Fake Explanations

Once upon a time, there was an in­struc­tor who taught physics stu­dents. One day the in­struc­tor called them into the class­room and showed them a wide, square plate of metal, next to a hot ra­di­a­tor. The stu­dents each put their hand on the plate and found the side next to the ra­di­a­tor cool, and the dis­tant side warm. And the in­struc­tor said, Why do you think this hap­pens? Some stu­dents guessed con­vec­tion of air cur­rents, and oth­ers guessed strange met­als in the plate. They de­vised many cre­ative ex­pla­na­tions, none stoop­ing so low as to say “I don’t know” or “This seems im­pos­si­ble.”

And the an­swer was that be­fore the stu­dents en­tered the room, the in­struc­tor turned the plate around.1

Con­sider the stu­dent who fran­ti­cally stam­mers, “Eh, maybe be­cause of the heat con­duc­tion and so?” I ask: Is this an­swer a proper be­lief? The words are eas­ily enough pro­fessed—said in a loud, em­phatic voice. But do the words ac­tu­ally con­trol an­ti­ci­pa­tion?

Pon­der that in­no­cent lit­tle phrase, “be­cause of,” which comes be­fore “heat con­duc­tion.” Pon­der some of the other things we could put af­ter it. We could say, for ex­am­ple, “Be­cause of phlo­gis­ton,” or “Be­cause of magic.”

“Magic!” you cry. “That’s not a sci­en­tific ex­pla­na­tion!” In­deed, the phrases “be­cause of heat con­duc­tion” and “be­cause of magic” are read­ily rec­og­nized as be­long­ing to differ­ent liter­ary gen­res. “Heat con­duc­tion” is some­thing that Spock might say on Star Trek, whereas “magic” would be said by Giles in Buffy the Vam­pire Slayer.

How­ever, as Bayesi­ans, we take no no­tice of liter­ary gen­res. For us, the sub­stance of a model is the con­trol it ex­erts on an­ti­ci­pa­tion. If you say “heat con­duc­tion,” what ex­pe­rience does that lead you to an­ti­ci­pate ? Un­der nor­mal cir­cum­stances, it leads you to an­ti­ci­pate that, if you put your hand on the side of the plate near the ra­di­a­tor, that side will feel warmer than the op­po­site side. If “be­cause of heat con­duc­tion” can also ex­plain the ra­di­a­tor-ad­ja­cent side feel­ing cooler, then it can ex­plain pretty much any­thing.

And as we all know by this point (I do hope), if you are equally good at ex­plain­ing any out­come, you have zero knowl­edge. “Be­cause of heat con­duc­tion,” used in such fash­ion, is a dis­guised hy­poth­e­sis of max­i­mum en­tropy. It is an­ti­ci­pa­tion-iso­mor­phic to say­ing “magic.” It feels like an ex­pla­na­tion, but it’s not.

Sup­pose that in­stead of guess­ing, we mea­sured the heat of the metal plate at var­i­ous points and var­i­ous times. See­ing a metal plate next to the ra­di­a­tor, we would or­di­nar­ily ex­pect the point tem­per­a­tures to satisfy an equil­ibrium of the diffu­sion equa­tion with re­spect to the bound­ary con­di­tions im­posed by the en­vi­ron­ment. You might not know the ex­act tem­per­a­ture of the first point mea­sured, but af­ter mea­sur­ing the first points—I’m not physi­cist enough to know how many would be re­quired—you could take an ex­cel­lent guess at the rest.

A true mas­ter of the art of us­ing num­bers to con­strain the an­ti­ci­pa­tion of ma­te­rial phe­nom­ena—a “physi­cist”—would take some mea­sure­ments and say, “This plate was in equil­ibrium with the en­vi­ron­ment two and a half min­utes ago, turned around, and is now ap­proach­ing equil­ibrium again.”

The deeper er­ror of the stu­dents is not sim­ply that they failed to con­strain an­ti­ci­pa­tion. Their deeper er­ror is that they thought they were do­ing physics. They said the phrase “be­cause of,” fol­lowed by the sort of words Spock might say on Star Trek, and thought they thereby en­tered the mag­is­terium of sci­ence.

Not so. They sim­ply moved their magic from one liter­ary genre to an­other.