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.
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.