I think it is the other way around. Chomsky is trying to find the underlying structure of intelligence (just like gravity underlies planetary motion), and is saying that others are simply trying to generate a model of intelligence (through statistical methods) with no understanding of why the intelligence behaves that way. Gravity is the why, planetary motion is the model produced by data (acquired by Brahe).

What will prevent Chomsky from having an Earth-centric model of the solar system, with epicycles to explain all of those weird little ticks like dropped pronouns?

The only thing that could possibly break you out of that way of thinking is massive amounts of observational analysis to show you that your foundation is flawed.

Seeing the moons of Jupiter revolutionized physics. Chomsky says that observing the heavens is unnecessary, and a distraction from his studying of the motion of billiards balls.

He's got trigonometry down cold, but he'll never come up with calculus that way. And quantum mechanics would never fall into Chomsky's way of thinking, in my analogy.

But there is a WHY associated with F= G* m1 * m2 / r^2 -- an explanation for why gravity exists, which although isn't yet unified with quantum mechanics, is that mass deforms space. The statistical formula is cool on its own right though too of course -- because of its elegance.

However, a concise formula without an explanation is less interesting, and an enormous statistical model without any elegance or insight (perhaps driven by big-data) is less interesting still, although it may have practical applications.

There may be general principles to intelligence, how it evolved through natural selection, and what in general will make for an intelligent robot. These are some of the most interesting unmade discoveries. But it isn't a sharp dichotomy between "Chomsky" and "Norvig," although that is one way to frame the question.

We should explore all reasonable approaches to AI and make sure one method is not dominating the others, but otherwise let everyone explore what they will. Who really knows what actually will lead to AI?

First, Norvig is not rejecting Chomsky's approach - you can't rely only on stats and probabilities. Chomsky is absolutely rejecting Norvig's approach. So, you apparently agree with Norvig.

Second, you don't know WHY mass deforms space. You don't know why some particles have mass, and others don't. You don't know how space is deformed by mass.

You wouldn't even have that explanation, "mass deforms space," without starting from the mathematical models. The mathematical models came about by studying the observed data.

Remember, people thought that cannon balls moved in a straight line, until they ran out of energy, and then they fell straight down. That was a perfectly valid view of the universe, given the observations available at the time. It even allowed you to make predictions about how far a cannonball would go, if you gave it different amounts of energy. It was also wrong.

We then cleverly figured out that the cannon ball moves in a parabola, with gravity as a constant force, pulling the cannonball down. Also wrong.

Now we know that the gravitational force exerted on the cannonball by the Earth is inversely proportional to the square of the distance between them. Meaning that you can put a cannonball in orbit, or you can even get it to escape Earth's gravity well.

Knowing "mass deforms space" doesn't help you make any of those predictions. How it deforms space does. And we, in fact, figured out that it deforms space, before we had any idea WHY, or by which mechanism.

Again, my problem with Chomsky is that he thinks we will come up with "mass deforms space," and Kepler's laws of planetary motion, before we even make any observations about the natural world.

Or rather, given our ability to measure huge quantities of text, it seems absurd that Chomsky would have us ignore the corpus, and go back to first principles as the exclusive and only way to gain any insight, be able to make any predictions, before we build any applications.