incidence
Pluralincidences
- 1The extent to which something happens, or how often it occurs across a group or period.
Researchers noted a rising incidence of burnout among remote workers.
The survey measured the incidence of fraud across small businesses.
Similarrate, frequency, prevalence, occurrence
- 2The fact of something occurring; the actual happening of an event or action.
Historians debated the incidence of the rebellion and its underlying causes.
The incidence of so many coincidences in one day seemed almost impossible.
Similaroccurrence
Note
The broadest sense, and the one nearest the word's origin. It comes through Middle French incidence from Medieval Latin incidentia, "a falling upon", built on Latin incidere, from in "on" and cadere "to fall". An incidence is what befalls. That picture of something landing on something else runs through the technical senses too, from taxes to light rays to points on a line.
- 3A measure of the rate at which new cases of a medical condition appear in a population over a specified period.
The study reported a higher incidence of diabetes in urban areas.
Public health officials tracked the incidence of the virus throughout the year.
Similarrate
Note
Epidemiologists use it strictly for new cases arising in a defined population during a set interval. Its constant partner is prevalence, which counts all existing cases at one moment, old and new alike. A long-lasting condition can therefore show low incidence and high prevalence. In ordinary prose the looser sense of frequency is fine, but in a medical paper the incidence of diabetes means onset, not presence.
- 4The arrival or striking of radiation, light, or a projectile against a surface.
The angle of incidence equals the angle of reflection for a flat mirror.
Increasing the incidence of laser light improved the sensor's response.
Note
Optics turns it into a measurement. The angle of incidence is taken between the incoming ray and the normal, the line standing perpendicular to the surface, rather than between the ray and the surface itself. This is an easy slip when reading diagrams. The angle of reflection is measured from the same reference line, which is why the two can be compared directly.
- 5The way a burden falls, especially how the real cost of a tax is borne by particular groups.
Economists analyzed the incidence of the sales tax on low-income households.
The true incidence of the levy shifted from producers to consumers.
Similarburden
Note
Economists keep the word's literal picture of where something lands, the Latin "falling upon" behind the plain sense of occurrence. The question is who finally bears a tax, not who hands it over. The party legally obliged to pay can pass the cost on through prices, so a levy collected from producers may fall on consumers. The usual phrasing is the incidence of a tax on someone.
- 6The lying of a point on a line, or of a line within a plane.
The proof relied on the incidence of three points along a single line.
Projective geometry studies the incidence of lines and points without any reference to distance.
Note
Here the falling is pure position: a point is incident with a line when it lies on it, and a line is incident with a plane when it lies within it. Projective geometry builds whole axiom systems and incidence structures on this relation alone, with no reference to distance or size. The relation always pairs objects of different dimension.
- 7The relation connecting an edge of a graph to one of the vertices it joins.
The matrix records the incidence of every edge with each vertex.
Each edge contributes to the incidence of exactly two vertices in a simple graph.
Note
The graph-theory cousin of the geometric sense: an edge is incident to the vertices at its ends, much as a point lies on a line. The full pattern is recorded in the incidence matrix, whose rows stand for vertices and whose columns stand for edges. Keep it apart from adjacency, which links vertex to vertex. Incidence always pairs an edge with a vertex.
Practice
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Origin
From Middle French incidence, from Medieval Latin incidentia ("a falling upon"), from Latin incidens, the present participle of incidere ("to fall upon"), formed from in ("on") plus cadere ("to fall").