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Generally the defining feature of non linear mechanisms is that the long term behaviour is non-intuitive. I'd expect that to include not having a predictable me

by 8note 5y ago

Generally the defining feature of non linear mechanisms is that the long term behaviour is non-intuitive. I'd expect that to include not having a predictable mean

godelski 5y ago
Non intuitive doesn't mean not predictable. Nor does chaos. Chaos just means that a small perturbation in input parameters can result in a large change in the output. So to have good predictive power you need to pick good inputs with good accuracy. But chaos is also a spectrum so not all chaotic systems are as sensitive as others.
- avianlyric 5y ago
  Chaos is also different at different scales. At certain point chaos can be simulated as noise with a known distribution. You can’t make predictions within the noise, but you can describe the shape of the noise and it’s impact on macro scale systems. Perfect example of this is quantum effects. Zoom in far enough and quantum effects make the world entirely unpredictable, and yet I can still accurately predict where I throw is going to land with no knowledge of quantum effects. That doesn’t mean those effects don’t influence the ball, it just that noisy chaos of those influences is tightly bound enough that it doesn’t matter. Newtonian physics is enough to make a prediction, despite being an incomplete description of the physical system at play.
  - godelski 5y ago
    But different noises do different things and have different predictive powers. I think your statements about these systems being impossible to calculate are too strong. We use gaussian noise all the time. In fact there's plenty of machine learning models that use noise and change of variables (we learn the transforms) to represent different distributions. Ones that do actually have good clustering. We can be predictive in these domains. Chaos and randomness don't make inference impossible. This is the 21st century, we're not beholden to Newton nor to deterministic processes.
    - avianlyric 5y ago
      I think we in perfect agreement here. Like I said in my comment, we can accurately describe the shape of noise, and that’s incredibly useful for making predictions. But we can’t make absolute deterministic predictions within the noise. I.e. we can say thing X has a 90% probability of happening. But we can’t say thing X will happen. And of course a strong probabilistic prediction is incredibly powerful and useful. I don’t want to suggest that it isn't, but it’s not an absolute prediction. And once again usefulness of a probabilistic prediction is almost always as useful as an absolute prediction (I would also argue that absolute prediction don’t really exist in the real world, they’re just extremely high confidence probabilistic predictions, but you haven’t bothered to model the actual noise).

by 8note 5y ago

Generally the defining feature of non linear mechanisms is that the long term behaviour is non-intuitive. I'd expect that to include not having a predictable mean

godelski 5y ago

Non intuitive doesn't mean not predictable. Nor does chaos. Chaos just means that a small perturbation in input parameters can result in a large change in the output. So to have good predictive power you need to pick good inputs with good accuracy. But chaos is also a spectrum so not all chaotic systems are as sensitive as others.

avianlyric 5y ago
Chaos is also different at different scales. At certain point chaos can be simulated as noise with a known distribution. You can’t make predictions within the noise, but you can describe the shape of the noise and it’s impact on macro scale systems. Perfect example of this is quantum effects. Zoom in far enough and quantum effects make the world entirely unpredictable, and yet I can still accurately predict where I throw is going to land with no knowledge of quantum effects. That doesn’t mean those effects don’t influence the ball, it just that noisy chaos of those influences is tightly bound enough that it doesn’t matter. Newtonian physics is enough to make a prediction, despite being an incomplete description of the physical system at play.
- godelski 5y ago
  But different noises do different things and have different predictive powers. I think your statements about these systems being impossible to calculate are too strong. We use gaussian noise all the time. In fact there's plenty of machine learning models that use noise and change of variables (we learn the transforms) to represent different distributions. Ones that do actually have good clustering. We can be predictive in these domains. Chaos and randomness don't make inference impossible. This is the 21st century, we're not beholden to Newton nor to deterministic processes.
  - avianlyric 5y ago
    I think we in perfect agreement here. Like I said in my comment, we can accurately describe the shape of noise, and that’s incredibly useful for making predictions. But we can’t make absolute deterministic predictions within the noise. I.e. we can say thing X has a 90% probability of happening. But we can’t say thing X will happen. And of course a strong probabilistic prediction is incredibly powerful and useful. I don’t want to suggest that it isn't, but it’s not an absolute prediction. And once again usefulness of a probabilistic prediction is almost always as useful as an absolute prediction (I would also argue that absolute prediction don’t really exist in the real world, they’re just extremely high confidence probabilistic predictions, but you haven’t bothered to model the actual noise).