Great observation! I was struggling with the same issue when I moved from studying math to graduate ML research. Depth-first search is the right approach to reading a math textbook. Say, you started to learn homology theory and realized you don’t know what’s an Abelian group. You should stop and go read about Abelian groups, or you won’t understand what comes next.
However, the same approach was getting me in trouble when trying to understand state-of-the-art in voice processing. I would start reading an article in the morning, and by the evening I’d finish no articles and find myself stuck in the middle of a textbook reading about some 50 years outdated method which wasn’t relevant to modern research. So, I worked out that the effective approach to this task is breadth-first search: read the article from beginning to end, write down all unknown terms, go on to look up the most important one.
I think another reason why people might default to depth-first search is that BFS requires to store a list of unexplored nodes in memory and people don’t have a lot working memory. So a note-taking system like Zettelkasten really helps with applying this approach more broadly in one’s life.
Depth-first search is the right approach to reading a math textbook.
That’s a great point! I never explicitly thought of it like that but it’s clearly true now that you mention it. And not just math—nearly any scientific writing has the same quality where lack of knowledge about one idea or principle ruins your ability to understand any of it—these are examples of those “complex machines” which break if any part doesn’t work.
A friend of mine mentioned that reading Wikipedia tends to be like your second example—going depth-first (chasing links) instead of breadth-first when trying to learn about a topic. You end up with a hundred tabs and no smarter than you were before. That’s another failure mode where a breadth-first method like your note taking system presents advantages.
Great observation! I was struggling with the same issue when I moved from studying math to graduate ML research. Depth-first search is the right approach to reading a math textbook. Say, you started to learn homology theory and realized you don’t know what’s an Abelian group. You should stop and go read about Abelian groups, or you won’t understand what comes next.
However, the same approach was getting me in trouble when trying to understand state-of-the-art in voice processing. I would start reading an article in the morning, and by the evening I’d finish no articles and find myself stuck in the middle of a textbook reading about some 50 years outdated method which wasn’t relevant to modern research. So, I worked out that the effective approach to this task is breadth-first search: read the article from beginning to end, write down all unknown terms, go on to look up the most important one.
I think another reason why people might default to depth-first search is that BFS requires to store a list of unexplored nodes in memory and people don’t have a lot working memory. So a note-taking system like Zettelkasten really helps with applying this approach more broadly in one’s life.
That’s a great point! I never explicitly thought of it like that but it’s clearly true now that you mention it. And not just math—nearly any scientific writing has the same quality where lack of knowledge about one idea or principle ruins your ability to understand any of it—these are examples of those “complex machines” which break if any part doesn’t work.
A friend of mine mentioned that reading Wikipedia tends to be like your second example—going depth-first (chasing links) instead of breadth-first when trying to learn about a topic. You end up with a hundred tabs and no smarter than you were before. That’s another failure mode where a breadth-first method like your note taking system presents advantages.