Should MO perhaps give numerological abductive questions a little more benefit of the doubt

Question

Background:

This question is a much more specific version of a metaMO question which was deleted for some odd reason after one poster said in a comment that he agreed with everything said in the post. That was this question:

https://meta.mathoverflow.net/questions/3542/question-re-sufficient-vs-necessary-properties-of-mo-culture

Question:

"Should MO perhaps give numerological abductive questions a little more benefit of the doubt?"

By numerological abductive questions, I simply mean questions that are as "bad" or "not much better" than Johannes Kepler's famous question:

"Are the orbits of the planets (only five known in his time) related to the circumspheres of the five Platonic solids"?

Here is an actual MO case study which suggests that MO probably should extend a little more benefit of the doubt to such questions, but I am course interested in the thinking behind the opinions of those who think that NO benefit of the doubt should EVER be extended to such questions.

Case Study

In my last edit to this MO question:

Is it a coincidence that (1,6,15) occur in corresponding positions of OEIS A007318 and A050447

I mentioned that Dr. Richard Klitzing does in fact have an answer to the question as reworded: Are the two 84's in the {84,72,84} decomposition of $E_8$'s root-system non-coincidentally related to the two 84's in row 8 of OEIS A135278?

And here's the interesting thing.

When I followed-up the implications of Richard's answer (which he kindly gave me off-line, even though he could not actually post it), I immediately discovered something which would lead anyone to ask what appears to be yet another purely numerological and naive abductive question:

New Numerological and Naive Abductive Question

Consider the third row

1 14 1

of A022177 (Triangle of Gaussian binomial coefficients [ n,k ] for q = 13.)

Is the appearance of 14 in this row non-coincidentally related to the appearance of two 84's in both:

i) the {84,72,84} decomposition of $E_8$'s roots

ii) row 8 of OEIS A135278 ?

Before immediately forming the conclusion that this question is NOT MO-caliber, I strongly urge you to consider two well-known facts:

iii) $E_8$ supports quantum-theoretic physics in many different ways

iv) the Gaussian or "q-" binomial coefficients also show up in quantum groups, as discussed here:

https://en.wikipedia.org/wiki/Gaussian_binomial_coefficient

(See the passage right above the section entitled "Triangles".)

Answer 1

There's a fair bit to sort out here. I actually think the question adumbrated in the question title is not precisely the one you want answered. As I see it, we don't have to wring our hands over whether we're being sufficiently open or fair to questions that have a numerological character. Try entering 'numerology' into the MO search bar, and you'll see quite a few good questions pop up. As I see it, it's not that there is some innate prejudice in the Community against 'numerology' as mathematicians use the word (there probably is prejudice toward its more mystical contexts). Of course not. We all have struggles not tied to deductive reasoning per se, where we look for patterns, apply guesswork, etc. etc., and occasionally ask each other for help.

Speaking for myself, questions are approached on a case-by-case basis. Here are some of the criteria I apply. Is the question clear and precise? Does it seem likely that someone can answer it? Does the level seem appropriate for a professionalized community? Etc. And I think I'm not alone in taking that case-by-case approach.

I have seen some good faith effort from you to try to understand the norms of the community and make adjustments to your questions. There seems to be some disagreement with my casting a fifth vote to reopen the thread $E_6$, $E_8$, and Coxeter's (anti-)prismatic projections of the n-dimensional cross-polytopes where I had cast a fifth and final vote to reopen, based partly on my perception of good faith effort. And I must admit, I'm having some second thoughts. As mathematics goes, the question still seems pretty vague to me, which is to say I don't have a clear idea what's in your mind when you ask such questions, or how someone would know what you're after. That may be partly due to my shortcomings, but here again I don't think I'm alone in this, and I suspect you generally needs to work yet harder to bring some of these questions into a good useful shape for MO. The closures may be due to people who share these concerns.

[I do often worry about knee-jerk reactions from the community. Hey, I worry about them in myself. So I struggle daily to maintain an open mind, and to seek pragmatic constructive solutions to problems as they arise. But, I'm struggling alongside other people here. May I say that I bristle a little at being painted as some sort of hero of free thought at MO -- maybe not as much as I bristle when I am portrayed as an enemy of free expression (as has sometimes happened), but still. It's just a little too inviting of invidious comparisons with others who I think are also acting in good faith. Cf. some of the discussions over at Math.SE meta, where I think my actions and attitudes have been overstated by you.]

In addition to the suggestion that you endeavor to make your mathematical questions much clearer, I have some others that I hope you will take to heart, and which I think might help moving forward:

• Resist the urge to leave so many comments. Very often when someone leaves a comment, you leave four or five in return. In ordinary conversation this would likely be experienced as being talked at. Actually, leaving excessive comments is considered a site violation. The lack of follow-up from your presumed interlocutor should be a sign not to go on and on. Part of the StackExchange model and software is that it is expressly not designed for extended discussion.

• Resist the urge to philosophize. There has been way too much about Peircean abduction, or alleging an auto-immunity disorder within the community, to mention two specific things. As Lucia said succinctly: just stick to the math. I do think he (yes, he) is right that you've had a tendency to diagnose what is wrong in our community and what should be changed, and inevitably this provokes resentment, as you are still new here.

• Adding to the last bullet point: please avoid any urge to get defensive about how your MO questions are treated within the MO questions themselves. This includes invoking names like that of Coxeter to defend your question as being research level. Really, the mathematics should speak for itself, and that should be the main, perhaps even the sole focus moving forward.

Those are just a few general pointers; there may be more specific ones for individual questions.

As for the case study: as I advised in response to an earlier meta question, in general a better approach for meta might be to ask whether the specific "numerological, abductive" question would be good for MO Main. Not whether we need to be more open to numerology, as I said before.