Asymmetry

“ But in all probability, the dynamical polarity, or asymmetry of the cell is a very complicated phenomenon: for the obvious reason that, in any system, one asymmetry will tend to beget another. A chemical asymmetry will induce an inequality of surface-tension, which will lead directly to a modification of form; the chemical asymmetry may in turn be due to a process of electrolysis in a polarised electrical field; and again the chemical heterogeneity may be intensified into a chemical “polarity,” by the tendency of certain substances to seek a locus of greater or less surface-energy. ”

“ It is further established, that the degree of asymmetry of the convolution of the two sides in the human brain is subject to much individual variation; and that, in those individuals of the Bushman race who have been examined, the gyri and sulci of the two hemispheres are considerably less complicated and more symmetrical than in the European brain, while, in some individuals of the chimpanzee, their complexity and asymmetry become notable. ”

“ Asymmetry is characteristic of the distribution of organic data, and in certain instances, as for example writing 18 seconds, males, the choice of a 10-second class interval results in extreme asymmetry, and one is reminded of the tables which Fechner gave as examples of his logarithmic method in statistics. ”

“ Each of the three properties which we combined in defining series—namely, asymmetry, transitiveness, and connexity—has its own importance. We will begin by saying something on each of these three.
Asymmetry, i.e. the property of being incompatible with the converse, is a characteristic of the very greatest interest and importance. In order to develop its functions, we will consider various examples. The relation husband is asymmetrical, and so is the relation wife; i.e. if is husband of , cannot be husband of , and similarly in the case of wife. ”

“ The experimental treatment of geometrical symmetry, the analysis of the completely symmetrical products of civilized art, and the analysis of all forms of asymmetry except asymmetry in pictures will be omitted. If, however, the fact of an original æsthetic feeling for symmetry is established by the study of primitive art, and the theory of the balance of motor impulses through the substitution of factors is established by the experimental treatment of isolated elements, and further confirmed by the analysis of pictures, the general argument may be taken as sufficiently supported. ”

“ Just as the trees of his native land are stunted, so too his features become monstrous, irregular, and one-sided: the frontal bones are forced, as though by spasm, down on the maxillaries, producing the most singular combinations and contortions of the features. A not uncommon form of asymmetry, in more favored lands, is the presence of a dimple on one cheek, while the other has no such indentation, or but a very faint one. ”

“ In such cases the face has, as it were, a summer and a winter side, just like the apple, which is round and ruddy on its summer side, but on the shade-side flattened and wan.
We are too much inclined to regard these phenomena of asymmetry as merely accidental, whereas the fact is that they are the result of a universal law. Take, for instance, the case where the mustache is longer or thicker on one side of the lip than on the other; the law is everywhere the same: nothing is like any thing else, as Goethe has said. ”

“ But asymmetry is a much more difficult property to secure by construction. The method by which we derived husband from spouse is, as we have seen, not available in the most important cases, such as greater, before, to the right of, where domain and converse domain overlap. In all these cases, we can of course obtain a symmetrical relation by adding together the given relation and its converse, but we cannot pass back from this symmetrical relation to the original asymmetrical relation except by the help of some asymmetrical [Pg 43] relation. ”

“ At first the rope is pulled out of the ductile mass without difficulty; but as the work goes on it gets harder to do, until all the man’s force is used to stretch the rope. Here we have the phenomenon of increasing strength, following mechanically on a rearrangement of molecules, as the original isotropic condition is transmuted more and more into molecular asymmetry or anisotropy ”

“ Stand before a mirror; hold your arms in precisely the same position at each side, your head upright your body straight; divide your hair exactly in the middle, and get it as nearly as you can into exactly the same shape over each ear, and you will see the effect of accurate symmetry; you will see, no less, how all grace and power in the human form result from the interference of motion and life with symmetry, and from the reconciliation of its balance with its changefulness. Your position, as seen in the mirror, is the highest type of symmetry as understood by modern architects. ”

“ In things in which perfect symmetry is, from their nature, impossible or improper, a balance must be at least in some measure expressed before they can be beheld with pleasure.... Symmetry is the opposition of equal quantities to each other. Proportion the connection of unequal quantities with each other. The property of a tree in sending out equal boughs on opposite sides is symmetrical. Its sending out shorter and smaller towards the top, proportional. In the human face its balance of opposite sides is symmetry, its division upwards, proportion. ”

“ The psychic accompaniment is a feeling of balance; the mind is æsthetically satisfied, at rest. And through whatever bewildering variety of elements in the figure, it is this simple bilateral [551] equivalence that brings us to æsthetic rest. If, however, the symmetry is not good, if we find a gap in design where we expected a filling, the accustomed equilibrium of the organism does not result; psychically there is lack of balance, and the object is æsthetically painful. We seem to have, then, in symmetry, three aspects. ”

“ Having once established a theory of the æsthetic significance of real symmetry, we should next have to examine asymmetrical, beautiful objects with reference to the relation of their parts to a middle line; to isolate the elements which suggest motor impulses; to find out how far it is possible to establish a system of substitution of these psychological factors and how far such substitution takes place in works of art—i.e., to what extent a substitutional symmetry or balance is found in pleasing [469] arrangements. ”

“ It will of course be understood that by the term Symmetry I here intend, not that more indefinite attribute of form which belongs to the domain of the fine arts, as when we speak of the ‘symmetry’ of an edifice 68 or of a sculptured figure, but a certain definite relation or property, no less rigorous and precise than other relations of number and position, which is thus one of the sure guides of the scientific faculty, and one of the bases of our exact science. ”

“ Exterior human symmetry is surely a curious physiological fact where there is no symmetry interiorly. For the centres of life and movement within the body are placed with Oriental inequality. Man is Greek without and Japanese within. But the absolute symmetry of the skeleton and of the beauty and life that cover it is accurately a principle. It controls, but not tyrannously, all the life of human action. Attitude and motion disturb perpetually, with infinite incidents—inequalities of work, war, and pastime, inequalities of sleep—the symmetry of man. ”

“ The human body is symmetrical. When we stand face to face with a human being, his body appears to be composed of two halves united in the centre, and these two parts, without being identical, correspond in such a manner that the right side, if folded over on the left, would exactly cover it. This repetition in reverse is what is called symmetry, though the original meaning of the word signified what we now understand by proportion. Diagram 132 is a capital illustration of symmetrical braiding, and is a copy of a military design for a cuff. ”

“ For symmetry’s sake, however, it will be proper briefly to point out how the multiplication of effects, like the instability of the homogeneous, is a corollary from the persistence of force.
Things which we call different are things which react in different ways; and we can know them as different only by the differences in their reactions. When we distinguish bodies as hard and soft, rough and smooth, we simply mean that certain like muscular forces expended on them are followed by unlike sets of sensations—unlike re-active forces. ”

“ There is, likewise, a kind of symmetry, or proportion, which may properly be said to belong to deformity. A figure lean or corpulent, tall or short, though deviating from beauty, may still have a certain union of the various parts, which may contribute to make them on the whole not unpleasing.
When the Artist has by diligent attention acquired a clear and distinct idea of beauty and symmetry; when he has reduced the variety of nature to the abstract idea ”

“ Experience, to be sure, can teach us to regard unsymmetrical objects as wholes, because their elements move and change together in nature; but this is a principle of individuation, a posteriori, founded on the association of recognized elements. These elements, to be recognized and seen to go together and form one thing, must first be somehow discriminated; and the symmetry, either of their parts, or of their position as wholes, may enable us to fix their boundaries and to observe their number. ”

“ With this characteristic of uniformity we must closely connect that of symmetry. Form is unable long to rest in that barest abstraction of its determination, namely, undifferentiated equality. A diverse relation is sure to assert itself, breaking into the empty form of identity. In this way we obtain symmetry, which consists in no mere identical repetition of one form, but in a combination with some such form analogous to it, identical, that is to say, in its [Pg 186] self-determination, and yet manifesting a distinct contrast with it. ”

“ And it is reasonable to suppose that, for the preservation of this beauty, any part of the body's substance, which, if placed in one spot, would produce a deformity, shall be distributed through the whole of it, so that neither any part, nor the symmetry of the whole, may be lost, but only the general stature of the body somewhat increased by the distribution in all the parts of that which, in one place, would have been unsightly. ”

“ An animal destined to be beautiful must possess symmetry. Of symmetries we understand those which are small, but are ignorant of the greatest. And, indeed, no symmetry is of more importance with respect to health and disease, virtue and vice, than that of the soul toward the body. When a weaker and inferior form is the vehicle of a strong and in every way mighty soul, or the contrary ”

“ Thus to be defined from without is, in principle, to be distracted within. And, the smaller the element, the more wide is this dissipation of its essence—a dissipation too thorough to be deep, or to support the title of an intestine division. [6] But, on the contrary, the expansion of the element should increase harmony, for it should bring these external relations within the inner substance. By growth the element becomes, more and more, a consistent individual, containing in itself its own nature; and it forms, more and more, a whole inclusive of discrepancies and reducing them to system. ”

“ In every symmetrical system every deformation that tends to destroy the symmetry is complemented by an equal and opposite deformation that tends to restore it. In each deformation positive and negative work is done. One condition, therefore, though not an absolutely sufficient one, that a maximum or minimum of work corresponds to the form of equi­lib­rium, is thus supplied by symmetry. Regularity is successive symmetry. ”

“ That bilateral symmetry of the skeleton which is so invariable a characteristic of the vertebrata, that ordinary observers, who have eyes for only the rare and the uncommon, fail to remark it, but which a Newton could regard as so wonderful, and so thoroughly in harmony with the uniformity of the planetary system, has scarce any place in the asymmetrical head of the flounder. ”

“ Again since the one face, constant in symmetry, appears sometimes fair and sometimes not, can we doubt that beauty is something more than symmetry, that symmetry itself owes its beauty to a remoter principle? ”

“ The impossibility of two bodies existing together in the same space cannot be deduced from our idea of solidity, or of figure. As soon as we perceive the motions of objects that surround us, and learn that we possess a power to move our own bodies, we experience, that those objects, which excite in us the idea of solidity and of figure, oppose this voluntary movement of our own organs; as whilst I endeavour to compress between my hands an ivory ball into a spheroid. And we are hence taught by experience, that our own body and those, which we touch, cannot exist in the same part of space. ”

“ But it is significant to note that recent researches show that where greater specific gravity of brain occurs in the insane, it appears to be limited to the gray matter. [156] Professor Goodsir maintained that symmetry of brain has more to do with the higher faculties than bulk of form. It is, at any rate, apparent that two brains of equal weight may differ widely in quality. ”

“ That abundance of bodies are hard, we learn by experience; and because the hardness of the whole arises from the hardness of the parts, we therefore justly infer the hardness of the undivided particles not only of the bodies we feel but of all others. That all bodies are impenetrable, we gather not from reason, but from sensation. The bodies which we handle we find impenetrable, and thence conclude impenetrability to be an universal property of all bodies whatsoever. ”