The Theory of Game · Track 22 · middle
A Fair Game Has a Secret Geometry
Category theory of fairness: Goss and Ludo argue whether all fair games are isomorphic, and what symmetry means in competition.
Lyrics
[Intro] Whisper to me, old chalkboard, in the University of Chicago's winter chill, 1945, when Saunders Mac Lane first drew your lines. [Verse 1] You stand there, black slate scarred by ideas, Saunders gripping his mechanical pencil, 0.5mm lead clicking, age 36, sketching morphisms like veins in a leaf. Samuel Eilenberg, 32, leans in, breath visible at 55 degrees Fahrenheit, arguing equivalences over black coffee in a chipped mug. Is fairness a structure, hidden in your dust? [Chorus] Oh, chalkboard, tell Goss and Ludo their secret geometry— all fair games isomorphic, symmetries folding like branes. What bends in competition, unbreakable under the map? Address me, lover of lines, in this intimate debate. [Verse 2] Reverend Goss claims the soul's symmetry, no cheat in the functor, but Ludo counters with war's cold math, categories closed like fists. November 1942, Eilenberg's notebook, yellowed pages brittle, ink faded to sepia, entries on natural transformations. Fair play as equivalence, or just a morphism's lie? You, board, erase the fouls, redraw the bounds. [Bridge] Feel the musty scent of old books, metallic tang of ink, late afternoon, 4:30 PM, sun setting through cracked windows. Mac Lane's eraser, white dust falling like snow, wiping away gaps in the record—unnamed students' whispers, Dorothy Jones Mac Lane's undocumented gaze. Is every game a mirror, reflecting the same fair core? [Verse 3] Sisukiro speaking close, miked to your surface, neurology weaving with theory—hippocampus mapping the play. Chess openings as categorical structures, Mac Lane's quirky fact, from a 1970 interview, pawns morphing like athletes' strides. Goss prays for unbroken rules, Ludo quantifies the break. [Chorus] Oh, chalkboard, tell Goss and Ludo their secret geometry— all fair games isomorphic, symmetries folding like branes. What bends in competition, unbreakable under the map? Address me, lover of lines, in this intimate debate. [Outro] In your commutative diagrams, the argument resolves, fairness not a sin or sacrament, but a universal mapping. Wipe clean, old friend, for the next debate.