I'm currently testing a promising direction for a possible collection of units at CFAR. (For those who have attended some CFAR events or test sessions, this is a collection of refinements to the fudoshin/"panic" unit.) I've hit on what I think is a key puzzle whose answer might unlock a lot of the emerging art of rationality. I - and possibly most people here, eventually - would very much appreciate any insight you have to share.
The puzzle is how thought incubation works, ideally expressed in terms of neural systems or neuroanatomical structures. I'll first explain the phenomenon and then suggest the general reference class from which I'm hoping to get an answer.
The Phenomenon:
Mathematicians frequently report that often one of the most helpful things they can do to solve a problem they're stuck on is step away from it. Jacques Hadamard (1949) examined his own experiences and also talked to many of his colleagues to work out what the common structure of this experience was, and determined that there seems to be a fairly predictable sequence to it:
(1) Intensely focus on the problem, working through every permutation you can think of that's likely to produce an answer.
(2) Walk away from the problem and think about something else.
(3) The magic genie in your head might eventually, and often unexpectedly, yell a possible insight into your awareness.
For instance, Henri Poincaré reported struggling to work on Fuchsian functions over the course of several weeks and then being forced to walk away from the proof he had been stuck on due to a planned vacation. One day he was stepping onto a bus with his mind certainly not on mathematics, and suddenly the key insight he needed to finish the proof appeared in his mind. It was as though a part of his mind had been secretly working on the problem and then brought the finished product into his awareness. In this particular case it also came with a feeling of total confidence that verification would pan out (although Hadamard notes that the validation step after the insight is still essential because sometimes that feeling of total confidence is mistaken).
I definitely relate to this from when I was working on graduate mathematics. However, it also pattern-matches with other mental phenomena that are much more common. For instance, sometimes I think I know what a person's name is, but struggle as I might I can't quite remember it - and then a few minutes later after I've given up remembering the name the answer loudly announces itself, often quite out-of-context. Or when I'm trying to figure out a way of improving a throw in martial arts and then find the answer suddenly dawning on me at a random time.
I'm under the impression that this is a fairly universal kind of experience. I suspect you can think of examples in your own life where this has happened. ("Oh, now I remember where I put those keys!")
Reference Class for an Explanation:
I'm going to offer some overly simplistic examples of the kind of explanation I'm looking for. In this case, I think overly simplistic might be okay since I'm just trying to get a reasonable handle on how to munchkin the interaction between a few different neural systems. If it turns out that a more detailed and technically correct version is important, I'll probably dig into it (pending the VOI versus cost-of-information comparison).
There seems to be some evidence that one of the reasons children are as impulsive as they are is that they haven't yet developed their prefrontal cortices (PFCs) to the degree adults have. The prefrontal cortex seems to do at least two things: (1) hold long-term goals in mind and (2) engage executive function (i.e., halt orders on impulses, typically ones that don't match up with the long-term goals). This neuroanatomical structure seems to continue growing until sometime in one's early 20s - which might be why we also find that teenagers typically have less impulse control than twentysomethings but more than middle-schoolers, whereas we don't find such a clear distinction between twentysomethings and thirtysomethings. (Yes, this could also or even instead be cultural. I know it's complicated.) Incidentally, I understand that the PFC is also one of the neural structures most deactivated by alcohol - although my impression is that it shuts down the long-term goals thing and not the executive function. (This is based on my and others' experience that precommitment works perfectly well. It seems to me that saying things like "I couldn't help myself because I was drunk!" is more a social excuse than an actual explanation. But I'm only around 65% confident of this as a general claim.)
On a related note, it would seem that there's something in the same rough space as theory of mind that goes beyond the ability to pass the false-belief test. According to Rebecca Saxe, the capacity for empathy seems to come from a particular bit of the brain that doesn't finish growing until the mid-20s. Saxe also provides some evidence that a sufficiently strong and precisely directed magnet can basically deactivate that part of one's theory of mind temporarily. It seems quite plausible to me (though I really don't know) that activation of the sympathetic nervous system (SNS), such as in fight-or-flight reactions, decreases activation of this empathy part of the brain. This might be why, in a perceived crisis, some people switch to an almost tool-like view of others (e.g., knowing that overcoming the bystander effect requires pointing at a specific person and saying "You! Call 911!" but not really getting a sense in that moment of what that person's experience is like to be so singled out).
I'm quite aware that much of the above is speculation. I think speculation is fine, but having it grounded in some actual known neuroscience is ideal. That would give me something to dig into. E.g., if there's some reason to believe that this phenomenon is related to the enteric nervous system, I can start digging into the literature on that system to better understand how to munchkin its interactions with the (rest of the) autonomic nervous system.
An example of something outside the reference class I'm looking for is a "little man in the subconscious" explanation. I first read about this about twenty years ago as a model for how mental incubation works: you concentrate on a problem in order to communicate to a little man in your subconscious what you want to have done, and then you stop talking to him so he can go do what you just told him to do. Then he comes back with an answer once he's done, without regard to what you're doing when he's done. I agree that this seems to be a reasonable metaphor for what's going on, but it doesn't tell me for instance why the "little man" seems to respond so much more to SNS activity than parasympathetic activity, or why he can't go do his job once he has the instructions even if we continue to think about the problem.
More generally, psychodynamic "explanations" are unlikely to be helpful here. Talking about this as the "domain of the iNtuiting function" in reference to Jungian psychodynamic theory or Myers-Briggs won't tell me hardly anything about how this relates to stress oscillation.
So... Any suggestions about what this mysterious "little man" might actually be made of?
One thing that I'm pretty sure is going on and that might be a sufficient explanation is that it takes time to develop fluency in a hard problem. You can solve a simple problem in one go if you can hold enough of it in your mind to see the next steps of a plan that prove useful, and the same happens with the results of those steps, and eventually you reach a solution. For a harder problem, you might fail to see a specific plan, so you develop various observations about the problem and additional representations of its aspects, without having a clear sense of which of them will be useful, and there are too many of these to hold in your mind at the same time, as even though the new observations may be obtained by the methods you know well, they are in themselves new facts that are not yet thoroughly familiar.
To get to the next step, it might be necessary to be able to access a lot of these observations easily, without spending attention on recreating them. It takes time to familiarize yourself with the new observations (and with the way they connect to the original problem and to each other), to commit all these details to long term memory and to train your imagination to easily retrace the connections between them. But once you've done so, you obtain new superpowers with respect to that problem (and perhaps others analogous to it). A proof that would've taken 15 steps in terms of the ideas you had when you started working on the problem (and so wasn't apparent), now takes only 4 steps in terms of the new auxiliary ideas you've developed in the meantime, and you can see it at a glance. (Perhaps if your mind wanders when you're stepping onto a bus, and spends a few seconds on the problem, this proves sufficient to take advantage of the prior training and notice the solution.)
This analysis suggests that if you are stuck on a problem you need to solve, and you have enough time on your hands, (1) you should deliberately and systematically study the observations associated with your problem, even the ones that don't seem immediately useful, and those that are easy to obtain, until these observations and their connections to the rest become obvious without the need to concentrate on reconstructing them, (2) revisit all (relevant) parts of the problem when you expect that new observations have been internalized since the last time you've revisited the problem.
This seems very insightful to me. In physics, it's definitely my experience that over time I gain fluency with more and more powerful concepts that let me derive new things in much faster and simpler ways. And I find myself consciously working ideas over in my mind with, I think, the explicit goal of advancing this process.
The funny thing about this is that before I gain these "superpowers," I'll read an explanation in a textbook, which is in terms of high-level ideas that I haven't completely grasped yet, so the reading doesn't help as much as ... (read more)