Dreams with Damaged Priors

Dream­ing is the clos­est I’ve got­ten to test­ing my­self against the challenge of main­tain­ing ra­tio­nal­ity un­der brain dam­age. So far, my tri­als have ex­hibited mixed re­sults.

In one mem­o­rable dream a few years ago, I dreamed that the Wall Street Jour­nal had pub­lished an ar­ti­cle about “Eliezer Yud­kowsky”, but it wasn’t me, it was a differ­ent “Eliezer Yud­kowsky”, and in the dream I won­dered if I needed to write a let­ter to clar­ify this. Then I re­al­ized I was dream­ing within the dream… and wor­ried to my­self, still dream­ing: “But what if the Wall Street Jour­nal re­ally does have an ar­ti­cle about an ‘Eliezer Yud­kowsky’ who isn’t me?”

But then I thought: “Well, the prob­a­bil­ity that I would dream about a WSJ ar­ti­cle like that, given that a WSJ ar­ti­cle like that ac­tu­ally ex­ists in this morn­ing’s pa­per, is the same as the prob­a­bil­ity that I would have such a dream, given that no such ar­ti­cle is in this morn­ing’s pa­per. So by Bayes’s The­o­rem, the dream isn’t ev­i­dence one way or the other. Thus there’s no point in try­ing to guess the an­swer now—I’ll find out in the morn­ing whether there’s an ar­ti­cle like that.” And, satis­fied, my mind went back to or­di­nary sleep.

I find it fas­ci­nat­ing that I was able to ex­plic­itly ap­ply Bayes’s The­o­rem in my sleep to cor­rectly com­pute the 1:1 like­li­hood ra­tio, but my dream­ing mind didn’t no­tice the dam­aged prior—didn’t no­tice that the prior prob­a­bil­ity of such a WSJ ar­ti­cle was too low to jus­tify rais­ing the hy­poth­e­sis to my at­ten­tion.

At this point even I must con­cede that there is some­thing to the com­plaint that, in real-world ev­ery­day life, Bayesi­ans dis­pense too lit­tle ad­vice about how to com­pute pri­ors. With a dam­aged in­tu­ition for the weight of ev­i­dence, my dream­ing mind was able to ex­plic­itly com­pute a like­li­hood ra­tio and cor­rect it­self. But with a dam­aged in­tu­ition for the prior prob­a­bil­ity, my mind didn’t suc­cess­fully check it­self, or even no­tice a prob­lem—didn’t get as far as ask­ing “But what is the prior prob­a­bil­ity?”

On July 20 I had an even more dra­matic dream—spark­ing this es­say—when I dreamed that I’d googled my own name and dis­cov­ered that one of my OBLW ar­ti­cles had been trans­lated into Ger­man and pub­lished, with­out per­mis­sion but with at­tri­bu­tion, in a spe­cial is­sue of the Jour­nal of Ap­plied Logic to com­mem­o­rate the death of Richard Thaler (don’t worry, he is in fact still al­ive)...

Then I half woke-up… and won­dered if maybe one of my OBLW ar­ti­cles re­ally had been “bor­rowed” this way. But I rea­soned, in my half-awake state, that the dream couldn’t be ev­i­dence be­cause it didn’t form part of a causal chain wherein the out­side en­vi­ron­ment im­pressed it­self onto my brain, and that only ac­tual sen­sory im­pres­sions of Google re­sults could form the base of a le­gi­t­i­mate chain of in­fer­ences.

So—still half-asleep—I wanted to get out of bed and ac­tu­ally look at Google, to see if a re­sult turned up for the Jour­nal of Ap­plied Logic is­sue.

And sev­eral times I fell back asleep and dreamed I’d looked at Google and seen the re­sult; but each time on half-awak­ing I thought: “No, I still seem to be in bed; that was a dream, not a sense-im­pres­sion, so it’s not valid ev­i­dence—I still need to ac­tu­ally look at Google.” And the cy­cle con­tinued.

By the time I woke up en­tirely, my brain had fully switched on and I re­al­ized that the prior prob­a­bil­ity was tiny; and no, I did not bother to check the ac­tual Google re­sults. Though I did Google to check whether Richard Thaler was al­ive, since I was le­gi­t­i­mately un­sure of that when I started writ­ing this post.

If my dream­ing brain had been talk­ing in front of an au­di­ence, that au­di­ence might have ap­plauded the in­tel­li­gent-sound­ing so­phis­ti­cated rea­son­ing about what con­sti­tuted ev­i­dence—which was even cor­rect, so far as it went. And yet my half-awake brain didn’t no­tice that at the base of the whole is­sue was a big com­pli­cated spe­cific hy­poth­e­sis whose prior prob­a­bil­ity fell off a cliff and van­ished. Eliez­erDream­ing didn’t try to mea­sure the length of the mes­sage, tot up the weight of bur­den­some de­tails, or even ex­plic­itly ask, “What is the prior prob­a­bil­ity?”

I’d mused be­fore that the state of be­ing re­li­gious seemed similar to the state of be­ing half-asleep. But my re­cent dream made me won­der if the anal­ogy re­ally is a deep one. In­tel­li­gent the­ists can of­ten be shep­herded into ad­mit­ting that their ar­gu­ment X is not valid ev­i­dence. In­tel­li­gent the­ists of­ten con­fess ex­plic­itly that they have no sup­port­ing ev­i­dence—just like I ex­plic­itly re­al­ized that my dreams offered no ev­i­dence about the ac­tual Wall Street Jour­nal or the Jour­nal of Ap­plied Logic. But then they stay “half-awake” and go on won­der­ing whether the dream hap­pens to be true. They don’t “wake up com­pletely” and re­al­ize that, in the ab­sence of ev­i­dence, the whole thing has a prior prob­a­bil­ity too low to de­serve spe­cific at­ten­tion.

My dream­ing brain can, in its sleep, rea­son ex­plic­itly about like­li­hood ra­tios, Bayes’s The­o­rem, cog­ni­tive chains of causal­ity, per­mis­si­ble in­fer­ences, strong ar­gu­ments and non-ar­gu­ments. And yet still main­tain a dream­ing in­abil­ity to rea­son­ably eval­u­ate pri­ors, to no­tice bur­den­some de­tails and sheer ridicu­lous­ness. If my dream­ing brain’s be­hav­ior is a true product of dis­so­ci­a­tion—of brain­ware mod­ules or soft­ware modes that can be in­de­pen­dently switched on or off—then the anal­ogy to re­li­gion may be more than sur­face similar­ity.

Con­versely it could just be a mat­ter of habits play­ing out in in my dream­ing self; that I ha­bit­u­ally pay more at­ten­tion to ar­gu­ments than pri­ors, or ha­bit­u­ally eval­u­ate ar­gu­ments de­liber­ately but pri­ors in­tu­itively.