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.)
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).