Where does arc collide?

Humphry Davy, working with the Royal Institution's large voltaic battery in the years around 1808 (Davy, 1808), produced powerful electrical discharges as an effect of that battery work, and by about 1809 to 1810 he demonstrated a bright, continuous discharge between carbon points before audiences at the institution (Anders, 2003). The glowing column of ionised gas bows upward into an arch when the two electrodes are drawn apart, and the phenomenon took its name from that arched shape. The referent is a sustained electrical discharge across a gap between conductors, carrying current through hot ionised gas, and it has nothing in common with a reflex route in the nervous system, a rising and falling story shape, or a directed link in a graph.[1][2]

Unit

One sustained discharge across an electrode gap, described by its current and arc voltage

Recovery means

Not applicable

Measured by

Characterised by the current it carries, the voltage across the gap, and the temperature of the ionised column

The physiology of the reflex begins with Marshall Hall's 1833 account of reflex action, which showed that the spinal cord can turn an incoming stimulus into an outgoing muscular response without conscious control (Hall, 1833). John Dewey's 1896 paper The reflex arc concept in psychology made the phrase current in the study of behaviour, and Charles Sherrington's 1906 The Integrative Action of the Nervous System set out the full route it names, from a sensory receptor through a spinal centre to the muscle that acts (Dewey, 1896; Sherrington, 1906). The referent is a signalling route through living nerve tissue, timed in milliseconds, and it is unrelated to an electrical discharge across a gap, the shape of a story, or an edge in a mathematical graph.[3][4][5]

Unit

One stimulus-to-response pathway through receptor, nerve, centre, and effector

Recovery means

The pathway returns to rest between stimuli as the nerve fibres repolarise

Measured by

Assessed by reflex latency and response amplitude, for example the timing and force of a tendon jerk

Gustav Freytag's 1863 Die Technik des Dramas analysed the shape of a classical play, an opening that rises through complication to a climax and then falls through reversal to a resolution, a pattern now often drawn as Freytag's pyramid (Freytag, 1863). In later storytelling and screenwriting this rising and falling shape of tension across a work, or the change a character undergoes across it, is called the dramatic or character arc. The referent is the trajectory of a narrative's tension or a character's change over the course of a story, and it bears no relation to an electrical discharge, a nerve pathway, or a directed edge in a graph.[6]

Unit

One story's or character's trajectory of rising and falling tension from beginning to end

Recovery means

Not applicable

Measured by

Described qualitatively by mapping stages of tension, or a character's change, across the work

In graph theory an arc is a directed edge: an ordered link that runs from one vertex to another, so that a connection from A to B is distinct from one from B to A. Claude Berge's 1958 Théorie des graphes et ses applications set the convention, in French, of calling a directed link an arc and an undirected one an arête (Berge, 1958), and Frank Harary's 1969 Graph Theory carried the term into the standard English vocabulary of the field (Harary, 1969). The referent is a formal object, an ordered pair of vertices in a directed graph, and it shares nothing with an electrical discharge, a reflex pathway, or the shape of a story beyond the word.[7][8]

Unit

One ordered pair of vertices, a single directed link in a graph

Recovery means

Not applicable

Measured by

Counted as entries in a directed graph and recorded in its adjacency or incidence matrix