The Principles of Psychology, Vols. 1-2

A certain maximum distance-value, however, being given to the field of view of the moment, whatever it be, the feelings that accompany the processes just enumerated become so many local signs of the gradation of distances within this maximum depth. They help us to subdivide and measure it. Itself, however, is felt as a unit, a total distance-value, determining the vastness of the whole field of view, which accordingly appears as an abyss of a certain volume. And the question still persists, what neural process is it that underlies the sense of this distance-value ?

Hering, who has tried to explain the gradations within it by the interaction of certain native distance-values belonging to each point of the two retinae, seems willing to admit that the absolute scale of the space-volume within which the natively fixed relative distances shall appear is not fixed, but determined each time by 'experience in the widest sense of the word ' (Beitrdge, p. 344). What he calls the Kernpunkt of this space-volume is the point we are momentarily fixating. The absolute scale of the whole volume depends on the absolute distance at which this Kernpunkt is judged to lie from the person of the looker. " By an alteration of the localization of the Kernpunkt, the inner relations of the seen space are nowise altered ; this space in its totality is as a fixed unit, so to speak, displaced with re-

Let us begin the long and rather tedious inquiry by tho most important case. Physiologists have long sought for spect to the self of the looker" (p. 345). But what constitutes the localization of the Kernpunkt itself at any given time, except ' Experience,' i.e., higher cerebral and intellectual processes, involving memory, Hering does not seek to define. Stumpf, the other sensationalist writer who has best realized the difficulties of the problem, thinks that the primitive sensation of distance must have an immediate physical antecedent, either in the shape of "an organic alteration accompanying the process of accommodation, or else given directly in the specific energy of the optic nerve. " In contrast with Hering, however, he thinks that it is the absolute distance of the spot fixated which is thus primitively, immediately, and physiologically given, and not the relative distances of other things about this spot. These, he thinks, are originally seen in what, broadly speaking, may be termed one plane with it. Whether the distance of this plane, considered as a phenomenon of our primitive sensibility, be an invariable datum, or susceptible of fluctuation, he does not, if I understand him rightly, undertake dogmatically to decide, but inclines to the former view. For him then, as for Hering, higher cerebral processes of association, under the name of 'Experience,' are the authors of fully one-half part of the distance-perceptions which we at any given time may have.

Hering's and Stumpf 's theories are reported for the English reader by Mr. Sully (in Mind, iii. pp. 172-6). Mr. Abbott, in his Sight and Touch (pp. 96-8), gives a theory which is to me so obscure that I only refer the reader to its place, adding that it seems to make of distance a fixed function of retinal sensation as modified by focal adjustment. Besides these three authors I am ignorant of any, except Panum, who may have attempted to define distance as in any degree an immediate sensation. And with them the direct sensational share is reduced to a very small proportional part, in our completed distance-judgments.

Professor Lipps, in his singularly acute Psychologische Studien (p. 69 ff.),argues, as Ferrier, in his review of Berkeley (Philosophical Remains, ii. 330 ff.), had argued before him, that it is logically impossible we should perceive the distance of anything from the eye by sight; for & seen distance can only be between seen termini ; and one of the termini, in the case of distance from the eye, is the eye itself, which is not seen. Similarly of the distance of two points behind each other : the near one hides the far one, no space is seen between them. For the space between two objects to he seen, both must appear beside each other, then the space in question will be visible. On no other condition is its visibility possible. The conclusion is that things can properly be seen only in what Lipps calls a surface, and that our knowledge of the third dimension must needs be conceptual, not sensational or visually intuitive.

But no arguments in the world can prove a feeling which actually exists to be impossible. The feeling of depth or distance, of farness oi awayness, does actually exist as a fact of our visual sensibility. All that Professor Lipps's reasonings prove concerning it is that it is not linear iu 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.

This theory starts from the truth that on both retinas 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 ? whole to the similar quadrant of its character, or in its immediacy fully homogeneous and consubstantial with the feeling of literal distance between two seen termini ; in short, ;.hat there are two sorts of optical sensation, each inexplicably due to a peculiar neural process. The neural process is easily discovered, in the case of lateral extension or spreadoutness, to be the number of retinal nerve-ends affected by the light ; in the case of pretension or mere farness it is more complicated and, as we have concluded, is still to seek. The two sensible qualities unite in the primitive visual bigness. The measurement of their various amounts against each other obeys the general laws of all such measurements. We discover their equivalencies by means of objects, apply the same units to both, and translate them into each other so habitually that at last they get to seem to us even quite similar in kind. This final appearance of homogeneity may perhaps be facilitated by the fact that in binocular vision two points situated on the prolongation of the optical axis of one of the eyes, so that the near one hides the far one, are by the other eye seen laterally apart. Each eye has in fact a foreshortened lateral view of the other's line of sight. In The London Times for Feb. 8, 1884, is an interesting letter by J. D. Dougal, who tries to explain by thia reason why two-eyed rifle-shootmg has such adv«jitages over shooting witb one eye closed.

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.* 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-

* Just so, a pair of spectacles held an inch or so from the eyes seem like one large median glass. The faculty of seeing stereoscopic slides single without an instrument is of the utmost utility to the student of physiological optics, and persons with strong eyes can easily acquire it. The only difficulty lies in dissociating the degree of accommodation from the degree of convergence which it usually accompanies. If the right picture is focussed by the right eye, the left by the left eye, the optic axes must either be parallel or converge upon an imaginary point some distance behind the plane of the pictures, according to the size and distance apart of the pictures. The accommodation, however, has to be made for the plane of the pictures itself, and a near accommodation with a far-oJQE convergence is something which the ordinary use of our eyes never teaches us to effect.

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.* 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 e-xpress 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 retinae 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.

* These two observations prove the law of identical direction only for objects which excite the foveae or lie in the line of direct looking. Ob- servers skilled in indirect vision can, however, more or less easily verify the law for outlying retinal points. jection of images on geometricoEy similar points that images which fall upon geoinetrically dispaeate pom^5 of the two retince should be projected in dispaeate directions^ and that their objects should consequently appear in two plaxjes, or look double. Take the parallel rays from a star falling upon two eyes which converge upon a near object, 0, 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 retinae, 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 nonsimilar 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 retinae. 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 tvouM 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,* showed that the disparateness of the

* This essay, published in the Philosophical TraDsactions, contains the germ of almost all the methods applied since to the study of optical perception. It seems a pity that England, leading off so brilliantly the modem 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.*

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 ;t finally, observe that the epoch of this study, should so quickly have dropped out of the field. Almost all subsequent progress has been made in Germany, Holland, and, longo intervallo, America. * This is no place to report this controversy, but a few bibliographic references may not be inappropriate. Wheatstone's own experiment is in section 12 of his memoir. In favor of hig interpretation see Helmholtz, Phys. Opt.,pp. 737-9; Wundt, Physiol. Psychol . 2teAufl. p. 144; Nagel, Sehen mit zwei Augen, pp. 78-82. Against Wheatstone see Volkmann, Arch. f. Ophth., v. 2-74. and Untersuchungen, p. 266 ; Bering, Beitragezui Physiologic, 29-45, also in Hermann's Hdbch. d Physiol., Bd. iii. 1 Th. p. 435 ; Aubert, Physiologic d Netzhaut, p. 322 ; SchSn, Archiv f. Ophthal., XXIV. 1. pp. 56-65 ; and Donders, iMd. xiii 1. p. 15 and note.

f When we see the finger the whole time, we usually put it in the line joining object and left eye if it be the left finger, joining object and right eye if it be the right finger. Microscopists, marksmen, or persons one of whose eyes is much better than the other, almost always refer directions to a single eye, as may be seen by the position of the shadow on their face when they point at a candle-flame. 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 f although a simple formula for expressing corwisely many fundamental phenomena^ is by no means an adequate account of the whole matter of retinxd perception."^

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 W and L' on geometrically dissimilar parts of the two retinae 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 direc-

* Professor Joseph Le Conte, who believes strongly in the identitytheory, has embodied the latter in a pair of laws of the relation between positions seen single and double, near or far, on the one hand, and convergences and retinal impressions, on the other, which, though complicated, seems to me by far the best descriptive formulation yet made of the normal facts of vision. His account is easily accessible to the reader in his volume * Sight ' in the International Scientific Series, bk. ii. c. 3, so I say no more about it now, except that it does not solve any of the diflaculties we are noting in the identity-theory, nor account for the other fluctuating perceptions of which we go on to treat.

tion, neither nearer nor farther than its point of intersection with the other line. Every point in the JIM 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 retinae ; 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, ice ought never to sec anything double. As a matter of fact we get too few double images for the identity-theory, and too many for the projection-theory.

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. Let 0 be the point looked at, M an object farther, and N an object nearer, than it. Then M and N will send the lines of visible direction MM and NN to the two retinae. If N be judged as far as O, it must necessarily lie where the two lines of visible direction NN intersect the plane of the arrow, or in two places, at W and at W. If M be judged as near as O, it must for the same reason form two images at M' and M''.

It is, as a matter of fact, true that we often misjudge the distance in the way alleged. If the reader will hold his forefingers, one beyond the other, in the median line, and fixate them alternately, he will see the one not looked at, double ; and he will also notice that it appears nearer to the plane of the one looked at, whichever the latter may be, than it really is. Its changes of apparent size, as the convergence of the eyes alter, also prove the change of apparent distance. The distance at which the axes converge seems, in fact, to exert a sort of attraction upon objects situated elsewhere. Being the distance of which we are most acutely sensible, it invades, so to speak, the whole field of our perception. If two half-dollars be laid on the table an inch or two apart, and the eyes fixate steadily the point of a pen held in the median line at varying distances between the coins and the face, there will come a distance at which the pen stands between the left halfdollar and the right eye, and the right half-dollar and the left eye. The two half-dollars will then coalesce into one ; and this one will show its apparent approach to the penpoint by seeming suddenly much reduced in size."^

Yet, in spite of this tendency to inaccuracy, we are never actually mistaken about the half-dollar being behind the pen-point. It may not seem far enough off, but still it is farther than the point. In general it may be said that where the objects are known to us, no such illusion of distance occurs in any one as the theory would require. And in some observers, Hering for example, it seems hardly to occur at all. If I look into infinite distance and get my finger in double images, they do not seem infinitely far off.

* Naturally it takes a smaller object at a less distance to cover by its image a constant amount of retinal surface. To make objects at different distances seem equidistant, careful precautions must be taken to have them alike in appearance, and to exclude all outward reasons for ascribing to the one a different location from that ascribed to the other. Thus Donders tries to prove the law of projection by taking two similar electric sparks, one behind the other on a dark ground, one seen double ; or an iron rod placed so near to the eyes that its double images seem as broad as that of a fixated stove-pipe, the top and bottom of the objects being cut off by screens, so as to prevent all suggestions of perspective, etc. The three objects in each experiment seem in the same plane.*

Add to this the impossibility, recognized by all observers, of ever seeing double with the/oveoe, and the fact that authorities as able as those quoted in the note on Wheatstone's observation deny that they can see double then with identical points, and we are forced to conclude that the projection-theory f like its predecessor, breaks doion. Neither formulates exactly or exhaustively a law for all our perceptions. What does each theory try to do ? To make of seen location a fixed funxition of retinal impression. Other facts may be

brought forward to show how far from fixed are the perceptive functions of retinal impressions. We alluded a while ago to the extraordinary ambiguity of the retinal image as a revealer of magnitude. Produce an after-image of the sun and look at your finger-tip : it will be smaller than your nail. Project it on the table, and it will be as big as a strawberry ; on the wall, as large as a plate ; on yonder mountain, bigger than a house. And yet it is an unchanged