In that case, I’d say that your response involves special pleading. SI priors are uncomputable. If the fine structure constant is uncomputable, then any uncomputable prior that assigns probability 1 to the constant having its actual value will beat SI in the long run. What is illicit about the latter sort of uncomputable prior that doesn’t apply to SI priors? Or am I simply confused somehow? (I’m certainly no expert on this subject.)
SI belongs to a class of priors that could be described as “almost computable” in a certain technical sense. The term is lower-semicomputable semimeasure. An interesting thing about SI is that it’s also optimal (up to a constant) within its own class, not just better than all puny computable priors. The uncomputable prior you mention does not belong to that class, in some sense it’s “more uncomputable” than SI.
When people talk about the impossibility of “winning” against SI, they usually mean it’s impossible to win by more than a constant in the long run.
In that case, I’d say that your response involves special pleading. SI priors are uncomputable. If the fine structure constant is uncomputable, then any uncomputable prior that assigns probability 1 to the constant having its actual value will beat SI in the long run. What is illicit about the latter sort of uncomputable prior that doesn’t apply to SI priors? Or am I simply confused somehow? (I’m certainly no expert on this subject.)
SI belongs to a class of priors that could be described as “almost computable” in a certain technical sense. The term is lower-semicomputable semimeasure. An interesting thing about SI is that it’s also optimal (up to a constant) within its own class, not just better than all puny computable priors. The uncomputable prior you mention does not belong to that class, in some sense it’s “more uncomputable” than SI.