THOUGHTS ON LINES
AS DEFINED IN PLANE GEOMETRY AND AS EXPERIENCED DRAWING
Why respond to a painted block of a single color on a page torn from a used book by marking it with one line or two connected or parallel lines?
That self-question led me to researching the very definition of line. And that generated more questions and further searches into lines. Basic geometry.
What is a line? As a 19th century mathematician stated, it definitely doesn’t wiggle! Euclid, the Father of Geometry, described it as breadthless length that could be extended indefinitely. A one-dimensional, “maximally taut” element. No end in either direction! Mathematical dictionaries offer a slew of mathematical terms referring to lines.
My home 3rd edition American Heritage Dictionary, copyright 1992, lists 35 definitions of line as a noun, plus the a, b, and c, etc., related meanings. Number 1 reads: The path traced by a moving point, and, lastly, number 35: (Archaic) One’s lot or position in life. I am thinking that the word line is said, used, thought about in one way or another every second of the day around the world. That’s what I’m beginning to think. Lines are foundational not only in the math world but everyday life.
Like cells, lines are building blocks.
The infinite quality of line transports me. From a solid, stationary, earthbound definition of ‘line,’ I’m soon travelling, so to speak, with the line through an endless universe.
All this delving into linear and plane geometry was entertaining me and interesting, but not quite yet answering my original question.
My question is based on hand drawn lines… Following this line!! of thinking, with the support of a theoretical definition of line, I was led to the thought that a drawn line with a pencil (whether free form or ruled) can be seen as sculptural, having width and depth by evidence of the graphite residue rising from the drawing plane. Imagine an enlarged image of a surface with graphite markings where dips and rises and curvatures would be on view. I then can think of the drawn line as a relief… I think so.
Hand drawn lines do wiggle and have a beginning and stopping point whether the end points are intentional, accidental or instinctual. The opposite of lines as mathematically defined. Yet…
Now I draw a line and think of the theoretical definition, as well as envision a 3-D image of it with a wavering course. Math and art together connecting to the mystery of life in the universe.
All this thinking and researching about lines have boosted my amazement. The word line now presents me with a fullness of meaning and importance I only semi-consciously acknowledged in my art or everyday speak.
Line, in all its manifestations, is a vital concept.
This statement is the answer to my original question. I understand my act of drawing a line/s on a rectangular block of color as symbolic. Symbolic of mystery (where will it continue to?) and beginnings (what will come next?). Lines articulating space, marking space, pointing to space, building on space. Lines defining paths, forms, and patterns of sound, words, images and emotions that rise and fall and wiggle. The breadth of drawn lines!
