The Level Above Mine
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 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 writing 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 had 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.