What Are You Tracking In Your Head?

A large chunk—plausibly the majority - of real-world expertise seems to be in the form of illegible skills: skills/​knowledge which are hard to transmit by direct explanation. They’re not necessarily things which a teacher would even notice enough to consider important—just background skills or knowledge which is so ingrained that it becomes invisible.

I’ve recently noticed a certain common type of illegible skill which I think might account for the majority of illegible-skill-value across a wide variety of domains.

Here are a few examples of the type of skill I have in mind:

  • While operating a machine, track an estimate of its internal state.

  • While talking to a person, track an estimate of their internal mental state—emotions, engagement, thoughts/​worries, true motivations, etc.

  • While writing an algorithm, track a Fermi estimate of runtime.

  • While reading or writing math, track a prototypical example of what the math is talking about.

  • While playing a competitive game, track an estimate of the other players’ plans, intentions and private information

  • While writing, track an estimate of the mental state of a future reader—confusion, excitement, eyes glossing over, etc.

  • While reasoning through a difficult search/​optimization problem, track an estimate of which constraints are most taut.

  • While working on math, physics, or a program, track types/​units

  • While working on math, physics, or a program, track asymptotic behavior

  • While in conversation, track ambiguous tokenization for potential jokes.

  • While presenting to a crowd, track engagement level.

  • While absorbing claims/​information, track an estimate of the physical process which produced the information, and how that process entangles the information with physical reality.

The common pattern among all these is that, while performing a task, the expert tracks some extra information/​estimate in their head. Usually the extra information is an estimate of some not-directly-observed aspect of the system of interest. From outside, watching the expert work, that extra tracking is largely invisible; the expert may not even be aware of it themselves. Rarely are these mental tracking skills explicitly taught. And yet, based on personal experience, each of these is a central piece of performing the task well—arguably the central piece, in most cases.

Let’s assume that this sort of extra-information-tracking is, indeed, the main component of illegible-skill-value across a wide variety of domains. (I won’t defend that claim much; this post is about highlighting and exploring the hypothesis, not proving it.) What strategies does this suggest for learning, teaching, and self-improvement? What else does it suggest about the world?

Pay Attention To Extra Information Tracking

I had a scheme, which I still use today when somebody is explaining something that I’m trying to understand: I keep making up examples. For instance, the mathematicians would come in with a terrific theorem, and they’re all excited. As they’re telling me the conditions of the theorem, I construct something which fits all the conditions. You know, you have a set (one ball) – disjoint (two balls). Then the balls turn colors, grow hairs, or whatever, in my head as they put more conditions on. Finally they state the theorem, which is some dumb thing about the ball which isn’t true for my hairy green ball thing, so I say, ‘False!’

- Feynman

A lot of people have heard Feynman’s “hairy green ball thing” quote. It probably sounds like a maybe-useful technique to practice, but not obviously more valuable than any of a dozen other things.

The hypothesis that extra-information-tracking is the main component of illegible-skill-value shines a giant spotlight on things like Feynman’s examples technique. It suggests that a good comparison point for the value of tracking a prototypical example while reading/​writing math is, for instance, the value of tracking the probable contents of opponents’ hands while playing poker.

More generally: my guess is that most people reading this post looked at the list of examples, noticed a few familiar cases, and thought “Oh yeah, I do that! And it is indeed super important!”. On the other hand, I’d also guess that most people also saw some unfamiliar cases, and thought “Yeah, I’ve heard people suggest that before, and it sounds vaguely useful, but I don’t know if it’s that huge a value-add.”.

The first and most important takeaway from this post is the hypothesis that the unfamiliar examples are about as important to their use-cases as the familiar examples. Take a look at those unfamiliar examples, and imagine that they’re as important to their use-cases as the examples you already use.

Ask “What Are You Tracking In Your Head?”

Imagine that I’m a student studying under Feynman. I know that he’s one of the great minds of his generation, but it’s hard to tell which things I need to pick up. His internal thoughts are not very visible. In conversation with mathematicians, I see him easily catch errors in their claims, but I don’t know how he does it. I could just ask him how he does it, but he might not know; a young Richard Feynman probably just implicitly assumes that everyone pictures examples in their head, and has no idea why most people are unable to easily catch errors in the claims of mathematicians!

But if I ask him “what were you tracking in your head, while talking to those mathematicians?” then he’s immediately prompted to tell me about his hairy green ball thing.

More generally: for purposes of learning/​teaching, the key question to ask of a mentor is “what are you tracking in your head?”; the key question for a mentor to ask of themselves is “what am I tracking in my head?”. These extra-information-tracking skills are illegible mainly because people don’t usually know to pay attention to them. They’re not externally-visible. But they’re not actually that hard to figure out, once you look for them. People do have quite a bit of introspective access into what extra information they’re tracking. We just have to ask.

Returns to Excess Cognitive Capacity

Mentally tracking extra information is exactly the sort of technique you’d expect to benefit a lot from excess cognitive capacity, i.e. high g-factor. Someone who can barely follow what’s going on already isn’t going to have the capacity to track a bunch of other stuff in parallel.

… which suggests that extra-information-tracking techniques are particularly useful investments for people with unusually high g. (Hint: this post is on LW, so “unusually high g” probably describes you!) They’re a way to get good returns out of excess cognitive capacity.

The same argument also suggests a reason that teaching methods aren’t already more focused on mentally tracking extra information: such techniques are probably more limited for the median person. On the other hand, if your goal is to train the great minds of the next generation, then figuring out the right places to invest excess cognitive capacity is likely to have high returns.

Other Examples?

Finally, the obvious question: what extra information do you mentally track, which is crucial to performing some task well? If the hypothesis is right, there’s probably high-value mental-tracking techniques which some, but not all, people reading this already use. Please share!