First, a brief story, then the punchline.

Elsewhere I mention a series of 0-1 matrices used for a combinatorial matrix result. This came about because of an aspiring undergraduate (Roger House) who was using a computer to search for 0-1 matrices of certain orders and determinant values.

He showed me a printout where he listed the first representative of each class (major key order, minor key absolute determinant value). He chose a lexicographical ordering of class members to pick this representative: this choice revealed a set of matrices with few differing entries, and those in just the first two or three columns. I would not blame someone else for saying it was a pattern screaming to be found.

Many a time since then, I think about how to organize computer-generated data (specifically, pick an explanatory set of representatives) that reveal patterns and structure. I think that experimental mathematics should not just include results, or even data analysis techniques, but heuristics on "how to make choices" so that patterns of note jump to the human eye. In the case above, lexicographic order was a choice made by one person that revealed a pattern of similarity to another person.

Gerhard "At Least, Raise Their Voices" Paseman, 2015.10.12

First, a brief story, then the punchline.

Elsewhere I mention a series of 0-1 matrices used for a combinatorial matrix result. This came about because of an aspiring undergraduate (Roger House) who was using a computer to search for 0-1 matrices of certain orders and determinant values.

He showed me a printout where he listed the first representative of each class (major key order, minor key absolute determinant value). He chose a lexicographical ordering of class members to pick this representative: this choice revealed a set of matrices with few differing entries, and those in just the first two or three columns. I would not blame someone else for saying it was a pattern screaming to be found.

Many a time since then, I think about how to organize computer-generated data (specifically, pick an explanatory set of representatives) that reveal patterns and structure. I think that experimental mathematics should not just include results, or even data analysis techniques, but heuristics on "how to make choices" so that patterns of note jump to the human eye. In the case above, lexicographic order was a choice made by one person that revealed a pattern of similarity to another person.

Gerhard "At Least, Raise Their Voices" Paseman, 2015.10.12