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The question is here. It is currently closed as opinion based, with +2/-5, 1 vote to reopen and 1 vote to delete. I need help understanding this local disaster.

As to close reason:

I can easily imagine a specific, mathematically true answer. I even show how one of the comments gets close to answering the question. I cannot imagine why anyone who understands the question could consider that it cannot be answered properly. Please help me understand why such conclusion was reached.

As to vote situation:

The question is as well-researched, clear and useful as any question I ever asked, so I cannot quite understand why it is voted down so much. I noticed a blip of 3 down votes after I added the tags logic and set-theory, so perhaps there are some obvious errors in my question that pertain to either field of study? But none were pointed out to me. Please help me understand how my post may be judged poorly researched, unclear or useless.

My suspicions:

I suspect that some of the unfavourable reactions garnered are not entirely rational. That is to say, I suspect that my post «rubbed a few people the wrong way», and in a world of power and opinion that has effect. I can understand that the question is somewhat off the beaten path and that it may step on some people's toes — particularly of those who may be called «dialectic» mathematicians as opposed to the «algorithmic». However, I cannot see how that can be a fair reason to have a question closed. Is there something offensive in the style of my writing? Please help me understand if there is anything to my suspicions or if not, what is the real reason for such unfortunate outcome.

Discussion of argument to close given in a comment:

The discussion below is surely biased, and I hope that is understandable. I hope the reader can be condescending.

See the comment. Verbatim:

JairTaylor (1) It is purely hypothetical because it deals with a fantasy world. (2) It has nothing to do with mathematics. (3) Everyone has the right to disagree, but such questions lead to nowhere, not even in theoretical mathematics, and I have also the right to consider it as a waste of time. (4) In a philosophy site, this question might be suitable. – Peter 1 hour ago

  1. It is purely hypothetical because it deals with a fantasy world.

    I cannot take this as anything but a joke. Any number of mathematical situations deal with a fantasy world, if not all. Then again, all references to fantasy may be erased from the question without much harm to its essence.

  2. It has nothing to do with mathematics.

    Hard to see how this is anything but a hyperbole. Surely I refer to a number of mathematical constructions and inquire according to mathematical methods. I grant that there is also an argument to common sense (such as «directly numerically checking it for any but the most trivial cases is impossible»), but it is not central to the question.

  3. Everyone has the right to disagree, but such questions lead to nowhere, not even in theoretical mathematics, and I have also the right to consider it as a waste of time.

    Any question leads any number of people nowhere. So this argument is general enough to close any question. It should therefore be enough that some people are led somewhere they want to arrive, and that is in evidence.

So it seems that I am unable to extract any practical advice from this comment. Undoubtedly so because of understandable personal bias, so please help me open my eyes.

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  • $\begingroup$ So now this question has 2 silent down votes. Way to go folks. $\endgroup$ – Ignat Insarov May 22 at 20:47
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    $\begingroup$ I took a look at the question. Firstly it gives an impression of rambling. Secondly, when I looked at all the sentences ending in question marks, I did not see anything that could be objectively solved with mathematics: it appeared they were all probing philosophy of mathematics, e.g. Are there numerically observable consequences to the diagonal argument?", "How can we possibly experimentally detect that any of the above assertions is true?", " What tangible result could not possibly be found in such a fantasy world?... $\endgroup$ – rschwieb May 22 at 20:58
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    $\begingroup$ (cont) What engineering could not be performed? What architecture could not be constructed?","Or else, could it be shown that a diagonal argument is not a key step on the way to any finitary positive result? Some of these approximate a real question but I typically dead-ended in a bit of terminology that looked suspiciously homegrown and couldn't find when I did some searching. It could also be, perhaps, that some people don't like waxing philosophical about the diagonal argument because sometimes it is a favorite of cranks. $\endgroup$ – rschwieb May 22 at 20:58
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    $\begingroup$ By the way, I did not vote either direction on this post or that post. I hope this feedback is somewhat helpful. What it all roughly means is that "It is not a mathematical question within the scope of this website." You might consider asking at the philosophy stackexchange? Or perhaps you can rewrite it to be more compact and more grounded in whatever mathematics you wish to do with it. $\endgroup$ – rschwieb May 22 at 21:00
  • $\begingroup$ @rschwieb  This is a curious report. I can certainly rewrite my question to be more compact, and I see how that may be an improvement. The terms can also be refined. However, can you explain why you consider «are there numerically observable consequences to the diagonal argument» not to be a question that could be solved with Mathematics? If this question is nonsense, I should certainly remove the whole thing and call it a day. But it seems to me that a decisive example would be easy to exhibit, should it exist. What is your line of thought? $\endgroup$ – Ignat Insarov May 22 at 21:22
  • $\begingroup$ The question has now been deleted. This is possible without delay for a closed question with a score of -3 or lower. $\endgroup$ – Matt Samuel May 22 at 21:40
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    $\begingroup$ Regarding your sarcastic comment "So now this question has 2 silent down votes. Way to go folks.": votes on meta mean something different than they do on the main page. An upvote mean "I agree with the statement being made by this post" while a downvote means "I disagree". There is no reputation at stake on meta, so folk are often freer with downvotes here. I would interpret the downvotes here to mean "I think that the question on the main site was appropriately closed" or something similar. $\endgroup$ – Xander Henderson May 23 at 4:16
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    $\begingroup$ @XanderHenderson  I am aware, but this question asks exactly to explain what down votes mean, so it is hard to interpret more silent down votes constructively. $\endgroup$ – Ignat Insarov May 23 at 6:48
  • $\begingroup$ I haven't yet read your question here, or any of the comments/answers, but in case you're interested, references #5 and #6 in this answer might be of interest (assuming you can find copies of the papers; you might have to visit a university library). I'm mentioning this here since your question Are there numerically observable consequences to the diagonal argument? has been closed. $\endgroup$ – Dave L. Renfro May 23 at 18:02
  • $\begingroup$ @DaveL.Renfro  Thank you. $\endgroup$ – Ignat Insarov May 23 at 18:53
  • $\begingroup$ @IgnatInsarov I don't know what a numerically observable consequence is. What would you say it is, specifically? $\endgroup$ – rschwieb May 24 at 16:48
  • $\begingroup$ @rschwieb  For example, if a theorem provides a novel series for π, and it gives the same digits as other algorithms as far as one cares to evaluate, that would be a numerically observable consequence that also seems to be correct, thus giving some reassurance that the logical system used to derive the series is acceptable. To paraphrase Mac Lane — despite mathematicians, computation is essential in Mathematics. I am taken aback by the recognition that I need to justify that. $\endgroup$ – Ignat Insarov May 26 at 3:46
  • $\begingroup$ I'm least bothered what's going on here. $\endgroup$ – SarGe May 26 at 15:22
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I can't comment on the mathematics of your question because I don't know logic, but I can critique your writing.

Is there something offensive in the style of my writing?

I wouldn't say your writing is offensive, but you need to work on clarity and brevity. To me, the question reads a lot like a direct transcription of from your own notes, or even a personal journal. It's like all your thoughts are there, instead of only those necessary to communicate the question to others.

I like that you have a tone to your exposition, and that you use metaphor and colorful language about hydras and dragon slaying. I wish more people would do this, because it can make questions much more fun and readable. However, to execute this style properly, it needs to be balanced out by more concrete mathematical content interspersed throughout the writing. When the majority of the question is written in this style, it risks coming off as too "soft" and non-serious. This is especially true when your question is very conceptual and high level.

Other tips:

  • Avoid emphasizing things «like this». It's unusual, and I don't know how to read it in my head-- are you yelling? Whispering? My best guess is that it voicelessly represents very heavy emphasis, similar to doing this, which is something people generally find obnoxious. Good writing rarely makes use of typographic emphasis at all (more here), so if you do use it, stick to regular italics.

  • In online writing, keep your paragraphs short. Walls of text deter people. I think you did a good job in this meta question, but in the question you linked, you could break the paragraphs up a bit more.

  • Quoting the dictionary definition of a word is a trope of bad arguments. There's a stereotype where college admissions essays and freshman English papers tend to begin with something like, "Bravery, defined in the Oxford English dictionary as..." Furthermore, the dictionary definition of a word often differs quite widely from its definition in a mathematical context. (And that's in the case that there is only one definition-- take, for example, the words "normal" or "regular".) If you're going to define something, do it in a mathematically explicit way, and format it like this:

    Definition. A process is called finitary if, something something, finite number of steps, etc.

  • Hyperlinks can be good, but if you include too many of them, it's overwhelming, and starts making your prose look like one of those pages with marketing links on every other word.

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  • $\begingroup$ Good points. And I'll second the point about on-line writing requiring more and shorter paragraphs than other types of writing. I notice it when reading, and when writing I often find that I have to go back and break up over-long paragraphs. $\endgroup$ – JonathanZ supports MonicaC May 23 at 1:20
  • $\begingroup$ This is a reasonable and welcome advice, I grant that it is fair. However, it hardly explains the amount of enmity the question evoked, so I am still uneasy. I hope to shortly roll out another version of my question, that takes some of the advice I collected into account, and check if there is an improvement. $\endgroup$ – Ignat Insarov May 23 at 7:00
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    $\begingroup$ @IgnatInsarov I suspect it is because there is a shadow of implied finitism in the question, which many people (especially in set theory) find recalcitrant. If I'm right, you might get something out of looking at my stubborn algebraist question from years ago. $\endgroup$ – Alexander Gruber May 23 at 9:19
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From a slight glance at your question to it seems to deal with mathematical philosophy which is very interesting to me at least, and deals with some computational and mathematical puzzle features, and logic. I have these two which could back your question being allowed on Math.SE the fact that it involves these two elements:

Solving mathematical puzzles

Understanding mathematical concepts and theorems

The fantasy portion is an exoskeleton to a real math problem that is there if I could give the reopen vote I would because its an interesting math topic which is displayed by theorems, and your citations good question I upvoted your question. Its quite interesting.

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  • $\begingroup$ Question is how is it not about understanding mathematical concepts and theorems? Explain that part? $\endgroup$ – EnlightenedFunky May 22 at 21:06

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