Drawbridges: Norbert Francis Attard in Japan
THE ARTIST IN PROGRESS
"The Japanese leave nothing to chance ... every tree, flower, pebble, blade of glass has its artistically proper place. The same is true of my art"
Way back in 1979 I was invited by Norbert Francis Attard to write an introduction to the catalogue of one of his first exhibitions. As a young artist, Attard had already caught my attention with his high quality production of immaculately made prints (1977-81) depicting mythical towns and fabled cities. These were inspired by Malta's cube-townscape forms and also influenced by the chimerical depictions and renderings of such artists as Folon and Escher. Almost prophetically, I had entitled my introduction, "The Graphics of Feng Shui", because of the spiral graphics employed by Attard to depict the surrounding areas of his castle-like structures. What had notably struck me in this particular series by this fledgling artist-architect, was the stark contrast, a form of tension of the opposites, between the architectural dominance of the built-form of the walled citadels and the sinuous labyrinthine earth force-lines of their setting. These earthbound, meandering, serpentine forms, read to me, as metaphors for the Ch'i dragon forces of the earth, as understood in the geomantic Oriental science of Feng Shui. The Medusa-like tresses of the telluric surroundings of Attard's urban cities sinuously merged into the geometry of his meticulously delineated ordered structures; which in turn rose and melted into celestial helix skies, also rendered in coiling convoluted spiral patterns. It was already obvious, that even in these early days, the artist was already haunted and captivated by the relationships of a man-made order to the rhythms and forces of nature. The artist's Japan works featured and discussed in this publication, may therefore be read as a culmination of the artist's long standing interest in these equations. The Kamiyama installations are a concrete manifestation of Attard's consistency in his growth and development as an artist; with many of the motifs found in these early works appearing again, in more complex format.
Attard followed this architecturally oriented collection with a series of graphics which focused on the more rigid geometric forms of the Muslim MIHRAB; the devotional focal point of the congregation in mosque buildings all over the world. In this series (1982-84), for the first time, he involved himself in a search for harmonic and spiritual acquiescence, through the discipline and rigour of the contemplative precision of geometry and its ordered forms. His next important exhibition journeyed him to the Far East and provided him with an initial encounter with the 'kimono' mind of Japan. Again, this print series was to prove somewhat prophetic, in terms of providing for the artist a thematic stepping stone to the 2004 'artist in residence' work-pieces in Kamiyama. In these visual 'kimono' essays (1985-86) Attard comes under the influence of the Orient and its religious beliefs of Zen Buddhism and Shinto. The designs of these Japanese vestments are delicately depicted, while also hinting at both the hidden symbolic overlays of the intricate patterns themselves and also the more complex ramifications of the whole thinking process of the Oriental mind. Worn by the Geisha, the kimono, introduced to Japan over 1200 years ago, combines both artistic achievement and allurement. A garment, that fuses elegance with discomfort, it is a perfect example of the Japanese capability of equating and combining the dichotomy of opposites. From the ebullient graphics of the kimono, Attard then passed to even more elaborate depictions; the symmetrical diagrams of the cosmological order of the Mandala (1987). With its multifarious symbolism of the universe, mandalic geometry is the most balanced and perfectly proportioned example of representation of symbolic order. In this series of graphic prints of these sacred cosmic geographies, the artist ventured for the first time into the exploration of the relationships and equations of mathematics, symmetry and their resultant harmony of form.
By 1995 Attard had initiated his departure from figurative art and ventured into the world of abstraction. His 1996 exhibition at the Foundation for International Studies in Malta's capital city, Valletta, featured his crossing over the threshold to a more organic and abstract lexicon. Although freer than his previous print series, the works exhibited were still bound and held together by a disciplined geometric overlay. The titles of many of these paintings, now in much larger format, were again to provide clues as to where the artist was eventually to go. His titles, "Sacred Geometry", "Listening to Nature" and "Measure of the Earth" are clear indications of Attard’s increasing interest, not only in the forces of nature, but more so in the underlying order of their geometry and propagation. Post the blurred opacity of a first glance, on closer examination, the paintings also revealed references to Malta’s mysterious Neolithic culture and its sophisticated art forms. Peter Serracino Inglott, in his catalogue introduction to this collection, refers to the "Hypogeum-like imagery" of the works.
Immediately post this exhibition, Attard passed from print-maker and painter to installation artist. Now no longer practising as an architect, this stepping over to a new realm of creation involved him passing from the confines of the limited spaces of museums and galleries to the wider arenas of workplace and site. As an interventionist, he now became both maker and creator of an inter-cultural art form. In this new field, the relationship of the artist to the workplace of the art-piece itself, became a paramount factor. No longer carrying his work with him, Attard now dialogued directly with the geography, geology, history and memory of place, while also participating with the community of the specific country or area in which he was working. His works became essentially site-specific and the meaning of the phrase "spirit of place" was extended to have broader and deeper meanings. Attard, here, metamorphoses himself into a quintessential map-maker, establishing longitude and latitude equations between remembrance and desire, yet time-framed to the mystical co-ordinates of the not yet and the no longer. Now an installation artist, Attard transforms his audience from spectators to participants. The artist has turned mediator, engaging with society through direct interactive and dialogical participation. Attard is no longer object maker, but service provider. From this body of work, worthy of particular notice are the artist's creations of "Beyond Conflict" set up at the Biennial of Liverpool in 2002, where he wrapped red and green fabric round the city’s oratory building; the explosive orgasm of colours which revitalised the dilapidated Manning Mills in Bradford in 2003; the "Palestrina and Hell" intervention at the Johanniterkirche Feldkrich in Austria; and the haunting mirrored water installation of Salina’s Lament at the Borders exhibition at the rehabilitated Pinto Wharf Stores, in Valletta, Malta, also dating from 2003, for which I contributed to the catalogue text.
The following year, with a now established international reputation, Norbert Attard was invited as artist in residence, for a six-week period, to Kamiyama, on the Shikoku island of Japan. During his stay there, the artist combined transported memories of his own ethnic roots and his long-standing fascination with geometry and proportion, to merge them with his personal reading of the spirit of place and ethnic customs of Japan. All this generative material combined to produce a series of highly imaginative and original installation works, which involved cultural interchanges and amalgamations in a manifestation of a contemporary "global village" art-form, which at the same time read as specifically regional and local. The Kamiyama ‘artist in residence’ programme invites artists to create works of art, which, while reflecting the Zeitgeist of today are also specifically conceived in relationship to nature and more so to the particular local genius loci. During his stay in this province of Tokushima, Attard constructed intellectual drawbridges between the ancient cults of his isle of the Middle Sea and the still dominant love of nature of the land of the cherry blossom, in interventions which spanned and connected this shared common theme across millennia, from Stone to Internet Age, in installations at the same time conceived as equations to dissolve cultural barriers while constructing interchangeable space-time hyperlinks.
When, on arrival in Kamiyama, Attard discovered that two of the national holidays of Japan were the spring and autumn equinoxes, he immediately constructed a mental equation with the Malta Mnajdra Neolithic stone calendar complex and marker of these two paramount seasonal dates. Separated by thousands of kilometres in space and over five millennia in time, the cultures of Japan and Malta, share across space and time a common adhesion to, and respect of, the rules and rhythms of nature. These civilisations, though different and apart, both based their life patterns on these rhythms, which, in turn, are governed by the harmony and order of number. Nature’s progress, change and growth patterns all seem to be structured and ordered by a particular mathematical and geometrical overlay. Attard, in his Japan body of works, relies essentially on the mysticism and order of number, as the generative structuring grammar and underlying syntax for the core lexicon of his artistic creations.
THE COGNITIVE FOUNTAINHEADS
"The first law of ecology is that everything is related to everything else"
At this stage, before dealing with the mathematical syntax of knowledge of how all things are ordered through the overlying grammar of mathematics, it is worth examining the two spatial or place depositaries, from which Attard draws his inspiration for these latest of his creative interactions, Japan, as the location he is visiting and working in, and the Maltese archipelago as the formative cultural identity environment of the artist. Both these locations, together with their collective memory, act as the springboards for the artist’s poetic creations, conceived as cross-cultural and time-bridging equations, bringing together the peoples of two countries, through their common understanding of the
overriding rules and laws of the forces of nature.
THE LAND OF THE RISING SUN
"In Japan nature has not altogether lost its paradisiacal loveliness"
Perhaps the most apt definition of the enigmatic land of contrasts that is Japan is that provided in the title of Ruth Benedict’s book "The Chrysanthemum and the Sword". Commissioned in the early forties, the author, a cultural anthropologist, was assigned the task of preparing a study of this country in order to help the United States of America during that delicate period, to answer a multitude of questions relating to this land and its inscrutable people. Japan, to this day, remains to the western mind, essentially a country of divergent contrasts and ambiguities. To the West, the complex dualities of the Orient tend to read as apparent contradictions. The Yin-Yang dyad provides perhaps the best metaphor for outsiders to understand how the Japanese are able to combine elements that may well appear to others as dichotomies. Derived from ancient Taoist philosophies, the Yin-Yang composite circle is the Oriental symbol for symmetry and symbiosis. Yin, is read as the passive, earth-focused female principle and Yang as the active heaven-oriented male one. Following this equilibrated principle of duality, the people of Japan are able to combine and blend such delicate expressions as moon-viewing and insect-listening with the forceful cults of the Martial arts and Sumo wrestling, thus creating cross-over connections between nature's amiable aesthetics and militant rigour. Japan, in many respects, may be considered the Oriental counterpart of Ancient Greece, with its combination and co-existence of the antithetical divinities of Apollo and Dionysus. The Japanese milieu is a world of heraldic animals, double-edged swords and colourful kites. Here rocks have one hundred and thirty-eight names and each is meaningful in terms of its corresponding void. It is therefore not surprising that every gesture of each inhabitant is a studied portrait of elegancy and precision, that paper through Origami is precisely folded into poetry, in a land that may be considered the very quintessence of austerity. To this day, newspapers still carry items of news on the forthcoming efflorescence of the "Sakura" cherry blossom. In spring, the air is satiated with the pink misty clouds of this flower’s falling petals, offering a perfect example of nature's springtime opulence. The Samurai in typical adherence to the Oriental mind-frame adopted the cherry as their metaphor for death in combat ... to scatter in the wind while still in one's prime.
While the Western world regards man as the focus of all things, the Far Eastern holistic ideal focuses on man belonging to and being but a part of the whole continuum of nature. The Japanese believe it is nature and not man that does the creating. Both the religion of Zen and the indigenous Shinto, point to man being inseparable from his environment and the heart of nature. Zen, from the Chinese Ch’an meaning meditation, is an austere path to enlightenment; a world of conundrums and paradoxes, which cannot be reduced or equated to any verbal formulae. Its main object remains that of infusing the temporal with the infinite in a creed which teaches that nothingness is the totality through which one attains enlightenment. Shinto, which means "the way of the gods", was, on the other hand, developed in Japan. It has no moral teaching and its belief is that divinity manifests itself in all forms of nature. The focus is specifically on nature, together with the veneration of the sun goddess Amaterasu. Its thinking may perhaps be defined as a process which circles its target in contrast to the more linear Western thought processes. Shinto may, therefore, be understood to be an animistic and pantheistic relationship with nature; a creed which believes in regeneration, fertility and ritual purity. It developed from the needs of the country's dominant agrarian society, focused on rice farming. So important was the produce of the earth, that up to the end of the 19th century, Japan still adopted the Lunar Calendar, which was more attuned and suitable to the country’s agriculturally focused society. As such, the Japanese New Year, Risshun started in spring as opposed to the Gregorian Calendar's first day of January.
From these earth-oriented Japanese attitudes, Norbert Francis Attard draws his equational relationships between Japan and Malta’s Neolithic farming people. The Japanese have always believed that their gods and spirits are embedded in the earth, in the forms and shapes of the landscape itself. To this day, Japan is a land still obsessed with the myths and legends of earth gods and goddesses and it is through this parallel that Attard constructs his drawbridges linking the creeds of the land of the rising sun to his native island’s Neolithic culture and its own earth-focused beliefs.
In Japan, all is still governed by sets of meticulous rules applied as an overlay to an ordered and disciplined hierarchy. The still practised Japanese arts of Ikebana, Bonsai, Landscape Gardening and the Tea Ceremony, all demonstrate a complex lexicon typical of the country’s intricate multi-dimensional culture. The specific qualities of wabi, essentially the quality of sparsity and severity, together with that of sabi, interpreted as a sense of melancholy, are qualities which one constantly encounters in many of these exquisite arts and perhaps even more so in the design and layout of the traditional Japanese garden. In these arenas of contemplative mysticism, through man's mutation of nature, a deep elegiac meditative Tatazumai is established. Ultimately, the serenity of the relationship between man and nature in these arenas, may be read as the cosmicisation of nature, which in the process transfigures into a consecration. Space in these Zen gardens is qualitatively different. Mirroring the sparingness and in-depth meanings of the minimalistic poetry of the Zen koan and the traditional Haiku, the Japanese gardener through their his selective Sentei sparsity together with his overall understanding of nature, is able to equate and link the temporal with the timeless. These are spaces sensed not only through reason but more so through one’s senses and emotions. It is the combination of this land’s structured society; its particular indigenous spirit of place and traditional culture and the artist's own architecturally-ground passion for order, discipline and proportion, together with the collective memory of his own homeland, that serves Attard in his production of these fascinating and intriguing "Between Sky and Earth" works .
THE ISLE OF THE MIDDLE SEA
"The people of this clairvoyant isle
in allegiance to their land
cast amalgams human and divine
metaphysical symbols of unity
umbilical dyads of fertility and sterility
where death meets birth in an eternal cycle of return"
The Maltese Islands, at the crossroads of the history-laden Middle Sea, boast the most important of all architectural Neolithic remains of pre-history. Pre-dating the major ancient world monuments of the Middle East, Egypt, Crete and the standing stones of Northern Europe, the most imposing of the Maltese temple structures date from around 3500 to 2500 BC. This was an era when man was changing from hunter to farmer and consequently settler. Through the discovery of agriculture and the human habit change from roamer to settler, the first artificial man-made landmarks appeared as the precursors of architecture. From these markers of territory, which now became equated to power, an architecture that reflected its builders’ understanding of both earth and sky forces and nature was developed. A society, which relied almost entirely for its existence on the produce of the earth, soon became aware of the dependency of its agrarian product on the movement and cycles of the heavenly bodies. Many of the Malta temples, particularly the Mnajdra complex, were planned not only as sacral structures, but also as time-clock calendars to enable their builders to read seasonal changes in order to establish the correct time for both the planting and harvesting of crops. These peoples' interest, however was not limited and bonded solely to the forces of the sky but was also related to and concomitant with the reading and understanding of earth forms, their configuration and their underlying subterranean energy forces. It was through this understanding of both sky and earth forces, that this ancient society established precise spatial locations and alignment placings for their structures. The reading by these people of earth's force-lines was not dissimilar to the still existent Far Eastern geomantic practice of Feng Shui (wind-water).
Many believe that the layout plan form of the sacred temple buildings of Malta was based on an anthropomorphic reproduction of the Earth goddess herself. This deity, in the belief of Neolithic man, was not only the personification of the earth and the provider of nourishment, but also the archetypal symbol of the whole human psyche. There is little doubt that these Malta temple structures were constructed by a people obsessed by both eschatology and the rhythmical cycles of nature, together with an inherent umbilical relationship to and understanding of above and below energies and forces. Because of their interest in the cycles of woman, agriculture and seasons, besides those of the earth and the heavenly bodies, these people were quick to read time in a cyclic as opposed to a linear manner. Thus the spiral was an apt symbol for them to depict and explore, in their attempt to come to terms with, both the passage of time and also natural and human cycles. The concept of expanding growth and perpetual regeneration must have held a particular fascination for these people. No doubt, they would have observed the spiral and its patterns in the natural phenomena of whirlpools, whirlwinds, flowers and more so in land molluscs and sea shells. Their interest in this labyrinthine symbol must have also provided them with a metaphor for the evolution of their own life pattern, from origin to indefinable destination through the cycle of birth, life, death and eventual re-birth. The amorphous matriarchal buildings of Malta's pre-history, with their complex artifacts and symbols, together with the whole intricate spectrum of the islands' cultural identity, provided Norbert Attard with an inspirational launch pad to establish his imaginative links and connections with the converse paradoxical spirit of place of ‘God’s Mountain’ in Kamiyama.
The terrestrial and celestial alignments of the Malta temples, together with their complex layout plan-form, demonstrate not only ancient man's in-depth comprehension of nature and the earth, but also hint at a more sophisticated knowledge and practice of measurement, geometry and geomancy. Through the combination of both an inherent and instinctive knowledge, combined with a far from "primitive" intellect, Neolithic man was able to forge successful equations to be able to live in peace and harmony with not only his fellow brethren, but also with the forces of nature. The materialistic desacralisation of our contemporary culture will never permit us today to understand the philosophies of these ancient people, their rituals or the guiding grammar of their architecture. Their relationship to path-finding and place-making together with their interactions between form and meaning are now irretrievable. Man today has in fact lost his memory of this knowledge of the past. Japan, on the other hand, remains one of the few countries which still manages to achieve a consistent and healthy relationship with nature, its environment and its produce. It is still a country where ritual is an enactment of myth and nature is understood, above all, in terms of its animistic qualities. In Japan the understanding of geography is still given an extra dimension in terms of a spiritual and sacred comprehension. Hence the dialectics of dualities and dichotomies, constructed by Norbert Attard in Kamiyama, become even more pertinent and apposite contemporary manifestations; for above all, they hint at a possible way for modern man to once more re-reconcile himself with nature, in a new and vital spiritual ecology, so essential for the survival of our species.
THE MATHEMATICAL LEXICON
"Art is a shadow of divine perfection"
It is a well known truism that life today is almost totally controlled by number. Through number, man is constantly gauging and measuring both material loss and gain. The idea of number being used with a sense of deeper meaning has become a far removed and distant concept for contemporary man. Yet the rupture between the rational and mystical understanding of number is only a recent one. Up to the time of scientists and mathematicians such as Kepler and Newton, the esoteric overlay of number was still prevalent and considered to be an essential and inseparable property. From ancient Babylon, Egypt, through to the Greeks, and up to the time of the pioneers of the sciences and mathematics of the Enlightenment, mysticism and number were intertwined and inseparable. Even the societies of the ancient Mediterranean and Europe understood the spiritual meaning of number. It was Alexander Thom who confirmed that one of the earliest applications of Pi in architecture was in the building of the ancient stone circles of northern Europe. For the later Pythagoreans everything was related to number; and they even understood that the movements of the planets and stars were fashioned on numerical and geometrical frequencies. Around this period of the 6th century BC, mathematics was believed to be an intellectual Mandala which helped man to focus his vision on the structure and make up of the divine. For ancient people mysticism of number always related to the sacred; an understanding which was carried on into later Christian thought processes. St Augustine perhaps the greatest of the Christian thinkers and philosophers saw in number "an image of the Creator". It was only with the birth of modern science that mysticism and magic were removed. Yet today, as scientists probe the seemingly endless realms of astrophysics to peer into the very origins of the universe, it seems that this overlay of magic is creeping back in. Perhaps it was science itself that removed much of the metaphysical meaning of mathematics. Yet today the qualitative is returning, as complex new calculations are being derived to answer challenging contemporary questions. It may therefore be said that the soul is once again creeping back into science. Einstein himself seemed convinced of this when he stated that "mathematical theories cannot be true unless they are also beautiful".
Norbert Francis Attard as an installation artist applies a poetic magical overlay onto his recent works by not only instilling a deep mathematical content to his creations, but by actually using the mystical aspect of number as the generating force of his works. In his venture into the realm of numbers, Attard lays a qualitative and a symbolic mantle to add to the depth and meaning of his work. The tools and vocabulary utilised by the artist in this research have led him to investigate and bring into play both the mystical and magical significance of specific numbers and the fascinating mathematical patterns which have intrigued man for millennia. The numbers and series which have particularly haunted Attard, may be listed as Pi, Phi, the Fibonacci Series and the Spiral. Some explanatory notes on these captivating items, may not be out of place, to help the reader further appreciate Attard's work-approach and thought process in the making of his works.
Pi or Π
Pi or Π is the ratio of the circumference of a circle to its diameter. Its mathematical value is 3.14159 ... This endless number has both puzzled and fascinated mathematicians ever since its discovery. It seems that its earliest use was by the ancient Egyptians. The Greeks however were also aware of Pi through geometry, but since it could not be expressed as a whole or as an exact ratio, they did not classify it as a number. To this day, Pi still holds a particular fascination; so much so that a film with Pi as its title was released in 1998 and only recently Givenchy marketed a men's cologne of that name. The whole concept of sacred geometry has constantly incorporated Pi as one of its essential elements. It may in fact be said that sacred geometry is the magical relationship between Pi and that other captivating number Phi, also used as an even more important tool by Attard in the working and making of his current art pieces.
Phi or Φ
Phi or Φ, a function of division as opposed to Pi, which is a function of the circle, remains perhaps the most fascinating number within the whole spectrum of mathematics. Described by Johannes Kepler as "one of the two treasures of geometry" (the other being Pythagoras’ theorem), and already referred to in the 16th century as the "Divine Proportion", Phi is established when the ratio between the larger and smaller unit of a divided line is equal to the ratio between the sum of the two and the larger one. In the following figure, if the ratio of AC to CB is the same as AB to AC, then the line is said to have been divided in a "Golden Ratio" proportion. In numerical terms the exact value of Phi is that of 1.6180339887 ... while its mathematical formula is Φ = (1 + √5)
A C B
This ratio which provides the most aesthetically pleasing of proportions is found constantly in botany, biology and astronomy as the consistent form-maker and generator of the whole order of nature.
The fact that Phi is neither a whole nor rational number and is also a never ending number, has endowed it with even further mystique, intrigue and mystery. The name Phi was only given to this ratio in the last century by the American mathematician Mark Barr, who took the first Greek letter Φ of the name Phidias. Phidias was the great Greek sculptor (490-430 BC) author of the sculptures of the immaculate friezes of the Parthenon on the Acropolis, which he proportioned on the Golden Ratio. The temple itself was also designed, by its architects Ictinus and Callicrates, using Golden Ratio proportions.
Throughout history, mathematicians, artists, architects, biologists, musicians and practitioners of other disciplines have both utilised and been beguiled by this ratio. Omnipresent in nature and consistently utilised as a design tool in architecture and art, Phi has been glorified as the sacred canon of perfect proportion. The first definition of Phi was given by Euclid, the founder of geometry, in his book Elements, in Ancient Greece, around 300 BC. The Ancient Greeks believed that harmony was divine and that divine proportion could only be achieved through special numerical ratios. In the 4th and 5th centuries, mathematics adopted a philosophical and intellectual overlay to add to its quantative and qualitative qualities. Later, it was Arab mathematicians who continued research into Phi. However, it was in the 12th and 13th century, through the work of Leonardo Fibonacci, that the Golden Ratio assumed its apex of importance and significance. Through his study of a problem not remotely connected to Phi, Fibonacci developed and expanded the already mythical properties of the Golden Ratio even further. It was through a study of the breeding habits of rabbits that he developed his theory of sequential growth. (Vide the section on the Fibonacci Series below) The later Renaissance produced many artists and mathematicians, who utilised and further studied and developed the qualities of this proportion. Piero Della Francesca and Leonardo Da Vinci himself, both wrote about and made use of the Golden Ratio in their work. However, it was the mathematician and painter Luca Pacioli (1445-1517) who made the most valid contributions to the study of Phi. In his book "Divina Proporzione" he went as far as to compare its properties to the infallibility and incomprehensibility of God himself. Later, Pacioli's blending of the mystical and maths was continued in the studies of Johannes Kepler (1571-1630) leading to the Golden Ratio being understood to be present in all natural phenomena and its also being consistently utilised by man as a proportional tool in all creative arts.
The last years of the 19th century then provided numerous literary publications on the subject and this renewed interest also flowed into the work of the artists of that period. This curiosity was carried into the 20th century, the most valid contribution being that of the iconic master-architect Le Corbusier, in his acclaimed publication Le Modulor. The Modulor, according to its author provided "a harmonic measure to the human scale, universally applicable to architecture and mechanics". Le Corbusier established his proportional theorem on the fact that the ratio of a man's height to the height of his navel was that of the Golden Ratio. Other bisections based on similar sub-divisional proportions were developed and Le Corbusier believed that by using these ratios one could provide a standard universal harmony. Einstein, on viewing Corbusier’s Modulor, is said to have commented that it was "a scale of proportions which makes the bad difficult and the good easy." To this day, the Golden Ratio continues to appear in many guises and aspects in the creation of the arts, from music to painting, sculpture and architecture. Mario Livio, Head of the Science Division at the Hubble Telescope Science Institute has stated that "humans had no idea, however, into what magical fairyland this product (the Golden Ratio) was going to lead them". There is little doubt that Phi does provide fascinating ratios and that it does in fact govern growth, development and expansion patterns in nature, and the whole of the universe. It remains, to this day, a most fascinating and intriguing scale applicable from miniscule micro to endless macro.
The Fibonacci Series
Leonardo Fibonacci (1170-1240) in his 1202 book "Liber Abaci" contributed fascinating and novel interpretations and applications in his studies of what he termed 'new maths' A mathematician, with a virtuosic command of number and its use, Fibonacci was able to also extend and expand the essential properties, meaning and use of Phi. Studying the mating habits of rabbits, he discovered a recursive sequence of vital mathematical importance. This, now termed Fibonacci Series, follows an expansion growth pattern wherein each number is equal to the sum of the two preceding ones, i.e. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 .... The particular fascinating property of this series is that as the sequence expands further, it converges to the Golden Ratio. Again, as with Phi itself, the Fibonacci Series was found to be existent in the basic syntax of the whole of nature. All propagation in fact seems to be governed by this growth pattern, with plants and fruits offering perfect examples. The Fibonacci Series is inherent in both the micro and macro worlds; from that viewed through the microscope to that detected only through the telescope.
The spiral, utilised by Norbert Francis Attard, as another generating form-maker in his Japan works, is one of man's oldest symbols of transition. It has, from ancient times, been read as not only the representation of regeneration, but also as an allegorical metaphor for spiritual development and progression. The unfurling whorls of this curve have constantly evoked in man connotations of growth. Man also read in the depiction of the spiral, seasonal changes and other expansion and contraction cycles in nature. Post the Paleolithic era, the spiral is consistently found in Neolithic, Egyptian, Muslim, Indian and Japanese cultures. From the time of Attard's native island's Neolithic temple carvings, to this day, the spiral symbolises symbiosis, transition, life cycles, perpetual regeneration and spiritual progression. The spiral is present and prevalent in the sciences, in magic and mysticism, as also in the arts of all ages. As an ever expanding infinite continuum, man has adopted it, over the ages, as his symbol for eternity, since it embodies both expansion and contraction, together with the combined aspects of genesis and decline.
Spirals may be generated in two forms, either the Archimedean or the logarithmic. The former discovered by Archimedes in the 3rd century BC, the latter also termed equiangular, by Descartes in the 17th century. In the Archimedean spiral, the distance between the developing coils remains constant, as the spiral itself expands, while the differentiating property of the logarithmic spiral lies in the gradual growth of the radius as the spiral itself develops. One of the most fascinating properties of the logarithmic spiral is that it can be constructed from a rectangle with the proportions of the Golden Ratio, demonstrating an intriguing mathematical relationship between this growth form and the ever magical number of Phi. It is on this equational correlation that Attard modelled his ± 1.618034 installation in the Fureai Park in Kamiyama.
The spiral, to this day, remains one of the archetypal symbols of mankind. Its existence in nature, from the minutiae of monocellular organisms to the galactic entities of the universe, provides proof of the paramount importance of this form. It is also worth noting that the double helix in the make up of the human DNA is made up of two concentrically twisted spiral tapes. Not dissimilar to the coiling umbilical cord linking child to mother, the geometric format of the spiral has fascinated man from pre-history to today. It is therefore not surprising, that an artist of the calibre of Attard, should return to its form and utilise it as one of his basic generative forces in his innovative and avantgarde mathematical songlines.
THE ART WORKS
"The senses delight in things duly proportional"
Norbert Attard’s interventions in Kamiyama focus specifically on, and draw their energy from primarily the power of place chosen for his art works. This relationship to site, together with the inborn influence of the artist's island origins, are brought together in a series of ebullient anachronistic visceral mutations. Yet Attard's fundamental anchoring tie in all these works, is his profound understanding of the discipline and order to be found in the refined order of mathematics and its numerical framework. The artist brings together time past and time present through the use of a revived esoterical magic of number. Attard is reviving from ancient times the use of the quality of number as opposed to its computative quantity. He is expanding and extending its day to day quantative function to that of an elevated qualitative one. Number, as understood and utilised by our ancient ancestors, as discussed before, was not only a functional mathematical tool, but its practical aspect was always embedded with a strong symbolic overlay. Numbers were read not only as computational, but also as possessing higher values related to both cosmic and divine revelation. Ancient civilisations all believed that mathematics was a ladder and bridge, which assisted man to reach out to the realm of the divine; in the process knowing full well that number was also the prime form maker and propagator of harmony.
Attard, as an artist of today, returns us to these creeds. In the ancient world, as we have seen before, all was number. Today, dialectic mathematics is a rigorous non-variable science of logic, where statements are either true or false. In ancient times, although solving real world problems, mathematics was variable and pragmatic in its relationship to individual and particular problems. Attard, in his Japan works, metamorphoses himself to become a rationalising artist as well as an irrationalising mathematician. His preoccupation with proportion led him to the obvious investigations, studies and use of extraordinary and special numbers. From the remarkable qualities of Pi, to the satisfying proportions of the Golden Section or Phi, together with the fascinating sequence of the Fibonacci Series and the eternal patterns of the spiral, Attard utilises this bewitching alphabet to establish an intriguing lexicon and vocabulary, which he in turn then employs in relationship to the collective memory of Malta and Japan to formulate formidable and valid art works. Much of his work in this direction may be said to evoke Nietzsche’s concept of the eternal recurrence of time. As such, much of the work in Kamiyama could be defined as a combination of the aesthetic of place in a particular time, brought together through the underlying chain-link of mathematics. This body of works is above all characterised by an aesthetic rigour and sparsity, arrived at through Attard's capability, in his maturity as an artist, of a spartan, lucid and discerning sense of selectivity. In away, it may be said that in these installations Attard has remarried myth and maths.
The following analysis on the individual works in Kamiyama, will I hope further inform and elucidate the reader as to the philosophy, work methodology and thinking process utilised by Attard, in the making of these site-specific and number-ordered creations.
"I do not know if God is a mathematician, but mathematics is the loom upon which God weaves the fabric of the universe"
Clifford A. Pickover
±1.618034 is a permanent sculpture installation located in the Souzou no Mori, Fureai Park, on the outskirts of Kamiyama. In this work utilising concrete and water, perhaps more than in the others of the series, one sees the return of the architect-builder in the artist’s work. Consisting of a cut-out cast-concrete logarithmic spiral platform containing water, and based on the Fibonacci Series, the prime function of this creative piece is to enable the spectator to equate its man-made geometry to the natural landscape of the site. Primarily an art work which incorporates nature into its surroundings, it also allows one to reflect on the hidden order of number, inherent in the generating grammar of its form. Specifically site-oriented, it also provides viewers with reflected images of Kamiyama’s "God’s Mountain". Because of its black-tinted reflective water surfaces, the piece brings into play not only the location, but also the people who visit it. Shinto-oriented in terms of its relationship to nature and place, it remains however a work which emanates from the essence of its mathematical proportions. Its beauty is realised through the harmony of Phi, and the aesthetic order and elegance it constantly generates and displays. Here Attard establishes a bridge between earth, sky, man and nature, and also a geographical connection between the isle of his origins and the site-specificity of the works location. This "spiral mirabilis" hints to its spectators, answers to man's ever enigmatic question of "where do we come from and where are we going?" With its water glimmering mirror surfaces evoking Ovid's Metamorphoses myth of Narcissus, the installation provides an inverted variety of static and kinetic symmetrical connotations, recalling the artist's 2003 Malta installation "Salina’s Lament", where the dialectics of image and reality were also expressed in profound poetic intensity. Attard's doubling of the real with the reflected in a Japanese setting provides a reference to the mirror, an important mythological symbol in the country's folklore, while also recalling mirror myths relating to the sun goddess Amaterasu.
Attard's ±1.618034 art work exists not only as an artifact on its own, but is extended into a reflective duality, through its mirrored image, while also allowing the observers' vision to expand through these visual echoes into a labyrinth of doubled infinities. As in music, the work's negative voids and silences are as important as its positive form-making elements. Attard's concept demonstrates visceral interplays of inversions, dualities and binary images all of which pulsate in fascinating and playful interchangeabilities. The artist has here created an enchanting visual poem that unifies image and reality and echoes in diametric symmetries observer and observed in advancing and receding interchanges between spatial hereness and thereness. This work is an interventionalist's subtle poetry, the verses of which must be sensed holistically, perhaps as best expressed
in Juhani Pallasma’s words through "the eyes of the skin".
"The footprints we leave behind us are of those who have passed before us"
Maria Cristina Crespo
A work of A-Oishi stone, sand and stone aggregate, located at the Kamiyama stone factory, Kamiyama, on the banks of the river Akui, in between two randomly dumped mounds of discarded factory bluestone. The installation emanates from a single anti-clockwise spiral, then develops into a true, undeviating line, culminating in two interconnecting spirals at its termination. Attard's concept of paving a disused intermediate zone recalls the Japanese concept of Ma, while the artist's chosen iconography of the spiral form is a particularly apt metaphor for the regenerative birth of an abandoned refuse-site. Attard seeks through this form to establish a temporal equation of resuscitation and revival, between the chaos and disorder of the previous condition of the site and the new order superimposed by the geometry of the applied artwork. Attard's bridge-building takes place, not only in the form of a physical link between the two sides of the discarded stone mounds, but also in the more vital crossover and change in the character and nature of the site; from that of disuse to a pulsating and vital art-form, the spiral forms providing excellent exponential symbols for the restored heart-beat given back to the site. Here Attard is super-imposing a man-made order over a pre-existent arbitrary chaos. These whirling motifs are the expressed symbols of cyclic expansion and growth in contrast to the linear passage flow of the river. The artist is also establishing a relationship to the linear concept of time, expressed by the etched Euclidean central line in the installation. Contrasting this with the whorl patterns of the end spirals, Attard establishes a connection between ancient and contemporary understandings of time. This synthesis of contrasting time-readings is a duality which, to the Japanese mind, could evoke and echo the essential essence of the Yin-Yang principle. The installation's sparsity, together with the somewhat melancholy overlay of the grey tones of the bluestone, re-kindles recollections of wabi and sabi. Attard’s symbiosis of time and space, interpreted also in terms of inter-relationships between the indigenous and the imported, may perhaps be best summed up in the words of the Japanese architect Kisho Kurokawa: "Our tradition is the challenge which exists in change... we are not afraid to learn from others".
"Numbers are fundamental realities alive with memories and eloquent with meaning"
Vincent Foster Hopper
Again, etched on the banks of the River Akui, Attard creates a downsized artwork which may be interpreted as an echo of the ancient art of land modelling. Only in the last century did the enthusiasm for shaping and forming the landscape wane. Here the artist re-designs the natural form of the riverbank, re-modelling it as a poetry-garden inviting the waters of the river to enter. The artist is now no longer representing a landscape but actually using it to re-evoke the lung-mei spirits and dragon-paths of Oriental geomancy. This specifically site-bound intervention, is a land-art piece reminiscent of the earth works of Walter De Maria, Richard Long, Herbert Bayer and perhaps even more of Robert Smithson’s "Spiral Jetty" 1970 intervention on Great Salt Lake, Utah, U.S.A.
Earth Galaxy, although exiguous in scale, still provides considerable impact on its observers, in its recollection of the Japanese art of Bonseki, those delectable Lilliputian miniscule stone and sand tray landscapes. Despite its diminutive proportions, Attard’s creation is an impressive example of the artist's fertile imagination. Furrowed into the earth, it remains, similar to the others in this series, a work essentially disciplined, by the order of its overlying canvas of mathematics, number and geometry. Earth Galaxy simultaneously recalls, utilises and reflects cosmic rhythmic laws and rules. This is a work, which to my mind, also recalls the enigmatic crop circles and their geometries, with its elegance, symbolism and similar geometries echoing the synchronicities of these mysterious phenomena, as also their makers' (whoever they are) grasp of number and pattern-making.
"Why does mathematics fit so excellently the objects of physical beauty?"
An indoor installation constructed within the walls of the Josei High School of the town, based on a three-dimensional interpretation of the Fibonacci Series. Each new square generated has a side whose length is that of the sum of the last two squares’ sides. On the floor, within the areas defined by the lower construction sides of the developing squares, a spiral is created, made up by drawing a quarter circle in each of the generated squares. This floor spiral is composed of 12,000 sudachi fruits, an indigenous citrus lime of the region. While not site-specific in relation to a specific external context, the work, through its utilisation of a local product, also relates specifically to place. It also involved work and participation by the local community in the labour intensive and arduous work process of the collection of the sudachi, for its manifestation. The artist, here, is not working with the landscape but with its produce. Golden Sudachi is a time-toil bricolage work that invites a haptic sensory exploration. It is worth recalling that space and matter are measured, not only by the eye, but also by the ear, nose, skin and tongue. In this work, the bouquet of the fruit evokes, in the observer’s memory, recollections of particular events or special places; for as we know too well, the nostrils are capable of awakening forgotten images. It was Gaston Bachlelard who reminded us of the power of this sense in his "Poetics of Space". The sudachi aroma also provides added thresholds and gateways for the observer to cross, in order to enable him or her to participate with greater depth in the work's multi-dimensional qualities.
"Geometry and number are the ideal philosophical language"
Food Cycle is an art-work installation consisting of a spectacular array of ethnic Maltese foods organised at the Kaizen Centre in Kamiyama. The ingredients were particularly chosen by the artist to equate and mirror local Japanese produce. Rice and beans common to both Malta and Japan, but cooked and presented in different ways are utilised by Attard to prepare and lay out this edible-art piece. The choice of boat shaped containers hints at the journey undertaken by the Mediterranean items to their far eastern destination and perhaps also to the journey of the artist himself. Mediterranean dietary habits, not unlike the Japanese, are also considered to be among the most nutritious and beneficial, providing their respective countries' inhabitants with a healthy longevity. It is interesting to again see that the ingredients of Attard's art piece, are laid out and arranged in strong geometric patterns within an ordered symmetry. The artist contrasts and combines edible products from the two countries to draw parallels and divergences between their cultures. References are also made to the spring and autumn equinoxes, the time when day and night both have equal 12-hour durations. For agrarian societies, equinoxes were always time-frames of paramount importance, establishing and mapping the date and time for both planting and sowing of their crops In the layout of this piece, Attard also echoes Japan's aesthetic considerations, in not only the preparation of food but more so in its artistic presentation. The Japanese, perhaps more than other nations, have always regarded their food as a form of natural medicine; thus each season has its particular food, and their diets are adjusted according to weather changes, and what is naturally in season. This affinity with nature and its products remains to this day the main influential element of the Japanese cuisine. Of all the works in the series, "Food Cycle" is the one which actions all five of the human senses, and its enactment may be viewed as a haptic polyphony of the senses, inviting visitors to a multifarious participation, including that of finally consuming the art-work.
"Geometry has two great treasures; one is the theorem of Pythagoras, the other is the Golden Mean: the first is gold, the second silver"
Situated within the sacred shrine of the Kami Ichinomija Oawa in Kamiyama, Earth Mother is a work that merits particular interest and attention. For its making, Attard reorganised oversized wooden beads from the shrine itself into a tri-cellular layout plan based on a stylised version of a Maltese Neolithic temple plan. The concept of a temple within a temple, distanced in time and space and yet connected in terms of a common dedication to a deity, conceived as both provider of nature and protector of human life, presents a fascinating equation of sacrality installed within sacrality. The Maltese temple plan is based on the articulated Ggantija layout of the island of Gozo. Its symmetrical amorphous curvilinear forms contrast with the rigid linear sparsity of the orthogonally planned Shinto shrine, in an interesting interplay between content and container. The organised axiality of the ascetic Shinto shrine (based on the Japanese Ken module) is also to be found in the curvaceous Malta temple (proportional on the ancient measuring unit of the megalithic yard), since both are laid out symmetrically around a central axis, reminding us that the ancients never read symmetry as uniformity, but always as unity, i.e. as a binding rather than dividing process. So much so that the Greek word for symmetry may be interpreted as the 'harmony of parts with each other, and with the whole'. The Orient and Occident through the forms of their buildings fashioned for divinatory and cosmological purposes, millennia apart, are drawn together by Attard, through contrasts and similarities in their purpose and layouts, to remind modern man of the value and importance of nature in today's contemporary world. This typology of space-time translocation takes its viewers back to the two countries' indigenous sacred structures and emphasises not only the uniqueness and individuality of the buildings themselves but also their builders' respective beliefs, creeds and habits. The whole is replete with a play of both differentiating and parallel elements. In today's complex electronic world, despite Global Positioning System computers, which enable us to exactly locate ourselves in spatial co-ordinates, man still has an uneasy relationship with his planet. On the other hand, both the practitioners of Shinto and the worshippers of the Earth Mother of ancient Malta, considered mapping, morphing and place-making paramount to the establishment of an ecological linkage to the earth and its natural habitat. Attard's Earth Mother art-work reminds us of the importance of reinstating man's relationship with his planet. In the making of this man-nature link paradigm, Attard extends his activity from that of an installation artist to that of an admonitory environmentalist, heeding more
than necessary warnings to today’s desacralised contemporary life style.
"What is God? He is length, width, height and depth"
St Benedict of Clairvaux
This intervention, again constructed in the Josei High School, Kamiyama, consists of an installation of two large intertwining spiral forms, together with four smaller spirals, all created by using Japanese slippers in a combination with other indigenous materials. The larger spiral is then combined with other spirals, projected on the wall surface. The piece, which could be termed Attard's glorification of the spiral, also featured music by Keiju Nakajima. The two large major whorls intertwine, radiating outwardly and inwardly respectively; the first as a metaphor of growth and generation, the second alluding to decline and degeneration.
The slipper, as the constituent element of this intervention, brings to mind its prime function of aiding human motion and movement, i.e. the transference in three dimensional space by means of the passage of the fourth dimension, time. This work of fusion and separation, establishes an equation between the two opposing spirals forming a constituent whole of progressive and regressive forces. The ancillary materials, consisting of bluestone, dry leaves, sudachi and rice, utilised with the slippers in the composition, evoke the four seasons of summer, autumn, spring and winter, as do also the four smaller spiral forms. The combination of positive and negative in the larger elements once again reiterates the artist's interest in antithetic yet integral relationships; for Attard understands all too well the necessity of marrying the centrifugal and the centripedal to produce the balanced equilibrium of nature's orderly and equitable life. In this work, the artist again creates a fascinating relationship and connection between spatial distance and temporal space. Imaginative installationist that he is, Attard here performs as a magician crossing the threshold of lost knowledge, while, diagramming mythical messages and metaphors for members of our contemporary myth lacking society to read.
"Make a round circle of the man and the woman,
and draw out of this a square ...."
Sacred Geometry, an installation again organised in one of the halls of the Josei High School, was created in collaboration and with the help of twenty-four of the school's pupils within the duration of a two-hour workshop. Utilising the ultimate non-art material of toilet paper, Attard unwrapped the micro scaled spiral rolls to re-wrap them again around eight students positioned and laid out on a square plan. This process provided an interesting curvilinear spiral form genealogy, as developed and evolved from the linear geometry of the four sides of a square. The remaining sixteen students then formed a surrounding outer circle and they in turn were wrapped in toilet paper by the artist. The internal square formed by the schoolchildren, was conceived as a symbol of the earth encircled by the outer circle, which Attard related to the planet’s revolving celestial bodies, thus creating a micro representational form of a world-universe equation. The artist, again working in close collaboration with the local community, utilises computations and combinations of mathematical data to create in a contemporary language re-echoes of Oriental space-time concepts. As in all the works of this series, Attard is once more able to dissolve obscure barriers through his imaginative utilisation of new methodologies thus enabling him to provide new understandings of the old.
“If we trace the artistic forms of things made by man to their origin, we find imitation of nature”
Attard’s Sparticles works are a post-Japan visit series, originating from the photographic records of the making processes of his Kamiyama community works. On return to his Gozo studio, the artist digitally manipulated his photographic images to metamorphose them into new art forms, again relying, as on the works themselves, on a mathematical and symmetrical order for their generation.
Based on the same symmetry and order exemplified in the Maltese Neolithic temple plans and Japanese Shinto temple layouts, Attard manipulates his recorded images into complex mirror compositions evoking the super symmetries of fractal geometry. The term fractals was first coined by the Polish mathematician Benoit Mandelbrot. It refers to the irregular geometry found in nature and to the whole system normally referred to as chaos. Fractals provide frames of reference capable of describing forms, which cannot be depicted or portrayed in terms of Euclidean geometry. Mandelbrot, in his research, noticed that many natural forms such as snow flakes, crystals, etc., displayed endless sequences of repeatable motifs. It was his attempts to mathematically describe the components of such structures, that led him to the discovery of the theory of fractals.
Fractals in nature are characterised by branching. It is exactly this property that Attard echoes and applies to this section of his work. Through digital transformation, the artist takes portions of his recorded images and gradually manipulates and layers them frame by frame, to achieve seamless symmetrical morphologies of repetitive patterns. Recalling ancient Islamic and Celtic patterns, and re-echoing sacred Mandelic geometry, these juxtaposed sequences also mirror the inherent hidden chaos to be found in all natural phenomena.
Appearing, initially, as simple pattern-making exercises Attard’s Sparticles however revel in the more complex and profound depths of super symmetry, twin imagery and the convolution of recently evolved mathematical theories. Their intricate, yet ordered play on symmetry and their compounded grammar are scripted in the throbbing theatre of Attard’s fertile imagination, and may indeed be termed mythical palaces of the artist’s alchemistic mind. Attard’s current interest in these modern mathematical theories lies in the fact that they are based on symmetries, a theme which has long fascinated and intrigued him. Yet, this is a new symmetry termed 'broken symmetry' which exists in situations where the properties of configuration remain the same after manipulation in rotation or in size. This body of work may initially give the impression that the artist may have initially plunged into chaos; but on further study one becomes aware that he has, in fact, emerged artistically baptised as an architect of the imagination with a production of highly organised and ordered images.
“Plan your castle in the air and then build a ship to take you there”
In all of the works carried out during his four-week stay in Japan, Norbert Francis Attard demonstrated, not only his thought provoking creative abilities through his penchant for number and geometry, but also his ability to meld and brew the mystical and alluring alchemy of mathematics into visual poetics. In the process of making these installations, Attard, eclectic artist that he is, also reminds us of a past which man today has chosen to forget. All the works point to the fact that contemporary man and his techno-sphere should be more cognizant of their place in the universe, and also that they should relate more to the spiritual forces and sacrality of nature’s cyclic rhythms. As an artist, Attard repeatedly emphasises the importance of this relationship, while clearly issuing a caveat against modern man’s destruction of his ecological habitat. Attard’s plea sounds timely, for man has distanced himself from his planet and the resulting consequences have been calamitous. The ancients, as we have seen, had a more understanding and pro-active attitude to nature and its forces, through their understanding of geomancy. This art of placement embodied a multi-disciplinarian coalescence of concepts borrowed from geography, geometry, number, religion, astronomy and mythology; all of which were applied to architecture in relation to its site-specificity. In today’s world of specialisation, pigeon-holing and categorising, man may well have made great progress in each of the individual disciplines; but he has surely lost his understanding of the power of their amalgam. Ecological disasters such as the greenhouse effect, deforestation and global pollution are all a result of man’s loss of this comprehension, and his consequential insensitivity to nature and its forces. Through an art modelled on the rules of nature, Attard, in his installations, opens our mind to a pathway towards our re-understanding and returning to a nature oriented life-style through the applied disciplines and grammar of nature’s very own formative syntax of number and geometry.
The structured mathematical clarity of Attard’s Kamiyama works, together with their dependency on context for content, evidence his own reverence of place, while also reflecting his nostalgia for the demise of a nature focused life-style. In this age of the encroachment of technology over the laws of nature, it is welcoming to have an erudite artist like Attard metamorphose into a shaman and poet to walk us out of the disorderly chaos of today’s world, and allow us to realise that we must return to once again embrace the ancient forces, to combine the mythological and the mystical with the ecological. Through his always interactive audience-sensitive installations and the manifest synergy of opposing energies, inherent in the works, Attard, seeker of transcendence, restores to the contemporary world of megabytes and megacities, a series of visual and intellectual poems, which only an artist of his sensitivity and calibre could devise. These are art works in which many disciplines and creative imagination come together to recall archetypal memories, and decode ancient understandings of long vanished metaphors.
Attard’s artistic vision and imagination, together with his impeccable eye for detail, are further codified and ordered by the mathematical genesis of the works, which besides being a delight to experience through the senses, also provide both intellectual and celebral stimulation in their search and pursuit for the sublime. The European-Oriental cultural hybrid, together with the anachronistic time-frame coupling of the pieces, make this series both intriguing and thought provoking. Forever a perennial seeker of magic, myth and mystery, Attard is an artist, who, above all, is an exploratory chronicler of the intellect, linking the microscopic to the astronomical, yet always drawing from and utilising the site and its surroundings as his proscenium. He constantly reminds us that we do not have to live in a Robo-Cop, Blade Runner world and that there are alternative pathways to a return, through the symbiosis and re-combination of art and mathematics, for man to once again understand and relate to the world as a sacred place.