The Anthropic Trilemma

Speak­ing of prob­lems I don’t know how to solve, here’s one that’s been gnaw­ing at me for years.

The op­er­a­tion of split­ting a sub­jec­tive wor­ldline seems ob­vi­ous enough—the skep­ti­cal ini­ti­ate can con­sider the Eb­bo­ri­ans, crea­tures whose brains come in flat sheets and who can sym­met­ri­cally di­vide down their thick­ness. The more so­phis­ti­cated need merely con­sider a sen­tient com­puter pro­gram: stop, copy, paste, start, and what was one per­son has now con­tinued on in two places. If one of your fu­ture selves will see red, and one of your fu­ture selves will see green, then (it seems) you should an­ti­ci­pate see­ing red or green when you wake up with 50% prob­a­bil­ity. That is, it’s a known fact that differ­ent ver­sions of you will see red, or al­ter­na­tively green, and you should weight the two an­ti­ci­pated pos­si­bil­ities equally. (Con­sider what hap­pens when you’re flip­ping a quan­tum coin: half your mea­sure will con­tinue into ei­ther branch, and sub­jec­tive prob­a­bil­ity will fol­low quan­tum mea­sure for un­known rea­sons.)

But if I make two copies of the same com­puter pro­gram, is there twice as much ex­pe­rience, or only the same ex­pe­rience? Does some­one who runs re­dun­dantly on three pro­ces­sors, get three times as much weight as some­one who runs on one pro­ces­sor?

Let’s sup­pose that three copies get three times as much ex­pe­rience. (If not, then, in a Big uni­verse, large enough that at least one copy of any­thing ex­ists some­where, you run into the Boltz­mann Brain prob­lem.)

Just as com­puter pro­grams or brains can split, they ought to be able to merge. If we imag­ine a ver­sion of the Eb­bo­rian species that com­putes digi­tally, so that the brains re­main syn­chro­nized so long as they go on get­ting the same sen­sory in­puts, then we ought to be able to put two brains back to­gether along the thick­ness, af­ter di­vid­ing them. In the case of com­puter pro­grams, we should be able to perform an op­er­a­tion where we com­pare each two bits in the pro­gram, and if they are the same, copy them, and if they are differ­ent, delete the whole pro­gram. (This seems to es­tab­lish an equal causal de­pen­dency of the fi­nal pro­gram on the two origi­nal pro­grams that went into it. E.g., if you test the causal de­pen­dency via coun­ter­fac­tu­als, then dis­turb­ing any bit of the two origi­nals, re­sults in the fi­nal pro­gram be­ing com­pletely differ­ent (namely deleted).)

So here’s a sim­ple al­gorithm for win­ning the lot­tery:

Buy a ticket. Sus­pend your com­puter pro­gram just be­fore the lot­tery draw­ing—which should of course be a quan­tum lot­tery, so that ev­ery ticket wins some­where. Pro­gram your com­pu­ta­tional en­vi­ron­ment to, if you win, make a trillion copies of your­self, and wake them up for ten sec­onds, long enough to ex­pe­rience win­ning the lot­tery. Then sus­pend the pro­grams, merge them again, and start the re­sult. If you don’t win the lot­tery, then just wake up au­to­mat­i­cally.

The odds of win­ning the lot­tery are or­di­nar­ily a billion to one. But now the branch in which you win has your “mea­sure”, your “amount of ex­pe­rience”, tem­porar­ily mul­ti­plied by a trillion. So with the brief ex­pen­di­ture of a lit­tle ex­tra com­put­ing power, you can sub­jec­tively win the lot­tery—be rea­son­ably sure that when next you open your eyes, you will see a com­puter screen flash­ing “You won!” As for what hap­pens ten sec­onds af­ter that, you have no way of know­ing how many pro­ces­sors you run on, so you shouldn’t feel a thing.

Now you could just bite this bul­let. You could say, “Sounds to me like it should work fine.” You could say, “There’s no rea­son why you shouldn’t be able to ex­ert an­thropic psy­chic pow­ers.” You could say, “I have no prob­lem with the idea that no one else could see you ex­ert­ing your an­thropic psy­chic pow­ers, and I have no prob­lem with the idea that differ­ent peo­ple can send differ­ent por­tions of their sub­jec­tive fu­tures into differ­ent re­al­ities.”

I find my­self some­what re­luc­tant to bite that bul­let, per­son­ally.

Nick Bostrom, when I pro­posed this prob­lem to him, offered that you should an­ti­ci­pate win­ning the lot­tery af­ter five sec­onds, but an­ti­ci­pate los­ing the lot­tery af­ter fif­teen sec­onds.

To bite this bul­let, you have to throw away the idea that your joint sub­jec­tive prob­a­bil­ities are the product of your con­di­tional sub­jec­tive prob­a­bil­ities. If you win the lot­tery, the sub­jec­tive prob­a­bil­ity of hav­ing still won the lot­tery, ten sec­onds later, is ~1. And if you lose the lot­tery, the sub­jec­tive prob­a­bil­ity of hav­ing lost the lot­tery, ten sec­onds later, is ~1. But we don’t have p(“ex­pe­rience win af­ter 15s”) = p(“ex­pe­rience win af­ter 15s”|”ex­pe­rience win af­ter 5s”)*p(“ex­pe­rience win af­ter 5s”) + p(“ex­pe­rience win af­ter 15s”|”ex­pe­rience not-win af­ter 5s”)*p(“ex­pe­rience not-win af­ter 5s”).

I’m re­luc­tant to bite that bul­let too.

And the third horn of the trilemma is to re­ject the idea of the per­sonal fu­ture—that there’s any mean­ingful sense in which I can an­ti­ci­pate wak­ing up as my­self to­mor­row, rather than Brit­ney Spears. Or, for that mat­ter, that there’s any mean­ingful sense in which I can an­ti­ci­pate be­ing my­self in five sec­onds, rather than Brit­ney Spears. In five sec­onds there will be an Eliezer Yud­kowsky, and there will be a Brit­ney Spears, but it is mean­ingless to speak of the cur­rent Eliezer “con­tin­u­ing on” as Eliezer+5 rather than Brit­ney+5; these are sim­ply three differ­ent peo­ple we are talk­ing about.

There are no threads con­nect­ing sub­jec­tive ex­pe­riences. There are sim­ply differ­ent sub­jec­tive ex­pe­riences. Even if some sub­jec­tive ex­pe­riences are highly similar to, and causally com­puted from, other sub­jec­tive ex­pe­riences, they are not con­nected.

I still have trou­ble bit­ing that bul­let for some rea­son. Maybe I’m naive, I know, but there’s a sense in which I just can’t seem to let go of the ques­tion, “What will I see hap­pen next?” I strive for al­tru­ism, but I’m not sure I can be­lieve that sub­jec­tive self­ish­ness—car­ing about your own fu­ture ex­pe­riences—is an in­co­her­ent util­ity func­tion; that we are forced to be Bud­dhists who dare not cheat a neigh­bor, not be­cause we are kind, but be­cause we an­ti­ci­pate ex­pe­rienc­ing their con­se­quences just as much as we an­ti­ci­pate ex­pe­rienc­ing our own. I don’t think that, if I were re­ally self­ish, I could jump off a cliff know­ing smugly that a differ­ent per­son would ex­pe­rience the con­se­quence of hit­ting the ground.

Bound to my naive in­tu­itions that can be ex­plained away by ob­vi­ous evolu­tion­ary in­stincts, you say? It’s plau­si­ble that I could be forced down this path, but I don’t feel forced down it quite yet. It would feel like a fake re­duc­tion. I have rather the sense that my con­fu­sion here is tied up with my con­fu­sion over what sort of phys­i­cal con­figu­ra­tions, or cas­cades of cause and effect, “ex­ist” in any sense and “ex­pe­rience” any­thing in any sense, and flatly deny­ing the ex­is­tence of sub­jec­tive con­ti­nu­ity would not make me feel any less con­fused about that.

The fourth horn of the trilemma (as ’twere) would be deny­ing that two copies of the same com­pu­ta­tion had any more “weight of ex­pe­rience” than one; but in ad­di­tion to the Boltz­mann Brain prob­lem in large uni­verses, you might de­velop similar an­thropic psy­chic pow­ers if you could split a trillion times, have each com­pu­ta­tion view a slightly differ­ent scene in some small de­tail, for­get that de­tail, and con­verge the com­pu­ta­tions so they could be re­unified af­ter­ward—then you were tem­porar­ily a trillion differ­ent peo­ple who all hap­pened to de­velop into the same fu­ture self. So it’s not clear that the fourth horn ac­tu­ally changes any­thing, which is why I call it a trilemma.

I should men­tion, in this con­nec­tion, a truly re­mark­able ob­ser­va­tion: quan­tum mea­sure seems to be­have in a way that would avoid this trilemma com­pletely, if you tried the analogue us­ing quan­tum branch­ing within a large co­her­ent su­per­po­si­tion (e.g. a quan­tum com­puter). If you quan­tum-split into a trillion copies, those trillion copies would have the same to­tal quan­tum mea­sure af­ter be­ing merged or con­verged.

It’s a re­mark­able fact that the one sort of branch­ing we do have ex­ten­sive ac­tual ex­pe­rience with—though we don’t know why it be­haves the way it does—seems to be­have in a very strange way that is ex­actly right to avoid an­thropic su­per­pow­ers and goes on obey­ing the stan­dard ax­ioms for con­di­tional prob­a­bil­ity.

In quan­tum copy­ing and merg­ing, ev­ery “branch” op­er­a­tion pre­serves the to­tal mea­sure of the origi­nal branch, and ev­ery “merge” op­er­a­tion (which you could the­o­ret­i­cally do in large co­her­ent su­per­po­si­tions) like­wise pre­serves the to­tal mea­sure of the in­com­ing branches.

Great for QM. But it’s not clear to me at all how to set up an analo­gous set of rules for mak­ing copies of sen­tient be­ings, in which the to­tal num­ber of pro­ces­sors can go up or down and you can trans­fer pro­ces­sors from one set of minds to an­other.

To sum up:

  • The first horn of the an­thropic trilemma is to con­fess that there are sim­ple al­gorithms whereby you can, in­de­tectably to any­one but your­self, ex­ert the sub­jec­tive equiv­a­lent of psy­chic pow­ers—use a tem­po­rary ex­pen­di­ture of com­put­ing power to per­ma­nently send your sub­jec­tive fu­ture into par­tic­u­lar branches of re­al­ity.

  • The sec­ond horn of the an­thropic trilemma is to deny that sub­jec­tive joint prob­a­bil­ities be­have like prob­a­bil­ities—you can co­her­ently an­ti­ci­pate win­ning the lot­tery af­ter five sec­onds, an­ti­ci­pate the ex­pe­rience of hav­ing lost the lot­tery af­ter fif­teen sec­onds, and an­ti­ci­pate that once you ex­pe­rience win­ning the lot­tery you will ex­pe­rience hav­ing still won it ten sec­onds later.

  • The third horn of the an­thropic trilemma is to deny that there is any mean­ingful sense what­so­ever in which you can an­ti­ci­pate be­ing your­self in five sec­onds, rather than Brit­ney Spears; to deny that self­ish­ness is co­her­ently pos­si­ble; to as­sert that you can hurl your­self off a cliff with­out fear, be­cause who­ever hits the ground will be an­other per­son not par­tic­u­larly con­nected to you by any such ridicu­lous thing as a “thread of sub­jec­tive ex­pe­rience”.

  • The fourth horn of the an­thropic trilemma is to deny that in­creas­ing the num­ber of phys­i­cal copies in­creases the weight of an ex­pe­rience, which leads into Boltz­mann brain prob­lems, and may not help much (be­cause al­ter­na­tively de­signed brains may be able to di­verge and then con­verge as differ­ent ex­pe­riences have their de­tails for­got­ten).

  • The fifth horn of the an­thropic trilemma is to ob­serve that the only form of split­ting we have ac­cu­mu­lated ex­pe­rience with, the mys­te­ri­ous Born prob­a­bil­ities of quan­tum me­chan­ics, would seem to avoid the trilemma; but it’s not clear how to have analo­gous rules could pos­si­bly gov­ern in­for­ma­tion flows in com­puter pro­ces­sors.

I will be ex­tremely im­pressed if Less Wrong solves this one.