[Verse 1]
Fyhn and Hafting dropped the knowledge in oh-seven
Place cells remap completely when environments shift direction
But grid cells hold their hexagons, just rotate and translate
Phase shifts keep the lattice while the anchoring updates
Hippocampus scrambles all its spatial memories clean
While entorhinal cortex keeps geometry pristine
[Chorus]
Grid cells bend but never break their sacred lattice dance
Flexible scaffolds shifting with each environmental chance
From Barry's stretching chambers to Krupic's trapezoid maze
The neural compass adapts while keeping metric ways
Realignment, rescaling, goals attracting every field
Entorhinal cortex shows us how space-time gets revealed
[Verse 2]
Barry's lab stretched the arena, watched the grids expand
Spacing rescales with the walls, not rigid but so grand
A flexible metric ruler that anchors to the scene
Not carved in neural stone but fluid and marine
When corridors get longer, the hexagons stretch wide
Environmental deformation becomes the spatial guide
[Chorus]
Grid cells bend but never break their sacred lattice dance
Flexible scaffolds shifting with each environmental chance
From Barry's stretching chambers to Krupic's trapezoid maze
The neural compass adapts while keeping metric ways
Realignment, rescaling, goals attracting every field
Entorhinal cortex shows us how space-time gets revealed
[Verse 3]
Krupic found the perfect grids distort in crooked rooms
Trapezoids make ellipses, geometry assumes
New shapes when walls aren't parallel, challenging the models
CAN networks predict perfection but reality just wobbles
Environmental geometry sculpts the neural terrain
Square rooms make square grids, but odd shapes break the chain
[Bridge]
Carpenter watched two chambers slowly drift apart
Same visual features but grids develop different hearts
Boccara showed the future when rewards shift the fields
Cognitive maps aren't neutral, value always yields
Goals attract the vertices like magnets pull iron filings
Spatial representation bends to motivational stylings
[Verse 4]
From coherent phase rotations to reward-biased attraction
Grid cells paint the canvas of spatial satisfaction
Not just measuring distance but encoding what we seek
Flexible neural networks make spatial memory unique
Context changes everything but structure stays intact
Entorhinal cortex bridges geometry with abstract
[Outro]
So remember when you're learning how the spatial system flows
Grid cells hold their patterns while adapting as it goes
The medial entorhinal keeps our navigation true
Through shifting phase and stretching space and goals we're walking to