Guessing the Teacher’s Password

When I was young, I read pop­u­lar physics books such as Richard Feyn­man’s QED: The Strange The­ory of Light and Mat­ter. I knew that light was waves, sound was waves, mat­ter was waves. I took pride in my sci­en­tific liter­acy, when I was nine years old.

When I was older, and I be­gan to read the Feyn­man Lec­tures on Physics, I ran across a gem called “the wave equa­tion.” I could fol­low the equa­tion’s deriva­tion, but, look­ing back, I couldn’t see its truth at a glance. So I thought about the wave equa­tion for three days, on and off, un­til I saw that it was em­bar­rass­ingly ob­vi­ous. And when I fi­nally un­der­stood, I re­al­ized that the whole time I had ac­cepted the hon­est as­surance of physi­cists that light was waves, sound was waves, mat­ter was waves, I had not had the vaguest idea of what the word “wave” meant to a physi­cist.

There is an in­stinc­tive ten­dency to think that if a physi­cist says “light is made of waves,” and the teacher says “What is light made of?” and the stu­dent says “Waves!”, then the stu­dent has made a true state­ment. That’s only fair, right? We ac­cept “waves” as a cor­rect an­swer from the physi­cist; wouldn’t it be un­fair to re­ject it from the stu­dent? Surely, the an­swer “Waves!” is ei­ther true or false, right?

Which is one more bad habit to un­learn from school. Words do not have in­trin­sic defi­ni­tions. If I hear the syl­la­bles “bea-ver” and think of a large ro­dent, that is a fact about my own state of mind, not a fact about the syl­la­bles “bea-ver.” The se­quence of syl­la­bles “made of waves” (or “be­cause of heat con­duc­tion”) is not a hy­poth­e­sis ; it is a pat­tern of vibra­tions trav­el­ing through the air, or ink on pa­per. It can as­so­ci­ate to a hy­poth­e­sis in some­one’s mind, but it is not, of it­self, right or wrong. But in school, the teacher hands you a gold star for say­ing “made of waves,” which must be the cor­rect an­swer be­cause the teacher heard a physi­cist emit the same sound-vibra­tions. Since ver­bal be­hav­ior (spo­ken or writ­ten) is what gets the gold star, stu­dents be­gin to think that ver­bal be­hav­ior has a truth-value. After all, ei­ther light is made of waves, or it isn’t, right?

And this leads into an even worse habit. Sup­pose the teacher asks you why the far side of a metal plate feels warmer than the side next to the ra­di­a­tor. If you say “I don’t know,” you have no chance of get­ting a gold star—it won’t even count as class par­ti­ci­pa­tion. But, dur­ing the cur­rent semester, this teacher has used the phrases “be­cause of heat con­vec­tion,” “be­cause of heat con­duc­tion,” and “be­cause of ra­di­ant heat.” One of these is prob­a­bly what the teacher wants. You say, “Eh, maybe be­cause of heat con­duc­tion?”

This is not a hy­poth­e­sis about the metal plate. This is not even a proper be­lief. It is an at­tempt to guess the teacher’s pass­word.

Even vi­su­al­iz­ing the sym­bols of the diffu­sion equa­tion (the math gov­ern­ing heat con­duc­tion) doesn’t mean you’ve formed a hy­poth­e­sis about the metal plate. This is not school; we are not test­ing your mem­ory to see if you can write down the diffu­sion equa­tion. This is Bayescraft; we are scor­ing your an­ti­ci­pa­tions of ex­pe­rience. If you use the diffu­sion equa­tion, by mea­sur­ing a few points with a ther­mome­ter and then try­ing to pre­dict what the ther­mome­ter will say on the next mea­sure­ment, then it is definitely con­nected to ex­pe­rience. Even if the stu­dent just vi­su­al­izes some­thing flow­ing, and there­fore holds a match near the cooler side of the plate to try to mea­sure where the heat goes, then this men­tal image of flow­ing-ness con­nects to ex­pe­rience; it con­trols an­ti­ci­pa­tion.

If you aren’t us­ing the diffu­sion equa­tion—putting in num­bers and get­ting out re­sults that con­trol your an­ti­ci­pa­tion of par­tic­u­lar ex­pe­riences—then the con­nec­tion be­tween map and ter­ri­tory is sev­ered as though by a knife. What re­mains is not a be­lief, but a ver­bal be­hav­ior.

In the school sys­tem, it’s all about ver­bal be­hav­ior, whether writ­ten on pa­per or spo­ken aloud. Ver­bal be­hav­ior gets you a gold star or a failing grade. Part of un­learn­ing this bad habit is be­com­ing con­sciously aware of the differ­ence be­tween an ex­pla­na­tion and a pass­word.

Does this seem too harsh? When you’re faced by a con­fus­ing metal plate, can’t “heat con­duc­tion?” be a first step to­ward find­ing the an­swer? Maybe, but only if you don’t fall into the trap of think­ing that you are look­ing for a pass­word. What if there is no teacher to tell you that you failed? Then you may think that “Light is wakalixes” is a good ex­pla­na­tion, that “wakalixes” is the cor­rect pass­word. It hap­pened to me when I was nine years old—not be­cause I was stupid, but be­cause this is what hap­pens by de­fault. This is how hu­man be­ings think, un­less they are trained not to fall into the trap. Hu­man­ity stayed stuck in holes like this for thou­sands of years.

Maybe, if we drill stu­dents that words don’t count, only an­ti­ci­pa­tion-con­trol­lers, the stu­dent will not get stuck on “Heat con­duc­tion? No? Maybe heat con­vec­tion? That’s not it ei­ther?” Maybe then, think­ing the phrase “heat con­duc­tion” will lead onto a gen­uinely helpful path, like:

  • “Heat con­duc­tion?”

  • But that’s only a phrase—what does it mean?

  • The diffu­sion equa­tion?

  • But those are only sym­bols—how do I ap­ply them?

  • What does ap­ply­ing the diffu­sion equa­tion lead me to an­ti­ci­pate?

  • It sure doesn’t lead me to an­ti­ci­pate that the side of a metal plate farther away from a ra­di­a­tor would feel warmer.

  • I no­tice that I am con­fused. Maybe the near side just feels cooler, be­cause it’s made of more in­su­la­tive ma­te­rial and trans­fers less heat to my hand? I’ll try mea­sur­ing the tem­per­a­ture . . .

  • Okay, that wasn’t it. Can I try to ver­ify whether the diffu­sion equa­tion holds true of this metal plate, at all? Is heat flow­ing the way it usu­ally does, or is some­thing else go­ing on?

  • I could hold a match to the plate and try to mea­sure how heat spreads over time . . .

If we are not strict about “Eh, maybe be­cause of heat con­duc­tion?” be­ing a fake ex­pla­na­tion, the stu­dent will very prob­a­bly get stuck on some wakalixes-pass­word. This hap­pens by de­fault: it hap­pened to the whole hu­man species for thou­sands of years.