automorphism

== English == === Etymology === From auto- +‎ morphism. === Pronunciation === === Noun === automorphism (countable and uncountable, plural automorphisms) (algebra) An isomorphism of a mathematical object or system of objects onto itself. The ascription to others of one's own characteristics or of one's own perceived characteristics. Synonym: heautomorphism 1895 Hiram M. Stanley: Studies in the Evolutionary Psychology of Feeling. MacMillan Sensation for us is a complex of sensations plus perceptions and other cognitive and emotional elements which lie beyond early mind, but which by an inevitable automorphism we interpret into early forms. This automorphism with the child is complete, and is never perfectly effaced even in the most accomplished psychologist.. . .But when we come to interpret the psychoses of the lower animals in connection with sexuality we may still more easily slip into a doubtful automorphism. Thus to say with Darwin, "When we behold a male bird elaborately displaying ... before the female, ... it is impossible to doubt that she admires the beauty of her male partner" (Descent of Man), or more strongly still with Grant Allen, "Every crow must think its own mate beautiful" (Mind, v. 448), we too easily take for granted that these birds would feel like ourselves in corresponding circumstances. ==== Usage notes ==== (algebra): An automorphism is characterised by the structure it preserves, which is usually specified as an object type. Thus one may speak of a group automorphism or ring automorphism. The identity mapping is sometimes called the trivial automorphism; any other automorphism may then be called a nontrivial automorphism. ==== Synonyms ==== (isomorphism of a mathematical object or system of objects onto itself): self-map (ascription to others of one's own characteristics): projection ==== Hypernyms ==== (algebra): isomorphism, endomorphism ==== Hyponyms ==== (algebra): inner automorphism, outer automorphism, Möbius transformation ==== Derived terms ==== ==== Translations ==== === See also === anthropomorphism self-map === Further reading === Automorphism in the Encyclopædia Britannica (11th edition, 1911)