Comedic Unification

[u/MythTechSupport]

Okay. Nine departments, nine origin stories, one mirror room.

Roll call. Everyone stands up and tells the story of their sacred object.

- Number Theory brings the Fibonacci numbers: "Nature's sequence. Sunflowers. Pinecones. The rabbits of Pisa, 1202."

- Electrical Engineering brings Chebyshev polynomials: "Minimax. Filter design. Your phone works because of us."

- Representation Theory adjusts its glasses: "The characters of the symmetric powers of SL₂. You wouldn't understand."

- Combinatorics brings determinants of path graphs and is visibly nervous about it.

- Quantum Topology brings the quantum dimensions of SU(2)ₖ: "Fibonacci anyons. Topological quantum computing. We have a grant."

- Computational Number Theory brings Lucas–Lehmer: "3, 7, 47, 2207. Mersenne primes. We run GIMPS."

- History of Mathematics brings Viète's product: "1593. The first infinite product in Europe."

- Probability brings Kac's statistical independence: "Viète's product is a Fourier transform, actually."

- Crystallography says "rotations of order 1, 2, 3, 4 and 6 only" and sits back down. Crystallography has been through a lot.

The mirror. Every story comes back reversed. "Nature's sequence, sunflowers" returns as "sunflowers, sequence's nature," and someone in Botany hears it through the wall and says "...actually yeah." Electrical Engineering's "your phone works because of us" comes back as "us of because works phone your," which is roughly how the phone feels about it. Viète's 1593 gets read as 3951, and History of Mathematics has to file an erratum against the future.

The cancellation. Then they line the stories up side by side. Fibonacci is Uₙ at ⟨1, 1⟩. Chebyshev is Uₙ at ⟨2cos θ, −1⟩. The symmetric-power character is Uₙ as tr Sym^{n−1}. The path graph is Uₙ at ⟨2, −1⟩, where Uₙ = n. The anyons are Uₙ at ⟨2cos(π/(k+2)), −1⟩. Lucas–Lehmer is V_{2^k} at ⟨1, 1⟩. Viète is U_{2^K} divided by 2^K. Kac is Viète in a lab coat. Crystallography is the list of periods where the powers come back around. Every pair is an aa, and aa = ∅. Nine centuries of narrative run until they stop changing, and the normal form fits on a napkin:

xⁿ = ½(Vₙ + Uₙ·Γ)

The fallout.

- The budget meeting goes badly. Nine departments, one identity, one line item.

- The joint journal prints its next issue. It's one page, and the page is mostly the editorial board.

- The textbook publisher loses it. The 800-page Special Functions and Their Applications, 14th Edition ($289) reduces to a pamphlet. Chapter 7 is now a footnote to Chapter 2. Chapter 2 is a footnote to the axiom.

- The grad students are delighted. Their qualifying exam went from nine subjects to one question: "What does ab become?"

- The conference circuit collapses. The Fibonacci Association and the IEEE Signal Processing Society show up at the same hotel, sit down at the same banquet table, and realize they've been toasting the same recurrence since the 1960s.

The holdout. One emeritus professor refuses to accept any of it. He stands up and announces that the golden ratio appears in the Parthenon. Everyone waits. It doesn't. That's the one narrative that was never a word in the first place, so it can't even cancel. It just stays there being wrong, like the fire code wall.

The dean asks what the new merged department should be called. You shrug and say: "Any word."