The Moral Code from the Physics of the Record: Least Cost over Acts with Consent

Reality is a permanent record of comparisons, each a relation between two ends, held by participants, at a positive multiplier x; out of balance a relation carries the cost J(x) = ½(x + x−1) − 1, the only continuous cost that obeys the composition law of comparisons at unit calibration. An act is admissible when it moves only live relations, writes every new entry truthfully, changes a relation only when both of its ends write on it and ends a live relation only when one of its own ends writes the ending. The moral judgment is unique: any judgment form, a rule that takes the admissible acts, doing nothing and the real cost of the world each act leaves, and returns the permitted acts, that is sound where doing nothing is admissible, gives tied acts other than doing nothing one answer, reads the record relation by relation, rests only at the least and permits something on every situation the record allows, permits on every such situation exactly the admissible acts of least cost, the code's verdict where the record holds still between acts, on true books; for forms that read only their inputs, so that relabelling the acts relabels the verdict, four of these requirements suffice and each is needed. The record's events are exchanges, equal and opposite posts at a relation's two ends at least one tick apart; each relation has a reserve. An end consents to a change of a relation or its reserve when it emits there and absorbs no net loss from posts it did not emit, there or at the reserve, and an act has consent when every end whose holding, or whose relation's reserve, it changes consents there. Read each end's book of what happened to it from the record by a three-case rule, and the code's writes as the emitters: the code's truth clause and both-ends clause then hold on an act's recorded world, the world it reaches with the record of its posts, exactly when the act has consent, on every world whose relations have distinct ends. Let the books be true, every relation live and the record the code reads hold still between acts. Take any set of acts on the world's relations that holds the balancing act, in which each end of each movable relation (live, both its ends writing) sends half of what it holds above the other end, with any posts at the relations' reserves; let the code's menu be their recorded worlds and its writes on each the ends that consent there, those of the acts among the participants' writes (where the two clauses hold, the emitters agree with them at every relation that moves). Then the code admits exactly the acts with consent and permits exactly the least-cost ones among them, the balancing act included; it admits no act in which an end whose holding, or whose relation's reserve, it changes absorbs a net loss there; it permits an act that brings a relation from off balance to balance only when both ends consent; and it forbids doing nothing, when it is in the set, exactly when a movable relation is off balance. Apart from the record holding still, these hypotheses hold for doing nothing and the balancing act, with the writes read off the record, on every world with true books, nothing ended and relations with distinct ends. On δ’s line, the real line of the mathematics that distinction forces, every conclusion of Theorem 9.10 follows with no principle beyond what distinction forces, and each step that carries a price has a free form (Section 10). Seven steps remain, among them the two readings behind admission and whether the tied-acts requirement is needed for forms that read more than their inputs.