What should I learn?

thoughts about how I’m picking what to learn right now

Originally published on Medium.

I have limited time and a long list of things to learn. My own knowledge is a tiny bucket compared to an ocean of blah yada ladeeda… I know how that goes, the refrain about how little you know and the implication that curiosity is thus naive. Is it not enough for me to be curious, do I also need others to be ignorant in order to be happy about learning something? It really is okay to be curious about things that are already known by others; that much is enough to make me very happy.

Curiosity is an obvious good. But how do I map out what I already know? I want to figure out what to learn next so I think I need a map first.

I know the cached response in my brain: a wiki-like solution to store arbitrary amounts of detail and variety of content but with a focus on smart links and brevity. And there are some who’ve done interesting things here and there.

The voice of efficiency pipes up:

“Why do you even need a map? You’ll feel that rush of recognition if you know $new_topic, you won’t if you don’t! And come on, stop sneering at a Google Sheet, it’s enough for the job if it really needs doing”

Well, thanks for asking and the reason is: I want to invest learning time in those things that I know least about and that I expect to be useful. And I get the feeling that I’m not looking at a complete-enough map when I just toy with this in my brain, so I think my decisions are not as good as they could be with an actual map.

Okay, let’s say you have a wiki or a spreadsheet or something. What do you put on that map? And how do you organize it? Depends on the nature of what you know, I think. So, what do you know?

Imagine being a high schooler. You have a certain number of years of education in many different subject areas, and also a condensed external description of what you learned in every subject in every year (syllabus), and actually you also have a measure of how well you know it too (grades). But you also remember that debate competition you placed 4th in, and that great scrapbook you made a couple of years ago. And don’t forget the lyrics to that one band’s entire album kicking around in your brain!

How do you organize this information? Hmm, exhaustive representations are out, they would take too long. What should the map contain? Well, probably some notion of what the big “chunks” of your knowledge are. And probably the constituents of those chunks themselves. So, one chunk could be math, and a constituent could be high school algebra. And you also need some notion of how well you know it. A grade is one consistent way to do it.

Let’s say you have a simple map (in a condensed form): Knowledge(3.625, Math(3.75, HSAlgebra(4.0), HSGeometry(3.5)), English(3.5, HSWriting(3.5), HSReading(3.5))). How do I evaluate whether this is a good map?

Hmm, a good map would help me answer certain questions better than other maps. What questions would those be? Let’s brainstorm a list:

  • Can I get a general sense of what I know in under 1 minute?
  • Can I tell what I know least about?
  • Can I lookup each topic easily? (I want to somehow figure out how useful it will be)

Well, I see the tree-like structure, and I know how to climb trees quickly with my fancy pants CS degree. Also, those grades in every topic tell me how well I know it, and if there are subtopics I can further tell why it’s low/high and where the deficiencies really are. I could lookup each topic in Google because I based them on the subject names that occur in syllabuses all over, and I could perhaps add links.

Hmm, what are other ways of creating maps?

  • I could make a flat list of very finely specified topics (or skills), along with a percentage indicating how well I know it and perhaps a simple rank ordering to communicate importance.
  • I could make Venn diagrams and size the topics I know least the biggest
  • I could make directed acyclic graph of topics to communicate the flexible dependencies that exist between them. This could take a lot of 2D space to represent (or require a tool) but it could in fact communicate usefulness. What I mean is that if you used this to represent topics as nodes and gave them each a weight corresponding to a grade and then drew arrows to indicate dependencies, the most important nodes are those with the least weight and the most dependents. I imagine that in practice this might be noisy, not actually useful week to week, or might just be a glorified Pretty Thing.

I’m attracted to DAGs as a way to represent knowledge. Thinking with SQL, I can imagine a pretty simple way to do this. Here’s a sql fiddle I made to show this point (a table of topics with name and grade, and a table of dependencies with start-topic and end-topic references). I imagine it’s not hard to query this database to answer questions like: what do I need to learn most? I also imagine it’s trivial to add arbitrary groupings if needed (think tags). That would make it easier to group ‘science’ topics separately from ‘humanities’ topics, etc. But this does add the weight of tools and specialized knowledge.

Mr. Efficiency again:

“I know! Take one sheet of A4 paper and a pencil, write down a nested, bulleted list of topics/sub-topics, noting grades alongside the name of each topic. Then, draw arrows representing relationships as you see them. Finish first draft as such, critique it, make another draft, and call it a day. You can now use this to decide what to learn first over the next $time_period. Remember: the value of this whole chunk of work is measured by the cost to make the final decision about what to learn first. Over-engineered solutions are thus costlier.”

Pencil and paper, we meet again!

Any other ideas, dear reader?


Oct 12 2015 Update:
I took myself up on the task of creating a draft of this ‘map of what I know,’ and… it’s quite humbling, haha. Here’s what I learned:

  • Estimating grades for topics is a bit difficult. I imagine it’s the biggest tar pit in this technique.
  • I didn’t end up using arrows at all and I also identified a new need: efficient ways of testing myself.
  • Those tests that lead to the most updates to grade-estimates of topics are the most valuable ones to take, I imagine.
  • Sure I could reference my transcript or standardized scores, but there is a rub: staleness of knowledge. I decided to discount the grade by a point for around 2 years of interim time, but boost it a bit above completely unknown topics (easier to revise previously known topics). But then… to make things quick, I thought about my gut answer, waited until it settled after trying to pull it apart, and just used that.
  • I actually did figure out a few candidate topics to study already, so I figure I need to think about next steps.