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MrHen comments on A Request for Open Problems - Less Wrong
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Comments (104)
See Wikipedia's list for a few examples.
The distinction between clearly defined and otherwise is somewhat subjective. I have not heard anyone talking about the subject yet, so brought it up.
Since Rationality seems to be strongly related to Bayes' theorem, it makes some sense that a lot of problems could be presented in a fashion where we only have to answer a few questions about priors to understand which actions to take.
I don't know if this answers your question.
It's the best possible kind of answer to my question - a link to a load of interesting stuff - thanks!
I see where I went wrong, in missing out the entire physical universe as a source of questions that can be clearly stated but are about real things rather than mathematical descriptions of them.