The Manifold Hypothesis in SAT Prep

Want to get notified about new posts? Join the mailing list and follow on X/Twitter.

“In developing the SAT curriculum, we came face-to-face with the manifold hypothesis playing out again.

The manifold hypothesis being that all of life takes place in this very high-dimensional space – there’s tons of possibilities of things that in theory could potentially happen – but the things that actually happen lie in a much lower-dimensional subspace within that space.

On the SAT, there are all these foundational skills, and they can be pulled together in so many different ways. You can do the calculation – there are hundreds of subskills, and you’re computing how many ways there are to combine a few. You get an astronomically large number and there’s no way that you can explicitly hit all those combinations.

But, once you actually look at the exam and you see combinations that show up over and over again, you realize it’s a much, much smaller space. It’s not this astronomically large number. It’s like 115 “missing middle” topics. It’s not a trivially small number, but you can enumerate it if you’re willing to put in some elbow grease and do the work.

You can build a highly scaffolded that takes a student – even one who’s not particularly mathematically gifted – and get them explicitly filling in these gaps that normally only highly gifted students would typically infer on the fly. At least, on the subset of knowledge that’s covered on the SAT. It’s small enough to get them highly trained on that.”

(weaving together snippets from our discussion starting ~1:08:11)

Want to get notified about new posts? Join the mailing list and follow on X/Twitter.