Etymology
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Words related to commute

com- 
Origin and meaning of com-

word-forming element usually meaning "with, together," from Latin com, archaic form of classical Latin cum "together, together with, in combination," from PIE *kom- "beside, near, by, with" (compare Old English ge-, German ge-). The prefix in Latin sometimes was used as an intensive.

Before vowels and aspirates, it is reduced to co-; before -g-, it is assimilated to cog- or con-; before -l-, assimilated to col-; before -r-, assimilated to cor-; before -c-, -d-, -j-, -n-, -q-, -s-, -t-, and -v-, it is assimilated to con-, which was so frequent that it often was used as the normal form.

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*mei- (1)
Proto-Indo-European root meaning "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].

It forms all or part of: amiss; amoeba; azimuth; common; commune; communicate; communication; communism; commute; congee; demean; emigrate; emigration; excommunicate; excommunication; immune; immutable; incommunicado; mad; mean (adj.1) "low-quality;" mew (n.2) "cage;" mews; migrate; migration; mis- (1) "bad, wrong;" mistake; Mithras; molt; Mstislav; municipal; munificent; mutable; mutant; mutate; mutation; mutatis mutandis; mutual; permeable; permeate; permutation; permute; remunerate; remuneration; transmutation; transmute; zenith.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit methati "changes, alternates, joins, meets;" Avestan mitho "perverted, false;" Hittite mutai- "be changed into;" Latin mutare "to change," meare "to go, pass," migrare "to move from one place to another," mutuus "done in exchange;" Old Church Slavonic mite "alternately;" Czech mijim "to go by, pass by," Polish mijać "avoid;" Gothic maidjan "to change."
commuter (n.)

"one who goes back and forth to work," 1865, American English, originally "holder of a commutation ticket," agent noun from commute (v.).

A commutation ticket (1848) was a ticket issued (by a railroad, etc.) at a reduced rate entitling the holder to travel over a given route a limited number of times or an unlimited number of times over a certain period. It is from commute in its sense of "to change one kind of payment into another" (1795), especially "to combine a number of payments into a single one, pay a single sum instead of a number of successive payments" (1845). 

commutation (n.)

mid-15c., commutacioun, "act of giving one thing for another," from Old French commutacion "change, transformation, exchange, barter" (13c., Modern French commutation), from Latin commutationem (nominative commutatio) "a change, alteration," noun of action from past participle stem of commutare "to change, alter entirely" (see commute (v.)).

From c. 1500 as "a passage from one state to another;" 1590s as "act of substituting one thing for another."

commutative (adj.)

"relating to exchange, interchangeable, mutual," 1530s, from Medieval Latin commutativus, from Latin commutat-, past participle stem of commutare (see commute (v.)). Commutative justice regulates interactions between two persons. Related: Commutatively.

commutator (n.)

1839, "apparatus for reversing the currents from a battery without rearranging the conductors," agent noun from Latin commutare (see commute (v.)). From 1880 as "contrivance for varying the strength of an electric current."

telecommute (v.)
by 1974 (as a hypothetical experience), from tele- + commute. Related: Telecommuted. Compare telecommuting.