Charles Cajori

Charles Florian Cajori (March 9, 1921—December 1, 2013) was an abstract expressionist painter who, through his drawing, painting and teaching, made a significant contribution to the New York School of artists that emerged in the 1950s.
Early life.
Charles Cajori was born in Palo Alto, CA to Florian Cajori and Marion Huntington Haynes. They moved to Wayne, PA when Charles was one year old. Florian Cajori was a bio-chemist and taught in the medical school at the University of Pennsylvania. Marion was a pianist and educator who gave piano lessons and started a school inspired by John Dewey’s philosophy of inclusion and social reform.
Cajori went to school on the Main Line in the western suburbs of Philadelphia before enrolling in Colorado Springs Art Center in 1939 and the Cleveland Art School from 1940-42. He was drafted in 1942, and spent four years in the US Air Force. Upon his discharge, he went to Columbia University on the G.I. Bill and studied there with Jack Heliker. He attended the Skowhegan School of Painting & Sculpture of in the summers of 1947 and 1948.
Early on Cajori discovered New York's downtown scene, and began attending the lively (and sometimes feisty) gatherings at the Cedar Tavern and the panels at the fabled Eighth Street Club. He became especially close to Willem de Kooning and Franz Kline, and in 1952 he joined with Lois Dodd, Angelo Ippolito, William King and Fred Mitchell to found the Tanager Gallery on East 10th St. The gallery was to become central to the lives of many of the contemporary working artists.
In 1950 he began his teaching career at Notre Dame University in Maryland, and by 1956 he was teaching at The Cooper Union. He was awarded a Fulbright Grant to Italy in 1959. After returning to the states, he resumed his life in New York. In 1959-60, he taught at the University of California at Berkeley, where he regularly joined Richard Diebenkorn and Elmer Bischoff in figure drawing sessions.
He met his wife, Barbara Grossman, at Cooper Union and they married in 1967. They had one child, Nicole Antonia born in 1969. In 1972 they moved to a rural farm house with land in Connecticut where they could both have large studios.
Career.
In the 1950s Cajori had solo exhibitions at the Tanager Gallery, Bertha Schaefer Gallery and the Oakland Art Museum. His work appeared in numerous group shows including annual and biennial shows at the Stable Gallery, the Whitney Museum, the Brooklyn Museum and the Corcoran Gallery of Art.
In 1964, joining with former students of Pratt Institute and several artists including Mercedes Matter, Sidney Geist, Georgio Spaventa, and Esteban Vicente, he founded the New York Studio School of Drawing, Painting and Sculpture. He was to teach at the school for the remainder of his active years. For 20 years he taught also at Queens College, and was a visiting artist at numerous other schools, including Yale University, Dartmouth College and Cornell University. He retired from full-time teaching in 1986 to devote his time to painting and drawing.
Cajori exhibited in New York City at the Howard Wise Gallery, Ingber Gallery, Lohin-Geduld Gallery, and at the Gross-McCleaf Gallery in Philadelphia as well as numerous colleges and universities, including Dartmouth College, American University, Cornell University, Wright State University, the New York Studio School, Central Connecticut State University, Cincinnati Art Academy, University of Texas at Austin, Bennington College, and the University of Washington at Seattle.
Legacy.
Cajori was recognized as an important second-generation Abstract Expressionist. His work was reviewed in all the major art journals and newspapers of the day.
The paintings of Cajori, with the exception of his early formative work, always revolved around the figure and the space. He keenly focused on the ideas about perception and the way we as humans are encompassed by the environment we found ourselves in. Thus the figure—always female, for Cajori—was activated by our vivid experience of occupying a section of life. All of his images were invented, using color and drawing to concretize this experience.
Cajori drew from the model all his life. He drew about once a week in his studio, hiring people with whom he often developed friendships. He exhibited those drawings along with the paintings and sometimes mixed-media inventions. He relished working large and could work on paintings over a long period of time, sometimes going back in to them long after declaring them “finished.” He lived his life as an artist, preferring the studio to any other place.
In 2011, Cajori submitted a statement to E. Ashley Rooney for inclusion in his book on New England artists:
“First is the acknowledgment of chaos: its contradictions and wayward forces. Then the struggle for coherence. Not a coherence of illusion but one of time and space—of form. The mode of attack is improvisational, multileveled, and non-rational. The resulting structures may seem complete, but they contain a hint of another stage. New attacks are called for. Structures evolve endlessly."
Reviews of Cajori's work appeared in the "New York Times, The New York Observer, Art News, Art in America, Arts Magazine, Art New England, Review, SoHo Weekly News, Art International, The New York Post, The Brooklyn Rail" and "artcritical.com," among many other publications.
Cajori's work is represented in numerous public collections, including the Metropolitan Museum of Art, the Hirshhorn Museum, the Whitney Museum, the Denver Art Museum, the Walker Art Center, the Weatherspoon Art Museum, the Arkansas Art Center, the Honolulu Art Academy and the National Academy of Design.
In addition to his Fulbright grant, Cajori was awarded a Distinction in the Arts by Yale University, a Longview Foundation Purchase Award, a Ford Foundation Purchase Award, several awards from the American Academy of Arts and Letters (the Jimmy Ernst Award, the Arts and Letters Award, and three Childe Hassam Purchase Awards), the Louis Comfort Tiffany Award, a National Endowment for the Arts Grant, several awards from the National Academy of Design (the Henry Ward Ranger Fund Purchase Award, the Ralph Fabri Prize, and four Benjamin Altman Prizes) and a Guggenheim Fellowship. In 1982 he was elected as an Academician of the National Academy of Design.
Further reading.
Ken Johnson, "Art in review: Charles Cajori, ”"The New York Times," April 28, 2000.
"A Talk Between Old Friends," Painter Charles Cajori & Sculptor Tom Doyle, video discussion presented by Behnke Doherty Gallery, Washington Depot.
Tom Reney, “Charles Cajori, R.I.P.: The jazz inspiration of a New York painter,” New England Public Radio, March 7, 2014.
Harry I. Naar, “Artist Conversation: Barbara Grossman and Charles Cajori,” interview with Barbara Grossman and Charles Cajori about their exhibit "Forming the Figure," on view at Rider University November 5-December 6, 2009.


The Luxury Institute

The Luxury Institute is a premium goods and services research, training and consulting firm based in New York City, New York and Boca Raton, Florida. It has the largest global network of luxury experts. It has conducted more quantitative and qualitative research on affluent consumers than any other entity. Over the last 17 years, the firm has served over 1,100 luxury and premium goods and services brands.
The Luxury Institute's reports, as well as CEO Milton Pedraza, have been cited in luxury industry articles by publications including Marketing Week, The Wall Street Journal, Women's Wear Daily, and the CEOWORLD magazine.
Luxury Brand Status Index (LBSI).
The Luxury Institute publishes annual Luxury Brand Status Index surveys, which aggregate the brand preferences of high-net-worth individuals within various luxury market categories. In 2009, some available categories included:


Tastiera shqip

Tastiera Shqip DK is an Albanian modified keyboard layout, fully compliant with the new way Albanians use the computers. The layout was studied by the teams of Pasioni and Albword. The software is free to download, use and distribute for personal use only.


Emilio Scanavino

Emilio Scanavino (Genoa, 28 February 1922 – Milan, 28 November 1986) was an Italian painter and sculptor.
Early life.
Scanavino was born in Genoa. In 1938 he enrolled to the Art School Nicolò Barabino where he met Mario Calonghi, who was teaching at the school and was due to be a great influence on Scanavino's artistic formation. In 1942 he had his first exhibition at the Salone Romano of Genoa. In the same year he enrolled at the Faculty of Architecture at the Milan University. In 1946 he married Giorgina Graglia.
In 1947 Scanavino moved to Paris where he met poets and artists such as Edouard Jaguer, Wols and Camille Bryen. This experience proved to be inspirational. He was especially interested in Cubism, which he rendered into a personal interpretation when he exhibited at the Gallery Isola in Genoa in 1948.
In 1950 Scanavino and Rocco Borrella joined "I sette del Numero", an artistic group revolving around the Numero Gallery in Florence. In the same year he was invited to the 27th edition of the Venice Biennale and in 1951 he had a two-person exhibition with the sculptor Sarah Jackson at the Apollinaire Gallery in London.
During his time in London Scanavino met Philip Martin, Eduardo Paolozzi, Graham Sutherland and Francis Bacon. In the same year he opened his first studio in Milan in an attic in Foro Bonaparte. Critic Guido Ballo and dealers Guido Le Noci and Arturo Schwartz were early champions of his works.
In 1952, Scanavino worked at the Marzotti's Ceramic Factory in Albissola Marina, where he met and befriended many artists, including Lucio Fontana, Asger Jorn, Corneille, Roberto Matta, Wifredo Lam, Giuseppe Capogrossi, Enrico Baj, Sergio Dangelo, Roberto Crippa, Gianni Dova, Agenore Fabbri and Aligi Sassu.
In 1954 he exhibited again at the Venice Biennale and in 1955 he received the Graziano Prize. In 1958 he won the Lissone Prize and the Prampolini Prize for a solo presentation at the Venice Biennale. In the same year he moved to Milan where he joined the Naviglio Gallery directed by Carlo Cardazzo with whom he established a long-standing friendship and proficuous working relation. In Milan he also met the art collector Gianni Malabarba with whom he established a strongfriendship.
Later life.
In 1962 Scanavino bought an old house in Calice Ligure, which he later converted into a studio space. In 1963, after winning the La Spezia Prize, Scanavino learned of the sudden death of Carlo Cardazzo. Cardazzo's brother, Renato, continued to run the Naviglio Gallery but the loss of Carlo had a huge impact in scanavino's life. After participating for the fourth time to the Venice Biennale, when he won the Pininfarina Prize, Scanavino permanently moved to Calice Ligure in 1968. In 1970 he won the Gran Prix at the 10th Mentone Biennale and met Franco Castelli, then editor of "L'uomo e l'Arte", who became one of his closest friends and supporters
In 1971 Scanavino had to undergo a major surgery operation. The recovery period signaled the start of a new creative phase in his painting. He travelled to Belgium, France and Germany, and in 1974 the Darmstadt Kunsthalle organized a comprehensive antological exhibition that later travelled to Venice's Palazzo Grassi and Milan's Royal Palace.
In 1982, Scanavino's health started to decline. His last exhibition was the 1986 edition of the Rome Quadriennale.
Scanavino died in Milan on 28 November 1986.
Art.
After an initial interest in figurative art, Scanavino's paintings took Post-Cubist nuances. His forms became increasingly stylized, until being completely obliterated in the works from the early 1950s. In 1954 his characteristic sign, “stylized knot”, started to appear. That is the, eventually marking his whole production. In the late 1970s years paintings, the “knot” became perfectly defined and recognizable, although his work became darker, sometimes even threatening due to the conspicuous presence of red stains resembling blood. Although Scanavino is difficult to place inside a specific artistic movement, he can be considered an informal abstractist, close to the Abstract Expressionism and Hans Hartung and Georges Mathieu's art.


Heap (data structure)

In computer science, a heap is a specialized tree-based data structure which is essentially an almost complete tree that satisfies the heap property: in a "max heap", for any given node C, if P is a parent node of C, then the "key" (the "value") of P is greater than or equal to the key of C. In a "min heap", the key of P is less than or equal to the key of C. The node at the "top" of the heap (with no parents) is called the "root" node.
The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root. However, a heap is not a sorted structure; it can be regarded as being partially ordered. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority.
A common implementation of a heap is the binary heap, in which the tree is a binary tree (see figure). The heap data structure, specifically the binary heap, was introduced by J. W. J. Williams in 1964, as a data structure for the heapsort sorting algorithm. Heaps are also crucial in several efficient graph algorithms such as Dijkstra's algorithm. When a heap is a complete binary tree, it has a smallest possible height—a heap with "N" nodes and for each node "a" branches always has log"a" "N" height.
Note that, as shown in the graphic, there is no implied ordering between siblings or cousins and no implied sequence for an in-order traversal (as there would be in, e.g., a binary search tree). The heap relation mentioned above applies only between nodes and their parents, grandparents, etc. The maximum number of children each node can have depends on the type of heap.
Operations.
The common operations involving heaps are:
Implementation.
Heaps are usually implemented with an array, as follows:
In the array, the first index contains the root element. The next two indices of the array contain the root's children. The next four indices contain the four children of the root's two child nodes, and so on. Therefore, given a node at index i, its children are at indices 2i + 1 and 2i + 2, and its parent is at index floor((i-1)/2). This simple indexing scheme makes it efficient to move "up" or "down" the tree.
Balancing a heap is done by sift-up or sift-down operations (swapping elements which are out of order). As we can build a heap from an array without requiring extra memory (for the nodes, for example), heapsort can be used to sort an array in-place.
After an element is inserted into or deleted from a heap, the heap property may be violated, and the heap must be re-balanced by swapping elements within the array.
Different types of heaps implement the operations in different ways, but notably, insertion is often done by adding the new element at the end of the heap in the first available free space. This will generally violate the heap property, and so the elements are then shifted up until the heap property has been reestablished. Similarly, deleting the root is done by removing the root and then putting the last element in the root and sifting down to re-balance. Thus replacing is done by deleting the root and putting the "new" element in the root and sifting down, avoiding a sifting up step compared to pop (sift down of last element) followed by push (sift up of new element).
Construction of a binary (or "d"-ary) heap out of a given array of elements may be performed in linear time using the classic Floyd algorithm, with the worst-case number of comparisons equal to 2"N" − 2"s"2("N") − "e"2("N") (for a binary heap), where "s"2("N") is the sum of all digits of the binary representation of "N" and "e"2("N") is the exponent of 2 in the prime factorization of "N". This is faster than a sequence of consecutive insertions into an originally empty heap, which is log-linear.
Applications.
The heap data structure has many applications.


Robert Motherwell

Robert Motherwell (January 24, 1915 – July 16, 1991) was an American abstract expressionist painter, printmaker, and editor. He was one of the youngest of the New York School, which also included Philip Guston, Willem de Kooning, Jackson Pollock, and Mark Rothko.
Trained in philosophy, Motherwell became an artist, regarded as among the most articulate of the abstract expressionist painters. He was known for his series of abstract paintings and prints which touched on political, philosophical and literary themes, such as the "Elegies to the Spanish Republic".
Early life and education.
Robert Motherwell was born in Aberdeen, Washington on January 24, 1915, the first child of Robert Burns Motherwell II and Margaret Hogan Motherwell. The family later moved to San Francisco, where Motherwell's father served as president of Wells Fargo Bank. Due to the artist's asthmatic condition, Motherwell was reared largely on the Pacific Coast and spent most of his school years in California. There he developed a love for the broad spaces and bright colours that later emerged as essential characteristics of his abstract paintings (ultramarine blue of the sky and yellow ochre of Californian hills). His later concern with themes of mortality can likewise be traced to his frail health as a child.
Between 1932 and 1937, Motherwell briefly studied painting at California School of Fine Arts, San Francisco and received a BA in philosophy from Stanford University. At Stanford, Motherwell was introduced to modernism through his extensive reading of symbolist and other literature, especially Mallarmé, James Joyce, Edgar Allan Poe, and Octavio Paz. This passion stayed with Motherwell for the rest of his life and became a major theme of his later paintings and drawings.
At the age of 20, Motherwell took a grand tour of Europe, accompanied by his father and sister. They began in Paris, then traveled to Amalfi, Italy. The next stops were Switzerland, Germany, The Netherlands and London. The group ended their tour in Motherwell, Scotland.
According to Motherwell, the reason he went to Harvard was that he wanted to be a painter, although his father urged him to pursue a more secure career: "And finally after months of really a cold war he made a very generous agreement with me that if I would get a Ph.D. so that I would be equipped to teach in a college as an economic insurance, he would give me fifty dollars a week for the rest of my life to do whatever I wanted to do on the assumption that with fifty dollars I could not starve but it would be no inducement to last. So with that agreed on Harvard then—it was actually the last year—Harvard still had the best philosophy school in the world. And since I had taken my degree at Stanford in philosophy, and since he didn't care what the Ph.D. was in, I went on to Harvard."
At Harvard, Motherwell studied under Arthur Oncken Lovejoy and David Wite Prall. He spent a year in Paris to research the writings of Eugène Delacroix, where he met American composer Arthur Berger who advised him to continue his education at Columbia University, under Meyer Schapiro.
The New York School and the Surrealists.
In 1940, Motherwell moved to New York to study at Columbia University, where he was encouraged by Meyer Schapiro to devote himself to painting rather than scholarship. Schapiro introduced the young artist to a group of exiled Parisian Surrealists (Max Ernst, Duchamp, Masson) and arranged for Motherwell to study with Kurt Seligmann. The time that Motherwell spent with the Surrealists proved to be influential to his artistic process. After a 1941 voyage with Roberto Matta to Mexico—on a boat where he met Maria Emilia Ferreira y Moyeros, an actress and his future wife—Motherwell decided to make painting his primary vocation. The sketches Motherwell made in Mexico later evolved into his first important paintings, such as "The Little Spanish Prison" (1941) and "Pancho Villa, Dead and Alive" (1943).
Matta introduced Motherwell to the concept of "automatic" drawing or automatism, which the Surrealists used to tap into their unconscious. The concept had a lasting effect on Motherwell, further augmented by his meeting with the artist Wolfgang Paalen. Motherwell's encounter with Paalen prompted him to prolong his stay in Mexico for several months, in order to collaborate with him. Motherwell's noted "Mexican Sketchbook" visually reflects the resulting change: while the first drawings are influenced by Matta and Yves Tanguy, later drawings associated with Motherwell's time with Paalen show more plane graphic cadences and details distinguished from the earlier period. Paalen also introduced Motherwell to André Breton, via a letter. Motherwell's seminal trip to Mexico has been described as a little-known but important factor in the history and aesthetics of abstract expressionism. In 1991, shortly before his death, Motherwell remembered a "conspiracy of silence" regarding Paalen's innovative role in the genesis of abstract expressionism.
Upon return from Mexico Motherwell spent time developing his creative principle based on automatism: "What I realized was that Americans potentially could paint like angels but that there was no creative principle around, so that everybody who liked modern art was copying it. Gorky was copying Picasso. Pollock was copying Picasso. De Kooning was copying Picasso. I mean I say this unqualifiedly. I was painting French intimate pictures or whatever. And all we needed was a creative principle, I mean something that would mobilize this capacity to paint in a creative way, and that's what Europe had that we hadn't had; we had always followed in their wake. And I thought of all the possibilities of free association—because I also had a psychoanalytic background and I understood the implications—might be the best chance to really make something entirely new which everybody agreed was the thing to do."
Thus, in the early 1940s, Robert Motherwell played a significant role in laying the foundations for the new movement of abstract expressionism (or the New York School): "Matta wanted to start a revolution, a movement, within Surrealism. He asked me to find some other American artists that would help start a new movement. It was then that Baziotes and I went to see Pollock and de Kooning and Hofmann and Kamrowski and Busa and several other people. And if we could come with something. Peggy Guggenheim who liked us said that she would put on a show of this new business. And so I went around explaining the theory of automatism to everybody because the only way that you could have a movement was that it had some common principle. It sort of all began that way."
In 1942 Motherwell began to exhibit his work in New York and in 1944 he had his first one-man show at Peggy Guggenheim's "Art of This Century" gallery; that same year the MoMA was the first museum to purchase one of his works. From the mid-1940s, Motherwell became the leading spokesman for avant-garde art in America. His circle came to include William Baziotes, David Hare, Barnett Newman, and Mark Rothko, with whom he eventually started the Subjects of the Artist School (1948–1949). In 1949 Motherwell divorced Maria and in 1950 he married Betty Little, with whom he had two daughters.
Motherwell was a member of the editorial board of the Surrealist magazine "VVV" and a contributor to Wolfgang Paalen's journal "DYN", which was edited from 1942-44 in six issues. He also edited Paalen's collected essays "Form and Sense" in 1945 as the first issue of "Problems of Contemporary Art".
In 1948 Motherwell executed the image which would prove to be the germ of the "Elegies to the Spanish Republic", one of his best known series of works. During 1947-48, Motherwell collaborated with the art critic Harold Rosenberg and others to produce "Possibilities", an art review. During the latter year Motherwell created an image incorporating Rosenberg's poem "The Bird for Every Bird", meant for inclusion in the review's second issue. The top half was a handwritten, stylized rendering of the poem's final three lines, and the bottom half was a visual element consisting of roughly rendered black ovoid and rectangular forms against a white background. The stark image was meant to "illustrate" the violent imagery of the poem in an abstract, non-literal way; Motherwell therefore preferred the term "illumination". The second issue of "Possibilities" did not materialize, and Motherwell placed the image in storage. He rediscovered it roughly one year later and decided to rework its basic elements. This led to the "Elegies to the Spanish Republic" which Motherwell continued to produce for the rest of his life; several years later Motherwell retroactively titled the original image "Elegy to the Spanish Republic No. 1", recognizing it as the series' starting point. A representative example is "Elegy to the Spanish Republic No. 110" (1971) which employs the same visual motif of rough ovoid and rectangular forms. The series' abstract imagery has been interpreted as representing violence in Hispanic culture, not necessarily related to the Spanish Civil War of its title. For example Motherwell himself and others have compared the images to the display of a dead bull's genitalia in the Spanish bullfighting ring.
Throughout the 1950s Motherwell also taught painting at Hunter College in New York and at Black Mountain College in North Carolina. Cy Twombly, Robert Rauschenberg and Kenneth Noland studied under and were influenced by Motherwell. At this time, he was a prolific writer and lecturer, and in addition to directing the influential Documents of Modern Art Series, he edited "The Dada Painters and Poets: An Anthology", which was published in 1951.
From 1954 to 1958, during the break-up of his second marriage, he worked on a small series of paintings which incorporated the words Je t'aime, expressing his most intimate and private feelings. His collages began to incorporate material from his studio such as cigarette packets and labels, becoming records of his daily life. He was married for the third time, from 1958 to 1971, to fellow abstract painter Helen Frankenthaler. Because Frankenthaler and Motherwell were both born into wealth and known to host lavish parties, the pair were known as "the golden couple".
Mature years.
In 1958–59, Motherwell was included in "The New American Painting" exhibition, initiated by the Museum of Modern Art, which traveled across Europe. In 1958 he and Frankenthaler spent a three-month honeymoon in Spain and France, during which he began painting with a new energy that he attributed to her influence. The "Two Figures" series he made that year shows "the brightening power of Helen's colors" on his work.
During the 1960s, Motherwell exhibited widely in both America and Europe and in 1965 he was given a major retrospective exhibition at the Museum of Modern Art; this show subsequently traveled to Amsterdam, London, Brussels, Essen, and Turin. In 1962, Motherwell and Frankenthaler spent the summer at the artists' colony at Provincetown, Massachusetts, where the coastline inspired the "Beside the Sea" series of 64 paintings, the oil paint splashed with full force imitating the sea crashing on the shore in front of his studio. The 1963 untitled oil on canvas painting in the collection of the Honolulu Museum of Art exemplifies this stage in the artist's career.
In 1964, Motherwell created a mural-sized painting entitled "Dublin 1916, with Black and Tan", which is in the Governor Nelson A. Rockefeller Empire State Plaza Art Collection in Albany, NY. The size and content suggest that Motherwell intended to create a monument to heroism in the tradition of Picasso's "Guernica".
In 1965 Motherwell worked on another prominent series called the "Lyric Suite", named after Alban Berg's string quartet. Motherwell recalled, "I went to a Japanese store to buy a toy for a friend's kid, and I saw this beautiful Japanese paper and I bought a thousand sheets. And I made up my mind, this was in the beginning of April 1965, that I would do the thousand sheets without correction. I'd make an absolute rule for myself. And I got to 600 in April and May, when one night my wife and I were having dinner and the telephone rang. And it was Kenneth Noland in Vermont saying that I should come immediately. And I said, 'what's happened?' And he said, 'David Smith's been in an accident'." Smith, the sculptor, was Motherwell and Frankenthaler's friend. The couple drove hastily to Vermont, arriving 15 minutes after Smith had died. Motherwell stopped work on the series. He said of them: "And then one year I had them all framed, and I like them very much now. I should also say that I half painted them and they half painted themselves. I'd never used rice paper before except occasionally as an element in a collage. And most of these were made with very small, I mean very thin lines. And then I would look at amazement on the floor after I'd finished. It would spread like spots of oil and fill all kinds of strange dimensions."
In 1967 Motherwell began to work on his "Open" series. Inspired by a chance juxtaposition of a large and small canvas, the Open paintings occupied Motherwell for nearly two decades. The Opens consist of limited planes of colour, broken up by minimally rendered lines in loosely rectangular configurations. As the series progressed, the works became more complex and more painterly, as Motherwell worked through the possible permutations of such reduced means.
The late 1960s saw Motherwell using Gauloises packets and cartons in many collages, including an extensive series with the packets surrounded by bright red acrylic paint, often with incised lines in the painted areas. In the introduction to his 2015 book "Robert Motherwell, The Making of an American Giant", gallery owner Bernard Jacobson says, "Motherwell smoked Lucky Strikes, but in his collage life he smokes Gauloises, around whose blue packets he now organises one composition after another, 'exotic to me precisely because in the normal course of things I don't smoke French cigarettes'. And by incorporating Gauloises packets he makes deft and condensed allusion to 'French blue': to the Mediterranean and the palette of Matisse ... to the smoke coiling up in a Cubist assemblage."
In 1972, Motherwell married the artist-photographer Renate Ponsold and moved to Greenwich, Connecticut, where they lived in a carriage house with a hayloft aerie, a barn and a guest cottage adjoining a large studio—the whole surrounded by parklike grounds. During the 1970s, he had retrospective exhibitions in several European cities, including Düsseldorf, Stockholm, Vienna, Paris, Edinburgh, and London. In 1977, Motherwell was given a major mural commission for the new wing of the National Gallery of Art, Washington, D.C.
In 1983, a major retrospective exhibition of Motherwell's work was held at the Albright-Knox Art Gallery in Buffalo, New York; this exhibition was subsequently shown in Los Angeles, San Francisco, Seattle, Washington, D.C., and New York City. Another retrospective was shown in Mexico City, Monterey, and Fort Worth, Texas, in 1991.
In 1985, Motherwell was awarded the Edward Macdowell Medal.
In 1988, Motherwell worked with the publisher Andrew Hoyem of Arion Press on a limited edition of the modernist novel "Ulysses", by James Joyce. Motherwell produced 40 lithographs for the project.
Death and legacy.
Motherwell died in Provincetown, Massachusetts on July 16, 1991. On his death, Clement Greenberg, champion of the New York School, left in little doubt his esteem for the artist, commenting that "although he is underrated today, in my opinion he was one of the very best of the abstract expressionist painters".
The Dedalus Foundation was set up by Robert Motherwell in 1981 to foster public understanding of modern art and modernism through its support of research, education, publications, and exhibitions. When Motherwell died, he left an estate then estimated at more than $25 million and more than 1,000 works of art, not including prints. His will was filed for probate in Greenwich and named as executors his widow, Renate Ponsold Motherwell, and longtime friend Richard Rubin, a professor of political science at Swarthmore College.
On July 20, 1991, several hundred people attended a memorial service for Motherwell on the beach outside his Provincetown home. Among them were the writer Norman Mailer and the photographer Joel Meyerowitz, both Provincetown summer residents. Speakers included the poet Stanley Kunitz, who read a poem that was a favorite of Motherwell's, William Butler Yeats's "Sailing to Byzantium". Others in attendance included family members, friends, other artists, and Senator Howard Metzenbaum, an acquaintance of Motherwell's.
Selected exhibitions.
Several major exhibitions of Motherwell's work have been held.


Antonio Asis

Antonio Asis (1932-2019) is an Argentine painter, an exponent of Op Art. His works were presented at the Paris Biennale (1967) and in "Casa de Cultura de Grenoble" (1968).
Biography.
From 1946 to 1950 he attended the Escuela National de Belles Artes in Buenos Aires, Argentina. In 1956 he arrived in Paris and immediately befriended the Denise Rene group of artists such as Jesus Rafael Soto, Pol Bury, and Yaacov Agam. Asis was one of the first Argentines to arrive in Paris, and started working in his typical style of 'interference' works like the "Interferences concentriques" paintings and his "Vibrations" sculptures with a metal grille.
There is a strong group of Argentinian artists (Antonio Asis, Julio Le Parc, Luis Tomasello, Horacio Garcia-Rossi) as well as a strong group of Venezuelan artists (Jesús Rafael Soto, Carlos Cruz-Diez, Dario Perez-Flores, Narciso Debourg) working with the possibilities of vision, movement, and light.
He works and lives in Paris.


Francis Celentano

Francis Michael Celentano (May 25, 1928 – November 20, 2016) was one of the seminal artists in the Op art movement that started in the 1960s. He was one of the featured artists in an exhibition called "The Responsive Eye", which was held at the Museum of Modern Art in New York City in 1965. He continued to contribute to the art form throughout his life, working in black and white, color, kinetic paintings and three dimensional studies.
Artistic work.
Among public collections are the Museum of Modern Art, the Whitney Museum of Contemporary Art, The Albright-Knox Gallery, the Museum of Contemporary Art in Buenos Aires and the Seattle Art Museum. He is represented by the Lee Russo Gallery, Oregon, David Richard Gallery, New Mexico, and D. Wigmore Fine Arts, New York.


Systems Research and Behavioral Science

Systems Research and Behavioral Science is a scientific journal for theory and research in the fields of systems sciences. It is the official publication of the International Federation for Systems Research.
"Systems Research and Behavioral Science" originated from the merger of two journals, "Systems Research" (1974–1996) and "Behavioral Science" (1956–1996). The combined series commenced in January/February 1997 with volume 14, continuing the numbering of "Systems Research". According to the "Journal Citation Reports", the journal has a 2016 impact factor of 1.034, ranking it 44th out of 96 journals in the category "Social Sciences Interdisciplinary" and 148th of out of 194 journals in the category "Management".


Ludwig Wilding

Ludwig Wilding (19 May 1927 – 4 January 2010) was a German artist whose work is associated with Op art and Kinetic art. Wilding was born in Grünstadt, Germany. He studied at the University of Mainz Art School.
Wilding's works are three-dimensional structures that create shifting patterns through their black and white designs. He has shown at the Museum Leverkusen (1953), Zimmergallery, Frankfurt (1958) and Studio F, Ulm (1965). His work was included in "The Responsive Eye" (Museum of Modern Art, New York, 1965), "Eyes, Lies, and Illusions" (Hayward Gallery, London, 2004) and "Optic Nerve: Perceptual Art of the 1960s" (The Columbus Museum of Art, Ohio, 2007). Ludwig Wilding lived in Westheim, Germany.
References.
"The Responsive Eye". William C. Seitz, New York: The Museum of Modern Art, 1965.
"Ludwig Wilding. Retrospektive 1949-1987" Kaiserslautern: Pfalzgalerie des Bezirksverbands Pfalz, 1987.
"Ludwig Wilding. Una traiettoria cinetica". Getulio Alviani, Milano: Edizioni Arte Struktura, 2004.
"Ludwig Wilding. Visuelle Phanomen". Wienand Verlag Edizioni, 2007.
"Ludwig Wilding. kunst= traum = illusion = tauschung". Hamburg: Galerie Renate Kammer, 2012.
"Ludwig Wilding. Kinetische und Programmierte Kunst: 1967/2008". Milano: Galleria Dep Art Edizioni, 2013.


Ranks and insignia of the Reichsluftschutzbund

Ranks and insignia of Reichsluftschutzbund were paramilitary titles adopted by the "Reichsluftschutzbund" ("State Air Protection Corps" – RLB) for wear on the paramilitary uniforms of the RLB.


Ashot Avagyan

Ashot Avagyan (; born May 20, 1958) is an Armenian painter. Many of his works depict the suffering and loss he experienced during the First Nagorno-Karabakh War, and inspired by ancient megalithic structures and ancient petroglyphs found in Syunik Mountains. In November 2020 he was arrested for his participation in a phone call, calling for the assassination of Armenia's Prime Minister Nikol Pashinyan, after Armenia's capitulation in the Second Karabakh War.
Early life.
Ashot Avagyan was born in 1958 in Sisian, Armenia. He defeated the region, the city and the megalithic structures during the war in Nagorno Karabakh.
Career.
In 1981 graduated from the Yerevan Art College after P. Terlemezyan. He lives and develops his work in Sisian. From 1981 till now teaches at Children Art School in Sisian.
Having the cultural heritage of different time periods of his living area as a standing point, the artist always seeks for searching new perspectives of world-perception.
The conceptual and artistic prospects of Neolithic petroglyphs to Middle Age iconographic culture are transposed from the surface of canvas into the forms of modern art, appearing in the context of performance. Ashot is regularly creating art exhibitions in Sisian and attracts thousands of people to take part.
Personal life.
Ashot Avagyan devoted his life to teaching children in the remote town in South Armenia.
One – Man Shows.
2000 – "The seven papers of Demiurge", Chamber Theatre, Yerevan, Armenia
2004 – "Magic double circle", Gevorgyan Gallery, Yerevan, Armenia
2008 – "Memories from previous life", Gevorgyan Gallery, Yerevan, Armenia
Performances.
Involve the areas of cultural and cult monuments of Neolithic period in Sisian (Ukhtasar petroglyphs, Zorats Karer, Portakar).
1999 – "Dialogue"
2000 – "The Way"
2001 – "Forgive me, Mama!"
2002 – "Magic Double Circle"
2003 – "Reincarnation"
2004 – "Fertility"
2006 – "Return". With Azat Sargsyan in the frame of the 5th Gyumri Biennale
2007 – "Return - 2"
2008 – "Sacrifice"
2010 – "Return – 3"
2011 – "Return – 4"
2012 – "Sacrifice – 2"
Group Shows.
2001 – "Four Armenian artists", Toronto, Canada; Copenhagen, Denmark
2002 – "Show of avant-garde art", ACCEA, Yerevan, Armenia
2003 – "Transcendents", Albert and Tove Boyajyan Gallery, Yerevan, Armenia
Dublin, Ireland; New York, USA; Montreal, Canada
2004 – The 4th Gyumri International Biennale, Gyumri, Armenia
Art Expo "ART CAUCASUS", Tbilisi, Georgia
2005 – Art Expo "ART CAUCASUS", Tbilisi, Georgia
2006 – Abdala Al-Salem Hall, Kiewit, Kiewit
"The colors of Armenia", IFEFEL, Saint –Petersburg, Russia
"Meeting with Saryan", National Gallery, Yerevan, Armenia
2007 – "Colors of Armenia", G.Gyulbenkian center, Aleppo, Syria;
"Colors of Armenia", AGBU, Damascus, Syria
"From Ararat to Fuji", National Gallery, Yerevan, Armenia
"Contemporary artists from Armenia", Armenian General Benevolent Union,
Pasadena, USA
Armenian Landscapes in Contemporary Art", Untewerk Selnau, Kultur und
Eventhaus, Zurich, Switzerland
2008 – The 6th Gyumri International Biennale, Stil Gallery, Gyumri Armenia;
"Recovering wounds", Museum of Spitak Earthquake, Spitak, Armenia; branch of National Gallery in Vanadzor, Vanadzor, Armenia
"Generation Freedom: Armenia's New Vanguard", InterArt Gallery, New York,
USA
Catalogues.
1. Art Caucasus. Art Expo-2004. Tbilisi: Art Caucaus, 2004, [Eng.]
2. Gevorgyan Gallery. Yerevan: Gevorgyan Gallery, 2004, [Arm., Eng.]
3. Art Caucasus. Art Expo-2005. Tbilisi: Art Caucaus, 2005, [Eng.]
4. The 4th Gyumri International Biennale. Yerevan: GCCA, 2005, [Arm., Eng.]
5. The colors of Armenia, contemporary Armenian artists. Yerevan: Tigran Mets, 2006, [Russ.]
6. The 5th Gyumri International Biennale. Yerevan: GCCA, 2006, [Arm., Eng.]
7. Armenian Landscapes in Contemporary Art. Yerevan, 2007, [Germ., Eng.]
8. Contemporary Artists from Armenia. Pasadena: AGBU, 2007, [Eng.]
9. Generation Freedom: Armenia's New Vanguard. New York: RAH, 2008, [Eng.]
10. Recovering wounds. Yerevan: GCCA, 2008, [Arm., Eng.]
Work with Qarahunge archaeological site.
Since December 2010 Ashot Avagyan has been the Director of Qarahunge (Zorats Karer) megalithic
historical complex in Sisian. He assisted with the Oxford University Expedition to Qarahunge. Avagyan continues to work with expedition leader Mihran Vardanyan to create a healthy scientific and cultural climate around the monument in order to attract more tourists.


Ayoayo

Ayoayo is a traditional mancala played by the Yoruba people in Nigeria. It is very close to the Oware game that spread to the Americas with the atlantic slave trade. Among modern mancalas, which are most often derived from Warri, the Kalah is a notable one that has essentially the same rules as Ayoayo.
There are games with identical rules also in other areas of Africa. One such game is the Endodoi, played by the Maasai people of Kenya and Tanzania.
Rules.
The Ayoayo board is composed of two rows of six holes each, and 48 seeds are used; at the beginning, 4 seeds are placed in each hole. These are exactly the same equipment and setup as those of Warri and many other 2-row mancalas such as Layli Goobalay. Each player owns one of the rows.
Each turn the player takes all seeds from one of the holes and relay sows them counterclockwise. During each individual sowing, the starting hole is skipped (i.e., no seeds are dropped there even if more than 12 seeds are to be sown). When the last seed is sown in an empty hole, the player captures any seen in the opposing hole if this hole belongs to the player.
When one of the players cannot move anymore, the game is over. The opponent captures all the seeds that are left on the board and the winner is the player who captured most seeds.
If a turn ends with no seeds left in their row, the opponent "must" (if it is possible) choose their move in such a way to bring one or more seeds into the other's row. This scheme is found in many mancalas and sometimes referred to as "feeding" the opponent (i.e., save the opponent from starving).


Donald Cole (painter)

Donald Cole (October 31, 1930 in New York, New York) is an American abstract expressionist painter. He received a BS from Bucknell University and an MFA from the University of Iowa. He served in the Navy during the Korean War. He now lives on Vashon Island in Washington with wife Joan Wortis, also a visual artist.
His work has been exhibited in New York at 55 Mercer Gallery, French & Co., the Nancy Hoffman Gallery and the Frank Marino Gallery. Northwest showings include the Foster/White Gallery, the Jeffrey Moose Gallery and the ArtXchange Gallery in Seattle, two Tacoma Art Museum biennials and Gallery 070 on Vashon Island. He has work in a number of private and public collections, including the Portland Art Museum, the Worcester Art Museum, and the ARCO Center for Visual Art, Los Angeles.


Sergey Bashkirov

Sergey Gennadievich Bashkirov (born December 17, 1971 in Siberia), known as Sergey Bashkirov, is a contemporary Russian painter.
Early life and education.
Bashkirov was born in Siberia on December 17, 1971. He graduated from two different universities in St. Petersbrug. One of them - the Sport Academy named after Lesgaft (major- hockey trainer) and the other one - the East European Institute of psychoanalysis (major- psychological correction and positive psychology).
He furthered his career in Northern India. For 12 years, Bashkirov was living and studying at the university of Human Ecology in Northern India (major - Yoga Trainer and Art Therapist).
Currently he lives and works in St-Petersburg. He has his own studio in the heart of the city.
Works.
In 2006, being impressed by the exhibition of Filonov, he first tried painting. Today, after several years of experiments and studies of various schools of painting, Bashkirov is concentrated on abstract and colorful vision, using different techniques.
He uses hardened brushes, spatula, and even his hands as paint applicators. Bashkirov's technique of pouring, sprinkling paint gives the impression of spontaneity. In his paintings a wide gamma of colours is used and still they are harmonic for the viewer.


Yvonne Thomas

Yvonne Thomas (1913 Nice – August 7, 2009 Aspen, Colorado) was an American abstract artist.
Life.
Yvonne Thomas was born in Nice, France, in 1913, and arrived with her family in the United States in 1925. After first settling in Boston, the family moved to New York, where Thomas studied briefly at Cooper Union. When her parents could not afford her tuition due to the Great Depression, she turned to commercial work, supporting herself as a fashion illustrator.
In 1938, she chose to devote herself to art, enrolling at the Art Students League, where she studied with Vaclav Vytacil and took lessons in the figure and portraiture from the Russian painter Dmitri Romanovsky. She also attended the Ozenfant School of Fine Art, where the French Cubist emigrée Amadée Ozenfant introduced her to the modernist precepts to which she would be devoted throughout the rest of her career. In 1948, Patricia Matta, the wife of the artist Roberto Matta, provided Thomas with an introduction to the Subjects of the Artists School. Situated in a loft at 23 East 8th Street, the school consisted of participants who were considered “collaborators” rather than teacher-and-student. The artists in the school were leading figures in the American avant-garde, with whom Thomas interacted on an equal footing. They included William Baziotes, David Hare, Willem de Kooning, Arshile Gorky, Adolph Gottlieb, Hans Hofmann, Lee Krasner, Robert Motherwell, Barnett Newman, Jackson Pollock, Richard Pousette-Dart, Mark Rothko, and Clyfford Still . At the Subjects of the Artists School, Thomas felt she had “finally come home.”
In 1950, Thomas studied with Hofmann at his school in Provincetown, Massachusetts. She credits him with giving her the “courage of color.” In the next year, she took part in the first of a series of annual exhibitions of abstract art, that became legendary. The first—the "Ninth Street Exhibition of Paintings and Sculpture"—was held at 60 East 9th Street in Greenwich Village in May and June 1951. The Stable Gallery on Seventh Avenue at Fifty-Eighth Street was the venue for the subsequent shows, held from 1953 to 1957. The exhibitions enabled women artists to exhibit abstract works for which they had few opportunities otherwise, whereas male colleagues, who had more representation, were gaining recognition more broadly. Thomas was one of few artists to be included in all five of the Ninth Street shows. She was also a member the exclusive Artist’s Club, a gathering of artists and intellectuals, which was only for male artists when it began in 1949.
In the mid-1950s, Thomas loosened the Cubist structures she had used earlier, employing more gestural handling to create works that were more expressively free. The personal quality in these paintings was deemed “American” by Stuart Preston in a review of a three-artist show at Tanager Gallery in 1954, in which Thomas was included. Preston singled out the work of Thomas and Miriam Schapiro, calling both “talented” and “comparatively unknown” artists who distilled “non-specific emotional moods in a language of restless brushwork and fitful color.” Also reviewing the show, Dore Ashton observed the “landscape feeling” in Thomas’s oils and commented: “Hers is a delicate, very subtle intonation, adjusted to atmospheric rather than energetic forces in nature.” Thomas’s first solo exhibition occurred that year at Hendler Gallery in Philadelphia. In a review in "Art Digest", Sam Feinstein noted that Thomas seemed “not at all concerned with the opposition of horizontals and verticals,” but instead created works consisting of “soft, curvilinear brushings harmonized into a pictorial lyricism.”
In the following year, Thomas was one of eleven artists represented in a show at the Riverside Museum, New York, where her work was shown alongside that of Franz Kline, Milton Avery, Kenzo Okada, and Leon Polk Smith. In a review, Howard Devree gave recognition to Thomas’s “vigorous loose color arrangements.” In 1956, a solo show of her work was held at Tanager. "Art News" commented that the works on view were larger than those at the gallery two years earlier and demonstrated more control, in their “deliberately selected forms.” "Arts Magazine" observed that Thomas had succeeded in “establishing a really plastic tension and strength” in works such as "Aspen" and "By the Sea".
In April 1960, after a year spent in Paris, Thomas had her second New York show, which was held at the Esther Stuttman Gallery in New York. It included some paintings rendered in Paris along with recent New York works. "Art News" stated that in her work Thomas did not “disguise who she is in her “personal color harmonies” and in imagery that was “not readily identifiable,” but “close to the free-form spirit of place.” "The New York Times" commented: “Big, brave gestures with paint and color parade on energetic action paintings.” Of the works on view, "Arts magazine" observed that: “wide brush-strokes and sweeps of color glissade to the plane of the bare canvas” while stating: “adept knowledge implements a personal, fresh, clear and uncomplicated lyricism—the kind one thinks of first, enjoyable, joyous, and a little pristine.” The show was sent on to Stuttman’s Gallery in Paris, located in the twelfth arrondissement. A reviewer in "Les Arts" observed that the forms in some of Thomas’s paintings surged forward while in others they were skillfully harmonized.
When Thomas had another solo exhibition in 1961, held at Galerie Agnes Lefort in Montreal, a reviewer for the "Montreal Gazette" noted that Thomas was moving from action painting to a “more analytical observation of her wildly careening or stolid forms and receding planes in limitless space,” categorically denying the first impression made by a work. In 1962 through 1964, Thomas was featured in one-artist shows in New York; Aspen, Colorado; and East Hampton, New York. By the time her work was featured at the Rose Fried Gallery in May 1965, she had developed the more geometric and structural approach of the art in the current exhibition.
Thomas continued to paint and actively exhibit her art until the end of her life. A show of her “Yellow Paintings” was held in 2006 at Lohin Geluld Gallery in New York. She was featured in several group shows in 2008, a year before her death. In 2016, she was one of the artists included in "Women of Abstract Expressionism" exhibition catalogue, a traveling exhibition organized by the Denver Art Museum. The accompanying catalogue, consisting of essays by several scholars, celebrated “the special contributions of women to Abstract Expressionism,” providing an “essential corrective” to what has been the “unequal accounting of women’s contributions” to the movement. Like other women who embraced abstraction, Thomas did not gain renown equal to that of the male artists of her time. However, a consideration of her career reveals that the issues she addressed, the organizations in which she took part, and the zeitgeist of her art gave her a central role in the avant-garde movement that she embraced.
 Berry Campbell's exhibition, "Yvonne Thomas: Windows and Variations (Paintings 1963 - 1965)" was reviewed by Roberta Smith for The New York Times, in which Smith wrote that Thomas, "... kept her hand in, adding a fresh directness of touch, and the results give her a place in the still-emerging saga of postwar American abstraction." Berry Campbell, New York represents the Estate of Yvonne Thomas.
Thomas' work is represented in many private and public collections, including the Atlantic Richfield, Los Angeles; Brandeis University, Waltham, Massachusetts; Ciba-Geigy Collection, Greensboro, North Carolina; First Pennsylvania Bank, Philadelphia, Pennsylvania; Fonds National d’art Contemporain, Paris, France; The Foundation for Art and Preservation in Embassies; Loeb Center, New York University, New York; Metropolitan Insurance Company, New York; Mougins Musee, France; New York University, New York; National Gallery of Art, Washington, DC; Riverside Museum, New York; Seattle Art Museum, Washington.


Wolf Hilbertz

Wolf Hartmut Hilbertz (April 16, 1938August 11, 2007) was a German-born futurist architect, inventor, and marine scientist. Notable contributions to science include the discovery of artificial mineral accretetion / biorock and its use to create electrified reefs.
Personal life.
Early life.
Wolf Hilbertz was born in Gütersloh, (Germany) in 1938, the first child of Rudolf Hilbertz (1909–1995) and Erna Hilbertz, née Uslat (1906–2008). His parents had quite different personalities; whereas his father was artistic and inventive, thinking up one of the first electric razors, his mother had a more down to earth, practical approach. While his father would have liked to become an artist, circumstances forced him to start working in a bank, whereas his mother enjoyed her occupation, channeling her forceful personality into her job as a school teacher.
After Wolf Hilbertz was born, the family moved to Ústí nad Labem / Aussig in the Czech Republic. When World War II began, his father volunteered for the Wehrmacht and became a member of the Brandenburger special forces. Wolf's sister Uta was born in 1940. His father was badly wounded in Greece in 1944 and fled from the Red Army with his family towards the west in 1945.
As war refugees, he and his family settled in Detmold, Germany in 1946. He attended the Gymnasium (secondary school) there, which he didn't complete. This would normally have precluded his attending a German university. However, after completing his compulsory military service, he went to Berlin in 1959 and signed up for a high school equivalency entrance exam. He was one of the very few to earn a "pass". Thus he was able to attend the Hochschule der Künste Berlin, the Berlin University of the Arts, where he studied architecture. He married Regina Piper in December, 1962 in Berlin and, upon earning his architecture diploma in 1965, immigrated to New York City with his family in July of that year. 1966 he moved to Ann Arbor, Michigan, where he earned his Masters of Architecture at the University of Michigan in 1967.
Final years.
After suffering what were initially diagnosed as stomach problems in the spring and summer of 2007, he was diagnosed with terminal lung cancer at the end of July. Hilbertz died August 11, 2007 in Munich. He was survived by his mother († 2008), sister, his wife and two ex-wives, and five children: two sons and three daughters. The urn with his ashes was buried at the cemetery "Städtischer Friedhof Wilmersdorf" in Berlin.
Professional career.
Hilbertz worked in architects' offices in Berlin, New York, and Detroit. His first teaching position was in 1967 as an Assistant Professor at Southern University in Baton Rouge, Louisiana. Together with Phil Harding, he founded a new Architecture Department at the University. After several years there, he conceived and published the concept of Cybertecture.
In 1970 he was appointed to the faculty of the School of Architecture at the University of Texas, along with several other highly innovative new faculty, by then-Dean Alan Y. Taniguchi (1969–1972). At the University of Texas, he founded the Responsive Environments Laboratory, where he and his students developed and extended his thinking about the automated creation of the built environment. Within a very few years, he was tenured as a full professor for his work. After several years, the focus of the lab shifted to the construction of underwater structures by a method not unlike that used by living corals. The material produced has since become commonly known as accretion, seacrete or biorock.
Hilbertz' work was influenced by and influenced the work of such notables as Nicholas Negroponte. Important students and associates include Joe Mathis, Bob Swaffar, Gene Lucas, Geoffrey Wright, Forrest Higgs, Frances Carvey, Eric Vanderzee, Ed Seiber, Dr. Thomas J. Goreau, Frank Gutzeit and Ari Spenhoff.
Hilbertz laid the foundation for the discipline of Cybertecture, emergent all-encompassing evolutionary environmental systems, and invented the artificial mineral accretion process in seawater in 1976. For the rest of the 1970s, he concentrated more and more on accretion, continuing to develop and refine the process. By the time he left the University of Texas in the early 1980s, accretion had become the sole focus of his work. Starting in the late 1980s, he partnered with Dr. Thomas J. Goreau to install, maintain and monitor accretion / biorock projects in many countries.
He published extensively on his R & D and lectured widely in the Americas, Europe, and Asia, conducting hands-on workshops. His work has been exhibited on several continents. He authored several US and international patents. In 1998 he and Dr. Thomas Goreau were awarded the Theodore M. Sperry Award for Pioneers and Innovators, the top award of the Society for Ecological Restoration.
With the help of a host of dedicated associates, students, and volunteers, Hilbertz designed and implemented seascaping projects focusing on coral conservation / fish habitat, mariculture, and erosion control. Whenever possible, this was done with direct local government or community involvement and participation. Ongoing projects and concerns were the production of building materials and components, metals, minerals and gases from seawater, direct or indirect solar energy conversion, sustainable brine use and model seacology artificial/natural islands like Autopia Saya. The Autopia Saya Project in the Indian Ocean was initiated in 1997 and continued in 2002. After his death, work on accretion projects has continued.
His academic affiliations as an environmental educator and researcher included Southern University, McGill University, the University of the Arts Bremen, and The University of Texas, where he also held an appointment as Sr. Research Scientist in Marine Sciences. He founded the Symbiotic Processes Laboratory (UT). Hilbertz formed and directed The Marine Resources Co., was a co-founder and Director of Biorock Inc., and founder and President of Sun & Sea e.V., a non-profit NGO.


Paul Chidlaw

Paul Chidlaw (April 5, 1900April 25, 1989) was an American painter and art instructor who spent most of his career in Cincinnati, Ohio.
Early life, studies and travels.
Paul Chidlaw was born in Cleves, Ohio on April 5, 1900 to Edward H. and Carolyn (Guise) Chidlaw. He resided in Cincinnati for the majority of his life. He was obsessed with the art world since the age of eight when he would get clay from the fields and creeks to make ceramics. When he was growing up in Cincinnati his aunts would take him to the Cincinnati Art Museum and they would point out the "finished" and "unfinished" works. The Frank Duveneck paintings were "unfinished."
He studied at the Art Academy of Cincinnati from 1919 to 1923.
In 1927, after working as a designer for commercial firms in Cincinnati for several years, he traveled to France and studied at L'Ecole des Beaux-Arts in Fontainebleau. He later moved to Paris and studied with Jean Despujols and André Lhote. Chidlaw found that his formal academic art training was restrictive. In 1989 while reflecting on his studies in France, Chidlaw remarked: "Because of my academic training, my painting was rather reserved. I was always trying to imitate nature. I wasn't as free. I was more less in a box." Not having yet achieved renown as an artist himself, Chidlaw had to finance his stay in Paris by finding employment in a foreign exchange section at a banker's trust.
After traveling extensively in Europe, Chidlaw lived in Morocco for a year.
Professional career.
Chidlaw returned to Cincinnati in 1935 and taught and painted various commissions including Works Progress Administration (WPA) murals under the Federal Art Project. During World War II, he served in the United States Army Corps of Engineers.
He taught at the Art Academy of Cincinnati from 1947 until his retirement in 1963.
After retirement, he taught drawing and painting in a studio in the Rookwood Building in Mount Adams from 1964 to 1977, when he was appointed artist-in-residence at Edgecliff College. In 1979 Edgecliff awarded him an honorary doctorate.
Toward the end of his life, his eyesight failed due to macular degeneration but he then turned to music to inspire his final abstract paintings.
Recognition and legacy.
His paintings include: "At the Wailing Wall" (an oil painting on canvas), and "The Farm Has a Song" (an oil painting on canvas in 1978). He painted in oil, watercolor, acrylic, etchings, pastel, charcoal and pencil. In his 1980 painting "Boogie Woogie", a "cheerful pastiche of color suggests a deluge of bright streamers and confetti drifting down from a pale winter sky at New Year's. The mood is upbeat and celebratory."
As part of the sensory process involved in creating his art, Chidlaw used a music motif as a form. Pigments vibrated in dulcet violin tones, or reverberated as percussion, and the notes of color blended in an exultant symphony of emotion. Chidlaw felt that his use of color was one of his greatest strengths, and he gave close consideration to how colors "sounded" and mingled optically on the canvas.
His colorful abstract paintings often suggested landscapes. He also was known for his calligraphy-like gesture drawings. He mentored numerous aspiring artists at the Art Academy of Cincinnati.
In 1985, the Miami University Art Museum held a major retrospective of his work entitled, "Paul Chidlaw: Paintings and Graphics".
In 1986, the Art Academy of Cincinnati named the Chidlaw Gallery after him because they considered him to be one of the finest artists (and certainly the earliest abstract expressionist) in the 20th Century in the Cincinnati area.
Family.
Childlaw married Madge Smith, a librarian at the Cincinnati Art Museum, in 1952.
He died of heart failure on April 25, 1989 at his Hyde Park home at the age of 89. He is buried at Spring Grove Cemetery in Cincinnati.


Nsolo

Nsolo also called Chisolo is the Zambian version of mancala. Nsolo game is usually played by scooping holes in the ground and using small stones or Mongongo nuts for playing pieces. Two players scoop four rows of holes in the ground and begin to play, usually with the help of a number of bystanders. However, carved wooden game boards exist from earlier years and can also still be bought at tourist markets in Livingstone and Lusaka. Several variations of the game exist.


Malcolm Hughes

Malcolm Hughes (22 July 1920 – 19 September 1997) was a British constructive artist.
Biography.
Hughes was born in Manchester and during the Second World War, he was a radio operator in the Royal Navy. After the war he became influenced by British abstract artists of the period whilst training at the Regional College of Art in Manchester and then later at the Royal College of Art in London. Whilst he was a student in London his work was in the socialist realism style and he was involved in painting a large mural at the Royal Courts of Justice. By the 1960s he had developed his own form of constructivism and his work was exhibited at the Institute of Contemporary Arts in London and the Salon des Réalités Nouvelles in Paris.
He taught at a number of institutions during his life. During the 1960s he taught part-time at the architecture department of the Polytechnic of Central London, Bath Academy of Art and Chelsea School of Art, where he taught alongside two other constructive artists, John Ernest and Anthony Hill. In 1970 he began to teach part-time at the Slade School of Art and in 1973 began to run the graduate programme there.
His works are in a number of collections, including at the Tate, Warwick University, Manchester City Art Gallery, Sussex University and the British Council.
In 2008, his work featured in an exhibition at Southampton City Art Gallery alongside other constructive artists, including Peter Lowe and Mary Martin.


Winthrop Poll

The Winthrop Poll, also known as the "Winthrop University Poll," is a long-term survey initiative conducted by Winthrop University's Center for Public Opinion & Policy Research (CPOPR). It informs public policy makers and the general public about the attitudes and opinions of citizens in the state of South Carolina and the southern region of the United States. During the 2020 US Democratic primary, the Democratic National Committee (DNC) designated the Winthrop Poll as one of the threshold polls used to qualify presidential candidates for debates. Topics of the poll typically include political candidates and politically-relevant issues. Results of the poll are cited regularly by national and international news organizations such as Time (magazine), Politico, The Hill, the BBC, Washington Post, MSNBC, and CNN.
The Social and Behavioral Research Lab at Winthrop, which originally conducted the poll, was a charter member of the American Association for Public Opinion Research.
History.
Professor Scott Huffmon began the polling initiative in 2002 as part of a Winthrop University “Scope and Methods” research class. The first intrastate polling was conducted in 2003 and the first statewide poll took place in 2006.
In 2019, the CPOPR received over three million dollars in grants from the U.S. Centers for Disease Control and Prevention and the S.C. Department of Health and Environmental Control to support social behavior and health research.
Criticism.
Some have criticized the poll for being inaccurate or questionable. However, the poll's director, Scott Huffmon, has defended the methodology used.


Latho

Latho is a traditional solitaire game played by the Dorzé people of Ethiopia. The equipment needed to play the game is similar to that used for mancala games, i.e., a board with 2 rows of 6 "pits", and 30 counters ("seeds"). The game was first described by British academic Richard Pankhurst in 1971.
Rules.
At game setup, the 30 seeds are placed in the 2x6 pits according to the following scheme:
Although the game is technically a solitaire, it requires a second person besides the player, who has the function of a "dealer". The dealer and player must first agree about the pit of the board from which to start. The player then closes his eyes (or is blindfolded) and must declare out loud the number of seeds in each of the pits of the board, counterclockwise from the starting pit. The traditional declarations used in Ethiopia are:
As long as the declaration is correct (i.e., the pit has that exact number of seeds), the dealer will remove one seed from the pit. The game will thus continue until the board is empty (in which case the player has succeeded) or the player fails to declare the correct number of seeds.
See also.
There are several other solitaires based on mancala boards, for example:


Ryan Sullivan (artist)

Ryan Sullivan (born 1983) is an American artist, best known for his paintings.
About.
Sullivan attended the Rhode Island School of Design and graduated in 2005.
He has exhibited at various museums and galleries worldwide, including MoMA PS1; Kunstmuseum Bonn; Institute of Contemporary Art, Miami; Hydra Workshop, Greece, Flag Art Foundation, New York; Sadie Coles HQ, London; Maccarone, New York; Rubell Family Foundation, Miami; White Flag Projects, Saint Louis; and Palazzo delle Esposizioni, Rome.
In 2013, he was artist-in-residence at Chinati Foundation, Marfa, Texas and the Robert Rauschenberg Foundation, Captiva, Florida.


The Complete Stories of Franz Kafka

The Complete Stories of Franz Kafka is a compilation of all of Kafka's short stories. With the exception of three novels ("The Trial", "The Castle" and "Amerika"), this collection includes all of his narrative work. The book was originally edited by Nahum N. Glatzer and published by Schocken Books in 1971. It was reprinted in 1995 with an introduction by John Updike.
The collection includes all the works published during Kafka's lifetime, with the exception of "The Stoker" which is usually incorporated as the first chapter of his unfinished novel "Amerika". Some of the stories included in the book are fragmented or in various states of incompletion. Most of the stories are translated by Willa and Edwin Muir, with occasional translations by Tania and James Stern.
Several fables, parables and philosophical pieces are not included in this collection, as they were never meant to be independent stories or never intended for publication. These can be found in Kafka's diaries, notebooks and letters.
Contents.
Foreword by John Updike (1995 edition only)
Postscript.
By Nahum N. Glatzer
On the material included in this volume.
Notes on the writing and publication history of the stories and fragments.
Chronology.
Chronology of Kafka's life and writing.
Selected writings on Kafka.
A list of critical and biographical essays on Kafka.


David Bolduc

David Bolduc (1945–2010) was an abstract artist who used colour and central imagery in his paintings, inspired by artists such as Jack Bush. Critics suggest that he and artists such as Daniel Solomon formed a bridge between the second and third generations of Toronto modernists or even form part of the third generation of Toronto abstract painters which includes artists such as Alex Cameron and Paul Sloggett.
Biography.
The son of Eugenie and Bernard Bolduc, he attended the Ontario College of Art, Toronto (1962–63) and the School of Art and Design at the Montreal Museum of Fine Arts, studying with Arthur Lismer and Jean Goguen (1964–65). While in Montreal, he was given a solo exhibition at the city's Elysee Theatre and included in a group showing at Galerie Soixante. To earn money, Bolduc worked part time in a plastics factory. In 1966, he returned to Toronto and worked in the Royal Ontario Museum's conservation department, his only full-time job except for painting.
In 1970, Bolduc attended a major retrospective exhibition of Henri Matisse in Paris. It had 208 paintings, 28 sculptures, 13 gouaches and the monumental designs for the stained‐glass windows for the chapel of Vence as well as a ceramic wall executed after Matisse's specifications. Matisse provided a model for what Bolduc wanted, Bolduc said, "To be complex within what would seem to be a simple structure".
In 1967, his work featured groupings of shaped canvases with contoured surfaces carrying simple geometric colour designs. He subsequently abandoned colour to work with minimal constructions of stretched white vinyl and then with simple structures made of rope, wood, and mirrors.
By the mid-1970s, Bolduc had developed his personal territory, central imagery abstracts. Bolduc`s signature as a painter was a main motif articulated in impasto colour drawn directly from the tube on top of a stained background. Bolduc once said that for him the "vertical member – a figure, a tree, a stamen, a column, a mast, a pylon, a stele, a stack of colours, a line of organizational force, an armature upon which the rest of the painting was wound – began as the hands of a watch, both of them pointing straight upward to midnight". He also compared it with grass, although by that he meant grass as it is found in a Persian miniature or in a Matisse cutout.
These canvases incorporated a bold central image which, at times, was repeated across the canvas. The main motif, described by Bolduc as a carrier for colour, was rendered in bright colours and set upon a textured backdrop. Bolduc remarked on his use of colour:"I'm interested in taking a nothing colour and giving it some bite to make it warmer. I'm not trying to be innovative. I'm not trying to make an object you haven't seen before. Colour is all that I am working with".
Shows of the mid-1970s which drew together significant groupings of Toronto`s abstract painters featured Bolduc, along with other painters such as Daniel Solomon. The most important international exhibition in which Bolduc`s work was featured occurred in 1977. It was called "14 Canadians: a Critic`s Choice", and the exhibition was held at the Hirshhorn Museum in Washington, DC, curated by Andrew Hudson. For the exhibitors, it was of primary importance.
Bolduc drew inspiration for his painting from different exotic locales and travelled often to attain it, such as his 1968 trip across Europe to Turkey, overland to Nepal, returning home via Uzbekistan and Moscow. He went to India (at least 15 times), Turkey, Mexico, North Africa, China, the Himalayas, Sri Lanka, Costa Rica, Paris, Spain, Portugal. For several years in the 1990s, Bolduc lived and worked in Paris and Morocco. In Canada, Bolduc and his friend Alex Cameron made regular trips to the Rockies and Newfoundland.
He showed his work in Toronto at the commercial gallery of Carmen Lamanna from 1967 until 1975. When Bolduc decided to leave the dealer, Lamanna decided to keep most of Bolduc's unsold paintings. Naturally, Bolduc asked for them back.
Lamanna refused. Bolduc hired a lawyer to sue for the return of his work, but there are different accounts about whether the suit succeeded.
In 1976, Bolduc exhibited at the David Mirvish Gallery and, when it closed in 1977, with Alkis Klonaridis, who opened his own gallery after working for Mirvish. Later, Bolduc was affiliated for 27 years with Calgary's Paul Kuhn Gallery. A memorial show in May 2010 was held at Christopher Cutts Gallery in Toronto. Between 1968 and 2008, there was only one year – 1994 – in which new work was not featured in a solo or group exhibit.
Bolduc’s paintings can be found in major collections across Canada, including the National Gallery of Canada, the Art Gallery of Ontario, the Art Gallery of Alberta, as well as the Mirvish Collection.
Bolduc was a lifelong student of modern poetry, and he provided illustrations for numerous volumes of poetry, often for his friend Michael Ondaatje as well as for Roy Kiyooka, Wayne Clifford, Victor Coleman, and David Rosenberg. Bolduc was also a regular contributor of illustrations for the biannual literary magazine Brick, edited by Michael Ondaatje and his wife, the writer Linda Spalding.
His death followed a diagnosis of brain cancer in September 2009.


Random-access machine

In computer science, random-access machine (RAM) is an abstract machine in the general class of register machines. The RAM is very similar to the counter machine but with the added capability of 'indirect addressing' of its registers. Like the counter machine the RAM has its instructions in the finite-state portion of the machine (the so-called Harvard architecture).
The RAM's equivalent of the universal Turing machinewith its program in the registers as well as its datais called the random-access stored-program machine or RASP. It is an example of the so-called von Neumann architecture and is closest to the common notion of computer.
Together with the Turing machine and counter-machine models, the RAM and RASP models are used for computational complexity analysis. Van Emde Boas (1990) calls these three plus the pointer machine "sequential machine" models, to distinguish them from "parallel random-access machine" models.
Introduction to the model.
The concept of a random-access machine (RAM) starts with the simplest model of all, the so-called counter machine model. Two additions move it away from the counter machine, however. The first enhances the machine with the convenience of indirect addressing; the second moves the model toward the more conventional accumulator-based computer with the addition of one or more auxiliary (dedicated) registers, the most common of which is called "the accumulator".
Formal definition.
A "random-access machine" (RAM) is an abstract computational-machine model identical to a multiple-register counter machine with the addition of indirect addressing. At the discretion of an instruction from its finite state machine's TABLE, the machine derives a "target" register's address either (i) directly from the instruction itself, or (ii) indirectly from the "contents" (e.g. number, label) of the "pointer" register specified in the instruction.
By definition: A "register" is a location with both an "address" (a unique, distinguishable designation/locator equivalent to a natural number) and a "content"a single natural number. For precision we will use the quasi-formal symbolism from Boolos-Burgess-Jeffrey (2002) to specify a register, its contents, and an operation on a register:
Definition: A "direct" instruction is one that specifies "in the instruction itself" the address of the source or destination register whose contents will be the subject of the instruction.
Definition: An "indirect instruction" is one that specifies a "pointer register", the contents of which is the address of a "target" register. The target register can be either a source or a destination (the various COPY instructions provide examples of this). A register can address itself indirectly.
Definition: The contents of "source register" is used by the instruction. The source register's address can be specified either (i) directly by the instruction, or (ii) indirectly by the pointer register specified by the instruction.
Definition: The contents of the "pointer register" is the "address" of the "target" register.
Definition: The contents of the "pointer register" points to the "target register"the "target" may be either a source or a destination register.
Definition: The "destination register" is where the instruction deposits its result. The source register's address can be specified either (i) directly by the instruction, or (ii) indirectly by the pointer register specified by the instruction. The source and destination registers can be one.
Refresher: The counter-machine model.
The register machine has, for a memory external to its finite-state machinean unbounded (cf: footnote|countable and unbounded) collection of discrete and uniquely labelled locations with "unbounded" capacity, called "registers". These registers hold only natural numbers (zero and the positive integers). Per a list of sequential instructions in the finite state machine's TABLE, a few (e.g. 2) types of primitive operations operate on the contents of these "registers". Finally, a "conditional-expression" in the form of an "IF-THEN-ELSE" is available to test the contents of one or two registers and "branch/jump" the finite state machine out of the default instruction-sequence.
Base model 1: The model closest to Minsky's (1961) visualization and to Lambek (1961):
Base model 2: The "successor" model (named after the successor function of the Peano axioms):
Base model 3: Used by Elgot-Robinson (1964) in their investigation of bounded and unbounded RASPsthe "successor" model with COPY in the place of CLEAR:
Creating "convenience instructions" from the base sets.
The three base sets 1, 2, or 3 above are equivalent in the sense that one can create the instructions of one set using the instructions of another set (an interesting exercise: a hint from Minsky (1967)declare a reserved register e.g. call it "0" (or Z for "zero" or E for "erase") to contain the number 0). The choice of model will depend on which an author finds easiest to use in a demonstration, or a proof, etc.
Moreover, from base sets 1, 2, or 3 we can create "any" of the primitive recursive functions ( cf Minsky (1967), Boolos-Burgess-Jeffrey (2002) ). (How to cast the net wider to capture the "total" and "partial" mu recursive functions will be discussed in context of indirect addressing). However, building the primitive recursive functions is difficult because the instruction sets are so ... primitive (tiny). One solution is to expand a particular set with "convenience instructions" from another set:
Again, all of this is for convenience only; none of this increases the model's intrinsic power.
For example: the most expanded set would include each unique instruction from the three sets, plus unconditional jump J (z) i.e.:
Most authors pick one or the other of the conditional jumps, e.g. Shepherdson-Sturgis (1963) use the above set minus JE (to be perfectly accurate they use JNZJump if "Not" Zero in place of JZ; yet another possible convenience instruction).
The "indirect" operation.
Example of indirect addressing.
In our daily lives the notion of an "indirect operation" is not unusual.
Indirection specifies a location identified as the pirate chest in "Tom_&_Becky's_cave..." that acts as a "pointer" to any other location (including itself): its contents (the treasure map) provides the "address" of the "target" location
"under_Thatcher's_front_porch" where the real action is occurring.
Why the need for an indirect operation: Two major problems with the counter-machine model.
In the following one must remember that these models are abstract models with two fundamental differences from anything physically real: unbounded numbers of registers each with unbounded capacities. The problem appears most dramatically when one tries to use a counter-machine model to build a RASP that is Turing equivalent and thus compute any partial mu recursive function:
So how "do" we address a register beyond the bounds of the finite state machine? One approach would be to modify the "program"-instructions (the ones stored in the registers) so that they contain more than one command. But this too can be exhausted unless an instruction is of (potentially) unbounded size. So why not use just one "über-instruction"one really really big numberthat contains "all" the program instructions encoded into it! This is how Minsky solves the problem, but the Gödel numbering he uses represents a great inconvenience to the model, and the result is nothing at all like our intuitive notion of a "stored program computer".
Elgot and Robinson (1964) come to a similar conclusion with respect to a RASP that is "finitely determined". Indeed it can access an unbounded number of registers (e.g. to fetch instructions from them) but only if the RASP allows "self modification" of its "program" instructions, and has encoded its "data" in a Gödel number (Fig. 2 p. 396).
In the context of a more computer-like model using his RPT (repeat) instruction Minsky (1967) tantalizes us with a solution to the problem (cf p. 214, p. 259) but offers no firm resolution. He asserts:
He offers us a "bounded" RPT that together with CLR (r) and INC (r) can compute any primitive recursive function, and he offers the unbounded RPT quoted above that as playing the role of μ operator; it together with CLR (r) and INC (r) can compute the mu recursive functions. But he does not discuss "indirection" or the RAM model per se.
From the references in Hartmanis (1971) it appears that Cook (in his lecture notes while at UC Berkeley, 1970) has firmed up the notion of indirect addressing. This becomes clearer in the paper of Cook and Reckhow (1973)Cook is Reckhow's Master's thesis advisor. Hartmanis' modelquite similar to Melzak's (1961) modeluses two and three-register adds and subtracts and two parameter copies; Cook and Reckhow's model reduce the number of parameters (registers called out in the program instructions) to one call-out by use of an accumulator "AC".
The solution in a nutshell: Design our machine/model with unbounded indirectionprovide an "unbounded" "address" register that can potentially name (call out) any register no matter how many there are. For this to work, in general, the "unbounded" register requires an ability to be cleared and then incremented (and, possibly, decremented) by a potentially infinite loop. In this sense the solution represents the unbounded μ operator that can, if necessary, hunt ad infinitim along the unbounded string of registers until it finds what it is looking for. The pointer register is exactly like any other register with one exception: under the circumstances called "indirect addressing" it provides "its" contents, rather than the address-operand in the state machine's TABLE, to be the address of the target register (including possibly itself!).
Bounded indirection and the primitive recursive functions.
If we eschew the Minsky approach of one monster number in one register, and specify that our machine model will be "like a computer" we have to confront this problem of indirection if we are to compute the recursive functions (also called the μ-recursive functions )both total and partial varieties.
Our simpler counter-machine model can do a "bounded" form of indirectionand thereby compute the sub-class of primitive recursive functionsby using a primitive recursive "operator" called "definition by cases" (defined in Kleene (1952) p. 229 and Boolos-Burgess-Jeffrey p. 74). Such a "bounded indirection" is a laborious, tedious affair. "Definition by cases" requires the machine to determine/distinguish the contents of the pointer register by attempting, time after time until success, to match this contents against a number/name that the case operator "explicitly" declares. Thus the definition by cases starts from e.g. the lower bound address and continues ad nauseam toward the upper bound address attempting to make a match:
"Bounded" indirection will not allow us to compute the partial recursive functionsfor those we need "unbounded" indirection aka the μ operator.
To be Turing equivalent the counter machine needs to either use the unfortunate single-register Minsky Gödel number method, or be augmented with an ability to explore the ends of its register string, ad infinitum if necessary. (A failure to find something "out there" defines what it means for an algorithm to fail to terminate; cf Kleene (1952) pp. 316ff "Chapter XII Partial Recursive Functions", in particular p. 323-325.) See more on this in the example below.
Unbounded indirection and the partial recursive functions.
For "unbounded" indirection we require a "hardware" change in our machine model. Once we make this change the model is no longer a counter machine, but rather a random-access machine.
Now when e.g. INC is specified, the finite state machine's instruction will have to specify "where" the address of the register of interest will come from. This "where" can be either (i) the state machine's instruction that provides an "explicit label", or (ii) the "pointer-register" whose "contents" is the address of interest. Whenever an instruction specifies a register address it now will "also" need to specify an additional parameter "i/d""indirect/direct". In a sense this new "i/d" parameter is a "switch" that flips one way to get the direct address as specified in the instruction or the other way to get the indirect address from the pointer register (which pointer registerin some models every register can be a pointer registeris specified by the instruction). This "mutually exclusive but exhaustive choice" is yet another example of "definition by cases", and the arithmetic equivalent shown in the example below is derived from the definition in Kleene (1952) p. 229.
The indirect COPY instruction.
Probably the most useful of the added instructions is COPY. Indeed, Elgot-Robinson (1964) provide their models P0 and P'0 with the COPY instructions, and Cook-Reckhow (1973) provide their accumulator-based model with only two indirect instructionsCOPY to accumulator indirectly, COPY from accumulator indirectly.
A plethora of instructions: Because any instruction acting on a single register can be augmented with its indirect "dual" (including conditional and unconditional jumps, cf the Elgot-Robinson model), the inclusion of indirect instructions will double the number of single parameter/register instructions (e.g. INC (d, r), INC (i, r)). Worse, every two parameter/register instruction will have 4 possible varieties, e.g.:
In a similar manner every three-register instruction that involves two source registers rs1 rs2 and a destination register rd will result in 8 varieties, for example the addition:
will yield:
If we designate one register to be the "accumulator" (see below) and place strong restrictions on the various instructions allowed then we can greatly reduce the plethora of direct and indirect operations. However, one must be sure that the resulting reduced instruction-set is sufficient, and we must be aware that the reduction will come at the expense of more instructions per "significant" operation.
The notion of "accumulator A".
Historical convention dedicates a register to the accumulator, an "arithmetic organ" that literally accumulates its number during a sequence of arithmetic operations:
However, the accumulator comes at the expense of more instructions per arithmetic "operation", in particular with respect to what are called 'read-modify-write' instructions such as "Increment indirectly the contents of the register pointed to by register r2 ". "A" designates the "accumulator" register A:
If we stick with a specific name for the accumulator, e.g. "A", we can imply the accumulator in the instructions, for example,
However, when we write the CPY instructions without the accumulator called out the instructions are ambiguous or they must have empty parameters:
Historically what has happened is these two CPY instructions have received distinctive names; however, no convention exists. Tradition (e.g. Knuth's (1973) imaginary MIX computer) uses two names called LOAD and STORE. Here we are adding the "i/d" parameter:
The typical accumulator-based model will have all its two-variable arithmetic and constant operations (e.g. ADD (A, r), SUB (A, r) ) use (i) the accumulator's contents, together with (ii) a specified register's contents. The one-variable operations (e.g. INC (A), DEC (A) and CLR (A) ) require only the accumulator. Both instruction-types deposit the result (e.g. sum, difference, product, quotient or remainder) in the accumulator.
If we so choose, we can abbreviate the mnemonics because at least one source-register and the destination register is always the accumulator A. Thus we have :
The notion of indirect address register "N".
If our model has an "unbounded accumulator" can we "bound" all the other registers? Not until we provide for at least one unbounded register from which we derive our indirect addresses.
The minimalist approach is to use itself (Schönhage does this).
Another approach (Schönhage does this too) is to declare a specific register the "indirect address register" and confine indirection relative to this register (Schonhage's RAM0 model uses both A and N registers for indirect as well as direct instructions). Again our new register has no conventional nameperhaps "N" from "iNdex", or "iNdirect" or "address Number".
For maximum flexibility, as we have done for the accumulator Awe will consider N just another register subject to increment, decrement, clear, test, direct copy, etc. Again we can shrink the instruction to a single-parameter that provides for direction and indirection, for example.
Why is this such an interesting approach? At least two reasons:
(1) An instruction set with no parameters:
Schönhage does this to produce his RAM0 instruction set. See section below.
(2) Reduce a RAM to a Post-Turing machine:
Posing as minimalists, we reduce all the registers excepting the accumulator A and indirection register N e.g. r = { r0, r1, r2, ... } to an unbounded string of (very-) bounded-capacity pigeon-holes. These will do nothing but hold (very-) bounded numbers e.g. a lone bit with value { 0, 1 }. Likewise we shrink the accumulator to a single bit. We restrict any arithmetic to the registers { A, N }, use indirect operations to pull the contents of registers into the accumulator and write 0 or 1 from the accumulator to a register:
We push further and eliminate A altogether by the use of two "constant" registers called "ERASE" and "PRINT": [ERASE]=0, [PRINT]=1.
Rename the COPY instructions and call INC (N) = RIGHT, DEC (N) = LEFT and we have the same instructions as the Post-Turing machine, plus an extra CLRN :
Turing equivalence of the RAM with indirection.
In the section above we informally showed that a RAM with an unbounded indirection capability produces a Post–Turing machine. The Post–Turing machine is Turing equivalent, so we have shown that the RAM with indirection is Turing equivalent.
We give here a slightly more formal demonstration. Begin by designing our model with three reserved registers "E", "P", and "N", plus an unbounded set of registers 1, 2, ..., n to the right. The registers 1, 2, ..., n will be considered "the squares of the tape". Register "N" points to "the scanned square" that "the head" is currently observing. The "head" can be thought of as being in the conditional jumpobserve that it uses indirect addressing (cf Elgot-Robinson p. 398). As we decrement or increment "N" the (apparent) head will "move left" or "right" along the squares. We will move the contents of "E"=0 or "P"=1 to the "scanned square" as pointed to by N, using the indirect CPY.
The fact that our tape is left-ended presents us with a minor problem: Whenever LEFT occurs our instructions will have to test to determine whether or not the contents of "N" is zero; if so we should leave its count at "0" (this is our choice as designersfor example we might have the machine/model "trigger an event" of our choosing).
The following table both defines the Post-Turing instructions in terms of their RAM equivalent instructions and gives an example of their functioning. The (apparent)location of the head along the tape of registers r0-r5 . . . is shown shaded:
Example: Bounded indirection yields a machine that is not Turing equivalent.
Throughout this demonstration we have to keep in mind that the instructions in the finite state machine's TABLE is "bounded", i.e. "finite":
We will build the indirect CPY ( i, q, d, φ ) with the CASE operator. The address of the target register will be specified by the contents of register "q"; once the CASE operator has determined what this number is, CPY will directly deposit the contents of the register with that number into register "φ". We will need an additional register that we will call "y"it serves as an up-counter.
The CASE "operator" is described in Kleene (1952) (p. 229) and in Boolos-Burgess-Jeffrey (2002) (p. 74); the latter authors emphasize its utility. The following definition is per Kleene but modified to reflect the familiar "IF-THEN-ELSE" construction.
The CASE operator "returns" a natural number into φ depending on which "case" is satisfied, starting with "case_0" and going successively through "case_last"; if no case is satisfied then the number called "default" (aka "woops") is returned into φ (here x designates some selection of parameters, e.g. register q and the string r0, ... rlast )):
"Definition by cases" φ (x, y):
Kleene require that the "predicates" Qn that doing the testing are all mutually exclusive"predicates" are functions that produce only { true, false } for output; Boolos-Burgess-Jeffrey add the requirement that the cases are "exhaustive".
We begin with a number in register q that represents the address of the target register. But what is this number? The "predicates" will test it to find out, one trial after another: JE (q, y, z) followed by INC (y). Once the number is identified explicitly, the CASE operator directly/explicitly copies the contents of this register to φ:
Case_0 ( the base step of the recursion on y) looks like this:
Case_n (the induction step) looks like this; remember, each instance of "n", "n+1", ..., "last" must be an explicit natural number:
Case_last stops the induction and bounds the CASE operator (and thereby bounds the "indirect copy" operator):
If the CASE could continue ad infinitum it would be the mu operator. But it can'tits finite state machine's "state register" has reached its maximum count (e.g. 65365 = 11111111,111111112 ) or its table has run out of instructions; it is a "finite" machine, after all.
Examples of models.
Register-to-register ("read-modify-write") model of Cook and Reckhow (1973).
The commonly encountered Cook and Rechkow model is a bit like the ternary-register Malzek model (written with Knuth mnemonicsthe original instructions had no mnemonics excepting TRA, Read, Print).
Schönhage's RAM0 and RAM1 (1980).
Schönhage (1980) describes a very primitive, atomized model chosen for his proof of the equivalence of his SMM [[pointer machine]] model:
RAM1 model: Schönhage demonstrates how his construction can be used to form the more common, usable form of "successor"-like RAM (using this article's mnemonics):
RAM0 model: Schönhage's RAM0 machine has 6 instructions indicated by a single letter (the 6th "C xxx" seems to involve 'skip over next parameter'. Schönhage designated the accumulator with "z", "N" with "n", etc. Rather than Schönhage's mnemonics we will use the mnemonics developed above.
Indirection comes (i) from CPYAN (copy/transfer contents A to N) working with store_A_via_N STAN, and from (ii) the peculiar indirection instruction codice_25.
Footnotes.
Finite vs unbounded.
The definitional fact that any sort of counter machine without an unbounded register-"address" register must specify a register "r" by name indicates that the model requires "r" to be "finite", although it is "unbounded" in the sense that the model implies no upper limit to the number of registers necessary to do its job(s). For example, we do not require r < 83,617,563,821,029,283,746 nor r < 2^1,000,001, etc.
We can escape this restriction by providing an unbounded register to provide the address of the register that specifies an indirect address.
References.
With a few exceptions, these references are the same as those at [[Register machine]].
[[Category:Register machines]]


Jonathan S Hooper

Jonathan S Hooper (born 1962) is a British painter and sculptor.
Jonathan Hooper was brought up in Cornwall, southwest England, in the 1960s. His father, Harry Hooper, was also a painter. He studied structural engineering at university, followed by a master's degree from Imperial College London.
Hooper worked in Japan for three years. After returning from Japan, Hooper worked on painting and sculpture, influenced by his interest in Japanese calligraphy and printing techniques. Hooper has held exhibitions at The Nine British Art and elsewhere. He has also produced books.