Biological Architectures
Eleven entries examining nervous-system designs in biology and their analogues in the geometric engine. Primary sequence (entries 01-04) argues from a minimum biological case to a large-scale navigational one, via a control. Entries 05-11 are per-capability deep dives isolating specific behaviours of the primary case (gait, phototaxis, behavioural modes, concept formation, depletion adaptation, trajectory learning, and prediction as constraint maintenance). Read in order; the deep dives assume familiarity with the primary sequence.
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01
The Tardigrade
The minimum biological case exhibiting non-linear state resolution by settling rather than branching. Eight legs, two eyes, four ganglia, one shared neuropeptide field. Twelve levels of cognition stacked on the same primitive, 12/12 pass, no training loop.
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02
C. elegans — The Control
The other side of the Ecdysozoan fork. Identical graph, with and without a field. Baseline freezes on every input; upgraded worm separates its states. The field is the single missing ingredient.
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03
The Squirrel — Topology vs Coordinates
Scatter-hoarding rodents navigate by reading a landscape rather than memorising coordinates. Hippocampal growth and pruning as scheduled scaffold removal. The same architecture is what lets a distributed basin system outperform a permanent index when the landscape moves.
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04
Navigation Energy
The settling-step count is an intrinsic loss signal. Well-consolidated basins resolve quickly; unfamiliar territory costs more steps. A loss that is discovered rather than inflicted — no labels, no gradient, auditable at the decision level.
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05
Gait Emergence
A walking rhythm appears from field dynamics alone — no central pattern generator, no walk command. The oscillation of a shared field settling toward its attractor is the gait. Opposite-sign output legs turn the oscillation into paired alternation.
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06
Phototaxis Without Rules
Light on one eye. No `if left > right` anywhere in the loop. The bilateral differential flows through the ganglion chain as a lateral bias; the body turns toward the light because the geometry of the differential is the decision.
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07
Behavioural Modes
IDLE, ASSESS, APPROACH, AVOID — named basins on a one-dimensional scalar manifold. The mode label is an `argmin` over distances to chosen basin positions. The `if/elif` reporting chain is replaced by basin proximity.
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08
Concept Formation
A pain event on a red plant transfers its valence to the red channel. The next unseen red plant inherits the danger. Learning as geometric attachment of valence to a feature channel; no reward model, no training set.
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09
Depletion Adaptation
A resource goes toxic after prolonged use. The system flips its valence from safe to avoid on a single event, without forgetting the rest of what it knows. Adaptive unlearning by local basin update, not a global retrain.
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10
Trajectory Learning
A moving object is recognised as the same object across frames because the trajectory is a single basin in spacetime rather than a set of disconnected positions. Object permanence, predictive tracking, and anticipation as properties of trajectory geometry.
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11
The Dragonfly — Prediction As Constraint Maintenance
A 97% interception rate without a ballistics solver. The dragonfly holds a constant bearing angle — keeping prey at a fixed angle in its visual field — and lets the physics deliver the catch. Prediction as geometric constraint, not computational extrapolation.