Attention conservation notice: if you’ve read Michael Nielsen’s stuff about Anki, this probably won’t be new for you. Also, this is all very personal and YMMV.
In a number of discussions of Anki here and elsewhere, I’ve seen Anki’s value measured in terms of time saved by not having to look stuff up. For example, Gwern’s spaced repetition post includes a calculation of when it’s worth it to Anki-ize threshold, although I would be surprised if Gwern hasn’t already thought about the claim going to make.
While I occasionally use Anki to remember things that I would otherwise have to Google, e.g. statistics, I almost never Anki-ize things so that I can avoid Googling them in the future. And I don’t think in terms of time saved when deciding what to Anki-ize.
Instead, (as Michael Nielsen discusses in his posts) I almost always Anki-ize with the goal of building a connected graph of knowledge atoms about an area in which I’m interested. As a result, I tend to evaluate what to Anki-ize based on two criteria:
Will this help me think about this domain without paper or a computer better?
In the Platonic graph of this domain’s knowledge ontology, how central is this node? (Pedantic note: it’s easier to visualize distance to the root of the tree, but this requires removing cycles from the graph.)
To make this more concrete, let’s look at an example of a topic I’ve been Anki-izing recently, causal inference. I just started Anki-izing this topic a week ago, so it’ll be easier for me to avoid idealizing the process. Looking at my cards so far, I have questions about and definitions of things like “d-separation”, “sufficient/admissible sets”, and “backdoor paths”. Notably, for each of these, I don’t just have a cloze card to recall the definition, I also have image cards that quiz me on examples and conceptual questions that clarify things I found confusing upon first encountering these concepts. I’ve found that making these cards has the effect of both forcing me to ensure I understand concepts (because writing cards requires breaking them down) and makes it easier to bootstrap my understanding over the course of multiple days. Furthermore, knowing that I’ll remember at least the stuff I’ve Anki-ized has a surprisingly strong motivational impact on me on a gut level.
All that said, I suspect there are some people for whom Anki-izing wouldn’t be helpful.
The first is people who have the time and a career in which they focus on a narrow enough set of topics such that they repeatedly see the same concepts and rarely go for long periods without revisiting them. I’ve experienced this myself for Python—I learned it well before starting to use Anki and used it every day for many years. So even if I forget some stuff, it’s very easy for me to use the language fluently after time away from it.
The second is, for lack of a better term, actual geniuses. Like, if you’re John Von Neumann and you legitimately have an approximation of a photographic memory (I’m really skeptical that he actually had an eidetic memory but regardless...) and can understand any concept incredibly quickly, you probably don’t need Anki. Also, if you’re the second coming if John Von Neumann and you’re reading this, cool!
To give another example, Terry Tao is a genius who also has spent his entire life doing math. Probably doesn’t need Anki (or advice from me in general in case it wasn’t obvious).
Finally, I do think how to use Anki well is an under-explored topic given that there’s on the order of 10 actual blog posts about it. Given this, I’m still figuring things out myself, in particular around how to Anki-ize stuff that’s more procedural, e.g. “when you see a problem like this, consider these three strategies” or something. If you’re also experimenting with Anki, I’d love to hear from you!
I would be surprised if Gwern hasn’t already thought about the claim going to make
I briefly looked at gwern’s public database several months ago, and got the impression that he isn’t using Anki in the incremental reading/learning way that you (and Michael Nielsen) describe. Instead, he seems to just add a bunch of random facts. This isn’t to say gwern hasn’t thought about this, but just that if he has, he doesn’t seem to be making use of this insight.
In the Platonic graph of this domain’s knowledge ontology, how central is this node?
I feel like the center often shifts as I learn more about a topic (because I develop new interests within it). The questions I ask myself are more like “How embarrassed would I be if someone asked me this and I didn’t know the answer?” and “How much does knowing this help me learn more about the topic or related topics?” (These aren’t ideal phrasings of the questions my gut is asking.)
knowing that I’ll remember at least the stuff I’ve Anki-ized has a surprisingly strong motivational impact on me on a gut level
In my experience, I often still forget things I’ve entered into Anki either because the card was poorly made or because I didn’t add enough “surrounding cards” to cement the knowledge. So I’ve shifted away from this to thinking something more like “at least Anki will make it very obvious if I didn’t internalize something well, and will give me an opportunity in the future to come back to this topic to understand it better instead of just having it fade without detection”.
there’s O(5) actual blog posts about it
I’m confused about what you mean by this. (One guess I have is big-O notation, but big-O notation is not sensitive to constants, so I’m not sure what the 5 is doing, and big-O notation is also about asymptotic behavior of a function and I’m not sure what input you’re considering.)
I think there are few well-researched and comprehensive blog posts, but I’ve found that there is a lot of additional wisdom the spaced repetition community has accumulated, which is mostly written down in random Reddit comments and smaller blog posts. I feel like I’ve benefited somewhat from reading this wisdom (but have benefited more from just trying a bunch of things myself). For myself, I’ve considered writing up what I’ve learned about using Anki, but it hasn’t been a priority because (1) other topics seem more important to work on and write about; (2) most newcomers cannot distinguish been good and bad advice, so I anticipate having low impact by writing about Anki; (3) I’ve only been experimenting informally and personally, and it’s difficult to tell how well my lessons generalize to others.
I feel like the center often shifts as I learn more about a topic (because I develop new interests within it). The questions I ask myself are more like “How embarrassed would I be if someone asked me this and I didn’t know the answer?” and “How much does knowing this help me learn more about the topic or related topics?” (These aren’t ideal phrasings of the questions my gut is asking.)
Those seem like good questions to ask as well. In particular, the second one is something I ask myself although, similar to you, in my gut more than verbally. I also deal with the “center shifting” by revising cards aggressively if they no longer match my understanding. I even revise simple phrasing differences when I notice them. That is, if I repeatedly phrase the answer to a card one way in my head and have it phrased differently on the actual card, I’ll change the card.
In my experience, I often still forget things I’ve entered into Anki either because the card was poorly made or because I didn’t add enough “surrounding cards” to cement the knowledge. So I’ve shifted away from this to thinking something more like “at least Anki will make it very obvious if I didn’t internalize something well, and will give me an opportunity in the future to come back to this topic to understand it better instead of just having it fade without detection”.
I think both this and the original motivational factor I described apply for me.
I’m confused about what you mean by this. (One guess I have is big-O notation, but big-O notation is not sensitive to constants, so I’m not sure what the 5 is doing, and big-O notation is also about asymptotic behavior of a function and I’m not sure what input you’re considering.)
You’re right. Sorry about that… I just heinously abuse big-O notation and sometimes forget to not do it when talking with others/writing. Edited the original post to be clearer (“on the order of 10”).
I think there are few well-researched and comprehensive blog posts, but I’ve found that there is a lot of additional wisdom the spaced repetition community has accumulated, which is mostly written down in random Reddit comments and smaller blog posts. I feel like I’ve benefited somewhat from reading this wisdom (but have benefited more from just trying a bunch of things myself).
Interesting, I’ve perused the Anki sub-reddit a fair amount, but haven’t found many posts that do what I’m looking for, which is both give good guidelines and back them up with specific examples. This is probably the closest thing I’ve read to what I’m looking for, but even this post mostly focuses on high level recommendations and doesn’t talk about the nitty-gritty such as different types of cards for different types of skills. If you’ve saved some of your favorite links, please share!
I agree that trying stuff myself has worked better than reading.
For myself, I’ve considered writing up what I’ve learned about using Anki, but it hasn’t been a priority because (1) other topics seem more important to work on and write about; (2) most newcomers cannot distinguish been good and bad advice, so I anticipate having low impact by writing about Anki; (3) I’ve only been experimenting informally and personally, and it’s difficult to tell how well my lessons generalize to others.
Regarding other topics being more important, I admit I mostly wrote up the above because I couldn’t stop thinking about it rather than based on some sort of principled evaluation of how important it would be. That said, I personally would get a lot of value out of having more people write up detailed case reports of how they’ve been using Anki and what does/doesn’t work well for them that give lots of examples. I think you’re right that this won’t necessarily be helpful for newcomers, but I do think it will be helpful for people trying to refine their practice over long periods of time. Given that most advice is targeted at newcomers, while the overall impact may be lower, I’d argue “advice for experts” is more neglected and more impactful on the margin.
Regarding takeaways not generalizing, this is why I think giving lots of concrete examples is good because it basically makes your claims reproducible. That is, someone can go out and try what you described fairly easily and see if it works for them.
If you’ve saved some of your favorite links, please share!
I like CheCheDaWaff’s comments on r/Anki; see here for a decent place to start. In particular, for proofs, I’ve shifted toward adding “prove this theorem” cards rather than trying to break the proof into many small pieces. (The latter adheres more to the spaced repetition philosophy, but I found it just doesn’t really work.)
Richard Reitz has a Google doc with a bunch of stuff.
I like this forum comment (as a data point, and as motivation to try to avoid similar failures).
One thing I should mention is that a lot of the above links aren’t written well. See this Quora answer for a view I basically agree with.
I couldn’t stop thinking about it
I agree that thinking about this is pretty addicting. :) I think this kind of motivation helps me to find and read a bunch online and to make occasional comments (such as the grandparent) and brain dumps, but I find it’s not quite enough to get me to invest the time to write a comprehensive post about everything I’ve learned.
So… I just re-read your brain dump post and realized that you described an issue that I not only encountered but the exact example for which it happened!
so i might remember the intuition behind newton’s approximation, but i won’t know how to apply it or won’t remember that it’s useful in proving the chain rule.
I indeed have a card for Newton’s approximation but didn’t remember this fact! That said, I don’t know whether I would have noticed the connection had I tried to re-prove the chain rule, but I suspect not. The one other caveat is that I created cards very sparsely when I reviewed calculus so I’d like to think I might have avoided this with a bit more card-making.
I want to highlight a potential ambiguity, which is that “Newton’s approximation” is sometimes used to mean Newton’s method for finding roots, but the “Newton’s approximation” I had in mind is the one given in Tao’s Analysis I, Proposition 10.1.7, which is a way of restating the definition of the derivative. (Here is the statement in Tao’s notes in case you don’t have access to the book.)
Although I haven’t used Anki for math, it seems to me like I want to build up concepts and competencies, not remember definitions. Like, I couldn’t write down the definition of absolute continuity, but if I got back in the zone and refreshed myself, I’d have all of my analysis skills intact.
I suppose definitions might be a useful scaffolding?
You’re right on both accounts. Maybe I should’ve discussed this in my original post… At least for me, Anki serves different purposes at different stages of learning.
Key definitions tend to be useful in the early stages, especially if I’m learning something on and off, as a way to prevent myself from having to constantly refer back and make it easier to think about what they actually mean when I’m away from the source. E.g., I’ve been exploring alternate interpretations of d-separation in my head during my commute and it helps that I remember the precise conditions in addition to having a visual picture.
Once I’ve mastered something, I agree that the “concepts and competencies” (“mental moves” is my preferred term) become more important to retain. E.g., I remember the spectral theorem but wish I remembered the sketch of what it looks like to develop the spectral theorem from scratch. Unfortunately, I’m less clear/experienced on using Anki to do this effectively. I think Michael Nielsen’s blog post on seeing through a piece of mathematics is a good first step. Deeply internalizing core proofs from an area presumably should help for retaining the core mental moves involved in being effective in that area. But, this is quite time intensive and also prioritizes breadth over depth.
I actually did mention two things that I think may help with retaining concepts and competencies—Anki-izing the same concepts in different ways (often visually) and Anki-izing examples of concepts. I haven’t experienced this yet, but I’m hopeful that remembering alternative visual versions of definitions, analogies to them, and examples of them may help with the types of problems where you can see the solution at a glance if you have the right mental model (more common in some areas than others). For example, I remember feeling (usually after agonizing over a problem for a while) like Linear Algebra Done Right had a lot of exercises where the right geometric intuition or representative example would allow you to see the solution relatively quickly and then just have to convert it to words.
Another idea for how to Anki-ize concepts and competencies better that I haven’t tried (yet) but will share anyway is succinctly capturing strategies pop up again and again in similar forms. To use another Linear Algebra Done Right example, there are a lot of exercises with solutions of the form “construct some arbitrary linear map that does what we want” and show it… does what we want. I remember this technique but worry that my pattern matching machinery for the types of problems to which it tends to apply has decayed. On the other hand, if I had an Anki card that just listed short descriptions of a few exercises and asked me which technique was core to their solutions, maybe I’d retain that competency better.
Anki’s Not About Looking Stuff Up
Attention conservation notice: if you’ve read Michael Nielsen’s stuff about Anki, this probably won’t be new for you. Also, this is all very personal and YMMV.
In a number of discussions of Anki here and elsewhere, I’ve seen Anki’s value measured in terms of time saved by not having to look stuff up. For example, Gwern’s spaced repetition post includes a calculation of when it’s worth it to Anki-ize threshold, although I would be surprised if Gwern hasn’t already thought about the claim going to make.
While I occasionally use Anki to remember things that I would otherwise have to Google, e.g. statistics, I almost never Anki-ize things so that I can avoid Googling them in the future. And I don’t think in terms of time saved when deciding what to Anki-ize.
Instead, (as Michael Nielsen discusses in his posts) I almost always Anki-ize with the goal of building a connected graph of knowledge atoms about an area in which I’m interested. As a result, I tend to evaluate what to Anki-ize based on two criteria:
Will this help me think about this domain without paper or a computer better?
In the Platonic graph of this domain’s knowledge ontology, how central is this node? (Pedantic note: it’s easier to visualize distance to the root of the tree, but this requires removing cycles from the graph.)
To make this more concrete, let’s look at an example of a topic I’ve been Anki-izing recently, causal inference. I just started Anki-izing this topic a week ago, so it’ll be easier for me to avoid idealizing the process. Looking at my cards so far, I have questions about and definitions of things like “d-separation”, “sufficient/admissible sets”, and “backdoor paths”. Notably, for each of these, I don’t just have a cloze card to recall the definition, I also have image cards that quiz me on examples and conceptual questions that clarify things I found confusing upon first encountering these concepts. I’ve found that making these cards has the effect of both forcing me to ensure I understand concepts (because writing cards requires breaking them down) and makes it easier to bootstrap my understanding over the course of multiple days. Furthermore, knowing that I’ll remember at least the stuff I’ve Anki-ized has a surprisingly strong motivational impact on me on a gut level.
All that said, I suspect there are some people for whom Anki-izing wouldn’t be helpful.
The first is people who have the time and a career in which they focus on a narrow enough set of topics such that they repeatedly see the same concepts and rarely go for long periods without revisiting them. I’ve experienced this myself for Python—I learned it well before starting to use Anki and used it every day for many years. So even if I forget some stuff, it’s very easy for me to use the language fluently after time away from it.
The second is, for lack of a better term, actual geniuses. Like, if you’re John Von Neumann and you legitimately have an approximation of a photographic memory (I’m really skeptical that he actually had an eidetic memory but regardless...) and can understand any concept incredibly quickly, you probably don’t need Anki. Also, if you’re the second coming if John Von Neumann and you’re reading this, cool!
To give another example, Terry Tao is a genius who also has spent his entire life doing math. Probably doesn’t need Anki (or advice from me in general in case it wasn’t obvious).
Finally, I do think how to use Anki well is an under-explored topic given that there’s on the order of 10 actual blog posts about it. Given this, I’m still figuring things out myself, in particular around how to Anki-ize stuff that’s more procedural, e.g. “when you see a problem like this, consider these three strategies” or something. If you’re also experimenting with Anki, I’d love to hear from you!
I briefly looked at gwern’s public database several months ago, and got the impression that he isn’t using Anki in the incremental reading/learning way that you (and Michael Nielsen) describe. Instead, he seems to just add a bunch of random facts. This isn’t to say gwern hasn’t thought about this, but just that if he has, he doesn’t seem to be making use of this insight.
I feel like the center often shifts as I learn more about a topic (because I develop new interests within it). The questions I ask myself are more like “How embarrassed would I be if someone asked me this and I didn’t know the answer?” and “How much does knowing this help me learn more about the topic or related topics?” (These aren’t ideal phrasings of the questions my gut is asking.)
In my experience, I often still forget things I’ve entered into Anki either because the card was poorly made or because I didn’t add enough “surrounding cards” to cement the knowledge. So I’ve shifted away from this to thinking something more like “at least Anki will make it very obvious if I didn’t internalize something well, and will give me an opportunity in the future to come back to this topic to understand it better instead of just having it fade without detection”.
I’m confused about what you mean by this. (One guess I have is big-O notation, but big-O notation is not sensitive to constants, so I’m not sure what the 5 is doing, and big-O notation is also about asymptotic behavior of a function and I’m not sure what input you’re considering.)
I think there are few well-researched and comprehensive blog posts, but I’ve found that there is a lot of additional wisdom the spaced repetition community has accumulated, which is mostly written down in random Reddit comments and smaller blog posts. I feel like I’ve benefited somewhat from reading this wisdom (but have benefited more from just trying a bunch of things myself). For myself, I’ve considered writing up what I’ve learned about using Anki, but it hasn’t been a priority because (1) other topics seem more important to work on and write about; (2) most newcomers cannot distinguish been good and bad advice, so I anticipate having low impact by writing about Anki; (3) I’ve only been experimenting informally and personally, and it’s difficult to tell how well my lessons generalize to others.
Those seem like good questions to ask as well. In particular, the second one is something I ask myself although, similar to you, in my gut more than verbally. I also deal with the “center shifting” by revising cards aggressively if they no longer match my understanding. I even revise simple phrasing differences when I notice them. That is, if I repeatedly phrase the answer to a card one way in my head and have it phrased differently on the actual card, I’ll change the card.
I think both this and the original motivational factor I described apply for me.
You’re right. Sorry about that… I just heinously abuse big-O notation and sometimes forget to not do it when talking with others/writing. Edited the original post to be clearer (“on the order of 10”).
Interesting, I’ve perused the Anki sub-reddit a fair amount, but haven’t found many posts that do what I’m looking for, which is both give good guidelines and back them up with specific examples. This is probably the closest thing I’ve read to what I’m looking for, but even this post mostly focuses on high level recommendations and doesn’t talk about the nitty-gritty such as different types of cards for different types of skills. If you’ve saved some of your favorite links, please share!
I agree that trying stuff myself has worked better than reading.
Regarding other topics being more important, I admit I mostly wrote up the above because I couldn’t stop thinking about it rather than based on some sort of principled evaluation of how important it would be. That said, I personally would get a lot of value out of having more people write up detailed case reports of how they’ve been using Anki and what does/doesn’t work well for them that give lots of examples. I think you’re right that this won’t necessarily be helpful for newcomers, but I do think it will be helpful for people trying to refine their practice over long periods of time. Given that most advice is targeted at newcomers, while the overall impact may be lower, I’d argue “advice for experts” is more neglected and more impactful on the margin.
Regarding takeaways not generalizing, this is why I think giving lots of concrete examples is good because it basically makes your claims reproducible. That is, someone can go out and try what you described fairly easily and see if it works for them.
I like CheCheDaWaff’s comments on r/Anki; see here for a decent place to start. In particular, for proofs, I’ve shifted toward adding “prove this theorem” cards rather than trying to break the proof into many small pieces. (The latter adheres more to the spaced repetition philosophy, but I found it just doesn’t really work.)
Richard Reitz has a Google doc with a bunch of stuff.
I like this forum comment (as a data point, and as motivation to try to avoid similar failures).
I like https://eshapard.github.io
Master How To Learn also has some insights but most posts are low-quality.
One thing I should mention is that a lot of the above links aren’t written well. See this Quora answer for a view I basically agree with.
I agree that thinking about this is pretty addicting. :) I think this kind of motivation helps me to find and read a bunch online and to make occasional comments (such as the grandparent) and brain dumps, but I find it’s not quite enough to get me to invest the time to write a comprehensive post about everything I’ve learned.
So… I just re-read your brain dump post and realized that you described an issue that I not only encountered but the exact example for which it happened!
I indeed have a card for Newton’s approximation but didn’t remember this fact! That said, I don’t know whether I would have noticed the connection had I tried to re-prove the chain rule, but I suspect not. The one other caveat is that I created cards very sparsely when I reviewed calculus so I’d like to think I might have avoided this with a bit more card-making.
I want to highlight a potential ambiguity, which is that “Newton’s approximation” is sometimes used to mean Newton’s method for finding roots, but the “Newton’s approximation” I had in mind is the one given in Tao’s Analysis I, Proposition 10.1.7, which is a way of restating the definition of the derivative. (Here is the statement in Tao’s notes in case you don’t have access to the book.)
Ah that makes sense, thanks. I was in fact thinking of Newton’s method (which is why I didn’t see the connection).
Although I haven’t used Anki for math, it seems to me like I want to build up concepts and competencies, not remember definitions. Like, I couldn’t write down the definition of absolute continuity, but if I got back in the zone and refreshed myself, I’d have all of my analysis skills intact.
I suppose definitions might be a useful scaffolding?
You’re right on both accounts. Maybe I should’ve discussed this in my original post… At least for me, Anki serves different purposes at different stages of learning.
Key definitions tend to be useful in the early stages, especially if I’m learning something on and off, as a way to prevent myself from having to constantly refer back and make it easier to think about what they actually mean when I’m away from the source. E.g., I’ve been exploring alternate interpretations of d-separation in my head during my commute and it helps that I remember the precise conditions in addition to having a visual picture.
Once I’ve mastered something, I agree that the “concepts and competencies” (“mental moves” is my preferred term) become more important to retain. E.g., I remember the spectral theorem but wish I remembered the sketch of what it looks like to develop the spectral theorem from scratch. Unfortunately, I’m less clear/experienced on using Anki to do this effectively. I think Michael Nielsen’s blog post on seeing through a piece of mathematics is a good first step. Deeply internalizing core proofs from an area presumably should help for retaining the core mental moves involved in being effective in that area. But, this is quite time intensive and also prioritizes breadth over depth.
I actually did mention two things that I think may help with retaining concepts and competencies—Anki-izing the same concepts in different ways (often visually) and Anki-izing examples of concepts. I haven’t experienced this yet, but I’m hopeful that remembering alternative visual versions of definitions, analogies to them, and examples of them may help with the types of problems where you can see the solution at a glance if you have the right mental model (more common in some areas than others). For example, I remember feeling (usually after agonizing over a problem for a while) like Linear Algebra Done Right had a lot of exercises where the right geometric intuition or representative example would allow you to see the solution relatively quickly and then just have to convert it to words.
Another idea for how to Anki-ize concepts and competencies better that I haven’t tried (yet) but will share anyway is succinctly capturing strategies pop up again and again in similar forms. To use another Linear Algebra Done Right example, there are a lot of exercises with solutions of the form “construct some arbitrary linear map that does what we want” and show it… does what we want. I remember this technique but worry that my pattern matching machinery for the types of problems to which it tends to apply has decayed. On the other hand, if I had an Anki card that just listed short descriptions of a few exercises and asked me which technique was core to their solutions, maybe I’d retain that competency better.