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Symmetry and asymmetry in aesthetics and the arts


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Symmetry and beauty are often claimed to be linked, particularly by mathematicians and scientists. However philosophers and art historians seem generally agreed that although symmetry is indeed attractive, there is also a somewhat sterile rigidity about it, which can make it less attractive than the more dynamic, less predictable beauty associated with asymmetry. Although a little asymmetry can be beautiful, an excess merely results in chaos. As Adorno suggested, asymmetry probably results most effectively in beauty when the underlying symmetry upon which it is built is still apparent. This paper examines the ways in which asymmetries, particularly left-right asymmetries, were used by painters in the Italian Renaissance. Polyptychs often show occasional asymmetries, which are more likely to involve the substitution of a left cheek for a right cheek, than vice-versa. A hypothesis is developed that the left and right cheeks have symbolic meanings, with the right cheek meaning like self and the left cheek meaning unlike self . This principle is evaluated in pictures such as the Crucifixion, the Annunciation and, the Madonna and Child. The latter is particularly useful because the theological status of the Madonna changed during the Renaissance, and her left right portrayal also changed at the same time in a comprehensible way. Some brief experimental tests of the hypothesis are also described. Finally the paper ends by considering why it is that the left rather than the right cheek is associated with unlike self , and puts that result in the context of the universal dual symbolic classification of right and left, which was first described by the anthropologist Robert Hertz.
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European Review, Vol. 13, Supp. No. 2, 157–180 (2005) © Academia Europaea, Printed in the United Kingdom
Symmetry and asymmetry in
aesthetics and the arts
Department of Psychology, University College London, Gower Street,
London WC1E 6BT, UK. E-mail:
Symmetry and beauty are often claimed to be linked, particularly by
mathematicians and scientists. However philosophers and art historians seem
generally agreed that although symmetry is indeed attractive, there is also a
somewhat sterile rigidity about it, which can make it less attractive than the
more dynamic, less predictable beauty associated with asymmetry. Although
a little asymmetry can be beautiful, an excess merely results in chaos. As
Adorno suggested, asymmetry probably results most effectively in beauty
when the underlying symmetry upon which it is built is still apparent. This
paper examines the ways in which asymmetries, particularly left-right
asymmetries, were used by painters in the Italian Renaissance. Polyptychs
often show occasional asymmetries, which are more likely to involve the
substitution of a left cheek for a right cheek, than vice-versa. A hypothesis is
developed that the left and right cheeks have symbolic meanings, with the
right cheek meaning ‘like self’ and the left cheek meaning ‘unlike self’. This
principle is evaluated in pictures such as the Crucifixion, the Annunciation
and, the Madonna and Child. The latter is particularly useful because the
theological status of the Madonna changed during the Renaissance, and her
left–right portrayal also changed at the same time in a comprehensible way.
Some brief experimental tests of the hypothesis are also described. Finally
the paper ends by considering why it is that the left rather than the right
cheek is associated with ‘unlike self’, and puts that result in the context of
the universal ‘dual symbolic classification’ of right and left, which was first
described by the anthropologist Robert Hertz.
… symmetric means something like well-proportioned, well-balanced, and
symmetry denotes that sort of concordance of several parts by which they
integrate into a whole. Beauty is bound up with symmetry. (Hermann Wegl;
Emphasis in original)
In the first paragraph of his famous book, Symmetry, Hermann Weyl discussed
158 I. C. McManus
the possible link between symmetry and beauty.
Certainly it is not difficult to see
how symmetries of various forms, be they in the natural world or the artificial
world of human aesthetics, are credited with beauty: the reflection of a mountain
in a lake, a starfish, flowers of many types, a honeycomb, snowflakes, the
symmetry of a face, the facade of a cathedral, a Byzantine mosaic of Christ
Pantocrator in a Greek church the list could be endless. Neither does the
symmetry have to be visual or spatial: music with the A-B-A structure of sonata
form, a play with its balanced structure of beginning, middle, and end, the Doppler
shift as a whistling train screams by, the lists could be endless. Symmetry is also
an obvious feature of good, practical and effective design a chair or table stands
most squarely (a revealing term) when it is symmetric, a clock face is symmetric,
tea-cups and dinner plates have their symmetries, and so on.
Ornamental or crystallographic symmetry
Weyl’s examples from the arts concentrated mostly on what he called ‘ornamental
or crystallographic symmetry’, with the manifold variations of the tilings of the
Alhambra being the paramount example. It was sketching these tiles on several
visits to the Alhambra, the first in 1922, that inspired the graphic work of M. C.
Escher, perhaps the most mathematically sophisticated of all twentieth century
Weyl tells how it was only in 1924 that George Po´lya showed there that
are exactly 17 mathematically distinct ways of tiling or tessellating a surface
if one likes, there are 17 fundamentally different types of wallpaper.
All of the
17 distinct types of pattern have been used by craftsmen using tiles or weaving
or decorating walls or any of the other myriad ways in which humans cover their
everyday objects with patterns,
imposing what Gombrich has called ‘the sense
of order’.
Interestingly, although all of the 17 types of pattern can be found in
art from around the world, not all types are found in all cultures (and that may
be because although the patterns are mathematically fundamental, it is not clear
that they are easily distinguished psychologically.
Although it is sometimes
claimed that all of the 17 types can be found in the Alhambra, it seems that only
13 of the types are actually there. Of the remaining four types it is said that two
have been found elsewhere in Islamic art,
but that the other two, specifically
pg and pgg, are not found anywhere in Islamic Art (although examples exist
elsewhere from, for instance, Zaire and the Navajo
The tension between symmetry and asymmetry
Although undoubtedly aesthetically satisfying from a mathematical point of view,
it is not so clear to aestheticians that the strict symmetries of tessellations are as
159Symmetry and asymmetry in aesthetics and the arts
satisfying as some other less symmetric patterns. Weyl hints at this when he quotes
from an article by the art historian, Dagobert Frey:
Symmetry signifies rest and binding, asymmetry motion and loosening, the one
order and law, the other arbitrariness and accident, the one formal rigidity and
constraint, the other life, play and freedom.
That pure symmetry is somehow too harsh, too rigid and unlifelike, was suggested
by Immanuel Kant, who commented on how,
All stiff regularity (such as borders on mathematical regularity) is inherently
repugnant to taste, in that the contemplation of it affords us no lasting
entertainment … and we get heartily tired of it.
The art historian, Ernst Gombrich was of a similar mind,
seeing a banality within
Once we have grasped the principle of order, we are able to learn the thing by
heart. […] We have easily seen enough of it because it holds no more surprise,
so that, symmetry and asymmetry are seen as,
a struggle between two opponents of equal power, the formless chaos, on which
we impose our ideas, and the all too formed monotony, which we brighten up
by new accents.
That same struggle was also emphasized by the psychologist Rudolf Arnheim,
Symmetry means rest and tie, asymmetry means movement and detachment.
Order and law here, arbitrariness and chance there; stiffness and compulsion here,
liveliness, play, and freedom there. […] On the one extreme … the stiffness of
complete standstill; on the other … the equally terrifying formlessness of chaos.
Somewhere at the ladder between the two extremes, every style, every individual,
and every artwork finds its own particular place.
Weyl recognized this tension, and described how ‘occidental art, like life itself,
is inclined to mitigate, to loosen, to modify, even to break strict symmetry’. That
indeed seems to be true of the social, biological and physical worlds, where despite
an overwhelming desire on the part of scientists to find symmetries, the world does
seem resolutely to be asymmetric at all levels, despite the best efforts to make it
Nevertheless there is an argument that symmetry forms the basis on
which asymmetry can be built, manipulated and used: ‘even in asymmetric
designs one feels symmetry as the norm from which one deviates under the
influence of forces of non-formal character’, as Wyle puts it. The philosopher and
aesthetician, Theodor Adorno, also saw the relationship of symmetry and
asymmetry in a similar way, in a sort of dialectic: ‘In artistic matters, asymmetry
can be grasped only in relation to symmetry.’
Symmetry is the basis on which
asymmetry can be built, just as the curves, irregularities and organic forms of a
160 I. C. McManus
Gaudı` building are predicated on an underlying geometry of horizontal and
vertical structures.
has also argued that there is an underlying cognitive scale beneath
the dimension of symmetric–asymmetric, which corresponds to simplicity–
complexity. In strict information theoretic terms that must be correct, for it
requires more bits of data to specify an asymmetric object than a symmetric object.
Amheim however takes the argument further in cognitive terms: ‘a taste for
symmetry is based on a more elementary propensity of the mind than its
Lurking here is also a suggestion that art develops, with symmetry
as a more primitive, simpler form of representation or portrayal which evolves,
with all the (non-biological) connotations of progress, into asymmetry. Certainly
that seems to be implicit in Wo¨lfflin’s distinction between the symmetry of
Byzantium and the early Renaissance, and the asymmetry of the High Renaissance
and the Baroque period,
and it is surely also a good description of the evolution
of Greek art, from the near symmetric kouroi of pre-Classical Greece, to the
elegant, fluid, lifelike forms of the fourth and fifth centuries BC.
Table 1 summarizes these psychological and aesthetic properties of symmetry
and asymmetry. Demonstrating them is easy, and has perhaps been most
straightforwardly shown by Gombrich
using a leaflet designed to teach amateur
photographers about composition. The two sketches in Figure l(a) are as
Gombrich prints them, and, as he says, ‘a sailing-boat photographed in the centre
Table 1. Summary of the psychological
and aesthetic properties of symmetry
and asymmetry according to art
historians and philosophers.
Symmetry Asymmetry
Rest Motion
Binding Loosening
Order Arbitrariness
Law Accident
Formal rigidity Life, play
Constraint Freedom
Boredom Interest
Stillness Chaos
Monotony Surprise
Fixity Detachment
Stasis Flux
Simplicity Complexity
161Symmetry and asymmetry in aesthetics and the arts
Figure 1. (a) Gombrich’s demonstration that asymmetry results in a sense of
movement. Because the boats are not identical in the left and right hand
images, the images have been manipulated in (b) and (c) so that the boat is
identical. Still the effect is compelling.
of a picture will look becalmed, one shown off-centre will appear to move’. And
he then goes on to add, ‘Of course, this applies with much greater force to
sailing-boats than, for instance, to trees, which suggests that even here meaning
has a large share in the resultant impression’. A potential problem with
Gombrich’s demonstration is that the boats in the original images are not quite
identical, the sails in the ‘moving’ image billowing more than in the ‘becalmed’
162 I. C. McManus
image. Figures l(b) and1(c) show the original images manipulated so that the boat
is in fact identical in each image; the effect is still compelling.
The continuum of symmetry
That there is also a continuum between pure symmetry and its total absence is
shown in another example from Gombrich, the computer-generated image
Schotter (Gravel Stones) by Georg Nees,
seen in Figure 2. The strict symmetries
of the original squares are slowly lost as the location and the angle of the squares
is jittered progressively more and more as one moves down through the image.
It is particularly interesting that, although in some sense the amount of symmetry
drops away monotonically as one passes from the top to the bottom, the interest
of the image is greatest perhaps a third of the way down. The original symmetries
are still discernable but new possibilities and relationships are also opening up.
Something here is reminiscent of the arguments of Stuart Kauffman,
suggests that the evolution of life that statistically most unlikely event – could
neither occur in the rigid, frozen, ordered world of ice crystals, nor in the booming,
Boltzmannian confusion of an ideal gas, but perhaps where ice is melting to water,
where there is fluidity and change, but order is not lost to noise as soon as it is
formed. Life evolved, he suggests, ‘at the edge of chaos’, and intriguingly that
area is also the most interesting and pleasurable.
The investigation of the way artists use symmetry and asymmetry requires
reference to images that are used repeatedly by many artists over a long period
of time, in a cultural context that is relatively well understood. One such situation
is the Italian Renaissance, with many examples being available and catalogued
for pictures such as the Crucifixion, the Annunciation, the Madonna and Child,
or the Madonna with Saints. Such images allow detailed statistics to be collected
and analysed, as a test of ideas about the nature of symmetry and asymmetry in
art. Nevertheless, not all art historians would see anything of use or interest
in such work. For, as the great Bernard Berenson once said,
The value of research depends on the field where it is carried out. The
most meagre adept may make elaborate statistics of the number of times in
the art of the middle ages our Lord blesses with three fingers, how many
times with two and a half, and how many times with two only; or how
frequently St. Catherine has her wheel, or St. Andrew his cross, to right or again
to left.
Despite his doubts about the enterprise, the data below could not have been
analysed had it not been for Berenson’s own industry in assembling his wonderful
catalogues of Italian paintings.
163Symmetry and asymmetry in aesthetics and the arts
Figure 2. Schotter (Gravel stones). Computer-generated image by Georg
Nees, 1968–1971. The work is also known as Wu¨rfel-Unordnung (Cubic
Disarray). Reprinted with permission of the artist.
Symmetry and asymmetry in Italian Renaissance art
Renaissance polyptychs
The polyptych was a standard form of the early Italian Renaissance. One of the
first, great pieces was the Baroncelli Polyptych of 1334 by Giotto and his school,
164 I. C. McManus
in the church of Santa Croce in Florence (Figure 3). The central panel shows the
crowning of the Virgin, and there are two panels to the left and to the right, each
containing portrayals of saints and of angels playing musical instruments. The two
left-hand panels show 51 saints and 10 angels, and the two right-hand panels also
show 51 saints and 10 angels. The overwhelming impression is of symmetry. And
yet a closer examination shows a curious deviation from symmetry. All of the 51
saints and 10 angels in the right-hand panels are looking to the viewer’s left,
towards the Virgin who is being crowned (and therefore each is turned to their
own right, and hence is showing the viewer their left cheek). However, although
50 of the saints and all 10 angels in the left-hand panels are looking towards the
Figure 3. The Broncelli Polyptych by Giotto and his school (1334). The
lower parts show an enlargement of the inner, left-hand panel.
165Symmetry and asymmetry in aesthetics and the arts
viewer’s right, once more towards the Virgin, and hence showing their right
cheeks, a solitary saint in the inner of the two left-hand panels is looking to the
viewer’s left and showing the left cheek. The apparent symmetry is broken. Quite
clearly that cannot be attributed to chance or error, for Giotto must have known
what he was doing, and it raises a question as to the underlying meaning.
Polyptychs are common in Italian Renaissance art. The eight volumes of
describing the paintings of this period contain 605 examples (for
further statistical details on this and other pictures, see McManus
). Most
polyptychs are simpler than the Baroncelli Polyptych, typically having two or four
saints arranged to either side of the central image. Symmetry breaking is relatively
common in these paintings, being found in 181 of the 605 cases (29.9%). More
intriguingly, in 105 of these (58.0%), the substitution is of a left cheek for a right
cheek, with only 76 cases (42.0%) where a right cheek is substituted for a left
cheek; the difference is significantly different from chance expectations (
l d.f., p 0.031). Thus, not only are asymmetries frequent, but they are more likely
to show an additional left cheek than a right cheek; the asymmetries are themselves
The meaning of the right and the left cheek
The ‘errors’ in the polyptychs predominantly involve the substitution of a left
cheek for a right cheek. The implication must, therefore, be that left and right
cheeks somehow differ in their meaning, for why else should a directional
asymmetry override the otherwise overwhelmingly symmetric structure of this
image? And understanding the meaning of the cheeks requires a more detailed
analysis of left and right cheeks in a range of paintings.
My first involvement with this problem was through the chance observation that
painted portraits are more likely to show the left cheek than the right cheek; and
of particular interest is that portraits of women are more likely to show the left
cheek than are portraits of men:
68% of 551 female portraits showed the left
cheek rather than the right, as did 56% of 932 male portraits in art galleries. The
proportions in each case were highly significantly different from 50%, and that
has since been confirmed in other studies.
The excess of left cheeks is unlikely
to result from the right-handedness of the artists since the same excess has been
reported in photographs.
Soon after we had published our data, Professor Walter Landauer wrote saying
that he had looked at 302 self-portraits in a book devoted to the subject, and only
39% showed the left cheek, a significant excess of right cheeks. Once we had
166 I. C. McManus
Figure 4. The use of the left and right cheeks in the portraits of Rembrandt.
Male and female portraits are sub-divided according to whether the subjects
are Rembrandt’s kin or non-kin.
become interested in self-portraits, an obvious artist to look at was Rembrandt,
and we rapidly confirmed that only 16% of the 57 self-portraits then recognized
as being by Rembrandt showed the left cheek. Although complex hypotheses
could be erected around the right-handedness of artists, the relative ease of
drawing left rather than right profiles with the right hand, the possibility that
self-portraits were painted using a mirror (Rembrandt certainly had mirrors in his
) and the role of the sitter of the portrait,
we were becoming interested
in a more subtle hypothesis that left and right had a symbolic meaning, rather
than being mere artefacts of handedness or turning tendencies. The key result was
when we broke down the rest of Rembrandt’s portraits by both sex and the
relationship of the sitter to Rembrandt.
Portraits of kin were more likely to
show the right cheek than were portraits of non-kin, be they male or female (see
Figure 4). Such effects could not be explained away by mechanical factors, nor
could other data showing that van Gogh was more likely to paint left cheeks for
his middle-class subjects than when he painted peasants.
The hypothesis we created was that left and right represented a continuum, with
the right cheek representing ‘like me’ (and hence self-portraits particularly fitted
into that category), and the left cheek representing ‘unlike me’ (and hence women
and non-kin were unlike the predominantly male artists). Of course many other
accidental, compositional features could also determine which might be shown
in a particular portrait, but the broad picture could not be explained away in those
167Symmetry and asymmetry in aesthetics and the arts
terms. The next step therefore was to explore the hypothesis further in the much
more tightly constrained subject matter of the Italian Renaissance, where there
were a large number of images that could be analysed.
The Crucifixion
The crucifixion of Christ is a very common picture in the Italian Renaissance, and
nowadays there is hardly a church that does not have such an image. Intriguingly,
of the 147 examples in Berenson’s volumes, 99.3% show Christ with the left
cheek, the sole exception being painted by Titian when an old man. There are also
a host of other asymmetries associated with the crucifixion, many of symbolic or
other value, such as the spear wound in Christ’s right side, and the tradition that
there was a good and a bad thief, with the good thief on Christ’s right (to where
he is looking), and the bad thief on his left. From the point of view of the present
theory, it is sufficient to note that the crucified Christ is about as unlike self as
The Annunciation
A more complex situation than either a typical portrait, or the Crucifixion, is the
Annunciation, in which the Angel Gabriel informs the Virgin Mary that she is to
be the mother of Christ. This situation is complicated because there are now two
principle actors in the scene, each being important. The data in Berenson’s
volumes are clear enough: of 209 Annunications, the angel enters from the left
side in 96.7% of cases, and hence the angel shows the right cheek and Mary shows
the left cheek. Compositional constraints mean it is nearly impossible to create
a satisfactory composition in which both the actors show their left cheek (and both
are unlike the artist, that is clear enough). There is also a further constraint here,
as can be seen in Figure 5, in which Veneziano’s Annunciation is shown correctly
and left-right reversed. The annunciation is about a message being conveyed from
one person to another, and there is a strong tendency, in Western art at least, for
such messages naturally to be read from left to right. The reversed version in the
lower part of Figure 5 looks wrong in some sense, although that in part may be
related to familiarity (see Blount et al.
). What is undoubtedly clear is that the
Annunciation shows a strong asymmetry, with artists choosing to break symmetry
in a highly consistent fashion.
The Madonna and Child
The Madonna and Child is another complex image, and as with the Annunciation,
two major figures, the Madonna and the newborn Christ Child, dominate the
168 I. C. McManus
Figure 5. The Annunciation by Domenico Veneziano (ca 1442–1448);
(Fitzwilliam Museum, Cambridge). The upper panel shows the picture in its
original form, and the lower panel shows the picture left-right reversed.
composition (although sometimes there are other figures as well). The Madonna
and Child is one of the most common images in Berenson’s volumes, representing
913 (16.8%) of the 5432 images. Such numbers provide unparalleled opportunities
for a detailed statistical analysis and, in particular, the consistency of the patterns
can be assessed across the different Italian schools of art, and across time. Previous
analyses of the Madonna and Child had concentrated on the side on which Mary
holds the Child. Salk
found that in 80% of cases the child is held on the left side,
a feature that he postulates is related to the natural tendency of mothers to hold
children on the left side, which he suggests is close to the heart, which comforts
the child. That explanation is now regarded as controversial,
and not particularly
relevant to present purposes. What is interesting is that Salk obtained his data from
a book entitled The Christ-Child in Devotional Images in the Italy during the XIV
However, as Figure 6 makes clear, although during the fourteenth
169Symmetry and asymmetry in aesthetics and the arts
Figure 6. The percentage of portrayals of the Madonna and Child with the
Child held on the Madonna’s left side, according to date and school. Solid
points are significantly different from 50%, whereas open points are not
significantly different from 50%.
century a majority of Madonnas do carry the child on the left side, the figure before
that is closer to 100%, and by the second half of the fifteenth century it has dropped
to below 50%. The pattern in the four main schools of Italian art is remarkably
consistent. Some explanation for these changes is required, and it is unlikely to
come from real changes in the actual manner in which women held babies, and
therefore a symbolic, compositional or other art-historical explanation must be
Although Salk’s analysis only considered the side on which the child was held,
it is also the case that the Madonna and Child each typically show one particular
cheek. At the beginning of the Renaissance the composition is fairly stereotyped,
and is shown as a schematic in Figure 7: the child is held on the Madonna’s left
side, the Madonna looks at the child, and therefore almost always shows her right
cheek, and the Child usually looks at the Madonna and therefore tends to show
his left cheek. Figure 8 shows the actual proportions of right and left cheeks,
for the Madonna, the Child and the two combined. Once again there are
clear historical changes, but these are most marked for the Madonna, who starts
the Renaissance almost always showing her right cheek and by the end of the
Renaissance is most typically shown with her left cheek.
The data in figure 8 show an important problem. The Madonna has shifted the
child from her left to her right side, and, quite naturally, for a mother would be
170 I. C. McManus
Figure 7. Schematic representations of the most frequent representations of
the Madonna and Child at the beginning of the Renaissance (top) and at the
end of the Renaissance (bottom).
Figure 8. The percentage of portrayals of the Madonna and Child in which
the Madonna, the Child and the Madonna and Child combined show the left
171Symmetry and asymmetry in aesthetics and the arts
expected to be looking at her child, now also shows her left rather than her right
cheek. However, the Child, who in the early Renaissance tends to return the gaze
of the mother by showing his left cheek, continues to show his left cheek, and
therefore looks away from the mother, which gives such images an awkward
appearance. The compositional solution, often found at the end of the
Renaissance, was either to have the Madonna and the Child looking at another
figure, perhaps a well placed Saint, or the Infant St John. Alternatively it was to
have the child holding an object towards which he is looking, perhaps a goldfinch,
a book or a rose. Although these devices solve the compositional problems, they
do not explain why the problem arose in the first place. The answer to that may
lie in the changing status of the Virgin Mary.
The Cult of the Virgin Mary
The status of the Virgin Mary in Catholic theology is complex, and can only be
touched upon here, but is discussed in detail elsewhere.
The important thing
for understanding the changes in the pictorial representation of the Madonna and
Child is the phenomenon known as the Cult of the Virgin Mary. Fundamental to
Roman Catholicism is the doctrine of Original Sin, which all individuals have
from conception onwards. To begin with, the only exception to this doctrine was
Christ himself, since he was conceived not of man but of the Holy Ghost. In
particular, as was emphasized by St Augustine (AD 354–430), the Virgin Mary
was not an exception to the rule of Original Sin. During the 6th and 7th centuries,
the Western and Eastern churches of Rome and Constantinople were splitting
apart, and about AD 700, the Eastern Church began to celebrate a festival of the
conception of the Virgin Mary. It should be emphasized however that this festival
did not suggest that the conception of Mary was immaculate, and Mary would
still have been seen as subject to the doctrine of Original Sin. In the 11th century,
the Normans were in Sicily where there were also large numbers of Greeks
celebrating the rites of the Eastern Church. With the invasion of England by the
Normans, the Eastern Churches’ festival of the conception of the Virgin Mary
spread from Sicily to England, and thence to France, Germany and eventually
Italy. In Italy, it caused much embarrassment, since it had mutated at some point
to become the festival of the immaculate conception of Mary, an idea strongly
opposed to church doctrine. The festival developed a populist momentum, and
despite attempts by St Bernard (ca 1140) to neutralize it by declaring the Virgin
Mary to be a Saint, the movement could not be stopped, despite the efforts of the
thirteenth century church, including that of St Thomas Aquinas. The movement
continued in the ensuing years, and further devices, such as suggesting that Mary
was cleansed of Original Sin during her intra-uterine life were not sufficient
to halt it; after a while it was supported even by scholars such as Duns Scotus
172 I. C. McManus
Figure 9. The ratio of portrayals of the Madonna and Child to those of the
Crucifixion in the Mediaeval Period and in the Italian Renaissance. Data for
the Renaissance are from the eight volumes of Berenson, and for the
Mediaeval Period from the publicly displayed collections of the British
Museum and Victoria and Albert Museums, and from three major reference
(AD 1265–1308). The belief was then taken up by the Franciscans, after which
it was only a matter of time before the Immaculate Conception became official
church dogma, although that occurred only in 1854.
The effect of the Cult of the Virgin Mary on painting can readily be seen in
Figure 9, which shows a rapidly rising proportion of paintings of the Madonna
and Child compared with those of Crucifixions. The challenge therefore is to see
whether the Cult of the Virgin Mary, which clearly developed throughout the
Renaissance, can also explain the changing portrayal of the Madonna and Child,
and in particular the shift of the child from the left to the right side.
At the beginning of the Renaissance, the two figures of the Madonna and the
Christ Child are very different in status; Mary is an ordinary mortal, subject to
Original Sin, whereas Christ was conceived immaculately and is the Son of God.
It is clear which is the more important, the Christ Child, and since he is very
different from the artist he is, therefore, like Christ in the Crucifixion, portrayed
showing his left cheek. Since it makes sense for Mary to look at the Child and
the Child to look at Mary, the child is therefore held on Mary’s left side, and Mary,
who is of less importance than Christ, has, faute de mieux, to show her right cheek.
However, as the Renaissance progresses, and Mary is perceived, by popular
acclamation as conceived immaculately, so she becomes of equivalent status to
173Symmetry and asymmetry in aesthetics and the arts
that of the Christ Child. The immediate requirement is that since neither Mary
nor the Child is now like the artist, then both should therefore show their left
cheeks. If, however, the Child were to continue to be held on the left of Mary,
then Mary would be looking away from the child, which would make little
pictorial sense. The solution, as we have seen, is to move the child to Mary’s right
side, which immediately solves the problem of Mary otherwise looking away from
the child, but introduces the new problem of the Child looking away from his
mother. The introduction of some other object into the left hand foreground, be
it saint, donor or a physical object, then solves that problem; the standard
composition of the Madonna and Child at the end of the Renaissance has come
into being.
Experimenting with the left and right cheeks
The analyses in this paper so far have been entirely descriptive. However, in
principle it ought to be possible to carry out experimental analyses of the meaning
of pictures showing the right or the left cheek. I did this many years ago in two
experiments, which were never published (Ref. 24, ch. 14). The design of each
study was similar. Subjects saw a series of slides of portraits, which were projected
either as they were painted or with left/right reversed and so shown in mirror image
(so that those painted showing the left cheek now showed the right cheek, and
vice versa). Subjects rated their perceptions of the pictures using a semantic
differential technique, in which there were 20 pairs of adjectives, such as
good–bad, strong–weak or spiritual–physical. As is common in such studies, three
factors were found to underlie the 20 judgements, which were labelled Evaluation,
Dynamism, and Spirituality.
Since some subjects saw a picture showing its left cheek, and other subjects
saw the same picture showing the right cheek, it is possible to compare the
judgements, to see whether the left and right cheeks have different meanings to
a typical viewer (the subjects in the studies were undergraduates who were not
studying art history). The results were extremely straightforward: although there
were clear differences in perception between the different portraits (some
depending on head tilt
and head canting
), the judgements showed no difference
at all according to whether, in the version seen by the subjects, a portrait showed
its right or its left cheek.
At first sight that result seems to throw the ‘like-self unlike-self’ hypothesis into
some doubt. However further analysis showed a much more intriguing result.
Although subjects reported no difference in the perception of portraits, which were
presented as showing the right or the left cheek, when the analysis was repeated
in terms of the cheek the artist had chosen to portray, the portraits originally
showing the right cheek were regarded more positive and more dynamic
174 I. C. McManus
than those showing the left cheek. In other words, even though viewers could not
ascribe a difference in meaning to left and right cheek versions of the same picture,
the artists had used the right and left cheeks differently. Clearly such a result needs
repeating (the results of Schirillo
are a partial replication), but the findings do
suggest that the cheeks may have different meanings, at the least to the artists
The origin of the meaning of left and right
If the ‘like-self unlike-self’ theory is correct (and even if it is not, then the
large-scale changes in the use of left and right in paintings still need to be
explained), there still remains one particularly difficult question, of why it is the
left cheek that is associated with ‘unlike self’, and the right cheek that is associated
with ‘like self’.
Left and right have symbolic meanings in many societies,
so-called dual
symbolic classifications. Even in classical Greece, the founts of rational,
philosophical and scientific thought are everywhere touched with right–left
Pythagoras said one should enter a sacred place from the right,
which is the origin of even numbers, and leave from the left, which is the origin
of odd numbers. In the Metaphysics, Aristotle describes how the Pythagoreans
identified ten first principles, which were listed in the two parallel columns shown
in Table 2, and which prominently include right and left. Right and left also have
different meanings in a range of other cultures. For instance, Needham
analysed the right–left symbolisms of the Purum,
a tribe living on the
Indo-Burmese border, and found a host of left–right symbolisms, which are
Table 2. The ten Pythagorean prin-
ciples described by Aristotle.
Limited Unlimited
Odd Even
One Plurality
Right Left
Male Female
At rest In motion
Straight Crooked
Light Darkness
Good Evil
Square Oblong
175Symmetry and asymmetry in aesthetics and the arts
Table 3. The dual symbolic classification of the Purums in relation to right and left.
Right Left Right Left
Male Female Kin Affines
Masculine Feminine Private Public
Moon Sun Superior Inferior
Sky Earth Above Below
East West Auspicious Inauspicious
Life Death South (North)
Good death Bad death Sacred Profane
Odd Even Sexual Abstinence Sexual activity
Family Strangers Village Forest
Wife givers Wife takers Prosperity Famine
Gods, Ancestral spirits Mortals Beneficent spirits Evil spirits, ghosts
Back Front
summarized in Table 3, and show a striking similarity to the Pythagorean
symbolisms. Western churches are also a rich source of symbolisms, which
has summarized in the diagram shown in Figure 10.
The first anthropologist to think seriously about the meaning of left and right
was Robert Hertz,
who in 1909 published a monograph on the symbolism of left
and right across a series of geographically and culturally disparate societies.
Figure 10. The symbolic meaning of the left and right sides of a Christian
Church. Based on Sattler.
176 I. C. McManus
Hertz’s earlier work had studied funerary and mortuary practices in a similar way,
and he had then been struck by the sheer variety of different ways in which humans
dispose of their dead. It is therefore all the more powerful a conclusion when Hertz
realized that there is universality in the meanings that societies attribute to right
and left; everywhere, in all societies, it is the case that right equates to good and
left to bad. As he puts it in his almost poetic introduction,
To the right hand go honours, flattering designations, prerogatives: it acts, orders,
and takes. The left hand, on the contrary, is despised and reduced to the roˆle of
a humble auxiliary: by itself it can do nothing; it helps, it supports, it holds.
Hertz understood biology, and he realized that the universal symbolism of right
and left must inevitably tie in with the universal predominance of right-
handedness over left-handedness (and there is no known society in which the
majority of people are left-handed rather than right-handed).
As Hertz puts it,
‘We must therefore seek in the structure of the organism the dividing line which
directs beneficent flow of supernatural favours towards the right side’ (my
emphasis); in other words by their handedness, and directly following on from
that, from their brain asymmetry. Why most humans are right-handed is another
story, and not one to be told here. What does matter for present purposes is that
right–left symbolisms are not arbitrary, but are constrained by biology, and by a
biology that extends back not merely to asymmetries of behaviour, but to
asymmetries of the brain, to asymmetries of viscera (such as the heart), and indeed
to asymmetries of the chemicals of which life is built, such as amino-acids and
Symmetry is a wonderful theoretical concept for science, providing structure,
organization and simplification for a host of complex, apparently unrelated
phenomena across many disciplines. However, seductive though symmetry is as
a concept, there is much evidence that not only is asymmetry found in the
sub-atomic world of physics, and throughout the biological world at all levels,
from biochemicals to brains, but that asymmetry is also exploited and developed
in the arts as well. Symmetry, although mathematically fascinating, also has a
coldness, a rigidity, a fixity, a sense of stasis, which is less interesting, less
attractive, indeed less beautiful than asymmetry. Too much asymmetry is however
mere chaos. Asymmetry, when it is used in the arts, is used to season symmetry.
The ur-structure of much art, just as in biology, is symmetry, but some asymmetry
is added to that symmetry to generate interest and excitement, for a little
asymmetry, correctly used, makes objects optimally satisfying. When artists do
use asymmetry they must also make choices, as symmetry can break in several
177Symmetry and asymmetry in aesthetics and the arts
different ways. Even left–right symmetry can break in two ways, to left and to
right, and an intriguing finding is that there are large-scale historical continuities
in the ways artists choose to use left or right. The Italian Renaissance, with its
large number of pictures portraying similar subject matter in the context of a
well-understood theology, provides a good situation for studying such asym-
metries. The origins of the symbolic meanings attached to left and right are
not entirely clear, but probably have a universal human component, driven by
the universal human predominance of right-handedness, which in turn is
driven by brain asymmetries, body asymmetries and chemical asymmetries.
However, without an understanding of the deep mathematical structures of
symmetry we would not be able to realize how asymmetry is generated.
Symmetry and asymmetry are therefore an essential dialectic for both science
and aesthetics.
I am grateful to Professor Onur Gu¨ntu¨rku¨n for assistance in the preparation of this
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About the Author
Chris McManus is Professor of Psychology and Medical Education at University
College, London. He is author of Right Hand, Left Hand, which was awarded
the 2003 Aventis Prize and is co-editor of Laterality. He is a Fellow of the
International Association for Empirical Aesthetics.
... The phenomenon of symmetry has fascinated people since ancient civilisations. Directly or indirectly, it is increasingly the subject of investigation in the arts [1], architecture [2], biology [3], medicine [4], mathematics [5], and various engineering disciplines [6][7][8]. ...
... We may now formally define B (1) = {u; (u ∈ G) ∧ ((u is on the border of U) ∨ (∃v, (v ∈ U\G) ∧ (v and u are neighbours)))}. The cells of B (1) are plotted in grey in Figure 1d. 6. (2) where |B (1) | denotes the cardinality of B (1) , and Centre(k) = (u k,x , u k,y , u k,z ) is the central point of a cell u k ∈ B (1) . ...
... The cells of B (1) are plotted in grey in Figure 1d. 6. (2) where |B (1) | denotes the cardinality of B (1) , and Centre(k) = (u k,x , u k,y , u k,z ) is the central point of a cell u k ∈ B (1) . The origin of the coordinate system is then moved to C (1) as seen in Figure 1e. ...
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A new algorithm is presented for detecting the global reflection symmetry of geometric objects. The algorithm works for 2D and 3D objects which may be open or closed and may or may not contain holes. The algorithm accepts a point cloud obtained by sampling the object’s surface at the input. The points are inserted into a uniform grid and so-called boundary cells are identified. The centroid of the boundary cells is determined, and a testing symmetry axis/plane is set through it. In this way, the boundary cells are split into two parts and they are faced with the symmetry estimation function. If the function estimates the symmetric case, the boundary cells are further split until a given threshold is reached or a non-symmetric result is obtained. The new testing axis/plane is then derived and tested by rotation around the centroid. This paper introduces three techniques to accelerate the computation. Competitive results were obtained when the algorithm was compared against the state of the art.
... Here, the observer has found the presence of regularity in the image with effort, and pleasure may follow from this discovery [41]. Note also that some authors have suggested that perfect symmetry can be too regular and slight deviations from it may be better at driving preference [58]. This hypothesis, however, does not have empirical support [59]. ...
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symmetric patterns are generally preferred to less regular patterns. Here, we studied 2D patterns presented as 2D images in the plane, and therefore producing a symmetric pattern on the retina, and the same patterns seen in perspective. This perspective transformation eliminates the presence of perfect symmetry in terms of retinotopic coordinates. Stimuli were abstract patterns of local coplanar elements, or irregular polygons. In both cases they can be understood as 2D patterns on a transparent glass pane. In the first study we found that perspective increased reaction time and errors in a classification task, even when the viewing angle was kept constant over many images. In a second study we tested a large sample (148 participants) and asked for a rating of beauty for the same images. In addition, we used the Cognitive Reflection Test (CRT) to test the hypothesis that people who tend to give the more immediate and intuitive answer would also show a stronger preference for the symmetry presented in the frontoparallel plane (in the image and on the retina). Preference for symmetry was confirmed, and there was a cost for perspective viewing. CRT scores were not related to preference, thus not supporting the hypothesis of a stronger preference for symmetry in the image when people follow a more immediate and intuitive gut response.
... Symmetry, an obvious kind of order and regularity, has often been linked to harmony and beauty (for a review, see McManus, 2005). Although symmetric patterns are generally found to be more beautiful (e.g., Jacobsen and Höfel, 2002), recent research shows that the extent to which this is the case depends on the type of task and the level of expertise of the participants (Leder et al., 2019;Weichselbaum et al., 2018). ...
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Perceptual organisation is hypothesised as a key in the perception and appreciation of abstract art. Here, we investigated how relational and compositional features affected the perception and aesthetic appreciation of Black Square and Red Square by Kazimir Malevich (1915). We studied how (i) the presence and obliquity of the red square and (ii) the relative configuration of the black and red square affected the detectability of the obliquity of the black square in this artwork. Results showed that the simultaneous presence and obliquity of the red square masked the obliquity of the original black square. The likelihood of the black square being incorrectly perceived as an exact square was always maximum in the original configuration and even slight alterations in the original configuration of the work resulted in the obliquity of the black square to be noticed. The original artwork was more aesthetically preferred compared to its alternatives. We argue that the artist may have intentionally set the configuration to mask the obliquity of the black square and maximise the aesthetic preference.
... liking and tourism) could be grounded on the "liking" and "wanting" facets of the reward system [8], with the tourist judgments anchored to observer's intention of exploration; • Symmetry did not predict liking with these images. This is new but it is not surprising [9]. Further research may investigate the role of subjective evaluations of other aesthetic components; • The no predictive role of the CNN measures for both judgments suggests that beholders' evaluation of real-world stimuli is influenced more by personal experience and sense of engagement; • The predictive role of the CNN left-right symmetry for subjective symmetry suggests that observers explore photographs in line with motor possibilities. ...
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[ABSTRACT: Perception, 50(1S), 108. ] Photographs as cognitive sources might have an impact on the development of a tourist destination image (TDI). When we look at pictures of places to visit, we imagine being in the represented place, “as if” we would be physically present exploring that place. This mechanism is grounded on the match between perception and action advocated by the embodied cognition account. Besides, it has been demonstrated that the aesthetic appearance of the place has a significant impact on the TDI. Since images can influence TDI, we aimed to test the role of embodied and aesthetic components in the choice of tourism destinations. In an online study, we presented 50 photographs of tourist places. Participants (N=121)provided ratings to evaluate three embodied components (bodily engagement, sense of exploration and the will to explore behind the scene) and symmetry. They also indicated how much they like each photograph and how much they would visit the place. All ratings were provided on a 0-100mm visual analogue scale. In addition, image aesthetics (symmetry, self-similarity and variance) were extracted with a Convolutional Neural Network (CNN) deep learning algorithm. We found that bodily engagement and sense of exploration predicted both liking and tourist judgments, whereas the intention to explore further predicted only the tourist judgment. None of the CNN components accounted for liking and tourism judgments. Interestingly, left-right mirror symmetry predicted subjective symmetry, reflecting a left-right exploration strategy through the images. Taken together these results lend support to the involvement of embodied processing in TDI.
... In Art, symmetry is also often linked to the concept of elegance. This is not to say that symmetric artworks are more beautiful, as it is known that most humans prefer faces, musical pieces, paintings and photographs where the symmetry is not exact, but slightly imperfect or broken [1,2]. In Physics as well, deviations around a symmetric situations are often considered as a useful approximation technique, since perfect symmetries are seldom found in Nature. ...
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We explore whether Neural Networks (NNs) can {\it discover} the presence of symmetries as they learn to perform a task. For this, we train hundreds of NNs on a {\it decoy task} based on well-controlled Physics templates, where no information on symmetry is provided. We use the output from the last hidden layer of all these NNs, projected to fewer dimensions, as the input for a symmetry classification task, and show that information on symmetry had indeed been identified by the original NN without guidance. As an interdisciplinary application of this procedure, we identify the presence and level of symmetry in artistic paintings from different styles such as those of Picasso, Pollock and Van Gogh.
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Abstract: Façade aesthetics is among the main areas of interest in architecture, urban design, and environmental psychology. In the interaction between the observer and the environment, the façades have a kind of communication value. Façades have repetition and similarity features and also represent various differences and uniqueness potentials. These properties show their aesthetic value. Within this aspect, symmetry is an important factor in the architectural and aesthetic value of the façades. However, the question of to what extent a façade should have symmetry and similarities, and to what extent it should have diversity and unique qualities, is among the discussion topics of the design field. These debates have the context of mathematics and science as well as design, psychology and philosophy. Digital aesthetics issues contribute to the interpretation of symmetry relations such as the golden ratio, fractal geometry and information entropy. Relationships of information entropy with Gestalt psychology and symmetry in visual studies led to the development of a different methodology of the subject defined as symmetropy. The architectural façade, symmetry, and entropy issues have different relationships with each other. The aim of this study is to discuss and interpret this trio of relationships among the façades, symmetry, and entropy with a literature-based review. This review will include critical approaches and the contextual origin of information entropy. The metaphorical, philosophical, and methodological content of the approach is discussed together with its controversial aspects. Keywords: architectural façades, information aesthetics, environmental psychology, symmetry, information entropy, symmetropy
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Abe Forsythe's Down Under (2016) is the first narrative feature film about the Cronulla riots, the infamous event on 11 December 2005 where over 5000 white Australians, responding to a minor local incident, descended on Cronulla Beach in Sydney and proceeded to harass, chase and bash anybody who they perceived to be of Middle Eastern appearance. In the following nights, a series of violent retaliatory attacks took place, as community leaders called for calm. Suvendrini Perera identifies how a symmetrical narrative had emerged in the wake of the riot and its aftermath, whereby Cronulla Beach "comes to stand for a paired sequence of events, the riot and the revenge, in a fable of equivalence in which two misguided groups . . . mirror each other's ignorance and prejudices". This article considers how Down Under reinforces the distortive implications of this "riot and revenge" narrative by maintaining a structural equilibrium, through the rigorous balancing of its narrative and characters, and formally, via its soundtrack, cinematography and editing patterns. In so doing, and despite its antiracist sentiments, the film ultimately dilutes the issue of race and obscures the power imbalances that informed the riot, and which continue to this day
Conference Paper
In the Iranian Islamic architecture, the existence of geometry as a principle has produced valuable and magnificent works over time and these properties are often founded in Islamic Iranian architecture phenomena. In this research, we have investigated some of the geometrical principles in Islamic Iranian architecture, also have studied thesis expression and influence in the Iran carpet. The main question of this research: What are the geometric principles in the Islamic Iranian architecture and how are these principles manifested in the Iran carpet? In this study, some geometrical patterns such as symmetry, circle, square and rectangle have been investigated thoroughly and compared in Iranian carpet and architecture. The results of this research showed that in the Islamic Iranian architecture were used geometry in theirs plan just like that in the carpet, this pattern of design and geometric principles have been taken always into consideration, and the full manifestation of geometry in Iranian handmade carpets were evident also, and this commonality of thought has given rise to the idea of Iranian artists and carpet weavers.
This study took the dial interface of smartwatches as its experimental sample and investigated screen shapes (square and round) of smartwatches and how the interaction between symmetrical type and complex type in the screen interface of different shapes affects the user’s hedonic and pragmatic qualities. Then, we further evaluated the relationship between perceived hedonic quality and pragmatic quality and the continuous usage intention of the smartwatch. Results from a between-subjects experiment (N = 200) indicated that the interaction between objective attributes in interface design esthetics affects the users’ quality perceptions. The results also revealed that perceived hedonic quality and pragmatic quality could be positively associated with continuance intention to use a smartwatch. This study explored the relationship between the objective attributes and the perceived subjective process in interface design esthetics, and provided empirical evidence for the relationship between the objective attributes and the user’s quality perceptions in interface design esthetics. Moreover, connecting the interface design esthetics of the smartwatch indirectly with the continuous usage intention, it is helpful to better understand how the related attributes of the interface design esthetics can stimulate the user’s quality perceptions, confirm the user’s demand for the qualities of the smartwatch more accurately, and consider how to use esthetics to improve the user’s continuous usage intention to the smartwatch.
The functional left-right asymmetry of the human brain (Table 1) appears to be determined, at least in part, by genetic factors. Hemispheric laterality found in some birds and subhuman primates1,2, statistics on structural asymmetry of cerebral hemispheres in human neonates3, the well-documented clinical studies on functional asymmetries as revealed by localized brain lesions4–8, and the findings on congenital left-handedness correlated with speech dominance of the right hemisphere provide the main evidence supporting this premise (see chapter 9). The following considerations ensue from these ideas. Before we discuss the possible effects of left-right brain asymmetry on aesthetic performance in the second part of this paper, we shall present some thoughts on potential environmental factors in the development of left-right asymmetry in the human brain, which are believed to modify the genetically controlled postnatal brain development.9
First published in English 1960.
Repetitive interface patterns are one of the hallmarks of Islamic and Moorish art. Through the study of various collections of such patterns, it is easy to verify that, despite the considerable complexity of the designs, most of the interlaces are formed by strands of a small number of shapes – often just a single shape stretching over many repeats of the design. This observation is described and documented by the authors, who present a simple explanation for this phenomenon.