§ 10. SPATIAL IDEAS.



1. Spatial and temporal ideas are fully distinguished from intensive ideas by the fact that the parts of spatial and temporal ideas are united, not in an arbitrarily variable order, but in a definitely fixed order, so that when the order is thought of as changed the idea itself changes. Ideas with such a fixed arrangement are called in general extensive ideas (p. 101).

Of the possible forms of extensive ideas, spatial ideas are distinguished by the fact that in them it is only in respect to the relation of the parts to one another, that there is a fixed arrangement. With respect to the relation of the parts to the ideating subject there is no such fixed arrangement. This relation of the parts to the subject may be thought of as varied indefinitely. The objective independence of spatial compounds from the ideating subject is expressed by saying that spatial compounds are capable of movements backwards and forwards and of rotation around any axis. The number of directions in which movement and rotation may take place, is limited. They may all be reduced to three dimensions, in each of which it is possible to advance in two opposite directions. The number of directions in which the parts of a single compound may be arranged, as well as the number of directions in which various compounds may be arranged with reference to one another, is the same as the maximal number of directions in which movement and rotation are possible. This is what we call the three-dimensional character of space. A single spatial idea may, accordingly, be defined as a three-dimensional compound whose parts are fixed in their location with reference to one another, but capable of indefinite variation in their location with reference to the ideating subject. This definition neglects, of course, the frequent changes which occur in reality in the arrangement of the parts of spatial compounds. When these changes take place, they are to be regarded as transitions from one idea to another. This three-dimensional arrangement must of necessity include one-dimensional and two-dimensional arrangements as special cases. In such cases, however, the wanting dimensions must always be recognized as added as soon as the relation of the idea to the ideating subject is taken into account.

2. This relation to the ideating subject, which is really present in all spatial ideas, renders it from the first psychologically impossible that the arrangement of the elements in such an idea should be an original attribute of the elements themselves, in any such way as intensity or quality of sensations are original attributes of these elements. It is obvious, rather, that this arrangement results from the bringing together of these elements, and arises from some new psychical conditions which depend upon this coexistence. If this is not admitted, it becomes necessary not only to attribute a spatial quality to every single sensation, but also to postulate for every sensation, however limited, a simultaneous idea of the whole of three-dimensional space in its location with regard to the ideating subject. This would lead to the acceptance of an a priori space-perception, prior to all concrete sensations, which is not only contradictory to all our experiences as to the conditions of the rise of psychical compounds in general, but also contradictory to our knowledge of all the influences that underlie spatial ideas.

3. All spatial ideas are arrangements either of tactual or of visual sensations. Indirectly, through the connection of other sensations with either tactual or visual ideas, the spatial relation may be carried over to other sensations through association of ideas (§ 16). In the cases of touch and sight, it is obvious that the extended surface of the peripheral sense-organs, and their equipment with organs of movement, which render possible a varying location of the impressions in regard to the ideating subject, are both favorable conditions for an extensive, spatial arrangement of the sensations. The tactual sense is the earlier of the two here in question, for it appears earlier in the development of organisms and shows the structural relations in much coarser, but for that reason in many respects much plainer form than does the more delicately organized visual organ. Still, it is to be noted that where vision is present, the spatial ideas from touch are greatly influenced by the ideas from sight, because of the higher development of vision.

A. SPATIAL TOUCH IDEAS.

4. The simplest possible touch idea is that of a single impression from a point on the skin. If such an impression is presented even when the eyes are turned away, there arises a definite idea of the place touched. Introspection shows that this idea, which is called the localization of the stimulus, is not, under the usual condition where vision is present, immediate, as we should expect it to be if the spatial quality were an original attribute of sensations, but it depends upon a secondary, generally very obscure, visual idea of the region touched. Localization is, therefore, more exact near bounding lines of the touch-organs than on the uniform intervening surfaces, since these bounding lines are more prominent in the visual images. The rise of a visual idea from the tactual impression, even when the eyes are turned away, is possible because every point of the organ of touch gives to the touch sensation a peculiar qualitative coloring, which is independent of the quality of the external impression, and is probably due to the character of the structure of the skin. This qualitative coloring varies from point to point and is never exactly the same in two separate regions.

This local coloring is called the local sign of the sensations. It varies from point to point in different regions of the skin at very different rates, rapidly on the tip of the tongue, on the ends of the fingers, and on the lips, slowly on the broader surfaces of the limbs and trunk. A measure of this variation may be obtained by applying two impressions near each other to any region of the skin. So long as the distance of the impressions is less than that of distinguishable local signs, the two impressions are perceived as a single one, but so soon as they pass this limit they are perceived as spatially separate. The smallest, just noticeable distance between two impressions is called the space threshold for touch. It varies from one or two millimetres (tips of tongue and fingers) to sixty-eight millimetres (back, upper arm, and leg). On the pressure-spots (p. 53), when the stimuli are favorably applied, still shorter distances can be perceived. Then, too, the threshold is dependent on the condition of the tactual organ and on practice. As a result of the first the threshold is smaller for children than for adults, since the differences in structure which condition the local signs, are obviously more crowded together. As a result of practice, the threshold is smaller in the case of the blind than it is in the case of those who have vision. This is especially true of the ends of the fingers which are most used for touching.

5. The influence, just described, of visual ideas of the regions touched, teaches that the localization of tactual impressions and the spatial arrangement of a number of such impressions is not due to an original spatial quality of cutaneous points or to any primary space-forming function of the tactual organ. On the contrary, it presupposes spatial ideas of sight. These can be used, to be sure, only because the various parts of the tactual organ have certain qualitative attributes, local signs, which arouse the visual images of the parts touched. But there is no reason for attributing an immediate spatial relation to the local signs themselves; it is obviously enough that they act as qualitative signals to arouse the appropriate visual images. This connection with vision depends upon the frequent union of the two. The keenness of localization will, therefore, be aided by all the influences that increase either the clearness of the visual images or the qualitative differences in local signs.

We may describe the formation of spatial ideas in this case as the arrangement of tactual impressions in visual images already present. The whole process is a consequence of the constant connection of visual images with the qualitative local signs of the tactual impression. The union of the local signs and the visual images of the corresponding region may (according to § 9, p. 102), then, be regarded as an incomplete, but very constant, fusion. The fusion is incomplete because both visual image and tactual impression retain their independent character; but it is so constant that, when the state of the tactual organ remains the same, the fusion seems of be invariable. This last fact explains the relative certainty of localization. The predominating elements of this fusion are the tactual sensations. For many persons the visual images are pushed so far into the background that they can not be perceived with any certainty, even when examined with the greatest attention. The perception of space, in such cases, is perhaps an immediate function of tactual and motor sensations, as for the blind (v. inf. 6). As a rule, however, more careful observation shows that it is possible to recognize the position and distance of the impressions only by attempting to make more distinct the indefinite visual image of the region touched.

6. The conditions which obtain when vision is present, are essentially different from those found in cases of blindness, especially blindness which is congenital or acquired early in life. Persons who become blind later retain for a long time memory images of familiar visual objects, so that the spatial ideas of touch always remain, to some extent, products of a fusion between tactual sensations and visual images. But these visual images can not be continually renewed, so that the persons in question make large use of movements. The tactual sensations which arise from the joints and muscles when the hand passes from one tactual impression to another (p. 51), serve as a measure for the movement executed and, at the same time, as a measure for the distance between the two impressions. These sensations of movement, which in acquired blindness are additions to the gradually fading visual images and in part substitutes for them, are in congenital blindness the only means present from the first for the formation of an idea of the relative position and distance of the single impressions. We observe in congenital blindness continual movements of the touch-organs, especially the fingers, over the object. Added to these movements are more concentrated attention to tactual sensations and greater practice in their discrimination. Still, the low grade of development of touch as compared with sight, always shows itself in the fact that the perception by the blind of continuous lines and surfaces is much less perfect than the perception of points arranged in various ways. The necessity of making a blind-alphabet of arbitrary figures formed by various combinations of raised points, is a proof of this. Thus, for example, in the ordinary blind-alphabet (braille's) one point represents A, two points in a horizontal line B, two points in a vertical line C, etc. With six points at most all the letters can be formed, but the points must be far enough apart to be perceived as separate with the end of the index finger. The way in which this alphabet is read shows clearly how the space ideas of the blind have developed. As a rule the index fingers of both hands are used in blind reading. The right finger precedes and apprehends a group of points simultaneously (synthetic touch), the left finger follows somewhat more slowly and apprehends the single points successively (analytic touch). Both the synthetic and analytic impressions are united and referred to the same object. This method of procedure shows clearly that the spatial discrimination of tactual impressions is no more immediately given in this case than in the case where vision was present, but that in the case of the blind the movements by means of which the finger which is used for analytic touch passes from point to point, play the same part as did the accompanying visual ideas in the normal cases with vision.

An idea of the extent and direction of these movements can arise only under the condition that every movement is accompanied by an inner tactual sensation (p. 51, 6). The assumption that these inner tactual sensations are immediately connected with an idea of the space which is traversed in the movement, would be highly improbable, for it would not only presuppose the existence of a connate perception of surrounding space and of the position of the subject in respect to the same (p. 114), but it would also include another particular assumption. This is the assumption that inner and outer touch sensations, although they are otherwise alike in quality and physiological conditions, differ in that inner sensations give, along with the sensation, an image of the position of the subject and of the spatial arrangement of the immediate environment. This would really necessitate a return to the Platonic doctrine of the memory of innate ideas, for the sensations arising from touch are here thought of as the mere external occasional causes for the revival of innate transcendental ideas of space.

7. Apart from its psychological improbability, such an hypothesis as that just mentioned can not be reconciled with the influence exercised by practice on the discrimination of local signs and on the discrimination of differences in movements. There is, therefore, no way, except to attribute the rise of spatial ideas of the blind, as we did the spatial ideas of normal individuals (p. 117), to the combinations of the sensations as presented, in experience. These combinations result from the fact that every pair of sensations, a and b, with their difference in local signs, always have a corresponding inner touch sensation, b , accompanying the movement from one to the other, while two sensations, a and c, with a greater difference in local signs, have a more intense sensation of movement, g. For the blind there is always such a regular combination of inner and outer touch sensations. It can not, therefore, be affirmed that either of these sensational systems, in itself, brings the idea of spatial arrangements; we can only say that the spatial arrangement results regularly from the combination of the two. On this basis the spatial ideas of the blind, arising, as they do, from external impressions, may be defined as products of the fusion of external tactual sensations and their qualitatively graded local signs, with internal tactual sensations graded according to intensity. The external sensations with their attributes as determined by the external stimulus, are the predominating elements in this fusion. They push the local signs with their qualitative peculiarities and the inner tactual sensations with their intensive attributes, so far into the background, that, like the overtones of a clang, all these secondary elements can be perceived only when the attention is especially concentrated upon them. Spatial ideas from touch are, accordingly, due to a complete fusion (p. 103). Their characteristic peculiarity, in contrast with such fusions as intensive tonal fusions, is that the subordinate and supplementary elements are different in character, and are at the same time related to one another according to definite laws. They are different, for the local signs form a purely qualitative system, while the inner touch sensations which accompany the movements of the tactual organs, form a series of intensities. They are related, in that the motor energy used in passing through an interval between two points increases with the extent of the interval, so that, in proportion as the qualitative difference between the local signs increases, there must also be an increase in the intensity of the sensations which accompany the movement.

8. The spatial arrangement of tactual impressions is thus the product of a twofold fusion. First, the subordinate elements fuse. That is, the various qualities of the local sign system, which is spread out in two dimensions, are related to one another according to the grades of intensity of the inner tactual sensations. Second, the tactual impressions as determined by the external stimuli, fuse with the product of the first union. Of course, the two fusions do not take place successively, but in one and the same process, for the local signs and movements are aroused directly by the external stimuli. Yet, while the external sensations vary with the nature of the objective stimulus, the local signs and internal tactual sensations are subjective elements, the mutual relations of which always remain the same even when the external impressions vary. This is the psychological condition for the constancy of attributes which we ascribe to space itself, in contrast with the great changeableness of the qualitative attributes of objects in space.

9. After the spatial fusion of tactual sensations has once been effected, either one of the elements which took part in the fusion is able by itself, though perhaps in a limited degree, to bring about a localization of the sensations. In this way not only normal individuals with vision, but also the blind, even the congenitally blind, have an idea of the place touched, and can perceive as spatially separate two impressions that are far enough apart, even when the touch-organs remain perfectly quiet. Of course, the congenitally blind can have no visual image of the region touched, but they have instead of this an idea of a movement of the part touched and where several impressions are received, they have the idea of a movement from one to the other. The same fusion takes place in ideas thus formed as takes place in the ordinary cases where movements are really present. The difference is that one factor, namely, the inner tactual sensation, is merely a memory image.

10. In the same way, we have the converse process. The real contents of experience may be a sum of inner tactual sensations which arise from the movement of some part of the body, while no noticeable external tactual sensations whatever are given, and yet these internal sensations which accompany the movement may be the basis of a spatial idea. This is regularly the case when we have pure ideas of our own movements. If, for example, we shut our eyes and then raise an arm, we have at every moment an idea of the position of the arm. To be sure, external tactual sensations which arise from the torsion and folding of the skin, play some part here too, but they are unimportant in comparison with the internal sensations from the joints, tendons, and muscles.

It can easily be observed that where vision is present, this idea of position comes from an obscure visual image of the limb with its surroundings, which image is aroused even when the eyes are closed or turned away. This connection is so close that it may arise between the mere memory image of the inner tactual sensation and the corresponding visual idea, as is observed in the case of paralytics, where sometimes the mere will to execute a certain movement arouses the idea of a movement really executed. Evidently, the ideas of one's own movements depend, when vision is present, on incomplete fusions just as do the external spatial ideas of touch. The only difference is that here the internal sensations play the part which the outer sensations play in the former case. This leads to the assumption that the inner tactual sensations also have local signs, that is, the assumption that the sensations in the various joints, tendons, and muscles show certain series of local differences. Introspection seems to confirm this view. If we move alternately the knee-joint, hip-joint, and shoulder-joint, indeed, if we move successively the corresponding joints on the right and left sides, the quality of the sensation varies a little each time, even if we neglect the fact that there is a visual image of the limb which can never be entirely suppressed.

11. From the relations which exist in the normal cases of persons who have vision, we can understand the way in which persons who are congenitally blind form ideas of their own movements. Here, instead of a fusion with a visual image, there must be a fusion of sensations of movement with the local signs. Outer tactual sensations also act as aids in this case. In fact, they are much more important here than when vision is present. The ideas of the blind as to their own movements are exceedingly uncertain so long as they are unaided by contact with external objects. When, however, the blind touch such objects, they have the advantage of greater practice with the external tactual sense and a keener attention to the same. The so-called "distance-sense of the blind" is a proof of this greater practice. It consists in the ability to perceive from some distance, without direct contact, a resisting object, as for example a neighboring wall. Now, it can be experimentally demonstrated that this distance-sense is made up of two factors, a very weak tactual stimulation of the forehead by the atmospheric resistance, and a change in the sound of the step. The latter acts as a signal to concentrate the attention so that the weak tactual stimulations can be perceived. The "distance-sense" disappears, accordingly, when the tactual stimulations are prevented by binding a cloth around the forehead or when the steps are rendered inaudible.

12. Besides our ideas of the position and movements of the various parts of our body, we have also an idea of the position and movement of our whole body. The ideas of the position of parts of the body can never have anything but a relative significance; it is only when considered in connection with the idea of the body as a whole that they become absolute. The organ of orientation for this general idea is the head. We always form a definite idea of the position of the head; the other organs are localized, generally, indeed, very indefinitely, with reference to the head, each idea depending on the particular complexes of inner and outer tactual sensations presented in that case. The specific organ of orientation in the head is the system of semicircular canals, to which are added, as secondary aids, the inner and outer tactual sensations resulting from the action of the muscles of the head. The function of these canals as an organ of orientation can be most easily understood by assuming that inner tactual sensations with especially marked differences in local signs, arise in them through the influence of the changing pressure of the fluid medium which fills them. It is highly probable that dizziness, which comes from rapid rotation of the head, is due to the sensations caused by the violent movements of this fluid. This is in accord with the observations that partial derangements of the canals bring about constant illusions in localization, and complete derangement of the same is followed by an almost total suspension of the ability to localize.

12a. The antagonistic theories in regard to the psychical formation of spatial ideas, are generally called nativism and empiricism. The nativistic theory seeks to derive localization in space from connate properties of the sense-organs and sense-centers, while the empiristic theory seeks to derive it from the influence of experience. This antithesis does not give proper expression to the actual opposition which exists, for the assumption of connate spatial ideas may be attacked without affirming that these ideas arise through experience. This is the case when, as above, space perceptions are regarded as products of psychical fusions due both to the physiological properties of the organs of sense and organs of movement, and to the general laws governing the rise of psychical compounds. Such processes of fusion and the arrangements of sense impressions based upon them, are everywhere the conditions of our experience, but for this very reason it is inadmissible to call them "experience" itself. It is much more in keeping with the facts to point out the opposition which really exists as the opposition between nativistic and genetic theories. Genetic theories may then be subdivided into empirical theories and theories of fusion. In view of the fact that the associative processes in the fusion theories, are necessary even for the first formulation of experience, we may designate these theories as the praeempirical forms of genetic theory. It is to be noted that the widely accepted nativistic theories contain empirical elements, while, on the other hand, empirical theories contain nativistic elements, so that the difference is sometimes very slight. Supporters of the nativistic view assume that the arrangement of impressions in space corresponds directly to the arrangement of sensitive points in the skin and retina. The special way in which the projection outward is effected, especially in ideas of the distance and magnitude of objects and in the reference of a plurality of spatially separated impressions to a single object, is accounted for as dependent upon "attention", "will", or even "experience". Supporters of the empirical theory, on the other hand, generally presuppose space as given in some way or other, and then interpret each single idea as a case of localization in this space, the particular localization being in each case due to some empirical motive. In the theory of spatial ideas from sight, tactual space is generally regarded as this originally given space; in the theory of tactual ideas, original spatial qualities have sometimes been attributed to inner tactual sensations. Thus, in the actual concrete theories empiricism and nativism are very ill-defined concepts. They agree in the use of the complex concepts of popular psychology, such as "attention", "will", and "experience", without any examination or analysis. In this respect they are different from the fusion theory, which seeks to discover, by means of a psychological analysis of the ideas, the elementary processes from which the ideas arise.

The special influence of the head on ideas of bodily position and movement shows itself in the phenomena of dizziness, and in the ideas which we form of movement through space when the body is carried along without effort on our own part. This special influence was originally attributed to certain parts of the brain, especially to the cerebellum. And it is not unlikely that the cerebellum participates in a measure directly, and in a measure indirectly as the center for the peripheral organ of orientation, in the processes of orientation and in the disturbances of orientation. As to the peripheral organs of orientation the partial and total extirpations which have been performed on the semicircular canals, especially on the canals of birds make it evident that the most important of these peripheral organs of orientation are the semicircular canals. In addition, however, it must not be overlooked that external touch sensations and visual perceptions are of supplementary importance, especially in that they make possible a gradual correction of the disturbances of orientation which arise when the semicircular canals are disabled. Further confirmation of a striking type is found for the belief that the canals are of great importance in the observation that deaf mutes very frequently suffer from disturbances in orientation. In deaf mutes the pathological disturbances in the inner ear, which cause deafness, usually occur early in life. Abnormalities in orientation probably occur in all those cases in which these early disturbances affect the semicircular canals as well as the cochlea.

References. E. H. Weber, Tastsinn und Gemeingefühl, Handwörterbuch der Physiol., vol. III, pt. 2, 1846. Lotze, Medizinische Psychologie, 1852. (On p. 324, appears the first statement of the concept local signs. This presentation was essentially metaphysical in motive.) Wundt, Beitrage zur Theorie der Sinneswahrnehmung, sect. I, 1862. Vierordt, Grundriss der Physiol., 5th ed. (1877) p. 340. Washburn, Phil. Stud., vol. II. judd, Phil. Stud., vol. 12. Goldscheider, Ges. Abhandlungen, vol. I. Wundt, Grundz. 5th ed., vol II, Chap. 13; Lectures, lecture 9. Lipps, Grundtatsachen des Seelenlebens, Chap. 22, 1883. On the Blind: heller, Phil. Stud., vol. II. On the Blind who are also deaf and dumb: Jerusalem, Laura Bridgman, 1890. Helen Keller, The Story of my Life. On Ideas of the Position of the Body as a Whole: Goltz, Pflüger's Archiv, vol. 3. Breuer, Pflüger's Archiv, vol. 48. Mach, Grundlinien der Lehre von den Bewegungsempfindungen, 1875. Delage-Aubert, Studien über die Orientirung, 1888. Ewald, Physiol. Untersuch. über das Endorgan des Nervus octavus, 1892. Kreidl, Pflüger's Archiv, vols. 51 and 54 (on the ability of the deaf and dumb to stand).





B. SPATIAL SIGHT IDEAS.

13. The general properties of the touch sense are repeated in the visual sense, but in a more highly organized form. Corresponding to the sensory surface of the outer skin, we have in the visual sense the retina with its rods and cones arranged in rows and forming an extraordinarily fine mosaic of sensitive points. (Fig. 2, p. 42.)

The fibers of the optic nerve enter the eyeball at a single point, (O, Fig. 11), and from this point spread out in all directions to form the inner layer of the retina (R). The ends of these fibers turn toward the outer surface of the eyeball and connect with the other layers of the retina. The outermost layer consists of the rods and cones, which are long slender organs having respectively the forms of a loaded cartridge and a cylinder, (Fig. 2, the layer in the upper part of the figure). The rods and cones are covered by a dark-colored pigment layer known as the choroid coat (A). This coat takes up the waste products given off by the retina, and is for this purpose richly supplied with blood vessels. Outside of the choroid is the outer protective coating of the eyeball, the sclerotic (5). The choroid coat develops in the front part of the eye into the iris (J), which has in its middle a round opening called the pupil (p). The sclerotic develops in the front part of the eye the transparent cornea (C). Between the cornea and the crystalline lens there lies a chamber filled with watery fluid known as the aqueous humor (W). The vitreous humor (G), which fills the eyeball, together with the cornea, aqueous humor, and crystalline lens (L), constitute the system of refracting media of the eye. They refract the light which comes into the eye so that in the normal condition of the eye an object placed at various distances casts a small inverted image on the retina. In order to determine approximately the position and size of such an image in a simple way, one can make use of the so-called optical center of the eye (K). This point lies at a distance of 0.5 mm. in front of the posterior surface of the lens. When a straight line is drawn from an outer point through this optical center, it may be continued and constitutes the line of direction from the outer point to the corresponding image-point on the retina. When objects are near at hand, the refracting organs are adjusted to these objects by an adjustment which renders the front surface of the crystalline lens very much more convex through the action of muscular fibers closely related to the iris and drawing upon a capsule which surrounds the lens. The iris is pushed forward by this change in the form of the lens, as is indicated in the dotted line in Fig. 11. In addition to these accomodations to near objects through change in the curvature of the lens, the eye possesses also the means of adapting itself to different degrees of brightness through the action of the muscle fibers of the iris. When the light strikes the eye, these fibers become reflexly active and operate to decrease the size of the pupil when brightness increases, and to increase the size of the pupil when the brightness diminishes. There are two points on the retina which are of special importance for vision. There is, first, the blind spot (b), which corresponds to the point of entrance of the optic nerve and is entirely unreceptive for light because of the absence of the rods and cones. The second point is the macula lutea (g), which includes the fovea centralis of the retina, the region in which are to be found only cones closely packed together. This region is especially adapted to the reception of clear images. The blind spot has a diameter of about 6° or 1.5 mm. The macula has a diameter of 41/2° or less than one millimeter, and it lies at a distance of 15° or 4 mm. toward the temporal side of the eye from the blind spot. The diameter of the whole eye is about 23 mm. These structural characteristics mark the eye as an organ which is constructed in all of its parts on the principle of a camera obscura. It has, in addition to the retina or surface which is sensitive to the light, two characteristics which could be possessed only by a living organ, namely, the characteristics of adjustability to light coming from different distances, and of adjustability to the different light intensities through the diaphragm which is provided in the iris. Since light is a form of energy which can traverse space and can provide clear images from objects at various distances, both far and near, the organ of vision comes to be, in a much higher degree than the organ of hearing, a distance sense. At the same time the visual organ is a spatial organ like the organ of touch.

14. With regard to its spatial attributes, every visual idea may be resolved into two factors: 1) the location of the single elements in relation to one another, and 2) their location in relation to the ideating subject. Even the idea of one single point of light contains both these factors, for we must represent a point in some spatial environment, and also in some direction and at some distance from ourselves. These factors can be separated only through deliberate abstraction, never in reality, for the relation of any point in space to its environment regularly determines its relation to the ideating subject. As a result of this dependence, the analysis of visual ideas may better start with the location of the elements in relation to one another, and then take up later the location of the compound in relation to the subject.

a. The Location of the Elements of a Visual Idea in Relation to One Another.
15. In the perception of the reciprocal relations between elements of a visual idea, the characteristics of space perception through the tactual sense are all repeated, only in a much more highly organized form, and with a few modifications which are important in determining the special character of the visual sense. Thus, in vision as in touch, we immediately connect with the simplest possible impression of a point the idea of its place in space; that is, we give it a certain definite position in relation to the parts of space about it. This localization is not effected, however, as in touch, by a direct reference of the impression to the corresponding point on the sense-organ itself; we project the impression rather into a field of vision, which lies at some distance outside of the ideating subject. Here as in tactual space we have a measure of the accuracy of localization in the distance at which two points can be just distinguished as spatially different. The distance is not given in this case as a directly measurable linear extension on the sensory surface itself, but as the shortest perceptible interval between two points in the field of vision. The field of vision may be at any distance whatever, so that it is best to use as a measure for the fineness of localization, not a linear extension, but an angle, the angle formed by the intersection of the lines passing from the points in the field of vision, through the optical center in the crystalline lens (the crossing point of all the lines of direction), to the corresponding retinal points. This angle of vision remains constant so long as the size of the retinal image is unchanged, while the distance between the points in the field of vision increases in proportion to their distance from the subject. If an equivalent linear distance is sought in place of the angle of vision, it can be found in the diameter of the retinal image. This may be calculated directly from the angle and the distance of the retina from the optical center of the eye.

16. Measurements of the keenness of visual localization made according to this principle show that there is a great difference in different parts of the field of vision, corresponding to the differences found for different regions of the tactual organs (p. 116). Only one spot on the retina is a notable exception in this respect, that is the blind point where the optic nerve enters and where no light stimulations can be received because of the absence of the sensory elements, the rods and cones. The blind spot can easily be demonstrated by means of a drawing such as that which is given in Fig. 12. If an observer closes the left eye and looks steadily with the right eye at the small cross on the left-hand side of the page, the black circle will fall on the blind spot of the eye if the book is moved backward and forward so as to bring it ultimately to a distance of about one foot from the face. The black circle then disappears and in its place the white background seems to be continuous over the whole area. This experiment is called by the name of its discoverer, Mariotte's experiment. In all other places the distances which are just perceptible are very small. In all parts of the retina these distances are much smaller than the least perceptible distances on the skin. Then too, while there are many regions of finer discrimination scattered over the tactual organ, there is only one region of finest discrimination in the field of vision. This is the middle of the field of vision which corresponds to the center of the retina. From this region toward the periphery, the fineness of localization diminishes very rapidly. The whole field of vision, or the whole retinal surface, is, accordingly, analogous to a single tactual region, as for example that of the index finger, except that the visual region much surpasses the tactual in fineness of localization, especially at the center where two impressions at a distance corresponding to 60"—90" in the angle of vision, are just distinguishable; at two and a half degrees from the center toward the periphery, the smallest perceptible extension is 3' 30"; and at eight degrees toward the periphery it increases to 1°.

In normal vision we turn the eye toward objects of which we wish to gain more accurate spatial ideas, in such a way that these objects occupy the middle of the field of vision, their images falling, as a result, on the center of the retina. We speak of such objects as seen directly, of all others, which lie in the eccentric parts of the field of vision, as seen indirectly. The center of the region of direct vision is called the point of regard, or the fixation-point. The line that unites the center of the retina with the fixation-point is known as the line of regard. The central region of the retina itself, that is, the region where impressions can be most clearly distinguished, the region with which we can read letters of the ordinary size used in printing, is, as noted above, about 41/2 degrees in diameter, and it lies at a distance of 15 degrees toward the temporal side of the eye from the blind spot, which in turn has a diameter of about 6 degrees (g and b, Fig. 11).

If we compute the distance on the retina which corresponds to the smallest angle of vision at which two points in the center of the field of vision may be perceived as separate, we shall find it to be .004 to .006 mm. This distance is about equal to the diameter of a retinal cone, and since the center of the retina has only cones and these are so close together that they are in direct contact, it may be concluded with probability that two impressions must fall upon at least two different retinal elements if they are to be perceived as separate in space. This view is supported by the fact that in the peripheral regions of the retina the rods and cones, which are the two forms of elements sensitive to light, are really separated by greater intervals. It may, then, be assumed that the keenness of vision is directly dependent on the proximity of the retinal elements to one another.

16a. Because of this relation between the keenness of vision and the arrangement of retinal elements, it has often been concluded that every retinal element has from the first the ability of localizing any stimulus which acts upon it, in that position in space which corresponds to its own projection in the field of vision. In this way the attempt has been made to explain the fact that the visual sense represents its objects in an external field of vision at some distance from the subject, as a connate energy of the retinal elements or of their central connections in the visual center in the brain. There are certain pathological disturbances of vision which seem at first sight to confirm this assumption. When some region of the retina is pushed out of place as a result of inflammation underneath, certain distortions in the images, the so-called metamorphopsia, arise. The extent and direction of these distortions can be fully explained when it is assumed that the displaced retinal elements continue to localize their impressions as they did when in their normal positions. But it is obvious that these distortions of the images, when they appear, as they do in most cases, as continually changing phenomena, during the gradual formation and disappearance of the excretion, furnish us with no more evidence of a connate energy of localization than does the readily observed fact that distorted images of objects are seen when one looks through prismatic glasses. Furthermore, if a stationary condition is gradually reached, the metamorphopsia disappear, and that, too, not only in cases where it may be assumed that the retinal elements return to their original position, but even in those cases where such a return is entirely improbable on account of the extent of the affection. In cases like the latter, the development of a new connection between the single retinal elements and their corresponding points in the field of vision, must be assumed. This conclusion is supported by observations made with normal eyes on the gradual adaptation to such distorted images as are produced by external optical appliances. If a pair of prismatic glasses be worn before the eyes, marked and disturbing changes in the images are the regular results. The straight bounding lines appear bent and the forms of the objects are thus distorted. These disturbances gradually disappear entirely if the glasses are worn some time. When the glasses are removed, the distortions may appear in the opposite direction.

17. Besides the retinal sensations there are other psychical elements which take part in the spatial arrangement of light impressions. The physiological properties of the eye point a priori to the sensations which accompany ocular movements, as such elements. These movements obviously play much the same part in the estimation of distances in the field of vision as do the tactual movements in the estimation of tactual impressions. Since the eye can be turned in all directions about its center of rotation, which is fixed in its relation to the head, it is very well adapted to follow continuously the bounding lines of objects or to pass each time in the shortest line from a given fixation-point to another. Furthermore, the movements of the two eyes are so adapted to one another through the synergy of their innervation, that normally the two lines of regard are always turned upon the same fixation-point. In this way a cooperation of the two eyes is made possible which not only permits a more perfect perception of the position of objects in relation to one another, but also furnishes the most essential means for the determination of the spatial relations of objects to the subject (24 seq.).

18. The phenomena of vision teach that the idea of the relative distance of two points from each other is dependent on the motor energy employed in passing through this distance, just as the discrimination of two distinct points in the field of vision depends on the arrangement of the retinal elements. The motor energy becomes a component of the idea through its connection with a sensation of tension which is perceived, especially in extensive movements and by comparing ocular movements in various directions.

The influence of these inner tactual sensations is most apparent in the fact that the disturbances in localization which arise from partial paralysis of single ocular muscles correspond exactly to the changes in the amount of energy required to move the eye. The general principle of such disorders is that the distance between two points seems greater when these points lie in the direction of the more difficult movement. The more difficult movement has a correspondingly more intense sensation of tension, which intense sensation under normal conditions accompanies a more extensive movement. As a result, the distance passed through appears greater. Furthermore, the same illusion may appear for distances which lie in the direction of difficult movement, but have not been actually passed through, for the standard acquired during movement determines the motor impulse in the eye even when it is not moved.

19. Similar variations can be demonstrated for the normal eye. Although the ocular muscles are so arranged that their movements in various directions require about the same amount of exertion, still, there is not exact equality in this respect. The reasons for the existing differences are connected with the adaptation of the eye to its functions. The neighboring objects, on which the lines of regard must be converged, are the ones at which we most often look. For this reason, the muscles of the eye have so adapted themselves that the movements for the convergence of the lines of regard are the easiest, particularly those directed downward as compared with other possible movements of convergence. This facilitation of convergent movements is brought about by the special mode of placing the muscles which move the eye upward and downward. These muscles, the superior rectus and the inferior rectus (Rsi, Fig. 13) do not lie exactly in the vertical median plane of the eye, from which position they would give the eye a simple upward and downward vertical movement; they lie rather at such an angle to this median plane that their contraction results in a slight inward, as well as an upward and downward movement. Furthermore, each of these superior and inferior recti muscles is supplemented by an oblique muscle, the superior rectus by the inferior oblique, and the inferior rectus by the superior oblique (Rsi, Fig. 13). These oblique muscles aid in producing upward and downward movements and at the same time counterbalance the rotation movements produced in the eyes by the asymmetrical placing of the recti muscles. As a result of the greater complexity of muscular activity in upward and downward directions, the exertion required to run over lines in these directions is greater than the exertion required in looking along horizontal lines, where only the internal and external recti act. Furthermore, the relative ease of downward movements of convergence as contrasted with upward movements shows itself partly in the differences in intensity of sensations accompanying the downward movements, as already remarked (p 136), and partly in the fact that downward convergence is involuntarily too great and upward convergence too small.

There are certain constant optical illusions depending on the position of a given object in the field of vision, which correspond to these differences in the motor mechanism. They are of two kinds, illusions of direction and illusions of length.

Both eyes are subject to an illusion as to the direction of vertical lines in the field of vision. Such a line, the upper end of which is inclined 1°—3° outward, appears vertical, and one really vertical, seems inclined inward. Since the illusion is in opposite directions for the two eyes, it disappears in binocular vision. It can obviously be explained by the fact just noted, that the downward movements of the eyes are connected with an involuntary increase in convergence, and the upward movements with a decrease in convergence. This deflection of the movement from the vertical is not noticed in itself, it is referred to the object as a deflection in the opposite direction.

An equally regular illusion of length appears when we compare straight lines extending perpendicularly to each other in the field of vision. This, too, is to be explained by the differences in the arrangement of the muscles which move the eye upward and downward as compared with those which move the eye outward and inward. The illusion consists in the fact that a vertical straight line is judged on the average 1/7 to 1/10 too long as compared with an equal horizontal line. A square, accordingly, appears as a rectangle whose base is shorter than its sides, and a square drawn by the eye is always too short in its vertical dimensions. As in the case of partially paralyzed eyes, so here in normal vision, distances in the direction of the more difficult movement appear greater.

Besides this difference between vertical and horizontal distances, which is most noticeable because it is so large, there are less marked differences between upward and downward and also between outward and inward distances. The upper half of a vertical line is overestimated on the average by 1/16 of its length, and the outer half of a horizontal line by 1/40. The first of these illusions corresponds to the facilitation of downward movements (described p. 136), the second corresponds to the general facilitation of movements of convergence.

20. In addition to these two constant illusions, which arise from the special structure of ocular muscles in their adaptation to the purposes of vision, there are certain other variable optical illusions which are due to certain attributes common to all our voluntary movements and which have their analogues in the movements of the tactual organs. These variable illusions may also be divided into those of direction, and those of length. The former follow the rule that acute angles are overestimated, obtuse angles underestimated, and that the direction of the lines forming the angles varies correspondingly. For the illusions of length we have the rule, that forced or interrupted movements require more exertion than free and continuous ones. Any straight line which necessitates fixation is, accordingly, overestimated in comparison with an open distance marked off by two points, and a straight line interrupted by several dividing lines is overestimated in comparison with an uninterrupted line.

20a. The tactual analogues of the illusion in visual angles is to be found in the tendency to overestimate small articular movements and to underestimate large ones. This comes under the general principle that a relatively greater expenditure of energy is required for a short movement than for a more extensive one, because it is relatively more difficult to begin a movement than to continue it after it is already started. The tactual phenomena analogous to the overestimation of interrupted lines, is that a distance estimated by a movement of one of the limbs always seems shorter when it is traversed in a single continuous movement, than it does when the movement is several times interrupted. Here too, the sensation corresponds to the expenditure of energy which is greater for an interrupted movement than for a continuous movement. The overestimation of interrupted lines by the eye takes place, as we can easily understand, only so long as no motives arise from the way in which the division is made, to hinder the movement of the eye. Such a hindrance is present, for example, when the line is interrupted only once. This one point of division makes fixation necessary. If we compare such a line with a continuous line, we tend to estimate the first without any movement, the point of division being the fixation-center, while the second is perceived by a movement of the eye. As a result the continuous line seems longer than the interrupted line. A similar explanation is to be offered for the illusion which appears in Fig. 14 and consists in the overestimation of the upper horizontal line which passes into the obliques extending outward from its end. These oblique lines tend to produce movements which extend beyond the straight line itself. On the other hand, there is an under-estimation of a like line which has its obliques turned inward, as shown in the lower part of the figure. The illusion of overestimated acute angles is most striking when the conditions for this illusion are repeated a number of times, as for example in Fig. 15. The long oblique lines in this figure are in reality parallel to each other, but on account of the apparent enlargement of the acute angles, which are formed between the long lines and the intersecting lines, the parallels seem to diverge and converge.

20b. All of these illusions of direction and length, whether variable or constant, are classified as "geometrical optical illusions", and are thus distinguished from certain other optical illusions which depend upon pure optical irregularities. The term geometrical is used because of the fact that it is in the construction of geometrical figures that the best opportunities for the discovery of such illusions appear. The term is extended so as to cover not only these illusions which have been described and which depend upon the characteristics of eye movements, but also to include other unusual forms of visual space perception which are due to the laws of association to be discussed later. These latter we may distinguish by the special designation "association illusions". Such association illusions are exemplified by the fact that a given line when placed near a very much shorter line is overestimated, and, conversely, when placed near a long line is underestimated. Similar underestimation or overestimation appears in the case of an angle compared respectively with a larger and smaller angle. These facts are obviously analogous to the facts of light and color contrast (§ 17, 11). Similar associations appear in the variable illusions of direction and length described above in certain cases in which the illusion due to differences in the energy of movement, is modified and the percept is brought into agreement with the retinal image by an apparent projection of the flat figure into depth. Thus, for example, we do not only see an interrupted straight line as longer than an uninterrupted line of equal length, but we also interpret the interrupted line as lying at a greater distance. This latter fact of interpretation depends upon the general rule of perception which has been established by a large number of associations, that of two objects casting retinal images of equal size the more remote is the larger. Such perspective association illusions appear more clearly in cases of rigid fixation than when the eye is moving freely, because such illusions depend very largely on the direct comparison of retinal images. They furnish also a means of distinguishing between variable illusions and constant illusions, for the constant illusions do not, as a rule, show any of these tendencies toward perspective interpretation. For further discussion of association illusions compare § 16, 9. For spatial contrast § 17, 11.

21. Both the variable and the constant optical illusions point to the immediate dependence of the perception of spatial directions and distances on ocular movements. As further evidence pointing in the same direction, we have the negative fact that the arrangement of the retinal elements, especially their proximity to one another, normally has no appreciable influence on the ideas of direction and magnitude. This is most strikingly evident in the fact that the distance between two points appears the same whether observed in direct or indirect vision. Two points which are clearly distinguished in direct vision, may become one in the eccentric parts of the field of vision, but so soon as they are distinguished at all, they will appear just as far apart in one region as in the other. The absence of any dependence of the perception of distance on the proximity of retinal elements to each other is shown, furthermore, in certain facts connected with the phenomenon which was mentioned above, (p. 131), that objects disappear when their images fall upon the blind spot. The size of the blind spot is about 6 degrees, so that images of considerable size can fall upon this area, for example, the image of a human face when seen from a distance of about six feet disappears altogether. Nevertheless, as soon as points become visible on the right or left, or above and below the blind spot, they always appear to be at the same distance from each other as points which are not separated by an interrupted region in the field of vision. Like facts are especially noticeable when some region of the retina has become blind by a pathological process.1)

22. The keenness of vision and the perception of directions and distances in the field of vision, are, as all these phenomena show, two functions, which depend upon different conditions: the first depends on the proximity of the retinal elements to one another, the second on ocular movements. It follows directly that spatial ideas from sight can not be regarded as original ideas or ideas arising from light impressions in themselves, any more than the spatial ideas of touch can be referred directly to the tactual impressions themselves. The spatial order is in both cases developed from the combination of certain sensation components which, taken separately, have no spatial attributes whatever. Other conditions also indicate that the elements are related in vision in the same way as in the case of touch, and that the development of visual space under normal conditions runs entirely parallel to the development of space in cases of congenital blindness, that is, under the only condition under which touch attains a similar independence. Retinal impressions correspond to impressions of contact, and ocular movements to touch movements. Tactual impressions can gain spatial qualities only through the local coloring of the sensations connected with them — that is, through the local signs — and in like manner, we must recognize the same to be true for retinal impressions.
 
 

1) In this connection we have the fact that the blind spot does not appear in the field of vision as a break, without sensation content, but as a continuation of the general brightness and color of the whole field. Thus, the field is seen as continuously white when we are looking at a white surface, as black when we look at a black surface. This filling out of the blind spot is possible only through reproduced sensations, and is to be considered as one of the phenomena of association to be discussed later (§ 16).
 
 

22a. To be sure, a qualitative gradation of local signs on the retina can not be demonstrated with the same evidentness as for the skin. Still, by the use of colors it can be established in a general way that at relatively great distances from the retinal center the sensation quality gradually changes. Colors are not as saturated in indirect vision, and the color-tone also changes; for example, yellow appears orange. There is, indeed, in these facts of retinal response no strict proof of the existence of pure local differences in the sensations, at least not in the fine gradations which must be assumed in the retinal center. Still, the facts show that local differences in sensations do exist, and this seems to justify the assumption of such differences even beyond the limits of demonstration. This assumption is all the more justifiable because in vision where the gradations are much finer than in touch, the tendency to translate sensation differences directly into local differences, a tendency which has already been noticed in the case of touch, would certainly do much more to destroy the specifically qualitative character of these local differences. As a confirmation of this view we have the fact that the demonstrable sensation differences at greater distances from the retinal center, can be observed only under favorable conditions, that is, when limited impressions are used; they disappear entirely when surfaces of uniform color are looked at. This disappearance of marked qualitative differences must be attributed in part at least to their relation to local differences.

23. We assume, accordingly, qualitative local signs, which judging from the data derived from the keenness of vision, are graded in the finest stages at the retinal center and more slowly in the eccentric parts. The formation of visual space may then be described as a combination of this system of local signs arranged in two dimensions, with a system of intensive inner tactual sensations. For any two local signs a and b there will be a corresponding sensation of strain a, arising from the movement through the distance a b, and serving as a measure of the same. A longer distance a c will have a more intense sensation of strain, g. Just as the point of finest discrimination on the finger is the center of reference, so in the same way the retinal center is such a point of reference for the eye. In fact, this is, because of the laws of ocular movements, more obvious for the eye than it is for the tactual organ. Any luminous point in the field of vision is a stimulus for the center of ocular innervation, and tends to turn the line of regard reflexly upon itself. This reflex relation of eccentric stimuli to the retinal center is probably an essential condition for the development of the synergy of ocular movements mentioned above, and is, at the same time, an explanation of the great difficulty of observing objects in indirect vision. This difficulty is evidently due to the greater reflex impulse toward a point in indirect vision when the attention is concentrated upon it. As a result of the preeminent importance which the retinal center has for ocular movements, the point of fixation becomes the center of reference in the field of vision, and all distances in this field are brought under a unitary standard by being determined with reference to the fixation-point. The excitation of local signs is due to the action of external impressions, and both together cause the movement toward the retinal center. The whole process of visual space arrangement is thus due to the fusion of three different sensation elements: first, the sensation qualities depending upon the character of the external stimulus, second the qualitative local signs depending on the points upon which the stimuli act, and third, the intensive motor sensations determined by the relation of the stimulated points to the center of the retina. The latter elements may either accompany actual movements — this is the original case — or, when the eye remains at rest, these elements are mere motor impulses of a particular intensity. Because of the regular connection between qualitative local signs and intensive sensations of strain which accompany the movements, the two factors may together be regarded as a single system of complex local signs. The spatial localization of a simple visual impression, is a product of a complete fusion of the sensation caused by the external stimulus with the two interconnected elements belonging to this system of complex local signs. The arrangement of a number of simple impressions in space consists in the combination of a great number of such fusions which are graded in quality and intensity according to the elements of the system of local signs. The predominating elements in these fusions are the sensations due to the external stimulation. In comparison with these, the elements of the system of local signs are little recognized, because in the immediate perception of objects the local signs are entirely swallowed up in their spatial interpretation.

b. The Location of Visual Ideas in Relation to the Ideating Subject.
24. The simplest case of a relation between an impression and the subject, which can appear in a visual idea, is evidently that in which the impression is limited in extent to a single point. If a single point of light is presented in the field of vision, both lines of regard are, as a result of the reflex impulse exerted by the stimulus (p. 144), turned upon it in such a way that in both eyes the images fall upon the retinal centers. Furthermore, the organs of accommodation are also adapted to the distance of the point. The point thus represented on the centers of both retinas is seen as single, and as situated in a certain particular direction, and at a certain particular distance from the ideating subject.

The subject is represented, as a rule, by a point which may be defined as the middle point of the straight line connecting the centers of rotation of the two eyes. We will call this the point of orientation for the field of vision, and the straight line drawn from this point to the intersection of the two lines of regard, that is, to the external fixation-point, we will call the line of orientation. When a point in space is fixated, there is always a fairly exact idea of the direction of the line of orientation. This idea is produced by the inner tactual sensations arising from the position of the two eyes. Such sensations are very noticeable because of their intensity when the eyes are rotated much out of the central position. They are just as perceptible for a single eye, so that localization in direction is as perfect in monocular as in binocular vision. In monocular vision, however, the line of orientation generally coincides with the line of regard2).

2) The habit of seeing with two eyes results in exceptions to this rule. Often when one eye is closed, the line of orientation remains the same as in binocular vision and does not coincide with the line of regard. In such cases the closed eye usually makes the movements of convergence to a fixation-point which is the same as that of the open eye.

25. The idea of the distance of objects from the subject, or of the absolute length of the line of orientation, is much more indefinite than the idea of direction. We are always inclined to represent this distance shorter than it really is, as may be shown by comparing it with a standard placed somewhere in the field of vision perpendicular to the line of orientation. In this way we find that the distance on the standard which is judged to be equal to the line of orientation, is always much shorter than the real length of the line of orientation. The discrepancy between the two increases as the point of fixation moves further away, that is, as the line of orientation becomes longer. The only sensation components which can produce this idea of distance, are the sensations of tension arising from the position of the two eyes. These sensations arise especially from the convergence of the lines of regard and give somewhat of a measure of the absolute extent of this convergence. In fact, it is possible to serve sensations when the convergence is changed: from the inner angle of the eye when the degree of convergence is increased, from the outer angle when the convergence is decreased. The sum of all the sensations corresponding to a given position of convergence distinguishes such a position completely from all others.

26. It follows that an idea of a definite, absolute length of the line of orientation can be developed only through experience, during which there appear, in addition to the sensation elements, a great many associations. This explains why these ideas not only remain indefinite but are also sometimes aided, sometimes disturbed by other components of visual ideas, especially by the size of the retinal images of familiar objects. On the other hand, we have in sensations of convergence, a relatively fine measure for differences in the distances of objects. For positions in which the lines of regard are nearly parallel, changes in convergence may be perceived when they correspond to an angle of vision of 60" or 70". When the convergence increases, the absolute amount of this least perceptible change in convergence also increases considerably, but, in spite of this increase in angular amount, the corresponding differences in the length of the line of orientation become smaller and smaller. Thus the purely intensive sensations which accompany movements of convergence, are translated directly into ideas of changes in the distance between the fixation-point and the point of orientation of the subject.

This translation of a certain particular sensation complex into an idea of distance, is not due to any connate energy, but to a particular psychical development, as is shown by a great number of experiences. Among these is the experience that the perception both of absolute distances and of differences in distance, is greatly improved by practice. Children are generally inclined to localize very distant objects in the immediate neighborhood; they grasp at the moon, at the slater on the tower, etc. In the same way, it has been observed that the congenitally blind are, immediately after an operation, entirely unable to distinguish near and far.

27. It is of importance for the development of this discrimination between far and near under the natural conditions of vision, that not mere isolated points be presented, but extended three-dimensional objects, or at least a number of points at different depths, to which we assign relatively different distances along their respective lines of orientation.

Let us consider first the simple case, where two points a and b are presented, lying at different depths and connected by a straight line. A change in the fixation from a to b. is always accompanied by a change in convergence, and brings about, first, the passage through a continuous series of retinal local signs corresponding to the points on the line a b, and, second, it produces an inner tactual sensation, a, corresponding to the difference in convergence between a and b. This gives us the elements of a spatial fusion. The product of this fusion is, however, peculiar in kind; it differs in both its components, that is, in the successive series of local signs and in the concomitant tactual sensations of movement, from the fusions which arise when we view a line in the field of vision (p. 144), which does not extend in the third dimension, but lies entirely in a given plane. In the latter case the changes in local signs and sensations of movement are alike for both eyes, while in the fanner case, that is, in changing the point of fixation from far to near, or the reverse, the changes in local signs are opposite in the two eyes. For when the convergence gives the right eye a rotation toward the left, it will produce a rotation toward the right in the left eye, and vice versa. The same must also hold for the movement of the retinal images; when the image of the point as it leaves the point of fixation, moves toward the right in the right eye, it moves toward the left in the left eye, and vice versa. The first takes place when the eyes turn from a nearer to a more distant point, the latter, when they move in the opposite direction. Such fusions arising from movements of convergence have, so far as their qualitative and intensive components are concerned, a composition analogous to the fusion on which the arrangement of the elements in the field of vision with regard to one another depends; but the special way in which these elements are united is entirely different in the two cases.

28. Thus, the fusions between local signs and inner tactual sensations form a system of complex local signs which is analogous to that described above (p. 144), but is in some respects unique in its composition. This second system of local signs adds to the reciprocal relation between the objective elements, a relation between the ideating subject and these elements. This relation to the subject divides into two ideational elements, characterized by distinctive sensation elements, the idea of direction and that of distance. Both refer primarily to the point of orientation in the head of the ideating subject, and are then secondarily applied to the relations of external objects in regard to one another. Thus, we come to assign to two points which lie at different distances along the line of orientation a certain direction and

a certain distance in relation to each other. All such ideas of spatial distance of various positions along the line of orientation when taken together, make up what are called ideas of depth, or when they are also ideas of particular single objects they constitute ideas of three-dimensional objects.

29. An idea of depth arising in the way described may vary according to objective and subjective conditions. The determination of the absolute distance of an isolated point in the field of vision, is always very uncertain. Even the determination of the relative distance between two points a and b lying at different depths is generally certain only under the condition assumed above, namely, the condition that the points are connected by a line along which the points of fixation for the two eyes can move in changing the convergence from one to the other. We may call such lines which connect different points in space with one another lines of fixation. The principle may then be formulated: points in space are perceived in their true relations, only when they are connected by lines of fixation, along which the points of fixation of the two eyes may move. This principle is explicable on the ground that the conditions for a regular union of the local signs of the retina with sensations of strain which accompany convergence, are obviously fulfilled only when impressions are presented which can arouse on the retina local signs appropriate to the particular sensations of strain given through the convergence.

30. When the conditions mentioned are not fulfilled there either arises an imperfect and indefinite idea of the differences in the relative distance of the two points from the subject, or else when there is steady fixation of one point, the two points may seem to be equally distant. In such cases there always arises in the idea another important change consisting in the fact that only the fixated point is seen as single, the other point is seen as double. The same thing happens in looking at extended objects when they are not conected with the binocular fixation-point by means of lines of fixation. The double images which are produced in this manner are either uncrossed or crossed. They are uncrossed, that is the right image belongs to the right eye and the left image to the left eye, when the fixated point lies nearer than the object which casts the double images. Thus in Fig. 16, if c is the fixated point and a is the object, the double images of a will appear at a' and a''. The double images are, on the other hand, crossed when the object lies nearer than the point of fixation. In Fig. 16, if the point of fixation is again c, the object b will be seen in double images at b' and b". The distance of the double images from each other in each of these cases will be determined by the size of the angles a' and a" and b' and b" which the lines of direction, drawn from the object to the retina through the optical center of the eye, form with the line drawn from the center of fixation to the center of the retina. The double images are seen, as a rule, not as represented in Fig. 16 in the same plane with the point of fixation, but a' and a" seem somewhat further than c, while b' and b" seem somewhat nearer. The apparent distances do not, however, correspond ordinarily to the real distances of the objects. This case of depth perception probably belongs to the general group of facts to be discussed later (34) under the head of monocular depth perception.

Binocular localization in depth and binocular double images are, accordingly, phenomena directly interrelated. Where localization is indefinite and imperfect we have double images, and where, on the other hand, double images are absent, the localization in depth is definite and exact. The two phenomena stand in such a relation to the line of fixation that when such a line is present it aids in forming the idea of depth and in doing away at the same time with double images. Still, this rule is not without exception, for when a point is rigidly fixated with both eyes, double images may arise in spite of any lines of fixation which may be present. This is explained by the general conditions mentioned above (p. 150) as necessary for ideas of depth. Just as the absence of lines of fixation results in the lack of the required succession of the local signs, so in a similar way the inner tactual sensations connected with movements of convergence are absent in rigid fixation.

c. Relations between the Location of the Elements in Regard to one another and their Location in Regard to the Subject.
31. When the field of vision is thought of merely as a series of locations of visual impressions in relation to one another, we represent this field to ourselves as a surface, and call the single objects lying in this surface two-dimensional, in contrast with those which have also depth. But even an idea of two dimensions must always be related to the seeing subject in two ways. For, in the first place, every point in the field of vision is seen in a particular direction on the subjective line of orientation mentioned above (p. 146), and second, the whole field of vision is localized at a more or less definite distance from the subject.

The location in a particular direction results in an erect ideational object corresponding to an inverted retinal image. This relation between the objective localization in direction and the retinal image is as necessary a result of ocular movements, as the inversion of the image is a result of the optical properties of the eye. Our line of orientation in space is the external line of regard, or, for binocular vision, the middle line resulting from the combined effects of movements of fixation. A direction upward on this line of orientation in external space corresponds to a direction downward in the internal ocular space where the retinal image lies, behind the center of ocular rotation. And the converse is true for directions downward on the line of orientation.

32. The location at some distance or other, which also is never absent, results in the fact that all the points of the field of vision seem to be arranged on the surface of a concave hemisphere the center of which is the point of orientation, or, in monocular vision, the center of the eye's rotation. Now a small area of a large curved surface appears plane, so that the two-dimensional ideas of single objects are as a rule plane; as examples of such figures, we may mention those which are taken up in plane geometry. But as soon as some parts of the general field of vision separate from this field in such a way that they are localized before or behind a single plane, that is in different planes, the idea of two dimensions gives place to an idea of three dimensions.

32a. The fusions formed between qualitative local signs and inner tactual sensations when we change from the fixation of a more distant point to the fixation of a nearer, or the reverse, may be called complex local signs of depth. Such local signs form for every series of points lying before or behind the fixation-point, or for every extended body which is nothing but a series of such points, a regularly arranged system in which a stereometric series of points located at a particular distance is always unequivocally represented by a particular group of complex local signs of depth. When one of two points lying at different distances is fixated, the other is represented in a definite and unequivocal manner by the positions of its images in the two eyes, which positions with their corresponding complex local signs are different in the two eyes. The same is true of connected series of points or extended bodies. When we look at a solid object, it throws images in the two eyes which are different from each other on account of the different relative positions of the object with reference to the two eyes. We designate the difference between the positions of a certain point in the image in the two eyes as the binocular parallax. This parallax is zero for the point fixated, and approximately zero for those points which are equally distant in depth; for all other points it has some real positive or negative value according as such points are more or less distant than the fixation-point. If we fixate solid objects with both eyes, only the point fixated, together with those points which are equidistant and in its neighborhood in the field of vision, will give rise to images corresponding in position in the two eyes. All points of the object located at different distances, give images varying in position and size. Thus, for example, in Fig. 17, the point d throws on the two retinas the images d and b, which are equally distant from the centers of the two retinas which are represented by a and b respectively. The point e, on the other hand, casts its image in the left eye on e and in the right eye on b. These two images are at different distances from the centers. The magnitude of the differences of these distances, or the magnitude of the two angles b band a e is what is known as binocular parallax. The differences, which are determined by the degree of parallax, are what determine the solid appearance of an object when there are lines of fixation between the points which give these different images. There is always some angle of parallax of the kind indicated in the figure for any point which lies either in front of the point of fixation or behind it and is connected with this center of fixation with a line. This angle of parallax, by its direction and magnitude and through the complex local signs which are connected with it, furnishes a measure of the relative distances in depth between the objective points. Thus, in Fig. 17, the parallax of the two images e and b determines the recognition of the nearer position of e as compared with the point d, and the parallaxes of all of the different points in the rod A B constitute the means of recognizing the total position of A B in depth as distinguished from the position of A' B'. This angle of parallax for given objective depth, decreases as the distance of the solid object from the subject increases, so that the impression of solidity diminishes the further off the objects are; and when the distance is so great that all angles of parallax disappear, the body will appear flat, unless the associations to be discussed later (§ 16, 9) produce an idea of depth.

33. The influence of binocular vision on the idea of depth may be investigated experimentally by means of a stereoscope. This instrument consists of two prisms with their angles of refraction turned toward each other in such a way that it renders possible a binocular combination of two plane drawings which correspond to the two retinal images from a three-dimensional object (Fig. 18). The binocularly fused figures a and b are referred to the region c, where the lines of vision of the two eyes come together, and the two images give us the same experience as that which would be given by an object which had real solidity and was placed in the position c. Furthermore, complex stereoscopic figures require for the most part backward and forward movements of convergence before a clear plastic image is formed. The effect of binocular parallax shows itself most clearly in the observation of stereoscopic figures the parts of which can be varied with reference to each other. The movement of the parts of such figures is accompanied by changes in the apparent solidity, which corresponds directly to the changes produced in binocular parallax. Thus, for example, the figure A, in Fig. 19, looks like a pyramid, the truncated end of which is turned toward the observer. When the small square, however, is moved into the position B, the whole figure is turned into a hollow pyramid into which the observer looks. The magnitude of binocular parallax is dependent on the distance of the two eyes from each other; it is therefore possible to produce ideas of depth even in the case of objects too distant in reality to give plastic effects. Plastic effects are secured in such cases by combining in the stereoscope, pictures taken from positions much further apart than the two eyes. This is done, for example, in making stereoscopic photographs of landscapes. The result is that these photographs when combined, do not look like real landscapes, but like plastic models regarded from a short distance.

34. In monocular vision all the conditions which are connected with movements of convergence are absent. There are, furthermore, no binocular differences in the retinal images such as may be artificially reproduced in the stereoscope. But even here certain factors are present which are capable of producing a localization in the third dimension, although this localization is more imperfect than in binocular vision.

The direct influence of movements of accommodation is, in comparison with other conditions, relatively small. Still, like movements of convergence, movements of accommodation are also accompanied by sensations which can be clearly perceived in the case of greater changes of accommodation from distant to neighboring points. For smaller changes in depth these sensations are very uncertain. As a result the movement of a point in the direction of the line of regard, when it is looked at with only one eye, is generally not clearly observed until a change in the size of the retinal image appears.

35. For the development of monocular ideas of depth the influences which the components of the so-called perspective exercise, are of the greatest importance. These are the relative magnitude of the angle of vision, the direction of limiting lines, the direction of shadows, the change in colors due to atmospheric absorption, etc. All these influences, depend on associations of ideas, and will, therefore, be treated in a later chapter (§ 16).

35a. We have in general the same opposing theories for the explanation of visual ideas as for tactual ideas (p. 125). The empirical theory has sometimes committed the fallacy of limiting itself to optics and turning the real problem of space perception over to touch. In such cases the empirical theory has confined its attention to explaining how a localization of visual ideas can take place with the aid of experience, on the basis of already existing spatial ideas from touch. Such an effort to reduce visual space to tactual is, however, not only self-contradictory, it also conflicts with experience, which shows that in normal persons with vision, visual space perception determines tactual, not the reverse (p. 116). The fact of general development, that touch is the more primitive sense, can not be applied to the development of the individual. The chief evidences in support of nativistic theories are, first, the metamorphopsia after dislocation of retinal elements (p. 134) and, second, the position of the line of orientation (p. 146), which indicates united functioning of the two eyes from the first. It has been noted already (p. 134) that the metamorphopsia and other related phenomena prove the exact opposite as soon as the changes to which they are due become stationary. Furthermore, the fact that in long continued use of only one eye the line of orientation comes to coincide with the line of regard (p. 146), proves that the position of this line is not given from the first, but that it has arisen under the influence of the conditions of vision. Still another fact against the nativistic and in favor of the genetic theory, is the development in the child of the synergy of ocular movements under the influence of external stimuli and the organization of space perceptions which apparently accompanies it. Here as in many other respects the development of most animals is different. In animals the reflex connections of retinal impressions with movements of the eyes and head, function perfectly immediately after birth (v. inf. § 19, 2).

The fusion theory has gained the ascendency over older nativistic and empirical views, chiefly through the more thorough investigation of the phenomena of binocular vision. Nativism has difficulty in showing why we generally see objects single although they produce images in each of the two eyes. The effort is made to avoid the difficulty by assuming that two identical retinal points are connected with the same optic fiber which divides in the chiasma, and that in this way the two retinal points represent what in the sensorium is only a single point. This doctrine of the "identity of the two retinas" became, however, untenable as soon as the actual conditions of binocular vision in three dimensions began to be investigated.

References. Helmholtz, Physiol. Optik, sect. 3. Hering, Hermann's Handbuch Physiol., vol. Ill, pt. I, sect. 4. Bourdon, La perception visuelle de l'espace, 1892. zoth, in Nagel's Handbuch der Physiol., vol. 3, pt. 2. Wundt, Grundz. 5th ed., vol. II, Chap. 14; Lectures, lectures 10 to 13. On the Keenness of Vision: Aubert, Physiol. der Netzhaut, (1865) p. 187. Wertheim, Archiv f. Ophth., vol. 33, no. 2. A. F. Fick, Archiv f. Ophth., vol. 45. A. König, Ber. der Berliner Akad., 1897. On Eye Movements: Hering, Lehre vom binocularen Sehen, 1868. Wundt, Grundz. 5th ed., vol. II, Chap. 14. On Geometrical Optical Illusions: J. Oppel, Ber. des physik. Vereins zu Frankfurt, 1854, 1856 and 1860. MÜLLER-LYER, Archiv f. Physiol., Supplement for 1889, and Zeitschr. f. Psychol., vols. 9 and 13. Lipps, Raumästhetik und geometrisch-optische Täuschungen, 1897. Wundt, Abhandl. der sächs. Ges. d. Wiss., math.-phys. CL, vol. 24 (1898), and Phil. Stud., vol. 14, and Lectures, lecture 10. On the Influence of Convergence and Accommodation: Hillebrand, Zeitschr. f. Psych., vol. 7. Arrer, Phil. Stud., vol. 13. On Binocular Vision, and Stereoscopic Vision: Wheatstone, Philosophical Transactions, 1838. Donders, Archiv f. Ohpth., vol. 17. Wundt, Lectures, lectures 12 and 13. On the Behavior of the congenitally Blind after Operation: Helmholtz, Physiol. Optik, p. 428. Rählmann, Zeitschr. f. Psych., vol. 2. Uhthoff, Zeitschr. f. Psych., vol. 14. On Theories of spatial Vision: Nativistic Theories: J. Müller, Zur vergl. Physiol. des Gesichtssinns, 1826. Panum, Physiol. Untersuchungen über das Sehen mit zwei Augen, 1858. Hering, Hermann's Handb., vol. III, pt. 1. Empirical Theories: Berkeley, Essay toward a New Theory of Vision, 1709. Helmholtz, Physiol. Optik § 23. Fusion Theories: herbart, Psychologie als Wissenschaft, Pt. 2, sect. 1, chap. 3. Wundt, Beiträge zur Theorie der Sinneswahrnehmungen, (1862) pts. 3 and 4, and Phil. Stud., vol. 14. Lipps, Grundtatsachen des Seelenlebens, chap. 23, and Psychol. Untersuchungen, I, 1885.