Showing posts with label Art. Show all posts
Showing posts with label Art. Show all posts

Monday, July 08, 2013

Math and the Mona Lisa

How did Leonardo da Vinci use math to influence the way we see the Mona Lisa? And how does our visual system affect our perception of that, and other, works of art? A look at math, biology and the science of viewing art.Math and the Mona Lisa
Just to note this radio program at NPR was back in 2004.

New possibilities opened up by the concept of four-dimensional space (and difficulties involved in trying to visualize it) helped inspire many modern artists in the first half of the twentieth century. Early Cubists, Surrealists, Futurists, and abstract artists took ideas from higher-dimensional mathematics and used them to radically advance their work.[1]Fourth dimension in art

Sunday, May 06, 2012

A Path With a Heart

"All paths lead nowhere,so it is important to choose a path that has heart."
-- Carlos Castenada
Update: I am re-posting this article from 2006. I wanted to highlight this post in relation to the idea of intent. What it means to me.  I wanted as well to show the need for, to be enable conventionality into our own lives. If one cannot find such meaning,  does one find them self as if tossed on the waves of some chaotic life living by rote?

Yes, I find it important that this idea of "a tonal"  leaves the impression in my mind and others of the closeness with which sincerity is expressed through our own feelings and the need for such convictions.

If we understand the the anticipated future is part of our living our lives then it should come as no shock that we are the architects of the time we have in living our lives as we do. That the probable futures and probable pasts come from taking a position in life regardless of the idea that not only is it causal toward our projections, but it also within the scope of our reason that we can live or lives as true as possible.

What happens to a culture raised in the early years that we might have felt that we were getting the messages from someone who understood something greater then ourselves. The baby boomers were all part of the process. I was part of the process in that I wanted to explore unconventional thinking.

While I have move forward to the principles of scientific standards today in my explorations I have to say this was indeed part of my past too. So what has come of the points about sophistical questions about our existence?

Shall we stay so blinded then to what could have transpire in our lives to have the myths transported from our own generations past to  be carried forward to another today to have missed the understandings of the times then?

Some of the older folk probably have read the many books of Carlos Castaneda, like I have? Drawn into a strange world of thinking, it challenged my thought processes.  Most of it I was not accustom too. Did Carlos Castaneda actually exist? Was he some fictional character created, to tell the stories?

Anything is one of a million paths. Therefore you must always keep in mind that a path is only a path; if you feel you should not follow it, you must not stay with it under any conditions. To have such clarity you must lead a disciplined life. Only then will you know that any path is only a path and there is no affront, to oneself or to others, in dropping it if that is what your heart tells you to do. But your decision to keep on the path or to leave it must be free of fear or ambition. I warn you. Look at every path closely and deliberately. Try it as many times as you think necessary.

This question is one that only a very old man asks. Does this path have a heart? All paths are the same: they lead nowhere. They are paths going through the bush, or into the bush. In my own life I could say I have traversed long long paths, but I am not anywhere. Does this path have a heart? If it does, the path is good; if it doesn't, it is of no use. Both paths lead nowhere; but one has a heart, the other doesn't. One makes for a joyful journey; as long as you follow it, you are one with it. The other will make you curse your life. One makes you strong; the other weakens you.

Before you embark on any path ask the question: Does this path have a heart? If the answer is no, you will know it, and then you must choose another path. The trouble is nobody asks the question; and when a man finally realizes that he has taken a path without a heart, the path is ready to kill him. At that point very few men can stop to deliberate, and leave the path. A path without a heart is never enjoyable. You have to work hard even to take it. On the other hand, a path with heart is easy; it does not make you work at liking it.

I have told you that to choose a path you must be free from fear and ambition. The desire to learn is not ambition. It is our lot as men to want to know.

The path without a heart will turn against men and destroy them. It does not take much to die, and to seek death is to seek nothing.

Well I am not going to tell you what to think. I am just going to show some of the things that attracted my attention and brought me to some of the views I have garnered around what the heart actually meant. The lesson was given by a person who told me the story of the picture of the scale weighting the feather, was to be a important one in my recognition of something profound and true. Possibly, to those who understood the message as well?

That was part of my lesson of learning. That a path with a heart was something better then no path at all.

Tuesday, January 04, 2011

Maurits Cornelis Escher

A 1929 self-portrait
Born June 17, 1898
Leeuwarden, The Netherlands
Died 27 March 1972 (aged 73)
Laren, The Netherlands
Nationality Dutch
Field Drawing, Printmaking
Works Relativity, Waterfall, Hand with Reflecting Sphere
Influenced by Giovanni Battista Piranesi
Awards Knighthood of the Order of Orange-Nassau    

Maurits Cornelis Escher (17 June 1898 – 27 March 1972), usually referred to as M.C. Escher (English pronunciation: /ˈɛʃər/, Dutch: [ˈmʌurɪts kɔrˈneːlɪs ˈɛʃər]  ( listen)),[1] was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints. These feature impossible constructions, explorations of infinity, architecture, and tessellations.


Early life

Maurits Cornelis, nicknamed "Mauk",[2] was born in Leeuwarden, The Netherlands, in a house that forms part of the Princessehof Ceramics Museum today. He was the youngest son of civil engineer George Arnold Escher and his second wife, Sara Gleichman. In 1903, the family moved to Arnhem where he attended primary school and secondary school until 1918.

He was a sickly child, and was placed in a special school at the age of seven and failed the second grade.[3] Though he excelled at drawing, his grades were generally poor. He also took carpentry and piano lessons until he was thirteen years old. In 1919, Escher attended the Haarlem School of Architecture and Decorative Arts. He briefly studied architecture, but he failed a number of subjects (partly due to a persistent skin infection) and switched to decorative arts.[3] Here he studied under Samuel Jessurun de Mesquita, with whom he would remain friends for years. In 1922 Escher left the school, having gained experience in drawing and making woodcuts.

Later life

In 1922, an important year of his life, Escher traveled through Italy (Florence, San Gimignano, Volterra, Siena, Ravello) and Spain (Madrid, Toledo, Granada). He was impressed by the Italian countryside and by the Alhambra, a fourteenth-century Moorish castle in Granada, Spain. He came back to Italy regularly in the following years. In Italy he met Jetta Umiker, whom he married in 1924. The young couple settled down in Rome and stayed there until 1935, when the political climate under Mussolini became unbearable. Their son, Giorgio Arnaldo Escher, named after his grandfather, was born in Rome. The family next moved to Château-d'Œx, Switzerland, where they remained for two years.

Escher, who had been very fond of and inspired by the landscapes in Italy, was decidedly unhappy in Switzerland, so in 1937, the family moved again, to Ukkel, a small town near Brussels, Belgium. World War II forced them to move in January 1941, this time to Baarn, the Netherlands, where Escher lived until 1970. Most of Escher's better-known pictures date from this period. The sometimes cloudy, cold, wet weather of the Netherlands allowed him to focus intently on his works, and only during 1962, when he underwent surgery, was there a time when no new images were created.

Escher moved to the Rosa Spier house in Laren in 1970, a retirement home for artists where he had his own studio. He died at the home on 27 March 1972, at age 73.


Escher's first print of an impossible reality was Still Life and Street, 1937. His artistic expression was created from images in his mind, rather than directly from observations and travels to other countries. Well known examples of his work also include Drawing Hands, a work in which two hands are shown, each drawing the other; Sky and Water, in which light plays on shadow to morph the water background behind fish figures into bird figures on a sky background; and Ascending and Descending, in which lines of people ascend and descend stairs in an infinite loop, on a construction which is impossible to build and possible to draw only by taking advantage of quirks of perception and perspective.

He worked primarily in the media of lithographs and woodcuts, though the few mezzotints he made are considered to be masterpieces of the technique. In his graphic art, he portrayed mathematical relationships among shapes, figures and space. Additionally, he explored interlocking figures using black and white to enhance different dimensions. Integrated into his prints were mirror images of cones, spheres, cubes, rings and spirals.
In addition to sketching landscape and nature in his early years, he also sketched insects, which frequently appeared in his later work. His first artistic work, completed in 1922, featured eight human heads divided in different planes. Later around 1924, he lost interest in "regular division" of planes, and turned to sketching landscapes in Italy with irregular perspectives that are impossible in natural form.

Although Escher did not have mathematical training—his understanding of mathematics was largely visual and intuitive—Escher's work had a strong mathematical component, and more than a few of the worlds which he drew are built around impossible objects such as the Necker cube and the Penrose triangle. Many of Escher's works employed repeated tilings called tessellations. Escher's artwork is especially well-liked by mathematicians and scientists, who enjoy his use of polyhedra and geometric distortions. For example, in Gravity, multi-colored turtles poke their heads out of a stellated dodecahedron.
The mathematical influence in his work emerged around 1936, when he was journeying the Mediterranean with the Adria Shipping Company. Specifically, he became interested in order and symmetry. Escher described his journey through the Mediterranean as "the richest source of inspiration I have ever tapped."

After his journey to the Alhambra, Escher tried to improve upon the art works of the Moors using geometric grids as the basis for his sketches, which he then overlaid with additional designs, mainly animals such as birds and lions.
His first study of mathematics, which would later lead to its incorporation into his art works, began with George Pólya's academic paper on plane symmetry groups sent to him by his brother Berend. This paper inspired him to learn the concept of the 17 wallpaper groups (plane symmetry groups). Utilizing this mathematical concept, Escher created periodic tilings with 43 colored drawings of different types of symmetry. From this point on he developed a mathematical approach to expressions of symmetry in his art works. Starting in 1937, he created woodcuts using the concept of the 17 plane symmetry groups.

Circle Limit III, 1959
In 1941, Escher wrote his first paper, now publicly recognized, called Regular Division of the Plane with Asymmetric Congruent Polygons, which detailed his mathematical approach to artwork creation. His intention in writing this was to aid himself in integrating mathematics into art. Escher is considered a research mathematician of his time because of his documentation with this paper. In it, he studied color based division, and developed a system of categorizing combinations of shape, color and symmetrical properties. By studying these areas, he explored an area that later mathematicians labeled crystallography.
Around 1956, Escher explored the concept of representing infinity on a two-dimensional plane. Discussions with Canadian mathematician H.S.M. Coxeter inspired Escher's interest in hyperbolic tessellations, which are regular tilings of the hyperbolic plane. Escher's works Circle Limit I–IV demonstrate this concept. In 1995, Coxeter verified that Escher had achieved mathematical perfection in his etchings in a published paper. Coxeter wrote, "Escher got it absolutely right to the millimeter."

His works brought him fame: he was awarded the Knighthood of the Order of Orange Nassau in 1955. Subsequently he regularly designed art for dignitaries around the world. An asteroid, 4444 Escher, was named in his honour in 1985.

In 1958, he published a paper called Regular Division of the Plane, in which he described the systematic buildup of mathematical designs in his artworks. He emphasized, "Mathematicians have opened the gate leading to an extensive domain."

Overall, his early love of Roman and Italian landscapes and of nature led to his interest in the concept of regular division of a plane, which he applied in over 150 colored works. Other mathematical principles evidenced in his works include the superposition of a hyperbolic plane on a fixed 2-dimensional plane, and the incorporation of three-dimensional objects such as spheres, columns and cubes into his works. For example, in a print called "Reptiles", he combined two and three-dimensional images. In one of his papers, Escher emphasized the importance of dimensionality and described himself as "irritated" by flat shapes: "I make them come out of the plane."

Waterfall, 1961
Escher also studied the mathematical concepts of topology. He learned additional concepts in mathematics from the British mathematician Roger Penrose. From this knowledge he created Waterfall and Up and Down, featuring irregular perspectives similar to the concept of the Möbius strip.

Escher printed Metamorphosis I in 1937, which was a beginning part of a series of designs that told a story through the use of pictures. These works demonstrated a culmination of Escher's skills to incorporate mathematics into art. In Metamorphosis I, he transformed convex polygons into regular patterns in a plane to form a human motif. This effect symbolizes his change of interest from landscape and nature to regular division of a plane.
One of his most notable works is the piece Metamorphosis III, which is wide enough to cover all the walls in a room, and then loop back onto itself.

After 1953, Escher became a lecturer at many organizations. A planned series of lectures in North America in 1962 was cancelled due to an illness, but the illustrations and text for the lectures, written out in full by Escher, were later published as part of the book Escher on Escher. In July 1969 he finished his last work, a woodcut called Snakes, in which snakes wind through a pattern of linked rings which fade to infinity toward both the center and the edge of a circle.


The special way of thinking and the rich graphic work of M.C. Escher has had a continuous influence in science and art, as well as references in pop culture. Ownership of the Escher intellectual property and of his unique art works have been separated from each other.
In 1969, Escher's business advisor, Jan W. Vermeulen, author of a biography in Dutch on the artist, established the M.C. Escher Stichting (M.C. Escher Foundation), and transferred into this entity virtually all of Escher's unique work as well as hundreds of his original prints. These works were lent by the Foundation to the Hague Museum. Upon Escher's death, his three sons dissolved the Foundation, and they became partners in the ownership of the art works. In 1980, this holding was sold to an American art dealer and the Hague Museum. The Museum obtained all of the documentation and the smaller portion of the art works.

The copyrights remained the possession of the three sons - who later sold them to Cordon Art, a Dutch company. Control of the copyrights was subsequently transferred to The M.C. Escher Company B.V. of Baarn, Netherlands, which licenses use of the copyrights on all of Escher's art and on his spoken and written text, and also controls the trademarks. Filing of the trademark "M.C. Escher" in the United States was opposed, but the Dutch company prevailed in the courts on the grounds that an artist or his heirs have a right to trademark his name.
A related entity, the M.C. Escher Foundation of Baarn, promotes Escher's work by organizing exhibitions, publishing books and producing films about his life and work.
The primary institutional collections of original works by M.C. Escher are the Escher Museum, a subsidiary of the Haags Gemeentemuseum in The Hague; the National Gallery of Art (Washington, DC); the National Gallery of Canada (Ottawa); the Israel Museum (Jerusalem); Huis ten Bosch (Nagasaki, Japan); and the Boston Public Library.

Selected works

  • Trees, ink (1920)
  • St. Bavo's, Haarlem, ink (1920)
  • Flor de Pascua (The Easter Flower), woodcut/book illustrations (1921)
  • Eight Heads, woodcut (1922)
  • Dolphins also known as Dolphins in Phosphorescent Sea, woodcut (1923)
  • Tower of Babel, woodcut (1928)
  • Street in Scanno, Abruzzi, lithograph (1930)
  • Castrovalva, lithograph (1930)
  • The Bridge, lithograph (1930)
  • Palizzi, Calabria, woodcut (1930)
  • Pentedattilo, Calabria, lithograph (1930)
  • Atrani, Coast of Amalfi, lithograph (1931)
  • Ravello and the Coast of Amalfi, lithograph (1931)
  • Covered Alley in Atrani, Coast of Amalfi, wood engraving (1931)
  • Phosphorescent Sea, lithograph (1933)
  • Still Life with Spherical Mirror, lithograph (1934)
  • Hand with Reflecting Sphere also known as Self-Portrait in Spherical Mirror, lithograph (1935)
  • Inside St. Peter's, wood engraving (1935)
  • Portrait of G.A. Escher, lithograph (1935)
  • “Hell”, lithograph, (copied from a painting by Hieronymus Bosch) (1935)
  • Regular Division of the Plane, series of drawings that continued until the 1960s (1936)
  • Still Life and Street (his first impossible reality), woodcut (1937)
  • Metamorphosis I, woodcut (1937)
  • Day and Night, woodcut (1938)
  • Cycle, lithograph (1938)
  • Sky and Water I, woodcut (1938)
  • Sky and Water II, lithograph (1938)
  • Metamorphosis II, woodcut (1939–1940)
  • Verbum (Earth, Sky and Water), lithograph (1942)
  • Reptiles, lithograph (1943)
  • Ant, lithograph (1943)
  • Encounter, lithograph (1944)
  • Doric Columns, wood engraving (1945)
  • Three Spheres I, wood engraving (1945)
  • Magic Mirror, lithograph (1946)
  • Three Spheres II, lithograph (1946)
  • Another World Mezzotint also known as Other World Gallery, mezzotint (1946)
  • Eye, mezzotint (1946)
  • Another World also known as Other World, wood engraving and woodcut (1947)
  • Crystal, mezzotint (1947)
  • Up and Down also known as High and Low, lithograph (1947)
  • Drawing Hands, lithograph (1948)
  • Dewdrop, mezzotint (1948)
  • Stars, wood engraving (1948)
  • Double Planetoid, wood engraving (1949)
  • Order and Chaos (Contrast), lithograph (1950)
  • Rippled Surface, woodcut and linoleum cut (1950)
  • Curl-up, lithograph (1951)
  • House of Stairs, lithograph (1951)
  • House of Stairs II, lithograph (1951)
  • Puddle, woodcut (1952)
  • Gravitation, (1952)
  • Dragon, woodcut lithograph and watercolor (1952)
  • Cubic Space Division, lithograph (1952)
  • Relativity, lithograph (1953)
  • Tetrahedral Planetoid, woodcut (1954)
  • Compass Rose (Order and Chaos II), lithograph (1955)
  • Convex and Concave, lithograph (1955)
  • Three Worlds, lithograph (1955)
  • Print Gallery, lithograph (1956)
  • Mosaic II, lithograph (1957)
  • Cube with Magic Ribbons, lithograph (1957)
  • Belvedere, lithograph (1958)
  • Sphere Spirals, woodcut (1958)
  • Ascending and Descending, lithograph (1960)
  • Waterfall, lithograph (1961)
  • Möbius Strip II (Red Ants) woodcut (1963)
  • Knot, pencil and crayon (1966)
  • Metamorphosis III, woodcut (1967–1968)
  • Snakes, woodcut (1969)

[edit] See also

[edit] Notes

  1. ^ Duden Aussprachewörterbuch (6 ed.). Mannheim: Bibliographisches Institut & F.A. Brockhaus AG. 2005. ISBN 3-411-04066-1.
  2. ^ "We named him Maurits Cornelis after S.'s [Sara's] beloved uncle Van Hall, and called him 'Mauk' for short ....", Diary of Escher's father, quoted in M. C. Escher: His Life and Complete Graphic Work, Abradale Press, 1981, p. 9.
  3. ^ a b Barbara E, PhD. Bryden. Sundial: Theoretical Relationships Between Psychological Type, Talent, And Disease. Gainesville, Fla: Center for Applications of Psychological Type. ISBN 0-935652-46-9.


  • M.C. Escher, The Graphic Work of M.C. Escher, Ballantine, 1971. Includes Escher's own commentary.
  • M.C. Escher, The Fantastic World of M.C. Escher, Video collection of examples of the development of his art, and interviews, Director, Michele Emmer.
  • Locher, J.L. (2000). The Magic of M. C. Escher. Harry N. Abrams, Inc. ISBN 0-8109-6720-0.
  • Ernst, Bruno; Escher, M.C. (1995). The Magic Mirror of M.C. Escher (Taschen Series). TASCHEN America Llc. ISBN 1-886155-00-3 Escher's art with commentary by Ernst on Escher's life and art, including several pages on his use of polyhedra.
  • Abrams (1995). The M.C. Escher Sticker Book. Harry N. Abrams. ISBN 0-8109-2638-5 .
  • "Escher, M. C.." The World Book Encyclopedia. 10th ed. 2001.
  • O'Connor, J. J. "Escher." Escher. 01 2000. University of St Andrews, Scotland. 17 June 2005.
  • Schattschneider, Doris and Walker, Wallace. M. C. Escher Kaleidocycles, Pomegranate Communications; Petaluma, California, 1987. ISBN 0-906212-28-6.
  • Schattschneider, Doris. M.C. Escher : visions of symmetry, New York, N.Y. : Harry N. Abrams, 2004. ISBN 0-8109-4308-5.
  • M.C. Escher's legacy: a centennial celebration; collection of articles coming from the M.C. Escher Centennial Conference, Rome, 1998 / Doris Schattschneider, Michele Emmer (editors). Berlin; London: Springer-Verlag, 2003. ISBN 3-540-42458-X (alk. paper), ISBN 3-540-42458-X (hbk).
  • M.C. Escher: His Life and Complete Graphic Work, edited by J. L. Locher, Amsterdam 1981.

External links

Thursday, November 19, 2009

Gian Paolo Lomazzo

Self-portrait of Giovanni Paolo Lomazzo

Gian Paolo Lomazzo (26 April 153827 January 1592; his first name is sometimes also given as "Giovan" or "Giovanni") was an Italian painter, more remembered for his writings on art theory, belonging to the second generation that produced Mannerism in Italian art and architecture.

Gian Paolo Lomazzo was born in Milan from a family emigrated from the town of Lomazzo. His early training was with Giovan Battista della Cerva in Milan. He painted a large Allegory of the Lenten Feast for San Agostino in Piacenza (1567). He also painted an elaborate dome with Glory of Angels for the Capella Foppa in San Marco in Milan. He also painted the Fall of Simon Magus in the wall of the chapel.
Lomazzo became blind in 1571, and turning to writing, produced two complex treatises that are milestones in the development of art criticism. His first work, Trattato dell'arte della pittura, scoltura et architettura (1584) is in part a guide to contemporary concepts of decorum, which the Renaissance inherited in part from Antiquity, which controlled a consonance between the functions of interiors and the kinds of painted and sculpted decors that would be suitable; Lespingola offered a systematic codification of esthetics that typifies the increasingly formalized and academic approaches typical of the later sixteenth century.
His less practical and more metaphysical Idea del tempio della pittura ("The ideal temple of painting", 1590) offers a description along the lines of the "four temperaments" theory of the human nature and personality, containing the explanations of the role of individuality in judgment and artistic invention.
Lomazzo's criticism took into account three aspects of critical viewing of works of art: doctrina, the record of discoveries— such as perspective— that artists had made in the course of history; prattica, the personal preferences and maniera of the artist, and iconography, the literary element in arts. Lomazzo’s contribution to art criticism was his systematic extraction of abstract concepts from art, not merely a recounting of the marvels of verisimilitude and technique and anecdotes of the works' reception among contemporaries of the type that Giorgio Vasari had reported in the previous generation.
Giovanni Ambrogio Figino and Girolamo Ciocca were his pupils.

The Fall of Simon Magus is a subject taken from The Golden Legend of Jacobus de Voragine and it involves a contest between a sorcerer at the court of Emperor Nero and Saint Peter. Nero is seen enthroned on the left while Saint peter and Saint Paul are on the right. Simon Magus, endeavouring to prove his magical powers, attempts to launch himself from a wooden tower towards heaven, but even though supported by demons his experiment fails and he falls to the ground. See:Web Gallery of Art

Friday, April 10, 2009

To Stop the Hardening

Kaluza-Klein (Invisible Architecture III) by Dawn Meson

Gallery: Dawn Meson
by Raven Hanna

From cave paintings of bison to Monet landscapes, artists have studied and interpreted the natural world. Dawn Neal Meson, a San Francisco artist, has taken this theme one level further, or, rather, many orders of magnitude smaller.

The subjects of Sum Over Histories, Meson's latest series of acrylic paintings, feature aspects of nature at the particle physics level: colliding electrons, multidimensional surfaces, entangled particles, and string theory. Her goal is to illuminate invisible worlds, unseen and unseeable. Through these works she answers her own question, what can art contribute beyond photography?

Sunday, October 14, 2007

The Artist In Us All

""Deep play means no analysis, no explanation, no promises, no goals, no worries. You are completely open to the drama of life that may unfold.""-Dianne Ackerman

See more on Deep Play.

This post entry under the heading of the "Artist in us All," is a culmination of information that I had transmitted on Bee's discussion board, under the heading of Art and Communication.

The whole jest is a preclude to a much more detailed analysis of Art and Science and the following post to this one, prepares the readers for a understanding that I myself strongly advocate.

But before I move to far ahead of myself, let me take you to the post entries that will prepare one for future considerations.

The Format

A final aspect of beauty that was often cited by readers might be called "deep play". This is the sense that we are actively engaged with something outside ourselves that is responding to us - rather than watching a game of our own construction or watching nature from a detached distance.

The timing of "preparing the format" asks that any given time be considered as the source from which we will move human experiences further along it's path to growth. We can "remove names" and this exercise will be of value to who ever inserts their name or responds accordingly to the questions posted in that same name.

This is the valuation of interplay that is part of our own gathering system. This post then is the template for what is happening within your own self. A "perceived constant" is being examined in relation to your contact with reality? What ever that is for you at this time?


"It is sometimes the scientist who takes "to the edge." Then it is the artist, who takes us much further." Plato( this is my quote Bee :)

Susskind did exactly this, by envisioning a rubber band? Some may laugh, yet, it is a mathematical insight.

Penroses Influence on Escher

During the later half of the 1950’s, Maurits Cornelius Escher received a letter from Lionel and Roger Penrose. This letter consisted of a report by the father and son team that focused on impossible figures. By this time, Escher had begun exploring impossible worlds. He had recently produced the lithograph Belvedere based on the “rib-cube,” an impossible cuboid named by Escher (Teuber 161). However, the letter by the Penroses, which would later appear in the British Journal of Psychology, enlightened Escher to two new impossible objects; the Penrose triangle and the Penrose stairs. With these figures, Escher went on to create further impossible worlds that break the laws of three-dimensional space, mystify one’s mind, and give a window to the artist heart.

But on the other hand you speak about the longevity of the musician, in place of what artist can do, but I would remind you of Dali's picture "on time" as a masterpiece?

Not least to mention his geometrical views on the hypercube and the crucification?

Number theory is the type of math that describes the swirl in the head of a sunflower and the curve of a chambered nautilus. Bhargava says it's also hidden in the rhythms of classical Indian music, which is both mathematical and improvisational. He sees close links between his two loves -- both create beauty and elegance by weaving together seemingly unconnected ideas.

There is a "inherent beauty in the mathematics" when we think about this music?

Not to mention the relationship of the "Monte Carlo methods" in relation to the cubists.

Bee, you were to soft in your opinion of artists when I am showing you otherwise. :)

Here is another quote you might recognize in relation to a form of mathematics.

An equation means nothing to me unless it expresses a thought of God.Srinivasa Ramanujan

It is how Srinivasa Ramanujan received his "inspiration" and the place from which this mathematics emerged, that few people realize is of significance.

From "a chaotic mind" it resolved itself "to the subconscious" that we realize the pattern that is inherent underneath.

12:50 PM, October 10, 2007

Part of the understanding here is our connection to the "universality of the subconscious mind" and it's reservoir of impressions received, as we try to express our perspective of the world. "How deep" is your subconscious mind, that you would not understand the complexity of all "self evident information" makes you who you are? That this interplay that takes place with you and your environment, is an exchange that is taking place not only on a "deductive and inductive Archean constant" that all of us would then be writing the "postulate of experience" here?


It is not about God, but how we dress up the mathematics in our everyday lives. Then, we have to decipher the context of the mathematics other then the "resolved experience-science" we have in moving mathematics forward?

To Srinivasa Ramanujan it was about his dream and how he received his messages, yet, how absurd that such a place as the subconscious we could receive such inspiration?

It is not about "heliocentrism" that we are, "the centre of the universe," but rather, that we are connected to the universe in such a way?

Liminocentric structures?

Finally, we also hope that this series furthers the discussion regarding the nature and function of 'the mandala'. In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry. By offering a new view about how consciousness itself is structured - in a fundamentally paradoxical fashion - and how these structurings are reflected in principles according to which the mandala is organized, we are able in this series to show how personality itself may be thought of as having an essentially 'liminocentric' design.

The "source of symmetry" is our perfection with the universal inherent in each of us. Our delving into this large pool is in part the effort of our recordings, that what is gained in experience is mapped on the brain's structure, and beyond that. This interplay has to have consequence? Not just in the development of the brain's structure, but far beyond what we see of the physical body.

1:40 PM, October 10, 2007

Bee:I tend to believe we are taking ourselves too seriously. If there is a God how could we be sure we'd be able to understand his (her?) thoughts? Genderless for sure eh?:)

From a psychological perspective and I am no expert for sure, but our present state of consciousness has to be supported in one way or another. Animus and Anima, depending on that gender?

An "all wise mother figure" who appears in your dream( your higher self speaking to you), or for those men, who recognize that the higher self is talking to them in a way that they have their "wise white haired person offering insight."

But before I loose you here, I wanted to show you that on first appearance Jean Shinoda Bolen is telling a story. This is the artist aspect of herself, showing the depth of our natures. She is showing it in a way that is helping people identify aspects of themself. Showing underlying causes for such "fantasy development."

Richards Wagners's Ring of Nibelung Jean Shinoda Bolen, M.D. Ring of Power was interesting.

Strange that we could have seen A Jungian Understanding of the Wagner's Ring cycle, portrayed in todays world and how could have this been accomplished. But by re-introducing a fictional story and embuing it with the archetypal structures of what Jean Shinoda Bolen called, "The Abandon Child, The Authoritarian Father, and the Disempowered Feminine."

Under the search of "Jean Shinoda Bolen on my site." One reason the "nav bar" was of good use. If you have a search feature otherwise?

It's never clear from all appearances, yet there is a deeper understanding of what is culminating in a person's experiential life.

I follow your thoughts on Bohm for I read him a long time ago too, and somehow it seems fitting that art and communication, might have incorporated "language as a developmental phase" to seeing reality, in new ways?

Sort of like being initiated into string theory, to help get past some of the blockages that are stopping science from developing further?

7:56 AM, October 11, 2007

These blockages manifest within the self, and become impediments to our experience and progression to further learning. This is not to say learning stops. It is the "greatest effort" that what has become apparent in the state of self evidential experience, is the potential to great transport human experience beyond the self's own limitations. Provides for, the "intuitive leaps" necessary once the basis of this experience is resolved. How deep this blockages goes, that the subconscious mind will allow images to transport the self to a future place for consideration.

Bee:It might not be an universally applicable source of inspiration?

To Hardy I don't think that mattered one bit. It is just part of the process to understanding how we humans like to fabricate our realities. Yet, there is a universal connection that we have that is a very consistent. One in relation to the artist in us all.

Namagiri, the consort of the lion god Narasimha. Ramanujan believed that he existed to serve as Namagiri´s champion - Hindu Goddess of creativity. In real life Ramanujan told people that Namagiri visited him in his dreams and wrote equations on his tongue.

We are the best predictors of ourselves and our experiential conditions that we put forward. A model perhaps in developmental insight as to what we have to do in science?

So in the psychology......

If any such resolve is not forthcoming in our "supposed awake reality," then there is a culminating effect that someone(archetypal) is speaking to us to help us resolve these disputes. "Our universality" is there in us all. I see no race religion, or gender.

So like Jean above we write our own story, and show the affect our experiential life has on the new conditions if not resolved.

So I apply these things to our current search for understanding the math creation (calculus for Newton)and the derivatives needed to push insight further into "new realms of experience."

Would you denigrate Calculus as a language to helping you discern the nature of reality? Newton knew he had to do something. Einstein realize it when Grossman was developing a new language, as was Reinmann preparing us from his predecessors, on the issue of "non euclidean geometries?" Gauss was very delighted with his student

8:18 AM, October 11, 2007

Understanding that human experience is "cradling the times for breakthroughs to further understanding" is the incubation period necessary for preparing these intuitive leaps and future predictability.

Here 50% or 100% provides for whether the human side of us really understands and knows what is necessary for us to progress. How would the probability of all human experiences to know to draw for one own postulate, "the self evident" and then understand that the leap to growth in experiences requires this and this?

While such is th evastness of the human experience it is not without our understanding that each of us has repercussions of actions to every decision we make. I cannot tell which, only that this probability can be played out time and time again and it will result in the growth of each of us at varying times. There is a constancy that is being talked about here that can be debated, but as far as I can tell this is the postulate that has been written.

To them, I said,
the truth would be literally nothing
but the shadows of the images.

-Plato, The Republic (Book VII)

I used this quote in "your other thread" for a reason. Images? Think about this for a minute.

If one can "translate" and transfer the image mathematically for each other, then what has happened? A level of communication not understood before?

Arthur Miller

Miller has since moved away from conventional history of science, having become interested in visual imagery through reading the German-language papers of Einstein, Heisenberg and Schrödinger - "people who were concerned with visualization and visualizability". Philosophy was an integral part of the German school system in the early 1900s, Miller explains, and German school pupils were thoroughly trained in the philosophy of Immanuel Kant.

When I referred to Susskind I did so for a reason as well. This is the culmination of what mathematically is derived. Thus, the image is a culmination, yet, it is only a "shadow of the truth."

I used Magritte, When is a Pipe a Pipe painting, to illustrate this.

Hawking shows this in his book as well.

You have to remember Plato's analogy was even used by Gerardus t'Hooft. See here and Heisenberg so you are in good company.

P.A.M. Dirac was a gifted mathematical inventor who saw how quantum mechanics rises from classical mechanics, yet transcends it. Dirac did not know of the Bohr atom when he arrived at Cambridge in 1923; yet he quickly began contributing to the mathematical structure demanded by quantum phenomena, discovering the connection between the Poisson bracket and the commutator of Heisenberg”s matrix representation of observables. Then, with careful attention to its classical antecedent, Dirac found the equation governing the evolution of the matrix elements which had eluded Heisenberg in the operator ihdA/dt = [A,H]. He then went on to discover spinors in describing the relativistic electron and antimatter implied by the quantum in relativistic space-time. Dirac conceived the many-time formulation of relativistic quantum mechanics and laid the foundations of the Feynman path integral thereby opening the way to quantum electrodynamics. Newton synthesized the foundations of classical mechanics. In fitting kinship, Dirac, who did the equivalent for quantum mechanics, filled the chair at Cambridge held by Newton.

Some people are better suited to visualization then others, and this comes out in some mathematicians and in artists as I had shown you of Escher and Dali. I could never judge Dali for his character an his life, but I can say how important he tried to push the envelope. Maybe for all his indulges, he thought if he could think of the cross and his geometrically tendency he might have found some relation?

Of course, to Plato this story was just meant to symbolize mankind's struggle to reach enlightenment and understanding through reasoning and open-mindedness. We are all initially prisoners and the tangible world is our cave. Just as some prisoners may escape out into the sun, so may some people amass knowledge and ascend into the light of true reality.

What is equally interesting is the literal interpretation of Plato's tale: The idea that reality could be represented completely as `shadows' on the walls

12:19 PM, October 12, 2007

Sunday, February 25, 2007

The Colour of Gravity

I am not sure how this post is to unfold, yet in my mind different exercises were unfolding as to how I should explain it. Can I come from an artist's perspective I wondered? Say "by chance" anything that seems relevant here in writing, and any relation to science "is" metaphorical by nature?

Yellow, Red, Blue
1925; Oil on canvas, 127x200cm; Centre Georges Pompidou, Paris

These free, wild raptures are not the only form abstraction can take, and in his later, sadder years, Kandinsky became much more severely constrained, all trace of his original inspiration lost in magnificent patternings. Accent in Pink (1926; 101 x 81 cm (39 1/2 x 31 3/4 in)) exists solely as an object in its own right: the ``pink'' and the ``accent'' are purely visual. The only meaning to be found lies in what the experience of the pictures provides, and that demands prolonged contemplation. What some find hard about abstract art is the very demanding, time-consuming labour that is implicitly required. Yet if we do not look long and with an open heart, we shall see nothing but superior wallpaper.
I underlined for emphasis.

Does one want to gleam only what is coming across in geometrical form as a painting without understanding the depth of the artist in expression? Some may say, why any association at all, and just leave science to what it knows best without implicating any theoretical positions with the thought pertaining to gravity here.

Yes that's why I selected the title of this post as thus, and why I am going to give perspective to what I may, "as artist in writing" see with these words, and then you decide whether it is useful to you.

The Field as the Plane

An ancient thought penetrated my thinking as I thought of "the field" that a society can work in agriculture, and yet, by definition it was the plane, "length and width" that was also appealing here. I did not want to loose it's "origination" while I moved any thinking to the "abstract of brane" and the like, without firmly attaching it to the ground.

But who was to know that this plane could be moved to any "fifth dimensional understanding" without having studied the relationship to dimensional thinking and the like. The physics elevated.

I allow this one time escapism to "other thinking" to demonstrate what use the colour of gravity implies while at the same time "theoretical positions" talk about it's place in the universe. If one did not accept the moves in science and the way it expressed itself to allow geometrical inclination, then how the heck could non-euclidean thinking ever make it's way into how we will discuss "the fields" about us?

It meant that a perspective "on height" be adopted? As an observer I was watching from a position. While in that sleeping/dosing state, I wondered how else to express myself as these concepts were amalgamating themselves into a "conceptual frame of reference?"

The picture of the field(I am referring to the ancient interpretation) continued in my mind, and "by abstract" I thought to introduce a line extend from the centre of this field upward. So here I am looking at this field before me. Now I had wondered off previous by bring "the brane" in here, yet is not without that sight I thought how the heck could any idealization so ancient make sense to what the colour of gravity to mean.

Title page of Opticks .... by Sir Isaac Newton, 1642-1727. Fourth edition corrected by the author's own hand, and left before his death with the bookseller. Published in 1730. Library call number QC353 .N48 1730.

So "an idea" came to mind.

While correlating Newton's work here and the "extra dimensional thinking," I also wanted to include the work of the "Alchemist Newton". "To expand" the current thinking of our "emotive states" as a "vital expression of the biological being."

Draw into any further discussion of the "philosophical or other wise," these views of mine which are a necessary part of what was only held to a "religious and uneducated evolutionary aspect of the human being."

A cosmologist may still say that such thoughts of Einstein used in this vain is wrong, but I could never tear myself away from the views of "durations of time."

Colour Space and Colour Theory

The CIE 1931 colour space chromaticity diagram with wavelengths in nanometers. Note that the colors depicted depend on the color space of the device on which you are viewing the image.

So by having defined the "frame of reference," and by introducing "Colour of gravity" I thought it important and consistent with the science to reveal how dynamical any point within that reference can become expressive. The history in association also important.

In the arts and of painting, graphic design, and photography, color theory is a body of practical guidance to color mixing and the visual impact of specific color combinations. Although color theory principles first appear in the writings of Alberti (c.1435) and the notebooks of Leonardo da Vinci (c.1490), a tradition of "colory theory" begins in the 18th century, initially within a partisan controversy around Isaac Newton's theory of color (Opticks, 1704) and the nature of so-called primary colors. From there it developed as an independent artistic tradition with only sporadic or superficial reference to colorimetry and vision science.

So you tend to draw on your reserves for such comparatives while thinking about this. I knew to apply "chemical relations" to this idea, and the consequential evidenced, by the resulting shadings by adding. I wanted to show "this point" moving within this colour space and all the time it's shading was describing the "nature of the gravity."

Adding a certain mapping function between the color model and a certain reference color space results in a definite "footprint" within the reference color space

By adding that vertical line in the field, the perimeter of my field of vision had to some how be drawn to an apex, while all kinds of thoughts about symmetry and perfection arose in my pyramidal mind.

All these colours, infinite in their ability to express the human emotive state, as a consequence of philosophical and expressed as function of the emotive being?

CIE 1976 L*, a*, b* Color Space (CIELAB)

CIE L*a*b* (CIELAB) is the most complete color model used conventionally to describe all the colors visible to the human eye. It was developed for this specific purpose by the International Commission on Illumination (Commission Internationale d'Eclairage, hence its CIE initialism). The * after L, a and b are part of the full name, since they represent L*, a* and b*, derived from L, a and b. CIELAB is an Adams Chromatic Value Space.

The three parameters in the model represent the lightness of the color (L*, L*=0 yields black and L*=100 indicates white), its position between magenta and green (a*, negative values indicate green while positive values indicate magenta) and its position between yellow and blue (b*, negative values indicate blue and positive values indicate yellow).

The Lab color model has been created to serve as a device independent model to be used as a reference. Therefore it is crucial to realize that the visual representations of the full gamut of colors in this model are never accurate. They are there just to help in understanding the concept, but they are inherently inaccurate.

Since the Lab model is a three dimensional model, it can only be represented properly in a three dimensional space.


the quantum entanglement would become so spread out through these interactions with the environment that it would become virtually impossible to detect. For all intents and purposes, the original entanglement between photons would have been erased.

Never the less it is truly amazing that these connections do exist, and that carefully arranged laboratory conditions they can be observed over significant distances. They show us, fundamentally, that space is not what we once thought it was. What about time?
Page 123, The Fabric of the Cosmo, by Brian Greene

So many factors to include here, yet it is with the "idea of science" that I am compelled to see how things can get all mixed up, while I say emotive state, or Colours of gravity?

It gets a little complicated for me here, yet the "Fuzzy logic" introduced or "John Venn's logic" is not without some association here. Or, the psychology I had adopted as I learnt to read of models and methods in psychology that could reveal the thinking we have developed, and what it included.

Least I forget the "real entanglement" issues here, I have painted one more aspect with the "Colour of Gravity" to be included in this dimensional perspective, as we look to the models in science as well?

Working from basic principles and the history of spooky has made this subject tenable in today's world. A scientist may not like all the comparisons I have made based on it, I could never see how the emotive and mental statements of the expressive human being could not have been included in the making of the reality.

That I may of thought the "perfection of the human being" as some quality of the God in us all, would have granted sanction to some developing view of "religious virtuosity," against the goals of the scientist. So as ancient the views painted, there was something that may have been missed of the "Sensorium," and goes toward the basis of the philosophy shared currently by Lee Smolin.

This entanglement to me is a vital addition to our exploration of the universe. Our place and observation within it? It did not mean to discount our inclusion within it, within a larger "oscillatory perspective."

Sunday, January 07, 2007

PLATO:Mathematician or Mystic ?

Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry.--BERTRAND RUSSELL, Study of Mathematics

One should not conclude that such a bloggery as this is not without a heartfelt devotion to learning. That I had made no great claims to what science should be. other then what a layman point of view in learning has become excited about. What may be a natural conclusion to one who has spent a long time in science. Do not think me so wanting to knock on your door to enforce the asking of education that may be sent my way was truly as a student waiting for some teacher to appear.

This did not mean I should not engage the world of science. Not become enamoured with it. Or, that seeing the teachers at their bloggeries, were "as if" that teacher did appear many times. This is what is good about it.

I did not care how young you were, or that I, "too old" to listen to what scientists knew, or were theoretically endowed with in certain model selections.

More from the Heart?

"Let no one destitute of geometry enter my doors."

You know that by the very namesake of Plato used here, that I am indeed interested how Plato thought and his eventual conclusions about what "ideas" mean. So, of course there is this learning that has to take place with mathematics.

If I may, and if I were allowed to fast forward any thought in this regard, it would be to say, that the evolution of the human being is much appreciated in what can transfer very quickly "between minds" while a dialogue takes place. Hence the title of this bloggery.

Science demands clarity, and being deficient in this transference of "pure thought" would be less then ideal speaking amongst those scientists without that mathematics. Yet, I do espouse that such intuitiveness can be gained from the simple experiment, by distilling information, from the "general concepts" which have been mention many times now by scientists.

So it is of interest to me that the roads to mathematical understanding through it's development would be quick to point out this immediate working in the "world of the abstract imaging" is to know that such methods are deduced by it's numbers and their greater meaning.

That such meaning can be assign to a "natural objector function" and still unbeknownst to the thinking and learning individual "a numerical pattern that lies underneath it. A "schematics" if you like, of what can become the form in reality.

No reader of Plato can fail to recognize the important role which mathematics plays in his writing, as would indeed be expected for an author about whom the ancient tradition maintains that he had hung over the entry to his school the words "Let No One Un-versed in Geometry Enter". Presumably it was the level of ability to work with abstract concepts that Plato was interested in primarily, but if the student really had never studied Greek geometric materials there would be many passages in the lectures which would be scarcely intelligible to him. Modern readers, versed in a much higher level of mathematical abstraction which our society can offer, have sometimes felt that Plato's famous "mathematical examples'" were illustrations rather than central to his arguments, and some of Plato's mathematical excursuses have remained obscure to the present time.

A Musical Interlude

Plato's Academy-Academy was a suburb of Athens, named after the hero Academos or Ecademos.

I can't help but say that I am indeed affected by the views of our universe. In a way that encompasses some very intriguing nodal points about our universe in the way that I see it.

While I may not have shown the distinct lines of the Platonic solids, it is within context of a balloon with dye around it, that it could be so expressive of the Chaldni plate, that I couldn't resist that "harmonics flavour" as to how one might see the patterns underneath reality. How some gaussian coordinates interpretation of the "uv" lines, that were distinctive of an image in abstract spaces.