where you just take the uniform prior over all programs of length T, then let T to infinity
Sure, but because of language-dependence I’m not sure why we would want to apply the principle of indifference at this level. (Note that the quote says “if we can find a privileged parameterization to which we can apply the principle”.) I tend to think you should apply the POI at the “explanatorily basic” level (see here, here), which might be the properties of fundamental objects in the ontology (e.g., position and momentum in Newtonian mechanics, maybe?). Otherwise I think you run into unsatisfying-to-me arbitrariness.
In what sense does the universe have structure, such that a-priori bit strings of observations about the universe ought to be treated by us as more than members of the set of all possible bit strings?
Right, I think this is the kind of question you’re not going to be able to answer without thinking about the kinds of ontological considerations pointed to here.
Thanks!
Sure, but because of language-dependence I’m not sure why we would want to apply the principle of indifference at this level. (Note that the quote says “if we can find a privileged parameterization to which we can apply the principle”.) I tend to think you should apply the POI at the “explanatorily basic” level (see here, here), which might be the properties of fundamental objects in the ontology (e.g., position and momentum in Newtonian mechanics, maybe?). Otherwise I think you run into unsatisfying-to-me arbitrariness.
Right, I think this is the kind of question you’re not going to be able to answer without thinking about the kinds of ontological considerations pointed to here.
Thanks, will change.