# Complex

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Related to Complex: inferiority complex, complex sentence, B complex, superiority complex, Complex numbers

## complex

1. Maths of or involving one or more complex numbers
2. Psychoanal a group of emotional ideas or impulses that have been banished from the conscious mind but that continue to influence a person's behaviour
3. Informal an obsession or excessive fear
4. a chemical compound in which molecules, groups, or ions are attached to a central metal atom, esp a transition metal atom, by coordinate bonds
5. any chemical compound in which one molecule is linked to another by a coordinate bond

## Complex

(in mathematics), one of the fundamental concepts of combinatorial topology. It is essential to the aims of this science to regard geometric figures as being subdivided into more elementary figures. It is easiest to construct geometric figures out of simplexes, that is, in the case of three-dimensional space, out of points, lines, triangles, and tetrahedra. Thus, we are most often dealing with simplicial complexes.

A simplicial complex is a finite set of simplexes situated in a certain Euclidean (or Hilbert) space and possessing the following property: the intersection of two simplexes of this set is either empty or is a face of each of them. If a complex contains a γ-dimensional simplex and no simplexes of higher dimension, then the complex is termed γ-dimensional. This very simple concept has undergone many generalizations, proceeding in different directions. Together with the just-defined finite complexes it is possible to define countable complexes. It is further possible to proceed from simplicial complexes to analogously defined cell complexes, whose elements are not necessarily simplexes but any convex polyhedrons or even any figures homeomorphic to them; in the latter case, we speak of “curvilinear” complexes. Ordinarily, only those complexes are considered that satisfy the following closure condition: each face of a simplex belonging to a given complex must also belong to that complex. A set that can be represented as a union of simplexes forming an n-dimensional complex is termed an n-dimensional polyhedron.

### REFERENCES

Aleksandrov, P. S. Kombinatornaia topologiia. Moscow-Leningrad, 1947.
Pontriagin, L. S. Osnovy kombinatornoi topologii. Moscow-Leningrad, 1947.

## Complex

in psychology, in the most general sense, a particular combination of psychological processes into some sort of whole; in a narrower sense, the word is taken to mean a group of heterogeneous psychic elements connected by a single affect.

Complex, in the latter sense, has become one of the basic concepts of various schools of depth psychology. According to psychoanalysis (S. Freud, Austria), complexes form around tendencies that are displaced to the subconscious (for example, the Oedipus complex arises as a result of the displacement in early childhood of hostile impulses toward the father). Complexes produce deviations in human behavior that are manifested in the form of improper actions, neuroses, and obsessions. In individual psychology (A. Adler, Austria), an exceptional role is attributed to the inferiority complex—an individual’s feeling of his own organic or mental inadequacy. Overcoming this complex by means of compensation is regarded by Adler to be the principal factor in man’s mental development, character formation, and behavior.

D. N. LIALIKOV

## complex

[′käm‚pleks]
(geology)
An assemblage of rocks that has been folded together, intricately mixed, involved, or otherwise complicated.
(mathematics)
A space which is represented as a union of simplices which intersect only on their faces.
(medicine)
(mineralogy)
Composed of many ingredients.
(psychology)
A group of associated ideas with strong emotional tones, which have been transferred from the conscious mind into the unconscious and which influence the personality.
References in classic literature ?
Its motion was so swift, complex, and perfect that at first I did not see it as a machine, in spite of its metallic glitter.
Plots are either Simple or Complex, for the actions in real life, of which the plots are an imitation, obviously show a similar distinction.
It may, perhaps, come to this in time," observed Monte Cristo; "you know that human inventions march from the complex to the simple, and simplicity is always perfection.
In some of the larger towns there are artels of a much more complex kind-- permanent associations, possessing large capital, and pecuniarily responsible for the acts of the individual members.
The matter is of a nature so complex and crooked that probably a hundred years would be insufficient to unravel it; and, though it has now to a certain extent been cleared up, the merchant still holds the key to the situation.
Such a view would have been wrong there and then, and would, of course, be still more wrong now and in England; for as man moves northward the material necessities of life become of more vital importance, and our society is infinitely more complex, and displays far greater extremes of luxury and pauperism than any society of the antique world.
No wonder, therefore, that her faculties were bewildered by the complex movements of the cotillion: and, in short, as the good lady daily contemplated the improvements of the female youth around her, she became each hour more convinced of her own inability to control, or in any manner to superintend, the education of her orphan niece.
Indeed, I suspect that, leaving aside the protestations and tributes of writers who, one is safe in saying, care for little else in the world than the rhythm of their lines and the cadence of their phrase, the love of the sea, to which some men and nations confess so readily, is a complex sentiment wherein pride enters for much, necessity for not a little, and the love of ships - the untiring servants of our hopes and our self-esteem - for the best and most genuine part.
Jacob, you understand, was not an intense idiot, but within a certain limited range knew how to choose the good and reject the evil: he took one lozenge, by way of test, and sucked it as if he had been a philosopher; then, in as great an ecstacy at its new and complex savour as Caliban at the taste of Trinculo's wine, chuckled and stroked this suddenly beneficent brother, and held out his hand for more; for, except in fits of anger, Jacob was not ferocious or needlessly predatory.
He will perhaps turn round by and by, and in the meantime we can look at that stately old lady, his mother, a beautiful aged brunette, whose rich-toned complexion is well set off by the complex wrappings of pure white cambric and lace about her head and neck.
So strange and complex in its arrangements is this remarkable system, that I have in several cases met with individuals who, after residing for years among the islands in the Pacific, and acquiring a considerable knowledge of the language, have nevertheless been altogether unable to give any satisfactory account of its operations.
In this latter, where the pieces have different and bizarre motions, with various and variable values, what is only complex is mistaken (a not unusual error) for what is profound.
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