Extraordinary claims

Summary

What makes some­thing count as an ‘ex­traor­di­nary claim’ for the pur­poses of de­ter­min­ing whether it re­quires ex­traor­di­nary ev­i­dence?

Broadly speak­ing:

  • Not-yet-sup­ported com­plex­ity or pre­cise de­tails; by Oc­cam’s Ra­zor, this re­quires added sup­port from the ev­i­dence.

  • Vio­la­tion of (deep, causal) gen­er­al­iza­tions; be­hav­ing in a way that’s out of char­ac­ter for (the low­est level of) the uni­verse.

Some prop­er­ties that do not make a claim in­her­ently ‘ex­traor­di­nary’ in the above sense:

  • Hav­ing fu­ture con­se­quences that are im­por­tant, or ex­treme-sound­ing, or that would im­ply we need to take costly poli­cies.

  • Whether few or many peo­ple already be­lieve it.

  • Whether there might be bad rea­sons to be­lieve it.

The ul­ti­mate ground­ing for the no­tion of ‘ex­traor­di­nary claim’ would come from Solomonoff in­duc­tion, or some gen­er­al­iza­tion of Solomonoff in­duc­tion to han­dle more nat­u­ral­is­tic rea­son­ing about the world. Since this page is a Work In Progress, it cur­rently only lists out the de­rived heuris­tics, rather than try­ing to ex­plain in any great de­tail how those heuris­tics might fol­low from Solomonoff-style rea­son­ing.

Ex­am­ple 1: An­thro­pogenic global warming

Con­sider the idea of an­thro­pogenic global warm­ing as it might have been an­a­lyzed in ad­vance of ob­serv­ing the ac­tual tem­per­a­ture record. Would the claim, “Ad­ding lots of car­bon diox­ide to the at­mo­sphere will re­sult in in­creased global tem­per­a­tures and cli­mate change”, be an ‘ex­traor­di­nary’ claim re­quiring ex­traor­di­nary ev­i­dence to ver­ify, or an or­di­nary claim not re­quiring par­tic­u­larly strong ev­i­dence? We as­sume in this case you can do all the physics rea­son­ing or ecolog­i­cal rea­son­ing you want, but you can’t ac­tu­ally look at the tem­per­a­ture record yet.

The core ar­gu­ment (in ad­vance of look­ing at the tem­per­a­ture record) will be: “Car­bon diox­ide is a green­house gas, so adding suffi­cient amounts of it to the at­mo­sphere ought to trap more heat, which ought to raise the equil­ibrium tem­per­a­ture of the Earth.”

To eval­u­ate the or­di­nar­i­ness or ex­traor­di­nar­i­ness of this claim:

We don’t ask whether the fu­ture con­se­quences of the claim are ex­treme or im­por­tant. Sup­pose that adding car­bon diox­ide ac­tu­ally did trap more heat; would the Stan­dard Model of physics think to it­self, “Uh oh, that has some ex­treme con­se­quences” and de­cide to let the heat ra­di­ate away any­way? Ob­vi­ously not; the laws of physics have no priv­ileged ten­dency to avoid con­se­quences that are, on a hu­man scale, very im­por­tant in a pos­i­tive or nega­tive di­rec­tion.

We don’t ask whether the poli­cies re­quired to ad­dress the claim are very costly—this isn’t some­thing that would pre­vent the causal mechanisms be­hind the claim from op­er­at­ing, and more gen­er­ally, re­al­ity doesn’t try to avoid in­con­ve­nienc­ing us, so it doesn’t af­fect the prior prob­a­bil­ity we as­sign to a claim in ad­vance of see­ing any ev­i­dence.

We don’t ask whether some­one has a mo­tive to lie to us about the claim, or if they might be in­clined to be­lieve it for crazy rea­sons. If some­one has a mo­tive to lie to us about the ev­i­dence, this af­fects the strength of ev­i­dence, rather than low­er­ing the prior prob­a­bil­ity. Sup­pose some­body said, “Hey, I own an apart­ment in New York, and I’ll rent it to you for $2000/​month.” They might be ly­ing and try­ing to trick you out of the money, but this doesn’t mean “I own an apart­ment in New York” is an ex­traor­di­nary claim. Lots of peo­ple own apart­ments in New York. It hap­pens all the time, even. The mon­e­tary stake means that the per­son might have a mo­tive to lie to you, but this af­fects the like­li­hood ra­tio, not the prior odds. If we’re just con­sid­er­ing their un­sup­ported word, the prob­a­bil­ity that they’ll say “I own an apart­ment in New York”, given that they don’t own an apart­ment in New York, might be un­usu­ally high be­cause they could be try­ing to run a rent scam. But this doesn’t mean we have to call in physi­cists to check out whether the apart­ment is re­ally there—we just need stronger, but or­di­nary, ev­i­dence. Similarly, even if there was some­one tempted to lie about global warm­ing, we’d con­sider this as a po­ten­tial weak­ness of the ev­i­dence they offer us, but not a weak­ness in the prior prob­a­bil­ity of the propo­si­tion “Ad­ding car­bon diox­ide to the at­mo­sphere heats it up.”

(Similarly, want­ing strong ev­i­dence about a sub­ject doesn’t always co­in­cide with the un­der­ly­ing claim be­ing im­prob­a­ble. Maybe you’re con­sid­er­ing buy­ing a house in San Fran­cisco, and mil­lions of dol­lars are at stake. This im­plies a high value of in­for­ma­tion and you might want to in­vest in ex­tra-strong ev­i­dence like hav­ing a third party check the ti­tle to the house. But this isn’t be­cause it’s a Love­craf­tian anomaly for any­one to own a house in San Fran­cisco. The money at stake just means that we’re will­ing to pay more to elimi­nate small resi­dues of im­prob­a­bil­ity from this very or­di­nary claim.)

We do ask whether “adding car­bon diox­ide warms the at­mo­sphere” or “car­bon diox­ide doesn’t warm the at­mo­sphere” seems more con­so­nant with the pre­vi­ously ob­served be­hav­ior of car­bon diox­ide.

After we finish figur­ing out how car­bon diox­ide molecules and in­frared pho­tons usu­ally be­have, we don’t give pri­or­ity to gen­er­al­iza­tions like, “For as long as we’ve ob­served it, the av­er­age sum­mer tem­per­a­ture in Free­do­nia has never gone over 30C.” It’s true that the pre­dicted con­se­quences of car­bon diox­ide be­hav­ing like it usu­ally does, are vi­o­lat­ing an­other gen­er­al­iza­tion about how Free­do­nia usu­ally be­haves. But we gen­er­ally give pri­or­ity to deeper gen­er­al­iza­tions con­tin­u­ing, i.e., gen­er­al­iza­tions that are lower-level or closer to the start of causal chains.

  • The be­hav­ior of car­bon diox­ide is lower-level—it’s gen­er­al­iz­ing over a class of molecules that we can ob­serve in very great de­tail and make very pre­cise gen­er­al­iza­tions about. The weight of a car­bon diox­ide molecule (with the stan­dard iso­topes in both cases), or the amount of in­frared light the cor­re­spond­ing gas al­lows to pass, is some­thing that varies much less than the sum­mer tem­per­a­ture in Free­do­nia—it’s a very pre­cise, very strong gen­er­al­iza­tion.

  • The be­hav­ior of car­bon diox­ide is closer to the start of the chain of cause and effect. The sum­mer tem­per­a­ture in Free­do­nia is some­thing that’s caused by, or hap­pens as a re­sult of, a par­tic­u­lar level of car­bon diox­ide in Free­do­nia’s at­mo­sphere. We’d ex­pect changes that hap­pened to­ward the start of the causal chain to pro­duce changes in the effects at the end of the causal chain. Con­versely, it would be very sur­pris­ing if the Free­do­nia-sur­face-tem­per­a­ture gen­er­al­iza­tion can reach back and force car­bon diox­ide to have a differ­ent per­me­abil­ity to in­frared.

We don’t con­sider whether lots of pres­ti­gious sci­en­tists be­lieve in global warm­ing. If you ex­pect that lots of pres­ti­gious sci­en­tists usu­ally won’t be­lieve in a propo­si­tion like global warm­ing in wor­lds where global warm­ing is false, then ob­serv­ing an ap­par­ent sci­en­tific con­sen­sus might be mod­er­ately strong ev­i­dence fa­vor­ing the claim. But that isn’t part of the prior prob­a­bil­ity be­fore see­ing any ev­i­dence. For that, we want to ask about how com­pli­cated the claim is, and whether it vi­o­lates or obeys gen­er­al­iza­tions we already know about.

Another way of look­ing at a test of ex­traor­di­nar­i­ness is to ask whether the claim’s truth or falsity would im­ply learn­ing more about the uni­verse that we didn’t already know. If you’d never ob­served the tem­per­a­ture record, and had only guessed a pri­ori that adding car­bon diox­ide would warm the at­mo­sphere, you wouldn’t be too sur­prised to go look at the tem­per­a­ture record and find that noth­ing seemed to be hap­pen­ing. In this case, rather than imag­in­ing that you were wrong about the be­hav­ior of in­frared light, you might sus­pect, for ex­am­ple, that plants were grow­ing more and ab­sorb­ing the car­bon diox­ide, keep­ing the to­tal at­mo­spheric level in equil­ibrium. But in this case you would have learned a new fact not already known to you (or sci­ence) which ex­plained why global tem­per­a­tures were not ris­ing. So to ex­pect that out­come in ad­vance would be a more ex­traor­di­nary claim than to not ex­pect it. If we can imag­ine some not-too-im­plau­si­ble ways that a claim could be wrong, but they’d all re­quire us to pos­tu­late new facts we don’t solidly know, then this doesn’t make the origi­nal claim ‘ex­traor­di­nary’. It’s still a very or­di­nary claim that we’d start be­liev­ing in af­ter see­ing an or­di­nary amount of ev­i­dence.

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