There’s an important point which I think this misses.
Rather than imagining the bottom level of a 2D pyramid, imagine the bottom level of a 3D pyramid. As you fill in the bottom level of that 3D pyramid, at some point you go from “it’s mostly space with a few islands filled in” to “it’s mostly filled in with a few islands of space”. There’s this phase-transition-like-phenomenon where all the concepts/knowledge go from disconnected pieces to connected whole.
For instance, in studying mechanics, this transition came for me around the time I took a differential equations class (I’d already taken some physics and programming). I went from feeling like “I can only model the dynamics of certain systems with special, tractable forms” to “I can model most systems, at least numerically, except for certain systems with special, intractable weird stuff”. This was still only level 1 of the pyramid—the higher levels still provided important tools for solving mechanics problems more efficiently—but it gave me a unified framework in which everything fit together, and in which I could generally see where the holes were.
There’s an important point which I think this misses.
Rather than imagining the bottom level of a 2D pyramid, imagine the bottom level of a 3D pyramid. As you fill in the bottom level of that 3D pyramid, at some point you go from “it’s mostly space with a few islands filled in” to “it’s mostly filled in with a few islands of space”. There’s this phase-transition-like-phenomenon where all the concepts/knowledge go from disconnected pieces to connected whole.
For instance, in studying mechanics, this transition came for me around the time I took a differential equations class (I’d already taken some physics and programming). I went from feeling like “I can only model the dynamics of certain systems with special, tractable forms” to “I can model most systems, at least numerically, except for certain systems with special, intractable weird stuff”. This was still only level 1 of the pyramid—the higher levels still provided important tools for solving mechanics problems more efficiently—but it gave me a unified framework in which everything fit together, and in which I could generally see where the holes were.
I really like that point about connected vs disconnected pieces, but isn’t that true in a 2D pyramid as well?
In a 2D pyramid, the bottom layer is 1D, so any “hole” anywhere breaks it into two disconnected pieces.
Ah, gotcha.