| 释义 |
isomorphism|aɪsəʊˈmɔːfɪz(ə)m|
[mod. (Mitscherlich, 1819) f. as prec. + -ism: in mod.F. isomorphisme.]
The character of being isomorphous.
1. Chem. and Min. The property of crystallizing in the same or closely related forms, esp. as exhibited by substances of analogous composition.
The general law of isomorphism affirms that bodies having a similar chemical composition have also the same form; or, in other words, that analogous elements and groups of elements may replace one another in composition without essential alteration of crystalline form. (Watts.)
1828in Webster. 1830Herschel Stud. Nat. Phil. 295 The isomorphism of certain groups of chemical elements. 1841J. Trimmer Pract. Geol. 83 The discovery by Professor Mitscherlich, of what is called the isomorphism of crystals, diminishes in some degree the value of crystalline form as a distinctive character. 1851Richardson Geol. (1855) 78 Isomorphism is the law by which an equal number of atoms, combining in the same manner, may give birth to similar crystalline forms, although the constituent elements are of a different nature. 1865–72Watts Dict. Chem. III. 423 Mitscherlich's first observation, presented to the Berlin Academy of Science in 1819, related to the isomorphism of the phosphates and arsenates. 1879Rutley Stud. Rocks x. 97 Completely establishing the isomorphism of orthoclase and albite.
2. Math. (Also Logic and Linguistics.) Identity of form and of operations between two or more groups or other sets; an exact correspondence as regards the number of constituent elements and the relations between them; spec. a one-to-one homomorphism.
1892F. N. Cole tr. Netto's Theory of Substitutions iv. 83 The correspondence of two groups as just defined is called isomorphism. 1897W. Burnside Theory of Groups of Finite Order xi. 222 A correspondence between the operations of a group, such that to every operation S there corresponds a single operation S′, while to the product ST of two operations there corresponds the product S′T′ of the corresponding operations, is said to define an isomorphism of the group itself. 1941W. V. Quine in P. A. Schilpp Philos. A. N. Whitehead 160 The theory of relation numbers is the general theory of isomorphism, i.e., of structural identity among relations. 1949Hutten & Reichenbach tr. H. Reichenbach's Theory of Probability vi. §41. 207 By showing that both the frequency interpretation and the geometrical interpretation satisfy the axioms of the formal system of probability..we have demonstrated the isomorphism, or structural identity, of the two interpretations. 1956E. M. Patterson Topology iv. 81 An isomorphism ϕ between two groups G1, G2 is a one—one transformation ϕ: G1→ G2 of G1 onto G2 which preserves the group operation. 1962Anthropol. Ling. June 26 An analysis of the special uses that an individual may make of other dialects..may tell us something about the range of prestige variants and the relative isomorphism of prestige scales that are involved in inter-dialect interchange. 1963J. Lyons Structural Semantics ii. 17 In so far as semantic and distributional criteria converge on the establishment of the same [grammatical] units, this is due to the admitted partial isomorphism between the ‘expression-plane’ and the ‘content-plane’ of language. 1965Patterson & Rutherford Elem. Abstr. Algebra iii. 77 An isomorphism of a ring R1 onto a ring R2 is a one—one mapping f of R1 onto R2 such that, for all x1, x2 {elem} R1, we have f(x1 + x2) = f(x1) + f(x2), f(x1x2) = f(x1) f(x2)... In a similar manner, we define isomorphisms between integral domains and fields. 1971Sci. Amer. Aug. 96/3 Boole..noticed that there was a considerable similarity (in fact a mathematical isomorphism) between the rules that govern the use in logic of the connectives ‘and’, ‘or’ and ‘not’, and the operations on sets of, respectively, intersection, union and complementation. 1973J. Hintikka Logic, Lang.-Games & Information ii. 42 The basic idea of Wittgenstein's picture theory is the idea of an isomorphism obtaining between language and reality.., an isomorphism which can be established by any correlation or mapping.
3. Biol. A similarity of appearance displayed by organisms having different genotypes.
1902Encycl. Brit. XXVI. 255/2 A few fundamental characters are better indications of the affinities of given groups of birds than a great number of agreements if these can be shown to be cases of isomorphism or heterophyletic, convergent analogy. 1920I. F. & W. D. Henderson Dict. Sci. Terms 158/1 Isomorphism, apparent similarity of individuals of different race or species.
4. Psychol. The correspondence assumed to exist between mental perception and physiological processes.
1930W. Köhler Gestalt Psychol. ii. 46 But I should have ever so much difficulty in trying to relate definite experiences to definite processes so long as I failed to assume one specific relationship between the two orders, viz., that of congruence or isomorphism in their systematic properties. This principle is sometimes formulated more explicitly in a number of ‘psycho-physical axioms’. 1937R. H. Thouless Gen. & Social Psychol. (ed. 2) xii. 241 One of the boldest of the Gestalt speculations has been that of the ‘isomorphism’ of brain processes and mental processes. 1951R. B. MacLeod in Rohrer & Sherif Social Psychol. at Crossroads 223 In the doctrine of isomorphism, however, it is asserted that the all-important parallel to perceptual organization is to be found not in the patterning of stimulus processes but rather in the immediately underlying organization of brain activities. 1970H. C. Shands Semiotic Approaches to Psychiatry xviii. 290 The evidence suggests strongly that at every level there is an isomorphism between physiological and psychological mechanisms [in cancer patients] when both are abstractly considered. |