The X Y Axis and Visual Arts
Portrait of an Algebraic Equation
This is a work I did in Oakland, California, back in 1969. It is somewhat like
the style of cubism except that it has much more color. Maybe more
like cubism with a bit of fauvism thrown in. But there's something
else going on here.
Because the idea for this composition was not just arbitrary abstraction in the
mind the artist. Instead, it is an actual drawing and subsequent painting
of a quadratic equation drawn out on an x y axis. The actual axis itself is the
rectangular form in the lower center of the painting: The horizontal axis is portrayed
at the narrow end at the top the rectangle, which is green, and the vertical
axis is the side of the rectangle that is on your left as you face the painting.
Now as you know, these equations work out, that if done in the progression, it
animates the subsequent plotting of the equation so that it tends to form a
curve; a sort of ellipse as if it were an object, the trajectory of which orbits
a point in outer space.
But what I'm able to do in the composition, is by using freehand, I can continue
alternate patterns of the actual line itself, and in this case also right angles
or 90° intersections of this line. Also by using hard edges and soft edges of
the colors, I can produce very stunning visual effects that help assist the
viewer to be able to visually take his mind out of the mundane logic of the
basic algebra classroom and into other realms of possibilities. The bright
yellow angle, established by the equation, forming a point of a right triangle
along the horizon of the equation itself becomes a kind of golden pyramid with a
soft edge disappearing into the blue of the background .
The terrestrial greens on the southern aspect of the equation take on soft and
hard edges to become an assortment of different forms. The one on the left, with
its dark edge softening into a bright middle and then the a final dark edge
along the edge of the painting, suggests a cylindrical form, which blends into
the earthen reddish-brownish form with a soft edge that is not as soft as the
others, that begins to imply a line that runs parallel to the south of the
equation's plotted directional line, making it into a earthy rectangular form,
disappearing into the blue background in the upper left-hand corner. But at the
other aspect, before it meets a blue triangular form in the center of the
composition, it's browns begin to transform into a greenish brown towards the
south, and a reddish triangular form to the north of the plotted line.
As you run south, this forms a pyramid that fades into stripy greens and
yellows, that coincide with the triangle going the opposite direction with a
hard line into green that is rectangular at the bottom and triangular at the top
and abuts the initial rectangular form, which is not only a basic green, but
also tends to emulate, in a speckling effect, the tannish violet form towards the
right of the composition, which indicates the southern right aspect of the
implied line of the equation, taking on here greater significance, as it runs
practically through the center diagonal of the picture plane with yellows and
blues towards its north, which becomes a sort of blue triangle in the northeast
half of the composition, with an opposite earthy green and brownish
multiplannular triangular form in the southwest corner.
Here, I have a chance to suggest and, as it were, consider, parallel equations
running along the same axis in tandem and in combination, thus entering into new
forms, boundaries, implied lines, and new forms emerging. The blues take on a
stark, ethereal difference, contrasting with the earthen green colors on the
southern edge of the line created by the equation. But the actual equation
itself sets the tone for the entire painting. It is the beginning of the
statement of the design therein, especially the angle it implies.
But this visualization also aids in the concept of math, giving more gravity,
significance, and speeding up the thought patterns that can be associated with
the mathematical aspect it portrays. It takes the mathematics out of the
literature end of the mind; the sympathetic memory. It bridges the gap and takes
the mind to into the more active and faster visual realm where the thoughts
travel at nearly the speed of light, unimpeded by the hesitant and decelerating
logic of literature, often used as the tool of algebraic expression or
mathematical statements.
What practical value can you get from this? Well, look at the painting. It also suggests a landscape involving the critical time of the calculus of the growing season in a Nordic coniferous forest when the mean angle of the incoming sunlight at the height of the day affords the observation of the commencement of the optimum growing season. That's just one application since light tends to be indicated as streaming in a straight direction and the growth of the conifers indicate the verticals and the terrestrial mean level of growth the horizontal.
But far beyond this, the
visualizations and the application of aesthetics tend to cause the human
observer to attain a deeper grasp of the essence of the mathematics in that the
mind can then go to greater degrees of discovery in the discipline never before
attainable, and I'm quite serious about that. You who dismiss the
aesthetic as non-utilitarian are in fact holding back the very utilitarian
advancements attainable with the inference of said aesthetics and the potential
of those mathematicians that have become aesthetes.
Here you can make a visual statement with mathematics. And although it does not
seem to be that effective at this initial effort, when worked upon and extended,
I am certain, for one, that it may boost the functionality of mathematics into a
higher form of the computational, applicational, and, yes, theoretical realms of
the discipline. It could be a breakthrough. Anyway, that's what I was thinking
in my little, leaky, Broadway studio in Oakland, California, back there in the
depressing, rainy days of late November, in 1969.
--Fine art, digital art, music, several voice introductions by me about my work, articles about my artwork and other topics such as sociology, the cosmos, economics, education, medicine, poetry, humor, something I call premonitions, and a series about covered bridges, all by yours truly, the webmaster, Paul A.L. Hall. There are feedback, a website search engine, and exhaustive contents pages. Plus my weblogs are on site, an art school and classes.
A painting of a quadratic equation
drawn out on an x y axis.
Copyright (c) 2005 by Paul A. L. Hall. All rights reserved.
Taking mathematics out of the reticent sympathetic, left side of the mind.
03 April, 2005