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.

Contents

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.

Works

 
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.

Legacy

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.

References

  • 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.

External links


Monday, January 03, 2011

Concepts Fade to Moments

Relativity, by M. C. Escher. Lithograph, 1953.


Of course I struggle "with" as to be free and in liberation of, as if to liberate oneself from all the constraints that we have applied to our circumstance, "by choice." Can this be done? Can a human being actually float and defy gravity? I mean, how ridiculous?:) No....not one of those meditating bouncing beans either.


So it is ever the exercise in my mind to clarify and to seek an understanding of something given that holds great meaning, and may help me to understand an experience that will not let go..
  
Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi.


I was given an image in mind a long time ago that has stayed close to me even while I concertize myself to the very explanations that science has to offer as a basis of fact. That if one could in a sense "experience an opposing force of another body,"  that "through playing" one can come into what I had learn about the sensing of, as to blend with opposition. So as to move accordingly, while knowing that it could reach an extreme, I could in turn, turn it back on itself.

A body's mass also determines the degree to which it generates or is affected by a gravitational field. If a first body of mass m1 is placed at a distance r from a second body of mass m2, each body experiences an attractive force F whose magnitude is
 F = G\,\frac{m_1 m_2}{r^2} \, ,
where G is the universal constant of gravitation, equal to 6.67×10−11 kg−1 m3 s−2. This is sometimes referred to as gravitational mass (when a distinction is necessary, M is used to denote the active gravitational mass and m the passive gravitational mass). Repeated experiments since the 17th century have demonstrated that inertial and gravitational mass are equivalent; this is entailed in the equivalence principle of general relativity.


If you have ever expressed this physically, as in some Martial Art Form,  some competitive edge in reaction, then it will have been grokked at it's fullest, because you have blended the concept, with movement. It's as if structurally you are given lines to follow, but now have to extend those lines into actually movements,  from the mind, into the physical body.

View of inner parts of earth. # continental crust # oceanic crust # upper mantle # lower mantle # outer core # inner core * A : Mohorovičić discontinuity * B : Core-mantle boundary (Gutenberg discontinuity) * C : Lehmann discontinuity * Author : KronicTOOL * Software : Photoshop (Click on Image for larger viewing)


Now one would have to assume there is some mathematical basis to this exchange, yet I would rather focus on the exchange, as to define this in our life as something "sensual in movement and form." Is it perfectly systematical and symmetrical "that one side had to equal the other," in order for me to explain something about life as an expressive attitude about our dealings in society? How "justice might work" as a balancing scale? A balancing scale, about life and it's truths

Weight at Earth's Core

Would your body weigh more or less if standing on the Earth's core? What about above sea level?

As you go further inside the Earth, the force you feel due to gravity lessens, assuming the Earth is has a uniform density all the way throughout. Less force means you weigh less.

The reason is that the mass attracting you is inside a sphere, and is given by M = (4/3) * pi * (radius)3 * density

The force you feel is given by F = G * M * (your mass) / (radius)2

This means the net force is F = G * (4/3) * pi * radius * density * (your mass)

(pi=3.14159 and G = Newton's gravitational constant)

So as you go further inside the Earth, the radius is decreasing, so the force you feel is decreasing. The mass above you oddly enough doesn't contribute at all to any net force on your body.

In reality, of course, the Earth is not of uniform density, and there is a slight increase in force as you go down from the surface, before it begins to decrease again. Still, you weigh less standing on the Earth's core.

As far as what happens above sea level - you must realize that what happens outside the Earth is different from what happens inside the Earth. Inside, as you go deeper and deeper, the mass attracting you is less and less (as stated). Above sea level (the surface of the Earth, specifically) as you go further and further away, the mass remains constant (obviously), but the distance gets larger and larger, which makes the force (given by F = G * M(Earth) * M(you) / r2) smaller.

Notice that the formula that applies inside the Earth is different from the one that applies outside.

Dr. Louis Barbier
(October 2003)

So there is this ancient notion about gravity being the same at all places on the earth, that slighting the idea of such minute differences, one would have to say "that it is not the same" and hence has left oneself "back in time" before it could be understood that  the earth can be looked at in another way? That the length and distance to it's outer edge, as some inverse square law can be explained "of all things." Systemically explaining away,  by understanding that gravity "is the same according to the weight of" is not the same in all places.

Truth, is that slight difference?

So how does one break free inside, between the understanding of Feather and Iron, versus Feather and Heart?

Structurally, building any foundation there are exactitude's toward defining that space according to  dimensional attributes as to straight lines and angles of perception. If you actualize this in physical form, you may have constructed a building. There are rules according to Pythagorean theorem that allows you build square things.

The emergence of,  follows distinctive rules according to expression, artistically inclined, and for me, any point in space has such abilities. How structurally sound, any expressive display that for realities sake and purpose, we see where such expressions can arrive out of nothing? It was not logical and did not make sense to me that such expression can appear  out of nothing, to become something. So there is a bias here for me about what is being revealed in that point, as well as, of what is being revealed in that moment.


I am of course interested in the creative process of a scientist. I am trying to be as responsible as I can about our comparison of the Heart and Truth(Feather) on the same scale as to be lead by example so as to define this concept better as,  "If the heart was free from the impurities of sin," not as some religious perspective about good and evil, but about the slight differences in the changes in the gravity of earth, and about the object that occupies that space, as well as,  the inherent nature of that truth.


Composition of Earth's mantle in weight percent[16][citation needed]
Element Amount Compound Amount
O 44.8
Si 21.5 SiO2 46
Mg 22.8 MgO 37.8
Fe 5.8 FeO 7.5
Al 2.2 Al2O3 4.2
Ca 2.3 CaO 3.2
Na 0.3 Na2O 0.4
K 0.03 K2O 0.04
Sum 99.7 Sum 99.1



If I should point toward elemental considerations, each to its own,  then,  as some expression of some inverse square law toward that outer rim of physicality of earth's domain, then  it is with this insight that I look toward  the "weight" of the concept with which "entrance to freedoms of eternal life" are nothing more then the recognition of "what weighs" according to those truths and what we adopt in our own lives according to the choices we make. If I say Heart, then it is wise that such entrances into the human being, is but a mental thing about how we weight things according to our set of criteria according Truth?

Cross section of the whole Earth, showing the complexity of paths of earthquake waves. The paths curve because the different rock types found at different depths change the speed at which the waves travel. Solid lines marked P are compressional waves; dashed lines marked S are shear waves. S waves do not travel through the core but may be converted to compressional waves (marked K) on entering the core (PKP, SKS). Waves may be reflected at the surface (PP, PPP, SS).

Seismographs detect the various types of waves. Analysis of such records reveals structures within the Earth.

Monday, December 27, 2010

Measure and Half Measures

Pythagoras, the man in the center with the book, teaching music, in The School of Athens by Raphael
Most of  you will recognize the partial image of the much larger I have used as the heading of this blog.


The Greek Pythagoras, for instance, was able to use abstract but simple mathematics to describe a natural phenomenon very precisely. He discovered the fractions that govern the harmonious musical notes. For example, a stretched string on a violin that produces a C note when you strike it, will give a C an octave higher when you divide its length by two. (Similarly, when we cut of a quarter of the length of the original string, the new string will sound like an E note) This is a famous early example of the use of mathematics to describe a physical phenomenon accurately. Pythagoras used the mathematics of fractions to describe the frequency of musical notes. In the ages that followed, of Galilei, Kepler, Newton and Einstein, mathematics became the prime language to depict nature. The mathematics of numbers, sets, functions, surfaces et cetera turned out to be the most useful tool for those people that felt the urge to understand the laws governing nature. See: Beyond String Theory-Introduction-Natural Language

However esoteric the following may seem to you, I was always enchanted with the idea of sound  as a manifestation of the world we live in, or, as color,  as a meaningful expression of the nature of the world we live in. Not really the artist of sound and color, but much more the artist in conceptual makings of the relation of the world with such ideas, hence, the idea of "Color of gravity."

Hence my interest in gravity, and what we as human beings can gather around our selves, in the ever quest for understanding the consequences of our causal relations to the events that follow us in the making of the reality we live.

The future consequences of probabilistic outcomes according to those positions adopted....can we say indeed that we are predictors of our futures and that at some level this predictability is a far reaching effect of understanding our choices and positions in life? We know this deep down within ourselves, "so as we think" we may become some "ball bouncing on the ocean of life?" Emotive consequences, without recourse to our choosing to excel from the primitive natures of our being in the moment?



Major scale

In music theory, the major scale or Ionian scale is one of the diatonic scales. It is made up of seven distinct notes, plus an eighth which duplicates the first an octavesolfege these notes correspond to the syllables "Do, Re, Mi, Fa, Sol, La, Ti/Si, (Do)", the "Do" in the parenthesis at the end being the octave of the root. The simplest major scale to write or play on the piano is C major, the only major scale not to require sharps or flats, using only the white keys on the piano keyboard:

Could we every conceive of the human being as being one full Octave? I thought so as I read, and such comparisons however esoterically contrived by association I found examples to such "predictable outcomes" as ever wanting to be "divined by principle by such choices we can make."  However unassociated these connections may seem.

I mean,  if one was a student of esoteric traditions and philosophies, it might have been "as traveling through a span and phase of one's life time"  leads us to the issues where we sit,  where we are at,  in the presences of the sciences today. We demanded accountability of ourselves in  that presence within the world as to being responsible and true to ourselves on this quest for understanding.

So if I had ever given the comment as to some iconic symbol as the Seal of Solomon, not just on the context of any secular religion as ownership, it is with the idea that representation could have enshrine the relationship between what exists as a "trinity of the above"  with that of "the below,"  when we are centered as to choice being the position with that of the heart.

See also:New Synesthete Character on Heroes


It was with this understanding that the full Octave could be entranced as too, resonances in the human being, that we could be raised and raise ourselves from such a position, so as to be freed from our emotive and ancient predicaments arising from evolutionary states of beings of the past.




***



Monochord is a one-stringed instrument with movable bridges, used for measuring intervals. The first monochord is attributed to Pythagoras. 

The story is told that Pythagoras wished to invent an instrument to help the ear measure sounds the same way as a ruler or compass helps the eye to measure space or a scale to measure weights. As he was thinking these thoughts, he passed by a blacksmith's shop. By a happy chance, he heard the iron hammers striking the anvil. The sounds he heard were all consonant to each other, in all combinations but one. He heard three concords, the diaspason (octave), the diapente (fifth), and the diatessaron (fourth). But between the diatessaron (fourth) and the diapente (fifth), he found a discord (second). This interval he found useful to make up the diapason (octave). Believing this happy discovery came to him from God, he hastened into the shop and, by experimenting a bit, found that the difference in sounds were determined by the weight of the hammers and not the force of the blows. He then took the weight of the hammers and went straight home. When he arrived home, he tied strings from the beams of his room. After that, he proceeded to hang weights from the strings equal to the weights he found in the smithy's shop. Setting the strings into vibration, he discovered the intervals of the octave, fifth and fourth. He then transferred that idea into an instrument with pegs, a string and bridges. The monochord was the very instrument he had dreamed of inventing.
See: String Instruments including Oud, Folk Fiddle, and Monochord, dan bau, from Carousel Publications Ltd

***
So what is the theory, then?
Pythagoras could be called the first known string theorist. Pythagoras, an excellent lyre player, figured out the first known string physics -- the harmonic relationship. Pythagoras realized that vibrating Lyre strings of equal tensions but different lengths would produce harmonious notesratio of the lengths of the two strings were a whole number. (i.e. middle C and high C) if the

   Pythagoras discovered this by looking and listening. Today that information is more precisely encoded into mathematics, namely the wave equation for a string with a tension T and a mass per unit length m. If the string is described in coordinates as in the drawing below, where x is the distance along the string and y is the height of the string, as the string oscillates in time t, 


See: Official String Theory Web Site

Monday, December 20, 2010

Feather and Iron?

Weight and amount

Anubis weighing the heart of Hunefer, 1285 BC
 
Weight, by definition, is a measure of the force which must be applied to support an object (i.e. hold it at rest) in a gravitational field. The Earth’s gravitational field causes items near the Earth to have weight. Typically, gravitational fields change only slightly over short distances, and the Earth’s field is nearly uniform at all locations on the Earth’s surface; therefore, an object’s weight changes only slightly when it is moved from one location to another, and these small changes went unnoticed through much of history. This may have given early humans the impression that weight is an unchanging, fundamental property of objects in the material world.

In the Egyptian religious illustration to the above, Anubis is using a balance scale to weigh the heart of Hunefer. A balance scale balances the force of one object’s weight against the force of another object’s weight. The two sides of a balance scale are close enough that the objects experience similar gravitational fields. Hence, if they have similar masses then their weights will also be similar. The scale, by comparing weights, also compares masses. The balance scale is one of the oldest known devices for measuring mass.

The concept of amount is very old and predates recorded history, so any description of the early development of this concept is speculative in nature. However, one might reasonably assume[citation needed] that humans, at some early era, realized that the weight of a collection of similar objects was directly proportional to the number of objects in the collection:
w_n \propto n,
where w is the weight of the collection of similar objects and n is the number of objects in the collection. Proportionality, by definition, implies that two values have a constant ratio:
\frac{w_n}{n} = \frac{w_m}{m}, or equivalently \frac{w_n}{w_m} = \frac{n}{m}.
Consequently, historical weight standards were often defined in terms of amounts. The Romans, for example, used the carob seed (carat or siliqua) as a measurement standard. If an object’s weight was equivalent to 1728 carob seeds, then the object was said to weigh one Roman pound. If, on the other hand, the object’s weight was equivalent to 144 carob seeds then the object was said to weigh one Roman ounce (uncia). The Roman pound and ounce were both defined in terms of different sized collections of the same common mass standard, the carob seed. The ratio of a Roman ounce (144 carob seeds) to a Roman pound (1728 carob seeds) was:
\frac{ounce}{pound} = \frac{w_{144}}{w_{1728}} = \frac{144}{1728} = \frac{1}{12}.
This example illustrates a fundamental principle of physical science: when values are related through simple fractions, there is a good possibility that the values stem from a common source.

Various atoms and molecules as depicted 
in John Dalton's A New System of Chemical Philosophy (1808).
 
The name atom comes from the Greek ἄτομος/átomos, α-τεμνω, which means uncuttable, something that cannot be divided further. The philosophical concept that matter might be composed of discrete units that cannot be further divided has been around for millennia. However, empirical proof and the universal acceptance of the existence of atoms didn’t occur until the early 20th century.

As the science of chemistry matured, experimental evidence for the existence of atoms came from the law of multiple proportions. When two or more elements combined to form a compound, their masses are always in a fixed and definite ratio. For example, the mass ratio of nitrogen to oxygen in nitric oxide is seven eights. Ammonia has a hydrogen to nitrogen mass ratio of three fourteenths. The fact that elemental masses combined in simple fractions implies that all elemental mass stems from a common source. In principle, the atomic mass situation is analogous to the above example of Roman mass units. The Roman pound and ounce were both defined in terms of different sized collections of carob seeds, and consequently, the two mass units were related to each other through a simple fraction. Comparatively, since all of the atomic masses are related to each other through simple fractions, then perhaps the atomic masses are just different sized collections of some common fundamental mass unit.

In 1805, the chemist John Dalton published his first table of relative atomic weights, listing six elements, hydrogen, oxygen, nitrogen, carbon, sulfur, and phosphorus, and assigning hydrogen an atomic weight of 1. And in 1815, the chemist William Prout concluded that the hydrogen atom was in fact the fundamental mass unit from which all other atomic masses were derived.

Carbon atoms in graphite (image obtained with a Scanning tunneling microscope)
 
If Prout's hypothesis had proven accurate, then the abstract concept of mass, as we now know it, might never have evolved, since mass could always be defined in terms of amounts of the hydrogen atomic mass. Prout’s hypothesis; however, was found to be inaccurate in two major respects. First, further scientific advancements revealed the existence of smaller particles, such as electrons and quarks, whose masses are not related through simple fractions. And second, the elemental masses themselves were found to not be exact multiples of the hydrogen atom mass, but rather, they were near multiples. Einstein’s theory of relativity explained that when protons and neutrons come together to form an atomic nucleus, some of the mass of the nucleus is released in the form of binding energy. The more tightly bound the nucleus, the more energy is lost during formation and this binding energy loss causes the elemental masses to not be related through simple fractions.
Hydrogen, for example, with a single proton, has an atomic weight of 1.007825 u. The most abundant isotope of iron has 26 protons and 30 neutrons, so one might expect its atomic weight to be 56 times that of the hydrogen atom, but in fact, its atomic weight is only 55.9383 u, which is clearly not an integer multiple of 1.007825. Prout’s hypothesis was proven inaccurate in many respects, but the abstract concepts of atomic mass and amount continue to play an influential role in chemistry, and the atomic mass unit continues to be the unit of choice for very small mass measurements.

When the French invented the metric system in the late 18th century, they used an amount to define their mass unit. The kilogram was originally defined to be equal in mass to the amount of pure water contained in a one-liter container. This definition, however, was inadequate for the precision requirements of modern technology, and the metric kilogram was redefined in terms of a manmade platinum-iridium bar known as the international prototype kilogram.

Tuesday, December 14, 2010

How Observant is your Science Mind?



This image above I have discussed before on this website. It is also in the legend on the right hand side of this web page. Maybe you can see the "symmetry at play?":)


Dürer Magic Square with Lines







Albrecht Durer and His Magic Square

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For those scientifically minded you must see the outlay and thesis adaption of Prof.dr R.H. Dijkgraaf as he demonstrated the totality of the illumination of his thinking? While I captured a small part of it by referencing the magic square, there is lots more there for the observant eye to take hold of.


Melencolia II
[frontispiece of thesis, after Dürer 1514]by Prof.dr R.H. Dijkgraaf

Monday, December 13, 2010

Cosmic Screens

[Recommended] Five Showers (Windows only). This has five showers (alpha, proton. gamma, iron, etc) at 333 ns per time step, and with a much more user-friendly interface than the other showers below. The interface was made by Mark SubbaRao using a Director plugin written by Toshiyuki Takahei. 

See:COSMOS:AIRES Cosmic Ray Showers

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2010 ion run: completed!

First direct observation of jet quenching.

At the recent seminar, the LHC’s dedicated heavy-ion experiment, ALICE, confirmed that QGP behaves like an ideal liquid, a phenomenon earlier observed at the US Brookhaven Laboratory’s RHIC facility. This question was indeed one of the main points of this first phase of data analysis, which also included the analysis of secondary particles produced in the lead-lead collisions. ALICE's results already rule out many of the existing theoretical models describing the physics of heavy-ions.
See: 2010 ion run: completed!

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After a very fast switchover from protons to lead ions, the LHC has achieved performances that allowed the machine to exceed both peak and integrated luminosity by a factor of three. Thanks to this, experiments have been able to produce high-profile results on ion physics almost immediately, confirming that the LHC was able to keep its promises for ions as well as for protons.

A seminar on 2 December was the opportunity for the ALICE, ATLAS and CMS collaborations to present their first results on ion physics in front of a packed auditorium. These results are important and are already having a major impact on the understanding of the physics processes that involve the basic constituents of matter at high energies.

In the ion-ion collisions, the temperature is so high that partons (quarks and gluons), which are usually constrained inside the nucleons, are deconfined to form a highly dense and hot soup known as quark-gluon plasma (QGP). This type of matter existed about 1 millionth of a second after the Big Bang. By studying it, scientists hope to understand the processes that led to the formation of nucleons, which in turn became the nuclei of atoms. See:LHC completes first heavy-ion run

See Also: Jets: Article Updated