To the extent this is a correct summary, I note that it's not obvious to me that agents would sharpen their reasoning skills via test cases rather than establishing proofs on bounds of performance and so on. Though I suppose either way they are using logic, so it doesn't affect the claims of the post

Here is my attempt at a summary of (a standalone part of) the reasoning in this post.

• An agent trying to get a lot of reward can get stuck (or at least waste data) when the actions that seem good don't plug into the parts of the world/data stream that contain information about which actions are in fact good. That is, an agent that restricts its information about the reward+dynamics of the world to only its reward feedback will get less reward
• One way an agent can try and get additional information is by deductive reasoning from propositions (if they can relate sense data to world models to propositions). Sometimes the deductive reasoning they need to do will only become apparent shortly before the result of the reasoning is required (so the reasoning should be fast)
  • The nice thing about logic is that you don't need fresh data to produce test cases: you can make up puzzles! As an agent will need fast deductive reasoning strategies, they may want to try out the goodness of their reasoning strategies on puzzles they invent (to make sure they're fast and reliable (if they hadn't proved reliability))
• In general, we should model things that we think agents are going to do, because that gives us a handle on reasoning about advanced agents. It is good to be able to establish what we can about the behaviour of advanced boundedly-rational agents so that we can make progress on the alignment problem etc

Somehow you're expecting to get a lot of information about task B from performance on task A

Are "A" and "B" backwards here, or am I not following?

Most of the rituals were created by individuals that did actually understand the real reasons for why certain things had to happen

This is not part of my interpretation, so I was surprised to read this. Could you say more about why you think this? (Either why you think this being argued for in Vaniver's / Scott's posts or why you believe it is fine; I'm mostly interested in the arguments for this claim).

For example, Scott writes:

How did [culture] form? Not through some smart Inuit or Fuegian person reasoning it out; if that had been it, smart European explorers should have been able to reason it out too.

And quotes (either from Scholar's Stage or The Secret of Our Success):

It’s possible that, with the introduction of rice, a few farmers began to use bird sightings as an indication of favorable garden sites. On-average, over a lifetime, these farmers would do better – be more successful – than farmers who relied on the Gambler’s Fallacy or on copying others’ immediate behavior.

Which, I don't read as the few farmers knowing why they should use bird sightings.

Or this quote from Xunzi in Vaniver's post:

One performs divination and only then decides on important affairs. But this is not to be regarded as bringing one what one seeks, but rather is done to give things proper form.

Which doesn't sound like Xunzi understanding the specific importance of a given divination (I realise Xunzi is not the originator of the divinatory practices)

This link (and the one for "Why do we fear the twinge of starting?") is broken (I think it's an admin view?).

(Correct link)

Yes, you're quite right!

The intuition becomes a little clearer when I take the following alternative derivation:

Let us look at the change in expected value when I increase my capabilities. From the expected value stemming from worlds where I win, we have $(p\ast q{)}^{\prime }=p^{\prime }\ast q+p\ast q^{\prime }$. For the other actor, their probability of winning decreases at a rate that matches my increase in probability of winning. Also, their probability of deploying a safe AI doesn't change. So the change in expected value stemming fro m worlds where they win is $-p^{\prime }\ast r\ast q$.

We should be indifferent to increasing capabilities when these sum to 0, so $p^{\prime }\ast q+p\ast q^{\prime }=p^{\prime }\ast r\ast q$.

Let's choose our units so $k_m=1$. Then, using the expressions for $q^{\prime }$ from your comment, we have $r{q}_0{p}_0^{\prime }=p_0^{\prime }{q}_0+p_0{q}_0(r-1)$.

Dividing through by $q_0$ we get $r{p}_0^{\prime }=p_0^{\prime }+p_0(r-1)$. Collecting like terms we have $(r-1)\ast p_0^{\prime }=p_0\ast (r-1)$ and thus $p_0^{\prime }=p_0$. Substituting for $p_0^{\prime }$ we have $\frac{1}{2}-p_0=p_0$ and thus $p_0=\frac{1}{4}$

It seems like keeping a part 'outside' the experience/feeling is a big part for you. Does that sound right? (Similar to the unblending Kaj talks about in his IFS post or clearing a space in Focusing)

Now of course today's structure/process is tomorrow's content

Do you mean here that as you progress, you will introspect on the nature of your previous introspections, rather than more 'object-level' thoughts and feelings?

I think that though one may use the techniques looking for a solution (which I agree makes them solution-oriented in a sense), it's not right to so that in, say, Focusing, you introspect on solutions rather than causes. So maybe the difference is more the optimism than the area of focus?

This points to a lot of what the difference feels like to me! It jibes with my intuition for the situation that prompted this question.

I was mildly anxious about something (I forget what), and stopped myself as I was about to move on to some work (in which I would have lost the anxiety). I thought it might be useful to be with the anxiety a bit and see what was so anxious about the situation. This felt like it would be useful, but then I wondered if I would get bad ruminative effects. It seemed like I wouldn't, but I wasn't sure why.

I'm not sure if I should be given pause by the fact you say that rumination is concerned with action; my reading of the wikipedia page is that being concerned with action is a big missing feature of rumination