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How I've personally applied the Math Academy learning approach to areas outside of math (specifically biology and music).

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The transcript below is provided with the caveat that there may be occasional typos and light rephrasings. Typos can be introduced by process of converting audio to a raw word-for-word transcript, and light rephrasings can be introduced by the process of smoothing out natural speech patterns to be more readable via text.

Intro

I’m back, excited to get this Q&A thing going again.

Thank you guys for such really good questions. It was honestly pretty hard to choose which one to answer today. But I noticed a particular question that I see every once in a while over and over again. And actually two people asked it in the comments here. I figured I might as well address it.

The general question is: how do you apply math academy principles to another topic? How do you learn some other domain, leveraging the math academy way as much as possible?

But where there’s not all this knowledge graph infrastructure, space repetitions built into a service for you — you’re roughing it out in the wild. What do you do? You got to get from point A to point B, but you don’t have a car. How are you going to hack your way through this jungle of knowledge, of skills to acquire as efficiently as possible?

In particular, how do you do this in an incremental fashion, one step at a time, where it doesn’t depend on you having existing knowledge of the domain? And it doesn’t depend on you being a genius. All it depends on is that you’re willing to work hard and also work smart, efficiently, not screwing around, not wasting time. You came here to learn the thing, and that’s what you’re focused on. You’re going to put a full-ass effort into it, and you’re going to show up consistently.

What are you going to do? How are you going to learn the thing? What’s your game plan? What’s your approach?

Now, there’s a million questions you can ask about this. Do you already need to know a subject and break it down like that effectively? Do you have to make your own knowledge graph? Do you have to do a spaced repetition plug-in?

And I think the easiest way to actually answer all of these is just to give some concrete examples of personal experiences that I’ve had successfully mapping the math gap approach over to other things that I’ve wanted to learn.

Instead of trying to answer a bunch of abstract questions, let’s just take a trip to the zoo. From that zoo of examples, you can extract a lot of these general principles. In particular, I’m going to focus on some domains where it’s really not obvious, or at least it wasn’t obvious to me, how you’d go about learning it.

We’re not going to talk about math. We’re not going to talk about anything quantitative, because that’s kind of a canonical example where I talk about all these learning techniques. You guys already know about that.

We’re not going to talk about athletics, because that’s kind of the canonical analogy. These things are just so much more obvious than athletics. You want to lift weights? You want to get strong? Start with a weight. You want to put more weight on the bar? You want to learn a bunch of cool calisthenics moves? Find some good progression. Start at your level, work your way up. People have a general idea of that.

Now, we’re going to focus on two tricky cases that I’ve encountered in the past year. One is learning biology, and the other one is learning a musical artist.

To frame the goal, my end goal in my pursuits of learning these things was to be able to connect better with people that I know and love. I always find that you can connect a lot more deeply with somebody if you can talk coherently, have an interesting conversation about some area of passion in their life.

The main bottleneck to having an interesting conversation with somebody else about their area of interest is that you probably don’t know shit about it. And if you try to talk about it, you don’t know what the hell you’re talking about.

You just end up asking these really basic questions, which can be kind of an enjoyable conversation, but it gets old really fast.

When you have a good conversation with somebody, there’s a sort of uniqueness to the conversation. You’re not asking or answering a bunch of questions that are really easy to Google or just learn about on an LLM. By that point, both parties have serious foundational knowledge. Because of that, you don’t have to spend time going back and forth about really basic stuff. You’re closer to the edge of human knowledge about this, and that’s where it gets really interesting.

That was my goal. How do I spin up on base foundational knowledge to have really interesting conversations with people that I know and love about their passions that I started out really not knowing much about?

Learning Biology

Without further ado, let’s jump into the first one: biology. Last fall, I actually started learning biology. My wife’s doing a PhD, and beyond high school biology classes, I don’t really know a whole lot about the subject. I always made an effort to talk with her about it, but it always felt like there was just a ceiling on how interesting, how deep our conversations could go without me just stumbling over some really basic stuff.

Gene expression—what even is a gene? What does it mean to turn some genes on, some genes off? Don’t get me wrong. I know what a gene is at a high level. Genes are what make people different from one another. Turning it off or on means you’re basically enabling or disabling certain characteristics of an organism.

But that high-level, super simplistic surface-level understanding is not enough to have a really interesting conversation with somebody who’s an expert, who really cares about this. I wanted to really understand this down to the level of what’s happening in the cell, DNA.

If you asked me before I went down this biology studying rabbit hole, I just couldn’t tell you anything. DNA is in a nucleus, right? I knew that. But how does it get outside? What components of the DNA are genes? What converts genes into molecules that go places? I didn’t know any of this shit.

I went down this rabbit hole wanting to really understand at a nuts-and-bolts level what’s happening with the DNA, what’s happening with the organelles inside the cell, what are all the knobs and levers that are getting pulled in the pipeline from having a jump ball of DNA to governing the whole functioning of this organism.

The problem was, I never pulled the trigger on this before because it was just too painful. The learning experience just sucked. Crack open a textbook and it’s a thousand words on a page, really long-winded. I start reading through it, get to page two, and realize it’s talking about the nuances of something on page one—I forgot even what that thing does. By the time I’m just skimming, it’s so boring, my eyes are glazed over. There’s hundreds of pages to go. I was spinning my wheels, not really getting anywhere.

It sucks spinning your wheels and not really getting anywhere. It’s just not fun. I like coming away actually being able to do things and talk about things that I wasn’t able to before. That is measurable, demonstrable learning. You need to be able to do things that you weren’t able to do before you started learning the thing. If that’s not happening, you’re not learning. And if you’re not learning, what are you even doing? You’re just wasting your time spinning wheels. That’s what I was trying to avoid.

I know what you do: you read the chapter, you do the problems at the end of the chapter or whatever. But these cycles, these feedback loops, take way too long and there’s just too much friction. If I’m gonna pull the trigger on this, I need much more bang per buck, much more learning per unit time that I spend in this thing. If I’m actually gonna do it and not just fall off the wagon on day one.

My first step was poking around for other resources just to see if there’s a math academy sort of style thing that exists for biology. I did get some recommendations and I checked out all the recommendations. But what I was finding is so many of these recommendations were basically the same as three blue one brown but for biology. I’d explore some interesting questions, see some interesting visuals, some animations. That’s cool, that can be fun.

The problem is it’s still kind of passive. I want to learn this shit cold. If I wanted to go get rocks off on doing some basketball moves or whatever, I’m not gonna do that by just watching highlight videos on YouTube. It can be fun to watch, it can be inspiring, it can be motivating. But ultimately, you’re a spectator. You want to seriously elevate your game in anything—not just sports, not just math—literally anything.

You can’t come at it with a spectator mentality. You gotta be doing exercises, lots of exercises. Most of the time that you spend in your learning session should be doing exercises.

You need to consume information to know what exercises to do and how to do them. But if you’re trying to maximize efficiency, get the most bang for your buck, every piece of information that you consume should be consumed with the purpose of enabling you to produce. That’s how you get stuff to stick in your head—by practicing pulling it out of your head.

What I ended up doing with biology is I was like, all right, not gonna go down the textbook path. And I’m not just gonna spend my time watching videos. I’m gonna use an LLM to give me bite-sized pieces of information that enable me to do exercises based on that information.

I know it’s not gonna be as good as a carefully curated curriculum. I know that LLM’s gonna forget stuff. Spaced repetition isn’t gonna be amazing. I know it’s not gonna be fully comprehensive. But maybe I can get some halfway decent, quick learning loop going where it delivers a bite-sized piece of information, has me do a bite-sized piece of work wrestling with that information and retrieving it from my head so I actually retain it, and make sure I actually get things right so that I know I’m actually understanding this information and not just glossing over it at surface level while misunderstanding a lot of details about it.

Basically what I did was I just chucked the math academy way into the LLM, just a straight-up PDF. I didn’t even try this. I know you’re supposed to summarize these things, take it through a pipeline of consolidating the information so you don’t blow up the context window. But remember what we’re dealing with. I’m in this situation because I don’t have a whole lot of time. I just wanted to get on with things and just have the LLM and some base amount of information that would kind of orient it in the right direction.

It actually worked decently well. We started off with some diagnostic questions. It got a halfway decent sense of what I knew. Again, this is nothing near a precision system, but it’s better than a textbook. Not great, but just good enough to remove enough friction to keep me going with it.

It took a lot of correcting its actions. No, no, no, don’t give me a thousand words to read and then ten questions afterward. Don’t even give me big paragraphs—just really simple, bite-size, short snippets of information. Then just ask me two or three questions based on that information.

Don’t make them open-ended questions like “write me an essay on blah blah blah.” Make them basic questions to check that I understood what I read and force me to pull that understanding out of my head so I can actually start to chunk it up in long-term memory and use it fluently as I layer more information on top.

Another thing that I had to very explicitly fine-tune was that this is not about shaping the learning experience around my curiosity. I want to learn this stuff, but I don’t have a million burning questions. If I came up with a bunch, it would just be a waste of time, because all these questions are gonna be made trivial by the foundational knowledge that I’m gonna acquire. All I’d do is push the LLM to take me down some rabbit hole, and going down that rabbit hole I’d miss out on all the good stuff—like all that spaced review and interleaving.

For Christ’s sake, I’m always telling people to go through the question bank breadth first, not depth first. That’s something I had to very explicitly instruct the LLM to do. But after some initial fine-tuning, I actually got to a point where I had these halfway decent quick learning cycles, deliberate practice cycles.

I would do half an hour a day, and I could feel that it was really cognitively taxing, but in a good way. It really felt like a cognitive workout session. I would do twenty exercises in a thirty-minute session that included the bite-size pieces of information interspersed. All these exercises and bite-size pieces of information would be building on each other.

I came out learning a lot more than I ever did with any other resource. As a result, I had a lot of really interesting biology conversations with my wife.

She was pretty impressed. From her point of view, it was like each week somebody just injected a truckload of knowledge into my brain, matrix style. It just got uploaded, now it’s there, and now we can talk. I can use all of it in our conversations.

She didn’t have to remind me of stuff and re-explain things to me. It was like, no, no, no, I got this. Let’s go play some intellectual basketball. Show me some cool moves. I know how to dribble. I know how to shoot. I’m going to continue improving at this stuff, but I’m at a point where we can actually talk strategy. I can ask some interesting questions that aren’t made trivial by foundational knowledge.

Overall, a success. No, I should say if anyone’s out there building a really serious biology training arena, it’s really good and I would absolutely pay for a speed-up from that. Because this LLM stuff—it was better than a textbook, it was better than watching videos. But man, it was still pretty rough.

However much additional efficiency this LLM setup captured over the standard textbooks and videos, there’s still a way, way bigger efficiency gain on the table if a subject matter expert actually curates content, makes a really good fine-grained knowledge graph, a precise diagnostic and review mechanism, timed quizzes to really build that automaticity.

All this stuff is actually hard coded, so it’s just there, problem solved. You don’t have to worry about keeping the LLM on the rails, because it’s always drifting off. If you’re not continually aligning it, or you don’t even know how to detect that it’s drifting off, then your learning experience will just get eaten alive by the AI slop.

I guess that was kind of the overall conclusion of this LLM-based learning experience that I set out, where you really need to be an experienced driver behind the wheel. The secret sauce of this is that you really have to be an expert on what efficient learning is, what it looks like.

You need to be able to detect when things are starting to drift off course, go haywire, and then nudge and recalibrate technique to keep the experience on the rails, to keep you in that active learning loop. If you don’t really know what efficient learning looks like, or if you’re somebody who will drift off the moment somebody stops holding you accountable for learning, things will go completely off the rails.

You really have to be the coach or tutor or whatever to the LLM about what efficient learning is so that it can deliver that to you. If you want to learn a subject where there’s not a really good adaptive learning system, but you’re not a super nerd on maximizing learning efficiency, I don’t know how this solution would work out.

But if you are a super nerd on maximizing learning efficiency, then you can kind of roll your own learning experience and have it be more effective than typical textbooks and videos.

At least one person other than me has managed to pull this off. Rafael Travis actually did a similar sort of thing to improve his painting skills. I’m no painter, but that looks like serious progress to me. He went into great detail about how he made this happen, and he shared some chat logs.

His end result was pretty awesome. He said that in his painting group, a pro-level artist was amazed by how much progress he’d made in just a couple of months. And these are not just beginner gains. This is after beginner gains. He got stuck in a plateau, and this is what broke him out of the plateau.

If you want to do your homework, learning about learning efficiency and enrolling your own learning experience in an LLM, you can really come a long way with it, even though there’s still going to be a lot of efficiency left on the table.

If you are skilled enough at designing efficient learning experiences, then you can turn this into a significant speed-up over your typical textbook or video lecture series on YouTube.

That’s one approach. Worked for me for biology, worked for Raphael for painting. I think it’s a decent DIY technique for a lot of hierarchical domains.

Learning a Musical Artist

But what about less hierarchical domains? I just recently started writing about this here and there. I actually went on a second learning expedition to spin up on musical artists that my sister was lost into.

In terms of end goals, it’s basically the same situation as biology. There’s something that I don’t know shit about. But there’s somebody important in my life who’s really passionate about it. It would be an opportunity for us to connect over it. But that’s only going to happen if I actually know things when we talk about it.

It’s also similar in that I don’t have a ton of intrinsic interest in the domain. If these people weren’t in my life, then I probably wouldn’t bother with learning.

All these strategies are pretty inefficient, but you might be able to make it work. You put in enough volume and enough thinking about it on your own throughout the day based on just consuming information. That’s not going to work for me. I got max 30 minutes a day. I got to make that count.

What am I going to do? How am I going to spin up on these artists, their songs, to the point where I can actually make a meaningful contribution to conversations about it?

The one really interesting thing about this domain as opposed to biology is that the knowledge graph—if you were to make a knowledge graph for it—would be very, very, very wide. Way wider than biology, which is already way wider than math.

Now we’re getting into the domain of much less hierarchical knowledge structures. It’s not to say that it’s un-hierarchical, because there are levels of hierarchy to it.

For instance, know the lyrics to a song, really understand the meaning of the song, understand how that fits into the album as a whole, understand how that album fits into the artist’s journey as a whole.

What I’ve realized is that this domain of spinning up on an artist’s music looks a lot more like language learning than math learning. There’s just a lot more primitives that you have to have rock solid in memory before you’re able to keep building on top of them and connecting the dots and all that stuff.

What I’ve done so far is I’ve listened through some albums while working on other stuff, just so that when I look at the lyrics, I can be like, oh, I’ve heard that song before. And also so that I can prioritize what songs I wanted to study first. There are some that I like more than others.

This is a relatively flat knowledge domain. That means there’s more room to leverage even an inkling of intrinsic interest. You have more choice in the matter of what path you take through the knowledge domain. Whereas in domains that are relentlessly hierarchical, that hierarchy really constrains the efficient path that can be taken through that knowledge domain.

I listened to a bunch of songs. I got some songs I like more than others. Even before I dove into individual songs, I decided to put down a bunch of memory anchors throughout the whole space. I wrote down a bunch of lyrics that I liked or were relatable in some way, or just that I had some kind of connection with.

I put them in a spreadsheet and did spaced repetition with them. I know loading them up into an actual spaced repetition system would increase the efficiency of the spaced repetition. But I just wanted to do it in a flexible format, because I didn’t know exactly what my cues were going to be.

It turned out I was actually changing the cues over time. I started out shrinking the spreadsheet window so that I could only see the first two or three words of a line. Then I would try to predict the rest of the line. Eventually I got really good at that and added a new column where I wrote down a couple words describing my connection to that line of lyrics. That would be my cue, and I’d have to recall the whole line without seeing any part of it.

I did that for a while, and I got to the point where I was actually able to make a lot of lyric references in conversation.

Then I got to the point where I was like, OK, I’m ready for the next level up. We’re not just going to remember lines of lyrics in isolation. We’re going to learn the whole song. We’re going to fill in the connective tissue between these lines of lyrics.

That way it’s no longer just about my relationship with those lines, but I can actually start to better understand the artist’s relationship with those lines of lyrics in the context of their overall song. This was actually something I tried before putting down these individual lyric anchors, but before the lyric anchors it was just too hard.

The lyric anchors helped scaffold me up to recalling entire songs, which is another benefit of the breadth-first approach. You’re going down multiple parallel learning tracks, you get really solid on your primitives, and it’s easier to connect them together as you climb to higher and higher levels of cognitive scale.

I kind of visualize it like this: you’re building a brick house. You want to get a full layer of bricks down before you start building more layers on top. It’s a lot harder to just put down one brick, then the next brick right on top of it, and right on top of that, and right on top of that. You’re asking for things to go wrong. I’m no bricklayer, but it sounds like building the bricks tower by tower, which makes things way harder than they have to be and way less efficient.

That’s what the memory anchors were for me. That first layer of bricks that supports the next layer of bricks, which is recalling songs as a whole.

What I do to practice song recall is I’ll look up the lyrics on my phone, but I’ll cover the bottom half of the phone with a credit card or a piece of paper. That way I can’t see the rest of the lyrics. I incrementally try to predict the next line of lyrics and scroll up.

I’m also recalling not just the lyric, but the song—the whole melody and backing music. I’m trying to play the next couple seconds of the song in my head without actually listening to it. To measure my performance, I count how many lines I get incorrect or how many times I can’t remember how the song goes.

I actually just use a physical tally counter for that. I tally up the number of mistakes that I make as I go through the song. I put that in the spreadsheet and do some low-grade spaced repetition based on the number of mistakes I made.

That’s working out really well. I can see my number of mistakes going down. Maybe the first time I did a song, it took 35 mistakes. Then a while later, maybe 25. Then a longer period of time later, down to 18 mistakes or something.

Now I’ve reached the point where once I’m down between 10 and 20 mistakes, I really need to focus on the segment of the song where I’m making most of the mistakes. Oftentimes I’m a lot quicker to learn the chorus than the verses, just because it’s the same lyrics repeated over and over. And it’s catchier.

When I sense that happening, then each time I go through the song, I only recall the chorus once. Then I skip the other choruses to save time and focus on the areas where I’m actually making mistakes.

On other occasions, sometimes it turns out that there’s a song I thought I knew well enough to start doing retrieval practice on, but I’m forgetting basically every single line. I can’t really remember how the song goes. It’s just too difficult. I’m not really getting a whole lot of mileage out of that form of practice. It’s like I’m at the gym trying to lift the heaviest weight and just not getting it off the floor.

If that happens, I need to scaffold into the full song prediction. What I do is actively listen to the song while constantly trying to predict the next few words. I’m not just consuming the song. I’m actually having the song play, but I’m still doing this exercise where I’m trying to predict the next few seconds of the song.

That serves as pre-training. Right after that, I’ll try to do it again but without the song playing. Just scrolling up the lyrics on my phone, the normal song recall testing exercise that I’ve set up. I’ll track my performance on that. Once I’m able to get to a decent level of performance pre-trained, then I’ll level up to the usual spaced repetition. No pre-training—just trying to pull it from memory each time.

So far, I’ve found that’s pretty efficient. Most songs, if I have to pre-train, I only have to do it once. The next time I come back to it, I’m able to recall enough from memory to make the real deal of retrieval an effective form of practice.

I think there’s only one song where I had to do two sessions of pre-trained retrieval before moving on to non-pre-trained. I guess pre-training is not the right word to use here. It’s not like I’m doing it untrained. There’s a lot of training leading up to this. It was just whether or not there was an immediate review of the song before the real deal of retrieval.

I’m always trying to avoid consuming information right before I recall. The only time I’m doing that is when I just have no idea what the information is. I’ve completely forgotten. I tried my hardest to retrieve, but I need a reminder. It’s like the spotter at the gym. You don’t let the spotter lift the weight for you, because otherwise you’re not lifting the weight. You’re not going to get strong. But if you really cannot get the weight up, then okay, spotter, intervene.

What I’m trying to do is strike the perfect balance between the task not being too easy or too hard. It needs to be just at the edge of my abilities. The moment it gets comfortable is the moment that I jump up to the next level.

What you’re doing in this kind of training is building these chunks in your long-term memory. Not just one layer of chunks on top of some isolated information, but also chunks of those chunks. And then chunks of those chunks of those chunks. It’s basically like you build this brick wall of chunks high enough, you build it up into the sky. That’s how you can really engage in deep conversation at a high level.

Everything you’re talking about at a high level is actually deep. It’s built upon a tower of knowledge. These towers of knowledge don’t get built accidentally.

Outro

I hope this helps explain how to use the Math Academy way to learn other subjects as well. Break things down into bite-sized components. Get a lot of high-quality reps of those components. Really tight feedback loop—compound, compound, compound. Lay down the first layer of bricks. Lay down the next layer of bricks. Keep building this thing up.

Build chunks in long-term memory. Build chunks on top of chunks. Chunks of chunks of chunks all the way until you’re wielding these gigantic swaths of memory and information. Almost effortlessly. Things just pop into your head whenever they’re needed.

Just like Thor’s hammer flies into your hand. You’re swinging this thing around. It’s super massive, but it feels as light as a feather. That’s the experience you want. That is the experience of max-efficiency learning.

And that’s all I got for today. But I’m going to get back to doing this Q&A regularly. Maybe once every two weeks or so.

I’ll make a post inviting any requests just like this time. Feel free to put follow-up questions on there. Or if I didn’t get to your question this time, but it’s a good one, please feel free to post it again next time.

I really wish I could get to every single one of them. But in order for me to stay on the wagon with this, I got to really scope it down, really quick. Just one question every couple of weeks. Not a big thing. Not a big push. Something that I can stick with consistently into the future.

Thanks for listening. See you next time.

Prompt

The following prompt was used to generate this transcript.

You are a grammar cleaner. All you do is clean grammar, remove single filler words such as “yeah” and “like” and “so”, remove any phrases that are repeated consecutively verbatim, and make short paragraphs separated by empty lines. Do not change any word choice, or leave any information out. Do not summarize or change phrasing. Please clean the attached text. It should be almost exactly verbatim. Keep all the original phrasing. Do not censor.

I manually ran this on each segment of a couple thousand characters of text from the original transcript.

Follow-Up Questions

Would be great if you could expose a little bit what your llm generated biology questions / study sessions looked like. Even just for 1 day

See this post.

What about learning music production? Like more Creative endeavors that don’t really have a structured thing and aren’t like memorizing biology facts or in your case just memorizing song lyrics?

Quick answer: From personal experience, I think the most efficient way to successful creative production is 1) building rock-solid fundamentals and then 2) leaning into creative projects.

This worked out really well for me in math: I self-studied pretty much a full undergrad curriculum during high school and then leaned into research projects/internships towards the end of high school / beginning of college, and I even worked full time as a data scientist during college, and all that combined with my experience in math education set me up perfectly to help build Math Academy. More details/links in my bio.

During college I also leaned into music production projects, but the key difference was that I skipped step 1 of fundamental skill training, and that really limited what I was able to creatively produce. I made some progress, produced some stuff that I thought was cool for a relatively untrained amateur, but it just wasn’t anywhere the level needed to make a career out of it.

In hindsight I wish I had trained music the way I did math: prioritizing structured training first, then goal-oriented pursuits with economic value second, and relegating free play to a distant third – or better yet, folding it into creative approaches within those goal-oriented pursuits.

More info on my music page.

Also related: this post.

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