Once upon a time . . .

This is a story from when I first met Marcello, with whom I would later work for a year on AI theory; but at this point I had not yet accepted him as my apprentice. I knew that he competed at the national level in mathematical and computing olympiads, which sufficed to attract my attention for a closer look; but I didn’t know yet if he could learn to think about AI.

I had asked Marcello to say how he thought an AI might discover how to solve a Rubik’s Cube. Not in a preprogrammed way, which is trivial, but rather how the AI itself might figure out the laws of the Rubik universe and reason out how to exploit them. How would an AI invent for itself the concept of an “operator,” or “macro,” which is the key to solving the Rubik’s Cube?

At some point in this discussion, Marcello said: “Well, I think the AI needs complexity to do X, and complexity to do Y—”

And I said, “Don’t say ‘complexity.’ ”

Marcello said, “Why not?”

I said, “Complexity should never be a goal in itself. You may need to use a particular algorithm that adds some amount of complexity, but complexity for the sake of complexity just makes things harder.” (I was thinking of all the people whom I had heard advocating that the Internet would “wake up” and become an AI when it became “sufficiently complex.”)

And Marcello said, “But there’s got to be some amount of complexity that does it.”

I closed my eyes briefly, and tried to think of how to explain it all in words. To me, saying “complexity” simply felt like the wrong move in the AI dance. No one can think fast enough to deliberate, in words, about each sentence of their stream of consciousness; for that would require an infinite recursion. We think in words, but our stream of consciousness is steered below the level of words, by the trained-in remnants of past insights and harsh experience . . .

I said, “Did you read ‘A Technical Explanation of Technical Explanation’?”¹

“Yes,” said Marcello.

“Okay,” I said. “Saying ‘complexity’ doesn’t concentrate your probability mass.”

“Oh,” Marcello said, “like ‘emergence.’ Huh. So . . . now I’ve got to think about how X might actually happen . . .”

That was when I thought to myself, “Maybe this one is teachable.”

Complexity is not a useless concept. It has mathematical definitions attached to it, such as Kolmogorov complexity and Vapnik-Chervonenkis complexity. Even on an intuitive level, complexity i...