Essays-1

What is Cyclical Space Painting?

Su Hsin-tien 31 December, 2006

I. About cyclical Space Painting

In Euclidean geometry, the shortest distance between two points is a straight line - the two points of which, if extended indefinitely, would never connect and would only grow further and further apart. However, in the real physical world, due to gravity an extended straight line could actually connect back with itself. For instance, on the earth's surface a straight line that moves ahead in the direction of the shortest distance would wrap around the globe and intersect on a point with itself. It could also turn like a vortex. An observer standing on the moon looking at a straight line on earth would actually see a round arc, the perimeter of which is called a "cyclical line."


Similarly, on a plane surface, lines radiating out in all directions would merely extend out into space indefinitely and would not intersect. However, as with the above example, on the surface of the earth, such lines continuously extended outward would blanket the entire earth's surface, forming a spherical plane. Earthbound people always feel like it's a plane, while someone on the moon would say it's a globe. This globe could be termed a "cyclical surface."


The problem with this is, is there such thing as a "cyclical body?" An orthographic cube formed with straight Euclidean lines consists of six surfaces. If each of the cube's surfaces were extended indefinitely straight out, expanding the cube infinitely, each straight line would be curved by gravity to link into a cyclical line, yet it would be difficult to draw this cube of cyclical lines. This is what has led me to my thinking on this concept, and based on readings between 1965 and 1970 I came to learn of the tremendous difficulty involved (See Illustration 1).

Illustration 1



If each edge of an Orthographic cube is extended in a cyclical line, together does it form a sphere? Judging by the perspective, object, picture plane, and eye point are the three critical factors determining graphic form (See Illustration 2).

Illustration 2: The three critical factors of perspective: object, picture plane, and eye point



As shown in Illustration 1, whether the eye point is fixed at point A, B, C, or D, it is located within the cyclical form. As it is inseparable from the cube, its complete form cannot be drawn unless the spherical glass is treated as a picture plane. This is illustrated by man's inability to render the earth as round unless viewed from a remote perspective far from the earth (See Illustration 3).

Illustration 3: Perspective of the Earth



By the same token, only when the human eye point goes outside the solar system can a perspective of the nine planets orbiting the sun be rendered ( See Illustration 4 ).

Illustration 4: Perspective of Solar System



Continuing, we can know that the Milky Way can only be rendered as a barred spiral galaxy from a perspective standing outside the Milky Way(See Illustration 5), rather than a vortex galaxy. (Liberty Times, 18 August 2005. Researchers at the University of Wisconsin revealed a comprehensive image of the Milky Way as a barred spiral. The barred spiral stretches 27,000 light years wide at both extremes.)

Illustration 5: Perspective of Milky Way



Nowadays, astronomers note that there are approximately 100 billion galaxies in the universe, each galaxy containing approximately 100 billion fixed stars. If this description approximates the truth, then humans could render a galaxy, two galaxies, three galaxies and so forth based on perspective... to form a perspective distance diagram. If that is the case, then could a human render 100 billion galaxies in one picture? The question is whether humans could attain a remote perspective from which to draw all 100 billion galaxies in the universe. If humans can draw the earth, solar system, and the Milky Way, then we could conceivably find a way to get far enough removed from the universe to render these 100 billion galaxies. But how would one attain such a remote perspective outside the universe? (See Illustration 6)

Illustration 6: Finite and yet Unbounded Universe, the artist cannot completely draw the Entire Universe



In this picture, due to the weight of the universe, straight lines in the universe do not continue ahead as with Euclidean geometry, so the relative physical positions of the planets in the universe may not be consistent with the Euclidean geometric relationships human thinking is based upon (how do Cartesian coordinates change?) (Encyclopedia Americana, V.12, pp.498-499, "Geometry: 6 Non-Euclidean Geometry Relevance to Real Space and Space-Time")


In 1905 Albert Einstein (1879-1955) proposed his narrowly defined theory of relativity, followed by the broadly defined theory of relativity in 1916. The Riemann geometric interpretation of the curved spaced of the universe proposed in 1917 notes that the universe is a finite sphere without boundaries. This thinking is in line with that of Chinese Warring States period astronomer Hui Shi, who said, vastness without limit is the great unity, smallness without interior is the minor unity. However, by the time of China's six great astronomers in the Jin dynasty, no view describing the universe as a finite cyclical universe was extant. The issue being, in relation to the three critical factors of object, picture, and eye point composing perspective, is it possible for humans to stand outside the above-illustrated universal space to render the entire universe? The answer is that it is impossible, because since the universe is a finite sphere without boundaries it has no exterior, so it follows that there is no place for the painter to stand beyond the universe from which to render its likeness.


One can conceivably render one Solar System, the Milky Way, five galaxies, 35,000 galaxies, up to 99.9 billion galaxies (N-1), but just by adding the final galaxy would there be no place for the artist to stand? Is that the case?


Under the theory of relativity dynamics universal view, by the 1930s astrophysicists had verified that the universe is in a state of expansion. Observers standing at any point in the universe can see stars all around, and that the relatively closer galaxies recede slower, while relatively distant ones recede faster. (Encyclopedia Americana, Astronomy Universe) For a rendering of curved space in accordance with the universal view, see the following illustration (See Illustration 7).

Illustration 7:
Spatial structure where various gravity fields in the universe exert influence on one another. This illustration is merely a partial special picture and cannot be extended to form a cyclical one (it cannot only form a sphere).(Su Hsin-tien, CYCLIC SPACE: Su Hsin-Tien's Multi-Dimensional World in Painting, 1998, p.39 upper picture)



The vertical lines of a cube on the earth in relation to the ground plane necessarily extend vertically towards the center of the earth, but where in outer space do the ones pointing in the opposite direction come together? (See Illustration 8)

Illustration 8 Moon Earth



Universal space formed by Cartesian coordinates (See Illustration 9) is an illustration of the Orthographic Coordinate System.

Illustration 9 Ptolemy system The Newtonian celestial sphere infinite space transcends the celestial sphere The viewer is located within the glass sphere



If a person stands inside the glass sphere and draws straight lines outside its surface, unfolding the glass into a plane, the resulting image would resemble Illustration 10. Straight lines on the surface of the glass are curved lines in the unfolded illustration below. Thus it follows that a sphere composed of Cartesian coordinates, at the planetary distance of astronomical observation, must be fixed again in perspective. (Su Hsin-tien, CYCLICAL SPACE: Su Hsin-Tien's Multi- Dimensional World in Painting, 1998, pp. 34-35)

Illustration 10



The ancient Greeks believed that fixed stars lined up on a celestial sphere. Aristotle (384-322 BC) posited that the celestial sphere consisted of 55 "crystal ball" layers, one inside the other. Hippachus (C. 190-120 BC), drew meridian lines on the celestial sphere. Ptolemy (AD100?-165/70?) proposed further standardizations (See Illustration11). (Pan-Chinese Encyclopedia; World Book: Astronomy)

Illustration 11



The celestial sphere concept remained in use through the twentieth century, and photographic techniques were employed to fix anew meridian lines and poles. However, in the early twenty-first century, advancements in satellite observation enable us to measure the distance of more fixed stars, while computers can establish the distance between different fixed stars or galaxies and people can read related information via computer. However, although the proximity of various fixed stars can be expressed, celestial sphere meridians are still relied upon to plot locations. If the distance of the farthest star could be ascertained, would that star be "the end of the universe?" If so, then the universe would be caught in the finite vs. infinite controversy, so would it be possible to render a "finite, boundless universe?" (See Illustration12)

Illustration 12:
An ancient Greek man penetrated the celestial sphere with a cane, but asked what the outside of the outside was? If the viewer in the picture seeks to express the stars mapped out on the celestial sphere with a planar three-di-mensional perspective, he must specify whether the picture plane (glass) is flat or round.



This gives rise to two problems: 1. The phenomenology of perspective in the threedimensional geometric space between the fixed stars and galaxies of the universe; 2. Is there an outline for the entire universe? Or do different galaxies circulate and envelop one another? What does that picture look like?


As for the first question, that depends on the method of perspective (Addressed in CYCLICAL SPACE, 1998. pp. 23-42), as illustrated by the following four graphics (See Illustrations 13-16).

Illustration 13: Classical triangulated perspective Horizon Line



Illustration 14: If curved lines in place of straight receding lines are employed for triangular cones above and below the horizon line, the below picture results. Horizon Line



Illustration 15 : Upper illustration is analysis; lower is perspective




The cylinder perspective was first employed by Maurits Cornelis Escher (18981972) in 1947. This perspective revealed that straight lines parallel to the horizontal plane remain straight lines.


The spherical perspective has been described earlier in this essay (as in Illustration 10). In both approaches, due to the curvature of the glass picture plane, unfolded on a flat plane they become receding curved lines. Meanwhile, curved space is described by the theory of relativity as the tangible curvature of physical phenomena. These different approaches compel me to seek another method, explained in Part III of this essay.


As for the second issue above, I have practiced "cyclical space painting" since 1970; that is, experimenting with an approach in many areas, with "objects without exteriors," "multiple objects enveloping one another," "spaces in which insides connect with the outsides," "universes empty on the inside," and "landscapes with multiple horizons, where each horizon line represents a gravitational realm." Examples are illustrated in the following pictures(Illustrations 16-19). A rubber ball, with "trees" growing perpendicular to the inner surface (See Illustration 16 ).

Illustration 16: Imagine the inside of the ball can be turned to become the exterior.
Illustration 17: In a state of chaos, the ball's interior and exterior are swapped.




Illustration 18: The ball's interior has been
Illustration 19: A rubber ball is rotated into turned around so that the trees extend a sort of Klein Bottle, with no distinction outward. between inside and outside.




II. Motivations and Objectives of Cyclical Space Painting


What I described in part I is the combined discussion about heavenly body phenomenon and perspective, and it has been the difficulty on spatial logic in my mind for a long time. Because of this, I tried various ways on painting and had a long-term accumulation, that's why I named all my artwork as "Cyclical Space Painting".


In CYCLICAL SPACE, a catalogue of my paintings published (in Chinese) in 1998, I outlined and discussed systematically the general theoretical suppositions and critical elements of cyclical space painting, with particular attention to the possible phenomena of perspective. This essay simply endeavors to go over these key points once again for the sake of "content analysis and categorical delineation" in the following section.


Cyclical Space painting is the expression of the knowledge and hypotheses described above using the forms and methods of painting. Simply put, it would be impossible to complete a circuit of three-dimensional space and cubes within the realm of Euclidean geometry. To wit, I have not seen such an explicable and satisfactory picture. Accordingly, I have tried to "approximate" the above-detailed objectives using optical illusions and distorted spatial perspectives. I have put forth my creative motivation with several linguistic devices in the form of questions, as follow:

* Can the circulation of three-dimensional cubes be felt through optical illusions and make the inside of an object continue to existence?
* Can using warped perspective give rise to objects and empty space that enclose each other? What's more, it is not empty infinite existence,
* The total area of all the planets and objects in the time and space of the universe must not be enveloped by the vacuous space outside in order for there to be a cyclical universe, but what does it look like?
* What is the effect of the warping of three-dimensional objects due to the gravitational force of the universe?
* What are the possibilities of illusionary paintings and distorted objects?
* What is the significance of multiple horizon painting?
* What are the possibilities of warped horizons and cyclical horizons?


It is with these questions in mind that I proceed with my art.

Illustration 20: Three Intersectional Horizon Lines, 2006

Essays-2