From Wikipedia
http://en.wikipedia.org/wiki/Zeno%27s_paradoxThe dichotomy paradox
"You cannot even start."
"That which is in locomotion must arrive at the half-way stage before it arrives at the goal." (Aristotle Physics VI:9, 239b10)
Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a fourth, he must travel one-eighth; before an eighth, one-sixteenth; and so on.
This description requires one to travel an infinite number of finite distances, which Zeno argues would take an infinite time -- which is to say, it can never be completed. This sequence also presents a second problem in that it contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. Hence, the trip cannot even be begun. The paradoxical conclusion then would be that travel over any finite distance can neither be completed nor begun, and so all motion must be an illusion.
This argument is called the Dichotomy because it involves repeatedly splitting a distance into two parts. It contains some of the same elements as the Achilles and the Tortoise paradox, but with a more apparent conclusion of motionlessness. It is also known as the Race Course paradox.
I was explaining to a rocket scientist friend this idea I had gotten while working on an art project using only black and white, absolutes. During my work on the project, I was thinking about being required by my art teacher to draw from memory. I was not too keen on drawing from memory; 1.) because I'm not that good, and 2.) because there were so many details I couldn't remember. (During class, I would sneak my camera out and take a picture.) But even with digital photography, there are details that are lost. Despite the absolutes of ones and zeroes, it was still not an accurate representation of what was there. I started thinking about other absolutes, the big bang and the end of the universe, life and death. How long does it take to die? Will there be a moment, infinitely small, where someone is between the living and the dead? My rocket scientist friend told me about Zeno's Paradoxes. I was so blown away by the concept, it was all I could think about for a week.
Here is the paper I wrote on my project:
The Space Between is an exploration of kinetic energy and passage of time conveyed through the synergistic relation of value range, grouping strategies, balance conditions, and continuity and dissolution of line. The following images provide visual codes, interpreted by the viewer, to describe “movement”. While the code is innately interpreted, the syntax needs explanation.
There are only two values in the images, black and white. However, some pieces appear to be neither black nor white, but a value of grey. The pieces look grey because of grouping strategies that the viewer uses to organize information. Defining the object from its background, or figure/ground, is created this way.
Clusters of small white dots on a black background are grouped together by proximity to create the illusion of a value of grey. Depending on the amount of dots and their proximity to each other, the pieces can appear to look lighter or darker. The same conditions apply to black dots on a white background.
These values of grey give the impression of distance. Lighter objects appear to be in the foreground while darker ones recede. The opposite can also be true depending on how figure/ground was established.
Arrangement of these values in the visual field creates balance conditions that lead the viewer to follow a course set by the grouping strategies. This project uses four balance conditions: Symmetrical, an equal balance; Asymmetrical, an unequal balance; Radial, a gradation of value beginning at the corner and center with the emphasis of moving both directions simultaneously; and Crystallographic, an alternating “checkerboard” pattern where the gradation in one set of steps will run in one direction while the opposite gradation will run in the inverse.
Finally, continuity and dissolution of edge will allow the original mark, or unit form, to simultaneously move between figure/ground. As the viewer determines continuity of edge, the object will rise to the foreground. When there is dissolution of edge, the object will sink into the background.
By using the code described, the visual images in this project create an implied passage of state between two absolutes. Only black and white are present, yet there appears to grey. The images are stationary, yet there appears to be movement. Yes. No. On. Off. Ones and zeros. Being and not being. There is a space, a moment, where and when they are neither. What has happened ten seconds ago is as irretrievable as something that happened ten years past. What will happen in the future is equally distant. A ball hangs from a string. The ball is lowered to half its distance from the ground. If the distance from the ground is continually divided in half, how can the ball ever reach the ground? Yet it does. There is a transition where object becomes background and background becomes object, a land of ghosts that lies somewhere in the space between.
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