Problems We Don't Understand

Most problems can be separated pretty cleanly into two categories: things we basically understand, and things we basically don’t understand. Some things we basically understand: building bridges and skyscrapers, treating and preventing infections, satellites and GPS, cars and ships, oil wells and gas pipelines and power plants, cell networks and databases and websites. Some things we basically don’t understand: building fusion power plants, treating and preventing cancer, high-temperature superconductors, programmable contracts, genetic engineering, fluctuations in the value of money, biological and artificial neural networks. 

Problems we basically understand may have lots of moving parts, require many people with many specialties, but they’re generally problems which can be reliably solved by throwing resources at it. There usually isn’t much uncertainty about whether the problem will be solved at all, or a high risk of unknown unknowns, or a need for foundational research in order to move forward. Problems we basically don’t understand are the opposite: they are research problems, problems which likely require a whole new paradigm.

Another difficulty with problems we basically don’t understand is that they are generally the type of issues where experimentation is extremely expensive and sometimes unethical to perform, further hindering our ability to learn about them. We don't know what we don't know because we cannot easily obtain a lot of good quality information about the problem itself.

Problems we do understand mainly require relatively specialized knowledge and techniques adapted to solving particular problems. But problems we don’t understand mainly require general-purpose skills of empiricism, noticing patterns and bottlenecks, model-building, and design principles. Existing specialised knowledge and techniques don’t suffice - after all, if the existing specialised knowledge and techniques were sufficient to reliably solve the problem, then it wouldn’t be a problem.

So what does generalise well? 

Within technical subjects, think probability and information theory, programming and algorithms, dynamical systems and control theory, optimization and microeconomics,  linear algebra and numerical analysis. Systems and synthetic biology generalize well within biology, mechanics and electrodynamics are necessary for fermi estimates in most physical sciences, continuum mechanics and PDEs are useful for a wide variety of areas in engineering and science.

But just listing subjects isn’t all that useful - after all, a lot of the most generally-useful skills and techniques don’t explicitly appear in a university course catalogue (or if they do, they appear hidden in a pile of more-specialized information). Many aren’t explicitly taught at all. What we really need is to be able to apply them in new contexts, very different from any problem one has seen before. One needs to recognise, without prompting, situations-in-the-wild in which a model or technique applies.

If the bottleneck is to notice that a particular technique applies, then we don’t even necessarily need to be good at using the technique. We just need to be good at noticing problems where the technique applies, and then we can google it if and when we need it (especially these days with the ease of asking for help from AI). This suggests exercises pretty different from exercises in a lot of classes - for instance, a typical intro linear algebra class involves a lot of practice executing row reduction, but not as much recognising linear systems in the wild.

So when dealing with problems we basically don’t understand, the use-cases for learned knowledge are different, and therefore require different kinds of practice. Some example use-cases for the kinds of things one might formally study:

• Learn a skill or tool which you will later use directly. Ex.: programming classes.

• Learn the gears of a system, so you can later tackle problems involving the system which are unlike any you've seen before. Ex.: physiology classes for doctors.

• Learn how to think about a system at a high level, e.g. enough to do Fermi estimates or identify key bottlenecks relevant to some design problem. Ex.: intro-level fluid mechanics.

• Uncover unknown unknowns, like pitfalls which you wouldn't have thought to check for, tools you wouldn't have known existed, or problems you didn't know were tractable/intractable. Ex.: intro-level statistics, or any course covering NP-completeness.

• Learn jargon, common assumptions, and other concepts needed to effectively interface to some field. Ex.: much of law school.

• Learn enough to distinguish experts from non-experts in a field. Ex.: programming or physiology, for people who don't intend to be programmers/doctors but do need to distinguish good work from quackery in these fields.

These different use-cases suggest different strategies for study, and different degrees of investment. Some require in-depth practice (like skills/tools), others just require a quick first pass (like unknown unknowns), and some can be done with a quick pass if you have the right general background knowledge but require more effort otherwise (like Fermi estimates).

Either way, study in any particular topic has decreasing marginal returns. The first exposure or two gives you the basic frames, tells you what kinds of questions to ask and what kinds of tools are available, etc. You may not remember everything, but you can at least remember what things to look up later if you need them - which is a pretty huge improvement over not even knowing that X is a thing you can look up at all!

That said, consider still picking one (maybe two or three, but few) small-ish sub-fields / topics to go through in depth, taking them to an extreme. Past a certain point, something funny tends to happen, where what's normally perceived as boundaries starts to warp and the whole space suddenly looks completely different. You're unlikely to get these kinds of perspective shifts if you look only at the basics. So every once in a while, if you are interested in the topic, just run with it and see what happens.

Conclusion

To learn the sort of skills and knowledge which are likely to generalise well to new, poorly-understood problems, it’s useful to work on a fairly wide variety of problems which you basically don’t understand or know how to solve. Then, prioritize techniques and models which seem relevant to multiple such problems. The problems also provide natural applications in which to test new techniques, and in particular to test the crucial skill of recognising (without prompting) situations-in-the-wild in which the technique applies.

Content adapted from LessWrong.