Here is a model of mine, that seems related.

[Edit: Add Epistemic status]
Epistemic status: I have used this successfully in the past and found it helpful. It is relatively easy to do. $\frac{\text{utility}}{\text{time\_investment}}$ is large for me.

I think it is helpful to be able to emotionally detach yourself from your ideas. There is an implicit "concept of I" in our minds. When somebody criticizes this "concept of I", it is painful. If somebody says "You suck", that hurts.

There is an implicit assumption in the mind that this concept of "I" is eternal. This has the effect, that when somebody says "You suck", it is actually more like they say "You sucked in the past, you suck now, and you will suck, always and ever".

In order to emotionally detach yourself from your ideas, you need to sever the links in your mind, between your ideas and this "concept of I". You need to see an idea as an object that is not related to you. Don't see it as "your idea", but just as an idea.

It might help to imagine that there is an idea-generation machine in your brain. That machine makes ideas magically appear in your perception as thoughts. Normally when somebody says "Your idea is dumb", you feel hurt. But now we can translate "Your idea is dumb" to "There is idea-generating machinery in my brain. This machinery has produced some output. Somebody says this output is dumb".

Instead of feeling hurt, you can think "Hmm, the idea-generating machinery in my brain produced an idea that this person thinks is bad. Well maybe they don't understand my idea yet, and they criticize their idea of my idea, and not actually my idea. How can I make them understand?" This thought is a lot harder to have while being busy feeling hurt.

Or "Hmm, this person that I think is very competent thinks this idea is bad, and after thinking about it I agree that this idea is bad. Now how can I change the idea-generating machinery in my brain, such that in the future I will have better ideas?" That thought is a lot harder to have when you think that you yourself are the problem. What is that even supposed to mean that you yourself are the problem? This might not be a meaningful statement, but it is the default interpretation when somebody criticizes you.

The basic idea here is, to frame everything without any reference to yourself. It is not me producing a bad plan, but some mechanism that I just happened to observe the output of. In my experience, this not only helps alleviate pain but also makes you think thoughts that are more useful.

Adopted.

A few adjacent thoughts:

• Why is a programming language like Haskell that is extremely powerful in the sense that if your program compiles, it is the program that you want with a very high probability because most stupid mistakes are now compile errors?
• Why is there basically no widely used homoiconic language, i.e. a language in which you can use the language itself to <reason about the language/manipulate the language>.

Here we have some technology that is basically ready to use (Haskell or Clojure), but people decide to mostly not use them. And with people, I mean professional programmers and companions who make software.

• Why did nobody invent Rust earlier, by which I mean a system-level programming language that prevents you from making really dumb mistakes that can be machine-checked if you make them?
• Why did it take like 40 years to get a latex replacement, even though latex is terrible in very obvious ways?

These things have in common that there is a big engineering challenge. It feels like maybe this explains it, together with that people who would benefit from these technologies where in the position that the cost of creating them would have exceeded the benefit that they would expect from them.

For Haskell and Clojure we can also consider this point. Certainly, these two technologies have their flaws and could be improved. But then again we would have a massive engineering challenge.

Research Writing Workflow: First figure stuff out

• Do research and first figure stuff out, until you feel like you are not confused anymore.
• Explain it to a person, or a camera, or ideally to a person and a camera.
  • If there are any hiccups expand your understanding.
  • Ideally, as the last step, explain it to somebody whom you have not ever explained it to.
• Only once you made a presentation without hiccups you are ready to write post.
  • If you have a recording this is useful as a starting point.

The point is that you are just given some graph. This graph is expected to have subgraphs which are lattice graphs. But you don't know where they are. And the graph is so big that you can't iterate the entire graph to find these lattices. Therefore you need a way to embed the graph without traversing it fully.

—The realization that I have a systematic distortion in my mental evaluation of plans, making actions seem less promising than they are. When I’m deciding whether to do stuff, I can apply a conscious correction to this, to arrive at a properly calibrated judgment.

—The realization that, in general, my thinking can have systematic distortions, and that I shouldn’t believe everything I think. This is basic less-wrong style rationalism, but it took years to work through all the actual consequences on me.

This is useful. Now that I think about it, I do this. Specifically, I have extremely unrealistic assumptions about how much I can do, such that these are impossible to accomplish. And then I feel bad for not accomplishing the thing.

I haven't tried to be mindful of that. The problem is that this is I think mainly subconscious. I don't think things like "I am dumb" or "I am a failure" basically at all. At least not in explicit language. I might have accidentally suppressed these and thought I had now succeeded in not being harsh to myself. But maybe I only moved it to the subconscious level where it is harder to debug.

I might not understand exactly what you are saying. Are you saying that the problem is easy when you have a function that gives you the coordinates of an arbitrary node? Isn't that exactly the embedding function? So are you not therefore assuming that you have an embedding function?

I agree that once you have such a function the problem is easy, but I am confused about how you are getting that function in the first place. If you are not given it, then I don't think it is super easy to get.

In the OP I was assuming that I have that function, but I was saying that this is not a valid assumption in general. You can imagine you are just given a set of vertices and edges. Now you want to compute the embedding such that you can do the vector planning described in the article.

I agree that you probably can do better than ${10}^{100}$ though. I don't understand how your proposal helps though.

Yes right, good point. There are plans that go zick-sag through the graph, which would be longer. I edited that.

Yes, abstraction is the right thing to think about. That is the context in which I was considering this computation. In this post I describe a sort of planning abstraction that you can do if you have an extremely regular environment. It does not yet talk about how to store this environment, but you are right that this can of course also be done similarly efficiently.