"Which chains-of-thought was that faster than?"

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

I was in the context of having just asked myself “what’s the set of functions which have this function as its derivative?”
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.
For about ~10 seconds, I tried to hold the function $f$ in my mind while trying to directly generate the integral landscape from it.
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.
After making those steps more salient in the forward direction (integral→derivative), it was easier to retrace the path in the opposite direction.
And once the derivative→integral trace was salient for a few examples, it was easier to generalize from the examples to produce the landscape of all the integrals.
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

Yesterday I was writing out some plans explicitly with pen and paper—enumerating my variables and drawing arrows between them.
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).
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 seems related to the brain’s myopic tendency for hastening subgoal completion.^[2]
  2. So I resolved to try to notice exactly which subgoal(s) my brain biases motivation toward, so I can trigger this concept specifically in the contexts where top-down override is most needed—instead of relying on an overly general sense of “uuh I gotta do this more somehow”.

Why is it better?

While obviously both heuristics are good to use, the reasons I think asking “which chains-of-thought was that faster than?” tends to be more epistemically profitable than “how could I have thought that faster?” include:

It is easier to find suboptimal thinking-habits to propagate an unusually good idea into, than to find good ideas for improving a particular suboptimal thinking-habit.
- Notice that in my technique, the good ideais cognitively proximal and the suboptimal thinking-habits are cognitively distal, whereas in Eliezer’s suggestion it’s the other way around.
- A premise here is that good ideas are unusual (hard-to-find) and suboptimal thinking-habits are common (easy-to-find)—the advice flips in domains where it’s the opposite.
- It relates to the difference between propagating specific solutions to plausible problem-domains, vs searching for specific solutions to a specific problem.
  - The brain tends to be biased against the former approach because it’s preparatory work with upfront cost (“prophylaxis”), whereas the latter context sort of forces you to search for solutions.

TAP: “What’s the appropriate scope?”

WHEN you notice that a heuristic is usefwl in specific cases
THEN ask yourself, “can I generalize this to new domains?”

Especially notice that there’s nothing about the structure of “how could I have thought that faster?” that implies it’s only usefwl in the domain of specific short chains-of-thought. “Thought” here is an unconstrained variable. It generalizes to everything where the trace of specific examples is likely to contain information which profitably generalizes to other examples. The general pattern is:

“What went wrong this time?”
- And its more-profitable inverse: “What went right this time?”

So let’s propagate this pattern across some domains:

“How could I have learned that faster?”
- What’s the most usefwl lessons you acquired from studying X? And could you have predicted that in advance so you could avoid wasting time learning [useless subsets of X]?
“How could I have finished that faster?”
- I don’t know about you, but I have wasted an outrageous number of hours perfecting the UI of my programs when, realistically, the benefit was extremely marginal.
“How could I have failed that faster?”
- If you have a plan, go straight for the bottlenecks that have the largest probability of making you realize the plan is intractable. Also, the correct response to uncertainty is not half-speed.
- Failing projects as fast as you can, may feel like making no progress at all. But keep in mind that you’re sampling the search-space faster this way. I call it “horizontal progress” because that makes me feel better.
“How could I have remembered that more reliably?”
- Especially don’t forget the inverse: “What enabled me to recall that?”
“How could I have read that faster?”
- If you are guilty of reading this sentence after having read all previous sentences in this post, consider whether you ought to be skimming more. I’m pretty sure some of the above sentences were predictably less usefwl to you.

TAP: “How can I make this advice better?”

Lastly, another generally usefwl heuristic, which also happens to have caused the insights which led to this post:

WHEN you receive good advice
- AND you especially trust the author of that advice
THEN ask yourself, “how can I make this advice better?”

^
Formatted as a trigger-action-plan (TAP) to make the cue more separately salient, so you’re more likely to notice the event that should trigger the action.
^
We asked university students to pick up either of two buckets, one to the left of an alley and one to the right, and to carry the selected bucket to the alley’s end. In most trials, one of the buckets was closer to the end point. We emphasized choosing the easier task, expecting participants to prefer the bucket that would be carried a shorter distance. Contrary to our expectation, participants chose the bucket that was closer to the start position, carrying it farther than the other bucket. — Pre-Crastination: Hastening Subgoal Completion at the Expense of Extra Physical Effort