A case study in fooling oneself

Note: This post as­sumes that the Oxford ver­sion of Many Wor­lds is wrong, and spec­u­lates as to why this isn’t ob­vi­ous. For a dis­cus­sion of the hy­poth­e­sis it­self, see Prob­lems of the Deutsch-Wal­lace ver­sion of Many Wor­lds.

smk asks how many wor­lds are pro­duced in a quan­tum pro­cess where the out­comes have un­equal prob­a­bil­ities; Emile says there’s no ex­act an­swer, just like there’s no ex­act an­swer for how many ink blots are in the messy pic­ture; Tetro­n­ian says this anal­ogy is a great way to demon­strate what a “wrong ques­tion” is; Emile has (at this writ­ing) 9 up­votes, and Tetro­n­ian has 7.

My the­sis is that Emile has in­stead pro­vided an ex­am­ple of how to dis­miss a ques­tion and thereby fool one­self; Tetro­n­ian pro­vides an ex­am­ple of treat­ing an epistem­i­cally de­struc­tive tech­nique of dis­mis­sal as epistem­i­cally vir­tu­ous and fruit­ful; and the up­votes show that this isn’t just their prob­lem. [edit: Emile and Tetro­n­ian re­spond.]

I am as tired as any­one of the de­bate over Many Wor­lds. I don’t ex­pect the gen­eral cli­mate of opinion on this site to change ex­cept as a re­sult of new in­tel­lec­tual de­vel­op­ments in the larger world of physics and philos­o­phy of physics, which is where the ques­tion will be de­cided any­way. But the mis­sion of Less Wrong is sup­posed to be the re­fine­ment of ra­tio­nal­ity, and so per­haps this “case study” is of in­ter­est, not just as an­other op­por­tu­nity to ar­gue over the in­ter­pre­ta­tion of quan­tum me­chan­ics, but as an op­por­tu­nity to dis­sect a lit­tle bit of ir­ra­tional­ity that is not only play­ing out here and now, but which ev­i­dently has a base of sup­port.

The ques­tion is not just, what’s wrong with the ar­gu­ment, but also, how did it get that base of sup­port? How was a situ­a­tion cre­ated where one per­son says some­thing ir­ra­tional (or fool­ish, or how­ever the prob­lem is best un­der­stood), and a lot of other peo­ple nod in agree­ment and say, that’s an ex­cel­lent ex­am­ple of how to think?

On this oc­ca­sion, my quar­rel is not with the Many Wor­lds in­ter­pre­ta­tion as such; it is with the ver­sion of Many Wor­lds which says there’s no ac­tual num­ber of wor­lds. Else­where in the thread, some­one says there are un­countably many wor­lds, and some­one else says there are two wor­lds. At least those are mean­ingful an­swers (al­though the ad­vo­cate of “two wor­lds” as the an­swer, then goes on to say that one world is “stronger” than the other, which is mean­ingless).

But the propo­si­tion that there is no definite num­ber of wor­lds, is as fool­ish and self-con­tra­dic­tory as any of those other con­tor­tions from the his­tory of thought that ra­tio­nal­ists and ad­vo­cates of com­mon sense like to mock or bog­gle at. At times I have won­dered how to place Less Wrong in the his­tory of thought; well, this is one way to do it—it can have its own chap­ter in the his­tory of in­tel­lec­tual folly; it can be known by its mis­takes.

Then again, this “mis­take” is not origi­nal to Less Wrong. It ap­pears to be one of the defin­ing ideas of the Oxford-based ap­proach to Many Wor­lds as­so­ci­ated with David Deutsch and David Wal­lace; the other defin­ing idea be­ing the pro­posal to de­rive prob­a­bil­ities from ra­tio­nal­ity, rather than vice versa. (I re­fer to the at­tempt to de­rive the Born rule from ar­gu­ments about how to be­have ra­tio­nally in the mul­ti­verse.) The Oxford ver­sion of MWI seems to be very pop­u­lar among thought­ful non-physi­cist ad­vo­cates of MWI—even though I would re­gard both its defin­ing ideas as non­sense—and it may be that its ideas get a pass here, partly be­cause of their so­cial sta­tus. That is, an im­por­tant fac­tion of LW opinion be­lieves that Many Wor­lds is the ex­pla­na­tion of quan­tum me­chan­ics, and the Oxford school of MWI has high sta­tus and high visi­bil­ity within the world of MWI ad­vo­cacy, and so its ideas will re­ceive ap­pro­ba­tion with­out much ex­am­i­na­tion or even much un­der­stand­ing, be­cause of the so­cial and psy­cholog­i­cal mechanisms which in­cline peo­ple to agree with, defend, and laud their fa­vorite au­thor­i­ties, even if they don’t re­ally un­der­stand what these au­thor­i­ties are say­ing or why they are say­ing it.

How­ever, it is un­doubt­edly the case that many of the LW read­ers who be­lieve there’s no definite num­ber of wor­lds, be­lieve this be­cause the idea gen­uinely makes sense to them. They aren’t just string­ing to­gether words whose mean­ing isn’t known, like a Tal­iban who re­cites the Qu­ran with­out know­ing a word of Ara­bic; they’ve ac­tu­ally thought about this them­selves; they have gone through some sub­jec­tive pro­cess as a re­sult of which they have con­sciously adopted this opinion. So from the per­spec­tive of an­a­lyz­ing how it is that peo­ple come to hold ab­surd-sound­ing views, this should be good news. It means that we’re deal­ing with a gen­uine failure to rea­son prop­erly, as op­posed to a sim­ple mat­ter of recit­ing slo­gans or af­firm­ing alle­giance to a view on the ba­sis of some­thing other than thought.

At a guess, the thought pro­cess in­volved is very sim­ple. Th­ese peo­ple have thought about the wave­func­tions that ap­pear in quan­tum me­chan­ics, at what­ever level of tech­ni­cal de­tail they can muster; they have de­cided that the com­po­nents or sub­struc­tures of these wave­func­tions which might be iden­ti­fied as “wor­lds” or “branches” are clearly ap­prox­i­mate en­tities whose defi­ni­tion is some­what ar­bi­trary or sub­ject to con­ven­tion; and so they have con­cluded that there’s no definite num­ber of wor­lds in the wave­func­tion. And the failure in their think­ing oc­curs when they don’t take the next step and say, is this at all con­sis­tent with re­al­ity? That is, if a quan­tum world is some­thing whose ex­is­tence is fuzzy and which doesn’t even have a definite mul­ti­plic­ity—that is, we can’t even say if there’s one, two, or many of them—if those are the prop­er­ties of a quan­tum world, then is it pos­si­ble for the real world to be one of those? It’s the failure to ask that last ques­tion, and re­ally think about it, which must be the over­sight al­low­ing the non­sense-doc­trine of “no definite num­ber of wor­lds” to gain a foothold in the minds of oth­er­wise ra­tio­nal peo­ple.

If this di­ag­no­sis is cor­rect, then at some level it’s a case of “treat­ing the map as the ter­ri­tory” syn­drome. A par­tic­u­lar con­cep­tion of the quan­tum-me­chan­i­cal wave­func­tion is pro­vid­ing the “map” of re­al­ity, and the in­di­vi­d­ual thinker is per­haps mak­ing cor­rect state­ments about what’s on their map, but they are failing to check the prop­er­ties of the map against the prop­er­ties of the ter­ri­tory. In this case, the prop­erty of re­al­ity that falsifies the map is, the fact that it definitely ex­ists, or per­haps the corol­lary of that fact, that some­thing which definitely ex­ists definitely ex­ists at least once, and there­fore ex­ists with a definite, ob­jec­tive mul­ti­plic­ity.

Try­ing to go fur­ther in the di­ag­no­sis, I can iden­tify a few cog­ni­tive ten­den­cies which may be con­tribut­ing. First is the phe­nomenon of bun­dled as­sump­tions which have never been made dis­tinct and ques­tioned sep­a­rately. I sup­pose that in a few peo­ple’s heads, there’s a rapid move­ment from “sci­ence (or ma­te­ri­al­ism) is cor­rect” to “quan­tum me­chan­ics is cor­rect” to “Many Wor­lds is cor­rect” to “the Oxford school of MWI is cor­rect”. If you are used to en­coun­ter­ing all of those ideas to­gether, it may take a while to re­al­ize that they are not linked out of log­i­cal ne­ces­sity, but just con­tin­gently, by the nar­row­ness of your own ex­pe­rience.

Se­cond, it may seem that “no definite num­ber of wor­lds” makes sense to an in­di­vi­d­ual, be­cause when they test their own wor­ld­view for se­man­tic co­her­ence, log­i­cal con­sis­tency, or em­piri­cal ad­e­quacy, it seems to pass. In the case of “no-col­lapse” or “no-split­ting” ver­sions of Many Wor­lds, it seems that it of­ten passes the sub­jec­tive mak­ing-sense test, be­cause the in­di­vi­d­ual is ac­tu­ally rely­ing on in­gre­di­ents bor­rowed from the Copen­hagen in­ter­pre­ta­tion. A semi-tech­ni­cal ex­am­ple would be the co­effi­cients of a re­duced den­sity ma­trix. In the Copen­hagen in­ter­peta­tion, they are prob­a­bil­ities. Be­cause they have the math­e­mat­i­cal at­tributes of prob­a­bil­ities (by this I just mean that they lie be­tween 0 and 1), and be­cause they can be ob­tained by strictly math­e­mat­i­cal ma­nipu­la­tions of the quan­tities com­pos­ing the wave­func­tion, Many Wor­lds ad­vo­cates tend to treat these quan­tities as in­her­ently be­ing prob­a­bil­ities, and use their “ex­is­tence” as a way to ob­tain the Born prob­a­bil­ity rule from the on­tol­ogy of “wave­func­tion yes, wave­func­tion col­lapse no”. But just be­cause some­thing is a real num­ber be­tween 0 and 1, doesn’t yet ex­plain how it man­ages to be a prob­a­bil­ity. In par­tic­u­lar, I would main­tain that if you have a mul­ti­verse the­ory, in which all pos­si­bil­ities are ac­tual, then a prob­a­bil­ity must re­fer to a fre­quency. The prob­a­bil­ity of an event in the mul­ti­verse is sim­ply how of­ten it oc­curs in the mul­ti­verse. And clearly, just hav­ing the num­ber 0.5 as­so­ci­ated with a par­tic­u­lar mul­ti­verse branch is not yet the same thing as show­ing that the events in that branch oc­cur half the time.

I don’t have a good name for this phe­nomenon, but we could call it “bor­rowed sup­port”, in which a be­lief sys­tem re­ceives sup­port from con­sid­er­a­tions which aren’t le­gi­t­i­mately its own to claim. (Ayn Rand ap­par­ently talked about a similar no­tion of “bor­rowed con­cepts”.)

Third, there is a pos­si­bil­ity among peo­ple who have a ca­pac­ity for highly ab­stract thought, to adopt an ide­ol­ogy, on­tol­ogy, or “the­ory of ev­ery­thing” which is only ex­pressed in those ab­stract terms, and to then treat that the­ory as the whole of re­al­ity, in a way that reifies the ab­strac­tions. This is a highly spe­cific form of treat­ing the map as the ter­ri­tory, pe­cu­liar to ab­stract thinkers. When some­one says that re­al­ity is made of num­bers, or made of com­pu­ta­tions, this is at work. In the case at hand, we’re talk­ing about a the­ory of physics, but the on­tol­ogy of that the­ory is in­com­pat­i­ble with the definite­ness of one’s own ex­is­tence. My guess is that the main psy­cholog­i­cal fac­tor at work here is in­tox­i­ca­tion with the feel­ing that one un­der­stands re­al­ity to­tally and in its essence. The uni­verse has bowed to the im­pe­rial ego; one may not liter­ally di­rect the stars in their courses, but one has known the essence of things. Com­bine that in­tox­i­ca­tion, with “bor­rowed sup­port” and with the sim­ple failure to think hard enough about where on the map the im­pe­rial ego it­self might be lo­cated, and maybe you have a com­pre­hen­sive ex­pla­na­tion of how peo­ple man­age to be­lieve the­o­ries of re­al­ity which are flatly in­con­sis­tent with the most ba­sic fea­tures of sub­jec­tive ex­pe­rience.

I should also say some­thing about Emile’s ex­am­ple of the ink blots. I find it rather su­perfi­cial to just say “there’s no definite num­ber of blots”. To say that the num­ber of blots de­pends on defi­ni­tion is a lot closer to be­ing true, but that un­der­mines the ar­gu­ment, be­cause that opens the pos­si­bil­ity that there is a right defi­ni­tion of “world”, and many wrong defi­ni­tions, and that the true num­ber of wor­lds is just the num­ber of wor­lds ac­cord­ing to the right defi­ni­tion.

Emile’s pic­ture can be used for the op­po­site pur­pose. All we have to do is to scru­ti­nize, more closely, what it ac­tu­ally is. It’s a JPEG that is 314 pix­els by 410 pix­els in size. Each of those pix­els will have an ex­act color cod­ing. So clearly we can be en­tirely ob­jec­tive in the way we ap­proach this ques­tion; all we have to do is be pre­cise in our con­cepts, and en­gage with the gen­uine de­tails of the ob­ject un­der dis­cus­sion. Pre­sum­ably the image is a scan of a phys­i­cal ob­ject, but even in that case, we can be pre­cise—it’s made of atoms, they are par­tic­u­lar atoms, we can make ob­jec­tive dis­tinc­tions on the ba­sis of con­ti­guity and bond­ing be­tween these atoms, and so the ques­tion will have an ob­jec­tive an­swer, if we bother to be suffi­ciently pre­cise. The same goes for “wor­lds” or “branches” in a wave­func­tion. And the truly per­ni­cious thing about this ver­sion of Many Wor­lds is that it pre­vents such in­quiry. The ide­ol­ogy that tol­er­ates vague­ness about wor­lds serves to pro­tect the pro­posed on­tol­ogy from nec­es­sary scrutiny.

The same may be said, on a broader scale, of the prac­tice of “dis­solv­ing a wrong ques­tion”. That is a gam­bit which should be used spar­ingly and cau­tiously, be­cause it eas­ily serves to in­stead jus­tify the dis­mis­sal of a le­gi­t­i­mate ques­tion. A com­mu­nity trained to dis­miss ques­tions may never even no­tice the gap­ing holes in its be­lief sys­tem, be­cause the lines of in­quiry which lead to­wards those holes are already dis­missed as in­valid, un­defined, un­nec­es­sary. smk came to this topic fresh, and with­out a head clut­tered with ideas about what ques­tions are le­gi­t­i­mate and what ques­tions are ille­gi­t­i­mate, and as a re­sult man­aged to ask some­thing which more knowl­edge­able peo­ple had already pre­ma­turely dis­missed from their own minds.