Bayes and Paradigm Shifts—or being wrong af
So I’ve been thinking about Bayesian probability and paradigm shifts. One of the early examples that Price published after discovering Bayes’ theorem (after Bayes died) was of someone who, upon awakening for the first time with no other information on cosmology, if they knew Bayes theorem, could then update their probability that the sun would rise again the next day, each day they saw it rise again. So with time, as they see the sun rise more and more times, they become more and more ‘certain’ that it will rise again the next day (ie their priors become higher).
However, not having any knowledge of the universe or physics, they are unaware that there is a near certainty that this sun will someday supernova and no longer rise again. If they made thousands of generations of sun tracking bayesians, every day they would see the sun rise and update their probability, and become more certain that it would rise again. By the time it didn’t rise, they would be wildly certain that it would rise again. So the more certain they became, actually the more WRONG they became. That sun was always almost certainly doomed at the same 99.999....% level the whole time (maybe not to each given new day, but eventually) and they just didn’t have access to good enough priors to recognize this.
So as a result of bad priors, they are maybe increasing their accuracy relative to any given day (the sun only dies on 1 in a billion days) but decreasing their accuracy of it’s eventual transformation into a black hole or some such phenomena which will likely kill the shit out of them.
I think this kind of misinformed search for accuracy is very symbolic of a bayesian look at paradigm shifts (even as it could also b used as a limited critique of bayesian statistics). Once they get access to just the knowledge that other stars exist, it opens up a huge range of other variables they didn’t know about in the calculation of their priors. So while we’re chugging along in our search for accuracy, we may be building relative accuracy, while building absolute an error until our paradigm catches up with a new and deeper layer of information.