| 释义 |
involution|ɪnvəˈl(j)uːʃən|
[ad. L. involūtiōn-em, n. of action from involvĕre to involve: cf. F. involution (13–14th c. in Hatz.-Darm.).]
1. a. The action of involving or fact of being involved; implicit comprehension or inclusion; implication; also, quasi-concr., that which is involved.
1611Cotgr., Involution, an inuolution, enwrapping, infoulding. 1642Jer. Taylor Episc. (1647) 136 Often..a Bishop nay an Apostle is called a Presbyter..by reason of the involution or comprehension of Presbyter within Episcopus. 1790Gibbon Misc. Wks. (1814) III. 489 According to the philosophers, who can discern an endless involution of germs or organized bodies, the future animal exists in the female parent. 1798Coleridge Satyrane's Lett. ii. 223 Aristotle has..required of the poet an involution of the universal in the individual. 1867Stubbs Lect. Hist. (1886) 17 From his own involution in the matter of which he is to judge. 1892Newman Smyth Chr. Ethics ii. iii. 420 The instinct to discover the deeper moral involutions of current political questions is a power of great ethical value.
b. concr. Something that involves or enwraps; an envelope, covering, etc.
1646Sir T. Browne Pseud. Ep. v. xxi. 269 The involution or membranous covering..called the silly how, that sometimes is found about the heads of children upon their birth.
2. An involved or entangled condition; entanglement, complication; intricacy of construction or style (as in a literary work or the arrangement of words in a sentence); also concr., something complicated; an intricate movement, a tangle, etc.
1611Cotgr., Anfractueux, full of turnings, compasses, involutions. 1647May Hist. Parl. i. i. 73 All their acts and actions are so full of mixtures, involutions, and complications. 1751Johnson Rambler No. 168 ⁋7 Mackbeth proceeds to wish..that he may, in the involutions of infernal darkness, escape the eye of providence. a1763Shenstone Economy iii. 33 Such the clue Of Cretan Ariadne ne'er explain'd! Hooks! angles! crooks! and involutions wild! 1820Hazlitt Lect. Dram. Lit. 156 The style of the first act has..more involution, than the general style of Fletcher. 1837–9Hallam Hist. Lit. I. i. viii. §24. 433 He introduced..a sort of involution into his style, which gives an air of dignity and remoteness from common life. 1858G. Macdonald Phantastes xiv, The whole place..swam with the involutions of an intricate dance.
3. Anat. A rolling, curling, or turning inwards; concr. a part of a structure formed by this action.
1851Carpenter Man. Phys. (ed. 2) 494 A cavity..which is subsequently rendered more complex by the prolongation and involution of its walls in various parts. 1870Rolleston Anim. Life Introd. 36 The peripheral apparatus retains its typical character as an involution of the integument in the olfactory..organs. 1873Mivart Elem. Anat. ix. 392 The ear like the eye is formed by an involution of the skin. 1880― Cat 230 Glands..are..complex involutions of an epithelial surface.
4. Phys. ‘The retrograde change which occurs in the body in old age, or in some organ when its permanent or temporary purpose has been fulfilled’ (Syd. Soc. Lex.). Also attrib.
1860Tanner Pregnancy ii. 93 The whole process of degeneration and reconstruction is spoken of as the involution of the uterus. 1878A. Gamgee tr. Hermann's Hum. Phys. 530 The close of the period of fecundity and the arrest of menstruation are associated with certain bodily changes, especially of the generative apparatus, which are comprehended in the term ‘involution’. 1887Syd. Soc. Lex., Senile Involution, the shrinking of the whole body which accompanies old age. Ibid., Involution cysts, the cysts found in the shrivelled mammary glands of old women, being dilated acini or ducts of the gland filled with a thick fluid. 1898G. E. Herman Dis. Wom. ix. 87 During the last few days of pregnancy, and the first few days of involution, giant cells with many nuclei are to be seen.
5. Biol. A retrograde process of development; the opposite of evolution; degeneration. Chiefly in Comb., as involution-form.
1896Allbutt's Syst. Med. I. 761 Involution forms [of bacilli] being pretty constantly developed. 1897Ibid. II. 90 Evidence that the clubs are involution-forms.
6. Math.
a. Arith. and Alg. The multiplication of a quantity into itself any number of times, so as to raise it to any assigned power. Hence, in extended sense, the raising of a quantity to any power, positive, negative, fractional, or imaginary.
1706W. Jones Syn. Palmar. Matheseos 51 By the Involution of the Binomial Root. 1806Hutton Course Math. I. 197 Involution is the raising of powers from any proposed root; or the method of finding the square, cube, biquadrate, &c., of any given quantity.
b. Geom. A system of pairs of points on a right line, so situated that the product of the distances of the two points of each pair from a certain fixed point on the line (the centre of involution) is equal to a constant quantity. Hence in various extended uses (see quot. 1847).
[1837Chasles Aperçu Hist. 77 Desargues appelait la rélation qui constitue son beau théorème involution de six points.] 1847Cayley in Camb. & Dubl. Math. Jrnl. II. 52 When three conics have the same points of intersection, any transversal intersects the system in six points, which are said to be in involution. It appears natural to apply the term to the conics themselves; and then it is easy to generalize the notion of involution so as to apply it to functions of any number of variables. 1879Salmon Conics 311. 1885 C. Leudesdorf tr. Cremona's Proj. Geom. 101 In an involution the elements are conjugate to one another in pairs.
c. A function or transformation that is equal to its inverse.
1916E. Kasner in Amer. Jrnl. Math. XXXVIII. 177 It is easy to determine all regular transformations of period 2. In the direct type Z = f(z) the functional equation is f(f(z)) ≡ z, that is, f2 = 1; in the reverse type Z = f(z0) the functional equation is f(f0(z)) ≡ z, that is, ff0 = 1, where f0 denotes the series whose coefficients are the conjugates of the coefficients of series f. We shall call a transformation of the former type (excluding the identical transformation) a conformal involution, and one of the latter type a conformal symmetry. 1969F. M. Hall Introd. Abstr. Algebra II. ii. 31 If θ is a 1–1 correspondence between elements of A and itself such that θ= θ—1, then θ is said to be an involution. |