[Verse 1] Trondheim lab, two-thousand-five, electrode drops in Hafting threads a wire where the cortex starts spinning Rat runs free in an open box, no maze, no wall to guide her Moser's crew just watches dots turn into architecture Every spike a firing field, but not some random splatter Line 'em up and what you get is crystal-perfect matter Triangles link corner to corner, tile the whole arena Nature's floor plan hiding in a rodent's entorhinal schema [Chorus] Hexagon, hexagon, tessellating brain Spacing, orientation, phase — the geometric refrain Layer two is the ground zero, that's where the grid is born Autocorrelate the map and watch the pattern form Hexagon, hexagon, the cortex draws it clean Sixty-degree symmetry, the sharpest thing you've seen [Verse 2] Spacing is the gap between the peaks, how far they scatter Orientation's the tilt, the twist, the compass angle matter Phase is just the shift — same lattice, different starting corner Dorsal cells pack tight and small, ventral ones grow broader Modules cluster discrete scales, they don't blend like a gradient Jump in steps like octaves on a keyboard, that's the paradigm Three parameters, one hexagon, infinite positions Population coding space through vector-summed collisions [Verse 3] Wanna measure if it's real? Compute the autocorrelogram Slide the rate map over itself, correlate the whole exam Rotate it in degrees and watch the coefficient dance Peaks at sixty and one-twenty, troughs at thirty by chance Grid score is that peak minus that trough, a number, clean and stark Above threshold, you got yourself a bona fide hex mark Gardner's data's sitting free on figshare, CRCNS too Load the spikes, bin the space, let the correlogram prove true [Chorus] Hexagon, hexagon, tessellating brain Spacing, orientation, phase — the geometric refrain Layer two is the ground zero, that's where the grid is born Autocorrelate the map and watch the pattern form Hexagon, hexagon, the cortex draws it clean Sixty-degree symmetry, the sharpest thing you've seen [Verse 4] Stellate cells in layer two, that's the densest population Deeper layers three, five, six still show the calculation Cross the species line — Yartsev finds it flying in a bat cave Killian spots it in a monkey's entorhinal archive Humans too, fMRI grids and single units in the hippocampal border Same hexagon, different skull, evolution kept the order So whether wing or paw or thumb, the module never wavers Nobel-grade real estate, the brain's own land surveyors [Bridge] Pull the dataset, run the code, don't just take my word Compute the score yourself and watch the symmetry get stirred Bin by bin, rotate the map, let the numbers self-report Grid cells never lie, they just triangulate and sort [Outro] Spacing, orientation, phase — say it till it's carved in bone Hexagon, hexagon — the cortex built its own Layer two to layer six, the pattern travels deep Hafting's rat still runs the loop inside your memory's keep
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