on 26-Nov-2020 (Thu)

At the center or heart of the hurricane is called the eye. Within the eye of a hurricane, winds are light, precipitation is minimal, and occasionally the skies above are clear. It is the calm region of the tropical storm, but that is what makes it so dangerous. Many people tend to go outside as the eye moves overhead because they believe the storm is over. But what some don’t realize is that “round two” is coming from behind.

Over time, this is a form of what Mortimer Adler and Charles van Doren dubbed syntopic reading*. I build up an understanding of an entire literature: what's been done, what's not yet been done. Of course, it's not literally reading an entire literature. But functionally it's close. I start to identify open problems, questions that I'd personally like answered, but which don't yet seem to have been answered. I identify tricks, observations that seem pregnant with possibility, but whose import I don't yet know. And, sometimes, I identify what seem to me to be field- wide blind spots. I add questions about all these to Anki as well. In this way, Anki is a medium supporting my creative research. It has some shortcomings as such a medium, since it's not designed with supporting creative work in mind – it's not, for instance, equipped for lengthy, free-form exploration inside a scratch space. But even without being designed in such a way, it's helpful as a creative support

This captures something of the immense emotional effort I used to find required to learn a new field. Without a lot of drive, it was extremely difficult to make a lot of material in a new field stick. Anki does much to solve that problem. In a sense, it's an emotional prosthetic, actually helping create the drive I need to achieve understanding. It doesn't do the entire job – as mentioned earlier, it's very helpful to have other commitments (like a creative project, or people depending on me) to help create that drive. Nonetheless, Anki helps give me confidence that I can simply decide I'm going to read deeply into a new field, and retain and make sense of much of what I learn. This has worked for all areas of conceptual understanding where I've tried it*.

One surprising consequence of reading in this way is how much more enjoyable it becomes. I've always enjoyed reading, but starting out in a challenging new field was sometimes a real slog, and I was often bedeviled by doubts that I would ever really get into the field. That doubt, in turn, made it less likely that I would succeed. Now I have confidence that I can go into a new field and quickly attain a good, relatively deep understanding, an understanding that will be durable. That confidence makes reading even more pleasurable*.

Make most Anki questions and answers as atomic as possible: That is, both the question and answer express just one idea. As an example, when I was learning the Unix command line, I entered the question: “How to create a soft link from linkname to filename?” The answer was: “ln -s filename linkname”. Unfortunately, I routinely got this question wrong. The solution was to refactor the question by breaking it into two pieces. One piece was: “What's the basic command and option to create a Unix soft link?” Answer: “ln -s …”. And the second piece was: “When creating a Unix soft link, in what order do linkname and filename go?” Answer: “filename linkname”.

That meant I didn't focus sharply enough on the mistake, and so didn't learn as much from my failure. When I fail with the atomic questions my mind knows exactly where to focus.

Incidentally, just because a question is atomic doesn't mean it can't involve quite complex, high-level concepts. Consider the following question, from the field of general relativity: “What is the dr 2 term in the Robertson-Walker metric?” Answer: dr 2 /(1-kr^2). Now, unless you've studied general relativity that question probably seems quite opaque. It's a sophisticated, integrative question, assuming you know what the Robertson-Walker metric is, what dr 2 means, what k means, and so on. But conditional on that background knowledge, it's quite an atomic question and answer.

One benefit of using Anki in this way is that you begin to habitually break things down into atomic questions. This sharply crystallizes the distinct things you've learned. Personally, I find that crystallization satisfying, for reasons I (ironically) find difficult to articulate. But one real benefit is that later I often find those atomic ideas can be put together in ways I didn't initially anticipate. And that's well worth the trouble.

Anki isn't just a tool for memorizing simple facts. It's a tool for understanding almost anything. It's a common misconception that Anki is just for memorizing simple raw facts, things like vocabulary items and basic definitions. But as we've seen, it's possible to use Anki for much more advanced types of understanding. My questions about AlphaGo began with simple questions such as “How large is a Go board?”, and ended with high-level conceptual questions about the design of the AlphaGo systems – on subjects such as how AlphaGo avoided over-generalizing from training data, the limitations of convolutional neural networks, and so on. Part of developing Anki as a virtuoso skill is cultivating the ability to use it for types of understanding beyond basic facts. Indeed, many of the observations I've made (and will make, below) about how to use Anki are really about what it means to understand something. Break things up into atomic facts. Build rich hierarchies of interconnections and integrative questions. Don't put in orphan questions. Patterns for how to engage with reading material. Patterns (and anti- patterns) for question types. Patterns for the kinds of things you'd like to memorize. Anki skills concretely instantiate your theory of how you understand; developing those skills will help you understand better. It's too strong to say that to be a virtuoso Anki user is to be a virtuoso in understanding. But there's some truth to it. Use one big deck:

se one big deck: Anki allows you to organize cards into decks and subdecks. Some people use this to create a complicated organizational structure. I used to do this, but I've gradually* merged my decks and subdecks into one big deck. The world isn't divided up into neatly separated components, and I believe it's good to collide very different types of questions. One moment Anki is asking me a question about the temperature chicken should be cooked to. The next: a question about the JavaScript API. Is this mixing doing me any real good? I'm not sure. I have not, as yet, found any reason to use JavaScript to control the cooking of a chicken. But I don't think this mixing does any harm, and hope it is creatively stimulating, and helps me apply my knowledge in unusual contexts.

Don't share decks: I'm often asked whether I'd be willing to share my Anki decks. I'm not. Very early on I realized it would be very useful to put personal information in Anki. I don't mean anything terribly personal – I'd never put deep, dark secrets in there. Nor do I put anything requiring security, like passwords. But I do put some things I wouldn't sling about casually. As an example, I've a (very short!) list of superficially charming and impressive colleagues who I would never work with, because I've consistently seen them treat other people badly. It's helpful to Ankify some details of that treatment, so I can clearly remember why that person should be avoided. This isn't the kind of information that is right to spread casually: I may have misinterpreted the other person's actions, or have misunderstood the context they were operating in. But it's personally useful for me to have in Anki.

Construct your own decks: The Anki site has many shared decks, but I've found only a little use for them. The most important reason is that making Anki cards is an act of understanding in itself. That is, figuring out good questions to ask, and good answers, is part of what it means to understand a new subject well. To use someone else's cards is to forgo much of that understanding. Indeed, I believe the act of constructing the cards actually helps with memory. Memory researchers have repeatedly found that the more elaborately you encode a memory, the stronger the memory will be. By elaborative encoding, they mean essentially the richness of the associations you form.

Humanity had a telecommunications satellite before we had a digital standard for communicating text! Finding that kind of connection is an example of an elaborative encoding

Cultivate strategies for elaborative encoding / forming rich associations: This is really a meta-strategy, i.e., a strategy for forming strategies. One simple example strategy is to use multiple variants of the “same” question. For instance, I mentioned earlier my two questions: “What does Jones 2011 claim is the average age at which physics Nobelists made their prizewinning discovery, over 1980- 2011?” And: “Which paper claimed that physics Nobelists made their prizewinning discovery at average age 48, over the period 1980-2011?” Logically, these two questions are obviously closely related. But in terms of how memory works, they are different, causing associations on very different triggers.

gather up her courage

Westergaard's solution applies directly to cracks, not to an ellipse that approaches a crack in the limit. Second, the solution is expressed in rectangular coordinates rather than elliptical coordinates. Granted, Westergaard chose to express the rectangular coordinates as complex numbers, z = x + i y z = x + i y z = x + i y .

The use of Airy Stress Functions is a powerful technique for solving 2-D equilibrium elasticity problems. The component equations of equilibrium for 2-D problems without body forces are

∂ σ x x ∂ x + ∂ τ x y ∂ y = 0 and ∂ σ y y ∂ y + ∂ τ x y ∂ x = 0