Constant2 comments on Explainers Shoot High. Aim Low! - Less Wrong

40 Post author: Eliezer_Yudkowsky 24 October 2007 01:13AM

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Comment author: Constant2 24 October 2007 12:40:30PM 0 points [-]

the only sensible prior may be determined by those symmetries, and that in such cases you can save some mental effort by just talking about the symmetries

Okay, but that's really just treating other views of probability as convenient fictions, which isn't quite what I was hoping for.

I do not believe that the subjective interpretation of probability is a good match for the application of probability to the analysis of events that have already occurred. Conduct an experiment, observe (say) a normal distribution in some variable. That we subjectively expected a normal distribution prior to the run of the experiment, or that we now expect it in future runs, is all well and good, but it is not our expectation that accounts for the actual appearance of the normal distribution itself. If anything accounts for the actual appearance of a normal distribution, it is some property of the experimental setup, rather than an expectation of ours.

I am not denying that you can go ahead and talk about our degree of belief and the unique rational way to update that degree of belief. I think that's a perfectly legitimate topic. What I find unconvincing is the idea is that that's all that we can profitably apply the probability calculus to. I did google "bayesian quantum" and didn't find anything that answered my concern, though I did find assertions of the very position that I have a problem with. I don't deny that you can approach quantum mechanics from a bayesian perspective - obviously your beliefs can be informed by quantum mechanics and you can have beliefs about the results of experiments and so on; I simply think it leaves something out, because at the end we have not only our own belief about the result of the next quantum experiment to arrive at rationally based on our priors in combination with experiments we have observed, but also actual observed frequencies of past quantum experiments, and these are out there, they are not subjective, and the mathematical theory of probability strongly recommends itself as a tool in the analysis of the observed frequencies.