An Understanding of Nature

March 15th, 2012

A painting from Pseudo-Aquinas‘s 15th century Aurora Consurgens (McLean’s edition).

Appearing in the prologue to Book II, p49. Click for larger version.

“Those who wish to master this Science therefore need to sharpen their wits most subtly and ingeniously; to ponder and deliberate as much as possible upon both the inner and the outer meanings of the words of the Sages; and to show a willingness to examine them from various points of view… [For] like the dust that the wind raises from the face of the earth are the operations of those who perform such actions without intellect and an understanding of Nature… As Alexander says, ‘If you try to dissolve snow with coldness then you only coagulate it the more, and if you try to freeze water with fire then you only heat it the more, and if you change any nature into its opposite then you simply corrupt the Work all the more'” (p47-48).

Jensen’s Great Pyramid

February 2nd, 2012

A painting by Alfred Jensen, reproduced in the catalog for his 2001–2002 Concordance exhibition at the Dia Center for the Arts.

In an article from the catalog, Professor Michael Newman writes, “Jensen’s elaborate diagrams are drawn from various cosmological systems, including the Mayan calendar, the I Ching and other Chinese mathematical systems, the Egyptian number system, Pythagorean mathematics and geometry, and ancient Greek systems of proportion. [For example,] The Great Pyramid (1980) [below] has numbers written in an ancient Egyptian notation, in which a bar stands for the number 1 and a horseshoe for 10, on a pattern that suggests rectangular pyramids seen from above. The panels are set in a progression such that the sum of the top and bottom number of each pair is 13; each contains an even number at the top and an odd one at the bottom—this kind of opposition, echoed in the use of black and white at the cores and edges, is reminiscent of the I Ching” (p78).

The Great Pyramid, 1980, 90 x 360 inches (insert), rotated 90° clockwise to fit this blog’s format. Click for larger, horizontal version.

Critic Peter Schjeldahl writes, “Jensen’s works can be called ‘diagrams’, not because they explicate ideas, but because they delineate them; they are fields united by the purpose of signifying. His is a gesture of communication, rather than of conveyance” (p44).

Asks Newman, “[Jensen] puts the viewer in a position of conflict in relation to the painting: Are we to decipher, turning to books to help us, or are we to look?” (p88).

Dowd on Metaphor

January 16th, 2012

Seven diagrams from movement investigator and trainer Irene Dowd’s 1984 essay, On Metaphor, collected in Taking Root to Fly.

“Studying the history of the eye’s growth… through the depiction… of the developmental process in five arbitrarily determined stages… enabled me to develop a metaphoric model of the activity of ‘seeing’. In each developmental stage, except for the very first one, there is simultaneously both movement outward from the neural core toward the surface periphery of the body and movement inward from the outside toward the neural core. The stages successively provide a more and more complex and elaborate map of precisely how these oppositional streams of moving cells and light waves can travel, grow, and interrelate” (p74).

Each of the five figures below depicts the developmental model on the left and Dowd’s metaphorical model on the right.

Stage 1, 28-day-old embryo: The optic vesicles protrude from the head end of the neural tube toward the surface ectoderm (primitive skin, the interface between the inside and outside world of the embryo) (p72).

Stage 2, 30-day-old-embryo: As the optic vesicles or bulbs continue to grow outward from the neural core, they become concave, cupping as if to receive the outside world they approach (these optic cups are the primitive retina, ground for the light sensitive rods and cones). Stimulated by the approach of the optic cups, surface ectoderm begins to thicken and invaginate into the cups (p72).

Stage 3, 33-day-old embryo: The optic cups continue to enlarge, encircling and grasping the thickened surface ectoderm. As if the optic cups were inhaling it, the surface ectoderm continues to grow into the cups until it has itself inhaled, encircled tiny globes of the outside world (these globes are the primitive lens, which will be able to change shape to accommodate vision from things far to things near in the outside world, just as if still remembering that outer place) (p73).

Stage 4, 42-day-old embryo: Immediately filaments grow to join each optic cup (continuous with the neural core) with each lens vesicle (bubble of outside other). These filaments provide a rudimentary blood supply called the hyaloid artery which nurtures the rapidly differentiating and growing primitive eye (this is gradually replaced by the circulatory system that is fully mature at eight months) (p73).

Stage 5, 100-day-old embryo: Once the hyaloid artery has firmly tied each lens vesicle to its optic cup, the cup releases its suction-like hold on the lens. As the lens floats free, its cells and those of the surface of the skin it moves toward become transparent like windows to the outside, to light. At the same time, nerve cell fibers are growing from the base of the optic cup back through the optic stalk to the developing brain (eventually over one million nerve fibers are formed that pass from eye to brain, making the optic stalk into the optic nerve whose transmissions are finally made vision within the brain itself). All the cells in the eye continue to mature until they are capable of responding in concert to light to create the complex of stimuli the optic nerve feeds back to the brain to produce vision (p73).

“If all the stages are put together in a single composite picture, they form a complex but consistent pattern of fluid dynamics. As the core moves outward toward surface, it also expands to cover a broader area. Seeping out past the surface membrane, it dissipates even more widely into space. As the outside moves inward through the surface membrane, it coalesces as if compacting the whole of the boundless outside into a tiny enclosed globe. Concentrating even more, it continues to stream into and through the center of the central core itself” (p74).

A composite metaphorical model for the dynamics of ‘seeing’ (p74).

“With abstraction, this model of a developing and ‘seeing’ eye can be used as a metaphor for a way in which any cell, cellular organism, or organism segment with a self-enclosed membrane or skin might interact with its environment or world outside it” (p74).

“This fluid-dynamics metaphor that describes ‘seeing’ serves equally well as a model for the pathways of connection between feet and ground in such activities as standing and walking. The sole of each foot functions like a retina that grows developmentally outward from the pelvis, central core structure of the body, down through the leg to spread the bottom surface of the foot in an ever-widening base of support that is ‘looking’ down and out into the ground. The ground itself is visualized as a transparent cornea through which light passes from the living earth beneath. The light enters the foot which receives the light in the curved space beneath its central dome. The light continues to travel up through the dome and into the central axis of the leg, thrusting the bones—like light beams—straight up into the pelvis they support.

“…I verbally suggest to students that they might visualize their feet (or any other parts of themselves) as if these were eyes ‘seeing’ in the way I have just described…” (p75).

Metaphoric ‘seeing’ with the foot (p75).

“Metaphor can be the fist that breaks through the dark glass between what is already known and what is still mystery.

“Through the vehicle of metaphor, we can participate in that movement from what is to what can be.

“Once in the new land on the other side of the dark glass, we can use the metaphor as a landmark from which to foray into the new world.

“Eventually the metaphor dissipates in explosion outward from its core into the space of new landscape. Finally another metaphor coils around the landscape, coalescing into a new vehicle in which we continue the journey” (p69).

Scully’s Wall of Light

November 18th, 2011

Three paintings by Sean Scully collected in Wall of Light, a catalog for his 2005 exhibition at The Phillips Collection.

“Scully is conscious of the nature of inspiration. If he knows that being an artist is all about desire, he knows too that active pursuit of the muse is doomed to disappointment. For this reason, the artist cannot put himself under pressure to evolve. He must let questions go unanswered, go about his business, and then, when he least expects it, the muse will come. Scully simply makes himself available” (p19-20).

3.29.84, 1984 (p113). Click for larger version.

“Stripes became central to his work after a trip in 1972 to Morocco, where he was exposed to the bright light and striped textiles of North Africa. Similarly, the [1998] Wall of Light paintings evolved from [1983 and ’84] sojourns in Mexico” (p20).

Wall of Light Pink, 1998 (p81). Click for larger version.

“Scully also knows that he evolves very slowly and says that if he had pushed himself to innovate after Mexico, the Wall of Light paintings would have been different paintings—playful rather than melancholy. Instead, Scully developed other bodies of work, creating his construction canvases, inset paintings, and Durango composition while subconsciously absorbing the Mexican experience. This period of gestation resulted in works that reflect Scully’s emotional growth. As he says, ‘I am very interested in the idea of creating something that has already gained experience by the time it enters the world…'” (p20).

Wall of Light Yellow, 2002 (p124). Click for larger version.

Nine figures from Jonas Salk and Jonathan Salk’s 1981 pictographic essay, World Population and Human Values.

“In this essay, the sigmoidal curve will be used as a ‘thinking tool’ and as a symbol. Its shape reflects a law of nature that governs growth in living systems, and reflects the transformational character of change in our time” (p3).

The sigmoidal curve (p3).

“In this figure, and in those that follow, the horizontal axis represents time and the vertical axis represents number. In the first, upturned portion of the curve, population growth follows a pattern of acceleration; in the second part, growth decelerates and a plateau is reached. The gap in the curve emphasizes the point of inflection—the point of change from accelerating growth to decelerating growth” (p3).

“For thousands of years before agriculture, human population increased very slowly. In response to environmental adversity and population pressures, agriculture emerged, making more food available to support greater numbers of human beings. A pattern of gradual increase thus continued throughout the agricultural period. In the last several centuries, scientific, technologic, and industrial developments have further raised the carrying capacity of the plant, contributing to the recent sharp rise in population” (p27).

Human population trends (p27).

However, rates of human population growth, birth and death rates, fertility rates, population distributions by age and sex, median age, life expectancy, sex ratios, child/woman ratios, and other data suggest that the human population growth curve will follow a sigmoidal pattern. As well, “except for the sun as a constant source of energy, the earth can be seen as  a closed system and, by inference from the examples given [of  animal and yeast population growth in closed systems], we can expect the human population growth curve to follow a sigmoid pattern” (p23).

The following figure “shows the estimated increase in world population size in the period 1750 to 1975, with medium projections to the year 2200. This figure… illustrates the sigmoid pattern of human population growth and the estimated plateau at approximately 10.5 billion people. The high and low variants for the year 2125 are 14.2 and 8.0 billion respectively. The inflection of worldwide growth will become evident at about the turn of the century” (p64).

World population size (medium variant), 1750-2000 (p65).

From a longer-range perspective, the figure below “schematically describes the course of human population growth and population growth rates over a period extending from 8,000 years in the past to 8,000 years in the future. The curve indicates a plateau of world population at approximately 11 billion by the end of the twenty-first century and assumes that this level will remain or slowly decline” (p66).

World population size and rate of growth, 6500 B.C. to 9500 A.D. (p67).

“If these estimates and assumptions are valid, we can see that the present extended period of rapid population growth is unique when seen from a long-range perspective; it has never occurred before and is unlikely to occur again” (p66). “Intuitively, we sense from this image that, from a psychological and social standpoint, human beings may be better adapted to conditions associated with less rapid change (like those that existed in the more distance past and that are anticipated in the coming centuries) than they are to those that we presently experience” (p130).

“We use the sigmoid curve not only to represent numbers of human beings but also to provide a frame of reference for discussing the nature of human values, attitudes, and behavior before and after the point of inflection” (p73). “The difference in shape between the two portions of the curve suggests both quantitative and qualitative differences in human life between the two periods of time. It not only indicates differences in population growth patterns but also suggests differences in the characteristics of prevailing conditions and in the quality of human life in the two periods” (p74).

“In this figure, the two parts of the curve before and after the point of inflection have been separated for emphasis. One is designated as A and the other as B. The periods of time prior to and following the point of inflection are referred to as Epoch A and Epoch B, respectively” (p77).

Epoch A and Epoch B (p77).

“From the shape of the A curve, the future would appear to be unlimited in terms of growth and expansion of, for example, population, resources, and availability of energy. To someone born in Epoch B, however, the future would seem to be a time of multiple limitations with a ceiling on growth and expansion. The difference in shape between the two curves thus implies that there will be a fundamental, qualitative difference in circumstances between the two periods of time” (p77).

For example, “during Epoch A, because mortality rates were high at all ages, the control of disease and of premature death were of primary concern. Success in this regard has contributed to the recent sharp increase in population size. As a result of this, the concern in Epoch B can be expected to shift to the control of fertility and to a preoccupation with the enhancement of health” (p80).

Values of health in Epoch A versus Epoch B (p81).

Other changes in values and attitudes discussed by Salk include:

Epoch A Values Epoch B Values
quantity of children quality of children
persistent expansion of societies and industries dynamic equilibrium
extremes in growth and development balance
competition, independence, power collaboration, interdependence, consensus
either/or, win-lose both/and, win-win
present, short-range, parts future, long-range, whole

“This is a change from seeing the world as limitless in terms of growth to seeing it as limited. It is also a change from seeing ourselves in opposition to each other to seeing ourselves in collaboration with one another. It is due not only to a change in perception but to a necessary change in human attitudes and spirit that comes in response to a change in reality, as expressed by the shapes of the curves. The change from A to B can be seen in relationships to nature, our relationships to each other, and in our relationships to ourselves” (p94).

“Human beings possess the capacity for a wide range of attitudes and behavior. The idea underlying the preceding discussion is that those attitudes and behavior that are advantageous and therefore appropriate under one set of circumstances (the reality of Epoch A) may be disadvantageous and inappropriate under another (the reality of Epoch B)” (p101).

“In the region of inflection growth rates are highest, acceleration is changing to deceleration, and values are shifting most rapidly. This period can be expected to be a time of increased conflict” (p101).

The process of inversion of values (p111).

In the above figure, “the relative position of the two lines indicates that Epoch B values exist even in the period before inflection, but are less dominant than Epoch A values. In Epoch B, the relative dominance is reversed… [This] offers an explanation for the tension we feel at this time. It suggests that the conflicts are an inherent part of this developmental and evolutionary process. They are not necessarily a signal of an impending end of the human species but reflect the process of inversion that is now occurring” (p110).

“In the process of adapting to changing conditions, conflict may be most effectively resolved, as symbolized [below], with a both/and approach. For example, completely disregarding the technological and social developments of Epoch A in an effort to immediately halt growth would be inappropriate and unrealizable. On the other hand, attempting to resolve tensions by completely suppressing the tendencies of Epoch B would be equally disadvantageous. With a both/and approach, the developments that have been part of Epoch A can be combined with Epoch B values in order to develop solutions that are appropriate to changing conditions. A specific example of this might be the simultaneous short-term reliance on nonrenewable resources of energy with the long-term goal of reducing consumption and of developing efficient means for using renewable resources” (p112).

Resolution of tensions (p113).

“The patterns revealed in the preceding figures suggest that differing tendencies that have always been present in human beings have diverged in the course of the rapid changes of more recent history” (p134). For example, “at present, the tendency to make decisions based purely on material costs and benefits are in conflict with the tendency to base decisions on human considerations, such as quality of individual health or the quality of the physical environment. In contrast, economic decisions in the future will increasingly take into account both human and material value. The change will affect the nature of economic relationships and organizations in the years ahead” (p138).

Material value versus human value (p139).

“At this point, innovation in the area of human development and social relationships is as important as the advent of agriculture 10,000 years ago, or the understanding of microbes and machines in the past century. Just as some of the brightest minds of recent years turned their attention to the advancement of science and technology and to the prevention and cure of disease, many of the brightest minds of coming generations will turn their attention to the phenomenon of the human mind and the improvement of the quality of human life” (p164).

Itten on Expressive Forms

October 18th, 2011

Three student exercises from Johannes Itten’s first year art course at the Bauhaus, reproduced in his 1964 Design and Form.

Writes Itten, “Freeing and deepening the expressive ability of students is the teacher’s most difficult task.

“To execute the following exercises it is necessary to choose a very flexible, expressive medium which reacts immediately to the slightest motion of the hand, such as India ink brush…

“If a genuine feeling is to be expressed in a line or plane, this feeling must first resound within the artist. Arm, hand, finger, the whole body, should be permeated by this feeling. Such devotion to work requires concentration and relaxation.

“Brush drawing would never have reached the level shown here if the students had not prepared themselves through breathing, concentrating, and relaxing exercises” (p147).

Attempts to represent the course of an emotion in a line. This exercise demands relaxation and involuntary ‘letting it happen’ (pl154, p149).

Change and transition from plane feeling to line feeling (pl155, p150).

“Superficially fixed seeing, fluctuating thinking, and willful acting must give way to inner vision. This requires a readiness to be guided by inspiration. The painter must wait until his feeling urges him to create. In the moment of complete devotion all forms will be in the right relationship, as if they had created themselves. Nothing can be added or subtracted afterwards without alien and inorganic effect.

“Every work created in this way surprises by its unforeseen formation. A famous Chinese ink picture consists of a single circle, painted on silk. To draw a large circle freehand with a brush requires complete control of the body and the deepest concentration of the mind. Although this thin line is even all around, it is felt. One of the cardinal principles of the Chinese ink painter is: ‘Heart and hand must be one.’

“The beginner becomes aware of the elastic point of the brush only when he really feels the form and is ready to follow this feeling… When the student has reached a certain sureness of movement and knows the difference between forms he has experienced and others he has not, he should be confronted with nature” (p147).

Portrait studies. Such exercises serve to synchronize the eye and hand motion. When the eye ceases to observe, the hand stops to move. Only the spontaneously observed is produced in this way, not the previously known. Instantly experienced form relations are created instead of schematic designs of known details (pl167, p162).

Cramer’s Emblems

October 4th, 2011

Six of forty emblems from Daniel Cramer’s 1617 The Rosicrucian Emblems of Daniel Cramer, each presenting a contemplative exercise working upon the heart process of a Rosicrucian meditator. Prefaces Cramer:

“And so, Reader, you have the work of death and life,
The embossings of the Holy page, and a short epigram.
These will be able to show and teach your mind
What your state was once and what it may become today” (p16).

Emblem 2: I INCREASE

“‘But that on the good ground are they, which in an honest and good heart, having heard the word, keep it and bring forth fruit with patience.’ (Luke 8:15)

“I am not a road, or a thorn, or a stone, but the best earth;
And sweet ears of corn will rise from the bossom of my heart” (p25).


“‘In thy light shall we see light.’ (Psalms 36:9)

“I see the light in your light, let darkness be far away,
He is wise who gains wisdom from the book of the Lord” (p29).

Emblem 15: I MEDITATE

“‘As we have therefore opportunity, let us do good unto all men.’ (Galatians 6:9)

“The centuries fly by, the days pass away,
Every man must work for the good, while there is an hour of time” (p40).


“‘The words of the Lord are pure words as silver tried in a furnace of earth, purified seven times.’ (Psalms 12:6)

“The brick and hearth witness to the quality of gold;
The same may testify to the goodness of the mind” (p62).


“‘…we will not turn to the right hand nor to the left.’ (Numbers 20:17)

“Not in this place, not in that;
The heart will go more safely in the middle.
He who rushes from the mean, runs to destruction” (p63).


“‘By ye therefore wise as serpents, and harmless as doves.’ (Matthew 10:16)

“He whose heart is saved by simplicity, whose eye by wisdom,
Will be both serpent and dove to God” (p64).

Klee on Pluralism

July 14th, 2011

A diagram by James Klee from his 1982 Points of Departure.

“The use of the word ‘dimension’ creates a peculiar difficulty in that it is not clearly pluralistic in nature. When we analyze we also unwillingly tend to objectify. So if a whole is analyzed into four parts one is tempted to think of ending up with four different entities. But if the analysis merely stresses four aspects we have not an objective pluralism but rather an existential pluralism. We have made the analysis and taken responsibility for the selective emphasis but the whole is not considered as disturbed. Rather we have paid attention to something less than the whole. We have restricted ourselves. The whole is not cut up into a multitude of fragments now independent of each other and of the whole” (p162).

Definitions of Body, Mind and Soul from a Phenomenological Point of View, p154. I have reoriented labels and legend to better fit this format.

The diagram “intended to show body, mind, soul, and matter as four differend [sic] questions or contexts about the whole instead of the resynthesis of four discrete entities. The yang-yin form was to show the ever changing relationships among the various aspects. One saw the aspects in different contexts so as to selectively emphasize mind or body or soul… If it had been a motion picture it could have emphasized the temporal dimensions even more than the yang-yin does although as a static symbol it tries hard and is occasionally successful” (p162, n*).

Hankiewicz’s Hearts

July 13th, 2011

Four of eight panels of an abstract comic by John Hankiewicz appearing in Andrei Molotiu’s 2009 Abstract Comics anthology.

Hearts, p109.

Writes Hankiewicz, “Hearts shares many of the preoccupations of my non-abstract comics: repetition, variation, and transformation. The challenge of doing an abstract comic is to make those formal issues dramatic—which is a reversal of my usual strategy” (from the Artist Biographies appendix).

Gabo’s Kinetic Paintings

April 11th, 2011

Three paintings by Naum Gabo from his 1959 lectures, Of Divers Arts.

“All colors, even in their seemingly identical hues, have a different identity in our vision of them. One and the same color acts differently on different surfaces. Colors change with the change of their place in space or on a surface, and their identity also varies with the time at which they appear in the field of our vision. They change not only according to the neighboring color—a fact by now known to every schoolboy—but in relation to the frame of our vision and its axis, i.e., to right or left of the axis, and up or down from it” (p96).

Red Kinetic Painting, 1943 (p97). This painting is meant to be viewed from all four sides, rotating counter-clockwise. Click for larger version.

“Color affects the bounds of the shape in which it is enclosed and changes the form of surrounding space; it modulates distances, retards or accelerates the rhythm of our visual perception… Color is the flesh of our visual perception of the world, not its skin” (p98).

Yellow Painting, “Strontium”, 1945 (p95). This painting is meant to be viewed from all sides, rotating counter-clockwise. Click for larger version.

“Space in our vision is not the distance between far and near, not the above and below, not even the place which is there or here; it is penetrating, everywhere present in our conscious experience of vision… It is ever within our reach, and thus it carries an experience of palpability equal to any conveyed by the tactile sense… Space is not a part of the universal space surrounding the object; it is a material by itself, a structural part of the object—so much so that it has the faculty of conveying a volume as does any other rigid material” (p100).

And time “in the artist’s experience is not that static sequence of intervals measured by days and hours of past and future, it is not the mechanical phenomenon we measure by our clocks; neither it is that idea of contemporary science where it has become a relative term dissolved entirely in the idea of space-time so that both become one. Time to us is the faculty of experiencing the continuity of the present” (p100-101).

“My explanation of the function of [color and] space and time in the visual experiences of the artist may perhaps be clearer to you in the work to be seen in the following illustration…” (p102).

Blue Kinetic Painting, 1945-54 (p103). This painting is meant to be viewed in rotation. The panel is mounted on a motor making one revolution in two minutes. Click for an animation of this revolution.