Oh hey, are you trying to say that I got too overly invested in my own extended metaphor? Because that never happens to me. *rolls eyes at self* Okay, fine, you're right, that's kind of embarrassing. D, my husband (whom I should pressure to get a DW account so he can join in directly), also argued strongly for your point of view, pointing out that repeatability and predictability (and probably locality helps too) of a universe should be sufficient for some system of mathematics to be structured that describes it.
But in terms of Wigner's point, I still don't quite understand philosophically why it should be possible to design a mathematical system that regularly does have non-consciously-designed correspondences with physics (complex numbers; matrices -- I should say that D argued against this example because linear systems are sort of an obvious generalization, but I still like it because it doesn't seem obvious to me that it should be a good way to describe discrete quantum systems; group theory...). I tend to like to think that the universe is in fact based on something like a mathematical structure, but of course there are other explanations (a tendency to further develop branches of mathematics that have some empirical correspondences; selection bias by Wigner and me; perhaps even if the universe isn't based on mathematical structure, it's based on forms that reappear; etc.)
Sure, improbable events are "surprising" when they occur because any one person's experience is restricted to being a particular instantiation of a probability distribution, even if theoretically we understand the law of large numbers applies globally to a large population. And I think you're saying -- the same sort of thing for any of the explanations given above: they provide a global mechanism for which the correspondences may be surprising locally but make sense in the context of the mechanism. Now, I think it's mysterious (in a way that statistics is not) in the sense that I think there can be debate about the proper interpretation, whereas I don't think there's any debate about improbable events -- but I agree, not in the sense of not having an explanation.
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timeasmymeasure
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Date: 2013-01-13 05:36 am (UTC)But in terms of Wigner's point, I still don't quite understand philosophically why it should be possible to design a mathematical system that regularly does have non-consciously-designed correspondences with physics (complex numbers; matrices -- I should say that D argued against this example because linear systems are sort of an obvious generalization, but I still like it because it doesn't seem obvious to me that it should be a good way to describe discrete quantum systems; group theory...). I tend to like to think that the universe is in fact based on something like a mathematical structure, but of course there are other explanations (a tendency to further develop branches of mathematics that have some empirical correspondences; selection bias by Wigner and me; perhaps even if the universe isn't based on mathematical structure, it's based on forms that reappear; etc.)
Sure, improbable events are "surprising" when they occur because any one person's experience is restricted to being a particular instantiation of a probability distribution, even if theoretically we understand the law of large numbers applies globally to a large population. And I think you're saying -- the same sort of thing for any of the explanations given above: they provide a global mechanism for which the correspondences may be surprising locally but make sense in the context of the mechanism. Now, I think it's mysterious (in a way that statistics is not) in the sense that I think there can be debate about the proper interpretation, whereas I don't think there's any debate about improbable events -- but I agree, not in the sense of not having an explanation.