Margins

Looking for a progression forward from three-dimensional linear perspective.

Context of Artist Statement

Visualising a new space for the artist has always been important. Artists have always searched for new depictions of the world, the ultimate view, the panoramic, the camera obscura, or decrying social injustices, visually or mentally all try to communicate another view.

For art, a notable point was in 13th century when Brunelleschis developed the draughtsmanship of three-dimensional linear perspective. At this time art had a more advanced spatial understanding than mathematics, which was still dealing in two-dimensional Euclidean geometry with its parallel postulate. This however was to change radically at the beginning of the 1800’s with a paper published by the Russian mathematician Loboeskyi. Following on, a pivotal point in 1868 came when Beltramis depicted his proposed pseudosphere, a partial model of constant negative curvature. This prompted new interest in the mathematics community culminating with Einstein’s theories of relativity. Mathematics now worked not only in the third dimension, but also up to thirteenth dimension.

Mathematicians and physicists have no problem with the understanding of Einstein’s space-time and many attempts to depict it in mathematical terms have been made. Arrived at with formula, a mathematical algebraic abstract, we have been given fractals, tessellations and stereoscopic hypercubes. They are all important for different reasons in the journey but they are all still drawn in terms of Euclidean geometry.

Positive curvature as two-dimensions gives a circle whilst in three-dimensions gives the sphere, negative curvature in two-dimension gives the hyperbolic plane and in three-dimension hyperbolic space is much harder to visualise. Here the space you come across increases faster than it does in flat space and we can therefore place within this space more ‘things’ than we can ’see’ room for. Although hard to imagine is often described as being like a saddle curved downward in one direction and upwards in another. Often referred to as infinite negative curvature, becomes an even more difficult abstract to come to terms with other than in the form of an algebraic equation. In trying to grasp the theory of hyperbolic space it is worth considering the stages leading to this and how representation and application have been applied, in particular to that of the hyperbolic plane. Here the world touches on the mathematical theory of chaos, which has been translated into fractals. A system continually repeating on itself, which is used in plant, phylotaxy where measurement and movement of growth can be recorded plotted and predicted and is used everyday in the discipline of biology.

Symmetry and asymmetry.

Equally as patterns and views are important to artists so they are to mathematicians and physicists. Symmetry has been one of mathematics most powerful tools in gravity, magnetism and the weak force, however non-parity was found to exist in 1957 which opened the debate. Patterns have been studied and passed on since ancient civilisation with symmetry and asymmetry forming an integral part. An example being the many plan views showing the Japanese lotus flower seed head.

Morphology

Morphology is important, because it holds limitation within the biological system, that of our vision and that of our consciousness or understanding.
It is worth noting that the human vision of our world is not necessarily the only type or the best when it could be considered that other species have more defined vision or there can be considerable variation within species.

Robert L. Solso tentatively suggests “Abstract art as done by Mondrian, Nicholson, Malevich, Kline, Rothko, and others who use bold lines and simple geometric designs seems to engage more rudimentary cerebral sites, while artists who portray more realistic scenes, such as Leonardo, Courbet, Boucher, Ingres, and Rockwell, might appeal to more expansive sites.
This observation does not imply that abstract art is simple, as it is likely that it engages higher-order parts of the cortex (such as the frontal regions) for processing that supplies greater imagination and interpretation from the observer. Realistic art, on the other hand, seems to engage parts of the brain that seek associations in one’s memory systems, which maybe distributed widely. 1

Religion has always been very close to art and many artists dealing with the fourth dimension have thought theosophy was the route. It can be understandable when a mind out of body experience appears to expand consciousness and a vastness or oneness presents itself. Spirituality is linked with meditation or religion and today ground is being gained that higher dimensions are not a ‘thing’ but a process. The process could be that of thought and offers understanding to conceptual art where art is not just realistic but a different kind thinking.

This in effect acknowledges that we still have not seen a different dimension, we are still after years of cosmology, the very large, a fundamental break through in research with quantum, the very small we are still standing at the stage of seeing a geometric projection, hypercube, for the best offered visual clue of vast leaps forward in a primary discipline.

Throughout the world of different disciplines people refer to other dimensions, other perspectives, or new dimensions new perspectives in art and with the thorny issues of time and space entering our everyday language there is a need that art should aid this leap forward in understanding and reclaim the world of vision and depiction for itself.

The cubists who were directly influenced by developments in science, depicted form as four-dimensional geometry, Metzinger, Braque, Picasso, Gris, impressionists such as Monet in his waterlilies shows different ‘fields’ or concepts of multiple spaces, the surface of the water, reflection on the surface and under the surface. Marcel Duchamp who remained with the study of the fourth dimension long after the other Cubists used a process he developed and termed “elementary parallelism” as a formal decomposition of linear elements following each other like parallels and distorting the object. The object being completely stretched out as if elastic whilst the parallel lines following each other change subtly to form the movement. Many Cubists looked to non-Euclidean geometry primarily as a theoretical justification for Cubist distortion.

Their attempts on canvas were flawed as they worked with two-dimensional media. Later with the onset of film the fourth dimension was defined as the two-dimensional surface showing perspective with time added. Space and time still remain a tricky subject but examples of the thirteenth dimension and chronological horizons have been described in mathematics and physics. Artists like Diana Thater with her spatial projection work has stated, ‘Time and space, are the two hardest things to make a viewer consciously recognise and must be like trying to describe water to a fish. To them it must be as invisible as space and time are to us since we inhabit them.’ Culturally, space is perceived entirely differently, in the west man perceives the objects but not the spaces between them, in the east these spaces are revered. There is a movement in conceptual art today to look at these spaces and gaps. The sculptor Rachael Whiteread makes content of non-space. Modelling the space between a table and chair or the space under the bed she draws attention to that which is not seen. She has also used reflection in “Plinth” a glass sculpture in popular terms nicknamed the Glacier Mint, which was a copy of the plinth in glass reflected on top of stone plinth exhibited Trafalgar Square Summer 2001. Bill Viola with his videos of extreme slow motion of emotion and movement questions our perception of time and motion. Mirrors and reflection, with their promise of a different view, have often been referred to on works of dimensionality from Charles Dodgeson’s, Alice Through The Looking Glass and Marcel Duchamp’s, Large Glass, Bride Stripped Bare by Her Bachelors Even. The Reverend Charles Dodgeson an Oxford Don was an eminent mathematician and his seminal children’s story was a satire at the fourth dimensionlists.

Artists today tend to take a more tangential view as shown by Tony Robbins who has endeavoured to show us the fourth dimension by combining sculpture to the canvas. He not only has a deep understanding of eastern art with its spatial complexity where the possibility exists of placing the viewer in more than one place at the same time, but also the mathematics and its projection.

Reflection

Today, although video and projection offer the greatest potential to distort the perception of time to place emphasis on the continuous or discontinuous nature of events, limitation is contained within the mediums two dimensionality. The clips used for projection are of reflections and shadows ranging from matt surfaces such as concrete to the mirrored glass now often used by architects for building surfaces. They are the items taken from places on the margins, at the periphery, or under threat. Attention is being brought to what is barely noticed but contains complexity. The horizontal of the natural is emphasised against the vertical of the cityscape. Verticals could be looked at further, projecting onto a curved surface of not less than 90 degrees to simulate pheripery vision. Movement of the verticals can cause after image on the retina giving a sense of illusion. Many artists work in the margins or peripheries. Yoko Ono would aid people to see the usually unseen, but not many try to work directly with space-time, which has a problem of bringing together, the empirical and art. Signatures of the Invisble, an exhibition in collaboration with CERN brought in analogies, Monica Sand sculpted light in boxes and Paola Pivi made time lapse real time video.

Included is the organic aspect by looking at reflection from water The digital photographs of large format printing illustrate a fracturing of what we see in everyday life but pay little attention to as we perceive and understand our world to be a continuous stream. The increase in scale brings attention to the distortion on the solid surface of glass and the motile surface of water rippling. In some ways answering the quest for depiction of non-Euclidean space by forming a non-linear un-measurable geometry.
The space between the object and the reflection of the object or the reality surface and the virtual surface may have a number of abstract definitions; this line is a base for asymmetry or as reflected surface the line for bi-lateral asymmetry or in mathematical term’s parity and non-parity. A definition of scale enters the work through mathematics from the quantum to the cosmos, the large format being used as a test bed production. A video demands a portion of time to view therefore offers a past, present and future. The metaphor being offered is one of fracturing time, the gap allowing thought to enter. The art is in the courage to leave out the superfluous to obtain poetry.

Conclusion

Mathematicians have led the way showing future dimensions described on the computer with the interactive hypercube. There is a need of using the computer, primarily because of the complexity of further dimensions but there is still a lack of something tangible in everyday terms that is capable of being displayed outside of it.

Fractals with their recursive close connection to nature and chaos theory may offer a more intuitive route. Ian Clothier writing of rotational symmetry and drawing curved space states “All shapes conceivable provide encyclopaedic potential. There could be triangular or tetrahedron image spaces, ones made of doughnut shapes, those derived from a saddle, others composed of three spheres, a picture space could have a crystalline shape with unequal sides. The projection of three-dimensional forms should be continuous, layered or stepped, or asymmetric with unusual protrusions. Some of these shapes must be segmented parallel to the picture plane, though they could be projected forwards or backwards, or be derived from side on views and take as a starting point the peculiar view of looking at structures from above or underneath”.

He proceeds later by informing of work that has been investigated at MIT (Massachusetts Institute of Technology): -

“What of curvature in computer imaging? Tolba, Dorsey and McMillan of the Computer Graphics Group at the Massachusetts Institute of Technology have recently developed an approach whereby freehand sketching using a digital notepad provides source information. This is then imported into software where the information is projected onto the surface of a sphere, centred on the viewpoint”. 01.06.2004

Capture of Landscape including the Upper Terraces of Crystal Palace Park

Index