Geometric and Pictorial Elements

It is fascinating to read about Klee’s approach to his art. It is daunting, however, to read his own explanations. I checked his Pedagogical Sketchbook out of the library. I imagine that this would have been a great auxiliary text to the students at the Bauhaus, where he taught. I’m sure the students had the opportunity to ask Professor Klee to expand upon his notions of active lines, passive lines and medial lines, for example. As yet I have not read enough to make much sense out of this. It seems that I am not the only one who has been at sea regarding his philosophy. Bridget Riley, in her essay, Making Visible stated the following:

“As anybody who has ever looked into these books [Pedagogical Sketchbook and The Thinking Eye a posthumous collection of Klee’s essays] will understand I could not find any systematic coherence in either of them. It was only much later that I learned the reason for this confusion.” (from Kudielka, R.  Paul Klee: The Nature of Creativity, Works 1914 – 1940. London: Hayward Gallery Publishing, 2002 pg. 15)

In her introduction to the 1953 edition of Pedagogical Sketchbook, Sybyl Moholy-Nagy presented this quote from Paul Klee:

“For the artist communication with nature remains the most essential condition. The artist is human; himself nature; part of nature within natural space.” (quoted from Sibyl Moholy-Nagy’s Introduction to Pedagogical Sketchbook, New York: Frederick A. Praeger 1953; original quote from Klee’s Paths of the Study of Nature)

Different paths to understanding building blocks of nature

Euclid

Euclid, the progenitor of geometry took another approach to the study of nature. In the first volume of his thirteen volume treatise, Elements, he defines basic geometric concepts: points, lines, planes, angles, and so on. The remainder of his work concentrates on the relationships among these elements based on axioms, and proofs. According to Wikipedia, Elements is one of the oldest existing deductive treatments of mathematics and was very important in the development of logic and science.

Here are the first few definitions: (from Euclid’s Elements of Geometry 1883–1885 edited, and provided with a modern English translation, by Richard Fitzpatrick First edition – 2007 Revised and corrected – 2008)

1. A point is that of which there is no part.

2. And a line is a length without breadth.

3. And the extremities of a line are points.

4. A straight-line is (any) one which lies evenly with points on itself.

5. And a surface is that which has length and breadth only.

6. And the extremities of a surface are lines.

Klee

I did not find Klee’s definition of a point other than referring to the point of his pencil. He had a lot to say about the concept of the line. As far as I can tell from what I’ve read thus far, every kind of line Klee refers to is the result of an agent that propels the point of the pencil. On the first page of Pedagogical Sketchbook he demonstrates, “An active line on a walk, moving freely, without goal. A walk for a walk’s sake.”

What are the differences between Euclid and Klee’s approach?

Both Klee and Euclid seemed to recognize a relationship with nature. Euclid’s rigorous treatment developed into a better understanding of nature in terms of modeling and predicting the kind of outcomes that engineers or builders must have for successful designs.

We already know that communication with nature was of paramount importance to Klee. I can’t help think of the analogy of a photographic portrait. When one looks at such a portrait, one not only sees the subject, but also the effect that the photographer had on the subject. There is an interaction; one has an affect on the other. This is what I imagine Klee had in mind. The artist interacts with nature through the mediation of pictorial elements. The resulting work is the reaction of the artist to nature. (Quantum physics tells us that observation has an effect on the observed, but I’m sure this is not relevant in this case, so the metaphor with a photographic portrait is incomplete.)

I am still at the beginning of this exploration. I hope I’m headed in the right direction. I’ll find out soon enough if I’m not.

Today’s experiment

I left the Kiwi and Kiwano out overnight. I thought I’d try to re-sketch them in their slightly deteriorated form.

Watercolor Study - Decaying Kiwi and Kiwano

Decaying Kiwi and Kiwano
5″x7″ 140# Cold Pressed Watercolor Block

The edges bordering the cut surfaces are starting to pucker; the surfaces themselves are starting to dry out and sink. Since I used a smaller format (5×7”) I didn’t get all the detail that may have been necessary to depict the aging process. I used pen and ink to emphasize the edges. I used aureolin as the basic yellow, with Prussian blue to make the green; winsor red, cadmium orange with a tint of black in the shadows for the orange coloration.

4 thoughts on “Geometric and Pictorial Elements

  1. The connection between Klee and Euclid deserves deeper consideration, maybe. We have the advantage (however slim this may seem) in our interpretation of Klee’s words. We are immersed in his cultural weltanschung. Of the same general time in Western culture.

    Euclid and Pythagoras and the early geometers used their propositions and theorems as a language, in attempts to apply the principles of logic. Most prominently what we call inductive logic in their proof of theorems built on propositions – that could not be proven (less discussed is the process of choosing the basic propositions, but Russell and Whitehead discuss this in Principia Mathematica). This language of Euclid was developing, and as an incidental sidebar Euclidian Geometry, is fundamentally rooted in the physical world – in their ancient Greek physical and mythical world.

    If we begin with prehistoric cave drawings, through representations of ancient Greek and Roman still life, and onward to the Art of Paul Klee we can study the line and point as well. A History of the Geometry of Art. It is interesting to ask how our human ability to perceive the intent of the line has changed over our whole cultural history. Not too sure how to describe the function of the relationship between the Artist and his/her expression of the line’s intent (or propulsion); and the human ability to interpret the representation of the line. Interesting melons, by the way. Your ability to capture texture is truly amazing. How would you without a mask?

    • Yes, there is an interesting relationship between Klee’s world view and Euclid. They both use abstraction, but Klee seems to have a more personal relationship with it. More study is definitely worth while.
      As for the spines on the fruit, one just needs to allow complete drying of one layer and try preserving the lighter areas as much as possible.
      Thanks for your comment, THGg.
      J

      • This is, in part, my point. I agree completely regarding the genius of both Euclid and Klee in representational abstraction. Remember, Euclid and Pythagoras illustrated their arguments in the sand. Though their abstractions were calculable, their illustrations were only estimable. To my view, Klee is a man of his Time (well, that is to say, considerably ahead of his Time), like Euclid. Klee adds the vector of propulsion – as you indicated. Very quantum. Newton was not even a twinkle in Euclid’s eye. Euclid and Pythagoras sort of kicked Descartes and Newton in the butt. It is a vast jump in our cosmology. In the conceptualization of our cosmology. Likely, this affects the ability of perceivers to perceive the intent of a propulsed line. We could hope someday.

        It is about four months into a commitment, each day, to photograph the Garden. As suspected, it is not so difficult, and even enjoyable when incorporated into regular routine. To do this well, is a lifetime work to which I may, or may not, be suited. This is a stepping stone, for me, to a watercolor a day. A botanical illustration. You will admit an important link between practicing photography and painting. I am not nearly so accomplished an artist as you. My goal is a few hundred pen and ink drawings rendered with watercoloring technique. Then, I can tell you, if further practice toward my own free hand flowers are warranted. I suspect nothing serious. It is enough to attempt passage as far as one is suited by one’s nature.

        • Sounds like a great project. It can be very satisfying, if not a little frustrating to document something of great import to one’s self. You’ll find that you’ll improve with every attempt, however. Best of luck. Have you started posting your pen and inks yet?
          J

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