random mathematical entities like Chaitin's Omega? In fact, in such a universe, where do the bits for atomic random-number generators come from? After all, if they're not really random, there should be some deterministic model capable of predicting them, and yet, quantum mechanics tells us precisely that such a thing is impossible. You can try to have a Bayesian epistemology with a nonstochastic ontology, but it doesn't really make sense. Just let your ontology be stochastic: then and only then you can physically account for both physical randomness and probabilistic belief.
  - jamesrcole 10y ago
    > I think what I have to say, then, is welcome to quantum mechanics. Or, in fact, welcome to probability theory. Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world. I'm not talking about randomness. I'm talking about determinism, and as far as I can see what you're saying says nothing about determinism or differing degrees of determinism. > An interesting question is: how could a fully deterministic ontology give rise to beings capable of having probabilistic beliefs? I don't see that as a problem at all. It fits completely fine with the idea that probability is a matter of lack of knowledge. > Worse, how can a fully deterministic ontology give rise to truly random mathematical entities like Chaitin's Omega? In fact, in such a universe, where do the bits for atomic random-number generators come from? After all, if they're not really random, there should be some deterministic model capable of predicting them, and yet, quantum mechanics tells us precisely that such a thing is impossible. You're talking like it's already a settled matter as to whether reality is fundamentally deterministic or not. Are you saying that there's definitive proof that deterministic accounts of QM are incorrect?
    - dpark 10y ago
      > I'm not talking about randomness. I'm talking about determinism The difference being?
      - jamesrcole 10y ago
        The person I was replying to said "Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world." This is because randomness can be seen as a matter of incomplete knowledge. Determinism is independent of our knowledge. Now, perhaps there is randomness that is independent of our knowledge. But I was talking about randomness/determinism in the context of the quoted statement, which was a matter of knowledge.
        10y ago

jamesrcole 10y ago

I'm not familiar with those concepts (like Wiener Process), but I don't think notions of predictability should be mixed up with notions of determinism. Whether something is predictable or not does not change how deterministic it is.

eli_gottlieb 10y ago
I think what I have to say, then, is welcome to quantum mechanics. Or, in fact, welcome to probability theory. Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world. An interesting question is: how could a fully deterministic ontology give rise to beings capable of having probabilistic beliefs? Worse, how can a fully deterministic ontology give rise to truly random mathematical entities like Chaitin's Omega? In fact, in such a universe, where do the bits for atomic random-number generators come from? After all, if they're not really random, there should be some deterministic model capable of predicting them, and yet, quantum mechanics tells us precisely that such a thing is impossible. You can try to have a Bayesian epistemology with a nonstochastic ontology, but it doesn't really make sense. Just let your ontology be stochastic: then and only then you can physically account for both physical randomness and probabilistic belief.
- jamesrcole 10y ago
  > I think what I have to say, then, is welcome to quantum mechanics. Or, in fact, welcome to probability theory. Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world. I'm not talking about randomness. I'm talking about determinism, and as far as I can see what you're saying says nothing about determinism or differing degrees of determinism. > An interesting question is: how could a fully deterministic ontology give rise to beings capable of having probabilistic beliefs? I don't see that as a problem at all. It fits completely fine with the idea that probability is a matter of lack of knowledge. > Worse, how can a fully deterministic ontology give rise to truly random mathematical entities like Chaitin's Omega? In fact, in such a universe, where do the bits for atomic random-number generators come from? After all, if they're not really random, there should be some deterministic model capable of predicting them, and yet, quantum mechanics tells us precisely that such a thing is impossible. You're talking like it's already a settled matter as to whether reality is fundamentally deterministic or not. Are you saying that there's definitive proof that deterministic accounts of QM are incorrect?
  - dpark 10y ago
    > I'm not talking about randomness. I'm talking about determinism The difference being?
    - jamesrcole 10y ago
      The person I was replying to said "Mathematically, there's no difference between a process which can only be predicted probabilistically, and a process which really is random; no difference between incomplete knowledge in your head and stochasticity in the world." This is because randomness can be seen as a matter of incomplete knowledge. Determinism is independent of our knowledge. Now, perhaps there is randomness that is independent of our knowledge. But I was talking about randomness/determinism in the context of the quoted statement, which was a matter of knowledge.
      - 10y ago