hundred wise men together could not answer. You have heard, so far, only
five of these wise men. You will certainly want to be spared the
opinions of the other ninety-five. To the first you will reply that we
should look just as pretty if we were born with only one eye, like the
Cyclops; to the second we should be much better off, according to his
principle, if we had four or eight eyes, and that in this respect we are
vastly inferior to spiders; to the third, that you are not just in the
mood to weep; to the fourth, that the unqualified interdiction of the
question excites rather than satisfies your curiosity; while of me you
will dispose by saying that my pleasure is not as intense as I think,
and certainly not great enough to justify the existence of a double eye
in man since the fall of Adam.
But since you are not satisfied with my brief and obvious answer, you
have only yourselves to blame for the consequences. You must now listen
to a longer and more learned explanation, such as it is in my power to
give.
As the church of science, however, debars the question "Why?" let us put
the matter in a purely orthodox way: Man has two eyes, what _more_ can
he see with two than with one?
I will invite you to take a walk with me? We see before us a wood. What
is it that makes this real wood contrast so favorably with a painted
wood, no matter how perfect the painting may be? What makes the one so
much more lovely than the other? Is it the vividness of the coloring,
the distribution of the lights and the shadows? I think not. On the
contrary, it seems to me that in this respect painting can accomplish
very much.
The cunning hand of the painter can conjure up with a few strokes of his
brush forms of wonderful plasticity. By the help of other means even
more can be attained. Photographs of reliefs are so plastic that we
often imagine we can actually lay hold of the elevations and
depressions.
[Illustration: Fig. 20.]
But one thing the painter never can give with the vividness that nature
does--the difference of near and far. In the real woods you see plainly
that you can lay hold of some trees, but that others are inaccessibly
far. The picture of the painter is rigid. The picture of the real woods
changes on the slightest movement. Now this branch is hidden behind
that; now that behind this. The trees are alternately visible and
invisible.
Let us look at this matter a little more closely. For convenience sake
we shall remain upon the highway, I, II. (Fig. 20.) To the right and the
left lies the forest. Standing at I, we see, let us say, three trees (1,
2, 3) in a line, so that the two remote ones are covered by the nearest.
Moving further along, this changes. At II we shall not have to look
round so far to see the remotest tree 3 as to see the nearer tree 2, nor
so far to see this as to see 1. _Hence, as we move onward, objects that
are near to us seem to lag behind as compared with objects that are
remote from us, the lagging increasing with the proximity of the
objects._ Very remote objects, towards which we must always look in the
same direction as we proceed, appear to travel along with us.
If we should see, therefore, jutting above the brow of yonder hill the
tops of two trees whose distance from us we were in doubt about, we
should have in our hands a very easy means of deciding the question. We
should take a few steps forward, say to the right, and the tree-top
which receded most to the left would be the one nearer to us. In truth,
from the amount of the recession a geometer could actually determine the
distance of the trees from us without ever going near them. It is simply
the scientific development of this perception that enables us to
measure the distances of the stars.
_Hence, from change of view in forward motion the distances of objects
in our field of vision can be measured._
Rigorously, however, even forward motion is not necessary. For every
observer is composed really of _two_ observers. Man has _two_ eyes. The
right eye is a short step ahead of the left eye in the right-hand
direction. Hence, the two eyes receive _different_ pictures of the same
woods. The right eye will see the near trees displaced to the left, and
the left eye will see them displaced to the right, the displacement
being greater, the greater the proximity. This difference is sufficient
for forming ideas of distance.
We may now readily convince ourselves of the following facts:
1. With one eye, the other being shut, you have a very uncertain
judgment of distances. You will find it, for example, no easy task, with
one eye shut, to thrust a stick through a ring hung up before you; you
will miss the ring in almost every instance.
2. You see the same object differently with the right eye from what you
do with the left.
Place a lamp-shade on the table in front of you with its broad opening
turned downwards, and look at it from above. (Fig. 21.) You will see
with your right eye the image 2, with your left eye the image 1. Again,
place the shade with its wide opening turned upwards; you will receive
with your right eye the image 4, with your left eye the image 3. Euclid
mentions phenomena of this character.
3. Finally, you know that it is easy to judge of distances with both
eyes. Accordingly your judgment must spring in some way from a
co-operation of the two eyes. In the preceding example the openings in
the different images received by the two eyes seem displaced with
respect to one another, and this displacement is sufficient for the
inference that the one opening is nearer than the other.
[Illustration: Fig. 21.]
I have no doubt that you, ladies, have frequently received delicate
compliments upon your eyes, but I feel sure that no one has ever told
you, and I know not whether it will flatter you, that you have in your
eyes, be they blue or black, little geometricians. You say you know
nothing of them? Well, for that matter, neither do I. But the facts are
as I tell you.
You understand little of geometry? I shall accept that confession. Yet
with the help of your two eyes you judge of distances? Surely that is a
geometrical problem. And what is more, you know the solution of this
problem: for you estimate distances correctly. If, then, _you_ do not
solve the problem, the little geometricians in your eyes must do it
clandestinely and whisper the solution to you. I doubt not they are
fleet little fellows.
What amazes me most here is, that you know nothing about these little
geometricians. But perhaps they also know nothing about you. Perhaps
they are models of punctuality, routine clerks who bother about nothing
but their fixed work. In that case we may be able to deceive the
gentlemen.
If we present to our right eye an image which looks exactly like the
lamp-shade for the right eye, and to our left eye an image which looks
exactly like a lamp-shade for the left eye, we shall imagine that we see
the whole lamp-shade bodily before us.
You know the experiment. If you are practised in squinting, you can
perform it directly with the figure, looking with your right eye at the
right image, and with your left eye at the left image. In this way the
experiment was first performed by Elliott. Improved and perfected, its
form is Wheatstone's stereoscope, made so popular and useful by
Brewster.
By taking two photographs of the same object from two different points,
corresponding to the two eyes, a very clear three-dimensional picture of
distant places or buildings can be produced by the stereoscope.
But the stereoscope accomplishes still more than this. It can visualise
things for us which we never see with equal clearness in real objects.
You know that if you move much while your photograph is being taken,
your picture will come out like that of a Hindu deity, with several
heads or several arms, which, at the spaces where they overlap, show
forth with equal distinctness, so that we seem to see the one picture
_through_ the other. If a person moves quickly away from the camera
before the impression is completed, the objects behind him will also be
imprinted upon the photograph; the person will look transparent.
Photographic ghosts are made in this way.
Some very useful applications may be made of this discovery. For
example, if we photograph a machine stereoscopically, successively
removing during the operation the single parts (where of course the
impression suffers interruptions), we obtain a transparent view, endowed
with all the marks of spatial solidity, in which is distinctly
visualised the interaction of parts normally concealed. I have employed
this method for obtaining transparent stereoscopic views of anatomical
structures.
You see, photography is making stupendous advances, and there is great
danger that in time some malicious artist will photograph his innocent
patrons with solid views of their most secret thoughts and emotions. How
tranquil politics will then be! What rich harvests our detective force
will reap!
* * * * *
By the joint action of the two eyes, therefore, we arrive at our
judgments of distances, as also of the forms of bodies.
Permit me to mention here a few additional facts connected with this
subject, which will assist us in the comprehension of certain phenomena
in the history of civilisation.
You have often heard, and know from personal experience, that remote
objects appear perspectively dwarfed. In fact, it is easy to satisfy
yourself that you can cover the image of a man a few feet away from you
simply by holding up your finger a short distance in front of your eye.
Still, as a general rule, you do not notice this shrinkage of objects.
On the contrary, you imagine you see a man at the end of a large hall,
as large as you see him near by you. For your eye, in its measurement of
the distances, makes remote objects correspondingly larger. The eye, so
to speak, is aware of this perspective contraction and is not deceived
by it, although its possessor is unconscious of the fact. All persons
who have attempted to draw from nature have vividly felt the difficulty
which this superior dexterity of the eye causes the perspective
conception. Not until one's judgment of distances is made uncertain, by
their size, or from lack of points of reference, or from being too
quickly changed, is the perspective rendered very prominent.
On sweeping round a curve on a rapidly moving railway train, where a
wide prospect is suddenly opened up, the men upon distant hills appear
like dolls.[17] You have at the moment, here, no known references for
the measurement of distances. The stones at the entrance of a tunnel
grow visibly larger as we ride towards it; they shrink visibly in size
as we ride from it.
Usually both eyes work together. As certain views are frequently
repeated, and lead always to substantially the same judgments of
distances, the eyes in time must acquire a special skill in geometrical
constructions. In the end, undoubtedly, this skill is so increased that
a single eye alone is often tempted to exercise that office.
Permit me to elucidate this point by an example. Is any sight more
familiar to you than that of a vista down a long street? Who has not
looked with hopeful eyes time and again into a street and measured its
depth. I will take you now into an art-gallery where I will suppose you
to see a picture representing a vista into a street. The artist has not
spared his rulers to get his perspective perfect. The geometrician in
your left eye thinks, "Ah ha! I have computed that case a hundred times
or more. I know it by heart. It is a vista into a street," he continues;
"where the houses are lower is the remote end." The geometrician in the
right eye, too much at his ease to question his possibly peevish comrade
in the matter, answers the same. But the sense of duty of these punctual
little fellows is at once rearoused. They set to work at their
calculations and immediately find that all the points of the picture are
equally distant from them, that is, lie all upon a plane surface.
What opinion will you now accept, the first or the second? If you accept
the first you will see distinctly the vista. If you accept the second
you will see nothing but a painted sheet of distorted images.
It seems to you a trifling matter to look at a picture and understand
its perspective. Yet centuries elapsed before humanity came fully to
appreciate this trifle, and even the majority of you first learned it
from education.
I can remember very distinctly that at three years of age all
perspective drawings appeared to me as gross caricatures of objects. I
could not understand why artists made tables so broad at one end and so
narrow at the other. Real tables seemed to me just as broad at one end
as at the other, because my eye made and interpreted its calculations
without my intervention. But that the picture of the table on the plane
surface was not to be conceived as a plane painted surface but stood for
a table and so was to be imaged with all the attributes of extension was
a joke that I did not understand. But I have the consolation that whole
nations have not understood it.
Ingenuous people there are who take the mock murders of the stage for
real murders, the dissembled actions of the players for real actions,
and who can scarcely restrain themselves, when the characters of the
play are sorely pressed, from running in deep indignation to their
assistance. Others, again, can never forget that the beautiful
landscapes of the stage are painted, that Richard III. is only the
actor, Mr. Booth, whom they have met time and again at the clubs.
Both points of view are equally mistaken. To look at a drama or a
picture properly one must understand that both are _shows_, simply
_denoting_ something real. A certain preponderance of the intellectual
life over the sensuous life is requisite for such an achievement, where
the intellectual elements are safe from destruction by the direct
sensuous impressions. A certain liberty in choosing one's point of view
is necessary, a sort of humor, I might say, which is strongly wanting in
children and in childlike peoples.
Let us look at a few historical facts. I shall not take you as far back
as the stone age, although we possess sketches from this epoch which
show very original ideas of perspective. But let us begin our
sight-seeing in the tombs and ruined temples of ancient Egypt, where the
numberless reliefs and gorgeous colorings have defied the ravages of
thousands of years.
A rich and motley life is here opened to us. We find the Egyptians
represented in all conditions of life. What at once strikes our
attention in these pictures is the delicacy of their technical
execution. The contours are extremely exact and distinct. But on the
other hand only a few bright colors are found, unblended and without
trace of transition. Shadows are totally wanting. The paint is laid on
the surfaces in equal thicknesses.
Shocking for the modern eye is the perspective. All the figures are
equally large, with the exception of the king, whose form is unduly
exaggerated. Near and far appear equally large. Perspective contraction
is nowhere employed. A pond with water-fowl is represented flat, as if
its surface were vertical.
Human figures are portrayed as they are never seen, the legs from the
side, the face in profile. The breast lies in its full breadth across
the plane of representation. The heads of cattle appear in profile,
while the horns lie in the plane of the drawing. The principle which the
Egyptians followed might be best expressed by saying that their figures
are pressed in the plane of the drawing as plants are pressed in a
herbarium.
The matter is simply explained. If the Egyptians were accustomed to
looking at things ingenuously with both eyes at once, the construction
of perspective pictures in space could not be familiar to them. They saw
all arms, all legs on real men in their natural lengths. The figures
pressed into the planes resembled more closely, of course, in their eyes
the originals than perspective pictures could.
This will be better understood if we reflect that painting was developed
from relief. The minor dissimilarities between the pressed figures and
the originals must gradually have compelled men to the adoption of
perspective drawing. But physiologically the painting of the Egyptians
is just as much justified as the drawings of our children are.
A slight advance beyond the Egyptians is shown by the Assyrians. The
reliefs rescued from the ruined mounds of Nimrod at Mossul are, upon the
whole, similar to the Egyptian reliefs. They were made known to us
principally by Layard.
Painting enters on a new phase among the Chinese. This people have a
marked feeling for perspective and correct shading, yet without being
very logical in the application of their principles. Here, too, it
seems, they took the first step but did not go far. In harmony with this
immobility is their constitution, in which the muzzle and the bamboo-rod
play significant functions. In accord with it, too, is their language,
which like the language of children has not yet developed into a
grammar, or, rather, according to the modern conception, has not yet
degenerated into a grammar. It is the same also with their music which
is satisfied with the five-toned scale.
The mural paintings at Herculaneum and Pompeii are distinguished by
grace of representation, as also by a pronounced sense for perspective
and correct illumination, yet they are not at all scrupulous in
construction. Here still we find abbreviations avoided. But to offset
this defect, the members of the body are brought into unnatural
positions, in which they appear in their full lengths. Abridgements are
more frequently observed in clothed than in unclothed figures.
A satisfactory explanation of these phenomena first occurred to me on
the making of a few simple experiments which show how differently one
may see the same object, after some mastery of one's senses has been
attained, simply by the arbitrary movement of the attention.
[Illustration: Fig. 22.]
Look at the annexed drawing (Fig. 22). It represents a folded sheet of
paper with either its depressed or its elevated side turned towards you,
as you wish. You can conceive the drawing in either sense, and in either
case it will appear to you differently.
If, now, you have a real folded sheet of paper on the table before you,
with its sharp edges turned towards you, you can, on looking at it with
one eye, see the sheet alternately elevated, as it really is, or
depressed. Here, however, a remarkable phenomenon is presented. When you
see the sheet properly, neither illumination nor form presents anything
conspicuous. When you see it bent back you see it perspectively
distorted. Light and shadow appear much brighter or darker, or as if
overlaid thickly with bright colors. Light and shadow now appear devoid
of all cause. They no longer harmonise with the body's form, and are
thus rendered much more prominent.
In common life we employ the perspective and illumination of objects to
determine their forms and position. Hence we do not notice the lights,
the shadows, and the distortions. They first powerfully enter
consciousness when we employ a different construction from the usual
spatial one. In looking at the planar image of a camera obscura we are
amazed at the plenitude of the light and the profundity of the shadows,
both of which we do not notice in real objects.
In my earliest youth the shadows and lights on pictures appeared to me
as spots void of meaning. When I began to draw I regarded shading as a
mere custom of artists. I once drew the portrait of our pastor, a friend
of the family, and shaded, from no necessity, but simply from having
seen something similar in other pictures, the whole half of his face
black. I was subjected for this to a severe criticism on the part of my
mother, and my deeply offended artist's pride is probably the reason
that these facts remained so strongly impressed upon my memory.
You see, then, that many strange things, not only in the life of
individuals, but also in that of humanity, and in the history of general
civilisation, may be explained from the simple fact that man has two
eyes.
Change man's eye and you change his conception of the world. We have
observed the truth of this fact among our nearest kin, the Egyptians,
the Chinese, and the lake-dwellers; how must it be among some of our
remoter relatives,--with monkeys and other animals? Nature must appear
totally different to animals equipped with substantially different eyes
from those of men, as, for example, to insects. But for the present
science must forego the pleasure of portraying this appearance, as we
know very little as yet of the mode of operation of these organs.
It is an enigma even how nature appears to animals closely related to
man; as to birds, who see scarcely anything with two eyes at once, but
since their eyes are placed on opposite sides of their heads, have a
separate field of vision for each.[18]
The soul of man is pent up in the prison-house of his head; it looks at
nature through its two windows, the eyes. It would also fain know how
nature looks through other windows. A desire apparently never to be
fulfilled. But our love for nature is inventive, and here, too, much has
been accomplished.
Placing before me an angular mirror, consisting of two plane mirrors
slightly inclined to each other, I see my face twice reflected. In the
right-hand mirror I obtain a view of the right side, and in the
left-hand mirror a view of the left side, of my face. Also I shall see
the face of a person standing in front of me, more to the right with my
right eye, more to the left with my left. But in order to obtain such
widely different views of a face as those shown in the angular mirror,
my two eyes would have to be set much further apart from each other than
they actually are.
[Illustration: Fig. 23.]
Squinting with my right eye at the image in the right-hand mirror, with
my left eye at the image in the left-hand mirror, my vision will be the
vision of a giant having an enormous head with his two eyes set far
apart. This, also, is the impression which my own face makes upon me. I
see it now, single and solid. Fixing my gaze, the relief from second to
second is magnified, the eyebrows start forth prominently from above the
eyes, the nose seems to grow a foot in length, my mustache shoots forth
like a fountain from my lip, the teeth seem to retreat immeasurably. But
by far the most horrible aspect of the phenomenon is the nose.
Interesting in this connexion is the telestereoscope of Helmholtz. In
the telestereoscope we view a landscape by looking with our right eye
(Fig. 24) through the mirror _a_ into the mirror _A_, and with our left
eye through the mirror _b_ into the mirror _B_. The mirrors _A_ and _B_
stand far apart. Again we see with the widely separated eyes of a giant.
Everything appears dwarfed and near us. The distant mountains look like
moss-covered stones at our feet. Between, you see the reduced model of a
city, a veritable Liliput. You are tempted almost to stroke with your
hand the soft forest and city, did you not fear that you might prick
your fingers on the sharp, needle-shaped steeples, or that they might
crackle and break off.
[Illustration: Fig. 24.]
Liliput is no fable. We need only Swift's eyes, the telestereoscope, to
see it.