This question is entitled If there is an infinite number of universes doesn't that mean there is a universe where there is not an infinite number of parallel universes?. I downvoted this question and voted to close. I also left a comment that said:

If there are an infinite number of triangles in the plane, doesn't that mean there is a triangle where there is not an infinite number of triangles?

It seems to me that this was a pretty useful analogy for understanding what was wrong with the question (or at least one of the things that was wrong with the question), viz: universes are not elements of other universes, any more than triangles are elements of other triangles. I also think that the slightly flippant tone in no way detracted from the usefulness of the comment and in fact probably contributed toward making the point clear. This comment was deleted. I do not think it should have been, particularly because there have been quite a few posts on meta requesting that downvoters should attempt to leave informative comments.

One could perhaps argue that this comment was cryptic. But I think it was cryptic only in the sense that it's "cryptic" to offer hints rather than solutions to homework problems. It invites the OP to do a little thinking.

I realize there have been a great many discussions about comment deletion. Many of those have centered around long comment threads. This post, by contrast, is about the deletion of single comments that, by way of analogy, invite the OP to reflect for a moment or two on the internal logic of the question.

Another example: This question on meta asks

Why don't some questions on PSE have any answers for the past many years with many high votes? ... Do they really don't have answers like proof of Goldabach's conjecture or yet their answers are very hard?

I left a comment that said something like:

Why do some roads have so little traffic? Are they just too hard to get to, like Mars?

Once again, I believe the comment makes a point that is likely to be useful to the OP, and that the light-hearted tone does not detract from that usefulness. This comment was upvoted several times.

This sort of deletion has happened several times over the past couple of years, though I haven't kept records so I have no other examples at my fingertips. Many of the deleted comments were heavily upvoted. I hope the moderators can be encouraged to tread a little more lightly here.

Edited to add: Some of the answers below suggest that it would be better to turn these comments into answers. Here is why I don't think that's advisable:

I leave this kind of comment on posts where I think that the OP is making simple and fundamental errors in reasoning. I think most of those posts should be closed and that when a post should be closed, it should not receive answers that might encourage the OP to continue posting without thinking.

At the same time, I think it's helpful to the OP to point out those errors in reasoning --- and that one of the most effective way to point them out is to translate the same reasoning into another context where it's quite clear that the reasoning has gone haywire.

So in short: I want to be helpful, but I don't want to be encouraging (in the limited sense that I don't want to encourage future ill-considered posts). I think that a) a brief comment pointing out the problem (together with a vote to close) is a good way to further both goals, and b) that often the best brief comment is one that offers an analogy for the OP to ponder. If the OP is not in a pondering mood, the analogy might be lost, but often it will make a light go on. I often use this kind of analogy in the classroom. It seems pretty effective with reasonably good students who have made thoughtless errors, and entirely ineffective with students who are making no effort anyway, but I'm not sure there's any good alternative in those cases, and at the very least no harm is done.

I can't speak for mods, but I can give my perspective on why those comments shouldn't really stay.

If there are an infinite number of triangles in the plane, doesn't that mean there is a triangle where there is not an infinite number of triangles?

...I do not think it should have been, particularly because there have been quite a few posts on meta requesting that downvoters should attempt to leave informative comments.

One could perhaps argue that this comment was cryptic. But I think it was cryptic only in the sense that it's "cryptic" to offer hints rather than solutions to homework problems. It invites the OP to do a little thinking.

When you're downvoting, some people suggest that you explain your downvote (though I don't necessarily agree with that in all cases). Constructive criticism is generally also okay; the problem is I'm not sure if that comment alone is particularly constructive to the OP. I'm sure for you, it makes a lot of sense, but given OP's question, I'm not even sure if they could track the analogy. You say:

It seems to me that this was a pretty useful analogy for understanding what was wrong with the question (or at least one of the things that was wrong with the question), viz: universes are not elements of other universes, any more than triangles are elements of other triangles. I also think that the slightly flippant tone in no way detracted from the usefulness of the comment and in fact probably contributed toward making the point clear.

But did you actually mention that "universes are not elements of other universes, any more than triangles are elements of other triangles" or did you just expect OP to understand that implication? If your comment was just that one line, I can see how it could be seen as unhelpful.

To be fair, I'm guilty of this too sometimes, but I still think it's a decent reason for deletion. I wouldn't be that upset if a comment of mine got deleted for being clear to me but not clear to others.

For your second comment:

Why do some roads have so little traffic? Are they just too hard to get to, like Mars?

I really don't see how this is even a useful analogy... They are asking about why some questions with high votes have no answers. I feel like the analogy would have to be more like "Why is there multi-lane road with no traffic? Is it just hard to get to?"; but that is actually a somewhat interesting question. Why would there be a big road if no one was driving on it? Does anyone know why that happened?

They had an actual question about something they thought was strange that they noticed on the site, and your "analogy" seemed really dismissive of what the question was about, so I can definitely see why that was deleted.

• But did you actually mention that "universes are not elements of other universes, any more than triangles are elements of other triangles" or did you just expect OP to understand that implication? My hope was that the OP would be motivated to ponder the comment for a while and that a light might go on. My experience is that students retain the things they've learned a lot better when they have to do a little work than when someone just hands them the answer. Such comments can, in my experience, be pretty useful for a good student who has posted a thoughtless question. – WillO Oct 12 '20 at 1:56

In the current version of your question (v3) you write,

I leave this kind of comment on posts where I think that the OP is making simple and fundamental errors in reasoning. I think most of those posts should be closed and that when a post should be closed, it should not receive answers that might encourage the OP to continue posting without thinking.

At the same time, I think it's helpful to the OP to point out those errors in reasoning --- and that one of the most effective way to point them out is to translate the same reasoning into another context where it's quite clear that the reasoning has gone haywire.

These two impulses are both fine to have, but they are mutually exclusive. If you think that a question should closed unanswered so that future similar questions are discouraged, then close it without answering. If you think that the question deserves a response that will guide the asker towards a solution to their problem, then provide such a response in an answer. Please don't use comments as a mechanism to do both of these things.

There have been numerous discussions across the network about why blurring the line between comments and answers is unproductive and harmful; I will hopefully add some relevant links later today or tomorrow, but other folks who have different search-fu skills than I are welcome to contribute as well.

When I encounter a question which I think warrants some assistance but shouldn't be answered in its current form, I vote to close it and leave a comment like

Greetings! Your question is interesting but in its current form it's not a good fit for our community. Take the [tour] to get an idea of how we do things here.

In comment-MarkDown, [tour] becomes a link to the right part of the help pages.

• – rob Oct 12 '20 at 14:44
• – rob Oct 12 '20 at 14:46

Regarding the comment on the main site question: More than any other reason, I deleted the comment because it was an answer to the question rather than to request clarification or suggest improvements to the post. You acknowledge this in your post here by saying it's a useful analogy to help understand why their thought process is wrong.

It could have been posted as an answer, such as:

No, it does not mean that. As an analogy to consider: If there are an infinite number of triangles in the plane, doesn't that mean there is a triangle where there is not an infinite number of triangles?

Is it a good answer? Probably not the best. But it's also not a good comment because it is not aiming to improve the post it was attached to.

Since the core of the question is a misunderstanding of a concept, "helping point out what's wrong about the question" is just pointing out what they are misunderstanding about the concept -- it is an answer.

• Thank you for explaining. I've added a few paragraphs at the end of the post above to explain why I think that leaving these comments as answers would not be a good alternative, and a little more on why I think they're valuable as comments. – WillO Oct 12 '20 at 1:53
• @WillO Not all content --- not even all good, high-quality, polite, clever, and interesting content --- has a home here. If your response to a question isn't a good fit for a comment, and it isn't a good fit for an answer, then perhaps just set it aside. I do this several times a day, personally. – rob Oct 12 '20 at 14:28
• I am absolutely astonished that my response to @rob's comment here has been deleted. – WillO Oct 13 '20 at 2:53

It seems to me that this was a pretty useful analogy for understanding what was wrong with the question (or at least one of the things that was wrong with the question), viz: universes are not elements of other universes, any more than triangles are elements of other triangles.

But you didn't point this out as an analogy. You just posted your questions as a comment. What were you intending the questions to do? Were you intending the OP to improve their post? Were you intending for the OP to reach their open conclusions and answer their own comments? IMO your comment was not a suggestion to improve the post nor was it a request for a clarification from the OP. Therefore, it wasn't a valid comment. As tpg2114 has already pointed out, it would have been best to just make an answer instead.

I do not think it should have been, particularly because there have been quite a few posts on meta requesting that downvoters should attempt to leave informative comments.

First, there isn't any policy saying that down voters should leave comments. Of course this is a nice and helpful thing to do, but it certainly isn't required. Second, the comment should relate to why you down voted, and the connection should be clear. Based on your comment, it isn't clear that you were someone who down voted nor is it clear why you down voted. Based on this and what I discussed earlier, I honestly don't see how your comment was a useful comment.

One could perhaps argue that this comment was cryptic. But I think it was cryptic only in the sense that it's "cryptic" to offer hints rather than solutions to homework problems. It invites the OP to do a little thinking.

This isn't what comments are for. In homework posts comments shouldn't be used to give hints to how to solve the problem, and comments in general shouldn't be used to invite the OP to do some thinking. If you really want the OP to think about something in the right way, then make an answer. If you want to improve the post itself, then you make a comment. If neither, then move on.

Another example: This question on meta asks

Why don't some questions on PSE have any answers for the past many years with many high votes? ... Do they really don't have answers like proof of Goldabach's conjecture or yet their answers are very hard?

I left a comment that said something like:

Why do some roads have so little traffic? Are they just too hard to get to, like Mars?

From what I have seen the comment policy isn't as enforced (or isn't enforced at all) on the meta site. Meta is the place for discussions about the main site, and sometimes these discussions extend into the comments. Therefore, I don't think you can take how meta comments are treated and compare them to the main site.

This sort of deletion has happened several times over the past couple of years, though I haven't kept records so I have no other examples at my fingertips. Many of the deleted comments were heavily upvoted. I hope the moderators can be encouraged to tread a little more lightly here.

Votes aren't an indication of site policy adherence, so I don't see how number of votes is relevant here.

I also never understood how some users find comments to be so sacred and get upset with moderators when they are deleted. If you think something is that important, then just make an answer. Problem solved.

I leave this kind of comment on posts where I think that the OP is making simple and fundamental errors in reasoning. I think most of those posts should be closed and that when a post should be closed, it should not receive answers that might encourage the OP to continue posting without thinking.

The problem is that there isn't any way for you to know how much someone has thought about their question. I don't think it's fair to assume that just because there is a flaw in someone's reasoning that is obvious to you that it must mean the person didn't think carefully enough. Furthermore, what you think is a "simple and fundamental error in reasoning" could be exactly the answer the person is looking for, and to them it is anything but simple. A question containing an error in reasoning or thought that isn't careful enough according to some subjective measure isn't a reason to close a question, and it certainly isn't a reason to not answer a question nor to violate the comment policy.

Additionaly, if you think the question really should be closed, then you really shouldn't be providing any sort of aid. Providing aid would still encourage users to post bad questions. The thought would be, "I can still post bad questions and get help in the comments even if answers are blocked."

At the same time, I think it's helpful to the OP to point out those errors in reasoning --- and that one of the most effective way to point them out is to translate the same reasoning into another context where it's quite clear that the reasoning has gone haywire.

You can and should do this in an answer.

I often use this kind of analogy in the classroom. It seems pretty effective with reasonably good students who have made thoughtless errors, and entirely ineffective with students who are making no effort anyway, but I'm not sure there's any good alternative in those cases, and at the very least no harm is done.

I completely agree with this line of thought for the classroom and with students. I also agree that this is a great way to teach. However, this isn't a classroom, and we can't guarantee that we are dealing with students. This is a question and answer site. Users post questions, and if they do not violate site policy then other users can fully answer those questions rather than engage in an educational discussion found in the classroom.$$^*$$

Furthermore, I don't think the site should treat users differently based on who they are. All users, questions, answers, comments, etc. should have the same applicable policies applied in the same way equally.

$$^*$$Is this an ideal way to reach physics? Not always. But that is how this particular site works. I love teaching people math and physics in precisely the way you describe, which is why I also tutor. I definitely tutor way differently compared to how I participate in this site because they are not the same thing. While I'm tutoring I'm not going to take the question a student has and give a complete answer. I'm going to primarily ask the student questions, guiding their own reasoning from where they are to where they need to be. However, on this site there isn't that essential back and forth needed for this type of pedagogy. People have (valid) questions, and we fully answer them.