Symbiotic Breathing Toy Simulation

Status: designed comparison between two compute schedules. It is not evidence that a real agent will discover the schedule, that the schedule is uniquely optimal, or that "true symbiosis" has been achieved.

Question

Can alternating periods of high and low activity keep a slow-recovering substrate within a selected health range while still allowing useful work? The script represents this as a coupled dynamical system with a compute-rate variable \(\gamma\) and a host-health variable.

The language of cognitive breathing names the periodic schedule. The TEO dissipation limit \(D_{\max}\) supplies a model parameter, not a measured universal capacity. References to a "Gödelian agent" in earlier versions were metaphorical: Gödel's incompleteness theorems do not imply that an agent will recognize substrate limits or choose cooperation.

Compared Conditions

1. Monotone schedule: compute demand rises according to the stipulated rule, and host health falls in the selected parameter regime.
2. Oscillating schedule: compute alternates between active and recovery periods, and host health approaches a bounded rhythm in that regime.

The second outcome follows from a schedule designed around the recovery equation. A fair follow-up should match total work, vary delays and noise, sweep parameters, compare adaptive non-periodic controllers, and test failure when the health signal is wrong or manipulable.

Run

python symbiotic_breathing.py

The script writes symbiosis_plot.png. Read the image as a demonstration that rate scheduling can alter trajectories in this toy model—not as a biological or governance theorem.