Life tip: If you want to study X but aren’t sure if you need to study Y first, just start studying X.
If you read a textbook is too hard, you will quickly discover and correct your mistake. If you read a textbook is too easy, you risk wasting months on material below your capabilities, and you won’t find out until you move on to the textbook you should have started with in the first place.
Could you give a specific example of what that failure mode looks like? I’ve either never experienced it or never noticed myself experiencing it.
EDIT: Would you agree with my advice when reading textbooks with exercises? That is, where your understanding of the material can be falsified with incorrect answers?
Ideally the learning process should follow the Prerequisites from Abstruse Goose linked elsewhere in the comments (hopefully except for the last panel). In reality, however, there is an overwhelming temptation to just look up the unfamiliar concept on Wikipedia and plow on. As a result, the incomplete understanding quickly compounds and it becomes impossible to make any meaningful progress.
As for exercises, yes, one has to do all the exercises in textbooks, and then some. Inability to solve some of the chapter problems or taking too long to do it is a good indication of missing some prerequisites.
So, to modify your advice, “If you want to study X but aren’t sure if you need to study Y first”, get a Y textbook and make sure you can solve or at least set up all or most of the exercises in it.
This disagreement was the point I was trying to make. That sometimes, the right advice is to just get started, such as the guy who thought he couldn’t start programming without learning a bunch of math first that I mentioned in the OP. I actually advised him to just start and backfill later. However, in other cases, it definitely seems right to learn things in order.
I suspect at least one of the failure modes related to not learning things in the right order is slower, more arduous learning that isn’t fun. If you struggle with the whole thing and look up the requisite material as you go, you don’t get a sense for which parts of what you’re learning are interesting results of thattopic as opposed to just requisite knowledge gaps. You don’t have the experience of thinking “that doesn’t sound right...” and then having your confusion cleared up as you keep reading and it is explained. Instead, everything sounds foreign and you don’t appreciate which parts of it are the interesting results of the topic at hand. This leads to poor retention and a low ability to apply what you’ve learned, even if you manage to make it through and “feel like you understand it.”
I suspect at least one of the failure modes related to not learning things in the right order is slower, more arduous learning that isn’t fun.
And if you want everything to make sense anyway, you’re going to learn the prerequisites anyways. So not only are you having more difficulties now, but you’re spending time getting a tenuous grasp on a subject that you’ll want to revisit later anyways once you can put things into a coherent framework.
Life tip: If you want to study X but aren’t sure if you need to study Y first, just start studying X.
If you read a textbook is too hard, you will quickly discover and correct your mistake. If you read a textbook is too easy, you risk wasting months on material below your capabilities, and you won’t find out until you move on to the textbook you should have started with in the first place.
Not in my experience. It’s pretty hard to figure out what you don’t know.
Could you give a specific example of what that failure mode looks like? I’ve either never experienced it or never noticed myself experiencing it.
EDIT: Would you agree with my advice when reading textbooks with exercises? That is, where your understanding of the material can be falsified with incorrect answers?
Ideally the learning process should follow the Prerequisites from Abstruse Goose linked elsewhere in the comments (hopefully except for the last panel). In reality, however, there is an overwhelming temptation to just look up the unfamiliar concept on Wikipedia and plow on. As a result, the incomplete understanding quickly compounds and it becomes impossible to make any meaningful progress.
As for exercises, yes, one has to do all the exercises in textbooks, and then some. Inability to solve some of the chapter problems or taking too long to do it is a good indication of missing some prerequisites.
So, to modify your advice, “If you want to study X but aren’t sure if you need to study Y first”, get a Y textbook and make sure you can solve or at least set up all or most of the exercises in it.
This disagreement was the point I was trying to make. That sometimes, the right advice is to just get started, such as the guy who thought he couldn’t start programming without learning a bunch of math first that I mentioned in the OP. I actually advised him to just start and backfill later. However, in other cases, it definitely seems right to learn things in order.
I suspect at least one of the failure modes related to not learning things in the right order is slower, more arduous learning that isn’t fun. If you struggle with the whole thing and look up the requisite material as you go, you don’t get a sense for which parts of what you’re learning are interesting results of that topic as opposed to just requisite knowledge gaps. You don’t have the experience of thinking “that doesn’t sound right...” and then having your confusion cleared up as you keep reading and it is explained. Instead, everything sounds foreign and you don’t appreciate which parts of it are the interesting results of the topic at hand. This leads to poor retention and a low ability to apply what you’ve learned, even if you manage to make it through and “feel like you understand it.”
And if you want everything to make sense anyway, you’re going to learn the prerequisites anyways. So not only are you having more difficulties now, but you’re spending time getting a tenuous grasp on a subject that you’ll want to revisit later anyways once you can put things into a coherent framework.
See the post “Double Illusion of Transparency”.