Teaching the Unteachable

Pre­vi­ously in se­ries: Un­teach­able Ex­cel­lence
Fol­lowup to: Ar­tifi­cial Addition

The liter­ary in­dus­try that I called “ex­cel­lence pornog­ra­phy” isn’t very good at what it does. But it is failing at a very im­por­tant job. When you con­sider the net benefit to civ­i­liza­tion of War­ren Buffett’s su­per­star skills, ver­sus the less glamorous but more com­mu­ni­ca­ble trick of “rein­vest wealth to cre­ate more wealth”—there’s hardly any com­par­i­son. You can see how much it would mat­ter, if you could figure out how to com­mu­ni­cate just one more skill that used to be a se­cret sauce. Not the porno­graphic promise of con­sum­ing the en­tire soul of a su­per­star. Just figur­ing out how to re­li­ably teach one more thing, even if it wasn’t ev­ery­thing...

What makes a suc­cess hard to du­pli­cate?

Naked statis­ti­cal chance is always in­com­mu­ni­ca­ble. No mat­ter what you say about your his­tor­i­cal luck, you can’t teach some­one else to have it. The arts of seiz­ing op­por­tu­nity, and ex­pos­ing your­self to pos­i­tive ran­dom­ness, are com­monly un­der­es­ti­mated; I’ve seen peo­ple stopped in their tracks by “bad luck” that a Sili­con Valley en­trepreneur would drive over like a steam­rol­ler flat­ten­ing speed bumps… Even so, there is still an el­e­ment of gen­uine chance left over.

Ein­stein’s su­per­star­dom de­pended on his ge­net­ics that gave him the po­ten­tial to learn his skills. If a skill re­lies on hav­ing that much brain­power, you can’t teach it to most peo­ple… Though if the po­ten­tial is one-in-a-mil­lion, then six thou­sand Ein­steins around the world would be an im­prove­ment. (And if we’re go­ing to be re­ally cre­ative, who says genes are in­com­mu­ni­ca­ble? It just takes more ad­vanced tech­nol­ogy than a black­board, that’s all.)

So when we fac­tor out the gen­uinely un­teach­able—what’s left? Where you can you push the bor­der? What is it that might be pos­si­ble to teach—albeit per­haps very difficult—and isn’t be­ing taught?

I was once told that half of No­bel lau­re­ates were the stu­dents of other No­bel lau­re­ates. This source seems to as­sert 155 out of 503. (In­ter­est­ingly, the same source says that the num­ber of No­bel lau­re­ates with No­bel “grand­par­ents” (teach­ers of teach­ers) is just 60.) Even af­ter dis­count­ing for cherry-pick­ing of stu­dents and poli­ti­cal pull, this sug­gests to me that you can learn things by ap­pren­tice­ship—close su­per­vi­sion, free-form dis­cus­sion, on­go­ing er­ror cor­rec­tion over a long pe­riod of time—that no No­bel lau­re­ate has yet suc­ceed­ing in putting into any of their many books.

What is it that the stu­dents of No­bel lau­re­ates learn, but can’t put into words?

This sub­ject holds a fas­ci­na­tion for me, be­cause how it delves into the meta, the source be­hind, the gap be­tween the out­put and the gen­er­a­tor. We can ex­plain Ein­stein’s Gen­eral Rel­a­tivity to stu­dents, but we can’t make them Ein­stein. (If you look at it from the right an­gle, the whole trick of hu­man in­tel­li­gence is just an in­com­mu­ni­ca­ble in­sight that hu­mans have and can’t ex­plain to a com­puter.)

The amount of word­less in­tel­li­gence in our work tends to be un­der­es­ti­mated be­cause the words them­selves are so much eas­ier to in­tro­spect on. But when I’m pay­ing at­ten­tion, I can see how much of my search­power takes place in fast flashes of per­cep­tion that tell me what’s im­por­tant, which thought to think next.

When I met my ap­pren­tice Mar­cello he was already bet­ter at math­e­mat­i­cal proof than my­self, cer­tainly much faster. He’d com­peted at the na­tional level—but in com­pe­ti­tions like that you get told which prob­lems are im­por­tant. (And also in com­pe­ti­tions, you in­stantly hand in the prob­lem when you’re done, and rush on to the next one; with­out look­ing over your proof to see if you can sim­plify it, see it at a glance, learn some­thing more.) But the re­ally crit­i­cal thing I was try­ing to teach him—test­ing to see if it could even be taught at all—was this sense of which AI prob­lems led some­where. “You can pedal as well as I can,” I said to him early on when he asked how he was do­ing, “but I’m still do­ing ninety per­cent of the steer­ing.” And it was a con­stant, tremen­dous strug­gle to put any­thing into words about why I thought that we hadn’t yet found the re­ally im­por­tant in­sight that was lurk­ing some­where in a prob­lem, and so we were go­ing to dis­card Mar­cello’s cur­rent proof and re­for­mu­late the prob­lem and try again from an­other an­gle, to see if this time we would re­ally un­der­stand some­thing.

We go through our life events, and our brain uses an opaque al­gorithm to grind the ex­pe­riences to grist, and out­puts yet an­other opaque neu­ral net of cir­cuitry: the pro­ce­du­ral skill, the source of word­less in­tu­itions that you know so fast you can’t see your­self know­ing them. “The ze­roth step”, I called it, the step in rea­son­ing that comes be­fore the first step and goes by so quickly that you don’t re­al­ize it’s there.

I pride my­self on be­ing good at putting things into words, at be­ing able to in­tro­spect on the mo­men­tary flashes and see their pat­tern and trend, even if I can’t print out the cir­cuitry that is their source. But when I tried to com­mu­ni­cate my cut­ting edge, the bor­der­line where I ad­vanced my knowl­edge—then my words were defeated, and I was left work­ing with Mar­cello on prob­lem af­ter prob­lem, hop­ing his brain would pick up that un­spo­ken rhythm of the steer­ing: Turn left, turn right; this is prob­a­bly worth pur­su­ing, this is not; this seems like a valuable in­sight, this is just a black box around our ig­no­rance.

I’d ex­pected it to go like that; I’d never had the delu­sion that the most im­por­tant parts of thought would be easy to put in words. If it were that sim­ple we re­ally would have had Ar­tifi­cial In­tel­li­gence in the 1970s.

Civ­i­liza­tion gets by on teach­ing the out­put of the gen­er­a­tor with­out teach­ing the gen­er­a­tor. Ein­stein out­put his var­i­ous dis­cov­er­ies, and then the gen­er­ated knowl­edge is ver­bal enough to be passed on to stu­dents in uni­ver­sity. When an­other Ein­stein is needed, civ­i­liza­tion just holds its breath and hopes.

But if these word­less skills are the product of ex­pe­rience—then why not com­mu­ni­cate the ex­pe­riences? Or if fic­tion isn’t good enough, and it prob­a­bly isn’t even close, then why not du­pli­cate the ex­pe­riences—put peo­ple through the same events?

(1) Su­per­stars may not know what their crit­i­cal ex­pe­riences were.

(2) The crit­i­cal ex­pe­riences may be difficult to du­pli­cate—for ex­am­ple, ev­ery­one already knows the an­swer to Spe­cial Rel­a­tivity, and now we can’t train peo­ple by giv­ing them the prob­lem of Spe­cial Rel­a­tivity. Just know­ing that it has some­thing to do with space and time shift­ing around, is already too much of a spoiler. The re­ally im­por­tant part of the prob­lem is the one where you stare at a blank sheet of pa­per un­til drops of blood form on your fore­head, try­ing to figure out what to think next. The skills of ge­nius are rare, I’ve sug­gested, be­cause there is not enough op­por­tu­nity to prac­tice them.

(3) There may be luck or ge­netic tal­ent in­volved in your brain hit­ting on the right thing to learn—find­ing a solu­tion of high qual­ity in the space of word­less pro­ce­du­ral skills. Even if we put you through the same ex­pe­riences, there’s com­po­nents of true chance and ge­netic tal­ent left over in hav­ing your brain learn the same word­less skill.

But I think there’s still rea­son to go on try­ing to de­scribe the in­de­scrib­able and teach the un­teach­able.

Con­sider the tran­si­tion in gam­bling skill as­so­ci­ated with the in­ven­tion of prob­a­bil­ity the­ory a few cen­turies back. There’s still a lef­tover art to poker, word­less skills that poker su­per­stars can only par­tially de­scribe in words. But go back far enough, and no one would have any idea how to calcu­late the odds of rol­ling three dice and com­ing up with all ones. And maybe an ex­pe­rienced enough gam­bler would have a word­less in­tu­ition that some things were like­lier than oth­ers, but they couldn’t have put it into words—couldn’t have told any­one else what they’d learned about the chances; ex­cept, maybe, through a long pro­cess of watch­ing over an ap­pren­tice’s shoulder and su­per­vis­ing their bets.

The more we learn about a do­main, and the more we sys­tem­at­i­cally ob­serve the stars at work, and the more we learn about the hu­man mind in gen­eral, the more we can hope for new skills to make the tran­si­tion from un­teach­able to ap­pren­tice­able to pub­lish­able.

And you can hope to trailblaze cer­tain paths, even if you can’t set down all the path in words. Even if you your­self got some­where through luck (in­clud­ing ge­netic luck), you can hope to diminish the role of luck on fu­ture oc­ca­sions:

(A) Warn­ing against blind alleys that de­layed you, is one ob­vi­ous sort of help.

(B) If you lay down a set of thoughts that are the product of word­less skills, some­one read­ing through the set of thoughts may find their brain pick­ing up the rhythm, mak­ing the leap to the un­spo­ken thing be­hind; and this might re­quire less luck than the events that led to your own origi­nal ac­qui­si­tion of those word­less skills.

(C) There are good at­trac­tors in the solu­tion-space—clus­tered sub-solu­tions which make it eas­ier to reach other solu­tions in the same at­trac­tor. Then—even if some of the thoughts can’t be put into words, and even if it took a lot of luck to wan­der into the at­trac­tor the first time through—de­scribing ev­ery­thing that can be put into words, may be enough to an­chor the at­trac­tor.

(D) Some im­por­tant ex­pe­riences are du­pli­ca­ble: for ex­am­ple, you can ad­vise peo­ple what ar­eas to study, what books to read.

(E) And fi­nally, the sim­ple ad­vance of sci­ence may just de­scribe a do­main bet­ter, so that you re­al­ize what it is you know, and are sud­denly able to com­mu­ni­cate it out­right.

And of course the punch­line is that this is the tran­si­tion I hope to see in cer­tain as­pects of hu­man ra­tio­nal­ity—skills which have been up un­til now un­teach­able, or only passed down from mas­ter to ap­pren­tice. We’ve learned a lot about the do­main in the past few decades, and I think it’s time to take an­other shot at sys­tem­atiz­ing it.

I as­pire to diminish the role of luck and tal­ent in pro­duc­ing ra­tio­nal­ists of a higher grade.