From Schopenhauer's On the Fourfold Root of the Principle of Sufficient Reason, beginning on page 68:
"Now, if seeing consisted in mere sensation, we should perceive the impression of the object turned upside down, because we receive it thus; but in that case we should perceive it as something within our eye, for we should stop short at the sensation. In reality, however, the Understanding steps in at once with its causal law, and as it has received from sensation the datum of the direction in which the ray impinged upon the retina, it pursues that direction retrogressively up to the cause on both lines; so that this time the crossing takes place in the opposite direction, and the cause presents itself upright as an external object in Space, i.e., in the position in which it originally sent forth its rays, not that in which they reached the retina (see fig. 1). The purely intellectual nature of this process, to the exclusion of all other, more especially of physiological, explanations, may also be confirmed by the fact, that if we put our heads between our legs, or lie down on a hill head downwards, we nevertheless see objects in their right position, and not upside down; although the portion of the retina which is usually met by the lower part of the object is then met by the upper: in fact, everything is topsy turvy excepting the Understanding.
The second thing, which the Understanding does in converting sensation into perception, is to make a single perception out of a double sensation; for each eye in fact receives its own separate impression from the object we are looking at, each even in a slightly different direction: nevertheless that object presents itself as a single one. This can only take place in the Understanding, and the process by which it is brought about is the following: Our eyes are never quite parallel, except when we look at a distant object, i.e. one which is more than 200 feet from us. At other times they are both directed towards the object we are viewing, whereby they converge, so as to make the lines proceeding from each eye to the exact point of the object on which it is fixed, form an angle, called the optic angle ; the lines themselves are called optic axes. Now, when the object lies straight before us, these lines exactly impinge upon the centre of each retina, therefore in two points which correspond exactly to each other in each eye. The Understanding, whose only business it is to look for the cause of all things, at once recognises the impression as coming from a single outside point, although here the sensation is double, and attributes it to one cause, which therefore presents itself as a single object. For all that is perceived by us, is perceived as a cause that is to say, as the cause of an effect we have experienced, consequently in the Understanding. As, nevertheless, we take in not only a single point, but a considerable surface of the object with both eyes, and yet perceive it as a single object, it will be necessary to pursue this explanation still further. All those parts of the object which lie to one side of the vertex of the optic angle no longer send their rays straight into the centre, but to the side, of the retina in each eye ; in both sides, however, to the same, let us say the left, side. The points therefore upon which these rays impinge, correspond symmetrically to each other, as well as the centres in other words, they are homonymous points. The Understanding soon learns to know them, and accordingly extends the above-mentioned rule of its causal perception to them also ; consequently it not only refers those rays which impinge upon the centre of each retina, but those also which impinge upon all the other symmetrically corresponding places in both retinas, to a single radiant point in the object viewed : that is, it sees all these points likewise as single, a [page 71] object also. Now, it should be well observed, that in this process it is not the outer side of one retina which corresponds to the outer side of the other, and the inner to the inner of each, but the right side of one retina which corresponds to the right side of the other, and so forth ; so that this symmetrical correspondence must not be taken in a physiological, but in a geometrical sense. Numerous and very clear illustrations of this process, and of all the phenomena which are connected with it, are to be found in Kobert Smith s "Optics," and partly also in Kastner's German translation (1755). I only give one (fig. 2), which, properly speaking, represents a special case, mentioned further on, but which may also serve to illustrate the whole, if we leave the point R out of question. 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 [page 72] 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. For, no matter from what cause it may have derived its data, perception is invariably an operation of the Understanding.
"Now, if seeing consisted in mere sensation, we should perceive the impression of the object turned upside down, because we receive it thus; but in that case we should perceive it as something within our eye, for we should stop short at the sensation. In reality, however, the Understanding steps in at once with its causal law, and as it has received from sensation the datum of the direction in which the ray impinged upon the retina, it pursues that direction retrogressively up to the cause on both lines; so that this time the crossing takes place in the opposite direction, and the cause presents itself upright as an external object in Space, i.e., in the position in which it originally sent forth its rays, not that in which they reached the retina (see fig. 1). The purely intellectual nature of this process, to the exclusion of all other, more especially of physiological, explanations, may also be confirmed by the fact, that if we put our heads between our legs, or lie down on a hill head downwards, we nevertheless see objects in their right position, and not upside down; although the portion of the retina which is usually met by the lower part of the object is then met by the upper: in fact, everything is topsy turvy excepting the Understanding.
The second thing, which the Understanding does in converting sensation into perception, is to make a single perception out of a double sensation; for each eye in fact receives its own separate impression from the object we are looking at, each even in a slightly different direction: nevertheless that object presents itself as a single one. This can only take place in the Understanding, and the process by which it is brought about is the following: Our eyes are never quite parallel, except when we look at a distant object, i.e. one which is more than 200 feet from us. At other times they are both directed towards the object we are viewing, whereby they converge, so as to make the lines proceeding from each eye to the exact point of the object on which it is fixed, form an angle, called the optic angle ; the lines themselves are called optic axes. Now, when the object lies straight before us, these lines exactly impinge upon the centre of each retina, therefore in two points which correspond exactly to each other in each eye. The Understanding, whose only business it is to look for the cause of all things, at once recognises the impression as coming from a single outside point, although here the sensation is double, and attributes it to one cause, which therefore presents itself as a single object. For all that is perceived by us, is perceived as a cause that is to say, as the cause of an effect we have experienced, consequently in the Understanding. As, nevertheless, we take in not only a single point, but a considerable surface of the object with both eyes, and yet perceive it as a single object, it will be necessary to pursue this explanation still further. All those parts of the object which lie to one side of the vertex of the optic angle no longer send their rays straight into the centre, but to the side, of the retina in each eye ; in both sides, however, to the same, let us say the left, side. The points therefore upon which these rays impinge, correspond symmetrically to each other, as well as the centres in other words, they are homonymous points. The Understanding soon learns to know them, and accordingly extends the above-mentioned rule of its causal perception to them also ; consequently it not only refers those rays which impinge upon the centre of each retina, but those also which impinge upon all the other symmetrically corresponding places in both retinas, to a single radiant point in the object viewed : that is, it sees all these points likewise as single, a [page 71] object also. Now, it should be well observed, that in this process it is not the outer side of one retina which corresponds to the outer side of the other, and the inner to the inner of each, but the right side of one retina which corresponds to the right side of the other, and so forth ; so that this symmetrical correspondence must not be taken in a physiological, but in a geometrical sense. Numerous and very clear illustrations of this process, and of all the phenomena which are connected with it, are to be found in Kobert Smith s "Optics," and partly also in Kastner's German translation (1755). I only give one (fig. 2), which, properly speaking, represents a special case, mentioned further on, but which may also serve to illustrate the whole, if we leave the point R out of question. 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 [page 72] 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. For, no matter from what cause it may have derived its data, perception is invariably an operation of the Understanding.
