# Beauty bias: “Lost in Math” by Sabine Hossenfelder

This is tech­ni­cally just a link post for those who didn’t see the book yet. The main idea, as I un­der­stand it, is that while some phys­i­cal the­o­ries are beau­tiful, other are com­plex and “ugly”. Beauty should not be taken as ev­i­dence for truth.

It looks like some­times in AI safety re­search aes­thet­ics may be taken as an ev­i­dence (I will not provide ex­am­ples, as in each case it may be just my in­ter­pre­ta­tion), and thus pos­si­bil­ity of such beauty bias should be taken into ac­count.

• “Beauty should not be taken as ev­i­dence for truth.”

Shouldn’t it? Isn’t tak­ing “beauty” as ev­i­dence just a way of phras­ing Oc­cam’s ra­zor?

• Beauty is a hint and an in­spira­tion, not ev­i­dence. Some­times it guides you some place use­ful, and some­times it leads you com­pletely astray. Like it has with the String The­ory and countless unified field the­o­ries.

• Yes, but there is a prob­lem of what I called “me­dian com­plex­ity of the world de­scrip­tions”, which is prob­a­bly an­swered some­where but I don’t know where to look.

In other words, Oc­cam ra­zor doesn’t mean that the sim­plest ex­pla­na­tion is true. It means that the sim­pler ex­pla­na­tions are more prob­a­ble to be true than more com­plex ones. The differ­ence be­tween the two defi­ni­tions is the way how the truth is dis­tributed over com­plex­ity of the ex­pla­na­tions.

In the first case, the dis­tri­bu­tion is very steep, so the sim­plest ex­pla­na­tion is more prob­a­ble than all more com­plex ex­pla­na­tion com­bined. In the sec­ond case, the truth(com­plex­ity) func­tion de­clines slowly, so may be first 100 ex­pla­na­tions com­bined have 0.5 prob­a­bil­ity, - in that case, it is un­likely that the sim­plest ex­pla­na­tion will be true.

• This ar­ti­cle on Solomonoff in­duc­tion goes over a lot of the re­lated con­sid­er­a­tions.

• Yes, it is a good post, but doesn’t cover the prob­lem of me­dian com­plex­ity di­rectly.

• Sure, but the fact that the prob­a­bil­ity dis­tri­bu­tion is skewed in fa­vor of sim­pler (i.e. more “beau­tiful”) ex­pla­na­tions by Oc­cam’s Ra­zor is equiv­a­lent to say­ing that there should be such a bias—af­ter all, bias is es­sen­tially just a skew­ing of one’s prob­a­bil­ity func­tion. Of course this bias shouldn’t be taken to the ex­treme of as­sum­ing that just be­cause one hy­poth­e­sis is more beau­tiful than oth­ers, it au­to­mat­i­cally qual­ifies as the cor­rect ex­pla­na­tion. But dis­cred­it­ing such an ex­treme mind­set doesn’t mean that a mild bias in fa­vor of “beauty” is dis­cred­ited.

• Haven’t read the book, but her blog is one of half a dozen sites I fol­low reg­u­larly. It talks about how push­ing for sub­jec­tive “beauty” over other con­sid­er­a­tions is not the most use­ful ap­proach.