[be] -- Eclogue 8
Roman civilization produced no famous mathematicians. Does this mean that mathematical thought lay dormant during this time? Hardly. Instead, it was applied to poetry.
Let us consider Virgil’s Eclogue 8, which portrays a singing contest between two shepherds. The content is unremarkable, but the internal structure is fascinating. Rather than just monotonously repeating 4 line stanzas, the poet alternates between 3, 4, and 5 lines in a simple yet subtle pattern.
Shepherd 1
4, 3, 5 (A)
4, 5, 3 (B)
4, 5, 3 (B)
Shepherd 2
4, 3, 5 (A)
4, 5, 3 (B)
5, 3, 4 (C)
The contrast between Shepherd 1’s ABB and Shepherd 2’s ABC is intriguing. Why not ABB ABB or ABC ABC? Why vary this last line?
Thus far, we have been thinking “horizontally”. But what happens if we look at things “vertically”? If we add the first “column” of Shepherd 1, we obtain 4 + 4 + 4 = 12. Similarly, the second column is 3 + 5 + 5 = 13. The third column is 5 + 3 + 3 = 11. Viewed vertically, Shepherd 1 is 12, 13, 11.
Repeating the process with Shepherd 2 yields 13, 11, 12. This is perfectly conjugate with Shepherd 1’s 12, 13, 11. Now Virgil’s variation makes sense. The ABB ABC pattern creates horizontal irregularity in service of deeper vertical balance.
Mathematics is popularly conceived of as a dusty collection of proofs and theorems, but it is really the study of logic, order, and organization. At its best, poetry can be mathematics without definitions to memorize or symbols to decipher.