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Complexity mathematics systems

Rat on a Wheel: The Doughnut in your Mind

Recent research suggests that the underlying symmetry in neural patterns of geometric world mapping in the mammalian brain are toroidal.

“(…) the Mosers discovered the activity structure of single grid cells. What they found was a hexagonal grid pattern that functions as the brain’s metric and coordinate system for space. Today they have uncovered the activity structure from the population of grid cells representing a spatial module. What they found was the surface of a doughnut. The doughnut exists in the connectivity between the cells.”


The internal information (as representational) symmetries of the (rat) brain’s world map are efficiently looped back upon and through themselves as a higher-dimensional toroid.

Possibly one of the most interesting topologies in the context of any complex system for which self-organisation is asserted.

The negative space of the torus is a kind of torus.

Symmetry.

It also loops back upon and through itself and invokes foundational dynamics for principles of logical self-containment that self-organisational systems in biological models approximate.

The negative space (as topology) of a complex representational information system and dynamical mapping precisely is that system, topologically inverted.

Bounded continuity in logical incompleteness: two systems that each contain the other mirrored in and as one system that contains itself.

It’s a doughnut, just not as we know it.

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