The collapse, the expanse

A year ago, I wrote When it all comes together, about the magic of the "a-ha!" moment when things just seem to line up. I included a lot about Catenary, which I was working on at the time, but I think the idea is interesting enough to stand on its own, and I'd like to return to it in the context of some other things I've written since.

There are two feelings I think are particularly notable in the context of discovery. I don't know if anyone else has named them, but I call them the collapse and the expanse. I think of them in terms of fundamental complexity, specifically in the sense of the number of actual possibilities. I touched on the idea in Abstractions: if you have a piece of paper with a million numbers written on it, there are a lot of possibilities for what can be on the paper. But if you look at the numbers and recognise that they fit a pattern, there are much fewer possibilities, sometimes even only one.

That decrease is the collapse: a sudden reduction in complexity, often accompanied by the "a-ha!". When you first realise in basic physics that you can calculate horizontal and vertical motion separately, one hard problem collapses into two simple problems. When you suddenly discover there's an underlying rule behind something you had learned case-by-case, or even figure out how to solve a tricky puzzle, the number of things you have to know decreases dramatically.

It makes sense that this feels good; the collapse is a sign you are storing information more efficiently than before. Much the same way that you can store "the even numbers from 1 to 2,000,000" in less space than you can store the even numbers from 1 to 2,000,000, you can store a collapsed understanding in less space than the knowledge that went into it. Doing this is essential for fitting all the things we need to know into our limited mental storage.

The expanse is the opposite: suddenly discovering that there is more complexity in a thing you thought was simple. Oddly, it feels good even though it means your life has become harder. The feeling is the kind of surprised curiosity you get when you've only ever seen white swans and you see a black swan for the first time, or you visit a new country and everyone acts very differently from what you're used to. Even just learning some new information with a lot of implications can lead to that kind of mind opening expansive feeling.

So why does it feel good? I think it's because the expanse provides you with a lot more new knowledge. And since new understanding requires collapsing down existing knowledge, that knowledge is important fuel for the process. But it's also worth noting that understanding also leads to new knowledge in the form of predictions and constructions. Which means that they complement each other: each collapse leads to more expanses, which should hopefully lead to yet more collapses.

I think it's these complementary processes that really define intelligence: expanding understanding into knowledge, collapsing knowledge back into understanding, and all the while inching closer to a complete representation of the truth.