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...But seem natural to ask at the time?

I think this happens to me fairly frequently.

Just to be clear, I'm not talking about asking questions that I know nothing about. But on topics I haven't studied in a (very) long time and I'm asking out of curiosity: maybe I just need to jog my memory on a couple of things. But maybe I have forgotten everything - I don't really know until I spend time trying to understand the topic again.

For example, I haven't studied Inner Product Spaces in many years, but this question just came up and I thought it would be interesting to ask a follow-up question:

In an inner product space, is it necessarily true that $\langle u,v\rangle = 0 \implies ( u=0 \text{ or } v=0 )$? If not, does there even exist an inner product space such that: $\langle u,v\rangle = 0 \implies ( u=0 \text{ or } v=0 )$?

I think there are pros and cons to doing this. One con is that your time could be spent learning something more helpful to yourself now, or better spent doing something else altogether. On the other hand, if you did ask the question now, then you might come back to it a few weeks/months later with more knowledge and you'd be thankful to your past self that you did ask it at the time, because now you can have that "ahah!" moment in understanding the answer to your question.

I think this is clearly a matter of personal judgement also. But I thought it would be interesting to hear peoples' views on this, and how they decide if they should even ask a question if they know they're unlikely to understand the answer immediately or any time soon.

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    $\begingroup$ Personal view: I think it is very hard to ask a good question in a field one knows nothing about. The sort of thing you describe works well in a one-on-one situation with someone who knows you and who understands what you are familiar with and what you are not. That person can then relate the question to subjects you have considered. But in a (roughly) anonymous format, as here, I think it's unlikely to yield anything productive. $\endgroup$ – lulu Jan 16 at 19:24
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    $\begingroup$ I used to know about inner product spaces. But now I've forgotten it all. I could probably pick it up again reasonably quickly, but then I guess I should probably be bothered enough do that before asking questions about it. $\endgroup$ – Adam Rubinson Jan 16 at 19:26
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    $\begingroup$ A personal view, motivated by your sample question: You should spend at least 5-15 minutes thinking about it and playing around with examples before posting your question. If you posted just that question as currently written, I'd probably vote to close as lacking details. But if your question included what you thought was the answer, and stuff like "I tried to prove it this way ........, but got stuck at .....", or "I thought I had an example with ......, but it fails because ....." then I'd think it's good. $\endgroup$ – JonathanZ supports MonicaC Jan 16 at 20:20
  • $\begingroup$ BTW, there's a nice answer to precisely characterize inner product spaces with that property. Go think about it, and post your work as a question later! $\endgroup$ – JonathanZ supports MonicaC Jan 16 at 20:22
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    $\begingroup$ Tangentially the first part of your question is strange on formal grounds. If the answer to "Is proposition P true for class of objects C." is negative then it is of course also negative for a larger class of objects C'. Further there are case for which the second holds for the dot product too. It's true for dimension 0 and 1. $\endgroup$ – quid Jan 16 at 22:56
  • $\begingroup$ I think you answered the question well in your comment below your question. Of course, if after "brushing up a bit," your confused, or realize you may not have fully understood some concept back when you first covered it, by all means, ask here! You actually have a neat opportunity. I took a five year break from math while pursuing another major. So I spent a lot of time reviewing material I learned earlier. In doing so, I became a much stronger student, and was able to ask questions that were deeper than anything I could have asked five years previously. $\endgroup$ – amWhy Jan 16 at 23:53
  • $\begingroup$ I think one of my main problems in mathematics is that I have too many questions and not enough energy to address them all. If you can call that a "problem". $\endgroup$ – Adam Rubinson Jan 16 at 23:57
  • $\begingroup$ Adam, that's a good thing! Really. Because questions sit waiting, as you study and learn more, and permit a lot of "aha!" moments. Asking questions is what made me who I am. Sure, I sometimes had people to ask about them. But asking questions prepares your mind to be receptive to clues and ultimately, answers, when you find them in your reviews. Just don't get hung up on having to have all the answers before moving on. $\endgroup$ – amWhy Jan 17 at 0:02
  • $\begingroup$ Why the downvotes? This downvotes without a reason nonsense again... $\endgroup$ – Adam Rubinson Jan 18 at 15:40
  • $\begingroup$ Don't worry about downvotes. They are not related to quality of meta question, but indicate some disagreement with what you propose or ask. $\endgroup$ – Paramanand Singh Jan 22 at 3:45
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In general, I would avoid asking questions on topics where you are unable to define the basic objects you are asking about, or where you are unfamiliar with the elementary theory. It is not fair to ask answerers to address a question where providing an answer "at your level" would require them to teach you an entirely new topic. Moreover, after learning the requisite background, you might find out that the question you are asking is entirely trivial, or quite uninteresting.

In the case of the question you suggest, can you define an inner product space? Do you have any examples of inner product spaces to hand, and have you tried addressing your question with respect to those examples? Do you know any theorems related to inner product spaces? My guess is that if you understood the basic objects being talked about, then you would know how to answer your question, and wouldn't feel the need to ask about it here.

There is an expectation that users will do some basic research first, and then ask a question here only if that research doesn't yield anything useful. Asking a question where the answer is likely to be over your head indicates a lack of that basic research.

As a final thought, you might Google the meaning of "orthogonal" in an inner product space.

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  • $\begingroup$ I know the meaning of orthogonal in an IPS. I see how that answers my first question but not my second question (other than vacuously true examples). $\endgroup$ – Adam Rubinson Jan 16 at 19:35
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    $\begingroup$ "...teach you an entirely new topic..." I have studied IPS in the past, but not for a long time. So this is not a new topic for me: I just need to jog my memory on the definitions. But I do think the onus is on me to go back and do this then. $\endgroup$ – Adam Rubinson Jan 16 at 19:41
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It is a better criterion to understand the questions you ask, rather than pre-judging how quickly you will be able to understand the answers you get. Both "understandings" are intimately related, so let's try to parse out these aspects.

The mission is to "promote learning mathematics at all levels." Naturally many Questions will be based on a gap in understanding or on a substantial misunderstanding of mathematics. Because a person asking a Question becomes the expert on what it is that is being asked, the responsibility to do basic research and clarify the Question falls primarily on the asker. The Community can (and often tries to) help with clarification, but the OP asking is a priori gatekeeper of the Question's formulation.

For this reason I recommend that one only asks questions which one understands well enough to be able to recognize when an Answer is provided. Answers may take a variety of approaches to a problem, and a user cannot know in advance whether they will understand every possible solution. If the user lacks confidence to recognize when any reasoned mathematical argument solves their problem, my standard advice is to step back and ask instead a threshold question that proceeds from a place of their firmer understanding.

Types of threshold questions might concern definitions or their immediate consequences, preliminary propositions/lemmas toward a theorem, or reference requests (so a user's basic research could preface posting a "main" Question).

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