Describing a Circle, why is radix representation a ring isomorphism?

圈 Describing a Circle; 1305 Edmund Conf. 232 in Early Eng. Poems & Lives Saints (1862) 77  Þreo rounde cerclen heo wrot: in þe paume amidde., concentric; 1400 G. Chaucer Treat. Astrolabe (Cambr. Dd.3.53) (1872) i. §17. 10  The heued of capricorne turnyth euermo consentryk vp-on the same cercle.

Describing a Circle

x = sin( -5.009757041932 * y ) – cos( 5.0073237419122 * x );
y = sin( -5.006352424622 * x ) – cos( 5.0065770149236 * y );

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Lessons of Darkness

Minnesota Declaration

  1. By dint of declaration the so-called Cinéma Vérité is devoid of vérité. It reaches a merely superficial truth, the truth of accountants.
  2. One well-known representative of Cinéma Vérité declared publicly that truth can be easily found by taking a camera and trying to be honest. He resembles the night watchman at the Supreme Court who resents the amount of written law and legal procedures. ‘For me,’ he says, ‘there should be only one single law: the bad guys should go to jail.’ Unfortunately, he is part right, for most of the many, much of the time.
  3. Cinéma Vérité confounds fact and truth, and thus ploughs only stones. And yet, facts sometimes have a strange and bizarre power that makes their inherent truth seem unbelievable.
  4. Fact creates norms, and truth illumination.
  5. There are deeper strata of truth in cinema, and there is such a thing as poetic, ecstatic truth. It is mysterious and elusive, and can be reached only through fabrication and imagination and stylization.
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Paintings Should Stick in the Throat

A question and its answer … are the painters still those painters who are painting the great cave? Do they paint the buffalo on the wall as hunger, the eagle as freedom, and the woman with a big bottom as love? Do they paint the buffalo as the table that magically sets itself? Have they meanwhile left the cave, cleared out of the community, and forgotten all those universal, comprehensible agreements, because magic does not still hunger, because flying does not work and yearning for love does not breed love? Have they traded the cave for some other place? Propagandizing about needs, ‘What does man need?’ feeds upon a yearning for freedom and the fear of death and entices us into taking another way, off the painters’ course. The smart ones, hotshots, innovators, activists – in the forefront madmen and hotspurs – have remained within their own skulls. They proclaim plucky mottos: paintings should stick in the throat, eyelids should be nailed down, and hearts grabbed with pliers. Fish bone, air raid and separation. Well, one still sits together around the fire, warms up the studios, has had enough to eat, and is in love. On battered canvases are those sumptuous ornaments filled with jumbled lines and rich colours; crystalline galleries hang over the frames. All that once stood erect, the still life, has been knocked over, the landscape has been seized and uprooted, the interiors tangled, and the portraits scratched and pierced. Painting became music. Surrealism won. Everything durable has been kicked out of the paintings.

Now, the tone goes right through walls, the line stands upside down. Are the painters now unhappy and freezing? They dance and celebrate with their friends, they invite their fathers and drink Capri with them. A black painting is as white as the sky. The colours in the dark cave are aglow. Light is superfluous. Everything is utterly different, anyway. The paraphernalia of Venus, Zeus, the angels, Picasso were invented by the painters, as were the bull, the roast chicken and the lovers. The pear-wood palette became a pail, the brush a knife, an axe and a club. The largest paintings are larger, and the smallest are smaller than ever before. Someone painted a painting weighing five hundred pounds. A Chinese handwalked over the canvas. A Norwegian painted 168 acres of birch wood on one and one-half square inches of canvas. This is not the way I want to continue. Hygiene, I mean religion, is employed. Discipline is one thing, education another, and meditation, too. Intoxication is used to prepare or to stabilize an attitude. Some eat well, others purify themselves through fasting. While I see no point at all in bustling around, in being confused, zap, zap, my friend between New York and Cologne makes the best paintings in his trouser pocket, where his canary sits. Does one see more of the world by climbing a ladder, does one see still more by lying down flat on the field and by sticking one’s nose in the ground? Either way. The difference between a German and an Italian apple tree is enormously large. In Tuscany in the garden I made photos of such trees. Back home in Germany I was terribly excited by these exotic apple trees, these unpaintable fairy-tale-tree-inventions. I realized that I did not want to paint an apple tree at all. I was still under the mother and had stuck out only my nose. The world had not opened up, the secret remained hidden within the object, but now there was confusion. This is an experience, but not of the kind that broadens your mind through shifting horizons. The first la-la sounds and the first dot-dot-comma-dash are indeed vehement creations for the one who makes them. This is not theory. I composed Fidelio, I know precisely that as a six-year-old I conducted this very piece; hare and dog I painted when I was eight years old, signing them Albrecht Dürer. One of these watercolours is in Vienna, in the Albertina, the dog is lost.

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I Am for an Art

I am for an art that is political-erotical-mystical, that does something other than sit on its ass in a museum.

I am for an art that grows up not knowing it is art at all, an art given the chance of having a starting point of zero.


I am for an art that embroils itself with the everyday crap & still comes out on top.

I am for an art that imitates the human, that is comic, if necessary, or violent, or whatever is necessary.

I am for all art that takes its form from the lines of life itself, that twists and extends and accumulates and spits and drips, and is heavy and coarse and blunt and sweet and stupid as life itself.

I am for an artist who vanishes, turning up in a white cap painting signs or hallways.

I am for art that comes out of a chimney like black hair and scatters in the sky.

I am for art that spills out of an old mans purse when he is bounced off a passing fender.

I am for the art out of a doggys mouth, falling five stories from the roof.

I am for the art that a kid licks, after peeling away the wrapper.

I am for an art that joggles like everyone’s knees, when the bus traverses an excavation.

I am for art that is smoked, like a cigarette, smells, like a pair of shoes. I am for art that flaps like a flag, or helps blow noses, like a handkerchief.

I am for art that is put on and taken off, like pants, which develops holes, like socks, which is eaten, like a piece of pie, or abandoned with great contempt, like a piece of shit.

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Megjegyzések egy kiáltványhoz

Notes de manifeste
Vasarely erTf t

Here are the determining facts of the past which tie us together and which, among others, interest us: ‘plastic’ triumphs over anecdote (Manet) – the first geometrization of the exterior world (Cézanne) – the conquest of pure colour (Matisse) – the explosion of representation (Picasso) – exterior vision changes into interior vision (Kandinsky) – a branch of painting dissolves into architecture, becoming polychromatic (Mondrian) – departure from the large plastic synthetics (Le Corbusier) – new plastic alphabets (Arp, Taeuber, Magnelli, Herbin) – abandoning volume for SPACE (Calder) … The desire for a new conception was affirmed in the recent past by the invention of PURE COMPOSITION and by the choice of UNITY, which we will discuss later. Parallel to the decline of painting’s ancestral technique, followed experimentation with new materials (chemical applications) and adoption of new tools (discovery of physics) … Presently we are heading towards the complete abandonment of routine, towards the integration of sculpture and the conquest of the plane’s SUPERIOR DIMENSIONS.

From the beginning, abstraction examined and enlarged its compositional elements. Soon, form-colour invaded the entire two-dimensional surface, this metamorphosis led the painting-object, by way of architecture, to a spatial universe of polychromy. However, an extra-architectural solution was already proposed and we deliberately broke with the neo-plastic law. PURE COMPOSITION is still a plastic plane where rigorous abstract elements, hardly numerous and expressed in few colours (matte or glossy), possess, on the whole surface, the same complete plastic quality: POSITIVE-NEGATIVE. But, by the effect of opposed perspectives, these elements give birth to and make vanish in turn a ‘spatial feeling’ and thus, the illusion of motion and duration. FORM AND COLOUR ARE ONE. Form can only exist when indicated by a coloured quality. Colour is only quality when unlimited in form. The line (drawing, contour) is a fiction which belongs not to one, but to two form-colours at the same time. It does not engender form-colours, it results from their meeting. Two necessarily contrasted form-colours constitute PLASTIC UNITY, thus the UNITY of creation: eternal duality of all things, recognized finally as inseparable. It is the coupling of affirmation and negation. Measurable and immeasurable, unity is both physical and metaphysical. It is the conception of the material, the mathematical structure of the Universe, as its spiritual superstructure. Unity is the absence of BEAUTY, the first form of sensitivity. Conceived with art, it constitutes the work, poetic equivalent of the World that it signifies. The simplest example of plastic unity is the square (or rectangle) with its complement ‘contrast’ or the two-dimensional plane with its complement ‘surrounding space’.

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Manifest, a new consciousness with laws of dialectics

Een nieuw bewustzijn binnen de wetten van de dialectiek

The dissolution of Western classical culture is a phenomenon that can be understood only against the background of a social evolution which can end only in the total collapse of a principle of society thousands of years old and its replacement by a system whose laws are based on the immediate demands of human vitality. The influence the ruling classes have wielded over the creative consciousness in history has reduced art to an increasingly dependent position, until finally the real psychic function of that art was attainable only for a few spirits of genius who in their frustration and after a long struggle were able to break out of the conventions of form and rediscover the basic principles of all creative activity.

After Us

Together with the class society from which it emerged, this culture of the individual is faced by destruction too, as the former’s institutions, kept alive artificially, offer no further opportunities for the creative imagination and only impede the free expression of human vitality. All the isms so typical of the last fifty years of art history represent so many attempts to bring new life to this culture and to adapt its aesthetic to the barren ground of its social environment. Modern art, suffering from a permanent tendency to the constructive, an obsession with objectivity (brought on by the disease that has destroyed our speculative-idealizing culture), stands isolated and powerless in a society which seems bent on its own destruction. As the extension of a style created for a social élite, with the disappearance of that élite modern art has lost its social justification and is confronted only by the criticism formulated by a clique of its connoisseurs and amateurs.

Western art, once the celebrator of emperors and popes, turned to serve the newly powerful bourgeoisie, becoming an instrument of the glorification of bourgeois ideals. Now that these ideals have become a fiction with the disappearance of their economic base, a new era is upon us, in which the whole matrix of cultural conventions loses its significance and a new freedom can be won from the most primary source of life. But, just as with a social revolution, this spiritual revolution cannot be enacted without conflict. Stubbornly the bourgeois mind clutches onto its aesthetic ideal and in a last, desperate effort employs all its wiles to convert the indifferent masses to the same belief. Taking advantage of the general lack of interest, suggestions are made of a special social need for what is referred to as ‘an ideal of beauty’, all designed to prevent the flowering of a new, conflicting sense of beauty which emerges from the vital emotions.

As early as the end of the First World War the DADA movement tried by violent means to break away from the old ideal of beauty. Although this movement concentrated increasingly on the political arena, as the artists involved perceived that their struggle for freedom brought them into conflict with the laws that formed the very foundations of society, the vital power released by this confrontation also stimulated the birth of a new artistic vision.

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Toward an Architecture

LC Bouteilles


Aesthetic of the Engineer


Aesthetic of the Engineer, Architecture: two things firmly allied, sequential, the one in full flower, the other in painful regression.

The engineer, inspired by the law of Economy and guided by calculations, puts us in accord with universal laws. He attains harmony.

The architect, through the ordonnance of forms, realizes an order that is a pure creation of his mind; through forms, he affects our senses intensely, provoking plastic emotions; through the relationships that he creates, he stirs in us deep resonances, he gives us the measure of an order that we sense to be in accord with that of the world, he determines the diverse movements of our minds and our hearts; it is then that we experience beauty.

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