Today was much better than yesterday. I don’t exactly know why. I spent some time with my drawing board, compass and straight edge. For some reason, I found that to be calming. I found a way to divide the circumference of a circle into 12 equal segments (like a clock face). No big deal, but I enjoyed connecting each point to every other point around the circumference, with straight lines, and liked the resulting intricate network of intersecting lines.
Compass and Other Scribblings
11″x17″ 67# Bristol
I understand that it is possible to construct a 17-sided polygon using only a compass and straight edge. I would love to be able to figure this out myself.
[Note: Carl Friedrich Gauss (1777-1855) proved the more general theorem that a polygon of n sides (where n=2p+1 [sorry, apparently WordPress does not support superscripts. This equation should read: n = 2 to the pth power +1] p=2k , [p = 2 to the kth power] n is a prime number, k=0,1,2,3…) can be constructed with only a compass and ruler. (Struik, D.J A Concise History of Mathematics Volume 2, New York: Dover Publications 1948 p. 206).]
Never mind the proof, I’ll settle for being able to construct the 17-sided polygon.
Arthur’s progress
I have been thinking about Arthur, my pet avocado tree. After months of germination in the Mason jar, I had to set him free. My first attempt at planting was abortive. I had to return Art to the jar. Finally, with some good advice from The Healing Garden gardener (THGg), I re-planted Arthur in a clay pot with the right kind of soil. I hope that the crispy leaves do not portend his demise. We’ll see.
Today’s experiment
I have been struggling with the idea put forth by Paul Klee, Master at the Bauhaus in the early part of the 20th century (and my artistic hero), that an artist’s creativity is manifested in how he or she takes his or her pencil point ‘for a walk’. This is how Klee describes drawing. A point is just a point until some motivating force animates it. The motivating force is the idea inside the person wielding the pencil.
The Healing Garden gardener triggered a thought that has enabled me to combine the idea of taking my line for a walk in service of capturing an essence of Arthur at an earlier point in time. THGg mentioned that Art will develop a tap root, which has the capability to support a 60′ tall tree when fully developed.
When Arthur was in the Mason jar, his roots were a hopeless tangle. However, there was one thick extension from the avocado pit that curled around at a lazier tempo than the others. I assume that this was the ‘tap root’.
The idea of tangled roots in real life meshed perfectly with the artistic concept of walking my pencil point around the page.
In the study below, I constrained my line to the circle, which represents the top of the Mason jar. My motivation for animating the pencil point was connected to the idea of the tangled roots. My understanding of Klee’s concept of creativity is that the pencil point is not in service of representation of the physical, but rather an idea embedded somewhere within the artist.
Tap Root in Mason Jar
11″x17″ 67″ Bristol
I believe that I made some progress with this sketch even though it is representational. I do have some justification for the colors I used. The predominant yellow is for the brackish water after I transferred Arthur from the dirt back to the jar. The darker colors are for the tap root. The greens are wishful thinking about Arthur’s chances for survival.
‘THGg mentioned that Art will develop a tap root, which has the capability to support a 60′ tall tree when fully developed.’ I stumbled on ‘Art’, realised it was Arthur, then remembered that it was Sylvia Plath who described art (more specifically poetry) as her ‘tap root’. The tap root was an important image to her – most obviously perhaps in her poem Elm (‘I know the bottom, she says. I know it with my great tap root’). Great to be reminded of the small place where the tap root starts… thank you.
That is serendipitous. Arthur imitating Art. Thank you for that, Liz. ;>)
On viewing the watercoloring, without reading the text, we recognized the tap root immediately. This is true, because we have come to know you and Arthur through this blogosphere. To the Taoist Painter, I am thinking this is numero uno in rendering the invisible to the visible. One must have with it a relation of some sorts.
Many years before my coma when I was nine years old, a prestigious psychiatric clinic diagnosed me an idiot savant. These were discontinued by the medical professional and became something else. It has been enough to keep track of myself, without being reinvented every few years by a bunch of people I’ve never met.
A brain injury is an identity crisis. Who you were you are not. Yet you still are. Of course. This puts some strain on those of us whose egos have been trained to accommodate our personality. I had many years of excellent special education and tutors. I think I can understand Arthur’s vegetative state. And Michael’s. I think you are doing great and I am glad we have this opportunity to know each other.
My maths library is very extensive. I will look for the manner of constructing your irregular polygon. For Arthur’s watercolored requiem banners. I am at my cognitive limit, so I’ll rest for a few days. Catch up on my brush work and move on to the First Cannon of the Tao of Painting. Scheme on a copy of Klee’s notebooks. Your Arthur series is a great example of using a line as a service dog. These animals will guide us through if we let them. Thank you for the good paintings. THGg
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