[Verse 1]
McNaughton dropped the framework back in oh-six
Path integration, velocity tricks
Neural basis of the cognitive map
Medial entorhinal, bridging the gap
Velocity integration problem posed
MEC implements what motion knows
Computational question now exposed
How does the brain track where it goes
[Chorus]
Hexagonal grids in neural space
Continuous attractors hold their place
Bump dynamics, interference waves
Two models showing different ways
Path integration, position trace
Grid cells firing, time and space
[Verse 2]
Burak and Fiete brought the CAN
Two-dimensional sheet, the master plan
Center-surround connectivity
Stable bump with continuity
Conjunctive cells with offset wire
Push the pattern, never tire
Velocity coupling, bump moves clean
Hexagonal fields in the firing scene
[Chorus]
Hexagonal grids in neural space
Continuous attractors hold their place
Bump dynamics, interference waves
Two models showing different ways
Path integration, position trace
Grid cells firing, time and space
[Bridge]
Burgess showed oscillatory way
Theta rhythms lead the play
Three directions, sixty degrees apart
Interference patterns, nature's art
Constructive waves at lattice points
Membrane oscillations, neural joints
[Verse 3]
Torus topology, periodic bounds
Energy functional, minimal grounds
Hexagonal packing wins the race
Most efficient use of neural space
Robustness analysis stands the test
Noise resistance, nature's best
[Verse 4]
Bush and Barry referee the fight
Two model classes, both insight
CAN versus oscillatory scheme
Different paths, same grid cell dream
Navigation strategies compared
Neural mechanisms, truth declared
[Verse 5]
Experimental data validates the theory
O'Keefe and Hafting made it clearly
Electrode recordings, firing rates
Spatial patterns, neural states
Triangular lattice, crystal clear
Grid cell function, engineered
From rat to human, preserved design
Evolution's path, the perfect line
[Chorus]
Hexagonal grids in neural space
Continuous attractors hold their place
Bump dynamics, interference waves
Two models showing different ways
Path integration, position trace
Grid cells firing, time and space
[Outro]
From McNaughton's map to Fiete's equations
Burgess waves and Bush translations
Core papers guide the neural quest
MEC secrets, now expressed