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.