Alvin Kerber

math and computers and stuff

Studying things is hard. Motivating yourself to study, and finding the time and energy to follow through, is much harder. The MOOC revolution of the mid-2010s was foiled (in my own experience) by how easy it was to simply stop paying attention and drop out of a class. For years I had only slightly better luck in my own planning and studying. I’d pick a book/course to follow, make a schedule, stress the importance of it to myself, seriously attempt to go through it, and peter out after just a couple weeks. At most, I lasted a month or two. For the first five years of my PhD things were pretty much the same. After all my exams were done, everything left to study was long-term and self-imposed, and I got basically nowhere.

It’s been a few more years now and I think I’ve improved a bit. I thought it’d be good to write down some things that seem to work for me, both for my own reference and so maybe others can benefit!

Content. King, of course. This is where most of my learning efforts fail. For me, video lectures are too slow. (Yes, I know I can watch at faster speed, but at that point the hard parts start to become incomprehensible – lectures are not amenable to skimming). Books are best. Books for general audiences tend to be more lively, but less informative. Many general audience books are uselessly soft (like, for instance, anything recommended in a newspaper). Books need to not be boring. Chapters and sections each should provide interesting insights that aren’t too inaccessible, not just building up to something mysterious or (worst of all) providing unmotivated background content. Small victories in understanding motivate progress, while small frustrations soon pile up and make it easy to give up completely. It’s really key to pick the best book possible.

Rhythm. In school, I’d always been motivated by competitive pressure and last-minute deadlines, so on my own with only self-imposed ground rules it’s easy to fall back into just mirroring the school structure. But school syllabi are primarily built for convenience of assessment, not for understanding. Basic pedagogical ideas like webs of concepts, connections to real-world problems, and even such simple things like spaced repetition are skipped entirely or left up to the students. I think the best I can do here is stay flexible. A fixed calendar that plods through one chapter at a time can’t be adjusted to cover the same things over and over, or shift to front-load more interesting topics. Courses tend to be better than books in this way, but they can have problems too. It’s hard to tell if I want to change topics because I’m bored, the topic is too hard, or I’m just having a lazy day. The best approach I can find here is just to follow my gut, and skip around and come back to things as I need.

Repetition. One of the hardest things I find when studying alone is deciding when I know a topic well enough to move on. More important than any particular topic in the learning is staying motivated! There’s nothing more frustrating than getting “stuck” on a seemingly endless stream of busywork, or conversely getting overwhelmed by difficult problems. The best solution I’ve found here is, rather than trying to work through whole books, to pick realistic-difficulty university courses and follow their content. If I know how to do all the exercises from a serious online course, I should be all set for the time being. MIT OpenCourseWare is particularly good, but plenty of course content from Stanford, CMU, etc can be found online also. (Most MOOCs are not rigorous enough to test much, and don’t use standard books either so there isn’t much to work from).

I know that this contradicts my earlier point here about not marching through school syllabi, and this is still something I don’t really know how to resolve. Reading is fun, but exercises often are not. My goal here is to answer the question “have I learned this well enough” not necessarily to say that going through the course in order is the best way to learn it. Whether or not that’s true varies a lot depending on the approach, but usually a multi-pass/multi-text approach works better for me. Even then it’s important to realize that there’s no such thing as knowing something for good, only learning it for now. Without practicing or building off something, it will disappear. So it’s vitally important to study things that are either inherently useful or that I’ll actually be building from!

Fun. Unlike school, there is no real stick, only carrots. People go their whole lives without studying extra topics. Most of the stuff I want to study isn’t really fun in the same way that, say, video games are. It’s satisfying, but that doesn’t really help day to day. Stupid tricks like framing stories and anecdotes are surprisingly helpful. I should really focus on weird, cartoony treatments, trashy “fun fact” books, and these sorts of things. After all, it’s the trashiness of the internet (bite size articles! Pictures! Silly stories!) that makes it so fun to get information from. What books can provide the same stimulation should still be more reliable and organized.

(Lack of) Accountability. This is the part where I’m supposed to say that you find an different person to serve as your stern taskmaster. These people are really hard to come by, and really expensive when you do find them. So maybe I’ll just say that trying to motivate myself with accountability doesn’t really seem to work in this setting. There are too many external factors that can really throw things off, and at the end of the day it’s all just my own ideas. I think instead it’s more important to keep reminding myself why I’m doing this, stay bored enough to give it a try, and make sure to celebrate each success even if they’re disorganized and out-of-order!

Subconscious. Something deep down in people loves learning new things. This is the guiding principle of the unschooling movement. People also find satisfaction from slowly getting better at things they practice. And people naturally practice things they think are interesting. Sure, they don’t practice them enough to be truly world-class, but I have an actual day job and don’t need to have world-class expertise in anything I study. I’ve gone very far in the past by just picking up things as they interested me. Perhaps instead of organized study goals (which have done little beyond get me in trouble, ever since my organized classes ended) a more long-term productive strategy is to just gather books, go through parts of them when I feel like it, and slowly glue concepts together. Practice problems are good, but it might be best to just do them for fun – think “pop quiz” vs “problem set”. Organized study time might not be as good as just reading what I feel like when I feel like it. I made it pretty far that way, after all – and in much less time than people following the school strategy.

Boredom. The problem with relying on people’s love of learning new things is there’s too many easy to learn things nowadays. This is the heart of the information revolution – tons of interesting stuff. In some ways this is good, but for creative motivation it’s a terrible, terrible thing. Even worse, most of I find sort of feels like learning but doesn’t really teach me anything. But luckily, if I stay far enough away from them for long enough, I really do still get bored. And that’s when all the learning and creativity happens!