[Illustration: FIG. 4.--The black and white portions
of this design are precisely alike; but the effect of
looking at the figure as a pattern in black upon a
white background, or as a pattern in white upon a black
background is quite different, although the difference
is not easily described.]
There is a further interesting class of illustrations in which a
single outward impression changes its character according as it is
viewed as representing one thing or another. In a general way we see
the same thing all the time, and the image on the retina does not
change. But as we shift the attention from one portion of the view
to another, or as we view it with a different mental conception of
what the figure represents, it assumes a different aspect, and to our
mental eye becomes quite a different thing. A slight but interesting
change takes place if we view Fig. 4 first with the conception that
the black is the pattern to be seen and the white the background, and
again try to see the white as the pattern against a black background.
I give a further illustration of such a change in Fig. 5. In our
first and natural view of this we focus the attention upon the black
lines and observe the familiar illusion, that the four vertical black
bands seem far from parallel. That they are parallel can be verified
by measurement, or by covering up all of the diagram except the
four main bands. But if the white part of the diagram be conceived
as the design against a black background, then the design is no
longer the same, and with this change the illusion disappears, and
the four bands seem parallel, as they really are. It may require a
little effort to bring about this change, but it is marked when once
realized.
[Illustration: FIG. 5.--When this figure is viewed as
a black pattern on a white background, the four main
vertical black bands seem far from parallel; when it
is viewed as a white pattern on a black background the
pattern is different and the illusion disappears (or
nearly so), and the four black bands as well as the
five white ones seem more nearly parallel.]
A curious optical effect, which in part illustrates the change in
appearance under different aspects, is reproduced in Fig. 6. In
this case the enchantment of distance is necessary to produce the
transformation. Viewed at the usual reading distance, we see nothing
but an irregular and meaningless assemblage of black and white
blotches. At a distance of not less than fifteen to eighteen feet,
however, a man's head appears quite clearly. Also observe that
after the head has once been realized it becomes possible to obtain
suggestions of it at nearer distances.
[Illustration: FIG. 6.--This is a highly enlarged
reproduction taken from a half-tone process print of
Lord Kelvin. It appeared in the _Photographic Times_.]
A much larger class of ambiguous diagrams consists of those which
represent by simple outlines familiar geometrical forms or objects.
We cultivate such a use of our eyes, as indeed of all our faculties,
as will on the whole lead to the most profitable results. As a rule,
the particular impression is not so important as what it represents.
Sense-impressions are simply the symbols or signs of things or
ideas, and the thing or the idea is more important than the sign.
Accordingly, we are accustomed to interpret lines, whenever we
can, as the representations of objects. We are well aware that the
canvas or the etching or the photograph before us is a flat surface
in two dimensions, but we see the picture as the representation of
solid objects in three dimensions. This is the illusion of pictorial
art. So strong is this tendency to view lines as the symbols of
things, that if there is the slightest chance of so viewing them, we
invariably do so; for we have a great deal of experience with things
that present their contours as lines, and very little with mere lines
or surfaces. If we view outlines only, without shading or perspective
or anything to definitely suggest what is foreground and what
background, it becomes possible for the mind to supply these details
and see foreground as background, and _vice versa_.
[Illustration: FIG. 7.--This drawing may be viewed
as the representation of a book standing on its
half-opened covers as seen from the back of the book;
or as the inside view of an open book showing the
pages.]
[Illustration: FIG. 8.--When this figure is viewed
as an arrow, the upper or feathered end is apt to
seem flat; when the rest of the arrow is covered, the
feathered end may be made to project or recede like the
book-cover in Fig. 7.]
[Illustration: FIG. 9.--The smaller square may be
regarded as either the nearer face of a projecting
figure or as the more distant face of a hollow figure.]
A good example to begin with is Fig. 7. These outlines will probably
suggest at first view a book, or better a book-cover, seen with its
back toward you and its sides sloping away from you; but it may also
be viewed as a book opened out towards you and presenting to you an
inside view of its contents. Should the change not come readily,
it may be facilitated by thinking persistently of the appearance
of an open book in this position. The upper portion of Fig. 8 is
practically the same as Fig. 7, and if the rest of the figure be
covered up, it will change as did the book cover; when, however, the
whole figure is viewed as an arrow, a new conception enters, and the
apparently solid book cover becomes the _flat_ feathered part of the
arrow. Look at the next figure (Fig. 9), which represents in outline
a truncated pyramid with a square base. Is the smaller square nearer
to you, and are the sides of the pyramid sloping away from you toward
the larger square in the rear? Or are you looking into the hollow
of a truncated pyramid with the smaller square in the background?
Or is it now one and now the other, according as you decide to see
it? Here (Fig. 12) is a skeleton box which you may conceive as made
of wires outlining the sides. Now the front, or side nearest to me,
seems directed downward and to the left; again, it has shifted its
position and is no longer the front, and the side which appears to be
the front seems directed upward and to the right. The presence of the
diagonal line makes the change more striking: in one position it runs
from the left-hand _rear_ upper corner to the right-hand _front_
lower corner; while in the other it connects the left-hand _front_
upper corner with the right-hand _rear_ lower corner.
[Illustration: FIG. 10.--This represents an ordinary
table-glass,--the bottom of the glass and the entire
rear side, except the upper portion, being seen through
the transparent nearer side, and the rear apparently
projecting above the front. But it fluctuates in
appearance between this and a view of the glass
in which the bottom is seen directly, partly from
underneath, the _whole_ of the rear side is seen
through the transparent front, and the front projects
above the back.]
[Illustration: FIG. 11.--In this scroll the left half
may at first seem concave and the right convex; it
then seems to roll or advance like a wave, and the
left seems convex and the right concave, as though the
trough of the wave had become the crest, and _vice
versa_.]
[Illustration: FIG. 12.
FIG. 12_a_.
FIG. 12_b_.
FIGS. 12, 12_a_, 12_b_.--The two methods of viewing Fig.
12 are described in the text. Figs. 12_a_ and 12_b_
are added to make clearer the two methods of viewing
Fig. 12. The heavier lines seem to represent the nearer
surface. Fig. 12_a_ more naturally suggests the nearer
surface of the box in a position downward and to the
left, and Fig. 12_b_ makes the nearer side seem to be
upward and to the right. But in spite of the heavier
outlines of the one surface, it may be made to shift
positions from foreground to background, although not
so readily as in Fig. 12.]
Fig. 14 will probably seem at first glimpse to be the view of a
flight of steps which one is about to ascend from right to left.
Imagine it, however, to be a view of the under side of a series
of steps; the view representing the structure of overhanging solid
masonwork seen from underneath. At first it may be difficult to see
it thus, because the view of steps which we are about to mount is a
more natural and frequent experience than the other; but by staring
at it with the intention of seeing it differently the transition will
come, and often quite unexpectedly.
[Illustration: FIG. 13.--Each member of this frieze
represents a relief ornament, applied upon the
background, which in cross-section would be an
isosceles triangle with a large obtuse angle, or a
space of similar shape hollowed out of the solid wood
or stone. In running the eye along the pattern, it
is interesting to observe how variously the patterns
fluctuate from one of these aspects to the other.]
[Illustration: FIG. 14.
FIG. 14_a_.
FIG. 14_b_.
FIGS. 14, 14_a_, and 14_b_.--The two views of Fig. 14
described in the text are brought out more clearly in
Figs. 14_a_ and 14_b_. The shaded portion tends to
be regarded as the nearer face. Fig. 14_a_ is more
apt to suggest the steps seen as we ascend them. Fig.
14_b_ seems to represent the hollowed-out structure
underneath the steps. But even with the shading the
dual interpretation is possible, though less obvious.]
[Illustration: FIG. 15.--This interesting figure (which
is reproduced with modifications from _Scripture:
The New Psychology_) is subject in a striking way
to interchanges between foreground and background.
Most persons find it difficult to maintain for any
considerable time either aspect of the blocks (these
aspects are described in the text); some can change
them at will, others must accept the changes as they
happen to come.]
The blocks in Fig. 15 are subject to a marked fluctuation. Now the
black surfaces represent the bottoms of the blocks, all pointing
downward and to the left, and now the black surfaces have changed
and have become the tops, pointing upward and to the right. For some
the changes come at will; for others they seem to come unexpectedly,
but all are aided by anticipating mentally the nature of the
transformation. The effect here is quite striking, the blocks seeming
almost animated and moving through space. In Fig. 16 a similar
arrangement serves to create an illusion as to the real number of
blocks present. If viewed in one way--the black surface forming the
tops of the blocks--there seem to be six, arranged as in Fig. 17;
but when the transformation has taken place and the black surfaces
have become the overhanging bottoms of the boxes, there are seven,
arranged as in Fig. 18. Somewhat different, but still belonging to
the group of ambiguous figures, is the ingenious conceit of the
duck-rabbit shown in Fig. 19. When it is a rabbit, the face looks
to the right and a pair of ears are conspicuous behind; when it is
a duck, the face looks to the left and the ears have been changed
into the bill. Most observers find it difficult to hold either
interpretation steadily, the fluctuations being frequent, and coming
as a surprise.
[Illustration: FIG. 16.
FIG. 16_a_.
FIG. 16_b_.
FIGS. 16, 16_a_, and 16_b_.--How many blocks are
there in this pile? Six or seven? Note the change in
arrangement of the blocks as they change in number
from six to seven. This change is described in the
text. Figs. 16_a_ and 16_b_ show the two phases of a
group of any three of the blocks. The arrangement of
a pyramid of six blocks seems the more stable and is
usually first suggested; but hold the page inverted,
and you will probably see the alternate arrangement
(with, however, the black surfaces still forming the
tops). And once knowing what to look for, you will very
likely be able to see either arrangement, whether the
diagram be held inverted or not. This method of viewing
the figures upside down and in other positions is also
suggested to bring out the changes indicated in Figs.
12, 12_a_, 12_b_, and in Figs. 14, 14_a_, 14_b_.]