Involution
Collier's New Encyclopedia (1921)
in mathematics, the operation of finding any power of a given quantity, the multiplication of a number into itself any given number of times; thus the third power of 2 is found by involution, or multiplication of the number by itself, and the product by the same number; thus 2×2×2=8. It is the reverse of EVOLUTION (q. v.). The operation of involution may be directly performed by continued multiplication, performed but it is often formulas, particularly by the binomial formula. In grammar, the insertion of one or more clauses or members of a sentence between the agent or subject and the verb. In pathology, the restoration to its normal size of any part which has been abnormally developed. The opposite of evolution. ing to one of the most popular versions, a daughter of Inachus, King of Argos. The love of Zeus for this maiden roused, as in other myths, the jealousy of Hera, who transformed Io into a heifer, and placed her in charge of Argus Panoptes, y Hermes, who This guardian was slain by Her was thence called Argeiphontes, or the Slayer of Argus. Hera then sent a gadfly, which stung the heifer, and drove her in madness over the earth. Thus began those wanderings of Io which Æschylus has sketched in his drama of "Prometheus Chained." IO, in astronomy, (1) the first satellite of Jupiter, discovered by Galileo in 1610. The names of the four satellites of this planet are seldom used, especially as three of them have been assigned to asteroids as well, and they are generally known by the numbers I, II, III, and IV. I, (2) The name of the 85th asteroid, discovered by Peters at Clinton, N. Y., Sept. 19, 1865, the fourth of the small planets detected by him.
What Has Changed in the Last Century
When Collier's wrote this in 1921, "involution" was still the standard schoolroom name for raising a number to a power; that usage is now dead, replaced by "exponentiation," and the paired term "evolution" for root-extraction has vanished with it. In modern mathematics the word has been reassigned entirely: an involution is a function that undoes itself, so that applying it twice returns the original value, as with negation or matrix transposition. The pathological sense has held up best and is still current medicine, chiefly for the shrinking of the uterus after childbirth and the age-related involution of the thymus. Note that the text above runs on into an unrelated article on Io, the Argive maiden and the Jovian moon, apparently a printing or scanning accident; the moon's name, which Collier's said was "seldom used," became standard after the Voyager flybys of 1979 revealed it as the most volcanically active body in the solar system.
Written for this edition, 2026.