Learning with Sub-Parts

The following research article is overly optimistic in some ways. I don’t think it’s exactly correct but I do think the ideas are worth considering.

There are two intellectual tools you need to learn anything. One, you need to be able to learn simple things. Two, you need to be able to divide complex things up into simpler parts (sub-parts). If some sub-parts parts are still complex/big/hard, divide them again (sub-sub-parts). You can divide again to get sub-sub-sub-parts and repeat as necessary. Stop dividing parts when they’re simple enough for you to learn.

There are many ways to divide the same thing up. To enable learning well, you just need any reasonable division, not the best one. For example, want to learn philosophy? Philosophy is complex! So you need to divide it up, e.g. into schools of thought:

That’s not complete; it’s just a start. You can keep dividing those up, e.g. the books can be divided into chapters, pages, paragraphs, even sentences. Figuring out what one sentence says is usually simple. When it’s not, you can divide that learning project (learning the sentence) up into parts like figuring out what background knowledge might help, learning some of that background knowledge, making a grammar tree, and trying again.

Here’s a different way to divide up the project of learning philosophy (again, just a start, not complete):

Each node (oval plus text in it) can be further sub-divided which will create a sub-tree. The whole diagram is called a tree. Any node plus all the nodes connected under it are called a sub-tree, which is a way of looking at only a portion of the tree at once. When two nodes are connected, the top node is called the “parent” and the bottom is its “child”.

You could take the “Mario Odyssey” node and add more nodes under it. Alternatively, you could take a blank page, put “Mario Odyssey” as the root node (the node at the top with no parent node), and then put child nodes under it to elaborate on it. Either way, whether you made one giant diagram or two separate diagrams, the meaning is the same. Having it as one giant diagram makes it easier to see how the stuff under “Mario Odyssey” is related to “philosophy” by a string of connections. Having it as separate diagrams reduces clutter and makes it easier to focus on some stuff without the rest. They’re just different presentations or views of the same underlying reality (the same underlying nodes and connections).

So that’s it: learning is just two steps. Splitting complexity up and doing simple/easy things. So, in some sense, learning is fundamentally easy.

However, there can be a lot of parts. You can lose track. So there’s sort of a third step: staying organized and keeping track of what you split into what parts and which parts you’ve already done, as well as remembering to combine the parts together again after you finish them. This organization or management aspect is a common source of learning failures. Tree diagrams can help with this step.

And maybe combining the parts back together is a step. It shouldn’t be very hard since if you split something into parts yourself, then you should know how those parts go together. But maybe it’s hard sometimes for some reason.

Does everything complex really split up into simpler parts? Either it’s already simple and easy, or you can split it more? I think so! I could give some theoretical arguments about e.g. irreducible complexity, but maybe just try it and see. You’ll find ways to split lots of things. If you find something you think is both complicated and indivisible, you could share it for feedback.

Learning Chemistry Example

Example: Want to learn chemistry? Split that into finding out what books are good, reading the books, finding places to ask questions, asking questions, reading the answers, etc. Where is the hard step?

Maybe you think finding out what chemistry books are good sounds hard. That’s fair. But we did split up learning chemistry into easier parts. If you can do that, you’re making progress, even if the parts are still hard. You just have to keep splitting. How can we find out what books are good? One way is to try reading a bunch and compare. That’ll take a lot of time but time is a different issue than difficulty. A better approach is to read some Amazon reviews, Quora answers, Reddit threads, etc., then try a few highly recommended books and start forming your own opinions. For something more obscure you might want to ask some questions yourself, but for chemistry you’d be able to find questions people already asked and the answers they already got.

Next we have to try reading some books. Is that hard? Well, not really. First of all, we’re just trying books to see if they’re good. If a book is confusing, we’ve successfully gotten our answer. Also, if you can understand individual sentences then you can understand paragraphs. If you can understand paragraphs, you can understand sections. If you can understand sections, you can understand chapters. If you can understand chapters, you can understand the book. Is understanding the individual sentences too hard? I doubt it. You might have to look up some terminology or understand some math. Some sentences could take work, but that work can be divided into sub-parts like looking up each word you don’t know, doing practice problems, and reading something else that gives more details about a concept.

This wouldn’t work if a book is disorganized nonsense. But I’m sure there are lots of OK chemistry books. I don’t know if any are great, but some are reasonably organized, reasonably coherent, etc. The sentences do fit together into paragraphs which fit together into sections. And most of the individual sentences make sense. (You may occasionally have to conclude that a particular sentence has an error, rather than understanding it as the author intended. But if that isn’t too frequent, you can generally learn from the book anyway.)

A lot of books have flaws that make learning harder. Some parts are under-explained. Even if the book doesn’t have many errors, understanding every sentence isn’t good enough because they leave out some important points. How do you deal with this? How do you fill in the unstated blanks? By looking at other books and online resources, by thinking about it yourself, by asking people.

What if a sentence has technical jargon so you have a hard time understanding that sentence? Read more background material to find out what it means.

What if a sentence refers to a difficult concept? Read a separate book (or article or podcast) on that concept.

None of this is hard. Whenever you hit an apparent hard part, you make a sub-project to work on dealing with that.

It can take time and effort though. You have to actually do all these steps. It can expand into a big number of things to do. And that’s reasonable. I’m not trying to offer some shortcut so you can learn chemistry in three days. I’m just saying that you can learn it, and it’s not that hard, and I’m talking about what the method is. You don’t need some sort of innate genius or talent to do these steps.

Difficulties

So the big problem with learning is not the difficulty. And it’s not time either. It’s not some big problem that you can’t learn every field because you don’t have enough time. The big problem is that people aren’t methodical. It’s not particularly hard to make tree diagrams or otherwise keep track, in writing, of your learning project. You can record what you split into what, and record which parts you’ve finished. But people don’t know that’s what they need to do. Intuitively they do it some, which is how they learn some, but then for bigger projects they lose track and it falls apart. Or they don’t follow the method consistently; for some parts they decide it’s complicated and hard and they just give up and get stuck instead of splitting it up more.

There are other problems people run into like forgetting stuff they learned in the past. That often means they never learned it properly in the first place. E.g. they skipped practicing or never really understood it well. If they did learn it correctly and forgot, relearning it should go pretty quickly and smoothly (unless it’s been a really long time and they forgot too much, in which case it might take more work to relearn if they find the past learning isn’t coming back to them).

Another problem is inventing new, original ideas. That’s harder. I haven’t been trying to explain how to be a pioneer; I’ve been focusing on how to learn what’s already known. The splitting and doing small things method is useful for pioneering too but don’t try that until you’ve already had a lot of success with it.

It’s possible to use the splitting method for learning anything, even creating new ideas. You figure out what you want and split it into various different new pieces of knowledge to invent, and keep splitting until the parts get easy. But one of the hard parts is lots of the ways of splitting don’t end up working out. You can run into dead ends and have to go back and try some other splitting method. Whereas when you’re learning stuff that lots of other people already know, then standard splittings/sub-projects, like reading books that explain something, make it a lot easier to figure out good splits.

So maybe splitting can be hard in theory. Or maybe it’s just time-consuming to keep trying things until you succeed, but not exactly “hard”. It depends what it means for something to be “hard”. We have lots of intuitions about that but it’s hard to actually define it precisely.

In general, if lots of other people have learned something, then some reasonably effective splittings are available and you should be able to learn it too without a bunch of dead ends and failures. But if you’re breaking new ground, it may take more attempts and cleverness to get the splits right. (Just brute force trial and error, with no cleverness, won’t work because there are infinitely many ways to split things up, and there are vastly more ways to fail than succeed.)

Learning recently created knowledge, where not many educational materials exist, can also be more difficult. You could gradually work your way up through whatever educational materials do exist and then start networking with the few people at the top of the field and start going to their lectures and asking them questions. But my main goal is to discuss a method to let people learn stuff that has reasonable help and resources publicly available without needing to rely on help from any particular people.

Conclusion

In conclusion, it’s useful to know the method of splitting complexity up into smaller parts plus doing simple/easy things. You can conceptualize your learning that way and do it on purpose. It also helps to keep track of what you’re doing. Use project management techniques like tree diagrams or nested lists. Keep notes on what you’ve done and what you haven’t done yet. You should be able to remember or quickly look up how the thing you’re currently working on fits together with some other parts to make something bigger, and what that bigger thing fits into, and so on, all the way up to your goal at the top. People often don’t do this, so there’s a lot of room for improvement.