The Reservoir and the Stake

A monitor whose conscience is too faint to change what he does is invisible to selection, and the threshold below which that is true is set by how costly his task is. Because the threshold moves with the cost, an organisation facing cheaper tasks does not draw on its store of invisible conscience: the store shrinks, and the shrinking is the drawing. It is drawn down from the top, so the monitors whose conscience was closest to mattering are the first for whom it begins to. A companion paper establishes that what sits in such a store is put there by the process that supplies new conscience rather than left there by the organisation’s past, so the value of the store as memory is nothing in the long run. This paper asks what it is worth in the short run, and finds that the question has an answer with a shape. The store is forgotten slowly where the conscience in it is invisible, because the set it occupies is narrow and narrowness divides the rate. It is forgotten quickly once the cost has fallen far enough that the population has left that set, and there the rate is set by a discontinuity at the set’s own edge and the supply process does not enter. A reservoir of latent conscience is therefore not worth its stock, but its stock discounted by a clock that accelerates at exactly the moment the reservoir becomes useful. Two consequences follow and neither was anticipated. The quieter the process that filled the reservoir, the more violently it is spent, because the same narrowness that made the store durable makes it small. And the process that filled it has no influence whatever on the rate at which exposure consumes it: it governs the stock and nothing of the spending. Where the two régimes meet, the rate vanishes on one side and is discontinuous across, so a descent that halts near the meeting point preserves the store almost intact while one that completes spends it in a few dozen turnovers of the supply process. The stock is mostly uncovered before that point and almost all of the erosion is incurred after it — two divisions of the same fall that are near mirror images. The paper prices a discount and not a decision. What the sheltered lose is measured here on both of the model’s accountings and is, on both, a gain: what a falling cost takes from them is not payoff but invisibility, and pricing that would require a weight on what selection does to the exposed, which this model does not carry and which is left to a companion. Two literatures own the halves of the object — one supplies a decision-maker and no replenishment, the other replenishment and no decision-maker — and the acceleration lives at the join.