The brief deafness after every spike. For an absolute window no stimulus — at any strength — can fire a second spike, because the sodium channels are inactivated (h ≈ 0). Then a relative window where only a stronger-than-normal stimulus fires a smaller spike, as inactivation lifts. This caps the firing rate at f_max = 1/t_ref and forces the impulse to travel one way. Down the center the stimulus goes in, the membrane decides, the result comes out. Blue builds it; red breaks it.
source The refractory period — E. D. Adrian, J. Physiol. 61:49–72 (1926); sodium inactivation from A. L. Hodgkin & A. F. Huxley, J. Physiol. 117:500–544 (1952) — ncbi.nlm.nih.gov/pmc/articles/PMC1392413. AMBER: the concept has no single stable primary link; parameters below are illustrative. Rendered, not quoted. No medical advice.
After a spike the sodium inactivation gate h collapses toward 0: the channels that carry the upstroke are shut. They de-inactivate exponentially:
h(t) = 1 − e−t/τh (t = time since the last spike)
Two phases fall out of that one curve:
ABSOLUTE (t < t_abs): h is below the minimum needed to regenerate a spike — the current threshold is infinite. No stimulus fires, at any strength.
RELATIVE (t_abs ≤ t < t_rel): the threshold is raised above baseline and decays back as h recovers — a stronger-than-normal stimulus fires a smaller spike (amplitude tracks h).
Illustrative params AMBER: t_abs = 2 ms, t_rel = 5 ms, τh = 1.5 ms, baseline threshold = 1.
The recovery window is the child of the-hodgkin-huxley: its sodium inactivation h is exactly what shuts the door after each firing. The absolute window caps the rate at f_max = 1/t_ref and forces conduction to be one-way — the membrane just behind the advancing front is still deaf, so the impulse cannot double back.
That spacing is what turns a single event into a train: it sets the rhythm of the-action-potential. Each sphere is the next one's premise.
The blue team's live check: recompute the ceiling and both phases from the model right now — absolute blocks any current, relative raises the threshold, f_max = 1/t_abs, conduction one-way. If red tampers, this badge is where it shows.
Feed the membrane two numbers: t — how long since the last spike (ms) — and I — the stimulus strength (baseline threshold = 1). The engine returns whether a second spike fires, how big it is, which phase you are in, and the rate ceiling. Slide either value below.
| phase | window | what fires |
|---|---|---|
| ABSOLUTE | t < 2 ms | nothing (h ≈ 0) |
| RELATIVE | 2–5 ms | stronger only, smaller spike |
| RECOVERED | t ≥ 5 ms | normal spike at baseline |
Pink = live threshold(t); green dash = baseline; cyan = your stimulus I; red band = absolute, pink band = relative.
Everything is computed from h(t) = 1 − e−t/τ and the threshold law on the spot — never looked up.
What the membrane proves, live: during the absolute period no current fires a spike; during the relative period only a stronger stimulus fires a smaller one; the absolute window is a hard ceiling f_max = 1/t_abs = 500 Hz (2 ms); and refractoriness makes conduction unidirectional. The current verdict is above; these invariants are the output.
The blue witness (left) confirms these live; the red team (right) tries to make them wrong.
f_max = 1/t_abs is an upper bound the cell rarely reaches — spike-frequency adaptation pushes the real ceiling lower. And "one-way" describes a single advancing front: a mid-axon stimulus can still fire antidromically (backward) — refractoriness stops a front reversing on itself, not every possible backward spike.
"The refractory period is caused by potassium channels." Cut. The absolute period is sodium inactivation (h → 0); K⁺ afterhyperpolarization mostly shapes the relative period. Both matter; the hard floor is Na.
"During the relative refractory period the neuron cannot fire." Cut. It can — with a stronger-than-normal stimulus. The threshold is raised, not infinite; the spike is just smaller.
"A neuron can fire arbitrarily fast." Cut. f_max = 1/t_abs. A 2 ms absolute period caps it near 500 Hz — computed in the machine.
The red team's move: remove the absolute refractory period — allow a spike to re-fire immediately. Now f_max is unbounded and the impulse can reverse. The blue witness (window 7) is watching.
Delete the absolute window and immediate re-firing becomes legal — the ceiling f_max = 1/t_ref vanishes and back-propagation opens. The witness recomputes, disagrees, and turns red. Nothing is faked; the attack is real and it is caught.