If a common person is asked how he is enabled to see things as they are, he will simply reply, by opening his eyes and looking. This innocent answer has, however, long since been impossible for science. There are various paradoxes and irregularities about _what_ we appear to perceive under seemingly identical optical conditions, which immediately raise questions. To say nothing now of the time-honored conundrums of why we see upright with an inverted retinal picture, and why we do not see double; and to leave aside the whole field of color-contrasts and ambiguities, as not directly relevant to the space-problem,--it is certain that the same retinal image makes us see quite differently-sized and differently-shaped objects at different times, and it is equally certain that the same ocular movement varies in its perceptive import. It ought to be possible, were the act of perception completely and _simply_ intelligible, to assign for every distinct judgment of size, shape, and position a distinct optical modification of some kind as its occasion. And the connection between the two ought to be so constant that, given the same modification, we should always have the same judgment. But if we study the facts closely _we soon find no such constant connection between either judgment and retinal modification, or judgment and muscular modification, to exist._ The judgment seems to result from the combination of retinal, muscular and intellectual factors with each other; and any one of them may occasionally overpower the rest in a way which seems to leave the matter subject to no simple law.
The scientific study of the subject, if we omit Descartes, began with Berkeley, and the particular perception he analyzed in his New Theory of Vision was that of distance or depth. Starting with the physical assumption that a difference in the distance of a point can make no difference in the nature of its retinal image, since "distance being a line directed endwise to the eye, it projects only one point in the fund of the eye--which point remains invariably the same, whether the distance be longer or shorter," he concluded that distance could not possibly be a visual sensation, but must be an intellectual 'suggestion' from 'custom' of some non-visual experience. According to Berkeley this experience was tactile. His whole treatment of the subject was excessively vague,--no shame to him, as a breaker of fresh ground,--but as it has been adopted and enthusiastically hugged in all its vagueness by nearly the whole line of British psychologists who have succeeded him, it will be well for us to begin our study of vision by refuting his notion that depth cannot possibly be perceived in terms of purely visual feeling.
Berkeleyans unanimously assume that no retinal sensation can primitively be of volume; if it be of extension at all (which they are barely disposed to admit), it can be only of two-, not of three-, dimensional extension. At the beginning of the present chapter we denied this, and adduced facts to show that all objects of sensation are voluminous in three dimensions (cf. p. 136 ff.). It is impossible to lie on one's back on a hill, to let the empty abyss of blue fill one's whole visual field, and to sink deeper and deeper into the merely sensational mode of consciousness regarding it, without feeling that an indeterminate, palpitating, circling depth is as indefeasibly one of its attributes as its breadth. We may artificially exaggerate this sensation of depth. Rise and look from the hill-top at the distant view; represent to yourself as vividly as possible the distance of the uttermost horizon; and then _with inverted head_ look at the same. There will be a startling increase in the perspective, a most sensible recession of the maximum distance; and as you raise the head you can actually see the horizon-line again draw near.[210] Mind, I say nothing as yet about our estimate of the 'real' amount of this depth or distance. I only want to confirm its existence as a natural and inevitable optical consort of the two other optical dimensions. The field of view is always a _volume-unit_. Whatever be supposed to be its absolute and 'real' size, the relative sizes of its dimensions are functions of each other. Indeed, it happens perhaps most often that the breadth- and height-feeling take their absolute measure from the depth-feeling. If we plunge our head into a wash-basin, the felt nearness of the bottom makes us feel the lateral expanse to be small. If, on the contrary, we are on a mountain-top, the distance of the horizon carries with it in our judgment a proportionate height and length in the mountain-chains that bound it to our view. But as aforesaid, let us not consider the question of absolute size now,--it must later be taken up in a thorough way. Let us confine ourselves to the way in which the three dimensions which are seen, get their values fixed _relatively to each other_.
Reid, in his Inquiry into the Human Mind, has a section 'Of the Geometry of Visibles,' in which he assumes to trace what the perceptions would be of a race of 'Idomenians' reduced to the sole sense of sight. Agreeing with Berkeley that sight alone can give no knowledge of the third dimension, he humorously deduces various ingenious absurdities in their interpretations of the material appearances before their eyes.
Now I firmly believe, on the contrary, that one of Reid's Idomenians would frame precisely the same conception of the external world that we do, if he had our intellectual powers.[211] Even were his very eyeballs fixed and not movable like ours, that would only retard, not frustrate, his education. For the _same object_, by alternately covering in its lateral movements different parts of his retina, would determine the mutual equivalencies of the first two dimensions of the field of view; and by exciting the physiological cause of his perception of depth in various degrees, it would establish a scale of equivalency between the first two and the third.
First of all, one of the sensations given by the object is chosen to represent its 'real' size and shape, in accordance with the principles laid down on pp. 178 and 179. _One sensation measures the 'thing' present, and the 'thing' then measures the other sensations._ The peripheral parts of the retina are equated with the central by receiving the image of the same object. This needs no elucidation in case the object does not change its distance or its front. But suppose, to take a more complicated case, that the object is a stick, seen first in its whole length, and then rotated round one of its ends; let this fixed end be the one near the eye. In this movement the stick's image will grow progressively shorter; its farther end will appear less and less separated laterally from its fixed near end; soon it will be screened by the latter, and then reappear on the opposite side, and finally on that side resume its original length. Suppose this movement to become a familiar experience; the mind will presumably react upon it after its usual fashion (which is that of unifying all data which it is in any way possible to unify), and consider it the movement of a constant object rather than the transformation of a fluctuating one. Now, the _sensation of depth_ which it receives during the experience is awakened more by the far than by the near end of the object. But how much depth? What shall measure its amount? Why, at the moment the far end is ready to be eclipsed, the difference of its distance from the near end's distance must be judged equal to the stick's whole length; but that length has already been judged equal to a certain optical sensation of breadth. _Thus we find that given amounts of the visual depth-feeling become signs of fixed amounts of the visual breadth-feeling. The measurement of distance is, as Berkeley truly said, a result of suggestion and experience. But visual experience alone is adequate to produce it, and this he erroneously denied._ Suppose a colonel in front of his regiment at dress-parade, and suppose he walks at right angles towards the midmost man of the line. As he advances, and surveys the line in either direction, he looks more and more _down_ it and less and less _at_ it, until, when abreast of the midmost man, he feels the end men to be _most_ distant; then when the line casts hardly any lateral image on his retina at all, what distance shall he judge to be that of the end men? Why, half the length of the regiment as it was originally seen, of course; but this length was a moment ago a retinal object spread out laterally before his sight. He has now merely equated a retinal depth-feeling with a retinal breadth-feeling. If the regiment moved, and the colonel stood still, the result would be the same. In such ways as these a creature endowed with eyes alone could hardly fail of measuring out all three dimensions of the space he inhabited. And we ourselves, I think, although we _may_ often 'realize' distance in locomotor terms (as Berkeley says we must always do), yet do so no less often in terms of our retinal map, and always in this way the more spontaneously. Were this not so, the three visual dimensions could not possibly feel to us as homogeneous as they do, nor as commensurable _inter se_.
_Let us then admit distance to be at least as genuinely optical a content of consciousness as either height or breadth. The question immediately returns, Can any of them be said in any strictness to be optical sensations?_ We have contended all along for the affirmative reply to this question, but must now cope with difficulties greater than any that have assailed us hitherto.
_Helmholtz and Reid on Sensations_.
A sensation is, as we have seen in Chapter XVII, the mental affection that follows most immediately upon the stimulation of the sense-tract. Its antecedent is directly physical, no psychic links, no acts of memory, inference, or association intervening. Accordingly, if we suppose the nexus between neural process in the sense-organ, on the one hand, and conscious affection, on the other, to be by nature uniform, _the same process ought always to give the same sensation;_ and conversely, _if what seems to be a sensation varies whilst the process in the sense-organ remains unchanged, the reason is presumably that it is really not a sensation but a higher mental product, whereof the variations depend on events occurring in the system of higher cerebral centres._ Now the _size_ of the field of view varies enormously in all three dimensions, without our being able to assign with any definiteness the process in the visual tract on which the variation depends. We just saw how impossible such assignment was in the case where turning down the head produces the enlargement. In general, the maximum feeling of depth or distance seems to take the lead in determining the apparent magnitude of the whole field, and the two other dimensions seem to follow. If, to use the former instance, I look close into a wash-basin, the lateral extent of the field shrinks proportionately to its nearness. If I look from a mountain, the things seen are vast in height and breadth, in proportion to the farness of the horizon. But _when we ask what changes in the eye determine how great this maximum feeling of depth or distance_ (which is undoubtedly felt as a unitary vastness) _shall be, we find ourselves unable to point to any one of them as being its absolutely regular concomitant._ Convergence, accommodation, double and disparate images, differences in the parallactic displacement when we move our head, faintness of tint, dimness of outline, and smallness of the retinal image of objects named and known, are all processes that have _something to do_ with the perception of 'far' and of 'near'; but the effect of each and any one of them in determining such a perception at one moment may at another moment be reversed by the presence of some other sensible quality in the object, that makes us, evidently by reminding us of past experience, judge it to be at a different distance and of another shape. If we paint the inside of a pasteboard-mask like the outside, and look at it with one eye, the accommodation- and parallax-feelings are there, but fail to make us see it hollow, as it is. Our mental knowledge of the fact that human faces are always convex overpowers them, and we directly perceive the nose to be nearer to us than the cheek instead of farther of.
The other organic tokens of farness and nearness are proved by similar experiments (of which we shall ere long speak more in detail) to have an equally fluctuating import. They lose all their value whenever the collateral circumstances favor a strong intellectual conviction that the object presented to the gaze is _improbable_--cannot be either _what_ or _where_ they would make us perceive it to be.
Now the query immediately arises: _Can the feelings of these processes in the eye, since they are so easily neutralized and reversed by intellectual suggestions, ever have been direct sensations of distance at all_? Ought we not rather to assume, since the distances which we see _in spite_ of them are conclusions from past experience, that the distances which we see _by means_ of them are equally such conclusions? Ought we not, in short, to say unhesitatingly that distance must be an intellectual and not a sensible content of consciousness? and that each of these eye-feelings serves as a mere signal to awaken this content, our intellect being so framed that sometimes it notices one signal more readily and sometimes another?
Reid long ago (Inquiry, c. vi. sec. 17) said: "It may be taken for a general rule that things which are produced by custom may be undone or changed by disuse or by contrary custom. On the other hand, it is a strong argument that an effect is not owing to custom, but to the constitution of nature, when a contrary custom is found neither to change nor to weaken it."
More briefly, a way of seeing things that can be unlearned was presumably learned, and only what we cannot unlearn is instinctive.
This seems to be Helmholtz's view, for he confirms Reid's maxim by saying in emphatic print: "No elements in our perception can be sensational which may be overcome or reversed by factors of demonstrably experimental origin. Whatever can be overcome by suggestions of experience must be regarded as itself a product of experience and custom. If we follow this rule it will appear that only _qualities_ are sensational, whilst almost all _spatial_ attributes are results of habit and experience."[212] This passage of Helmholtz's has obtained, it seems to me, an almost deplorable celebrity. The reader will please observe its very radical import. Not only would he, and does he, for the reasons we have just been ourselves considering, deny distance to be an optical sensation; but, extending the same method of criticism to judgments of size, shape, and direction, and finding no single retinal or muscular process in the eyes to be indissolubly linked with any one of these, he goes so far as to say that all optical space-perceptions whatsoever must have an intellectual origin, and a content that no items of visual sensibility can account for.[213] As Wundt and others agree with Helmholtz here, and as their conclusions, if true, are irreconcilable with all the sensationalism which I have been teaching hitherto, it clearly devolves upon me to defend my position against this new attack. But as this chapter on Space is already so overgrown with episodes and details, I think it best to reserve the refutation of their general principle for the next chapter, and simply to assume at this point its untenability. This has of course an arrogant look; but if the reader will bear with me for not very many pages more, I shall hope to appease his mind. Meanwhile I affirm confidently that _the same outer objects actually_ FEEL _different to us according as our brain reacts on them in one way or another by making us perceive them as this or as that sort of thing._ So true is this that one may well, with Stumpf,[214] reverse Helmholtz's query, and ask: "What would become of our sense-perceptions in case experience were _not_ able so to transform them?" Stumpf adds: "All wrong perceptions that depend on peculiarities in the organs are more or less perfectly corrected by the influence of imagination following the guidance of experience."
If, therefore, among the facts of optical space-perception (which we must now proceed to consider in more detail) we find instances of an identical organic eye-process, giving us different perceptions at different times, in consequence of different collateral circumstances suggesting different objective facts to our imagination, we must not hastily conclude, with the school of Helmholtz and Wundt, that the organic eye-process pure and simple, without the collateral circumstances, is incapable of giving us any sensation of a spatial kind at all. We must rather seek to discover _by what means_ the circumstances can so have transformed a space-sensation, which, but for their presence, would probably have been felt in its natural purity. And I may as well say now in advance that we shall find the means to be nothing more or less than association--_the suggestion to the mind of optical objects not actually present,_ but more habitually associated with the 'collateral circumstances' than the sensation which they now displace and being imagined now with a quasi-hallucinatory strength. But before this conclusion emerges, it will be necessary to have reviewed the most important facts of optical space-perception, in relation to the organic conditions on which they depend. Readers acquainted with German optics will excuse what is already familiar to them in the following section.[215] Let us begin the long and rather tedious inquiry by the most important case. Physiologists have long sought for a simple law by which to connect the seen direction and distance of objects with the retinal impressions they produce. Two principal theories have been held of this matter, the 'theory of identical points,' and the 'theory of projection,'--each incompatible with the other, and each beyond certain limits becoming inconsistent with the facts.
_The Theory of Identical Points_.
This theory starts from the truth that on both retinæ an impression on the upper half makes us perceive an object as below, on the lower half as above, the horizon; and on the right half an object to the left, on the left half one to the right, of the median line. Thus each quadrant of one retina corresponds as a whole to the _similar_ quadrant of the other; and within two similar quadrants, _al_ and _ar_ for example, there should, if the correspondence were consistently carried out, be geometrically similar points which, if impressed at the same time by light emitted from the same object, should cause that object to appear in the same direction to either eye. Experiment verifies this surmise. If we look at the starry vault with parallel eyes, the stars all seem single; and the laws of perspective show that under the circumstances the parallel light-rays coming from each star must impinge on points within either retina which _are_ geometrically similar to each other. The same result may be more artificially obtained. If we take two exactly similar pictures, smaller, or at least no larger, than those on an ordinary stereoscopic slide, and if we look at them as stereoscopic slides are looked at, that is, at one with each eye (a median partition confining the view of either eye to the picture opposite it), we shall see but one flat picture, all of whose parts appear sharp and single.[216] Identical points being impressed, both eyes see their object in the same direction, and the two objects consequently coalesce into one.
The same thing may be shown in still another way. With fixed head converge the eyes upon some conspicuous objective point behind a pane of glass; then close either eye alternately and make a little ink-mark on the glass, 'covering' the object as seen by the eye which is momentarily open. On looking now with both eyes the ink-marks will seem single, and in the same direction as the objective point. Conversely, let the eyes converge on a single ink-spot on the glass, and then by alternate shutting of them let it be noted what objects behind the glass the spot covers to the right and left eye respectively. Now with both eyes open, both these objects and the spot will appear in the same place, one or other of the three becoming more distinct according to the fluctuations of retinal attention.[217] Now what is the direction of this common place? The only way of defining the direction of an object is by _pointing to it_. Most people, if asked to look at an object over the horizontal edge of a sheet of paper which conceals their hand and arm, and then to point their finger at it (raising the hand gradually so that at last a finger-tip will appear above the sheet of paper), are found to place the finger not between either eye and the object, but between the latter and the root of the nose, and this whether both eyes or either alone be used. Hering and Helmholtz express this by saying that we judge of the direction of objects as they would appear to an imaginary cyclopean eye, situated between our two real eyes, and with its optical axis bisecting the angle of convergence of the latter. Our two retinæ act, according to Hering, as if they were superposed in the place of this imaginary double-eye; we see by the corresponding points of each, situated far asunder as they really are, just as we _should_ see if they were superposed and could both be excited together.
The judgment of objective singleness and that of identical direction seem to hang necessarily together. And that of identical direction seems to carry with it the necessity of a common origin, between the eyes or elsewhere, from which all the directions felt may seem to be estimated. This is why the cyclopean eye is really a fundamental part of the formulation of the theory of identical retinal points, and why Hering, the greatest champion of this theory, lays so much stress upon it.
_It is an immediate consequence of the law of identical_ _projection of images on geometrically similar points that images which fall upon geometrically_ DISPARATE _points of the two retinæ should be projected in_ DISPARATE _directions, and that their objects should consequently appear in_ TWO _places, or_ LOOK DOUBLE. Take the parallel rays from a star falling upon two eyes which converge upon a near object, O, instead of being parallel, as in the previously instanced case. If SL and SR in Fig. 55 be the parallel rays, each of them will fall upon the nasal half of the retina which it strikes.
But the two nasal halves are disparate, geometrically _symmetrical_, not geometrically _similar_. The image on the left one will therefore appear as if lying in a direction leftward of the cyclopean eye's line of sight; the image of the right one will appear far to the right of the same direction. The star will, in short, be seen double,--'homonymously' double.
Conversely, if the star be looked at directly with parallel axes, O will be seen double, because its images will affect the outer or cheek halves of the two retinæ, instead of one outer and one nasal half. The position of the images will here be reversed from that of the previous case. The right eye's image will now appear to the left, the left eye's to the right--the double images will be 'heteronymous.'
The same reasoning and the same result ought to apply where the object's place with respect to the direction of the two optic axes is such as to make its images fall not on non-similar retinal halves, but on non-similar parts of similar halves. Here, of course, the directions of projection will be less widely disparate than in the other case, and the double images will appear to lie less widely apart.
Careful experiments made by many observers according to the so-called haploscopic method confirm this law, and show that _corresponding points, of single visual direction,_ exist upon the two retinæ. For the detail of these one must consult the special treatises.
Note now an important consequence. If we take a stationary object and allow the eyes to vary their direction and convergence, a purely geometrical study will show that there will be some positions in which its two images impress corresponding retinal points, but more in which they impress disparate points. The former constitute the so-called horopter, and their discovery has been attended with great mathematical difficulty. Objects or parts of objects which lie in the eyes' horopter at any given time cannot appear double. _Objects lying out of the horopter would seem, if the theory of identical points were strictly true, necessarily and always to appear double._ Here comes the first great conflict of the identity-theory with experience. Were the theory true, we ought all to have an intuitive knowledge of the horopter as the line of distinctest vision. Objects placed elsewhere ought to seem, if not actually double, at least blurred. And yet no living man makes any such distinction between the parts of his field of vision. To most of us the whole field appears single, and it is only by rare accident or by special education that we ever catch a glimpse of a double image. In 1838, Wheatstone, in his truly classical memoir on binocular vision and the stereoscope,[218] showed that the disparateness of the points on which the two images of an object fall does not within certain limits affect its seen singleness at all, but rather the _distance_ at which it shall appear. Wheatstone made an observation, moreover, which subsequently became the bone of much hot contention, in which he strove to show that not only might disparate images fuse, but images on corresponding or identical points might be seen double.[219] I am unfortunately prevented by the weakness of my own eyes from experimenting enough to form a decided personal opinion on the matter. It seems to me, however, that the balance of evidence is against the Wheatstonian interpretation, and that disparate points may fuse, without identical points for that reason ever giving double images. The two questions, "Can we see single with disparate points?" and "Can we see double with identical points?" although at the first blush they may appear, as to Helmholtz they appear, to be but two modes of expressing the same inquiry, are in reality distinct. The first may quite well be answered affirmatively and the second negatively.
Add to this that the experiment quoted from Helmholtz above by no means always succeeds, but that many individuals place their finger between the object and _one_ of their eyes, oftenest the right;[220] finally, observe that the identity-theory, with its Cyclopean starting point for all lines of direction, gives by itself no ground for the _distance_ on any line at which an object shall appear, and has to be helped out in this respect by subsidiary hypotheses, which, in the hands of Hering and others, have become so complex as easily to fall a prey to critical attacks; and it will soon seem as if _the law of identical seen directions by corresponding points, although a simple formula for expressing concisely many fundamental phenomena, is by no means an adequate account of the whole matter of retinal perception._[221] Does the theory of projection fare any better? This theory admits that each eye sees the object in a different direction from the other, along the line, namely, passing from the object through the middle of the pupil to the retina. A point directly fixated is thus seen on the optical axes of both eyes. There is only one point, however, which these two optical axes have in common, and that is the point to which they converge. Everything directly looked at is seen at this point, and is thus seen both single and at its proper distance. It is easy to show the incompatibility of this theory with the theory of identity. Take an objective point (like O in Fig. 50, when the star is looked at) casting its images R' and L' on geometrically dissimilar parts of the two retinæ and affecting the outer half of each eye. On the identity-theory it ought necessarily to appear double, whilst on the projection-theory there is no reason whatever why it should not appear single, provided only it be located by the judgment on each line of visible direction, neither nearer nor farther than its point of intersection with the other line.
_Every point in the field of view ought, in truth, if the projection-theory were uniformly valid, to appear single,_ entirely irrespective of the varying positions of the eyes, for from every point of space two lines of visible direction pass to the two retinæ; and at the intersection of these lines, or just where the point is, there, according to the theory, it should appear. _The objection to this theory is thus precisely the reverse of the objection to the identity-theory. If the latter ruled, we ought to see most things double all the time. If the projection-theory ruled, we ought never to see anything double. As a matter of fact we get too few double images for the identity-theory, and too many for the projection-theory._ The partisans of the projection-theory, beginning with Aguilonius, have always explained double images as the result of an erroneous judgment of the _distance_ of the object, the images of the latter being projected by the imagination along the two lines of visible direction either nearer or farther than the point of intersection of the latter. A diagram will make this clear.