**See**:Colloquim January 30, 2014 - Quantum Mechanics and the Geometry of Spacetime

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Showing posts with label **Maurits Cornelis Escher**. Show all posts

Showing posts with label **Maurits Cornelis Escher**. Show all posts

Inspired on Escher's works. A free vision on how could be his workplace.

I was made aware of This Youtube video by Clifford of Asymptotia. He also linked, Lines and Colors.

A 1929 self-portrait | |||||

Born | June 17, 1898 Leeuwarden, The Netherlands | ||||
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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 |

## Contents |

He was a sickly child, and was placed in a special school at the age of seven and failed the second grade.

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.

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

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.

In 1941, Escher wrote his first paper, now publicly recognized, called

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

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

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."

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

Escher printed

One of his most notable works is the piece

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

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.

*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)

*Gödel, Escher, Bach*by Douglas Hofstadter- echochrome
- Giovanni Battista Piranesi
- Impossible object
- Ravello
- Strange loop

**^***Duden Aussprachewörterbuch*(6 ed.). Mannheim: Bibliographisches Institut & F.A. Brockhaus AG. 2005. ISBN 3-411-04066-1.**^**"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.- ^
^{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. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Escher.html.
- 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.

*M.C. Escher official website*.*Math and the Art of M.C. Escher*, USA: SLU.*Artful Mathematics: The Heritage of M. C. Escher*, USA: AMS.*Escherization problem and its solution*, CA: University of Waterloo.*Escher for Real*, IL: Technion — physical replicas of some of Escher's "impossible" designs.*M.C. Escher: Life and Work*, USA: NGA.*US copy right proctection for UK artists*, UK. Copyright issue regarding Escher from the Artquest Artlaw archive.- Schattschneider, Doris (June/July 2010). "The Mathematical Side of M. C. Escher" (PDF).
*Notices of the American Mathematical Society*(USA)**57**(6): 706–18. Retrieved 2010-07-09.

(Click on Image)

Friedman Equation What is_{p}density.

What are the three models of geometry? k=-1, K=0, k+1

Negative curvature

Omega=the actual density to the critical density

If we triangulate Omega, the universe in which we are in, Omega_{m(mass)}+ Omega(a vacuum), what position geometrically, would our universe hold from the coordinates given? ** **

**See Also**:

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I am not sure if it is proper to take such expressions of dark energy and dark matter as they are perceived in the universe and apply them to a "dynamical movement of a kind," as an expression of that Universe?

Part of that "Toposense" you might say?

*******IN their figure 2. Hyperbolic space, and their comparative relation to the M.C.Escher's Circle Limit woodcut, Klebanov and Maldacena write, " but we have replaced Escher's interlocking fish with cows to remind readers of the physics joke about the spherical cow as an idealization of a real one. In anti-de Sitter/conformal theory correspondence, theorists have really found a hyperbolic cow."

Click on image for larger version. See:Solving quantum field theories via curved spacetimes by Igor R. Klebanov and Juan M. Maldacena

**See**:

Friedman Equation What is

What are the three models of geometry? k=-1, K=0, k+1

Negative curvature

Omega=the actual density to the critical density

If we triangulate Omega, the universe in which we are in, Omega

I am not sure if it is proper to take such expressions of dark energy and dark matter as they are perceived in the universe and apply them to a "dynamical movement of a kind," as an expression of that Universe?

Part of that "Toposense" you might say?

Click on image for larger version. See:Solving quantum field theories via curved spacetimes by Igor R. Klebanov and Juan M. Maldacena

....a higher dimensional version of the Pringle's potato chip. Brian Greene, The Fabric of the Cosmos, pg 483, Para 2, line 29

Again I try remind good scientists that I have nothing to offer other then trying to keep pace with their thinking, and to find myself in world's of abstraction that I really find interesting. Of course, their metaphors too.

You see for me there are interesting correlations of thought that wake me up to the understanding of such abstract thinking, and what purposes it serves. I quote the Pringle Potato Chip to spell out the earlier realization of Maldacena, as well, the idea I have about, the Birth of Approximation. I was trying to tangle with such thoughts in a cosmological sense and here they speak to it in mathematical illustrations.

IN their figure 2. Hyperbolic space, and their comparative relation to the M.C.Escher's Circle Limit woodcut, Klebanov and Maldacena write, " but we have replaced Escher's interlocking fish with cows to remind readers of the physics joke about the spherical cow as an idealization of a real one. In anti-de Sitter/conformal theory correspondence, theorists have really found a hyperbolic cow."

Click on image for larger version. See:Solving quantum field theories via curved spacetimes by Igor R. Klebanov and Juan M. Maldacena

Thank you, too "Just Learning" andDavid Berenstein for the information about the article above.

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