Mathematical formulas describe and within reason predict the probability of any occurrence.
Stanley William Hayter slid a piece of paper my way and held two diagonal corners for me.
With my pencil perpendicular to the paper, I moved my arm and not my wrist, in free unconstrained motion. My elbow ran the show, so to speak and a fine, continuous, swirling line was deposited as a record of the movement on the sheet of paper.
Hayter then told me to put my pencil down and notice the frequency with which one line crossed another. One line intersecting another is what he called “expected”. Three lines intersecting at a single point was special. I was not so impressed and he saw that. He challenged me to make a conscious drawing and “TRY” to see how many triple points I could create in the same period of time, freehand. I think I made one and was close on another. It doesn’t count if you make a tiny triangle.
Stanley Hayter was a British painter and printmaker. He was also a Surealist artist. The concurrences held meaning for him: what happens when muscles twitch without mental control
Apparently the word for multiple intersections at a single point is concurrence. While it may be interesting that in the process of a free meander a pencil may pass through one point in space more than once, it would be more impressive to see the pencil points collide simultaneously.
Imagine visiting the frozen food aisle at the grocery store and standing at one spot occupied at that same moment by your younger and older self. That would excite me.
Yet, it only seemed mildly interesting and quite inevitable that on a small piece of paper a pencil may pass over the same dot. Undoubtedly there is some simple equation to correlate how many times within a certain space that a random loping line, of a particular length might be expected to produce how many intersections and concurrences.
At the point of dismissing any significance for three lines meeting at one point, I thought of Pollock’s One, Number 31, 1950 and how the happenstance of three parallel brown paint drips
have been given importance when they are coincidently three drips that could also be explained with another similar equation. The more one drags a pencil in free elliptical patterns, the more concurrent meeting points one will find in any drawing. Paint flung about in a studio will leave drips in predictable places and every so often a little bonus surprise. The more paint slung around, the more over-splatter landing other than the intended canvas. Stanley Hayter might have attached meaning to three drips on a Pollock painting. Jackson Pollock was a surrealist long before an abstract expressionist. Hayter might have believed Pollock’s drips were special and unconscious products, but he would not have accepted them as demonstration of skill, calculated contrivances.
Somewhere, I have a small drawing Hayter made for me with several points at which a random line meets with two other random lines at the same point.
It was on a regular piece of paper, not very big. Plus, he did it using a ball point pen; a Bic, if I recall. Now, if I could remember where it is.
It is very likely in the frozen food aisle at the grocery, guarded by my younger and older selves.Stanley William Hayter and the Point Where Three Lines Intersect