can be distinguished if the distance be- tween them subtends a visual angle of a little less than 1', or, in other words, if the distance between their retinal images is 4 (i: this distance just leaves room for an un- stimulated cone between those upon which the images are formed. Beyond the fovea, in indirect vision, the separation of ob- Fio. 54. A field of cones jective points necessary to their separate (shown schematically as localisation rapidly increases. Whether hexagons) is stimulated l J by a sheet of half-white juxtaposed cones give the perception of and half-black paper. jocai difference when successively stimu- The sheet has been cut through along the lated, the author does not know.
horizontal line, and the if the resting eye is required, not to upper portion has been...,.« shifted a trifle to the distinguish points in space, but to note the right. The black of this relative displacement of lines or edges of upper portion now leaves surfac localisation is far more accurate.
unstimulated cones which are still affected by the Two straight lines placed end to end are black of the lower por- percejve(i to \[e apart under a visual angle tion. Hence the dis-..
placement is perceived. — E. Hering, Btr. d. matk.-phys. Klasse d. k. sacks. Gesellschaft d. Wissenschaflen, li., 3, of only 5", or, in other words, when the distance between their retinal images is less than 0.5 /a. The most probable explanation of this fact is given in Fig. 54.
Precisely the same disparity of retinal images is sufficient, in binocular vision, to give a noticeable differ- ence of depth. The classical experiment is as follows: three fine needles are set up, in the transverse plane, at a short distance from the eyes; the two outer needles are fixed in position, while the middle needle is moved, in successive observations, back or forth in the median plane, until the difference in depth is remarked. In a particular case (interocular distance, 66 mm.), the needles were 0.7 §88. The Perception of Space: Locality 325 mm. in diameter, and were set up 3 mm. or 5' apart at a distance of 2 m. The limen of depth was reached when the middle needle was moved 1.5 mm. toward or away from the observer. This amount of displacement means a difference of 5" in the position of the retinal images of the two eyes.1 The Law of Identical Visual Direction. — The intimate cooper- ation of the two eyes in binocular vision is well shown by the fol- lowing experiment. Place yourself before a window from which you can see, in the distance, two salient objects — say a tree and a chimney — not too far apart. Make an inkspot on the window, fir a fixation-point, and stand in such a position that the spot, fixated by the one eye alone, covers the tree, and fixated by the other eye, without change of the position of the head, covers the chimney. Now fixate the spot with both eyes; you see the tree and the chimney — in rivalry, of course — directly behind the fixation- point. Inkspot, tree, and chimney have the same direction, lie in the same straight line; and this line, if prolonged to the observer's face, would pass between the eyes, or, as Hering puts it, would strike the fovea of a single, cyclopean eye, set midway between the actual eyes.
Internal Localisation. — A special question which belongs to this Section is that of internal localisation (§ 57). How do we localise the organic sensations? It may be noted, first, that if the sensations are at all intensive there is a tendency to move the hand over the skin of chest or abdomen. Whenever this explora- tory pressure sets up, diminishes, enhances, or puts an end to an internal sensation, a cue to localisation is given. Secondly, how- ever, certain organic sensations are regularly connected with other localised sensations. Thus, hunger and intestinal pain may get their place-reference from attendant contraction of the diaphragm, or from distension and contraction of the abdominal wall; stuffiness 1 The further limit of depth-perception, the limit beyond which no dif- ference of depth can be perceived in terms of retinal disparity, lies at the point at which the interocular distance itself is viewed under the smallest visual an;_;le that permits of depth-discrimination. As the average interocular distance is taken as 64 mm., and the visual angle in question is 5", the limit must be placed, approximately, at 2700 m. (p. 316).
326 Spatial Perceptions and exhilaration may be referred to chest or head through associ- ated contractions of the chest muscles, or constriction and relaxa- tion of the nasal passages and respiratory entrances. Here would fall, also, the cases of reflex reference (pp. 184, 186). Thirdly, in minds of visual constitution, organic sensations are directly localised by help of visual images. The author has a definite mental picture of the course of a draught of cold water through the alimentary canal, though he must confess that the picture is accurate neither in scale nor in directions. Visual association is probably responsible, also, for the general tendency to localise organic sensations towards the front of the body (p. 187). Alto- gether, then, organic localisation is an indirect affair, due to pal- pation, to connection with localised sensations, to visual associa- tions, and influenced, no doubt, by more or less accurate know- ledge of the position of the principal organs of the body.
§ 89. The Perception of Space: Magnitude. — The cutane- ous perception of magnitude may be determined either by linear stimuli or by point-distances. It is especially in- teresting to compare point-distances at different parts of the body. If the one distance is kept constant, and the other varied from observation to observation, we shall pres- ently arrive at subjective equality: it has been found, for instance, that a distance of 5 mm. on the finger-tip is the equivalent of a distance of some 16 mm. on the wrist. In general, as this instance shows, point-distances are perceived as larger at parts of the skin which have the more delicate discrimination of locality; so that the points of a pair of compasses, drawn across the face above and below the lips, or drawn down the inside of the arm from shoulder to finger- tips, seem to diverge and converge according to the local sensitivity of the regions traversed. There is, however, no direct proportionality between the two perceptions. More- over, if the point-distances are relatively large, local dif- § 89. The Perception of Space: Magnitude 327 f erences tend to disappear, and subjective tends to coincide with objective equality. Here we have evidence of the dominance of visual over cutaneous space; vision has in- formed us of the actual size of the areas stimulated, and we equate the stimuli by what we know rather than by what we feel.
Very many experiments have been made upon the com- parison of point-distances by the eye. The results show that, at any rate for stimuli of a middle range of magnitude, the differential limen is always the same fraction of the distances compared; in other words, the visual perception of magnitude obeys Weber's Law. Hence it is natural to suppose (and, indeed, there is introspective warrant for the hypothesis) that the distances are compared in terms of the sensations aroused by eye-movement; the greater the intensity of these sensations, the greater is the distance for perception (p. 219).
It is worth remarking that we get differences of perceived extent by the stimulation, at various intensities, of a single pres- sure-spot, and of a single retinal cone. Further: we have two cutaneous limens, for the perception of linear magnitude, whether we work with linear stimuli or with point-distances; for the per- ception of linear extent, as such, appears earlier than the percep- tion of its direction upon the skin.
The Perception of Form. — The cutaneous perception of form is, in general, very inaccurate. At the parts of greatest local sensi- tivity we find small liminal values: thus, the end of a glass tube pressed down upon the tip of the tongue or of the middle finger will be perceived as circular if the glass is 0.5 mm. thick and the outside diameter of the tube is 2 or 3 mm. There can be little doubt, however, that this perception is indirect, based chiefly upon visual association.
Contour lines are followed most easily by the eye if they are continuous, by the moving finger (active touch) if they are broken.
328 Spatial Perceptions You may test the latter statement by trying to read, with the finger-tips, two sentences, the one printed in ordinary raised print, the other in the dotted blind-print.
The Blind Spot. — The blind spot (p. 88) does not interfere with our perception of visual magnitude; points whose retinal images lie on either side of it do not run together, but retain their normal separation. Two factors appear to have contributed to this result. First, there is no blind spot in binocular vision; the part of the combined field to which the one eye is blind is seen by the other. But secondly, and more importantly, the eyes are constantly in motion; and the moving eyes ——————— — £ give us the perception of spatial continuity. Primarily, therefore, points are localised and magnitudes are esti- FlG.55. Blind Spot of the author's left eye, plane pro- mated in direct vision, jection. Reduced from a large diagram, in which and the habit of direct the distance from the inner edge of the fixation-.., mark a to the inner edge of the blind spot was vlsl0n save under 54.5 cm. The distance of the fixation-mark from special experimental the eye, in the experiments, was 2.2 m. conditions - is carried over to indirect vision. Our habitual disregard of double images (p. 309) is a fact of the same kind.
As to what happens at the blind spot itself, opinions are divided. Some psychologists think that the area which it occupies is filled, in the field of vision, either by irradiation from the light and coloured surfaces which surround it, or by imagination: in look- ing at a patterned wall-paper, e.g., we carry an image of the pattern over the blank space which represents the projection of the blind spot. Others declare that the blind spot is simply and literally blind; we see nothing at that part of the field; but, if we see nothing, we cannot see a gap or blank. The field is, then, in fact, continuous, although localisation, for the reasons given above, takes account of the existence of the blind area.
It has recently been asserted that if one looks suddenly, with a single eye, at some uniform and brightly illuminated surface, one § 89. The Perception of Space: Magnitude 329 sees the projection of the blind spot as a faint grey patch (the central grey, p. 90).
The Various Psychological Spaces. — Geometry and the physical sciences know of only one space, which is always and everywhere the same (p. 7). It is clear that a like statement cannot be made of psychology. We have already said something of four psycho- logical spaces: the bidimensional fields of the skin and the resting eye, and the tridimensional spaces of active touch and of the moving double-eye. But there are incongruities, again, within these four systems, for finger-space is not back-space, and the space of direct vision is not that of indirect vision; it would, in- deed, be difficult to say how many psychological spaces can be distinguished. At all events, instances of spatial conflict are not far to seek. The cavity of a hollow tooth seems larger to the explor- ing tongue than to the passively pressing finger; to both, it seems larger than it does to the eye. If you bite far out over the lower lip, the upper jaw seems narrow and small as compared with the tongue's report of it. The sight of the back of one's head in a mirror is — to a man, at any rate — curiously disconcerting, so different is the visual magnitude from the magnitude registered by the hollow hand.
Plainly, then, some sort of reconciliation or compromise is required. Reconciliation is possible, because the attribute of sensory extent, the fundamental spatial datum, is identical for all the spaces. A first practical step towards it is taken in the prefer- ence given to the spot of clearest vision and the spots of clearest touch, to the fovea and the finger-tips: the other spaces are usually ignored. But these two residual spaces are themselves not in accord. Which of them takes precedence of the other?
Helmholtz declares for touch. " We are continually controlling and correcting the notions of locality derived from the eye by the help of the sense of touch, and always accept the impressions on the latter sense as decisive." The author, if he were compelled to make a choice, would, despite the authority of Helmholtz, pro- nounce in favour of sight. In the daylight, our space world is surely, for all practical purposes, a world of space seen; and even in the dark most of us, probably, visualise our way about. Really, 330 Spatial Perceptions however, the issue is not drawn in these terms. We build up, in course of time, a composite idea of space, partly from data of visual, partly from data of tactual experience, but more especially from what we learn of measured, physical or mathematical space. This composite idea rarely appears as a whole, clear and well- defined, in consciousness; often, indeed, the nervous mechanism, inherited and acquired, works automatically, without consciousness at all; but often, again, and perhaps as a rule, our generalised or standardised space-experiences show as a total conscious attitude (§ 138). Then, in any given case, the attitude is particularised as circumstances determine; we apply now this and now that partial and temporary standard; we may act as if on the principle that seeing is believing, or as if on the opposite principle that ap- pearances are deceptive; we trust our eyes, or our fingers, or neither, or both. We follow the path laid out for us, not by sight or touch, but by the present trend and tendency of the cortex.
§ 90. Secondary Spatial Perceptions. — Odours and sounds, although they do not possess the attribute of extent, may yet be localised. They have their physical origin at some point in objective space, and if we can get any cue to this point of origin, we can place the sensations in the visual or tactual field.
Odours may sometimes be referred to a certain direction in space by a process of elimination: we get the scent if we hold the head in a certain way, and we lose it if we turn our face in any other direction. Where this direct cue fails, we rely upon intensity; we move to and fro, sniffing, in the hope that an unusually strong whiff of the odour will give us our bearings. But the quest is uncer- tain; the sense-organ soon becomes adapted (p. 124); and if the scent is weak, or the stimulus has had time to diffuse, localisation is impossible.
Sounds, on the other hand, are as a rule localised readily § 90- Secondary Spatial Perceptions 331 and with considerable accuracy. Under experimental con- ditions, localisation appears to depend on the cooperation of three principal factors. The first of these is the rela- tive intensity of the sound as heard by the two ears: it is difficult to distinguish front and back, in the median plane, and localisation is poor where changes in the binaural ratio are slight, e.g., at the sides, in the region of the axis of the ears. The second is absolute intensity: there are characteristic differences in intensity when the sound comes from different directions. And the third is com- plexity: musical tones, the human voice, complex noises, can be localised far more accurately than pure tones. At the same time it is not difficult to arrange conditions, whether for monaural or for binaural hearing, such that localisation of the auditory stimulus is impossible.
We saw, in § 86, that the congenitally blind might achieve the direct perception of tridimensional space. There is, however, no doubt that they live, very largely, in the secondary space of hear- ing. We have the testimony of a blind author that the blind idea of space " depends far more upon hearing than upon the sense of touch," and that the tactual idea of plasticity, of solidity, i.° only an occasional factor in the blind space-consciousness.
It has been suggested that what is known as the ' warning sense ' of the blind — their perception of the presence of some solid object in their near neighbourhood — may also be due, either directly or indirectly, to hearing. The perception may be aroused directly by the reflection of sound-waves from the surface of the object; or the auditory stimuli may react upon the kinaesthetic organs of the inner ear, and the perception may be based upon vestibular sensations which, in the seeing, are unremarked (§ 54). Since, however, the warning sense is present in deaf patients, and in patients with normal hearing whose ears are stopped, it seems that in these cases a change in temperature, or in the pressure of the air, is responsible for the perception; the sense is, in fact, 332 Spatial Perceptions referred by the blind to the face. There is, of course, no reason to think that the warning sense is confined to a single sense-organ; cochlea, vestibule, pressure-spot and temperature-spot may all, on occasion, be pressed into the service of space-perception.
§ 91. Illusory Spatial Perceptions. — In a certain sense, most of our space-perceptions are illusory. Distance, for instance, very soon closes up on itself; if we try to stop, halfway, a friend who is walking down a long corridor, we shall be likely to call out before he has gone more than a third of its length; at a little distance from the eyes, tridimensional space is perceived as a shallow relief. Mag- nitude, too, is illusory; the size of the moon in the sky is that of a pea held close to the eyes. Form is illusory; how often do we see a square table as square? Only di- rection is adequately perceived. Yet we do not, somehow, think of all these things as illusions: they represent the natural and normal way in which space is perceived; we are used to them, and can correct them, make allowance for them.
There are, on the other hand, certain simple arrange- ments of dots and lines that yield, in perception, a result markedly different from the result which measurement would lead us to expect. These figures, grouped together under the purely descriptive name of the geometrical illu- sions of sight, have in recent years been made the subject of detailed study: our Fig. 1 (p. 7) has, in particular, been repeatedly discussed and variously explained. The simplicity of the forms is, in fact, misleading; explanation is very difficult; and there is no present prospect of agree- ment among investigators. Three types of theory have emerged from the discussion: we may illustrate them by reference to Fig. 1.
§ gi. Illusory Spatial Perceptions 333 Theories of the first type explain the illusions in terms of the physiological mechanism of perception. It is pos- sible, for example, to explain the illusion of Fig. 1 by refer- ence to eye-movement. We are to compare the main lines of the figure, and we move the eyes along them with this comparison in view. But in the upper half of the figure the eyes are tempted to continue their move- ment beyond the proper point, from the shaft to the feathers of the arrow; in the lower half their movement is checked by the enclosing arrow-heads. Hence the upper vertical appears longer than the lower.
Theories of the second type declare that illusion is due to the associative sup- plementing of the perception; ideas are read into the figures. Thus, according to one authority, we tend, just because we are human beings, to humanise the forms -,„, ™.., about us; a column seems, according to Swallow Figure, showing that the illts proportions, to stretch up easily to its lusion of the Muiier- load, or to plant itself doggedly under a ^yer Figure- Fig- *> too heavy pressure, — precisely as a we read into it (in the sense of tlie man might do. So we read ourselves, or second type of feel ourselves, into the lines of the theory) foI\ces thuat are opposed to the figure; the upper vertical has room to direction of illusion.
expand, the lower is cramped and con- Grundzuge d. Psy- fined. The illusion of length results. ckohgu,^, 1908, 96.
Theories of the third type emphasise our own general attitude to the object of perception. If we take the figure as a whole, we get a pronounced illusion: the large open Spatial Perceptions area above, and the closed diamond-shaped area below, strike the attention; we say, from total impression, that the upper vertical is the longer. If, however, we take the figure critically, analytically, limiting our attention to the two verticals and disregarding the oblique lines, the illusion is greatly reduced, and may, with practice, entirely dis- appear.
There is no doubt that perception may be modified both by associated ideas and by general disposition (cortical set). The author remembers a vaudeville performance in which a professional strong man was mer- cilessly hissed; the man had gilded his dumb- bells, in honour of some holiday, and the audience took them for tinsel; only when he sent the mass of iron crashing through the nearest row of seats did the hissing change to applause. So with disposition; we are con- tinually misreading the headlines of the news- Fig. s7. Mach's Book, papers because we are prepared, predisposed, zur Analyse der EmP- for neVVS °f a Certain SOrt- We may grant, findungen, 1886, 97; then, that these factors are operative. Nevermovement theory goes to the heart of the matter. It is supported by many lines of evidence, and not least by the fact that actual record of eye-movement proves the eyes to move differently according as the observer is or is not subject to the illusion. It has the further advantage of bringing into line a series of illusions known as the illusions of reversible perspective. Thus, Fig. 57 shows an open book. Is the back or the front of the book turned towards you? Fixate the middle line, or move the eyes from its extremities out- ward, and you see the back; fixate an outer line, or move the eyes from its extremities inward, and you see the front. And, if you think that the book reverses when you expect it or mean it to reverse (cortical set), you will find — such, at least, is, the author's uniform experience — that, as a matter of fact, the fixation-point has also shifted. All these points, however, are still, so far as detailed explanation is concerned, matters of controversy.
Page 336 contains a number of the more familiar illusion-figures; the reader should try to explain them for himself.1 The cutaneous and tactual spaces show similar illusions; but the results vary greatly, both with variation of the experimental conditions and with the observer's attitude, so that no unitary principle of explanation can be offered.
§ 92. Theories of Space-Perception. — The psychological theories of space-perception range between two extremes. On the one side we have theories which derive, or generate, the perception of space from the intimate connection of sensations, though these are themselves considered to be entirely spaceless. On the other side we have theories which endow the individual sensation with all the funda- mental spatial characters. The theory implied in the fore- going §§85 ff. takes a middle position: it makes extent an attribute of certain classes of sensations, regards localisa- tion as a corollary of extent, and tries to find definite, secondary conditions for the perception of depth.
As an illustration of theories of the first class, the genetic theo- ries, we may take Wundt's account of the origin of spatial ideas. Every point upon the skin, Wundt says, gives to its sensation of pressure, however evoked, a peculiar qualitative colouring, which may be called a local sign. But, in passing from a sensation of local sign a to one of local sign b, we experience the movement-sen- sation B; whereas, in passing from a to the more different c, we 1 The three squares at the top of the page are known as Helmholtz' squares; the two horizontal figures below as Oppel's lines. The large diagram to the left, below the lines, is Zollner's pattern; that to the right is Poggen- dorffs figure. The single diagram below these is called Lipps' parallels. The broken circle to the left, at the bottom of the page, is Muller-Lyer's circle; the diagram to the right shows Muller-Lyer's semicircles.
Spatial Perceptions \ \ \ get the stronger movement-sensation C. The fusion of pressure- sensations and their qualitatively graded local signs with intensively graded movement-sensations furnishes, as its resultant, a bidimen- sional touch-space. It is then not difficult, if we grant qualitative local signs to the articular sensations, to pass to tridimensional perception. Wundt adds that the limbs tend to move in straight lines to and from objects in the field; hence the dimensions of space are naturally regarded as rectilinear. Similarly, every point upon the retina gives to its sensation, whatever that may be, a qualitative local sign, and this fuses with the intensively graded sensations of movement which serve to bring the stimuli upon the fovea: the result is a bidimensional sight-space. The perception of depth requires no additional factors. For, if the eyes move from a to b in the same transverse plane, the change in local sign and the movement-sensation are alike in both; whereas, if they move from a farther a to a nearer b, the retinal images of a move to the right in the left eye, to the left in the right eye, and the right eye itself turns to the left, the left eye to the right. The elements of space-perception are thus unchanged, but the special way in which they are united is entirely different in bidimensional and in tridimensional vision.
As an illustration of theories of the second class, the nativistic theories, we may take Hering's account of visual space-perception. Every retinal point, according to Hering, furnishes, besides its sensations of light and colour, three space-sensations, those of height, breadth and depth. The two former are identical at cor- responding retinal points; they give us, taken together, the percep- tion of direction. The sensations of depth are also identical at corresponding points, but are of opposite sign, — positive in the one eye, negative in the other; they are identical and of the same sign at symmetrically situated retinal points; they are, in fact, posi- tive (mean greater distance) on the outer halves of the retinas, and they are negative (mean less distance) on the inner halves. Every binocular perception of an object imaged on corresponding points has, then, the average direction and the average depth-value of all these space-sensations. But the average depth- value is zero; the depth-sensations are of opposite sign; so that all such percep- 33S Spatial Perceptions tions are localised, by a simple act of sensation, in a plane, Her- ing's nuclear plane, which has no depth-value at all. Let the point in this plane which corresponds to the two foveas be made the centre of a system of coordinates, such that the height and breadth coordinates lie in the plane itself, and the depth coordinate lies at right angles to it: then we have a geometrical construction which, subject to empirical correction, is adequate to space-percep- tion. Since the observer's body is included in this tridimensional space, the distance of objects from the eye is taken account of in the construction.
What is to be said in criticism? Against Wundt, principally this: that the theory does not explain. To say that space results from the fusion of quality and intensity, however plausibly the statement be made, is to leave us with a mystery; nowhere else, over the whole range of psychology, does the concurrence of attributes (pp. 54 f.) give rise to an absolutely new form of con- sciousness. And against Hering, this: that the theory is psy- chologically impossible. Sensations of height and breadth might pass muster, if we mean by them qualitative local signs, but a sensation of depth is an impossibility: depth has no specific quality that can be seen, and, if it had, we have no sense-organ where- with to see it. Here is, of course, only the barest outline of a criticism; we have no room for details. It may be added, how- ever, that the congeni tally blind, to whom sight has been restored by operation, see the world at once as a manifold of two dimen- sions; neither is surface generated by eye-movement, nor is there any primal perception of depth.
References for Further Reading