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This question was migrated to physics.se where it now is marked as a duplicate. I don't understand why it was moved there? The question is about forming a simple mathematical model for the "proof" presented in the question. I specifically stated that I'm interested in mathematical approach to the question but it was moved to physics and I was not consulted on the way. Now the question is marked as a duplicate but the two marked "duplicates" really don't answer the question, thus it is all in vain.

I understand the title could be better, but it can't be the title that caused the migration. Could someone elaborate this a bit? I don't understand why the question was moved away. Was it too broad or vague?

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    $\begingroup$ If the question is how to approach/formalize a claim/argument about the physical universe mathematically, then that sounds more like what physicists do than what mathematicians do. $\endgroup$
    – Trevor Wilson
    Commented Oct 9, 2013 at 19:47
  • $\begingroup$ That being said, I agree that the question is not a duplicate of what Physics.SE marked it as a duplicate of. $\endgroup$
    – Trevor Wilson
    Commented Oct 9, 2013 at 19:50
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    $\begingroup$ @TrevorWilson Problem is that physicists bring all physics - starting from expanding universe ending to string theory. The math tends to get lost once you ask something from a physicists... Dunno.. maybe a better subject with better tagging would have saved the trouble. $\endgroup$
    – user8523
    Commented Oct 9, 2013 at 20:02
  • $\begingroup$ It would also help if you attempt to formulate the problem in a precise mathematical way rather than in terms of stars, etc. For example, you could assume that the light source is uniformly distributed (rather than "spread somewhat uniformly") and then ask for help in setting up and solving an integral to find the light intensity at a point. $\endgroup$
    – Trevor Wilson
    Commented Oct 9, 2013 at 21:36
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    $\begingroup$ It seems to be open now over there, but as I said here migrating questions to Physics SE is always a bit risky ... $\endgroup$
    – Dilaton
    Commented Oct 9, 2013 at 23:19
  • $\begingroup$ I voted to migrate to physics. I feel that the answers given below clarify my reasons enough. $\endgroup$
    – Thomas Rot
    Commented Oct 10, 2013 at 10:27

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Just to chime in with my two cents.

First a note about the timeline: in case it was not clear, the question received 2 flags for migration to physics, and then 2 votes to close for migration for physics, and then 3 further votes to close for "primarily opinion based".

I saw the flags after the question has been closed, and decided to migrate the question for several reasons (in order of importance to me):

  1. The question does have some mathematical content. But a formal formulation of Olbers' paradox is somewhat of a standard textbook problem in Cosmology (by the way, the quoted version is actually incorrect mathematically; at the very least one needs to assume that the universe is static/nonexpanding for the argument to work. And spatial finiteness actually makes things worse [Einstein's static universe comes to mind].) Much of these, due to their standard textbook nature, I think can be much better explained by the folks over at Physics.SE. (This is especially the case since that to actually approach the problem mathematically one needs to first formulate it correctly. And the formulation of "physically reasonable assumptions" really is not the job of mathematicians.)

  2. The question has already been closed. I somewhat disagree with the "primarily opinion based" closure reason, and since the closure reason was decided by one vote (with two flags from lower reputation users), and had I not been a moderator I would've voted for migration directly, I am somewhat justified in overriding the closure reason and changing it to migration.

  3. I actually suspected that there might have been a duplicate question that is already answered on Physics.SE, and this may have been a good way of pointing the user to the discussion there. Unfortunately it seems that the so-called duplicates they found were not quite satisfactory.

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    $\begingroup$ Thanks, it is easier to understand what happened when the actions are unfold. Personally I find the result unsatisfactory because the question has now been edited almost unrecognizable. I would have preferred to have an option to modify the question after feedback (and reading about the Older's paradox which I did not know about at the time asking), but instead it was "taken away" from me and started to live a life on its own. It has now come evident asking the original question (better formulated) in physics would be waste of time. $\endgroup$
    – user8523
    Commented Oct 10, 2013 at 8:47
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I remember seeing this question in the review queue earlier, and whilst my initial thought was to close it, I ended up deciding to vote to leave it open. That being said, I can explain why my initial reaction was to migrate it and why it might be more appropriate on physics than maths (even though it is unfortunate that you didn't get a useful answer).

Your question, as it stands, looks for an answer which provides a model of a physical phenomenon, rather than an analysis of some given model. Much of theoretical physics and maths is strongly related, but one of the key differences is that maths is about the general case, whilst physics is about using maths to model specific phenomenon.

The question seems to be asking for an answer which makes some assumptions about the actual universe, and creates a mathematical model using those assumptions. The process of deciding how uniform you want stars, and arranged in what kind of pattern (A lattice? concentric spheres? The result of some form of random process? (And what kind of probability distribution should you use?)?) is fundamentally a physical problem.

However, suppose you specified a particular model, and asked a question that could be answered in full generality, where the answerer doesn't need to make any choices about the model. This would allow a purely mathematical approach and would enable users to give a "complete" answer and would then be a good fit for this site, even though the subject matter is physically motivated. One example would be the following:

"Assuming light travels infinitely quickly, and we place stars at every integer lattice point in $\mathbb{R}^3$ which give out light spherically symmetrically with intensity $f(r)$, what is the total intensity at the origin? What if we give light finite speed $v$ and turn all the stars on at $t=0$, how does the intensity at the origin vary with time?"

I seem to recall a comment with a lot of votes along the lines of "what do you mean by uniform?". I chose to leave the question open, hoping that you would answer that in a specific way, which would allow for a mathematical answer. I am sorry that I didn't express the above suggestion at the time in the hopes of keeping the question open, but as you can see I think my point would have been too long for a comment!

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    $\begingroup$ Nice answer. This is pretty much the same as I mean by the comment I left at Matt's answer (just before reading this one). $\endgroup$
    – Tobias Kildetoft
    Commented Oct 10, 2013 at 6:34
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I looked at the question, and it seemed like a math question to me, with a fairly easily penetrated physical overlay. An analogous question would be to ask why the electric field given off by an infinite charged plate is uniform, which again is a physics question to begin with, but quickly tuns into a question about certain integrals.

I would prefer such question to be on topic here, perhaps with a "physics" tag or something similar.

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    $\begingroup$ I would prefer that they only be on topic if the translation from physics to math has been done in the question. Translating a physical phenomenon to a mathematical one is pretty much what theoretical physicists do. What mathematicians do is then to study that mathematical problem. $\endgroup$
    – Tobias Kildetoft
    Commented Oct 10, 2013 at 6:32
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    $\begingroup$ @Matt: to nitpick, the difference is that to actually obtain a statement of the form that the OP is asking about one needs to add quite a lot of extra assumptions, and to properly answer the question one also needs to explain why the motivational paragraph is in fact incorrect. This pushes it across the line to a physics question (at least for me). $\endgroup$
    – Willie Wong
    Commented Oct 10, 2013 at 8:12
  • $\begingroup$ @TobiasKildetoft: Dear Tobias, I can appreciate your point of view, but we probably differ on how serious the translation has to be before the question becomes on topic here. Regards, $\endgroup$
    – Matt E
    Commented Oct 10, 2013 at 11:06
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    $\begingroup$ @WillieWong: Dear Willie, I can see your point, and I don't really have a strong argument against it. Perhaps it's a question of degree? Or I may well have underestimated the amount of physics involved in making the translation to calculus. One argument I'll try to make in support of my position is that these kinds of questions give interesting applications of calculus, and it's nice to have interesting calculus questions on our site! Cheers, $\endgroup$
    – Matt E
    Commented Oct 10, 2013 at 11:09
  • $\begingroup$ @MattE: I think it definitely is a question of degree, which requires a judgment call. But it also (to a lesser extent) is a question of language. A question exactly as you worded would've been a bit borderline in my opinion. I would have preferred if it is also specified somewhere that the usual laws of electrostatics is assumed to apply etc. My feeling is that as long as there is no confusion about the set-up and about the "physics portion" that is involved, a mathematical question in physics' guise can belong perfectly well here. $\endgroup$
    – Willie Wong
    Commented Oct 10, 2013 at 11:43
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I recalled posting a Comment on this very similar Question here to the effect that it might be better addressed at Physics.SE, and linking to a related (possibly duplicate) Question there, but the other responders favored leaving it open at Math.SE.

I suspect its one Answer could bear improvement, if anyone has time. I meant to get back to it but lost track until reminded by this meta post.

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