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Here is what I would do, in the hypothetical scenario, where I have taken over the world.
Though this is what I would do in any situation really. It is what I am doing right now. This is what I breathe for, and I won't stop until I am dead.
[EDIT 2023-03-01_17-59: I have recently realized that is is just how one part of my mind feels. The part that feels like me. However, there are tons of other parts in my mind that pull me in different directions. For example, there is one part that wants me to do lots of random improvements to my computer setup, which are fun to do, but probably not worth the effort. I have been ignoring these parts in the past, and I think that their grip on me is stronger because I did not take them into account appropriately in my plans.]
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 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.
In this post, I describe a toy setup, where I have a graph of vertices. I would like to compute for any two vertices A and B how to get from A to B, i.e. compute a path from A to B.
The point is that if we have a very special graph structure we can do this very efficiently. O(n) where n is the plan length.
If you have a 1GHz CPU you can do 1,000,000,000 operations per second. Let's assume that iterating through one one object takes only one operation.
In a year you can do 10^16 operations. That means it would take 10^84 years to iterate through 10^100 verticies.
The big bang was 1.4*10^10 years ago.
Maybe it is the same for me and I am depressed. I got a lot better at not being depressed, but it might still be the issue. What steps do you take? How can I not be depressed?
(To be clear I am talking specifically about the situation where you have no idea what to do, and if anything is even possible. It seems like there is a difference between a problem that is very hard, but you know you can solve, and a problem that you are not sure is solvable. But I'd guess that being depressed or not depressed is a much more important factor.)
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. utilitytime_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.