Substrate — the neuron is a switch with a slow recovery

A neuron is an R19 bistable switch with a slow recovery — a relaxation oscillator. Na⁺ in, K⁺ out gives an all-or-none spike at the cost of the ion pump (~20% of the body's energy). The fast switch but slow recovery makes the cell oscillate at very low frequency, and coupled neurons synchronise into one slow population rhythm.

A neuron is an R19 bistable switch with a slow recovery — a relaxation oscillator. Na⁺ in / K⁺ out gives an all-or-none spike; the metabolic price is the ion pump (≈1 ATP per 3 Na⁺), which is why the brain spends ~20% of the body's energy. The switch timescale is fast, but the recovery is slow, so the neuron oscillates at very low frequency; coupled neurons synchronise into one slow population rhythm, and fast external input is low-passed. The substrate speaks at low frequency.

The switch

A neuron is the R19 bistable switch in its simplest neural form. Sodium flows in, potassium flows out, and the membrane flips all-or-none: a spike either fires or it does not. There is no graded "half spike" — the read is discrete, exactly the on/off of the switch. This is the unit the rest of the chain is built from.

The energy

The switch is not free. After every flip the pump must restore the gradient, paying about 1 ATP for every 3 Na⁺ ions returned. This single cost dominates the brain's budget: the organ is ~2% of body mass but spends on the order of 20% of the body's energy, almost all of it on the pump. Energy in this chain is the price of switching, nothing more — it is not information (§9).

The slow oscillator

A switch with a fast threshold but a slow recovery is a relaxation oscillator: it fires, then waits out the recovery, then fires again. Because the recovery sets the period, the period is far longer than the switch timescale, so a neuron's intrinsic rhythm is very low frequency. This is the seed of the whole rhythmic story: the brain's internal communication is slow because its unit recovers slowly.

Low-pass

Couple many such oscillators and they synchronise into one slow population rhythm — an internal low-frequency channel. Drive them with a fast external input and the population does not track it cycle-for-cycle; it low-passes it. So an external fast signal is read as a low-frequency one. The substrate, left to itself and coupled, speaks at low frequency — which is what the next chapter turns into bands.