This post discusses a family of words that pertain to balance, impartiality, or uniformity.
The root equi-, which forms without the i when it precedes a vowel, ultimately derives from the Latin adjective aequus, meaning “even” (which is not related to equus, meaning “horse” and the source of equestrian). Equal refers to a state of balance, and the noun form is equality; a person or system that favors or promotes equality is an egalitarian. (The consonantal change occurred in French.)
Equity is the quality of fairness, though the word also has senses in finance and in property ownership of rights or value. The adjectival form is equitable, and equitably is the adverbial form. The antonym, with the same variations, is inequity, though iniquity, which means “wickedness,” stems from the same source. (Its adjectival form is iniquitous, and the noun is formed by attaching to that word the suffix -ness.)
To equate is to balance or compare, or to make even or smooth; the act of doing so is equation. (That noun also denotes a logical or mathematical expression.) Equanimity is fairness, and equilibrium is mental or physical balance. The root word of the former term is a form of animus, meaning “mind” or “spirit,” so a literal translation is “even mind,” and the root word of the latter term is derived from libra, meaning “balance” or “scale,” so equilibrium literally means “even balance.” (Equanimity has no adjectival form, but equilibrious, though rare, serves that function for equilibrium.)
Equivalence (equivalency is a variation) is literally “equal worth”; the adjectival form is equivalent. The source of the root of equivocation is also that of vocal and voice; literally “equal voice,” the word has pejorative senses of “avoiding commitment to what one says” or “using language to deceive.” One is described as equivocating or being equivocal.
Equinox derives from the Latin word for “equality of night (and day)”—the root nox is related to the first syllable of nocturnal (and both are cognate with night)—and refers to the two days of the year, six months apart, when day and night are of identical duration.
A word that may not be an apparent relative of those described above is adequate, which means “sufficient.” (Its Latin forebear literally means “make equal.”) Depending on context, the word can be neutral or disparaging. And the rare term equiparation means “equal treatment.” (The root syllable is related to par and per, which pertain to value.)
“Equipartition” is an important word in thermodynamics – the study of the flow of, gases, heat, and other forms of energy.
“Equanimity has no adjectival form” – ??
“equaniminous” There was a malfunction, and the computer system refused to include this prospective word.
From the Internet: equanimous:
DEFINITION: the adjective form of equanimity
e·qua·nim·i·ty
NOUN: mental calmness, composure, and evenness of temper, especially in a difficult situation: “Lee accepted both the good and the bad with equanimity.”
On the other hand, Sherman was very tempermental, to the point of insanity.
“equanimous”. The adjective form of “equanimity”.
The lieutenant felt equanimous about the whole wretched ordeal.
She felt equanimous about being pregnant with triplets.
I am equanimous on whether to walk or to take the shuttle bus.
Hamlet was equanimous on whether to live or to die.
“Poor Yorick, I knew him, Horatio…”
I am not equanimous about what that rakehell Osama did!
Feed him to the sharks.
Another word from the same family: “equipoise”.
“The two main opposing parties in Parliament stood in equipoise. Neither one could gather enough votes to elect a new Prime Minister or a Cabinet.”
“Equipoise” is also a word that is useful in thermodynamics and other kinds of physics, chemistry, and biology.
There are also the words “equipotential” and “equipotent”.
Equipotential is a term from electricity that is useful in physical and electrical engineering. By extension, it can be used elsewhere:
“The two main parties in Parliament are in an equipotential state. Neither one of them can muster enough strength to accomplish anything!’
Similarly for “equipotent”. “In the religion of the Lost Continent of Mu, there were two main gods who were equipotent. It did not matter which one that one prayed to.”
“The two armies on opposite sides of No Man’s Land were equipotent. Hence, the war went on for year after bloody year, with no end in sight.”
“Equivalence relationships” can be defined in mathematics, and one is symbolized by A ~ B. There are several basic rules:
1. A ~ A, rather obviously. (The reflexive law)
2. If A ~ B, then B ~ A. (The symmetric law)
3. If A ~ B, and B ~ C, then A ~ C. (The transitive law for equivalence)
It can be seen that equivalence has a lot in common with equality, but they are not exactly the same thing.
We have only just begun with these.
An “equilateral” triangle is a triangle with all three sides of equal length.
This can also be called a 60-60-60 triangle because all three of its angles work out to be 60 degree angles.
An equilateral triangle is a special case of an isosceles triangle, where the latter has any two sides of equal length.
An equilateral rectangle is a SQUARE because all four sides are of equal length. Likewise, there are equilateral polygons of as many sides as you would like. In ancient times, Archimedes made some calculations with equilateral polygons of 96 sides, and with these, he found a good approximation to the number pi.
Naturally, “equilateral” goes along with {equivalent, equipotential, equipotent, equipartition, equipoise, equiangular, equidiameter, equiperimeter}.
Two poisons are said to be equipotent if one would kill you, or your enemy, just as readily as the other.
There does not seem to be a similar word in the world of probability and random variables. When two or more events have equal probabilities, they are said to be “equally probable” or “equally likely”.