[Verse 1] Picture a sheet, neurons packed tight in a grid, Fold up the edges, that's the torus we hid, Not flat like a map, it's a donut disguise, Twist it once more so the wiring implies Six-fold neighbors, hexagons woven in wire, Fuhs and Touretzky lit the original fire, A bump of activity, glowing and round, Sits on this manifold, never touching the ground. [Chorus] Bump on a torus, pointer in the crowd, Velocity pushes it, quiet not loud, Phase on a wheel, oscillators keep time, Two ways to grid it, both roads make the rhyme, CAN's a vector, indexed on the ring, Interference counts the phase that the cell sings, Remember the twist, remember the beat, Two models, one hexagon, never obsolete. [Verse 2] Burak and Fiete built it clean in oh-nine, No boundary patchwork, just local weights in a line, Excite your neighbors close, inhibit ones far, Mexican-hat kernel, that's the shape of the scar, Feed in your speed, feed in your heading too, The bump glides smooth like a compass come true, Position's not stored as some number somewhere, It's WHERE the bump sits — the coordinate's there, That's the data structure: a pointer that moves, Read off the peak and you've measured your grooves. [Chorus] Bump on a torus, pointer in the crowd, Velocity pushes it, quiet not loud, Phase on a wheel, oscillators keep time, Two ways to grid it, both roads make the rhyme, CAN's a vector, indexed on the ring, Interference counts the phase that the cell sings, Remember the twist, remember the beat, Two models, one hexagon, never obsolete. [Verse 3] Now flip to Burgess, Barry, O'Keefe's design, Forget the sheet, forget the twisted line, Instead every neuron's a tiny metronome, Baseline ticking theta, calling it home, Three oscillators, each tuned sixty degrees apart, Speed and direction bend the beat like a dart, When phases align, you get a burst of a spike, Sum up the waves and hexagons strike, The structure here's a phase accumulator's chore, Counting the swing, not a bump anymore. [Bridge] Evidence stacks: CAN needs no clock in the skull, Fits grid cells surviving when theta goes null, But interference nails the phase-speed correlation, Each model's got holes, neither wins domination, Hybrid thinkers stitch them, oscillators feeding a sheet, Torus catches drift while oscillation keeps beat, Try it yourself — NumPy, matrix, and seed, Random-walk the rat, watch the hexagons breed, Update weights local, inject velocity in, Plot the firing field, hexagons under your skin. [Chorus] Bump on a torus, pointer in the crowd, Velocity pushes it, quiet not loud, Phase on a wheel, oscillators keep time, Two ways to grid it, both roads make the rhyme, CAN's a vector, indexed on the ring, Interference counts the phase that the cell sings, Remember the twist, remember the beat, Two models, one hexagon, never obsolete. [Outro] One's a bump, one's a beat, both draw the same six-sided seal, Code the manifold, code the clock — then tell me which is real.
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