On the Fourfold Root of the Principle of Sufficient Reason, and On the Will in Nature · Arthur Schopenhauer
THE UNDERSTANDING.
According to this illustration, we invariably direct both eyes equally towards the object, in order that the symmetrically corresponding places on both retinas may catch the rays projected from the same points. Now, when we move our eyes upwards and downwards, to the sides, and in all directions, the point in the object which first impinged upon the central point of each retina, strikes a different place every time, but in all cases one which, in each eye, corresponds to the place bearing the same name in the other eye. In examining (_perlustrare_) an object, we let our eyes glide backwards and forwards over it, in order to bring each point of it successively into contact with the centre of the retina, which sees most distinctly: we feel it all over with our eyes. It is therefore obvious that seeing singly with two eyes is in fact the same process as feeling a body with ten fingers, each of which receives a different impression, each moreover in a different direction: the totality of these impressions being nevertheless recognised by the Understanding as proceeding from _one_ object, whose shape and size it accordingly apprehends and constructs in Space. This is why it is possible for a blind man to become a sculptor, as was the case, for instance, with the famous Joseph Kleinhaus, who died in Tyrol, 1853, having been a sculptor from his fifth year.[80] For, no matter from what cause it may have derived its data, perception is invariably an operation of the Understanding.
But just as a single ball seems to me double, if I touch it with my fingers crossed--since my Understanding, at once reverting to the cause and constructing it according to the laws of Space, takes for granted that the fingers are in their normal position and of course cannot do otherwise than attribute two spherical surfaces, which come in contact with the outer sides of the first and middle fingers, to two different balls--just so also does an object seem double, if my eyes, instead of converging symmetrically and enclosing the optic angle at a single point of the object, each view it at a different inclination--in other words, if I squint. For the rays, which in this case emanate from one point of the object, no longer impinge upon those symmetrically corresponding points in both retinas with which my mind has grown familiar by long experience, but upon other, quite different ones which, in a symmetrical position of the eyes, could only be affected in this way by different bodies; I therefore now see _two_ objects, precisely because perception takes place by means of, and within, the Understanding.--The same thing happens without squinting when, for instance, I look fixedly at the furthest of two objects placed at unequal distances before me, and complete the optic angle at it; for then the rays emanating from the nearer object do not impinge upon symmetrically corresponding places in both retinas, wherefore my Understanding attributes them to two objects, _i.e._ I see the nearer object double (see fig. 2, page 70). If, on the contrary, I complete the optic angle at the nearer object, by looking steadily at it, the further object appears double. It is easy to test this by holding a pencil two feet from the eyes, and looking alternately at it and at some other more distant object behind it.
1^o. If seeing single were dependent upon an organic connection, the corresponding points in both retinas, on which this phenomenon is shown to depend, would correspond _organically_, whereas they do so in a merely _geometrical_ sense, as has already been said. For, organically speaking, the two inner and two outer corners of the eyes are those which correspond, and so it is with the other parts also; whereas for the purpose of single vision, it is the right side of the right retina which corresponds to the right side of the left retina, and so on, as the phenomena just described irrefutably show. It is also precisely on account of the intellectual character of the process, that only the most intelligent animals, such as the higher mammalia and birds of prey--more especially owls--have their eyes placed so as to enable them to direct both optic axes to the same point. 2^o. The hypothesis of a confluence or partial intersection of the optic nerves before entering the brain, originated by Newton,[81] is false, simply because it would then be impossible to see double by squinting. Vesalius and Cæsalpinus besides have already brought forward anatomical instances in which subjects saw single, although neither fusion nor even contact of the optic nerves had taken place. A final argument against the hypothesis of a mixed impression is supplied by the fact, that on closing our right eye firmly and looking at the sun with our left, the bright image which persists for a time is always in the left, never in the right, eye: and _vice versa_.
It is this which makes perspective drawing so difficult a problem, that it can only be solved by mathematics and has to be learnt; although all it has to do, is to represent the sensation of seeing as it presents itself to our Understanding as a datum for the third process: that is, visual sensation in its merely planimetrical extension, to the _two_ dimensions of which extension, together with the said data in them, the Understanding forthwith adds the _third_, in contemplating a drawing as well as in contemplating reality. Perspective drawing is, in fact, a sort of writing which can be read as easily as printed type, but which few are able to write; precisely because our intellect, in perceiving, only apprehends effects with a view to constructing their causes, immediately losing sight of the former as soon as it has discovered the latter. For instance, we instantly recognise a chair, whatever position it may be in; while drawing a chair in any position belongs to the art which abstracts from this third process of the Understanding, in order to present the data alone for the spectator himself to complete. In its narrowest acceptation, as we have already seen, this is the art of drawing in perspective; in a more comprehensive sense, it is the whole art of painting.
A painting presents us with outlines drawn according to the rules of perspective; lighter and darker places proportioned to the effect of light and shade; finally patches of colouring, which are determined as to quality and intensity by the teaching of experience. This the spectator reads and interprets by referring similar effects to their accustomed causes. The painter's art consists in consciously retaining the data of visual sensation in the artist's memory, as they are _before_ this third intellectual process; while we, who are not artists, cast them aside without retaining them in our memory, as soon as we have made use of them for the purpose described above. We shall become still better acquainted with this third intellectual process by now passing on to a fourth, which, from its intimate connection with the third, serves to elucidate it.
This _fourth_ operation of the Understanding consists in acquiring knowledge of the distance of objects from us: it is this precisely which constitutes that third dimension of which we have been speaking. Visual sensation, as we have said, gives us the _direction_ in which objects lie, but not their _distance_ from us: that is, not their _position_. It is for the _Understanding_ therefore to find out this distance; or, in other words, the distance must be inferred from purely _causal_ determinations. Now the most important of these is the _visual angle_, which objects subtend; yet even this is quite ambiguous and unable to decide anything by itself. It is like a word of double meaning: the sense, in which it is to be understood, can only be gathered from its connection with the rest. An object subtending the same visual angle may in fact be small and near, or large and far off; and it is only when we have previously ascertained its size, that the visual angle enables us to recognise its distance: and conversely, its size, when its distance is known to us. Linear perspective is based upon the fact that the visual angle diminishes as the distance increases, and its principles may here be easily deduced.
As our sight ranges equally in all directions, we see everything in reality as from the interior of a hollow sphere, of which our eye occupies the centre. Now in the first place, an infinite number of intersecting circles pass through the centre of this sphere in all directions, and the angles measured by the divisions of these circles are the possible angles of vision. In the second place, the sphere itself modifies its size according to the length of radius we give to it; therefore we may also imagine it as consisting of an infinity of concentric, transparent spheres. As all radii diverge, these concentric spheres augment in size in proportion to their distance from us, and the degrees of their sectional circles increase correspondingly: therefore the true size of the objects which occupy them likewise increases. Thus objects are larger or smaller according to the size of the spheres of which they occupy similar portions--say 10°--while their visual angle remains unchanged in both cases, leaving it therefore undecided, whether the 10° occupied by a given object belong to a sphere of 2 miles, or of 10 feet diameter.
Conversely, if the size of the object has been ascertained, the number of degrees occupied by it will diminish in proportion to the distance and the size of the sphere to which we refer it, and all its outlines will contract in similar proportion. From this ensues the fundamental law of all perspective; for, as objects and the intervals between them must necessarily diminish in constant proportion to their distance from us, all their outlines thereby contracting, the result will be, that with increasing distance, what is above us will descend, what is below us will ascend, and all that lies at our sides will come nearer together. This progressive convergence, this linear perspective, no doubt enables us to estimate distances, so far as we have before us an uninterrupted succession of visibly connected objects; but we are not able to do this by means of the visual angle alone, for here the help of another datum is required by the Understanding, to act, in a sense, as commentary to the visual angle, by indicating more precisely the share we are to attribute to distance in that angle. Now there are four principal data of this kind, which I am about to specify.
Thanks to these data, even where there is no linear perspective to guide us, if a man standing at a distance of 200 feet appears to me subtending a visual angle twenty-four times smaller than if he were only 2 feet off, I can nevertheless in most cases estimate his size correctly. All this proves once more that perception is not only a thing of the senses, but of the intellect also.--I will here add the following special and interesting fact in corroboration of what I have said about the basis of linear perspective as well as about the intellectual nature of all perception. When I have looked steadily at a coloured object with sharply defined outlines--say a red cross--long enough for the physiological image to form in my eye as a green cross, the further the surface on to which I project it, the larger it will appear to me: and _vice versa_. For the image itself occupies an unvarying portion of my retina, _i.e._ the portion originally affected by the red cross; therefore when referred outwards, or, in other words, recognised as the effect of an external object, it forms an unchanging visual angle, say of 2°.
Now if, in this case, where all commentary to the visual angle is wanting, I remove it to a distant surface, with which I necessarily identify it as belonging to its effect, the cross will occupy 2° of a distant and therefore larger sphere, and is consequently large. If, on the other hand, I project the image on to a nearer object, it will occupy 2° of a smaller sphere, and is therefore small. The resulting perception is in both cases completely objective, quite like that of an external object; and as it proceeds from an entirely subjective reason (from the image having been excited in quite a different way), it thus confirms the intellectual character of all objective perception.--This phenomenon (which I distinctly remember to have been the first to notice, in 1815) forms the theme of an essay by Séguin, published in the "_Comptes rendus_" of the 2nd August, 1858, where it is served up as a new discovery, all sorts of absurd and distorted explanations of it being given. _Messieurs les illustres confrères_ let pass no opportunity for heaping experiment upon experiment, the more complicated the better. _Expérience!_ is their watchword; yet how rarely do we meet with any sound, genuine reflection upon the phenomena observed! _Expérience! expérience!_ followed by twaddle.
To return to the subsidiary data which act as commentaries to a given visual angle, we find foremost among them the _mutationes oculi internæ_, by means of which the eye adapts its refractory apparatus to various distances by increasing and diminishing the refraction. In what these modifications consist, has not yet been clearly ascertained. They have been sought in the increased convexity, now of the _cornea_, now of the crystalline _lens_; but the latest theory seems to me the most probable one, according to which the lens is moved backwards for distant vision and forwards for near vision, lateral pressure, in the latter case, giving it increased protuberance; so that the process would exactly resemble the mechanism of an opera-glass. Kepler, however, had, in the main, already expressed this theory, which may be found explained in A. Hueck's pamphlet, "Die Bewegung der Krystallinse," 1841. If we are not clearly conscious of these inner modifications of the eye, we have at any rate a certain feeling of them, and of this we immediately avail ourselves to estimate distances. As however these modifications are not available for the purposes of clear sight beyond the range of from about 7 inches to 16 feet, the Understanding is only able to apply this datum within those limits.
Beyond them, however, the second datum becomes available: that is to say, the _optic angle_, formed by the two optic axes, which we had occasion to explain when speaking of single vision. It is obvious that this optic angle becomes smaller, the further the object is removed: and _vice versa_. This different direction of the eyes, with respect to each other, does not take place without producing a slight sensation, of which we are nevertheless only in so far conscious as the Understanding makes use of it, as a datum, in estimating distances intuitively. By this datum we are not only enabled to cognize the distance, but the precise position of the object viewed, by means of the parallax of the eyes, which consists in each eye seeing the object in a slightly different direction; so that if we close one eye, the object seems to move. Thus it is not easy to snuff a candle with one eye shut, because this datum is then wanting. But as the direction of the eyes becomes parallel as soon as the distance of the object reaches or exceeds 200 feet, and as the optic angle consequently then ceases to exist, this datum only holds good within the said distance. Beyond it, the Understanding has recourse to _atmospheric perspective_, which indicates a greater distance by means of the increasing dimness of all colours, of the appearance of physical blue in front of all dark objects (according to Göthe's perfectly correct and true theory of colours), and also of the growing indistinctness of all outlines. In Italy, where the atmosphere is very transparent, this datum loses its power and is apt to mislead: Tivoli, for instance, seems to be very near when seen from Frascati. On the other hand, all objects appear larger in a mist, which is an abnormal exaggeration of the datum; because our Understanding assumes them to be further from us.
Finally, there remains the estimation of distance by means of the size (known to us intuitively) of intervening objects, such as fields, woods, rivers, &c. &c. This mode of estimation is only applicable where there is uninterrupted succession: in other words, it can only be applied to terrestrial, not to celestial objects. Moreover, we have in general more practice in using it horizontally than vertically: a ball on the top of a tower 200 feet high appears much smaller to us than when lying on the ground 200 feet from us; because, in the latter case, we estimate the distance more accurately. When we see human beings in such a way, that what lies between them and ourselves is in a great measure hidden from our sight, they always appear strikingly small.
The fact that our Understanding assumes everything it perceives in a horizontal direction to be farther off, therefore larger, than what is seen in a vertical direction, must partly be attributed to this last mode of estimating distances, inasmuch as it only holds good when applied horizontally and to terrestrial objects; but partly also to our estimation of distances by atmospheric perspective, which is subject to similar conditions. This is why the moon seems so much larger on the horizon than at its zenith, although its visual angle accurately measured--that is, the image projected by it on to the eye--is not at all larger in one case than in the other; and this also accounts for the flattened appearance of the vault of the sky: that is to say, for its appearing to have greater horizontal than vertical extension. Both phenomena therefore are purely intellectual or cerebral, not optical. If it be objected, that even when at its zenith, the moon occasionally has a hazy appearance without seeming to be larger, we answer, that neither does it in that case appear red; for its haziness proceeds from a greater density of vapours, and is therefore of a different kind from that which proceeds from atmospheric perspective. To this may be added what I have already said: that we only apply this mode of estimating distances in a horizontal, not in a perpendicular, direction; besides, in this case, other correctives come into play. It is related of Saussure that, when on the Mont Blanc, he saw so enormous a moon rise, that, not recognising what it was, he fainted with terror.
The properties of the telescope and magnifying glass, on the other hand, depend upon a separate estimate according to the visual angle alone: _i.e._, that of size by distance, and of distance by size; because here the four other supplementary means of estimating distances are excluded. The telescope in reality magnifies objects, while it only seems to bring them nearer; because their size being known to us empirically, we here account for its apparent increase by a diminution of their distance from us. A house seen through a telescope, for instance, seems to be ten times nearer, not ten times larger, than seen with the naked eye. The magnifying glass, on the contrary, does not really magnify, but merely enables us to bring the object nearer to our eyes than would otherwise be possible; so that it only appears as large as it would at that distance even without the magnifying glass. In fact, we are prevented from seeing objects distinctly at less than from eight to ten inches' distance from our eyes, by the insufficient convexity of the ocular lens and cornea; but if we increase the refraction by substituting the convexity of the magnifying glass for that of the lens and cornea, we then obtain a clear image of objects even when they are as near as half an inch from our eyes. Objects thus seen in close proximity to us and in the size corresponding to that proximity, are transferred by our Understanding to the distance at which we naturally see distinctly, _i.e._ to about eight or ten inches from our eyes, and we then estimate their magnitude according to this distance and to the given visual angle.
I have entered thus fully into detail concerning all the different processes by which seeing is accomplished, in order to show clearly and irrefragably that the predominant factor in them is _the Understanding_, which, by conceiving each change as an _effect_ and referring that effect to its _cause_, produces the cerebral phenomenon of the objective world on the basis of the _à priori_ fundamental intuitions of Space and Time, for which it receives merely a few data from the senses. And moreover the Understanding effects this exclusively by means of its own peculiar form, the law of Causality; therefore quite directly and intuitively, without any assistance whatever from reflection--that is, from abstract knowledge by means of conceptions and of language, which are the materials of _secondary_ knowledge, _i.e._ of _thought_, therefore of _Reason_.
That this knowledge through the Understanding is independent of Reason's assistance, is shown even by the fact, that when, at any time, the Understanding attributes a given effect to a wrong cause, actually perceiving that cause, whereby _illusion_ arises, our Reason, however clearly it may recognise _in abstracto_ the true state of the matter, is nevertheless unable to assist the Understanding, and the illusion persists undisturbed in spite of that better knowledge. The above-mentioned phenomena of seeing and feeling double, which result from an abnormal position of the organs of touch and sight, are instances of such illusions; likewise the apparently increased size of the rising moon; the image which forms in the focus of a concave mirror and exactly resembles a solid body floating in space; the painted relievo which we take for real; the apparent motion of a shore or bridge on which we are standing, if a ship happens to pass along or beneath it; the seeming proximity of very lofty mountains, owing to the absence of atmospheric perspective, which is the result of the purity of the air round their summits. In these and in a multitude of similar cases, our Understanding takes for granted the existence of the usual cause with which it is conversant and forthwith perceives it, though our Reason has arrived at the truth by a different road; for, the knowledge of the Understanding being anterior to that of the Reason, the intellect remains inaccessible to the teaching of the Reason, and thus the _illusion_--that is, the deception of the Understanding--remains immovable; albeit _error_--that is, the deception of the Reason--is obviated.--That which is correctly known by the Understanding is _reality_: that which is correctly known by the Reason is _truth_, or in other terms, a judgment having a sufficient reason; _illusion_ (that which is wrongly perceived) we oppose to _reality_: _error_ (that which is wrongly thought) to _truth_.
The purely formal part of empirical perception--that is, Space, Time, and the law of Causality--is contained _à priori_ in the intellect; but this is not the case with the application of this formal part to empirical data, which has to be acquired by the Understanding through practice and experience. Therefore new-born infants, though they no doubt receive impressions of light and of colour, still do not apprehend or indeed, strictly speaking, see objects. The first weeks of their existence are rather passed in a kind of stupor, from which they awaken by degrees when their Understanding begins to apply its function to the data supplied by the senses, especially those of touch and of sight, whereby they gradually gain consciousness of the objective world. This newly-arising consciousness may be clearly recognised by the look of growing intelligence in their eyes and a degree of intention in their movements, especially in the smile with which they show for the first time recognition of those who take care of them.
Text from Project Gutenberg, public domain in the United States.