Wednesday, May 2, 2018

Simplicity, complexity, and snowflakes

Nikolai Timkov "A Bright Day" 1963

“Science is nothing other than the search to discover unity in the wild variety of nature, or more exactly, in the variety of our experience. Poetry, painting, the arts are the same search for unity in variety.” J. Bronowski (1908-1974) was a British mathematician, historian of science, theatre author, poet and inventor. He was also the presenter and writer of the 1973 BBC television documentary series and accompanying book The Ascent of Man.


“The measure of aesthetic value is in direct proportion to order and in inverse proportion to complexity.” George David Birkhoff (1884-1944) was another prominent mathematician who proposed a theory of measuring beauty in the book Aesthetic Measure.  

Birkhoff defined a typical aesthetic experience as a combination of three successive phases: (1) the act of attention, that increases proportionally to the observed object’s complexity (C); (2) the feeling of value or aesthetic measure (M); and (3) the realization that the object is characterized by a certain harmony or order (0). The mathematical formula he proposed defined the relationship of the three phases.

While the proposal of a formula to measure aesthetics may be interesting to some, most of us would probably just experience an eye-crossing moment of “huh?” But the take-away on this is the recognition of the relationship of simplicity and complexity, or as Bronowski pointed out – the unity in variety. Complexity is responsible for increasing the observer’s attention. Simplicity and the perception of order and pattern trigger a sense of answer or completion – a brief aha moment of “yes, this makes sense”. This is merely recognition of orderliness in a universe that is also dynamic and continually changing. 

Fedor Zakharov
Order and change, unity and variety, and simplicity and complexity are complementary. They co-exist in a continual feedback and response loop. How these elements coexist, and in what kind of proportional relationship, determine how a painting, or any other object we choose to create, looks and feels.





The visual aesthetics of snowflakes


Simplicity and complexity were the focus of researchers at Western Kentucky University who set out to quantify aesthetic experience by asking subjects to rate the perceived beauty of snowflakes and solid objects. Participants were presented with a set of ten snowflake silhouettes created from photographs of natural snowflakes that varied in complexity and ten randomly-shaped, computer-generated, solid objects that also varied in complexity. The results for the solid objects showed a preference for both the most and least complex objects, while moderately complex objects were rarely selected. The results for the snowflakes, however, were different. The least complex snowflakes were almost never chosen: 91 percent of participants perceived only the complex snowflakes as the most beautiful. 

The infinite variety of snowflakes

We have a tendency to overlook complexity when categorizing and visualizing information. The iconic image of a paper cut-out snowflake is probably the first visual that comes to mind when one mentions the word “snowflake”, but it’s suggested from the WKU study that people respond positively to complexity in natural forms when given a choice. It is also possible people are responding to complexity in conjunction with, not apart from, a sense of perceived order.

Chaos and order are defining features of the natural world. While the basic structure of a snowflake is determined by the scientific process of crystallization and all snowflakes start out in the same way, the actual formation of a snowflake is dependent on more chaotic atmospheric conditions, such as temperature and humidity. A snowflake’s growth is one of both order and chaos. No two falling snowflakes will meet precisely the same circumstances on their way to the ground; even the appearance of symmetry will be an illusion since the microscopic space of the growing crystal will contain subtle differences.

The process of snowflake formation is a perfect example of simplicity and complexity. It is also a perfect example of the dynamic forces of chaos and symmetry that create form in both nature and art.

Photo of natural snowflakes by Kenneth G. Libbrecht

Next winter, if you are fortunate enough to enjoy a bright, sunlit, snow-covered landscape, remember you are looking at all the colors of the rainbow. When sunlight hits snow, its full spectrum of wavelengths is almost entirely reflected back at us – every spectral color – red, orange, yellow, green, blue, and violet.

Notes for painters:
  • Simplicity and complexity coexist, just as light and shadow, and warmer and cooler colors coexist. This is all part of the variety in unity. A memorable painting is one in which all the pieces combine to form something new, one in which the whole is greater than the sum of its parts.
  • Complexity does not necessarily mean more detail. Texture, color pattern, and variety in shapes and edges all contribute to the perception of complexity.
  • Learning to see complexity is a form of understanding; editing the information one sees is the key to a strong and insightful painting.



Sunday, March 4, 2018

Breaking the "rules" and changing the parameters of perception

“When the great English painter Sir Joshua Reynolds explained to his students in the Royal Academy that blue should not be put into the foreground of paintings but should be reserved for the distant backgrounds . . . his rival Gainsborough – so the story goes – wanted to prove that such academic rules are usually nonsense. He painted the famous ‘Blue Boy’, whose blue costume, in the central foreground of the picture, stands out triumphantly against the warm brown of the background.”
(E. Gombrich, The Story of Art)

The complexity and endless variety of color information should make any painter wary of rules that limit possibilities. The history of art reveals a pattern of experimentation, innovation, and visual interpretation that form a fascinating time-line of both continuity and change.

We can see millions of colors, far more than we are able to mix with pigments. Also, the range of value (luminance) in a natural scene is almost always far larger than the range of values one can achieve with pigments. According to Margaret Livingstone (Vision and Art), the range of luminance in a room lit by a window or lamp may vary by hundreds of times, and the luminance in an outdoor scene can vary by a factor of a thousand. The range of values available using paint or photographic paper varies, at most, by a factor of twenty.

Artists have dealt with these limitations for centuries. There is not one solution for interpreting a three-dimensional scene on a two-dimensional surface using pigments which can never equal the contrast range or the colors we actually see.  But great artists throughout various periods of art history made one discovery after another that allowed them to interpret and create a convincing picture of the visible world.

The use of oil paint in the fifteenth century led to a greater range of rich colors and smooth gradations of tone.  There was the discovery of linear perspective, atmospheric perspective, and the use of strong tonal contrast known as chiaroscuro. Over the centuries artists refined these techniques and learned to optimize their command of value pattern and luminance to represent depth on a two-dimensional surface.

Value (luminance) determines our perception of depth, three-dimensionality, movement, and spatial organization. Perceiving light is simpler than discriminating what wavelength (color) it is.

Towards the end of the nineteenth century, there was a break with tradition when artists rebelled against the teachings of the academies and what they saw as predictable and uninspired painting. They realized traditional art, with its emphasis on defining objects with careful shading, did not reflect the reality of the scene outside the window. There are harsh contrasts in sunlight, shadows are not uniformly grey, black or brown, and reflections of light and the kind of light affect our perception of color.

These artists, known as Impressionists, set out on a path of discovery - the exploration of light and color. Empowered by the invention of the tin paint tube, they took painting outdoors to create unplanned and spontaneous paintings. Even those who remained studio painters, such as Edgar Degas, shared an interest in scenes that appeared unplanned and spontaneous, as if capturing a split-second glimpse of the world. The advent of photography and exposure to Japanese prints expanded the acceptance of compositions which were once considered unbalanced and incomplete.

The Impressionists, in a radical departure from Renaissance ideals, emphasized light and color, and the transitory nature of visual reality, instead of value and rounded, modeled, solid form. Their use of color changed painting in new and challenging ways, and the change was dramatic. What mattered in painting was not the subject, but the way in which it was translated into color. The old rules of predictable compositions, correct drawing and idealized or picturesque subject matter were set aside for new freedoms of expression in painting. But while the Impressionists were painting a new chapter in art history, some artists found the brushwork and flickering color too messy and incomplete. 


Mont Sainte Victoire by Paul Cezanne, 1895
Cezanne worked to bring solidity, order and design to the Impressionist’s use of light and color without resorting to the academic conventions of drawing and shading.

The Post-Impressionists, such as Cezanne, Seurat, Gauguin, and Van Gogh, brought a desire for order and solid form to the fleeting observations of the Impressionists, but did not want to return to the traditional methods for defining space and modeling form. These artists, while distinctively different from one another, worked to reconcile the pattern and solidity of visual reality with the brilliance and luminosity of color.


The Sower by Vincent Van Gogh, 1888
Van Gogh didn’t hesitate to distort and exaggerate information while using bright color and expressive brushwork.



 Self Portrait by Paul Gauguin, 1890-91
Images that looked flat did not bother Gauguin who sacrificed spatial depth in favor of pattern and color.
The pattern of innovation and change continued as each artist explored various facets of representation. Their work inspired other artists who moved in even different directions. The pointillism of George Seurat inspired Paul Signac’s paintings. Signac’s use of pure color in complementary pairs inspired Henri Matisse. Matisse and fellow painter Andre Derain continued the use of complementary color, but substituted painterly brushwork for the dots used by Signac and Seurat,  All of these painters expanded the dialogue of visual language and changed our ideas about visual interpretation.

The Pine Tree at Saint Tropez by Paul Signac, 1909


Montagne a Collioure by Andre Derain
Woman with the Hat by Henri Matisse,1905
This is an extreme example of Matisse' work during the Fauve period.  He discovered he could use any color as long as the value was accurate. Note the lack of any coherent color pattern. The warmer and cooler colors jump around at random with no reference to the actual light source. The darkest value in the painting is the anchor that holds everything together. Matisse's Self-Portrait-1906 still maintains strong color and brushwork, but has a more coherent, although unusual, color pattern.


Self Portrait by Henri Matisse 1906

Complementary colors are pairs of colors which, when combined, cancel each other out. When placed next to each other, they create strong and brilliant contrast. In the traditional red-yellow-blue color model, the complementary color pairs are red–green, yellow–purple, and blue–orange. The modern color model is cyan-magenta-yellow, and the complementary pairs are red-cyan, blue-yellow, and green-magenta.

Color is a property of light and light is not a random scattering of color. Wavelengths of light that we can see range from the longest (red) to the shortest (violet). The pattern of visible light is red, orange, yellow, green, blue, and violet. The colors merge seamlessly from one to the other. We see these colors because of the receptors in our eyes that are responsive to this narrow range of wavelengths. Objects absorb or reflect particular wavelengths of the visible spectrum. What we see are the wavelengths that are reflected back. 

We rarely perceive pure colors, and the colors we do see depend on the available light source. When the light changes, the number and ratio of wavelengths also change. 

Friday, September 8, 2017

Things with feathers

I’ve been painting birds off and on for many years. It’s an intermittent pursuit, and I’ve been met with resistance from galleries at times. “But,” they have said, “you are not ‘known’ for bird paintings.” Interesting how easily one can become a product instead of a painter. I would like to think I am just a painter, not a painter of ______. I choose subject matter because it is available, interesting, inspiring, and challenging.

With any subject, I initially try and decide what it is I don’t want my painting to look like. This makes the most sense to me. A painting is a possibility, good, bad, or mediocre. It is similar to a new day, somewhat constrained by routine and necessity, but open to whatever may transpire. So, from past experience and personal preference, I decide what to try and avoid.

Things to avoid in my paintings of birds:


1. The dead bird look (unless, of course, a dead bird is the subject).
2. The taxidermy bird look (similar to dead birds, frozen in time and lacking any sense of movement).
3. Painting an illustration for a bird identification book.
I am not an ornithologist. I do not need exact measurements and exquisitely detailed plumage. My painting should not be an Audubon print or a duck stamp. I am not Roger Tory Peterson, whom I hold in high regard for his exquisite drawings in the Peterson Field Guides.



What I would like in my painting:


I want complexity and simplicity. I would like to find the rhythm and pattern that is universal, but is also as individual as a single bird. I want the snowstorm and the snowflake.















Interesting and enlightening book:
"The Thing With Feathers" by Noah Strycker
The surprising lives of birds and what they reveal about being human. 

Friday, May 19, 2017

Stripey things, zebras, and the uncanny valley

Stripes and zebras
Stripes can mess with your brain. A recent study from research in the Netherlands and the U.S. suggests that “looking at intensely stripey things causes an increase in gamma oscillations in the brain” which can be linked to headaches and seizures. Many people just find stripes weird, but some experience very real visual distortions. What is even more interesting is that these effects are more likely to be caused by human-created stripes such as venetian blinds, rather than natural stripes, like those found on zebras. Researchers found that distorting the lines slightly or blurring their edges caused the oscillations to die down. And vertical stripes are not as disturbing as horizontal ones. “It seems that our brains are not designed to cope with such extreme regularity, as it doesn’t occur in nature.”

The Uncanny Valley
Natural realism and artificial realism are also the basis for ongoing research into an odd property of computer generation called “uncanny valley”. The closer the images get to total realism the more disturbing they seem to become. Japanese robotics engineer Mashahiro Mori coined the term in a paper he wrote in 1970 titled The Uncanny Valley. He proposed that we will accept a synthetic human that looks and moves realistically, but only up to a point. Once the resemblance comes close to, but not close enough to reality, we become more and more disturbed by slight anomalies. Mori’s theory made its way into computer animation. Stylized cartoons engender empathy but pseudo-human characteristics can easily go awry.

"Uncanny valley really does relate to painting! The closer the work gets to being
realistic the more cognitive dissonance is triggered. This causes a person to feel really uncomfortable, so the mind jettisons whatever is causing the dissonance." 
 Kathryn Fisher, Artist

When the first computer-generated elements began turning up in Hollywood films, technicians were capable of making things like dinosaurs, metal men, and spaceships, but creating a realistic human, with all its variety and subtle changes, seemed unattainable. The outward appearance of a human or human face could be created, but all the variables present in reality, especially having to do with subtle movement, were more difficult to achieve. Even slight imperfections in humans can create unsettling reactions in viewers. The closer to reality an animation becomes, the more likely it is to create cognitive dissonance and a sense of discomfort and conflict in the viewer.

We pay attention when something is changed,
 or different, or just seems weird.

Seeing is dependent on noticing and we notice only when we look for something. We cannot notice everything, but we do pay attention when something is changed, or different, or just seems weird. The process of visual observation is a complex one. We notice the most obvious information and tend to overlook all the nuanced information that actually underlies our perception.


Leonardo da Vinci’s painting Mona Lisa is probably the most iconic painting in the world. We also know how this painting “looks”. But art historian E. H. Gombrich pointed out how difficult it is to look at this painting with fresh eyes. He urged viewers to look anew, to try and forget what we think we know and focus on what we truly see. “She really seems to change before our eyes and to look a little different every time we come back to her.”

Neurobiologist Margaret Livingstone, author of Vision and Art, did just that. She looked anew at the painting and noticed the expression on Mona Lisa’s face was dependent on the discrepancy between our peripheral and central vision systems. The center of our gaze is optimized for small, detailed things, while our peripheral vision has a lower resolution and is better at big “blurry” things. We are usually not aware of this difference because we are constantly moving our eyes around, and we do not notice that our peripheral vision (blurry) can be just as important as our central vision (detail). If you move your eyes around the painting, her expression appears to change. Look directly at her mouth and she appears to smile less than when you’re staring at her eyes. Our peripheral vision picks up the slight shading around the mouth which gives the impression of a smile. When your gaze falls on the background or on her hands, this effect can be even more pronounced. 
(Livingstone notes this observation is more apparent when viewing the original painting instead of a reproduction.)

More stripes, more zebras
Dazzle camouflage was a type of ship camouflage used extensively in World War I and to a lesser extent in World War II. British marine artist Norman Wilkinson is usually credited as being the father of dazzle camouflage but this is not entirely accurate. The idea was initially proposed by the British zoologist John Graham Kerr. In writing to Winston Churchill in 1914 he explained the goal was to confuse, not to conceal, by disrupting a ship's outline. Kerr made the comparison to the patterns on land animals such as the zebra and suggested a similar pattern but with the use of countershading to also offer a measure of invisibility.


American artist Abbott Handerson Thayer wrote to Churchill in 1915 and suggested disruptive coloration and countershading based on his 1909 book Concealing-Coloration in the Animal Kingdom. Neither Thayer nor Kerr were able to win over the Admiralty, but along came Norman Wilkinson, a marine artist and Royal Naval Volunteer Reserve officer. He advocated "masses of strongly contrasted colour" to confuse the enemy about a ship's size, speed and heading. He also said the effect was not to conceal, but to cause the enemy to take up a poor firing position.  Kerr, whose proposal was based on years of study, lost out to the more socially connected Wilkerson. Later, Kerr was asked if he had, in fact, invented dazzle camouflage and he replied by saying "this principle was, of course, invented by nature."
Thanks to Artist Amber Blazina for this interesting tip on dazzle camouflage.


And for those of you who have read this far, here's a diagrammed selection from John Singer Sargent's painting The Daughters of Edward Boit. Any figure or any "thing" we paint needs a variety of edges, most notably from side to side. Too many similar or hard edges, especially on a horizontal plane, can negate our attempts at creating the illusion of three dimensions. I have illustrated a few obvious points of reference and also included some diagonals to illustrate the flow of information and the variety of edges.
Suggestion: Try squinting at the image to see value contrast more easily, and keep in mind edge information can be enhanced by value similarities or value differences between the object and the area around the object.


Friday, March 31, 2017

Making canvas panels - the easy way

The easiest and least expensive way to make panels is to use a Masonite or Gatorboard substrate and apply a sealer to the surface. Liquitex acrylic gesso provides an excellent surface without too much absorption. Note: Use the professional or standard Liquitex, not the Basics Liquitex. Three coats applied with a small foam roller works great. (Two coats on a white surface can be sufficient.) But if you want an easy and fast way to make canvas panels, here are a few tricks.

You will need the following: an iron, your choice of canvas, Gator Board or another substrate like Masonite, a heat-activated adhesive such as Raphael’s Miracle Muck, a lightweight cloth, and a paper-creasing block or tool, often called a bone folder. You will also need a brush or roller to apply the adhesive.A good source for Gator Board is Artgrafix. The Natural Kraft Gator Board works best and I often order 18x24 boards. This is an easy size to store and work with and panels can be cut as needed. The 18x24 size is not listed on their website, but you can call the company to order it. The 3/16" thickness works for this size if you are cutting the panels down, but if you work very large, use the 1/2" thick boards.  

If you have ever worked with a roll of canvas, you know one of the biggest problems is the curl in the canvas which makes it difficult to lay it flat and also difficult to adhere to the panel surface, which is usually done by rolling with a brayer. This is where the best trick of all comes in – use an iron.

1. First of all, cut your canvas to size. I add a half-inch to both width and height. Since I frequently use the 18x24” Gatorboard panels, I’ll cut my canvas to 18½ by 24½. Set your iron to a medium to medium high heat setting and iron the backside (unprimed) side of the canvas. You now have perfectly flat pieces of canvas. (I use Claussens oil-primed canvas, usually #66.) When you are done, turn the heat setting on the iron down to a little less than medium or less than half-way.



2. Apply a coat of adhesive to one side of your panel. The best and fastest way is to use a foam roller. You need an adhesive that is heat reactivated. Raphael’s Miracle Muck works great.  Raphaels.com Miracle Muck  



3. Lay your canvas face down (primed side down) and carefully align the panel to the canvas, allowing some of the canvas to extend past the edges of the panel.
Flip the canvas panel over and place a lightweight cloth on the primed surface of the canvas. Flour sack cloth works great, but any lightweight cloth will work. You just need something between the primed surface of the canvas and the iron. (Trust me, I learned this the hard way.)

4. With the iron turned down to a little less than halfway, iron the face of the panel, starting in the middle and working out. Do not over-iron. Three to five passes is usually sufficient. Avoid getting the canvas too hot. This is a fast process and so much easier than using a brayer/roller. Remove the cloth.



5.Take a smooth block of wood or a tool called a bone folder (used to crease paper) and firmly crease all the outside edges of the panel and also press down on the outside edges. (A sanding block should also work.) This step is critical for making sure the canvas adheres well on the edges and does not pull up from the sides or corners as the adhesive dries. Bone Folder.com - square bone folder

This wood block works great but not sure where to find another.

6. Stack the panels up and weight them down for a day. Trim the excess canvas from the sides and you should now have perfect canvas panels, ready to be used as is, or cut to any size.

Additional tips and tricks: Gator Board can be scored and cut with a utility knife. It will take several passes to get a good cut, but is easy to do. I quit rinsing out the roller tray to keep excess adhesive from going down the drains. I just put any extra adhesive back in the bottle and let what remains dry in the tray. I do wash out the roller but make sure to use some soap. I also keep brown paper on my framing table which can be easily replaced as necessary. No work table - no problem - just use newspaper or something. Years ago when I made most of my frames and did not have a separate work space, I did most of the finishing work in my kitchen. I just made sure to cover all the surfaces with plastic. As the saying goes - whatever works . . .





Wednesday, February 15, 2017

Rational control and intuitive flow

Summary: Painting is a combination of chess and making breakfast. Combining the two requires some dancing. Robots can’t dance. And the next time you’re in front of your easel, try actually listening to your painting instead of always talking over it. Feedback and response is a good thing. 

Robert Genn (1936-2014) was a well-known Canadian painter and author of the Painter's Keys web site which he started in 1998. The site mails out a twice-weekly newsletter, and is currently run by Robert’s daughter Sara. You can sign up for free at The Painter's Keys. Following is an excerpt from a letter titled “The Intuitive Flow” originally published by Robert Genn on February 11, 2000.

“To what degree do we pay attention to our progress and to what degree do we just let it flow? My observation has been that there are times to give thought and other times when thought may be dangerous. Most of us have noticed how too much thinking can lead to poor or contrived work. Many of my outright failures have occurred when I wanted so badly to succeed, brought every brain cell to bear and fell down miserably. It makes you realize that something other than the cerebral cortex is necessary. Consider the centipede. If this lowly being paused for only a moment to determine which foot to move forward next, it would undoubtedly stumble. The centipede has rhythm and flow in its hundred legs precisely because it does not have to think about it. Consider this the next time you move the instruments of your art. At what point in the act of art does a natural power or a mysterious intuition seem to guide and generate excellence?

"Among the artists I know, admire and compete with, I've noticed the following: They understand the basics. They train themselves. They perfect the details and trivialities of what they do. They master their stances and their strategies. Then they put their heads down, close out the crowd and let it flow.

"Balancing your calculating brain and your intuitive flow is an easy dream and a difficult task. I think it's one of the true miracles.” (Robert Genn)

In September of 2016 Uri Bram posted an article titled “The Limits of Formal Learning, or Why Robots Can’t Dance.” He interviewed David Chapman, one of the first researchers to apply the mathematics of computational complexity theory to robot planning. Chapman suggested AI researchers address the challenge of teaching a robot to dance. “Dancing,” Chapman said, “was an important model because there’s no goal to be achieved. You can’t win or lose. It’s not a problem to be solved… Dancing is paradigmatically a process of interaction.”

Since most AI research revolves around task-oriented problems, ones with definite goals and a rigid structure, teaching a robot to dance would present unique problems. Chapman emphasized development over learning. Learning implies completion while development is an “ongoing, open-ended process. There is no final exam in dancing, after which you stop learning.”

One could argue the successful use of formal reasoning in areas such as science, engineering and mathematics has placed too much emphasis on logic-based, linear thinking and overlooked all the information being processed and working in the background. As the German philosopher Martin Heidegger pointed out, routine practical activities, such as making breakfast, are skills that do not seem to involve formal rationality. Our ability to engage in formal reasoning seems more likely to rely on our ability to engage in practical, informal, and embodied activities. He suggested most of life is unlike chess, and more like breakfast.

Heidegger’s observation on chess and breakfast is similar to Annie Dillard’s explanation of the mind/body  dilemma.  “The mind wants to live forever, or to learn a very good reason why not. The mind wants the world to return its love, or its awareness; the mind wants to know all the world, and all eternity, even God. The mind’s sidekick, however, will settle for two eggs over easy. The dear, stupid body is as easily satisfied as a spaniel. And, incredibly, the simple spaniel can lure the brawling mind to its dish. It is everlastingly funny that the proud, metaphysically ambitious, clamoring mind will hush if you give it an egg.”

Somewhere between chess and breakfast, the innate movements of the centipede Genn mentioned and Chapman’s robot is a place where it is possible to exceed our own expectations.

In the book “The Wayward Gate” Philip Slater  wrote, "Imagine life as a complicated dance. When we're thoroughly "into" the dance we don't have to analyze it in order to participate in a creative and harmonious way, no matter how rapid and intricate it becomes. But occasionally we're distracted, get self-conscious, lose confidence, trip, collide with someone, get out of synchrony with the rest. At such times we may mentally step out of the situation, look around, and try to figure out where the dance is going and where we fit in. Like children jumping rope, we adjust our timing for a few turns and then, when we're back in tune, leap in and again relinquish rational control in favor of a more instinctive kind of coordination.”

Slater went on to say rational control is a necessary device and useful for restoring balance, but destructive when we become dependent on the illusion of control. “I said rational control was a way of getting back in the dance when we’d lost our footing. But sometimes we get dazzled by the intricacy of the dance and forget about getting back in.” The need to understand the whole dance, not just our part in it, leads us to want control, to “reproduce it, mechanize it, and make sure we never lose our place again."

"My wish to understand . . . comes from my particular place in the dance – nine thousand and thirty-third whirler from the left, spinning on one of those bumpy places that make people lurch every so often. Lurching gives me a desire to grasp that the dance as a whole doesn’t share. The most grandiose, ‘objective’ theory in the world, in other words, is just a complicated personal effort to find one’s own place in the dance.  . . . Of course, from another point of view even lurching is just part of the dance, and so is stepping outside the dance, and so is trying to analyze and control the dance . . . They’re all just dances . . . and you’re just dancing.”