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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:

https://mathoverflow.net/questions/288367/is-it-a-coincidence-that-1-6-15-occur-in-corresponding-positions-of-oeis-a0073

I mentioned that Dr. Richard Klitizing 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".)

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:

https://mathoverflow.net/questions/288367/is-it-a-coincidence-that-1-6-15-occur-in-corresponding-positions-of-oeis-a0073

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".)

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 question.

Case Study

In my last edit to this MO question:

https://mathoverflow.net/questions/288367/is-it-a-coincidence-that-1-6-15-occur-in-corresponding-positions-of-oeis-a0073

I mentioned that Dr. Richard Klitizing 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 84 in both:

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

ii) the two 84's in 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".)

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:

https://mathoverflow.net/questions/288367/is-it-a-coincidence-that-1-6-15-occur-in-corresponding-positions-of-oeis-a0073

I mentioned that Dr. Richard Klitizing 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".)