M. C.

ES C H E R
The Graphic Work

Introduced and explained by the artist

TASCH EN
HONG KONG KOLN LONDON LOS ANGELES MADRI D PAR IS TOKYO
 FRONT COVER:
Sky and water I, 1938
Woodcut, 44 x 44 em

BACK COVER:
M. C. Escher
Photo: Bruno Ernst

2007 TASCHEN GmbH

Hohenzollernring 53, D-50672 Kbl n
www.taschen.com
1989 for all M.C. Escher reproductions:
Cordon Art - Baarn - Holland
English translation: John E. Brigham
The title was published in 1959 by
Koninklijke Erven J.J. Tijl N.V., Zwolle,
under the title M.C. Escher "Grafiek en Tekeningen".

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 Contents

Introduction 5
Classif ication and Description 7

I. Early prints 43 Sphere spirals

7 Tower of Babel 44 Moebius band I
2 Ca strova lva 45 Rind
3 Palm 46 Bond of union
4 Portrait G.A. Escher
5 Fluorescent sea V. Mirror images
6 St. Peter, Rome 47 Rippled surface
1 Dream 48 Puddle
49 Three worlds
II. Regular division of a plane 50 Still life with reflecting globe
8 Swans 57 H and with reflecting globe
9 Horsemen 52 Three spheres II
70 Two intersecting planes 53 Dewdrop
77 Day and night 54 Eye
72 Sun and moon
73 Sky and water I VI. Inversion
74 Sky and water II 55 Cube w ith magic ribbons
75 Liberation 56 Concave and convex
76 Development I
77 Verbum
78 Sphere surface with fishes VII. Polyhedrons
79 Path of life II 57 Double planetoid
20 Smaller and smaller 58 Tetrahedral planetoid
27 W hirlpools 59 Order and chaos
22 Circle limit I 60 Gravitation
23 Square limit 67 Stars
24 Circle limit Ill 62 Flat worms
25 Circle limit IV
26 Fishes and scales VIII. Relativities
27 Butterflies 63 Another world II
28 Reptiles 64 High and low
29 Cycle 65 Curl-up
30 Encounter 66 House of stairs
37 Magic mirror 67 Relativity
32 Metamorphose
33 .Predestination IX. Conflict flat-spatial
34 Mosaic I 68 Three spheres I
35 Mosaic II 69 Drawi ng hands
10 Ba lcony
Ill. Unlimited spaces 77 Doric columns
36 Depth 72 Print gallery
37 Cubic space division 73 Dragon
38 Three intersecting planes
X. Impossible buildings
IV. Spatial rings and spirals 7 4 Belvedere
39 Knots 75 Ascending and descending
40 Moebius band II 16 Waterfall
47 Concentric rinds
42 Spirals
 Eight heads, wood cut stamped print, 1922.
Th is is the first regular division of a plane surface carried
out by the arti st when he was a pupil of the School of
Architecture and Decorative Art s in Haarlem . It indicates
at what an early stage he felt d rawn to rhyth mic repetition.
In th e origina l wood-block eight hea ds were cut, four
female and four male. Space can be filled to infi nity with
contiguous prints.
 Introduction

Anyone who applies himself, from his early yo uth, to the

practice of graphic techniques may wel l rea ch a stage at
wh ich he begins to hold as his highest ideal the complete
mastery of his craft. Excellence of crafts manship takes up
all his ti me and so completely absorbs his thoughts that he
wi ll even make his choice of subject subo rdi nate to his
desire to explore some particular facet of technique. True
enough, there is tremendous satisfaction to be derived
from the acquisition of artistic skill and the achievement of
a thorough understanding of the properties of the
material to hand, and in learning w ith true purposefu lness
and contro l to use the tools which one has available
- above all, one's own two hands!

I myself passed many years in this sta te of self-delusion. But

then there came a moment when it seemed as though
scales fell from my eyes. I discovered that technical Regular division of a plane nr. 99, VIII 1954
mastery wa s no longer my sole aim, for I b eca me gripped
by another desire, the existence of which I had never After this, to my great rel ief, there dawns the second
suspected. Ideas came into my mind quite un related to ph ase, that is the making of the graphic printi for now the
graphic art, notions w hich so fascinated me that I longed spirit con toke its rest w hil e the work is to ke n over by the
to co mmunicate them to oth er people. This could not be hands.
achieved through words, for these thoughts were not In 1922, w hen I left the School of Architecture and
literary ones, but mental images of a kind that can only be Ornamental Design in H oarlem, having learnt graphic
made comprehensible to others by presenting them as techniques from S. Jessurun de Mesquita, I was very much
visual images. Suddenly the method by which the ima ge under the influence of this teacher, whose strong
was to be presented became less importa nt than it used to personality certainly left its mark on the majo rity o f his
be. One does not of course stu dy graphic art for so many pupils. At that period the woodcut (that isto say the cutting
yea rs to no availi not only had the craft b ecome second with gouges in a side-grained block of wood, usually
nature to me, it had also become essential to continue pear) was more in vogue with graphic artists than is the
using some techniqu e of reproduction so that I could case today. I in herited from my teacher his predilection for
communicate simu ltaneously to a large number of my side-grained wood, and one of the reasons fo r my ever-
fellow men that w hich I was aiming at. lasting gratitude to him stems from the fact that he taught
me how to handle this material. During the first seven
If I compa re the way in which o graphic sheet from my yea rs of my time in Italy, I used nothing else. It lends itself,
technique period came into being with that of a print better than the costly end-g rained wood, to large-sized
expressing a particular train of thought, th en I realize th at figures. In my youthful recklessness I ha ve gouged away at
th ey are almost poles a part. W hat often happened in the eno rmous p ieces of pearwood, not short of three feet in
post was that I would p ick out from a pile of sketches one length and perhaps two feet w ide. It was not unti ll929 that
which it seemed to me might be suitable for reproduction I made my first lithograph, and then in 19311 tried my hand
by means of some techniq ue that'was interesti ng me at for the fi rst time at wood-engraving, that is to say
that moment in time. But now it is from amongst those engraving with burins o n an end-grain block. Yet even
tech niques, which I have to some degree mastered, that I today the woodcut remains for me an essential medium.
choose t he one w hich lends itself more than any other, to Whenever one needs a greater degree of tinting o r
the expression of the particular idea that has ta ken hold of colouring in order to communicate on e' s ideas, and for
my mind. this reason has to produce more than one block, the
woodcut offers many advantages over wood-eng ravi ng,
N owadays the g rowth of a graphic image can be divided and there have been many paints in recent years that I
in to two sh arply defined phases. The process begins w ith could not have produced had I not gained a thorough
the search for a visual form such as will interpret as clearly knowledge of the advanta ges of side-grained wood. In
as possible one's train of thought. Usually a long time making a colourp rint I have often combined both of these
elapses before I decide that I have got it clear in my mind . raised relief techniques, using end-grain for details in
Yet a mental image is something compl etely d ifferent from black, and side-grain for the colours.
a visual image, and how ever much one exerts oneself, one The period during which I devoted such enthusiasm to my
can neve r manage to capture the fullness of that perfec- research into the characteristics of graphic materials and
tion which hovers in th e mind and which one thinks of, during w hich I ca me to realize the limitations that one must
quite falsely, as something tha t is "seen". After a long impose on o neself when dealing with them, la sted from
series of attempts, at lost - when I am just about at the end 1922 until about 1935. During that time o Iorge nu mber o f
of my resources - I manage to cost my lovely dream in the prints came into being (about 70 woodcuts and
defective visual mould of a detailed conceptual sketch . engravings and some 40 lithographs) . The greater

5
 I ha ve never practised any other type of intaglio. From the
moment of my discovery, I have deliberately left etching
and copper-plate engraving to one side. The reason for
this can probably be traced to the fact that I find it
preferable to delineate my figures by means of tone-
contrast, rather than by linear contour. The thin black line
on a white background, which is characteristic of etching
and copper-engraving, would only be of use as a compo-
nent part of a shaded area, but it is not adequate for this
purpose. Moreover, with intaglio, one is much more tied to
white as a starting point than is the case with raised relief
and planography. The drawing of a narrow wh ite line on
a dark surface, for w hich raised relief methods are
eminently suitable, is practically impossible w ith intaglio,
while on the other hand, a thin black line on a white
background can be satisfactorily achieved, albeit as a
rather painstaking operation, in woodcuts and wood-
.....
Regular division of a plane with two congruent motifs
engravi ngs.

Apart from prints 1 to 5, all the numbered reproductions

in this book were made with a view to communicating a
specific line of thought. The ideas that are basic to them
often bear witness to my amazement and wonder at the
laws of nature which operate in the world around us. He
who wonders discovers that this is in itself a wonder. By
keenly confronting the enigmas that surround us, and by
considering and analyzing the observations that I had
made, I ended up in the domain of mathematics. Although
I am absolutely innocent of training or knowledge in the
exact sciences, I often seem to have more in common with
mathematicians than with my fellow artists.

On reading over what I wrote at the beginning of this

introduction , about the particular representational
character of my prints, I feel it may be rath er illogical to
devote so many words to it, not only here but beside each
Regular division of a plane with two different motifs
separate reproduction as well. It is a fact, however, that
number ofthese have little or no value now, because they most people find it easier to arrive at an understanding of
were for the most part merely practice exercises: at least an image by the round-about method of letter symbols
that is how they appear to me now. than by the direct route. So it is with a view to meeting this
need that I myself have written the text. I am well aware
The fact that, from 1938 onwards, I concentrated more on that I have done this very inadequately, but I could not
the interpretation of personal ideas was primarily the leave it to anyone else, for - and here is yet another
result of my departure from Italy. In Switzerland, Belgi um reason for my astonishment- no matter how objective or
and Holland where I successively established myself, I how impersonal the majority of my subjects appear to me,
found the outward appearance of landscape and so far as I have been able to discover, few, if any, of my
architecture less striking than that which is particularly to fellow- men seem to react in the same way to all that they
be seen in the southern part of Italy. Thus I felt compelled see around them.
to withdraw from the more or less direct and true-to-life M. C. Escher
illustrating of my surroundings. No doubt this circum-
stance was to a high degree responsible for bringing my
inner visions into being.
On one further occasion did my interest in the craft take
the upper hand again. This was in 1946 when I first made
the acquaintance of the o ld and highly respectable black
art technique of the mezzotint, whose velvety dark grey
and black shades so attracted me that I devoted a great
deal oftime to the mastery of this copper-plate intaglio, a
process that has today fallen almost entirely into disuse.
But before long it became clear that this was going to be
too great a test of my patience. It claim s far too much time
and effort from anyone who, rightly or wrongly, feels he
has no time to lose. Up to the present I have, in all,
produced no more than seven mezzotints, the last one
being in 1951.

6
 Classification and description
of the numbered reproductions

In the case of the portraiture of someone w ith strongly

asymetrical features, a great deal of the likeness is lost in
the print, for this is the mirror image of the original work.
In this instance a contra print was made; that is to say, w hile
the ink of the first print was still wet on the paper, this was
printed on to a second sheet, thereby annulling the mirror
image. The "proof" brings out the signature that he
himself wrote on the stone with lithographic chalk and
which is now to be seen, doubly mirrored, back in its
original form.

5 . Fluorescent sea, lithograph, 1933,

33 x 24.5 em

6. St. Peter, Rome, wood-engraving, 1935,

24 x 32 em
The convergence of the vertical lines towards the nadir
Regular division of a plane with two symmetrical and suggests the height of the building in which the viewer
congruent motifs finds himself, together with the feeling ofvertigothattakes
hold of him when he looks down.
I. Early prints 1-7
7. Dream, woodcut, 1935, 32 x 24 em
The seven prints in this group, selected from a Iorge Is the bishop dreaming about a praying locust, or is the
numberwhich were made before 1937, display no unity as whole conception a dream of the artist?
for os their subject matter is concerned. They are all
representations of observed reality. Even no. 7 (Dream),
although pure fantasy, consists of elements which, taken
separately, are rea listically conceived.

1. Tower of Babel, woodcut, 1928, 62 x 38.5 em

On the assumption that t he period of language confusion II. The regular division of a plane 8-35
coincided with the emergence of different races, some of
the building workers ore wh ite and others black. The work This is the richest source of inspiration that I have ever
is at a standstill because they are no longer able to under- struck; nor has it yet dried up. The symmetry drawings on
stand each other. Seeing that the climax of the drama the foregoing and following pages show how a surface
ta kes place at the summit of the tower which is under can be regularly divided into, or filled up with, similar-
construction, the building has been shown from above, as shaped figures which are contiguous to one another,
though from a bird' seyeview. Thiscalledfora verysharp ly without leaving any open spaces.
receding perspective. It was not until twenty years later The Moors were past masters of this. They decorated
that this problem was thoroughly thought out. (see 63, walls and floors, particularly in the Alhambra in Spain,
Another World et seq). by placing congruent, multi-coloured pieces of
majolica together without leaving any spaces
2. Castrovalva, lithograph, 1930, 53 x 42 em between. What a pity it is that Islam did not permit
A mountainous landscape in the Abruzzi. them to make "graven images". They always restricted
themselves, in their massed t iles, to designs of an abstract
3. Palm, wood-engraving printed from two blocks, geometrical type. Not one single Moorish artist, to the
1933, 39.5 x 29.5 em best of my knowledge, ever made so bold {or maybe the
idea never occurred to him) as to use concrete,
4. Portrait of the engineer G. A. Escher, father of the recognizable, naturistically conceived figures of fish,
artist, in his 92nd year, lithograph, 1935, 26.5 x 21 em birds, reptiles or human beings as e lements in their surface
7
 coverage. This restricti on is a ll the more unacceptable
to me i n that the recogniza b ility of the components of
my own designs is the reason fo r my unfaili ng interest
in this sphere.

a. Glide Reflexion 8-9-10

Anyone who wishes to achieve sym metry on a fla t surface

must ta ke acco unt of th ree fu nda mental principles of
crystallog raphy: repeated shifting {translation); turn ing
about axes (rotati on) and gliding mirror image
{reflexion). It would be an exaggeratio n to attempt to
d iscuss all th ree of them in this short treatise, but seeing
that g lide refl exion is defi nitely displayed in th ree of my
prints, I must pay specia l attention to it.

8. Swans, wood-e ng raving, 1956, 20 x 32 em

The swans in this exa mple of g lide reflexio n are flying
round in a closed ci rcuit for med like a recumbent fig ure
eight. In o rder to pass over to its mirror image, each bird
has got to raise itself up like a flat biscuit sprinkled wit h
sugar o n o ne si de a nd spread with chocolate o n the other.
In the mid dle, where th e white an d bl ack streams cross,
Symmetry drawing A
they fill up ea ch other's open spaces. So a completely
square surface pattern is created . {See also symmetry
drawing B.)

9. Horsemen, wood cut printed from three b locks,

1946, 24 x 45 em
In orderto indicatethatthe light-sha ded ho rsemen are the
mirror images of the dark-shaded ones, a circular band is
portra yed on w hich a procession of horsemen moves
forwa rd. One can imagine it to be a length of material,
with a pattern woven into it, the warp and woof being of
different colours. The dark knigh ts on the light
background thereby cha nge colour o n the reverse side of
th e band. In the midd le both front and back have become
enmeshed, and now it appears that lig ht and dark
horsemen together fill up the space completely. (See also
symmetry drawing A.)

10. Two intersecting planes, woodcut p rinted fro m

three blocks, 1952, 22 x 32 em
Symmetry drawing B Two thin, fla t rectangular boards intersect each other at a
slight angle. H oles have been sawn in each board leaving
openings shaped like fishes and birds. The ho les in one
board can be filled up by the remaining parts of the other
board. The jigsaw pieces of the one o re mirror images of
those in the other {see also symmetry drawing C).

b. The function of figures as a bac:kground 11 - 14

O ur eyes a re accustomed to fixing upon a specific object.

The moment this hap pens everything round about
becomes reduced to background.

11. Day and night, woodcut pri nted from two blocks,
1938, 39 x 68 em
Grey rectangu lar fields develo p upwards into si lhouettes
of white and b lack birds; the black ones a re flying towards
the left and the white ones towards the right, in two
o p posing formatio ns. To the left of the picture the white
birds flow together and merge to form a daylight sky and
Symmetry drawing C landscape. To the rig ht the black birds melt together into
night . The day and night landscapes are mirror images of
8
each other, united by means of the grey fields out of which, d. Infinity of number 18-27
once aga in, the birds emerge.
If all component ports are equal in size, it is impossible to
12. Sun and moon, woodcut printed from fo ur blocks, represent more tha n a fragment of a regular p lane-fi lling.
1948, 25 x 27.5 em If o ne wishes to illustrate on infinite number then one must
The subject of this coloured woodcut is once again the have recourse to a g radual red uction in the size of th e
contrast between day and night. But in this instance the figures, until one reaches- at any rote theoretically- the
two notions ore not, as in print 11, pictured as next to each limit of infinite small ness.
other but in the some place - tho ugh not simultaneous,
being sepa rated by a leap of the mind. It is day-time when 18. Sphere surface with fishes, woodcut printed from
there is a sun shining in the centre, w here the sun is two blocks, 1958, diameter 32 em
shooting out yellow and red rays. Aga inst this background The previous print demonstrated a return motion towards
stand out fourteen dark blue birds. As soon as one divests the starting point. There now follow va riations on that
them of their function as objects and regards them as theme, with two cores, a starting point and an end point
background, then there appear fourteen light coloured between which the chains of figures move. Here, as a first
bi rd s against a night sky, w ith a crescent moon in the centre example, is a sphere with two poles and a network of
and with stars, planets and a comet. longitudinal and latitudinal circles. Swimming spirally
outwards from the one visible pole, there come alternate
13. Sky and water I, woodcut, 1938, 44 x 44 em rows of white and black fishes. They attain their greatest
In the horizontal central strip there are birds and fish size on reaching the equator and thereafter they become
equivalent to each other. We associate flying with sky, and smaller and disap pear into the other, invisible, po le on the
so for each of the block birds the sky in w hich it is fly ing is for side of the sphe re.
formed by the four white fish which encircle it. Similarly
swimming makes us think of water, and therefore the four 19. Path of life II, woodcut printed from two blocks,
black b irds that surround a fish become th e water in which 1958, 37 x 37 em
it swims. Here, too, thepointof infinitesmallnessisinthecentre. This
time an attempt has been made to e li minate the
14. Sky and water II, woodcut, 1938, 62 x40 .5 em unsatisfactory fea tu re of an illogical limit. The area is filled
Similar in subjecttothatin no. 13 (Sky and Water 1), except with white and grey fish-shaped figures whose
that the bi rds and fishes are to be seen here in direct as well longitudinal axes ore accentuated by black lines. Out
as in mirror image. from the central point come fou r series of white fish {rays)
swimming head to tail in a spi ral motion. The four largest
c. Development of form and contrast 15-16-17 specimens, which close off the square surface, change
direction a nd colour; th eir wh ite tails still belong to th e
15. Liberation, lithograph, 1955, 43.5 x 20 em centrifugal movement, but their grey heads ore a lready
On the uniformly grey surface of a strip of paper that is tu rni ng inwards and so form part of the grey series which
being un ro lled, a simultaneous development in form and ore moving back towards the centre.
contrast is taking place. Triangles, at first scarcely visible,
change into more comp licated figures, whilst the colour 20. Smaller and smaller, wood-engraving printed from
contrast b etween them increases. In the midd le they are four blocks, 1956, 38 x 38 em
transformed into white and black b irds, and from there fl y The area of each of the reptil e-shaped e lements of this
off into the world as independe nt creatures. And so the pattern is regu la rly and contin uously halved in the direc-
strip of paper on which they were drawn disappears. tion of the centre, where theoretically both infinite
smallness of size and infinite greatness of number are
16. Development I, woodcut, 1937, 44 x 44 em reached. However, in practice, the wood-engraver soon
Scarcely visible g rey squares at the edges evolve in form comes to the end of hi s abi lity to carry on. He is depend ent
and contrast towards the centre. Their g rowth is on foudactors: 1. the qua lity of his wood-block, 2. the
completed in the middle. An unsatisfactory feature of th is sharpness of the instrument that he is using, 3. the
kind of inward -directed unfolding is that there is so little steadiness of his hand and , 4. his optical ability (good
space left for th.e freedom of movement of the most eyesight, plenty of light and a powerful magnifying lens).
greatly developed figures: two white and two black In this particular case, the halving of the figures is ca rried
reptil es. thro ug h ad absurdum . The smallest animal still possessing
a head, a ta il and four legs is about 2 mil limetres in le ngth.
17. Verbum, lithograph, 1942, 33 x 38.5 em From the point of view of composition, this work is only
An evolution working from the centre outwards, thus the partially satisfactory. In spite of the central li mit, it remains
opposite way round to the previous print, offe rs more only a fragment, b ecause the outer edge of the pattern
space a t the edges for the fully grown figures. The central has been arbitrarily fixed. So a complete composition has
word "Verbum" recalls the biblical story of creation. Out not been achieved.
of a misty grey th e re loom triangular primeval figures
which, by the time they reach the edges of the hexagon, 21. Whirlpools, wood-engraving printed from
have developed into birds, fishes and frogs, each in its own two blocks, 1957, 45 x 23.5 em
e le ment: air, water and e arth. Each kind is pictured by day Closely related to the foregoing picture, there is here
and by night, and the creatures merge into each other as displayed a flat surface with two visible cores. These are
they move forwa rd along the outline of the hexagon, in a bound together by two white S-shaped spirals, drawn
clockwise direction. through the bodily axes of, once again, fish swimm ing
9
head to tail. But in this case they move forward in opposite radiate from it. The disc is d ivided into six sections in which,
directions. The upper core is the starting point for the dark- turn and turn about, the angels on a black background
colo ured series, the component members of which attain and then the devils on a wh ite one, gain the upper hand.
their greatest size in the middle of the picture. From then In this way, heaven and hell change place six times. In the
on, they come within the sphere of influence of the lower intermediate, "earthly" stages, they are equivalent.
core, towards w hich they keep on swirling until they disap-
pear within it. The other, light-coloured, line makes the 26. Fishes and scales, woodcut, 1959, 38 x 38 em
same sort of journey but in the opposite direction. As a The final example in this group brings in two different sorts
matter of special printing technique, I would point out that of mutation, carried out at one and the same time, that is
only one wood-block is used for both colours, these to say both shape and size. Th e double process completes
having been printed one after the other on the same sheet itself twice over. In the upper part of th e print, from right
of paper, and turned 180 degrees in reflection to each to left, scales grow into fish that keep on increasing in size.
other. The two prints fill up each other's open spaces. In the lower half the same thing happens, but from left to
right .
22. Circle limit I, woodcut, 1958, diameter 42 em
Sofarfourexamples have been shown with pointsas limits 27. Butterflies, wood-engraving, 1950, 28 x 26 em
of infinite smallness. A diminution in the size of the figures Working downwards from the top to the centre, th e w hite
progressing in the opposite direction, i.e. from within area is divided up by black contours of increasing
outwards, leads to more satisfying results. The limit is no thickness which take on ever larger butterfly shapes; these
longer a point, but a line which bordersthewholecomplex continue to develop.
and gives it a logical boundary. In this way one creates, as
it were, a universe, a geometrical enclosure. If the e . Story pictures 28-33
progressive reduction in size radiates in all directions a t an
equal rate, then the limit becomes a circle. In the example Th e chief characteristic of the six foll owi ng prints is the
in qu~stion (chronologically the first of the three which transition from flat to spatial and vice versa. We think in
have been included in this book), the arrangement of the terms of an interplay between the stiff, crystallized two-
component parts still leaves much to be desired. All the dimensional figures of a reg ular pattern and the indivi-
lines, once again accentuated by the bodily axes, consist dual freedom of three-dimensional creatures capable of
of alternating pairs of fish, two white ones head to head moving about in space witho ut hindrance. On the one
and two black ones whose tails touch. So there is no hand, the members of planes of collectivity come to life in
continuity here, no direction offorward movement, nor is space; on the other, the free individ uals sink back and lose
there any unity of colour in each line. themselves in the com munity. A row of identical spatial
beings such as those to be found in the prints of this group
23. Square limit, woodcut printed from two blocks, often emerges to be treated as a single individual in
1964, 34 x 34 em motion. This is a static method of illustrating a dynamic
Design number 20 {Smaller and smaller) showed a fact. A few prints from each group, such as 11 {Day and
pattern composed of elements continuously reduced by night), 15 {Liberation) a nd 17 {Verbum) might also be
half as they move in the direction of the centre. A similar counted in this category, were it not for the fact that their
system of halving was adapted here, but this time moving chief characteristic differs from that of the ones we have
from with in outwards. The limit of the infinitely smal l just been considering.
shapes is reached on the straight sides of the square.
28. Reptiles, lithograph, 1943, 33.5 x 38.5 em
24. Circle limit Ill, woodcut printed from five blocks, The life cycle of a little alligator. A mid all kinds of objects,
1959, diameter 41.5 em a drawing book lies open, a nd the drawing on view is a
Here, the failings of the previous work are as far as mosaic of reptilian figures in three contrasting shades.
possible remedied. White cu r ved lines cut across each Evidently one of them has tired of lying flat and rigid
other and div ide one another into sections, each of which amongst his fellows, so he puts one plastic-looking leg
equals the length of a fi sh. They mark the routes along over th e edge of the book, wrenches himself free and
which series offish move forward, from the infinitely small, launches out into rea !life. He climbs up the back of a book
through the greatest size, to infinitely small. Each series on zoology and works his laborious way up the slippery
comprises fish of only one colour. It is necessary to have at slope of a set square to the highest point of his existence.
least four colours so as to get the lines of fish to contrast Then after a quick snort, tired but fulfilled, he goes
with each other. It is worth mentioning, from the point of downhill again, via on ashtray, to the level surface, to that
view of printing technique, that five wood-blocks were flat drawing paper, and meekly rejoins his erstwhile
made, oneforthe black lines and fourfor thecolours. Each friends, ta king up once more his function as an element of
block has the shape of a right-ang led segment and so has surface division.
to be printed four times over in order to fill the circle.
Therefore a complete copy of this print requires 4x 5 = 20 N .B. The little book of Job has nothing to do with the Bible,
impressions. but contains Belgian cigarette papers.

25. Circle limit iv, {Heaven a nd Hell), woodcut printed 29. Cycle, lithograph, 1938, 47.5 x 28 em
from two blocks,1960, diameter 41.5 em At the top right-hand corner a jolly young lad comes
Here, too, we have the components dimi nishing in size as popping out of his house. As he rus hes downstairs he loses
they move outwards. The six largest (three white angels his special quality and takes his place in a pattern of flat,
and three black devils) are arranged about the centre a nd grey, white and black fellow-shapes. Towards the left and
10
upwards these become simplified into lozenges. The quickly turn once more into black bird shapes. Small grey
dimension of depth is achieved by the combination of birds begin to appear in the white background and then
three diamonds which give the impression of a cube. The gain in size until their contours equal those of their fellows.
cube is joined on to the house from which the boy emerges. Such areas of white that still remain take on the form of a
The floor of a terrace is laid with the same familiar pattern third variety of bird so that there are now three different
of diamond-shaped tiles. The hilly landscape at the top is kinds, each with its own specific form and colour, filling the
intended to display the utmost three-dimensional realism, surface completely. Now for another simplification: each
while the periodic pattern at the lower part of the picture b ird turns into a lozenge. Just as in print number 29
shows the greatest possible amount of two-dimensional (CycleL this is an opportunity to pass over to the three-
restriction of freedom. dimensional, as three diamond shapes suggest a cube.
The blocks give rise to a c ity on the sea-shore. The tower
30. Encounter, lithograph, 1944, 34 x 46.5 em standing in the water is at the sometime a piece in a game
Out from the grey surface of a back wall there develops a of chess; the board for this game, with its light and dark
complicated pattern of white and black figures of little squares, leads back once more to the letters of the word
men. And since men who d esire to live need at least a floor "Metamorphose".
to wa lk on, a fl oor has been designed for them, with a
circ ul ar gap in the middle so that as much as possible can 33. Predestination, lithograph, 1951 , 29 x 42 em
still be seen of the back wal l. In this way they are forced, An aggressive, voracious fish and a shy and vulnerable
notonlytowalkin a ring , but a Isoto meet each other in the bird are the actors in this drama: such co ntrasting traits of
foreground: a white optimist and a black pessi mist character lead inevitably to the d e nouement. A regular
shaking hands with one another. pattern floats like a ribbon in space. Lower down, in the
middle, this picture strip is made up of fish and birds, but
31. Magic mirror, lithograph, 1946, 28 x 44.5 em by a substitution of figures, only birds remain on the left
On a tiled floor there stands a vertical reflecting screen out side and fish on the right. Out from these gradually fading
of which a fabulous animal is born. Bit by bit it emerges, extremities, one representative of each sort breaks loose
until a complete beast walks away to the right. His mirror - a black, devilish fish and a white bird, all innocence, but
image setsofftowards the left, but he seems fairly substan- sad to say irrevocably doomed to destruction. The fate of
tial, for behind the reflecting screen he appears in quite a each is played out in the foreground.
realistic guise. First of all they walk in a row, then two by
two, and finally both streams meet up four abreast. At the f. Irregular filling of plane surfaces 34-35
same time they lose their plasticity. Like pieces of a ji9saw
puzzle they slide into one anoth e r, fill up each other' s The next two prints consist offigures that do not in anyway
interstices and fade into the floor on which the mirror repeat themselves in similar form . So they do not really
stands. belong to group II; nevertheless they were added to it
because they do in fact have their surfaces filled up, with
32. Metamorphose, woodcut printed from twenty-nine no spaces left empty.
blocks, 1939-40 and 1967-68, 19.5 x 700 em
A long series of changing shapes. Out of the word What is more, they could never have been produced
"Metamorphose" placed vertically and horizontally o n without years of training in reg ular surface-filling . The
th.e level su rface, with the letters 0 and M ( = Greek E) as recognizability of their components as natural objects
points of intersection, there emerges a mosaic of white plays a more important role. The only reason for their
and black squares that changes into a carpet of flowers exist ence is one's enjoyment of th is difficult game, without
and leaves on which two bees have settled. The reupo n the any ulterior motive.
flowers and leaves change back into squares aga in, only
to be transformed once more, this time into animal shapes. 34. Mosaic I, mezzotint, 1951, 14.5 x 20 em
To use musical term inology, we are dealing here with four- Regularity of construction can be recognized in this
four time. rectangular mosaic in that, both as regards height and
breadth, three light and three dark figures alternate li ke
Now the rhyth m changes; a third shade is added to the the squares on a chessboard. With the exception of the
w hite and black and the measure changes to three-four shapes round the edge, every white one is surrounded by
time. Each figure becomes simplified and the pattern four black ones and every black by four white. The sum
which at first was composed of squ ares now consists of total can immediately be ascertained: 36 pieces, 18 white
hexagons. Then fol lows an association of ideas; hexagons and 18 black.
makeone think ofthecellsin a honeycomb, and so in every
cell there appears a bee larva . The full y grown larvae tu rn 35. Mosaic II, lithograph, 1957, 32 x 37 em
into bees w hich fly off into space. But they are not In this case the only regularity to be noted is the
vo uchsafed o long life of freedom, for soon their black rectangularity of the complete surface. There are but few
silhouettes join together to form a background for white of the inner figures bordered by four adjacent ones. The
fish. As these also fuse together, the interstices see m to direct environment of the frog consists of two figures; the
take on the form of b lock birds. Similar transformations of guitar is hemmed in by three, the cock by five and the
background objects now appear several times: dark ostrich (if that is what it really is) by six. The sum total can
birds... light-coloured boots ... dark fish ... light horses ... only be arrived at by careful counting.
dark birds. These become simplified into a pattern of
equilateral tria ngles which serve for a short whi le as a
canvas on which winged letters are depicted but then
11
Ill. Unlimited spaces 36-37-38 casing which, as a narrowing torus, returns to the place
where it began, penetrates within itself and starts on its
36. Depth, wood-engraving printed from three second round.
blocks,1955, 32 x 23 em
Here, too, space is divided up cubically. Each fish is found 43. Sphere spirals, woodcut printed from four blocks,
at the intersection of three lines of fish , all of which cross 1958, diameter 32cm
each other at right-angles. Here, just as in no. 18, a sphere is shown with a network of
longitudinal and latitudinal circles. Four spirals twist their
37. Cubic space division, lithograph, 1952, way around the spherical surface, infini tely small at the
27 x 26.5 em poles and broadest at the equator. Half of its yellow
Intersecting each other at right angles, girders d ivide exterior is visible. Through open la nes in its side the red
each other into equal lengths, each forming the edge of a interior can be followed to the opposite pole.
cube. In this way space is filled to infinity with cubes of the
same size. 44. Moebius band I, wood-engraving printed from four
blocks, 1961 , 24 x 26 em
38. Three intersecting planes, woodcut printed from An endless band has been cut through, down its whole
two blocks, 1954, 32.5 x 37.5 em length. The two sections have been drawn apart from
Three planes intersect each other at rightangles. They are each other a little, sothata clear space divides them all the
indicated by squa re tiles with the same number of squa re way round. Thus the band ought to fall apart into two
gaps between them. Each plane recedes in perspective to unattached rings, and yet apparently it consists of one
a vanishing point and the three vanishing points coincide single strip, made up of three fish, each biting the tai l of the
with the points of an equilateral triangle. one in front. They go round twice before regaining their
point of departure.

45. Rind, wood-engraving printed from four blocks,

1955, 34.5 x 23.5 em
IV. Spatial Rings and Spirals 39-46 Like the spirally shaped peel of a fruit and like a hollow,
fragmented sculpt ure, the image of a woman floats
39. Knots, woodcut printed from three blocks, 1965, through space. The sense of depth is enhanced by a bank
43 x 32 em of clouds which diminishes towards the horizon.
Three unbroken knots are displayed here; that is to say a
simpl e knot has been tied three times over in a cord, the 46. Bond of union, lithograph, 1956, 26 x 34 em
ends of wh ich run into each other. The perpendicular Two spirals merge and portray, on the left, th e head of a
cross-section of each knot is different. In the top right hand woman and, on the right, that of a man. As an endless
example the profile is round, as in a sausage; the top left band, their foreheads intertwined, they form a doubl e
one is cruciform, with two flat bands intersecting each unity. The suggestion of space is magnified by spheres
other at right angles; below is a square, hollow pipe with which float in front of, within and behind the hollow
gaps through w hich the inside can be seen. If we start at images.
any arbitrary point and fo llow a flat wall with the eye, then
it appears t hat we have to make four rounds before we
come back to our point of departure. So th e pipe does not
consist of four separate strips, but of one which runs
through the knot four times. The knot shown at the top V. Mirror images 47-54
right-hand corner is in principle every bit as interesting,
but it remains undiscussed here, as the draughtsman a. Reflections in water 47-48-49
hopes to devote a more detailed print to it in the future.
47. Rippled surface, lino cut printed from two blocks,
40. Moebius band II, woodcut, printed from three 1950, 26 x 32 em
blocks, 1963, 45 x 20 em Two raindrops fall into a pond and, with the concentric,
An endless ring-shaped band usually has two distinct expanding ripples thattheycause, disturb the still reflexion
surfaces, one inside and one outside. Yet on this strip nine of a tree with the moon behind it. The rings shown in
red ants crawl after each other and travel the front side as perspective afford the only means whereby the receding
well as the reverse side. Therefore the strip has only one surface of the water is indicated.
surface.
48 . Puddle,woodcutprintedfromthreeblocks, 1952,
41. Concentric rinds, wood -engraving, 1953, 24 x 32 em
24 x 24 em The cloudless evening sky is reflected in a puddle which a
Four spherical concentric rinds are illuminated by a recent shower has left in a woodland path. The tracks of
central source of light. Each rind consists of a network of two motor cars, two b icycles and two pedestrians are
nine large circles which divide the surface of the sphere impressed in the foggy ground.
into forty-eight similar shaped spherical triangles.
49. Three worlds, lithograph, 1955, 36 x 25 em
42. Spirals, wood-engraving printed from two blocks, Th is picture of a woodland pond is made up of three
1953, 27 x 33.5 em elements: the autumn leaves which show the receding
Four spiralli ng strips come together to form a curved surface of the water, the reflexion of three trees in the
12
background and, in the foreground, the fish seen through 55. Cube with magic ribbons, lithograph, 1957,
the clear water. 31 x 31 em
Two endless circular bands, fused together in four places,
b. Sphere reflexions 50-54 are curved around the diagonals of a cube. Each strip has
a row of button-like protuberances. If we follow one of
50. Still life with reflecting globe, lithograph, 1934, these series with the eye, then these nodules surreptitiously
28.5 x 32.5 em change from convex to concave.
The same reflecting globe as the one shown in no. 51
(Hand with Reflecting GiebeL but in this case viewed 56. Concave and convex, lithograph, 1955,
sideways on, like a bottle with a neck. 28 x 33.5 em
Three little houses stand near one another, each under a
51. Hand with reflecting globe, lithograph, 1935, crossvaulted roof. We have an exterior view of the left-
32 x 21.5 em hand house, an interior view of the right-hand one and an
A reflecting g lobe rests in the artist' s hand.ln this mirror he either exterior view or interior view of the one in the
can have a much more comp lete view of his surroundings middle, according to choice. There are several similar
than by direct observation, for nearly the whole of th e inversions illustrated in this print; let us describe one of
area around him- four walls, the floor and ceiling of his them. Two boys are to be seen, playing a flute. The one on
room- are compressed, albeit distorted, within this little th e left is looking down through a window on to the roof
disc. His head, or to be more precise, the point between his of the middle house; if he were to climb out of the window
eyes, comes in the absolute centre. Whichever way he he cou ld stand on this roof. And then if he were to jump
turns he remains at the centre. The ego is the unshakable down in front of it he would land up one storey lower, on
core of his world. the dark-coloured floor before the house. And yet the
right-hand flautist who regards that same cross-vault as a
52. Three spheres II, lithograph, 1946, 26 x 47 em roof curving above his head, will find, if he wants to climb
Three spheres, of equal size but different in aspect, are out of his w indow, that there is no floor for him to land on,
p laced next to each other on a shiny table. The one on the only a fathomless abyss.
left is made of glass and filled with water, so it is transpa-
rent but a lso reflects. It magnifies the structure of the table
top on which it rests and at the same time mirrors a
window. The right-hand sphere, with its matt surface,
presents a light side and dark side more clearly than the VII. Polyhedrons 57-62
other two. The attributes of the middle one are the same
as those described in connection w ith no. 51; the whole of 57. Double planetoid, wood-engraving, printed from
the surrounding area is reflected in it. Furthermore it four blocks, 1949, diameter 37.5 em
achieves, in two d ifferent ways, a triple unity, for not only Two regular tetrahedrons, piercing each other, float
does it reflect its companions to left and right, but all three through spa ce as a planetoid . The light-coloured one is
of them are shown in th e drawi ng on which the artist is inhabited by human beings who have completely
working. transformed their region into a co mplex of houses,
bridges and roads. The darker tetrahedron has remained
53. Dewdrop, mezzotint, 1948, 18 x 24.5 em in its natural state, w ith rocks, on w hich plants and
This leaf from a succulent plant was in fact about 1 inch in prehistoric animals live. The two bodies fit together to
length. On it lies a dewdrop which shows a reflection of a make a whole but they have no knowledge of each other.
window and yet at the same time serves as a lens which
magnifies the structure ofthe leaf-veins. Quaintly shaped 58. Tetrahedral planetoid, woodcut printed from two
air-pockets, shining white, are trapped between the leaf blocks, 1954, 43 x 43 em
and the dewdrop. This little plan et inhabited by humans has the shape of a
regular tetrahedron and is encircled by a spherical
54. Eye, mezzotint, 1946, 15 x 20 em atmosphere. Two of the four triangular surfaces, with
Here th e artist has drawn his eye, greatly enlarged, in a which this body is faced, are visib le. The edges w hich
concave shaving mirror. The pupil refl ects the one who separate them divide the picture into two. A ll the vertica l
watches us all. li nes: the walls, houses, trees and people, point in the
direction of the core of the body - its centre of gravity-
and all th e horizontal surfaces, gardens, roads, stretches
of water in pools and cana ls, are parts of a spherical crust.

59. Order and chaos, lithograph, 1950, 28 x 28 em

VI. Inversion 55-56 A stellar dodecahedron is placed in the centre and is
enclosed in a translucent sphere like a soap bubble. This
It was stated in connection with print no. 29 that a symbol of o rder and beauty reflects the chaos in the shape
combination of three diamond-shapes can make a cube. of a heterogeneous collection of all sorts of useless,
Yet it still remains an open question as to w hether we are broken a nd crumpled objects.
looking at this cube from within or without. The mental
reversal, this inward o r outward turning, this i nversion of 60. Gravitation, lithograph, coloured by hand, 1952,
a shape, is the game that is played in the two following 30 x 30 em
p rints. H ere once again is a stellar dodecahedron, encased in
13
twelve flat, five-pointed stars. On each of these platforms and show the horizon, while through the bottom pair one
lives a tailless monster with a long neck and four legs. H e looks straight up to the stars.
sits there with hi s lump caught beneath a fl at-side
pyramid, each wall o f which has an opening, and through Each plane of the building, which unites nadir, horizon
this opening t he creature sticks his head and legs. But the and zenith, has a threefold function. For instance, the rear
pointed extremity of one animal's dwelling platform is at plane in the centre serves as a wa ll in relation to the
the same time the wa ll of one of his fellow-sufferer's horizon, a floor in connection with the view through the
prisons. All these triangular protrusions function both as top opening and a ceiling so far as the view to towa rds the
floors and as wa lls; so it comes about that this print, the last starry sky is concerned.
in the series of polyhedrons, serves also as a transition to
t he relativity group. 64. High and low, lithograph, 1947, 50.5 x 20.5 em
In this print the same picture is presented twice over, but
61. Stars, wood -engraving, 1948, 32 x 26 em viewed from two different points. The upper half shows the
Single, double and triple regu lar bodies float like stars view that an observer would get if he were about three
through space. In the midst of them is a system of three storeys up; the lower half is the scene that would confront
regular octahedrons, indicated by their edges only. Two him if he were standing at ground level. If he shou ld take
chameleons have been chosen as denizens of this his eyes off the latter and look upwards, then he would see
framework, because they are able to cling by their legs the tiled floor on which he is standing, repeated as a
and tails to the beams of their cage as it swirls through ceiling in th e centre of th e composition . Yet t his acts as a
space. floor for the upper scene. At the very top, this tiled floor
repeats itself once again, purely as a ceiling.
62 . Flat worms, lithograph, 1959, 34 x 41.5 em
Bricks are usua lly rectangular, because in that way t hey 65. Curl-up, lithograph, 1951 , 17 x 23.5 em
are most suitable for building the vertical wa lls o f our The imaginary creature here portrayed and fully
houses. But anyone w ho has anything to do with the described goes into action in the following print.
stacking of ston es of a non-cubic typ e w ill b e well aware
of other possibilities. For instance, one can make use of 66 . House of stairs, lithograph, 1951, 47 x 24 em
tetrahedrons alternating with octahedrons. Such are the N ow comes a further development of the concept of
basic shapes w hich are used to raise the building relativity that was displayed in the foregoing prints. A
illustrated here. They are not practicable for human playful element is introduced, one wh ich came up for
beings to build with, because t hey make neither vertical discussion in connection w ith the regular dividing-up of
walls no r horizonta l floors. However, when this building is surfaces, in other words glide reflexion. Roughly the
filled with water, flat worms can swim in it. w hole of the top half of the print is th e mirror image of the
b ottom half. The topmost flight of steps, down w hich a
curl -up is crawling from left to right, is reflected tw ice over,
onceinthe middle and then agai n inthe lower part. On the
stairs in the top right-hand corner, in the same way as is
VIII. Relativities 63-67 also shown in number 67, the distinction between a scend-
ing and descending is eliminated, for two rows o f animals
The underlying ideo in the following pictures is basically are moving side by side, yet one row is going up and the
this: b efore photography was invented, perspective was other down.
always closely linked with horizon . Yet even at the time of
the Renaissance it was known that not only do the 67. Relativity, lithograp h, 1953, 28 x 29 em
horizontallinesofo building meet at a point on the horizon Here we have three forces of gravity working perpen-
(the famous "vanishing point" ), but also t he vertica l lines dicularly to one another. Three earth-planes cut across
meet downward s at the nadir and upwa rds at the zenith. each other at rig ht angles, and human beings are living on
This is obvious w ith old ceiling-paintings which have each of them .
vertical perspective recedi ng lines, such as pillars. But now
that photography is part of our everyday lives, we really It is impossible for the inhabitants of different worlds to
have come to understand vertical perspective. We have walk or sit or stand on the same floor, because they have
only to point our lens at the top or at the bottom of a differing conceptions of what is horizontal and w hat is
building to realize that architectural draughtsmen ore vertical. Yet they may well share the use of the same
simply taking the easy wa y out w hen they indicate stairca se. On the t op staircase illustrated here, two people
everything t hat stands vertically, in their perspective are moving side by side and in the some di recti on, and yet
projections, with parallel lines. In the following prin ts the one of th em is going downstairs and the ot her upstairs.
vanishing point has several different functions at one and Contact b etween them is out of the question because t hey
the-same time. Sometimes it is situated on the horizon, t he live in different worlds and therefore can have no
nadir and the zenith all at once. knowledge of each other's existence.

63. Another world II, wood-engraving printed fro m

three blocks, 1947, 31.5 x 26 em
The interior of a cube-shaped building. Openings in the
five visible walls give views of three different landscapes. IX . Conflict between the flat and the spatial68- 73
Through the topmost pair one looks down, almost
vertically, onto the ground; the middle two are at eye-level Our three-dimensional space is the only true reality that
14
we know. The two-dimensional is every bit as fictitious as his eye moves further on from left to right, to the ever
the four-dimensional, for nothing is flat, not even the most expanding blocks of houses. A wo man looks down
finely polished mirror. And yet we stick to the convention through her open window onto the sloping roof which
that a wa ll or a piece of paper is flat, and curiously covers the exhibition ga lleryi and this brings us back to
enough, we still go on, as we have done since time where we started our circuit. The boy sees al l these things
immemorial, producing illusions of space on just such as two dimensional details of the print that he is studying.
plane surfaces as those. Surely it is a bit absurd to draw a If his eye explores the surface further then he sees himself
few li nes and then claim: " This is a house". This odd situa - as a part of the print.
tion is the theme of the next live pictures.
73. Dragon, wood -engraving, 1952, 32 x 24 em
68. Three spheres I, wood-engraving, 1945, However much this dragon tries to be spatial, he remains
28 x 17 em comple tely flat. Two incisions are made in the paper on
At the top of this print the spatial nature of a g lobe is which he is printed. Then it is fo lded in such a way as to
brought out as strongly as possible. Yet it is not a globe at leave two square openings. But this dragon is an obstinate
all, merely the projection ofoneon a piece ofpaperwhich beast, and in spite of his two dimensions he pe rsists in
could be cut out as a disc. In the middle, just such a paper assuming that he has threei so he sticks his head through
disc is illustrated, but folded in two halves, one port vertical one of the holes and his tail through the other.
and the other horizontal, with the top sphere resting on
this Iotter. At the bottom another such disc is shown, but
unfolded this time, and seen in perspective as a circular
table top.

69. Drawing hands, lithograph, 1948, 28.5 x 34 em

A piece of paper is fixed to a base with drawing pins. A
right hand is busy sketching a shirt-cuff upon this drawing X. Impossible buildings 74-75-76
paper. Atthis point its wo rk is inco mplete, but a little further
to the rightithasalreadydrawna left hand e mergi ng from 74. Belvedere, lithograph, 1958, 46 x 29.5 em
a sleeve in such detail that this hand has come right up out In the lower left foreg round there lies a piece of paper on
of th e flat surface, and in its turn it is sketching the cuff from wh ich the edges of a cube are drawn . Two small circles
which the right hand is emerging, a s though it were a living mark the places where edges cross each other. Which
member. edge comes atthefront and wh ich at the back? In a three-
dimensional world simultaneous front and back is an
70. Balcony, lithograph, 1945, 30 x 23.5 em impossibility and so cannot be illustrated . Yet it is quite
The spatial nature of these houses is a fiction. The two- possible to draw an object which displays a different
dimensiona l nature of the paper on which it is drown is not reality when looked at from above and from below. The
disturbed- unl ess we give it a bang from behind. But the lad sitting on the bench has got just such a cube-like
bulge that can be seen in the centre is an illusion too, for absurdity in his hands. He gazes thoughtfully at this
the paper stays flat. incomprehensible object and seems oblivious to the fact
All that has been achieved is on expansion, a quadruple that the belvedere behind him has been built in the same
magnification in the centre. impossible style. On the floor of the lower platform, that is
to say indoors, stands a ladder w hich two people are busy
71. Doric columns, wood-engraving printed from three cl imbing. But as soon as they arrive a floor higher they are
blocks, 1945, 32 x 24 em back in the open air and ha ve to re-enter the building. Is
The lower part of the left-hand column suggests a heavy it any wonder that nobody in this company can be
three-dimensional stone object, and yet it is noth ing more bothered about the fate of the prisoner in the dungeon
than a bit of ink on a piece of paper. So is turns out to be who sticks his head through the bars and bemoans his
a flat strip of p aper which, having b een folded three times, fate?
has got itse lf jammed between the ceiling and the capital
ofthe right-hand column. Butthe something applies to the 75. Ascending and descending, lithograph, 1960,
right-hand column itself; from above it resem bles a ribbon 38 x 28.5 em
lying flat on the floor with the left-hand column resting The en dless stai rs which are the main motif of this picture
upon it. were taken from an a rticle by L.S. and R. Penrose in t he
February, 1958, iss ue of the British Journal of Psychology.
72. Print gallery, lithograph, 1956, 32 x 32 em A rectangular inner courtyard is bounded by a building
As a va riation on the theme of the print Balcony, namely, that is roofed in by a never-ending stairway. The
magnification towards the centre, we have here an expan- inhabitants of these living-q uarters wo uld a ppear to be
sion which curves around th e empty centre in a clockwise monks, adherents of some unknown sect. Perhaps it is their
direction. We come in through a door on the lower right ritua l duty to climb those stairs for a few hours each day.
to an exhibition ga llery where there are prints on stands It would seem that w hen they get tired they are allowed to
and wa lls. Firstofallwepassa visitor with his hands behind turn about and go downstairs instead of up. Yet both direc-
his back and then, in the lower left-hand corner, a you ng tions, though not without meaning, are equally useless.
man who is already four times as big . Even his head has Two recalcitrant individuals refuse, for the time being, to
expanded in relation to his hand. He is looking at th e last take any part in this exercise. They have no use for it at all,
print in a series on th e wa ll and glancing at its details, the but no doubt sooner or later they will be brought to see the
boat, the water and the houses in the background. Then error of their nonconformity.
15
76. Waterfall, lithograph, 1961, 38 x 30 em Maurits Corne lis Escher, born in Leeuwarden, 17 June
In the same article in the British Journal of Psychology as 1898, received his first instruction in drawing at the
was mentioned in connection with the foregoing print, R. secondary school in Arnhem, by F. W. van der Haagen,
Pen rose publishes the perspective drawing of a triangle. A who helped him to develop his graphic aptitude by
copy of this is reproduced here. teaching him the technique of the linoleum cut. From
It is composed of square beams which rest upon each 1919 to 1922 he studied at the School of Architecture
other at right-angles. If we follow the various parts of this and Ornamental Design in Haarlem, where he was in-
construction one by one we are unable to discover any structed in graphic techniques by S. Jesserun de Mes-
mistake in it. Yet it is an impossible whole because changes quita, whose strong personality greatly influenced
suddenly occur in the interpretation of distance between Escher's further development as a graphic artist. In 1922
our eye and the object. he went to Ita ly and settled in Rome in 1924. During his
This impossible triang le is fitted three times over into the ten-year stay in Italy he made many study tours, visiting
picture. Falling water keeps a millwheel in motion and Abruzzia, the Amalfi coast, Calabria, Sicily, Corsica
subsequently flows along a slopir.g channel between two and Spain. In 1934 he left Italy, spent two years in Swit-
towers, zigzagging down to the point where the waterfall zerland and five years in Brussels before settling in
begins again. The miller simply needs to add a bucketful Baarn (Holland) in 1941, where he died on 27 March
of water from time to time, in o rder to compensate for loss 1972, at the age of 73 years.
through evaporatio n. The two towers are the same height
and yet the one on the right is a storey lower than the one
on the left.

16
1.
Tower of Bobel
2.
Castrovalva
3.
Palm
4.
G. A. Escher
5.
Fluorescent sea
6.
St. Peter, Rome
7.
Dream
8.
Swans
9.
Horsemen
10.
Two intersecting planes
11.
Day and night
12 .
Sun and moon
13.
Sky a nd water I
14.
Sky ond woter II
15 .
Liberation
16.
Development I
17.
Verbum
18.
Sphere surface with fishes
19.
Path of life II
20.
Smaller and smaller
21.
Whirlpools
?..2.
Circle \imil I
23.
Squa re limit
2.A.
Circle \iroil Ill
25.
Circle limit IV
26.
Fishes and scales
27.
Butterflies
28.
Reptiles
29.
Cycle
30.
Encounter
3 1.
Magic mirror
32.
Metamorphose
33.
Predestination
34.
Mosaic I
35.
Mosaic II
36.
Depth
37.
Cubic space division
38.
Three intersecting planes
39 .
Knots
40
M~ebius bo nd II
4 1.
Concentric rinds
42.
Spirals
43 .
Sphere spirals
44.
Moebius bond I
45.
Rind
46.
Bond of union
/

47.
Rippled surface
48.
Puddle
49.
Three worlds
50.
Still life with reflecting globe
51.
Hand with reflecting globe
52.
Three spheres II
53 .
Dewdrop
54.
Eye
55.
Cube with magic ribbons
56.
Concave and convex
57.
Double planetoid
58.
Tetra hedral planetoid
59.
Order and chaos
60.
Gravitation
61.
Stars
62.
Flat worms
63.
Another world II
64.
High and low
 :De Pedalternorotani:'iomovens eentroeu1a.tu.s a-rHculosllS ontstonCI,(generatlos,P.Onta.neat)
uit onbevredigdheid over bet in denatuur ontbre'kenvan wielvormLgeJevenae sene~e:
len met net vermos-en zicllrollena_VOO!'t te bewegen.}{et nier'bjj a.fgebeelae di.ertj~' Ltl ae
volksmond genaa.m~ 11Wente1teefje"of,,rolpens~ trc1cht dus in etln diepgevoeloe be:
hoefte teVQOrZten.Bio1ogisc1le 'DUzonaerneden :zyn nog sena.a.rs :i.sbet een
zoogoier,eell repUel,of een Lnsel<t? Het neeft een 1angger-ekt uit ver= 1
noor.nd.e _gel~d l~~en ~~vorma licnaam en dri~ paren poten,waarvan
de uttemden geJukems vertonen met aemenseJy'Ke voet. Iq net midden
en van de oLKke,ronde kop,die voorz~n ts vane en ste-rk g~bo~
daaT>:. -sen papa~aatensnavel,"bevtnoen :dell ae bolvormige
toe een ogen,die,op atelen ?eplaa:tst ,ter weerszyden van
betrekkel9k de 1<oP. ver uitsLeKen.In ~estrel<te poslt ie l<an
vlal<l<e baan net di.er- zteh~tN:ag en bedaclltzaa.m ,door
tot z~nbescnik mLadel van zijn zes_poten~voortbewegen
"king Me{t,aru'kt het over et>n wlllel<eurl.g substraat
zijn koQ op de grond ~n {het ka.n eventueel steile tra.pp~n
rolt ztch o1Cksemsnel opldi.mmen of afdalen ,dOO'P
op,wa~rbU net zlcb afduwt str-u.tkgewas neendrtngen
met zun pot en ~oor zoveel aeze of ove-r rots blokken
da.n nog desrond raken,In O.P-~ l<laut ereJl). Zo=
gerolde toestand vertoont net dra. net echtep
de gedaante van een dlscus-senyf, eenlange
waarvan decentpaie as gevor>mo worat wegmoet
door de ogen-op-stelen.Door zien beurle-:. afleg:
lings ~f te zetten met een van zijn dpie paren ~en

~oten, han net een grote snel'heio bereLl<en. .

Oo"k trekt net naar believen tijdens net rollen (bY.b~ het
afdalen van een nelling,of om zun vaart uit te lopef!)de P9:.
ten in en gaat ,freewlleeleriae verder.Wanneerllet er aa.nlei.~
1

ding toe 'heeft ,1<an llet op tweewlizen weer in wanael-posi tLe

over~aan: ten eerate abrupt ,door zijn lichaam plotseJingte
stre"kken maar dan lfgtllt?t op'zijn rusr,met zijn poten in ae luent en
ten tweede doorgeJeideJUke snelneidsvermtnaerin$ (remming met ae
poten) en langzame acnterwaartse ontroll~ng l7l stustaande toestand.

65.
Curl-up
66. .
House of stairs
67.
Rela tivity
68.
Three spheres I
69.
Drawing hands
70.
Balcony
71.
Doric columns
72.
Print gallery
73_
Dragon
74.
Belvedere
75.
Ascending and descending
76.
Waterfall
 ..
BG -Art/Photo/Arch
I S BN 978 - 1 - 4 3 51 - 18 5 8 -4

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