Part 6
The soul of man is pent up in the prison-house of his head; it looks at nature through its two windows, the eyes. It would also fain know how nature looks through other windows. A desire apparently never to be fulfilled. But our love for nature is inventive, and here, too, much has been accomplished.
Placing before me an angular mirror, consisting of two plane mirrors slightly inclined to each other, I see my face twice reflected. In the right-hand mirror I obtain a view of the right side, and in the left-hand mirror a view of the left side, of my face. Also I shall see the face of a person standing in front of me, more to the right with my right eye, more to the left with my left. But in order to obtain such widely different views of a face as those shown in the angular mirror, my two eyes would have to be set much further apart from each other than they actually are.
Squinting with my right eye at the image in the right-hand mirror, with my left eye at the image in the left-hand mirror, my vision will be the vision of a giant having an enormous head with his two eyes set far apart. This, also, is the impression which my own face makes upon me. I see it now, single and solid. Fixing my gaze, the relief from second to second is magnified, the eyebrows start forth prominently from above the eyes, the nose seems to grow a foot in length, my mustache shoots forth like a fountain from my lip, the teeth seem to retreat immeasurably. But by far the most horrible aspect of the phenomenon is the nose.
Interesting in this connexion is the telestereoscope of Helmholtz. In the telestereoscope we view a landscape by looking with our right eye (Fig. 24) through the mirror _a_ into the mirror _A_, and with our left eye through the mirror _b_ into the mirror _B_. The mirrors _A_ and _B_ stand far apart. Again we see with the widely separated eyes of a giant. Everything appears dwarfed and near us. The distant mountains look like moss-covered stones at our feet. Between, you see the reduced model of a city, a veritable Liliput. You are tempted almost to stroke with your hand the soft forest and city, did you not fear that you might prick your fingers on the sharp, needle-shaped steeples, or that they might crackle and break off.
Liliput is no fable. We need only Swift's eyes, the telestereoscope, to see it.
Picture to yourself the reverse case. Let us suppose ourselves so small that we could take long walks in a forest of moss, and that our eyes were correspondingly near each other. The moss-fibres would appear like trees. On them we should see strange, unshapely monsters creeping about. Branches of the oak-tree, at whose base our moss-forest lay, would seem to us dark, immovable, myriad-branched clouds, painted high on the vault of heaven; just as the inhabitants of Saturn, forsooth, might see their enormous ring. On the tree-trunks of our mossy woodland we should find colossal globes several feet in diameter, brilliantly transparent, swayed by the winds with slow, peculiar motions. We should approach inquisitively and should find that these globes, in which here and there animals were gaily sporting, were liquid globes, in fact that they were water. A short, incautious step, the slightest contact, and woe betide us, our arm is irresistibly drawn by an invisible power into the interior of the sphere and held there unrelentingly fast! A drop of dew has engulfed in its capillary maw a manikin, in revenge for the thousands of drops that its big human counterparts have quaffed at breakfast. Thou shouldst have known, thou pygmy natural scientist, that with thy present puny bulk thou shouldst not joke with capillarity!
My terror at the accident brings me back to my senses. I see I have turned idyllic. You must pardon me. A patch of greensward, a moss or heather forest with its tiny inhabitants have incomparably more charms for me than many a bit of literature with its apotheosis of human character. If I had the gift of writing novels I should certainly not make John and Mary my characters. Nor should I transfer my loving pair to the Nile, nor to the age of the old Egyptian Pharaohs, although perhaps I should choose that time in preference to the present. For I must candidly confess that I hate the rubbish of history, interesting though it may be as a mere phenomenon, because we cannot simply observe it but must also _feel_ it, because it comes to us mostly with supercilious arrogance, mostly unvanquished. The hero of my novel would be a cockchafer, venturing forth in his fifth year for the first time with his newly grown wings into the light, free air. Truly it could do no harm if man would thus throw off his inherited and acquired narrowness of mind by making himself acquainted with the world-view of allied creatures. He could not help gaining incomparably more in this way than the inhabitant of a small town would in circumnavigating the globe and getting acquainted with the views of strange peoples.
* * * * *
I have now conducted you, by many paths and by-ways, rapidly over hedge and ditch, to show you what wide vistas we may reach in every field by the rigorous pursuit of a single scientific fact. A close examination of the two eyes of man has conducted us not only into the dim recesses of humanity's childhood, but has also carried us far beyond the bourne of human life.
It has surely often struck you as strange that the sciences are divided into two great groups; that the so-called humanistic sciences, belonging to the so-called "higher education," are placed in almost a hostile attitude to the natural sciences.
I must confess I do not overmuch believe in this partition of the sciences. I believe that this view will appear as childlike and ingenuous to a matured age as the want of perspective in the old paintings of Egypt does to us. Can it really be that "higher culture" is to be gotten only from a few old pots and palimpsests, which are at best mere scraps of nature, or that more is to be learned from them alone than from all the rest of nature? I believe that both these sciences are simply parts of the same science, which have begun at different ends. If these two ends still act towards each other as the Montagues and Capulets, if their retainers still indulge in lively tilts, I believe that after all they are not in earnest. On the one side there is surely a Romeo, and on the other a Juliet, who, some day, it is hoped, will unite the two houses with a less tragic sequel than that of the play.
Philology began with the unqualified reverence and apotheosis of the Greeks. Now it has begun to draw other languages, other peoples and their histories, into its sphere; it has, through the mediation of comparative linguistics, already struck up, though as yet somewhat cautiously, a friendship with physiology.
Physical science began in the witch's kitchen. It now embraces the organic and inorganic worlds, and with the physiology of articulation and the theory of the senses, has even pushed its researches, at times impertinently, into the province of mental phenomena.
In short, we come to the understanding of much within us solely by directing our glance without, and _vice versa_. Every object belongs to both sciences. You, ladies, are very interesting and difficult problems for the psychologist, but you are also extremely pretty phenomena of nature. Church and State are objects of the historian's research, but not less phenomena of nature, and in part, indeed, very curious phenomena. If the historical sciences have inaugurated wide extensions of view by presenting to us the thoughts of new and strange peoples, the physical sciences in a certain sense do this in a still greater degree. In making man disappear in the All, in annihilating him, so to speak, they force him to take an unprejudiced position without himself, and to form his judgments by a different standard from that of the petty human.
But if you should ask me now why man has two eyes, I should answer:
That he may look at nature justly and accurately; that he may come to understand that he himself, with all his views, correct and incorrect, with all his _haute politique_, is simply an evanescent shred of nature; that, to speak with Mephistopheles, he is a part of the part, and that it is absolutely unjustified,
"For man, the microcosmic fool, to see Himself a whole so frequently."
FOOTNOTES:
[Footnote 17: This effect is particularly noticeable in the size of workmen on high chimneys and church-steeples--"steeple Jacks." When the cables were slung from the towers of the Brooklyn bridge (277 feet high), the men sent out in baskets to paint them, appeared, against the broad background of heaven and water, like flies.--_Trans._]
[Footnote 18: See Joh. Müller, _Vergleichende Physiologie des Gesichtssinnes_, Leipsic, 1826.]
ON SYMMETRY.[19]
An ancient philosopher once remarked that people who cudgelled their brains about the nature of the moon reminded him of men who discussed the laws and institutions of a distant city of which they had heard no more than the name. The true philosopher, he said, should turn his glance within, should study himself and his notions of right and wrong; only thence could he derive real profit.
This ancient formula for happiness might be restated in the familiar words of the Psalm:
"Dwell in the land, and verily thou shalt be fed."
To-day, if he could rise from the dead and walk about among us, this philosopher would marvel much at the different turn which matters have taken.
The motions of the moon and the other heavenly bodies are accurately known. Our knowledge of the motions of our own body is by far not so complete. The mountains and natural divisions of the moon have been accurately outlined on maps, but physiologists are just beginning to find their way in the geography of the brain. The chemical constitution of many fixed stars has already been investigated. The chemical processes of the animal body are questions of much greater difficulty and complexity. We have our _Mécanique céleste_. But a _Mécanique sociale_ or a _Mécanique morale_ of equal trustworthiness remains to be written.
Our philosopher would indeed admit that we have made great progress. But we have not followed his advice. The patient has recovered, but he took for his recovery exactly the opposite of what the doctor prescribed.
Humanity is now returned, much wiser, from its journey in celestial space, against which it was so solemnly warned. Men, after having become acquainted with the great and simple facts of the world without, are now beginning to examine critically the world within. It sounds absurd, but it is true, that only after we have thought about the moon are we able to take up ourselves. It was necessary that we should acquire simple and clear ideas in a less complicated domain, before we entered the more intricate one of psychology, and with these ideas astronomy principally furnished us.
To attempt any description of that stupendous movement, which, originally springing out of the physical sciences, went beyond the domain of physics and is now occupied with the problems of psychology, would be presumptuous in this place. I shall only attempt here, to illustrate to you by a few simple examples the methods by which the province of psychology can be reached from the facts of the physical world--especially the adjacent province of sense-perception. And I wish it to be remembered that my brief attempt is not to be taken as a measure of the present state of such scientific questions.
* * * * *
It is a well-known fact that some objects please us, while others do not. Generally speaking, anything that is constructed according to fixed and logically followed rules, is a product of tolerable beauty. We see thus nature herself, who always acts according to fixed rules, constantly producing such pretty things. Every day the physicist is confronted in his workshop with the most beautiful vibration-figures, tone-figures, phenomena of polarisation, and forms of diffraction.
A rule always presupposes a repetition. Repetitions, therefore, will probably be found to play some important part in the production of agreeable effects. Of course, the nature of agreeable effects is not exhausted by this. Furthermore, the repetition of a physical event becomes the source of agreeable effects only when it is connected with a repetition of sensations.
An excellent example that repetition of sensations is a source of agreeable effects is furnished by the copy-book of every schoolboy, which is usually a treasure-house of such things, and only in need of an Abbé Domenech to become celebrated. Any figure, no matter how crude or poor, if several times repeated, with the repetitions placed in line, will produce a tolerable frieze.
Also the pleasant effect of symmetry is due to the repetition of sensations. Let us abandon ourselves a moment to this thought, yet not imagine when we have developed it, that we have fully exhausted the nature of the agreeable, much less of the beautiful.
First, let us get a clear conception of what symmetry is. And in preference to a definition let us take a living picture. You know that the reflexion of an object in a mirror has a great likeness to the object itself. All its proportions and outlines are the same. Yet there is a difference between the object and its reflexion in the mirror, which you will readily observe.
Hold your right hand before a mirror, and you will see in the mirror a left hand. Your right glove will produce its mate in the glass. For you could never use the reflexion of your right glove, if it were present to you as a real thing, for covering your right hand, but only for covering your left. Similarly, your right ear will give as its reflexion a left ear; and you will at once perceive that the left half of your body could very easily be substituted for the reflexion of your right half. Now just as in the place of a missing right ear a left ear cannot be put, unless the lobule of the ear be turned upwards, or the opening into the concha backwards, so, despite all similarity of form, the reflexion of an object can never take the place of the object itself.[20]
The reason of this difference between the object and its reflexion is simple. The reflexion appears as far behind the mirror as the object is in front of it. The parts of the object, accordingly, which are nearest the mirror will also be nearest the mirror in the reflexion. Consequently, the succession of the parts in the reflexion will be reversed, as may best be seen in the reflexion of the face of a watch or of a manuscript.
It will also be readily seen, that if a point of the object be joined with its reflexion in the image, the line of junction will cut the mirror at right angles and be bisected by it. This holds true of all corresponding points of object and image.
If, now, we can divide an object by a plane into two halves so that each half, as seen in the reflecting plane of division, is a reproduction of the other half, such an object is termed symmetrical, and the plane of division is called the plane of symmetry.
If the plane of symmetry is vertical, we can say that the body is vertically symmetrical. An example of vertical symmetry is a Gothic cathedral.
If the plane of symmetry is horizontal, we can say that the object is horizontally symmetrical. A landscape on the shores of a lake with its reflexion in the water, is a system of horizontal symmetry.
Exactly here is a noticeable difference. The vertical symmetry of a Gothic cathedral strikes us at once, whereas we can travel up and down the whole length of the Rhine or the Hudson without becoming aware of the symmetry between objects and their reflexions in the water. Vertical symmetry pleases us, whilst horizontal symmetry is indifferent, and is noticed only by the experienced eye.
Whence arises this difference? I say from the fact that vertical symmetry produces a repetition of the same sensation, while horizontal symmetry does not. I shall now show that this is so.
Let us look at the following letters:
d b q p
It is a fact known to all mothers and teachers, that children in their first attempts to read and write, constantly confound d and b, and q and p, but never d and q, or b and p. Now d and b and q and p are the two halves of a _vertically_ symmetrical figure, while d and q, and b and p are two halves of a _horizontally_ symmetrical figure. The first two are confounded; but confusion is only possible of things that excite in us the same or similar sensations.
Figures of two flower-girls are frequently seen on the decorations of gardens and of drawing-rooms, one of whom carries a flower-basket in her right hand and the other a flower-basket in her left. All know how apt we are, unless we are very careful, to confound these figures with one another.
While turning a thing round from right to left is scarcely noticed, the eye is not at all indifferent to the turning of a thing upside down. A human face which has been turned upside down is scarcely recognisable as a face, and makes an impression which is altogether strange. The reason of this is not to be sought in the unwontedness of the sight, for it is just as difficult to recognise an arabesque that has been inverted, where there can be no question of a habit. This curious fact is the foundation of the familiar jokes played with the portraits of unpopular personages, which are so drawn that in the upright position of the page an exact picture of the person is presented, but on being inverted some popular animal is shown.
It is a fact, then, that the two halves of a vertically symmetrical figure are easily confounded and that they therefore probably produce very nearly the same sensations. The question, accordingly, arises, _why_ do the two halves of a vertically symmetrical figure produce the same or similar sensations? The answer is: Because our apparatus of vision, which consists of our eyes and of the accompanying muscular apparatus is itself vertically symmetrical.[21]
Whatever external resemblances one eye may have with another they are still not alike. The right eye of a man cannot take the place of a left eye any more than a left ear or left hand can take the place of a right one. By artificial means, we can change the part which each of our eyes plays. (Wheatstone's pseudoscope.) But we then find ourselves in an entirely new and strange world. What is convex appears concave; what is concave, convex. What is distant appears near, and what is near appears far.
The left eye is the reflexion of the right. And the light-feeling retina of the left eye is a reflexion of the light-feeling retina of the right, in all its functions.
The lense of the eye, like a magic lantern, casts images of objects on the retina. And you may picture to yourself the light-feeling retina of the eye, with its countless nerves, as a hand with innumerable fingers, adapted to feeling light. The ends of the visual nerves, like our fingers, are endowed with varying degrees of sensitiveness. The two retinæ act like a right and a left hand; the sensation of touch and the sensation of light in the two instances are similar.
Examine the right-hand portion of this letter T: namely, T. Instead of the two retinæ on which this image falls, imagine feeling the object, my two hands. The T, grasped with the right hand, gives a different sensation from that which it gives when grasped with the left. But if we turn our character about from right to left, thus: T, it will give the same sensation in the left hand that it gave before in the right. The sensation is repeated.
If we take a whole T, the right half will produce in the right hand the same sensation that the left half produces in the left, and _vice versa_.
The symmetrical figure gives the same sensation twice.
If we turn the T over thus: T, or invert the half T thus: L, so long as we do not change the position of our hands we can make no use of the foregoing reasoning.
The retinæ, in fact, are exactly like our two hands. They, too, have their thumbs and index fingers, though they are thousands in number; and we may say the thumbs are on the side of the eye near the nose, and the remaining fingers on the side away from the nose.
With this I hope to have made perfectly clear that the pleasing effect of symmetry is chiefly due to the repetition of sensations, and that the effect in question takes place in symmetrical figures, only where there is a repetition of sensation. The pleasing effect of regular figures, the preference which straight lines, especially vertical and horizontal straight lines, enjoy, is founded on a similar reason. A straight line, both in a horizontal and in a vertical position, can cast on the two retinæ the same image, which falls moreover on symmetrically corresponding spots. This also, it would appear, is the reason of our psychological preference of straight to curved lines, and not their property of being the shortest distance between two points. The straight line is felt, to put the matter briefly, as symmetrical to itself, which is the case also with the plane. Curved lines are felt as deviations from straight lines, that is, as deviations from symmetry.[22] The presence of a sense for symmetry in people possessing only one eye from birth, is indeed a riddle. Of course, the sense of symmetry, although primarily acquired by means of the eyes, cannot be wholly limited to the visual organs. It must also be deeply rooted in other parts of the organism by ages of practice and can thus not be eliminated forthwith by the loss of one eye. Also, when an eye is lost, the symmetrical muscular apparatus is left, as is also the symmetrical apparatus of innervation.
It appears, however, unquestionable that the phenomena mentioned have, in the main, their origin in the peculiar structure of our eyes. It will therefore be seen at once that our notions of what is beautiful and ugly would undergo a change if our eyes were different. Also, if this view is correct, the theory of the so-called eternally beautiful is somewhat mistaken. It can scarcely be doubted that our culture, or form of civilisation, which stamps upon the human body its unmistakable traces, should not also modify our conceptions of the beautiful. Was not formerly the development of all musical beauty restricted to the narrow limits of a five-toned scale?
The fact that a repetition of sensations is productive of pleasant effects is not restricted to the realm of the visible. To-day, both the musician and the physicist know that the harmonic or the melodic addition of one tone to another affects us agreeably only when the added tone reproduces a part of the sensation which the first one excited. When I add an octave to a fundamental tone, I hear in the octave a part of what was heard in the fundamental tone. (Helmholtz.) But it is not my purpose to develop this idea fully here.[23] We shall only ask to-day, whether there is anything similar to the symmetry of figures in the province of sounds.
Look at the reflexion of your piano in the mirror.
You will at once remark that you have never seen such a piano in the actual world, for it has its high keys to the left and its low ones to the right. Such pianos are not manufactured.
If you could sit down at such a piano and play in your usual manner, plainly every step which you imagined you were performing in the upward scale would be executed as a corresponding step in the downward scale. The effect would be not a little surprising.