One Million Points
a random event that led to a catastrophe

“Aesthetics is no longer essentially a philosophy of beauty, but an experimental science based on psychology, sociology, and the theory of creativity.” -   Abraham A. Moles


“The function of repetition is to render the structure of the myth apparent.” - Claude Levi Strauss


“The only reasonable numbers are zero, one, and infinity.” - Bruce MacLean

Hewlett Packard 3000 Series II mainframe computer

When I was in graduate school in the Art Department at the University of Houston in the early 1980’s, I experimented with computers and used them for my work. I made drawings, sound work, some sculpture, and a few videos using computers. My fascination with computers went well beyond just using them as a tool to make things. I gravitated to the newest, most radical art and ideas, and it became evident to me that computers would soon dominate everything in society, including art. This view was not shared.  Most of the computer work that I did at UH was done in the Technology Department since they were one of the very few departments with computers at all. The art department had none. I didn’t really know what I wanted to do with computers or how I could generate anything that didn’t look like a beginning engineer’s drawing of a bolt circle (whatever that is). All I knew is that computers were the future and I wanted to use this tool that was new and virtually unknown in the art world.   

 I was led to the Technology Department and their computers by simple snooping around. Luckily and conveniently, the Technology Department was located adjacent to the Art Department building, just a short stroll westward across the lawn. There, I found a miraculously supportive teacher named Scott Carpenter who taught computer programming. Scott was intelligent, patient, open minded, and possessed a great sense of humor. Somehow, I convinced him to allow me to take some beginning classes so I could use computers in my art work. But first, I had to learn some code. Since I wasn't enrolled in the Technology Department, Scott wasn't concerned with fulfilling any faculty obligations through me, so he pretty much let me have the run of the place, as long as I didn't get in the way of the other students. Basically, Scott let me use the computers to play. I generated most of my drawings during "off hours" away from any class. Although Scott didn't know much about art, his good natured curiosity accounted for his interest in my experiments. And, luckily, we were both intrigued with many of the same ideas and questions. We became friends.

Department of Technology, University of Houston

L. to R. Scott Carpenter, Jack Massing, Michael Galbreth, 1987

The terminals in the classroom were connected to a mainframe computer on the floor below us. The plotters were clunky, small, flat bed types and used only ink styluses of black, blue or red inks. They had air vacuum systems built in that pulled the paper and held it in place during the printing.  You’d place the paper onto the surface of the plotter, turn it on, and the thing would suck the paper flat, sticking to it like glue, and off you’d go. The styluses were driven by small servo-motors that connected to a small metal arm that moved back and forth across the surface (the X axis), with small metal wires that moved the stylus up and down the metal arm (the Y axis).  It was a simple, flat, Cartesian coordinates plotter.  The largest size paper that would fit was tabloid size -  11 x 17 inches with an actual plotting area of 10 x 15 inches. Each plotter was shared by several terminals, so there could be lines of students waiting to make their plots of bolt circles or whatever their assignment was.


Initially, I did what everyone else in the class did in order to understand the rudimentary basics of programming. The first computer language that we were taught was called, appropriately, Basic. I learned how to generate and plot simple shapes like lines, rectangles, other polygons, and circles. It was easy at first, but then became difficult as the mathematical formulas necessary to generate complex shapes grew more complicated. But I hung in there with the engineers.

equipment used for One Million Points: L. Lear Siegler computer terminal; R. Tektronix 4662 flatbed plotter

It wasn’t long before I grew tired of the geometric shapes that we worked with and I wanted to use something more interesting. I had a drawing template of an outline of a human - both male and female - that I liked. It was a generic image that could be used for simple diagrams or for architectural renderings. Its plain shape suggested anonymity and universality. Scott showed me how to digitize this outline in order to use it with the computers. I used this image as a constant to explore complicated positions of the figure in space. I created algorithms that would scale, twist, and turn the figure resulting in rather trite looking “computeresque” drawings that had a “spirographic” quality. They were quintessential expectations of what someone might think a computer drawing would look like. I liked them, but there was something missing. There was still something else that I was looking for. 

computer drawings, 1982, pen on paper, 11 x 17 each

One day, Scott introduced to me the capability of a built-in random number generator that the computer had.  I was immediately intrigued. It had no application to anything anyone was doing in that beginning computer class. In the early 1980’s, computer generation of randomness was a relatively small field understood by few and used by fewer. I wanted to play with it.  


At that time, I was deeply involved with the concepts of chance and so-called chaos systems and their potential with making art. Like many others, my interest in chance operations began with studying the work and philosophy of John Cage. As is well known, John’s approach to making music was revolutionary, despite the fact that it was based on ancient systems and beliefs. To most of the music and art world, which largely cultivates the idea of “quality” and “talent,” employing chance operations in one's work was heresy. For me, anything heretical was interesting.  


I suppose the suspicions and doubts that some people may have had about John’s use of chance is the perceived lack of control, and the absence of predictability, which runs directly counter to almost all artists and musicians, and counter to audience’s expectations of expertise. Accusations of incompetence, laziness, and even nihilism were leveled at him and others who used chance operations to make art or music.  But the complexity and depth of these systems is fascinating.  Topics and questions regarding determinism, control, probability, and certainty goes to the core of belief systems, and perhaps to the core of all systems - that is, reality. It challenges everything, including objectivity, subjectivity, and truth.  


I began theorizing about the differences among chance, chaos, and random systems, if there were any. I wanted to know if these were different terms for the same thing or if each of these was distinct and different from each other. And I wasn't really sure that any of these systems were what they were claimed to be. I'm still not sure.


I had a some discussions with Scott regarding this random number generator. I wanted to know what it really was and how it worked. He explained that the random number generator was built into the computer, and if I recall, it was a timer, or counter, and he assured me it was truly random. My skepticism was immediate. I didn’t believe it and I wanted proof. I surmised that if the random number generator was based on a formula, then that formula must have a structure. And if it had a structure, then it must somehow be organized, and that that organization could be revealed visually. Scott disagreed, but in his inimitable graciousness, he was willing to entertain my challenge.  


I devised an experiment that I believed would prove my theory. My idea was to plot one million points using this random number generator onto a piece of paper. I surmised that as the marks accumulated, some sort of arranged pattern would emerge and that the marks would group themselves into a regular form. In other words, the marks would not be spread evenly across the surface. 


The decision to use one million points as the cutoff number was arbitrary. For me, and for most other people, the number one million was a large number, and I believed it was a number that was sufficiently large enough to reveal the structure of the random number algorithm that Scott used.  But I didn’t know for sure.  It was just a guess.  What were considered large numbers in the 1980’s would now not be. And the accompanying processing speed by computers to count in real time was painfully slow back then as compared to now. So, the minimum amount of superfluous data that the computer had to process, the faster it would operate. In an attempt to strip the formula and the experiment down to its essential basics, I decided to mark a point rather than a line or some other shape. A point, or a period, was the simplest, easiest, fastest mark to make.


It wasn’t the calculating speed of the computers that would be the deciding factor of how long it would take to plot one million points, it was the printing speed of the plotters. The number of points per second that could be plotted was approximately 2, or about 7,200 per hour. Given this plotting speed, even with the plotter printing continuously, 24 hours a day, Scott and I estimated that plotting one million points would take more than five days, an enormous length of time for a single plot. Nothing close to that had ever been attempted with that computer and with those plotters, and we weren’t sure what would happen. If we were going to plot one million points, it would have to be done in separate, manageable increments of a few hours each.


Scott calculated the parameters for the plot and wrote the short algorithm. We set aside a day to begin the experiment so as not to interfere with the other students and to be minimally disruptive.  We began the plot at 10:00 am on Tuesday, November 8, 1983, and watched. 

One Million Points, plot in progress, November 8, 1983

The computers and plotters set off doing what they do, and admirably so. The plotter was remarkably fast with the stylus zipping around the surface of the paper, jotting point after point in a different spot each time.  Zip, jot, zip, jot, zip, jot...  I snapped a few pictures for documentation. Since Scott was going to be around, he volunteered to babysit the process so that I would be allowed to leave and attend to whatever it was that I needed to do. The plan was to return in a few hours to assess the progress. Sometime later that afternoon, I went back to check on things.  


When I returned, the terminal and plotter were off and the drawing was gone. What happened? Scott walked in. He told me that after just a couple of hours the plotter broke. The strain placed on the arm of the plotter was just too much. It over heated, or something, and one of the small cables that drove the stylus snapped. Scott was gracious and forgiving about the whole thing, smiling as he explained what had happened. But I could tell he wasn’t happy.  Losing a plotter was a real loss. One fewer plotters in the class created a log jam for the other students who needed to make drawings for their assignments. And because the significant devotion of time and energy to this plotter had no relation, relevance, or use to the goals of the Technology Department, it was irritating. There would be no continuation of this experiment. Nevertheless, Scott diligently saved the drawing and fastidiously recorded the data of the plot.   

original statistical notes regarding final plot for One Million Points

The plotter broke after only a little more than three hours with just over 28,000 points plotted, or less than 3% of the targeted one million. With so few points drawn, nothing definitive could be seen. The experiment to visualize the formula for the random number generator was a failure.  Apologetically, I retrieved the drawing and left.


I felt bad and responsible for the broken plotter. But at the same time, I was secretly delighted. I thought that the entire affair was fascinating. My time in the Technology Department using the computers, doing seemingly useless art experiments, felt like an invasion, as if I were in a place I wasn’t properly supposed to be and doing things that I wasn’t properly supposed to do. Whatever I was able to accomplish seemed like a coup. Yes, the experiment to graphically portray a random number formula failed, but I considered the attempt at the endeavor a success. In the end, there was a result. Something did happen. A drawing was made.  Built into that drawing was the intent, the idea. That idea was to experiment with and challenge a system, or perhaps, rather, to reveal it.  


Another justification for considering the experiment a success was the nature of the drawing itself. The reasons for the marks, and the resulting image, were not based on aesthetics. They were based on something entirely different. The drawing was not a representation of something - a tree, for instance. The drawing was something. And that something was a process, a specific one. The drawing wasn’t drawn, it was informed. As such, it’s not so much a drawing as it is a document, an artifact, evidence.   


Perhaps the deeper, underlying revelation from the experiment, at least for me, was what might paradoxically be called the exactitude of indifference.  

The nature of the computer/plotter system, and the purpose for its use, is the translation of clear mathematical equations into logical programmatic formulations that can be accurately revealed visually. It is to render precision. The elimination of variance in the line quality is desired, and mainly necessary.  The stylus’ undifferentiated weight upon the page is uniform and designed to be so. For most, with traditional art drawing, it is the hand of the artist that reveals their talent. It is often the fluid, virtuosic, weight sensitive dance between the paper and marker that indicates the physical dexterity - the prowess - of the artist. But with this project, there was no hand, save for the tapping of fingers upon the adjacent keyboard.  The plotter is said to have an arm, but there is almost no resemblance to a human one. Not only was the hand of the artist removed (I prefer the term perpetrator), the decision making, and the accompanying value of how and where to make the mark, were virtually eliminated. 


What was not eliminated, and what is exactly, precisely present, is the experiment. Theoretically, the result of pure randomness is entropic uniformity.  But the pursuit of anything, like making a drawing, regardless of method, is the opposite. With this purposeful activity there emerges something. And for me, I believed that what would emerge was not entropic uniformity - randomness - but an organized structure.  


There is not a moral to this story, but there is a result, and perhaps, potential. This project is one of many that have led me to other ideas.  This one led me to thinking about another phenomenon: the sudden, often inexplicably abrupt change in a system, otherwise known as Catastrophe Theory. Randomness may not have structure, but the study of it does.

One Million Points, 1983, ink on paper, 11 x 17


(Although there are only 28,440 marks on the paper, I still call the drawing “One Million Points.”) 

July 22, 2017