A Biologically Grounded Theory of Physical Computation

Biological nervous systems reason through the coordinated activity of interacting neurons rather than through a single centralized computational element. Sensory signals are continuously integrated with recurrent activity, prior experience, adaptation, and competing interpretations. These processes motivate an investigation of whether analogous physical dynamics in neuromorphic hardware can support reasoning. This paper develops a framework for reasoning as collective state evolution and selection within coupled dynamical networks. It models reasoning, drawing on recurrent circuits and attractor dynamics, as two regimes of one continuous-time system: exploration, in which candidate interpretations compete, persist and reorganize, and commitment, in which dissipative relaxation stabilizes one. The regimes are generated by a candidate vector field combining a conservative (Hamiltonian-type) term and a dissipative (Lyapunov-type) term, constrained by metriplectic-type degeneracy conditions. We show these conditions cannot hold in two state dimensions with a non-constant landscape and a nonzero skew operator, and give a three-variable construction in which they hold exactly. The candidate substrate is a lattice of Mead-inspired transconductance–capacitor (Gm–C) cells with a self-field; the circuit realization of the conservative term remains open. A five-level hierarchy, from local physical law to task-relative semantic evaluation, is to be validated at each transition by a commuting-diagram condition and an intervention criterion. The framework does not assume that biological reasoning has been reproduced or that analog implementation guarantees efficiency. It specifies measurements against accumulator, attractor and digital baselines, an energy–time–accuracy accounting, and falsification conditions. No hardware or circuit results are reported. Numerical examples in Sections 5.1 and 7.4 are reproduced by the deposited Python script (reproduce_numerical_values.py; see README.md)