LW - "Which chains-of-thought was that faster than?" by Emrik

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: "Which chains-of-thought was that faster than?", published by Emrik on May 23, 2024 on LessWrong.
Here's some good advice from Eliezer:
TAP: "How could I have thought that faster?"
WHEN[1] you complete a chain-of-thought
THEN ask yourself, "how could I have thought that faster?"
I really like this heuristic, and it's already paid its rent several times over for me. Most recently today, so I'll share the (slightly edited) cognitive trace of it as an example:
Example: To find the inverse of something, trace the chain forward a few times first
1. I was in the context of having just asked myself "what's the set of functions which have this function as its derivative?"
2. This is of course its integral, but I didn't want to use cached abstractions, and instead sought to get a generalized view of the landscape from first-principles.
3. For about ~10 seconds, I tried to hold the function f in my mind while trying to directly generate the integral landscape from it.
4. This seemed awfwly inefficient, so I changed tack: I already know some specific functions whose derivatives equal f, so I held those as the proximal thing in my mind while retracing the cognitive steps involved in their derivation.
5. After making those steps more salient in the forward direction (integralderivative), it was easier to retrace the path in the opposite direction.
6. And once the derivativeintegral trace was salient for a few examples, it was easier to generalize from the examples to produce the landscape of all the integrals.
7. There are multiple takeaways here, but one is:
1. "If you struggle to generalize something, find a way to generate specific examples first, then generalize from the examples."
TAP: "Which chains-of-thought was that faster than?"
Imo, more important than asking "how could I have thought that faster?" is the inverse heuristic:
WHEN you complete a good chain-of-thought
THEN ask yourself, "which chains-of-thought was that faster than?"
Although, ideally, I wouldn't scope the trigger to every time you complete a thought, since that overburdens the general cue. Instead, maybe limit it to those times when you have an especially clear trace of it AND you have a hunch that something about it was unusually good.
WHEN you complete a good chain of thought
AND you have its trace in short-term memory
AND you hunch that something about it was unusually effective
THEN ask yourself, "which chains-of-thought was that faster than?"
Example: Sketching out my thoughts with pen-and-paper
1. Yesterday I was writing out some plans explicitly with pen and paper - enumerating my variables and drawing arrows between them.
2. I noticed - for the umpteenth time - that forcing myself to explicitly sketch out the problem (even with improvised visualizations) is far more cognitively ergonomic than keeping it in my head (see eg why you should write pseudocode).
3. But instead of just noting "yup, I should force myself to do more pen-and-paper", I asked myself two questions:
1. "When does it help me think, and when does it just slow me down?"
1. This part is important: scope your insight sharply to contexts where it's usefwl - hook your idea into the contexts where you want it triggered - so you avoid wasting memory-capacity on linking it up to useless stuff.
2. In other words, you want to minimize (unwanted) associative interference so you can remember stuff at lower cost.
3. My conclusion was that pen-and-paper is good when I'm trying to map complex relations between a handfwl of variables.
4. And it is NOT good when I have just a single proximal idea that I want to compare against a myriad of samples with high false-positive rate - that's instead where I should be doing inside-head thinking to exploit the brain's massively parallel distributed processor.
2. "Why am I so reluctant to do it?"
1. This se...