It is really, really, hard to find good math resources on the internet.
In my opinion, MSE provides an unmatched quality and talent compared to any other place on the internet. There are a lot of things I feel this site has to offer that could really help people love and understand math better, which is what this site is all about. But a lot of them are contained in "broad" questions. When I write a question on Math Stack Exchange, I spend 90% of my time just trying to frame the question so that it won't be downvoted; being broad is frowned upon, it is even a close reason.
The thing is, broad questions can be advantageous:
- You can't learn a subject by the asking specific questions; You can't learn arithmetic by just by looking at sums, just as you can't learn calculus by looking at specific integrals. Often times, it's the broad questions that are the most enlightening and useful.
- Sometimes, which at least I can speak to, learning a new subject is confusing. It's hard to know what's the right direction to take, how things are done in the biz, and especially, it's really hard to ask the right questions. I sort of just have to keep asking specific questions and hoping I'm asking the right thing (you can see on my profile this is what I've tried to do with Tensors, and I still don't really feel like I understand them). It has been said that the key to learning is about knowing how to ask the right questions. A broad question evokes broad answers; but broad answers then allow you to narrow your scope to pinpoint the specific thing you need to know. It helps you categorize specific information for future learning.
- It's hard to know how things are done in the biz. See this question of mine for an amusing example: Bilinear Functions Not Isomorphic to xy (geez, looking back at this I'm surprised it wasn't downvoted). Maybe the question is a bit fuzzy, and maybe you do or don't realize it. In any case, it should not be cause for alarm. If people knew they could get a better answer by adding more details they would. It's hard to know how things are done in the biz; sometimes broad questions don't get the answers you'd expect, but they are actually more useful. They might offer better methods, or let you know that "broad idea X" is not how working mathematicians think of something in the real world.
- There are no bad questions. In real life, we ask broad questions, and I don't know anyone who would deny that. It's what makes us human.
Hopefully I've clarified where I am coming from. Note that this is not an argument from reason, so please don't nitpick every detail; it is an argument based on my experiences, which I am sure many others share.
I also see that there are disadvantages of broad questions:
- Answer is opinionated (although broad certainly does not imply opinionated).
- The answer is not helpful or discusses things a bit besides the point.
- I have a vague idea that there's a ton more, so seriously, let me know in the comments and I will add it here.
I understand why we may want to limit broad questions, but is there nothing we could do? Maybe we could have a broad question tag - although please, I'm not ranting or complaining or asking why we can't do something about it, I just want to understand why this is the way it is.
Finally, I would also like to stress the distinction between a question which is not clear and one that is just broad. This is really important because without it I would be asking a different question. Moreover, I am talking about the functional definition of being too broad (or what some people would call, lazy - although the people who ask broad questions are not necessarily lazy in their attempts to understand something at all. Others might regard it as a question of scope. These different intuitive notions also seem to be a problem, but that is besides the point to what I am trying to say).
What I want to point out is, should we really be dismissive of the value of a broad question? Are we? My question is simply: