The Level Above Mine

(At this point, I fear that I must re­curse into a sub­se­quence; but if all goes as planned, it re­ally will be short.)

I once lent Xiaoguang “Mike” Li my copy of “Prob­a­bil­ity The­ory: The Logic of Science”. Mike Li read some of it, and then came back and said:

“Wow… it’s like Jaynes is a thou­sand-year-old vam­pire.”

Then Mike said, “No, wait, let me ex­plain that—” and I said, “No, I know ex­actly what you mean.” It’s a con­ven­tion in fan­tasy liter­a­ture that the older a vam­pire gets, the more pow­er­ful they be­come.

I’d en­joyed math proofs be­fore I en­coun­tered Jaynes. But E.T. Jaynes was the first time I picked up a sense of formidabil­ity from math­e­mat­i­cal ar­gu­ments. Maybe be­cause Jaynes was lin­ing up “para­doxes” that had been used to ob­ject to Bayesi­anism, and then blast­ing them to pieces with over­whelming fire­power—power be­ing used to over­come oth­ers. Or maybe the sense of formidabil­ity came from Jaynes not treat­ing his math as a game of aes­thet­ics; Jaynes cared about prob­a­bil­ity the­ory, it was bound up with other con­sid­er­a­tions that mat­tered, to him and to me too.

For what­ever rea­son, the sense I get of Jaynes is one of ter­rify­ing swift perfec­tion—some­thing that would ar­rive at the cor­rect an­swer by the short­est pos­si­ble route, tear­ing all sur­round­ing mis­takes to shreds in the same mo­tion. Of course, when you write a book, you get a chance to show only your best side. But still.

It spoke well of Mike Li that he was able to sense the aura of formidabil­ity sur­round­ing Jaynes. It’s a gen­eral rule, I’ve ob­served, that you can’t dis­crim­i­nate be­tween lev­els too far above your own. E.g., some­one once earnestly told me that I was re­ally bright, and “ought to go to col­lege”. Maybe any­thing more than around one stan­dard de­vi­a­tion above you starts to blur to­gether, though that’s just a cool-sound­ing wild guess.

So, hav­ing heard Mike Li com­pare Jaynes to a thou­sand-year-old vam­pire, one ques­tion im­me­di­ately popped into my mind:

“Do you get the same sense off me?” I asked.

Mike shook his head. “Sorry,” he said, sound­ing some­what awk­ward, “it’s just that Jaynes is...”

“No, I know,” I said. I hadn’t thought I’d reached Jaynes’s level. I’d only been cu­ri­ous about how I came across to other peo­ple.

I as­pire to Jaynes’s level. I as­pire to be­come as much the mas­ter of Ar­tifi­cial In­tel­li­gence /​ re­flec­tivity, as Jaynes was mas­ter of Bayesian prob­a­bil­ity the­ory. I can even plead that the art I’m try­ing to mas­ter is more difficult than Jaynes’s, mak­ing a mock­ery of defer­ence. Even so, and em­bar­rass­ingly, there is no art of which I am as much the mas­ter now, as Jaynes was of prob­a­bil­ity the­ory.

This is not, nec­es­sar­ily, to place my­self be­neath Jaynes as a per­son—to say that Jaynes had a mag­i­cal aura of des­tiny, and I don’t.

Rather I rec­og­nize in Jaynes a level of ex­per­tise, of sheer formidabil­ity, which I have not yet achieved. I can ar­gue force­fully in my cho­sen sub­ject, but that is not the same as writ­ing out the equa­tions and say­ing: DONE.

For so long as I have not yet achieved that level, I must ac­knowl­edge the pos­si­bil­ity that I can never achieve it, that my na­tive tal­ent is not suffi­cient. When Mar­cello Her­reshoff had known me for long enough, I asked him if he knew of any­one who struck him as sub­stan­tially more na­tively in­tel­li­gent than my­self. Mar­cello thought for a mo­ment and said “John Con­way—I met him at a sum­mer math camp.” Darn, I thought, he thought of some­one, and worse, it’s some ul­tra-fa­mous old guy I can’t grab. I in­quired how Mar­cello had ar­rived at the judg­ment. Mar­cello said, “He just struck me as hav­ing a tremen­dous amount of men­tal horse­power,” and started to ex­plain a math prob­lem he’d had a chance to work on with Con­way.

Not what I wanted to hear.

Per­haps, rel­a­tive to Mar­cello’s ex­pe­rience of Con­way and his ex­pe­rience of me, I haven’t had a chance to show off on any sub­ject that I’ve mas­tered as thor­oughly as Con­way had mas­tered his many fields of math­e­mat­ics.

Or it might be that Con­way’s brain is spe­cial­ized off in a differ­ent di­rec­tion from mine, and that I could never ap­proach Con­way’s level on math, yet Con­way wouldn’t do so well on AI re­search.

Or...

...or I’m strictly dumber than Con­way, dom­i­nated by him along all di­men­sions. Maybe, if I could find a young proto-Con­way and tell them the ba­sics, they would blaze right past me, solve the prob­lems that have weighed on me for years, and zip off to places I can’t fol­low.

Is it dam­ag­ing to my ego to con­fess that last pos­si­bil­ity? Yes. It would be fu­tile to deny that.

Have I re­ally ac­cepted that awful pos­si­bil­ity, or am I only pre­tend­ing to my­self to have ac­cepted it? Here I will say: “No, I think I have ac­cepted it.” Why do I dare give my­self so much credit? Be­cause I’ve in­vested spe­cific effort into that awful pos­si­bil­ity. I am blog­ging here for many rea­sons, but a ma­jor one is the vi­sion of some younger mind read­ing these words and zip­ping off past me. It might hap­pen, it might not.

Or sad­der: Maybe I just wasted too much time on set­ting up the re­sources to sup­port me, in­stead of study­ing math full-time through my whole youth; or I wasted too much youth on non-mathy ideas. And this choice, my past, is ir­re­vo­ca­ble. I’ll hit a brick wall at 40, and there won’t be any­thing left but to pass on the re­sources to an­other mind with the po­ten­tial I wasted, still young enough to learn. So to save them time, I should leave a trail to my suc­cesses, and post warn­ing signs on my mis­takes.

Such spe­cific efforts pred­i­cated on an ego-dam­ag­ing pos­si­bil­ity—that’s the only kind of hu­mil­ity that seems real enough for me to dare credit my­self. Or giv­ing up my pre­cious the­o­ries, when I re­al­ized that they didn’t meet the stan­dard Jaynes had shown me—that was hard, and it was real. Modest de­meanors are cheap. Hum­ble ad­mis­sions of doubt are cheap. I’ve known too many peo­ple who, pre­sented with a coun­ter­ar­gu­ment, say “I am but a fal­lible mor­tal, of course I could be wrong” and then go on to do ex­actly what they planned to do pre­vi­ously.

You’ll note that I don’t try to mod­estly say any­thing like, “Well, I may not be as brilli­ant as Jaynes or Con­way, but that doesn’t mean I can’t do im­por­tant things in my cho­sen field.”

Be­cause I do know… that’s not how it works.