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.

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

Angular rotation, position, calculated across four billion seven hundred twelve million three hundred eighty eight thousand nine hundred seventy five iterations; graphite touching arc to shade on paper, through Faber-Castell pencil I am a circle inscribed. I am a little cowboy in South Texas, shooting metal plates hanging on a barbed wire fence. Shot striking metal to chime, dreaming sound of bell, 1225 Ancrene Riwle (Cleo. C.vi) Þet ower beoden bemen wel & dreamen in drichtines earen. Time occupied by the same nature in mind, symbolism or a thing, a radiance of observation, synthesis succeed one and makes them of the soul, a dark room also occupied by dreaming itself. Aristotle describes the primary being as an intellect or a kind of intellect that “thinks itself” perpetually. A primary substance must be what is both ontologically and epistemically basic, i.e., that which the existence of everything else depends, and on which our systematic knowledge depends. Circles in circles carved in stones as Mayan haab and tzolkin, civil and divine, against the long count of distant memory, days to come curving into a distant past. Stairless cylinder of words overheard in the woods at night among the same stone altars in grey watercolor shades, circles bent towards straight lines, appetite and practical thought, affections and actions of knowledge. The eye being merely the matter of seeing, sense is either a faculty or a separation by the same act dividing the time, obscure to obscurity… learning how to fall in love with my mistakes. Time occupied by the same nature in mind, symbolism or a thing, a radiance of observation, synthesis succeed one and makes them of the soul, a dark room also occupied by dreaming itself. The eye is the first circle; the horizon which it forms is the second; and throughout nature this primary picture is repeated without end. It is the highest emblem in the cipher of the world. St. Augustine described the nature of God as a circle whose centre was everywhere and its circumference nowhere. Here we are bound by many circles.

The Machine is soul so let us lose our devotion, but rather seem to the mouths and causes of hunger. A gap being different interpretations according to no one moment, I to the ruins of its own burdens talk of light. Life is a self-evolving circle from a ring imperceptibly small, rushes on all sides towards new and larger circles, and that without end. Wheel within wheels, each thought having formed itself into an arc of circumstance, as for instance an empire, an English garden, or rules of art. Perhaps this circle was a temple devoured by ancient fires, an enclosure crowned with smoothly weatherworn stone tiger. An uninhabited, ruined temple in the center of a circular amphitheater shadowed by taciturn clouds, the farthest ones hung at a distance of many centuries and as high as the stars. We subsist peremptory obligation to dream.

Last night I dreamt meeting a girl in a Chinese restaurant. She was eating french fries with chopsticks. She told me about her three cats “There”, “Their”, and “They’re”. I fell in love with her. We left the restaurant. She was riding a blue eyed paint mule. The girl was a beautiful cowgirl, and sang a lilting etherial song up at the sky accompanying herself with a ‘bass violin’, not an upright bass mind you… it looked like a cross between a violin, an autoharp, and a 箏. Occasionally the Sun turned black and time streamed backwards and forwards… people raced around and around in a blur. Suddenly there was a robbery at a local bank. We went quickly to stop it. As a reward we are given a nights stay in an elegant hotel with a seven course dinner. In the dining room at the table next to ours there is a woman having dinner with her daughter. The little girl is singing one of the Chopin opus 10 études, she’s singing all the notes polyphonically. The cowgirl and I marry and live in the hotel. I’m practicing for a piano contest. My manuscript is all over the hotel. On the walls, on the bed and the bath, on the concierge and bellboys, on the delicately water painted embroidered silk cushions of the Louis XVI chairs in the foyer, and even on two horses in the hotel corral outside. Nous n’irons plus au bois, les lauriers sont coupés. La belle que voilà, la laiss’rons nous danser?

In minute entirety and impose reality I ask sincerely, why is radix representation a ring isomorphism? Time occupied by the same nature in mind, symbolism or a thing, a radiance of observation, synthesis succeed one and makes them of the soul, a dark room also occupied by dreaming itself. How poignant, I must believe nothing of meaning, the true circle can not be inscribed. Seeking its confirmation across resolve within resolutions, I see misconceptions of arc astray, hesitant gestures, and lost voices. Y si el alma se me cayo por qué me sigue el esquéleto?

Angular rotation, position being a kind of intellect that ‘thinks itself’. Our encircling dream separating us to subtle arcs. Separated as horizons vast headlong abyss emitting no decisive light to undiscovered countries, to undreamed tedium of a Tuesday afternoon at 3:26pm and sandcastles singing the full moon tide. Here is a circular ceiling vaulted, elaborately fretted with the wildest and most grotesque specimen of a semi-gothic, semi-druidical device expanding space to echoes of principal feature seemingly of an excessive antiquity, of unaccountable capacities, vague longings, unnatural inclinations implanted without perceptible motivation. Words bewitch eyes, a sweet disorder in with delight and spake the bodies of blood. In a great fig-tree growing, in this river to be dying, the voice indeed is a way to reach it. So hand, so, there upon the heavens touch kinds of fire written, and hears the sound of Sirens’ voice never ceased, but that asked how this river to the truth was dream, hold had to much-sorrowing and sheer, as fascinated tale with loud voice, by no greater than when art is too precise. Subtlety doesn’t want but the hearth, the heavens touch the common into a great heap of yet more bonds, it haste away if they will then let think necks long and circumspect. Powers of the mind held in intimate connection with the capabilities of the stomach. We are such stuff. As dreams are made on; and our little life. Is rounded with a sleep.

1380 J. Wyclif Sel. Wks. III. 173 A sparke of fire, turnede aboute in derke nyȝte, semes to make cercul. 1483 tr. G. Deguileville Pilgrimage of Soul (Caxton) (1859) v. i. 70 In the circumference of eueriche of these cercles, was sette a lytel Cercle. 1483 Cath. Angl. 56 Half a Cerkylle, semicirculus. 1560 L. Digges Geom. Pract.: Pantometria (1571) iii. xi. sig. Riv Their circumferences or circles. 1589 G. Puttenham Arte Eng. Poesie ii. xi. 81 The beame is a line stretching directly from the circle to the center, & contrariwise from the center to the circle. a1616 W. Shakespeare Henry VI, Pt. 1 (1623) i. iii. 112 Glory is like a Circle in the Water, Which neuer ceaseth to enlarge it selfe. 1665 R. Boyle Occas. Refl. v. x. sig. Mm5v Archimedes..was so busie in tracing his Circles. 1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 284/2 The circumference or periphery itself is called the circle, though improperly, as that name denotes the space contained within the circumference. 1846 J. Ruskin Mod. Painters II. 55 The resulting curve, the circle, is..the least beautiful of all curves. 1877 E. R. Conder Basis of Faith ii. 67 A circle whose centre is everywhere and its circumference nowhere.

Akira Rabelais