Showing posts with label Coxeter. Show all posts
Showing posts with label Coxeter. Show all posts

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, July 17, 2008

13th Sphere of the GreenGrocer

I suppose you are two fathoms deep in mathematics,
and if you are, then God help you, for so am I,
only with this difference,
I stick fast in the mud at the bottom and there I shall remain.

-Charles Darwin

How nice that one would think that, "like Aristotle" Darwin held to what "nature holds around us," that we say that Darwin is indeed grounded. But, that is a whole lot of water to contend with, while the ascent to land becomes the species that can contend with it's emotive stability, and moves the intellect to the open air. One's evolution is hard to understand in this context, and maybe hard for those to understand the math constructs in dialect that arises from such mud.

For me this journey has a blazon image on my mind. I would not say I am a extremely religious type, yet to see the image of a man who steps outside the boat of the troubled apostles, I think this lesson all to well for me in my continued journey on this earth to become better at what is ancient in it's descriptions, while looking at the schematics of our arrangements.

How far back we trace the idea behind such a problem and Kepler Conjecture is speaking about cannon balls. Tom Hales writes,"Nearly four hundred years ago, Kepler asserted that no packing of congruent spheres can have a density greater than the density of the face-centered cubic packing."

Kissing number problem
In three dimensions the answer is not so clear. It is easy to arrange 12 spheres so that each touches a central sphere, but there is a lot of space left over, and it is not obvious that there is no way to pack in a 13th sphere. (In fact, there is so much extra space that any two of the 12 outer spheres can exchange places through a continuous movement without any of the outer spheres losing contact with the center one.) This was the subject of a famous disagreement between mathematicians Isaac Newton and David Gregory. Newton thought that the limit was 12, and Gregory that a 13th could fit. The question was not resolved until 1874; Newton was correct.[1] In four dimensions, it was known for some time that the answer is either 24 or 25. It is easy to produce a packing of 24 spheres around a central sphere (one can place the spheres at the vertices of a suitably scaled 24-cell centered at the origin). As in the three-dimensional case, there is a lot of space left over—even more, in fact, than for n = 3—so the situation was even less clear. Finally, in 2003, Oleg Musin proved the kissing number for n = 4 to be 24, using a subtle trick.[2]

The kissing number in n dimensions is unknown for n > 4, except for n = 8 (240), and n = 24 (196,560).[3][4] The results in these dimensions stem from the existence of highly symmetrical lattices: the E8 lattice and the Leech lattice. In fact, the only way to arrange spheres in these dimensions with the above kissing numbers is to center them at the minimal vectors in these lattices. There is no space whatsoever for any additional balls.

So what is the glue that binds all these spheres in in the complexities that they are arrange in the dimensions and all that we shall have describe gravity along with the very nature of the particle that describe the reality and makeup that we have been dissecting with the collision process?

As with good teachers, and "exceptional ideas" they are those who gather, as if an Einstein crosses the room, and for those well equipped, we like to know what this energy is. What is it that describes the nature of such arrangements, that we look to what energy and mass has to say about it's very makeup and relations. A crystal in it's molecular arrangement?

Look's like grapefruit to me, and not oranges?:)

Symmetry's physical dimension by Stephen Maxfield

Each orange (sphere) in the first layer of such a stack is surrounded by six others to form a hexagonal, honeycomb lattice, while the second layer is built by placing the spheres above the “hollows” in the first layer. The third layer can be placed either directly above the first (producing a hexagonal close-packed lattice structure) or offset by one hollow (producing a face-centred cubic lattice). In both cases, 74% of the total volume of the stack is filled — and Hales showed that this density cannot be bettered.....

In the optimal packing arrangement, each sphere is touched by 12 others positioned around it. Newton suspected that this “kissing number” of 12 is the maximum possible in 3D, yet it was not until 1874 that mathematicians proved him right. This is because such a proof must take into account all possible arrangements of spheres, not just regular ones, and for centuries people thought that the extra space or “slop” in the 3D arrangement might allow a 13th sphere to be squeezed in. For similar reasons, Hales’ proof of greengrocers’ everyday experience is so complex that even now the referees are only 99% sure that it is correct....

Each sphere in the E8 lattice is surrounded by 240 others in a tight, slop-free arrangement — solving both the optimal-packing and kissing-number problems in 8D. Moreover, the centres of the spheres mark the vertices of an 8D solid called the E8 or “Gosset” polytope, which is named after the British mathematician Thorold Gosset who discovered it in 1900.

Coxeter–Dynkin diagram

The following article is indeed abstract to me in it's visualizations, just as the kaleidescope is. The expression of anyone of those spheres(an idea is related) in how information is distributed and aligned. At some point in the generation of this new idea we have succeeded in in a desired result, and some would have "this element of nature" explained as some result in the LHC?

A while ago I related Mendeleev's table of elements, as an association, and thought what better way to describe this new theory by implementing "new elements" never seen before, to an acceptance of the new 22 new particles to be described in a new process? There is an "inherent curve" that arises out of Riemann's primes, that might look like a "fingerprint" to some. Shall we relate "the sieves" to such spaces?

At some point, "this information" becomes an example of a "higher form "realized by it's very constituents and acceptance, "as a result."

Math Will Rock Your World by Neal Goldman

By the time you're reading these words, this very article will exist as a line in Goldman's polytope. And that raises a fundamental question: If long articles full of twists and turns can be reduced to a mathematical essence, what's next? Our businesses -- and, yes, ourselves.

Friday, April 06, 2007

Craftsman of Plato

Time is of your own making;
its clock ticks in your head.
The moment you stop thought
time too stops dead.
Angelus Silesius
See Status of Warp Drive Smolin had some deep questions and relevance "about" time? :)

Some "updates" within this article. Mainly for all those "couch potatoes" who watch Law and Order. I remembered Sean Carroll's portrayal as well on Preposterous Universe when Clifford showed the picture from "the lecture" Clifford is showing today.

Dark Matter and Dark Energy: from the Universe to the Laboratory-Conclusion

See comment here

Good show

Are Cosmologists Couch Potatoes?

Your asking for simplicity and without a geometrical/topological approach(quantum gravity), the cosmos from surveillance and interrogation, and without further introspection, it leaves one with a nice comfortable view, as is.

That's nice, for those who want to sit back and watch the show:)

That fellow, does he have his binoculars backwards!Hmmmmm:)How would this lensing affect his view of the stake out? So close, yet so far away?
plato | Homepage | Mon, February 21, 2005 @ 3:22 pm | #

Maybe Clifford is a Seer? Or, is he a Craftsman who became a seer, like Lee Smolin? Well, we'd have to delve into the reason a seer "became" or could possibly "become?"

The Craftsman

BEHOLDING beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities, for he has hold not of an image but of a reality, and bringing forth and nourishing true virtue to become the friend of God and be immortal, if mortal man may. Would that be an ignoble life? PLATO

If one had given their whole life to rote and memorization, how much smarter would they be, if they did not allow themselves to be "filled?" It is as if the universe said "look at the emptiness. This cannot be so?" It was at that moment the mind fills with all these "wonderful things" as if all that had taken place was ignited into a new view of the world. It is literally not the same world for them?

Tabula rasa (Latin: scraped tablet or clean slate) refers to the epistemological thesis that individual human beings are born with no innate or built-in mental content, in a word, "blank", and that their entire resource of knowledge is built up gradually from their experiences and sensory perceptions of the outside world. See Tabula rasa: The Glass Room

Predictions? Every tone spoken as if this new change took place, realized, that having enter a part of reality that was somehow away from, yet, existed in the reality until discovered. Coxeter shared these same views? So, every kind of geometry you know of, already exists, and is just waiting to be discovered. You had to be able to tap into the probabilities. You were always preparing the stage.


Genesis Timaeus 27c-34a

First then, in my judgment, we must make a distinction and ask, What is that which always is and has no becoming; and what is that which is always becoming and never is? That which is apprehended by intelligence and reason is always in the same state; but that which is conceived by opinion with the help of sensation and without reason, is always in a process of becoming and perishing and never really is. Now everything that becomes or is created must of necessity be created by some cause, for without a cause nothing can be created.
See Timaeus:Laying the Ground rules on Genesis

The Mechanism

See "The Cosmological Constant and the String Landscape by Joe Polchinski (UCSB, KITP)"

So one has to take into account the perspective being developed by others before we get to where we have some kind of mechanism of tunnelling the landscape? Is it right or not, to have a "potential hill" have evidence of some kind, having been traverse? You would then think, hmmm... the blackhole as a horizon?

Three Ring Circus: Dark Energy

"Of course this information is based on 2003 data but the jest of the idea here is that in order to go to a "fast forward" the conditions had to exist previously that did not included "sterile neutrinos" and were a result of this "cross over."

What reason did Lee Smolin called the string theorists craftsman? I think part of the fun for me is when somebody who sits out front in terms of being a science director of a kind, then one is immediately thinking "okay, why did he say this."

See The Entropic Principle by Raphael Bousso (UC Berkeley)

Now, why did he say that? Yes, it would be easier to go to him and get the reason right from the person's mouth. But hey their busy, and I do not want to be on the list of those knocking on doors being pesky. Besides, that's part of the fun of doing the detective work and trying to understand the basis of any argument they may have.

The Demiurge (Creator)

Literally, “craftsman.” The creator of Plato’s physical world is not a divine intelligence or a personal ruler, but (as it were) a manual laborer. Cf. Vlastos, Plato’s Universe (pp. 26-27):

That the supreme god of Plato’s cosmos should wear the mask of a manual worker is a triumph of the philosophical imagination over ingrained social prejudice. ... But this divine mechanic is not a drudge. He is an artist or, more precisely, what an artist would have to be in Plato’s conception of art: not the inventor of new form, but the imposer of pre-existing form on as yet formless material.

The Seer

So we now know to a degree how Lee Smolin assigned the Craftsman, but little is said about the Seer? The Seer, is one who knows how to use that blank slate. Knows how to find the departure point and is asking to be filled?

If there are any runners out there, you might know the "depletion point" one can reach after having expended the energy, one gains a sense of this new influx of energy and well being? Having once know these times in my youth, I am sad to say, I am to old to be ever running like I did.

So one sees the community is suffering and leaders in despair as to how new ideas can be generated and new ways to invigorate science come to the forefront. Is the privileged few who see themself pertaining to some model, that one would now say, hey they are getting all the incentives and the idea here about nurture is suffering?

No, there must be special way to invigorate the scientists of the future? Allow them to empty themselves after the intense involvement, to allow the mind, when empty to be filled?

(Thanks Bee for asking the question By the way, "Happy Easter" to you and Stefan)

Friday, March 23, 2007

Solidification of Geometrical Presence

While I might infer the "attributes of Coxeter here," it is with the understanding such a dimensional perspective which has it's counterpart in the result of what manifests as matter creations. Yet we have taken our views down to the "powers of ten" to think of what could manifest even before we see the result in nature.

When you go to the site by PBS of where, Nano: Art Meets Science, make sure you click on the lesson plan to the right.


Visitors' shadows manipulate and reshape projected images of "Buckyballs." "Buckyball," or a buckminsterfullerene molecule, is a closed cage-structure molecule with a carbon network. "Buckyball" was named for R. Buckminster "Bucky" Fuller (1895-1983), a scientist, philosopher and inventor, best known for creating the geodesic dome.
Photo Credit: © 2003 Museum Associates/Los Angeles County Museum
Fundamentally the properties of materials can be changed by nanotechnology. We can arrange molecules in a way that they do not normally occur in nature. The material strength, electronic and optical properties of materials can all be altered using nanotechnology.

See Related information on bucky balls here in this site. This should give some understanding of how I see the greater depth of what manifest in nature, as solids in our world, has some "other" possibilities in dimensional attribute, while it is given association to the mathematical prowess of E8.

I do not know of many who will take in all that I have accumulated in regards to how one may look at their planet, can have the depth of perception that is held in to E8.?

One may say what becomes of the world as it manifest into it's constituent parts, has this energy relation, that it would become all that is in the design of the world around us.

While some scientists puzzle as to the nature of the process of E8, little did they realize that if you move your perception to the way E8 is mapped to 248 dimensions, the image while indeed quite pleasing, you see as a result.

It can include so much information, how would you know that this object of mathematics, is a polytrope of a kind that is given to the picture of science in the geometrical structure of the bucky ball or fullerene.


Diamond and graphite are two allotropes of carbon: pure forms of the same element that differ in structure.
Allotropy (Gr. allos, other, and tropos, manner) is a behaviour exhibited by certain chemical elements: these elements can exist in two or more different forms, known as allotropes of that element. In each different allotrope, the element's atoms are bonded together in a different manner.

For example, the element carbon has two common allotropes: diamond, where the carbon atoms are bonded together in a tetrahedral lattice arrangement, and graphite, where the carbon atoms are bonded together in sheets of a hexagonal lattice.

Note that allotropy refers only to different forms of an element within the same phase or state of matter (i.e. different solid, liquid or gas forms) - the changes of state between solid, liquid and gas in themselves are not considered allotropy. For some elements, allotropes can persist in different phases - for example, the two allotropes of oxygen (dioxygen and ozone), can both exist in the solid, liquid and gaseous states. Conversely, some elements do not maintain distinct allotropes in different phases: for example phosphorus has numerous solid allotropes, which all revert to the same P4 form when melted to the liquid state.

The term "allotrope" was coined by the famous chemist Jöns Jakob Berzelius.

Saturday, September 23, 2006

Hydrogen, and the Law of Octaves

Alex Vilenkin - Many Worlds in One article by Mark of Cosmic Variance drew my interest again after reading with a new perspective gained from understandng some implications about the "anthropic principle."

Sometimes I even still hold to the idea it is better not to touch this topic because of the greeness with which insight has now taken over. This greeness resides against the reason with which such logic is necessary in regards ot the debate between Susskind and Smolin.

I do not want to be blinded by the razzle dazzle either of men leading this debate, so as to the layman's pursuite of understanding, I hope to show what I am seeing?

While I have not read the book either I am still "drawn to the debate" about what the "anthropic reasoning" is talking about at a fundamental level? Scared yes, and on wobbly legs so I continue.

So as a layman I am curious too ,about views here and what the basis could lead too, in terms of what our universe had become?

If "carbon" wasn't present at the beginning, then how would you explain our universe?

Because the triple-alpha process is unlikely, it requires a long period of time to produce carbon. One consequence of this is that no carbon was produced in the Big Bang because within minutes after the Big Bang, the temperature fell below that necessary for nuclear fusion.

Ordinarily, the probability of the triple alpha process would be extremely small. However, the beryllium-8 ground state has almost exactly the energy of two alpha particles. In the second step, 8Be + 4He has almost exactly the energy of an excited state of 12C. These resonances greatly increase the probability that an incoming alpha particle will combine with beryllium-8 to form carbon. The existence of this resonance was predicted by Fred Hoyle before its actual observation based on its necessity for carbon to be formed.

I too hate the idea of the "law of crackpostism," yet research back to mendeleev table in regards to Newland, raised interesting ideas about the future of testbility?

A "harmonical disseration" about the ways we will in the fuure be able to map the elements in "photonic imagery" devised to work within carbon processes?

What were the ground rules for this universe?

He is best known for discovering the element plutonium, with Edwin McMillan. He led the team that devised the chemical process for extraction of plutonium.

Seaborg served as chairman of the Atomic Energy Commission from 1961 until 1971.

He and McMillan shared the 1951 Nobel Prize in Chemistry for research into transuranic elements.

Having a framework here in which to establish the elemental nature of our universe, how is it that such principals inherent in "string theory" should not direct our attention to what is a viable indicator of what will fill the spaces between, as Mendeleev was able to do in prediction?

While one has been introduce to the "allotopes of Coxeter," it is not without some thought that "planck length," along with the understanding of what "geometrical inhernetness?" qunatum geometry, would also spew forth from the very basis of the beginning of that big bang?

So while I have shown the allotrope here, and dimensional perspective developed, what degrees of freedom say that the space would allow all constants of nature to be described here, and allowed such geometrical principals to form in the bucky ball of carbon, carbon nanotubes?

It was not wihtout directing our attention to the immediacy of that big bang in the microsecond of "planck time" that we are at a loss then?

The last major changes to the periodic table was done in the middle of the 20th Century. Glenn Seaborg is given the credit for it. Starting with his discovery of plutonium in 1940, he discovered all the transuranic elements from 94 to 102. He reconfigured the periodic table by placing the actinide series below the lanthanide series. In 1951, Seaborg was awarded the Noble prize in chemistry for his work. Element 106 has been named seaborgium (Sg) in his honor.


  • CNO and the Law of Octaves

  • Allotropes and the Ray of Creation
  • Tuesday, September 12, 2006

    Coxeter and Plato's Cave

    IN Beyond the Dance of the Sun I give an image of Plato's Cave for consideration, about dimensinal perspectve.

    This is not only held in my mind in terms of what free people are chained in their perspectives, but I also feel, that the leading characteristics were kindly put forward not only by my own position, but by those who I have listed throughout this blog.

    Bolya, Heisenberg and Hooft?

    There are "no wares" here to market(no advertising) other then what perception has granted me by "learning" and assuming the inherent nature of the leading perspectves in geometries and their relation to the real world.

    Visitors' shadows manipulate and reshape projected images of "Buckyballs." "Buckyball," or a buckminsterfullerene molecule, is a closed cage-structure molecule with a carbon network. "Buckyball" was named for R. Buckminster "Bucky" Fuller (1895-1983), a scientist, philosopher and inventor, best known for creating the geodesic dome.

    Imagine then, that such nanotechnology sites have taken us down to microperspectives and there are such things in the "geometry of being" that would dictate the technolgies that we use?

    Was it so distant from the real world that such "projective geometries" exposed the correlation of knowledge from a man like Coxeter, that you would say "I would rather demomnstrate the technological aspect because this is real?"

    You know you had to be more suttle then this. You knew you had to think of the sun's ray and "think" beyond in the Sun/Earth Relation in a lagrangian perspective. But you refuse?

    It is better then, that the cynics remain chained. And allow themselves to spread their venom about the callousness of "good people who had ventured forth" and asked about dimensional perspective. Who is it, that remains in the box?

    Focus then, on the science and what has been accomplished. You need no further explanation. No "back reaction" to what constituted this science.

    HOUSTON, Texas, Oct. 31 -- Nobel laureate Richard Smalley, co-discoverer of the buckyball and widely considered to be one of the fathers of nanotechnology, died Friday at the age of 62 after a long battle with cancer.
    Rice University professor Smalley shared the 1996 Nobel Prize in chemistry with fellow Rice chemist Robert Curl and British chemist Sir Harold Kroto for the 1985 discovery of a new form of carbon nicknamed buckyballs. Shaped like soccerballs and no wider than a strand of DNA, buckyballs each contain 60 carbon atoms arranged in a hollow sphere resembling two conjoined geodesic domes. Smalley coined the name "buckminsterfullerene" for the discovery in honor of architect and geodesic dome inventor Buckminster Fuller.

    Fullerenes -- the family of compounds that includes buckyballs and carbon nanotubes -- remained the central focus of Smalley's research until his death. According to colleagues, Smalley's belief that nanotubes were a wonder material that could solve some of humanity's problems -- such as clean energy, clean water and economical space travel -- led him to crusade for more public support for science and to help found a business, Carbon Nanotechnologies Inc., in 2000 to make sure his discoveries made it to the marketplace where they could benefit society. Smalley was convinced that nanotubes could only be used to solve society's problems if they were manufactured in bulk and processed economically.

    The socialogical foundation of thinking about our world here then is a far cry from the very foundationof the geometries and how human being may envision. How they may descend into mind. Thre posisbilties are endless,a nd I would just point to the images of flowers and the kalidescope they cause, as they reveal strange nodes and anti-nodes brought forth in mandalic pattern interpretations.

    What symmetry is this, that we can create such patterns and see how beautiful they are? Some like Clifford like th easymmetry of certain flowers?

    Again such liminocentric structure are a inhernet part of our consciousness developement and following this process, into reality is a very important step. Some will only like the pictures and some will venture deeper. That's always be the way of it.

    How would I know this?:)

    Monday, September 11, 2006

    Donald Coxeter: The Man Who Saved Geometry

    "I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Harold Scott Macdonald (H. S. M.) Coxeter

    Some would stop those from continuing on, and sharing the world behind the advancements in geometry. I am very glad that I can move from the Salvador Dali image of the crucifixtion, to know, that minds engaged in the "pursuites of ideas" as they may "descend from heaven," may see in a man like Donald Coxeter, the way and means to have ideas enter his mind and explode in sociological functions? Hmmmm. what does that mean?

    Geometry is a branch of mathematics that deals with points, lines, angles, surfaces and solids. One of Coxeter’s major contributions to geometry was in the area of dimensional analogy, the process of stretching geometrical shapes into higher dimensions. He is also famous for “Coxeter groups,” the inversive distance between two disjoint circles (or spheres).

    It is not often we see where our views are shared with other people?

    I was doing some reading over at Lubos Motl's blog besides just getting the link for Michio Kaku article, I noticed this one too.

    You might think the loss of geometry | like the loss of, say, Latin would pass virtually unnoticed. This is the thing about geometry: we no more notice it than we notice the curve of the earth. To most people, geometry is a grade school memory of fumbling with protractors and memorizing the Pythagorean theorem. Yet geometry is everywhere. Coxeter sees it in honeycombs, sun°owers, froth and sponges. It's in the molecules of our food (the spearmint molecule is the exact geometric reaction of the caraway molecule), and in the computer-designed curves of a Mercedes-Benz. Its loss would be immeasurable, especially to the cognoscenti at the Budapest conference, who forfeit the summer sun for the somnolent glow of an overhead projector. They credit Coxeter with rescuing an art form as important as poetry or opera. Without Coxeter's geometry | as without Mozart's symphonies or Shakespeare's plays | our culture, our understanding of the universe,would be incomplete.

    Now you know what fascination I have with the geometries, as they have moved us towards the comprehension of GR and Reimann? Could Einstein have ever succeeded without him?

    Michael Atiyah:
    At this point in the development, although geometry provided a common framework for all the forces, there was still no way to complete the unification by combining quantum theory and general relativity. Since quantum theory deals with the very small and general relativity with the very large, many physicists feel that, for all practical purposes, there is no need to attempt such an ultimate unification. Others however disagree, arguing that physicists should never give up on this ultimate search, and for these the hunt for this final unification is the ‘holy grail’.

    Without stealing the limelight from Donald, I wanted to put the thinking of Michael Atiyah along side of him too. So you understand that those who speak about the "physics" have things underlying this process which help hold them to the very fabric of thinking.

    Some do not know of "this geometric process" I speak, where such manifestation arise from the very essence of the thinking soul. If you began to learn about yourself you would know that such abstractions are much closer to the "pure thought" then any would have realized.

    Some meditate to get to this essence. Some know, that in having gone through a journey of discovery that they will find the very patterns sealed within each of the souls.

    How does it arise? You had to follow this journey through the "muddle maze" of the dreaming mind to know that patterns in you can direct the vision of things according to what you yourself already do inherently.

    Now some of you "know," don't you, with regards to what I am saying? I spoke often of "Liminocetric structures" just to help you along, and help you realize that the sociological standing of exchange houses many forms of thinking that we had gained previously. Why as a soul of the "thinking mind" should you loose this part of yourself?

    So you begin with the "Platonic Forms" and look for the soccer ball/football? THis process resides at many levels and Dirac was very instrumental in speaking about the basis of the geometer and his vision of things. Along side of course the algebraic way.

    (Picture credit: AIP Emilio Sergè Visual Archives)

    This is very real, and not so abstract that you may have departed form the real world to say, you have lost touch? Do you think only "in a square box" and cannot percieve anything beyond the "condensive thoughts and model apprehensions" which hold you to your own design?

    Maybe? :)

    But the world is vast in terms of discovery, that the question of mathematics again draws us back too, was "Mathematics invented or discovered?" So "this premise" as a question formed and with it "the roads" that lead to inquiry?

    Al these forms of geometrics leading to question about "Quantum geometry" and how would such a cosmological world reveal to the thinkingmind "the microscopic" as part of the dynamical world of our everyday living?

    Only a cynic casts the diversions and illusions to what is real. Because they cannot inherently deal with the "strange language of geometrics" that issues forth in model apprehensions. This is the basis from which Einstein solved the problems of his day.

    But the question is what geometrics could ever reside at such a microscopic level?