The Dilemma: Science or Bayes?

“Eli: You are writ­ing a lot about physics re­cently. Why?”
Shane Legg (and sev­eral other peo­ple)

“In light of your QM ex­pla­na­tion, which to me sounds perfectly log­i­cal, it seems ob­vi­ous and nor­mal that many wor­lds is over­whelm­ingly likely. It just seems al­most too good to be true that I now get what plenty of ge­nius quan­tum physi­cists still can’t. [...] Sure I can ex­plain all that away, and I still think you’re right, I’m just sus­pi­cious of my­self for be­liev­ing the first be­liev­able ex­pla­na­tion I met.”
Re­cov­er­ing irrationalist

RI, you’ve got no idea how glad I was to see you post that com­ment.

Of course I had more than just one rea­son for spend­ing all that time post­ing about quan­tum physics. I like hav­ing lots of hid­den mo­tives, it’s the clos­est I can eth­i­cally get to be­ing a su­pervillain.

But to give an ex­am­ple of a pur­pose I could only ac­com­plish by dis­cussing quan­tum physics...

In physics, you can get ab­solutely clear-cut is­sues. Not in the sense that the is­sues are triv­ial to ex­plain. But if you try to ap­ply Bayes to health­care, or eco­nomics, you may not be able to for­mally lay out what is the sim­plest hy­poth­e­sis, or what the ev­i­dence sup­ports. But when I say “macro­scopic de­co­her­ence is sim­pler than col­lapse” it is ac­tu­ally strict sim­plic­ity; you could write the two hy­pothe­ses out as com­puter pro­grams and count the lines of code. Nor is the ev­i­dence it­self in dis­pute.

I wanted a very clear ex­am­ple—Bayes says “zig”, this is a zag—when it came time to break your alle­giance to Science.

“Oh, sure,” you say, “the physi­cists messed up the many-wor­lds thing, but give them a break, Eliezer! No one ever claimed that the so­cial pro­cess of sci­ence was perfect. Peo­ple are hu­man; they make mis­takes.”

But the physi­cists who re­fuse to adopt many-wor­lds aren’t di­s­obey­ing the rules of Science. They’re obey­ing the rules of Science.

The tra­di­tion handed down through the gen­er­a­tions says that a new physics the­ory comes up with new ex­per­i­men­tal pre­dic­tions that dis­t­in­guish it from the old the­ory. You perform the test, and the new the­ory is con­firmed or falsified. If it’s con­firmed, you hold a huge cel­e­bra­tion, call the news­pa­pers, and hand out No­bel Prizes for ev­ery­one; any dod­der­ing old emer­i­tus pro­fes­sors who re­fuse to con­vert are quietly hu­mored. If the the­ory is dis­con­firmed, the lead pro­po­nent pub­li­cly re­cants, and gains a rep­u­ta­tion for hon­esty.

This is not how things do work in sci­ence; rather it is how things are sup­posed to work in Science. It’s the ideal to which all good sci­en­tists as­pire.

Now many-wor­lds comes along, and it doesn’t seem to make any new pre­dic­tions rel­a­tive to the old the­ory. That’s sus­pi­cious. And there’s all these other wor­lds, but you can’t see them. That’s re­ally sus­pi­cious. It just doesn’t seem sci­en­tific.

If you got as far as RI—so that many-wor­lds now seems perfectly log­i­cal, ob­vi­ous and nor­mal—and you also started out as a Tra­di­tional Ra­tion­al­ist, then you should be able to switch back and forth be­tween the Scien­tific view and the Bayesian view, like a Necker Cube.

So now put on your Science Gog­gles—you’ve still got them around some­where, right? For­get ev­ery­thing you know about Kol­mogorov com­plex­ity, Solomonoff in­duc­tion or Min­i­mum Mes­sage Lengths. That’s not part of the tra­di­tional train­ing. You just eye­ball some­thing to see how “sim­ple” it looks. The word “testable” doesn’t con­jure up a men­tal image of Bayes’s The­o­rem gov­ern­ing prob­a­bil­ity flows; it con­jures up a men­tal image of be­ing in a lab, perform­ing an ex­per­i­ment, and hav­ing the cel­e­bra­tion (or pub­lic re­can­ta­tion) af­ter­ward.

Science-Gog­gles on: The cur­rent quan­tum the­ory has passed all ex­per­i­men­tal tests so far. Many-Wor­lds doesn’t make any new testable pre­dic­tions—the amaz­ing new phe­nom­ena it pre­dicts are all hid­den away where we can’t see them. You can get along fine with­out sup­pos­ing the other wor­lds, and that’s just what you should do. The whole thing smacks of sci­ence fic­tion. But it must be ad­mit­ted that quan­tum physics is a very deep and very con­fus­ing is­sue, and who knows what dis­cov­er­ies might be in store? Call me when Many-Wor­lds makes a testable pre­dic­tion.

Science-Gog­gles off, Bayes-Gog­gles back on:

Bayes-Gog­gles on: The sim­plest quan­tum equa­tions that cover all known ev­i­dence don’t have a spe­cial ex­cep­tion for hu­man-sized masses. There isn’t even any rea­son to ask that par­tic­u­lar ques­tion. Next!

Okay, so is this a prob­lem we can fix in five min­utes with some duct tape and su­per­glue?

No.

Huh? Why not just teach new grad­u­at­ing classes of sci­en­tists about Solomonoff in­duc­tion and Bayes’s Rule?

Cen­turies ago, there was a wide­spread idea that the Wise could un­ravel the se­crets of the uni­verse just by think­ing about them, while to go out and look at things was lesser, in­fe­rior, naive, and would just de­lude you in the end. You couldn’t trust the way things looked—only thought could be your guide.

Science be­gan as a re­bel­lion against this Deep Wis­dom. At the core is the prag­matic be­lief that hu­man be­ings, sit­ting around in their arm­chairs try­ing to be Deeply Wise, just drift off into never-never land. You couldn’t trust your thoughts. You had to make ad­vance ex­per­i­men­tal pre­dic­tions—pre­dic­tions that no one else had made be­fore—run the test, and con­firm the re­sult. That was ev­i­dence. Sit­ting in your arm­chair, think­ing about what seemed rea­son­able… would not be taken to prej­u­dice your the­ory, be­cause Science wasn’t an ideal­is­tic be­lief about prag­ma­tism, or get­ting your hands dirty. It was, rather, the dic­tum that ex­per­i­ment alone would de­cide. Only ex­per­i­ments could judge your the­ory—not your na­tion­al­ity, or your re­li­gious pro­fes­sions, or the fact that you’d in­vented the the­ory in your arm­chair. Only ex­per­i­ments! If you sat in your arm­chair and came up with a the­ory that made a novel pre­dic­tion, and ex­per­i­ment con­firmed the pre­dic­tion, then we would care about the re­sult of the ex­per­i­ment, not where your hy­poth­e­sis came from.

That’s Science. And if you say that Many-Wor­lds should re­place the im­mensely suc­cess­ful Copen­hagen In­ter­pre­ta­tion, adding on all these twin Earths that can’t be ob­served, just be­cause it sounds more rea­son­able and el­e­gant—not be­cause it crushed the old the­ory with a su­pe­rior ex­per­i­men­tal pre­dic­tion—then you’re un­do­ing the core sci­en­tific rule that pre­vents peo­ple from run­ning out and putting an­gels into all the the­o­ries, be­cause an­gels are more rea­son­able and el­e­gant.

You think teach­ing a few peo­ple about Solomonoff in­duc­tion is go­ing to solve that prob­lem? No­bel lau­re­ate Robert Au­mann—who first proved that Bayesian agents with similar pri­ors can­not agree to dis­agree—is a be­liev­ing Ortho­dox Jew. Au­mann helped a pro­ject to test the To­rah for “Bible codes”, hid­den prophe­cies from God—and con­cluded that the pro­ject had failed to con­firm the codes’ ex­is­tence. Do you want Au­mann think­ing that once you’ve got Solomonoff in­duc­tion, you can for­get about the ex­per­i­men­tal method? Do you think that’s go­ing to help him? And most sci­en­tists out there will not rise to the level of Robert Au­mann.

Okay, Bayes-Gog­gles back on. Are you re­ally go­ing to be­lieve that large parts of the wave­func­tion dis­ap­pear when you can no longer see them? As a re­sult of the only non-lin­ear non-uni­tary non-differ­en­tiable non-CPT-sym­met­ric acausal faster-than-light in­for­mally-speci­fied phe­nomenon in all of physics? Just be­cause, by sheer his­tor­i­cal con­tin­gency, the stupid ver­sion of the the­ory was pro­posed first?

Are you go­ing to make a ma­jor mod­ifi­ca­tion to a sci­en­tific model, and be­lieve in zillions of other wor­lds you can’t see, with­out a defin­ing mo­ment of ex­per­i­men­tal triumph over the old model?

Or are you go­ing to re­ject prob­a­bil­ity the­ory?

Will you give your alle­giance to Science, or to Bayes?

Michael Vas­sar once ob­served (tongue-in-cheek) that it was a good thing that a ma­jor­ity of the hu­man species be­lieved in God, be­cause oth­er­wise, he would have a very hard time re­ject­ing ma­jori­tar­i­anism. But since the ma­jor­ity opinion that God ex­ists is sim­ply un­be­liev­able, we have no choice but to re­ject the ex­tremely strong philo­soph­i­cal ar­gu­ments for ma­jori­tar­i­anism.

You can see (one of the rea­sons) why I went to such lengths to ex­plain quan­tum the­ory. Those who are good at math should now be able to vi­su­al­ize both macro­scopic de­co­her­ence, and the prob­a­bil­ity the­ory of sim­plic­ity and testa­bil­ity—get the in­san­ity of a global sin­gle world on a gut level.

I wanted to pre­sent you with a nice, sharp dilemma be­tween re­ject­ing the sci­en­tific method, or em­brac­ing in­san­ity.

Why? I’ll give you a hint: It’s not just be­cause I’m evil. If you would guess my mo­tives here, think be­yond the first ob­vi­ous an­swer.

PS: If you try to come up with clever ways to wrig­gle out of the dilemma, you’re just go­ing to get shot down in fu­ture posts. You have been warned.