tau (optical time-to-contact invariant)

Compiled with AI assistance and selectively reviewed. Please consult the cited passages; the books remain the authoritative source. About this companion

Editorial synthesis · provisional

Definition

Tau is Lee’s optical time-to-contact variable, described in RB2 as the inverse relative rate of expansion of an approaching object’s image. It supports prospective control such as braking or landing without separately estimating distance and speed. The projection concerns contact if the relevant motion continues unchanged; the proposal does not treat tau as an exact forecast under arbitrary acceleration or as every organism’s sole control mechanism.

Explanation

The direct passage links image expansion to the time remaining before contact under continued motion. Its examples illustrate timing an action in relation to an optical signature, rather than first computing separate abstract magnitudes. The source’s unchanged-speed condition is retained; no further mathematical precision or measurement result is supplied beyond the local account.

Prospective control means adjusting now in relation to what would happen unless action changes the trajectory. The driver or diving-bird examples consequently concern regulation, not a prediction guaranteed to become actual. A successful use changes the very future the optical relation initially indicates.

AB repeats the accessible landing and braking comparison, with a native note attributing tau to David Lee and locating it within the direct-perception debate. The proposed subentry therefore records the defined optical variable and its illustrative use without claiming all interception tasks reduce to it or that a single account settles broader theories of anticipation.

Scope and attribution

Keep the local unchanged-motion qualification, prospective action role and bounded illustrative scope; invent no universal formula or measured accuracy.

AB — The Actual Book

The accessible examples retain the native Lee genealogy and direct-perception context.

Occurrence locators: 94; Notes: 242.

RB2 — The Real Book, Volume II: Becoming Is Being

Image expansion specifies prospective contact under continued motion, with Lee’s attribution.

Occurrence locators: 65, 66.

Background used in the editorial explanation

Named theories and mechanisms are distinguished from neighboring background, homonyms and the author’s own synthesis. Reproduced AI passages retain their separate voice.