coincidence
Pluralcoincidences
- 1The appearance of a meaningful connection between events that are in fact unrelated.
Like rolling the same number twice in a row: surprising, but really just chance.
The detective argued that the matching timestamps were no coincidence.
By sheer coincidence, both novelists set their stories in the same tiny village.
Similarchance, accident, fluke, happenstance
Oppositedesign
Note
The everyday meaning works as both a count noun and a mass noun, and each has its own habits. As a count noun it often follows just: it was just a coincidence. As a mass noun it drops the article and pairs with sheer: by sheer coincidence. The phrase no coincidence is the skeptic's version, used to insist that the connection is real after all.
- 2The state of two or more things occupying the same position or happening at the same moment.
Like laying one map over another so every road sits exactly on its match.
The coincidence of the planets along a single line is a rare event.
Surveyors confirmed the coincidence of the new marker with the old boundary wall.
Similaralignment, conjunction, concurrence, correspondence, simultaneity
Note
The literal meaning behind the everyday one. The word comes from French coïncidence and works as the noun of coincide: things that fall together in space or time. It usually takes of … with, as in the coincidence of the new marker with the old wall. The "mere chance" meaning keeps this picture of events lining up and adds the suspicion that the alignment means nothing.
- 3A point at which two functions or mappings take the same value.
Like finding the one moment two runners are side by side on the track.
Fixed-point theorems guarantee that certain pairs of maps possess at least one coincidence.
The proof reduces the problem to locating a coincidence of the two continuous functions.
Note
Analysts also use the full name, coincidence point. Given two maps f and g, they look for an x where f(x) = g(x). When g is the identity map, the search becomes ordinary fixed-point theory, so coincidence theory is its generalization. Compare the geometer's fixed point, where a single correspondence plays the role of the pair of maps.
- 4A fixed point of a correspondence: a point of a variety that maps to itself under the correspondence.
Like a pairing rule that, applied to one special point, hands back that same point.
Each coincidence corresponds to a point left fixed by the algebraic correspondence.
The number of coincidences of a correspondence on a curve follows a classical formula.
Note
Geometers usually meet these in the plural, because the interest lies in counting them: how many points of a curve a correspondence sends back to themselves. The classical answer is the Cayley–Brill formula. If you view the correspondence as a relation on the variety, a coincidence is simply a point related to itself. That is why the word sits so close to fixed point.
Practice
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Origin
From French coïncidence; by surface analysis, coincide plus the suffix -ence.