The following text was written collaboratively by Carolyn Pillers Dobler, Professor and Chair, Department of Mathematics and Computer Science, Gustavus Adolphus College, whose research and teaching is in statistics, with interests in mathematical origami, data visualization, and mathematics education; and Donald Myers, Director of the Hillstrom Museum of Art and Instructor in the Department of Art and Art History. It was produced as part of a recurring exhibition program of the Hillstrom Museum of Art titled FOCUS IN/ON, in which individual works in the Hillstrom Collection are explored in depth in a collaborative process that engages the expertise of College community members across the curriculum. The text was featured in the Museum’s exhibition FOCUS IN/ON: Henry Schnakenberg’s Dominoes, on view from February 15 through April 18, 2010, in which was displayed a 1956 oil painting by American artist Henry Schnakenberg (1892-1970), a gift to the Museum from Reverend Richard L. Hillstrom in 2000. That painting, a still life, was the impetus for the study, which considers Schnakenberg, his work, style and career, as well as the history of dominoes and mathematical circumstances and problems associated with them.
An Artist Characterized
A t a memorial service for American Realist Henry Schnakenberg (1892-1970), artist of the Hillstrom Museum of Art’s 1956 oil painting Dominoes, poet Louis Untermeyer (1885-1977) praised the late painter in a tribute that was reproduced in the Newtown (Connecticut) newspaper, the Bee. Untermeyer, a celebrated author and Poet Laureate to the Library of Congress in the early 1960s, had become friends with Schnakenberg when he moved to Newtown in 1947 after having spent the earlier part of his illustrious artistic career in New York City. The poet praised the artist not only for his artwork but also for his fine qualities as a person, calling him “Good at heart and good in deed, generous in act and in spirit,” concluding that “…Henry was loved by everyone.” About Schnakenberg and art, Untermeyer said, “To watch him handle a work of art or admire a painting was infectious to those who were with him,” and he quoted his friend as saying that “’an artist paints as he lives.’” An obituary for the artist in the New York Times echoed Schnakenberg’s self-assessment, calling him, in its headline, “An Artist of Everyday Themes,” and in the main text, “an imaginative realist.”
These descriptions are indicative of two frequently noted qualities of the artist. First, that he was a good and kind person who sought to help others and who was devoted to causes in which he believed. And second, that his art was solidly based in reality, as well as very accomplished. Schnakenberg’s characteristics had been described over thirty years earlier in a November 28, 1936 article in The New Yorker, by critic and social philosopher Lewis Mumford (1895-1990). In reviewing the third biennial exhibition at the Whitney Museum of American Art, he cited the artist along with two other highly admired and prominent Americans, Edward Hopper (1882-1967) and Reginald Marsh (1898-1954), as the best of a group of contemporary American painters he termed “the Poets of the Actual.” Noting the excellence of their craftsmanship, Mumford observed that what these three esteemed artists also had in common was their attitude towards their subject matter.
Schnakenberg’s painting Dominoes, donated to the Museum in 2000 by Reverend Richard L. Hillstrom, is characteristic of the artist’s generally prosaic approach, as is his Romantic Landscape (1939) in the collection of the Minneapolis Institute of Arts, an oil painting that, despite its suggestive title, was neither reflective of a particular character nor a depiction of a particular spot, but had its genesis in the artist’s chance viewing of a heron alighting on a tree stump (according to the artist’s description of the painting in a catalogue of a 1955 exhibition at the Wadsworth Atheneum in Hartford, Connecticut). Other works by Schnakenberg acquired by major American museums similarly consider, with neither nostalgia nor satire, their subject. The Art Institute of Chicago, for instance, acquired in 1933 a watercolor depicting a corner of the Spanish village of Ronda (1929), while an oil painting purchased by the Metropolitan Museum of Art, New York in 1937, titled Mourning Doves, shows several birds startled to flight from a wheat field. In all these works, the ordinary is not exactly elevated, but is considered with incisive sympathy and is depicted in an accomplished but unmannered way—the essence of Schnakenberg’s art.
Early Life and Career
The artist was born in 1892 in New Brighton, an independent village on Staten Island that was incorporated into New York City in 1898. His father Daniel was successful in the insurance industry, and Schnakenberg initially followed him into that business after graduating from Staten Island Academy. His interest in art was piqued by studies of painting at school, by the old master prints his father owned by artists like Albrecht Dürer (1471-1528) and Rembrandt van Rijn (1606-1669), and by watercolors of European travels made by his uncle, a professor at the University of Strasbourg. While working days in insurance, Schnakenberg was enrolled in night classes at the Art Students League in New York.
In 1913, he saw the famous Armory Show, the exhibit that introduced modernism to an eager American audience by highlighting contemporary European and American art. Like so many young artists, Schnakenberg was much affected by this experience. One group well represented in the exhibition was the Ash Can School. It was one of the first modern movements in American art, centered around a group of artists who eschewed late nineteenth century attitudes and themes, abandoning romantic landscapes and the like for more contemporary, sometimes gritty, often urban subject matter. Many of the artists associated with the Ash Can approach were also connected with the Art Students League where Schnakenberg was studying. He resolved to become an artist, leaving insurance and enrolling full-time at the League. There his principal mentor was the painter Kenneth Hayes Miller (1876-1952), whose insistence on clear forms, logical structure, and solid compositions that drew from the classic tradition dating back to the Renaissance, were to be a fundamental influence on Schnakenberg and his work, including the Hillstrom painting of Dominoes.
Schnakenberg found success quickly. In 1914, one of his paintings, titled Monday—a slice of urban life depicting wash hung out on the roof by a New York City apartment dweller who chats across the alley with a neighbor at her window balcony (private collection)—was chosen by a jury for exhibition at the National Academy of Design. A few years later, in 1917, he exhibited two works at the Society of Independent Artists. This organization held annual exhibits in which members could show without being juried and at which prizes were not awarded, an attitude that made an impression on Schnakenberg. Any member who paid the entry fee could participate, and although the Society tended to show avant-garde artists, that same year, its director, artist Marcel Duchamp (1887-1968) resigned when his infamous work Fountain, a urinal signed “R. Mutt,” was refused for exhibition by the Society.
The first major exhibition of the young Schnakenberg’s work was in 1921, when nineteen of his paintings were shown with works by American Futurist painter Joseph Stella (1877-1946). This was at the Whitney Studio Club, which had been formed by wealthy heiress and champion of contemporary American art Gertrude Vanderbilt Whitney. The Studio Club was a forerunner of the Whitney Museum of American Art, founded in 1931, an institution with which Schnakenberg had an enduring relationship. In 1944, he served as spokesperson for a group of over 150 artists who expressed to the President of the Whitney Board their appreciation of and fondness for the museum, a short time after its closure had been feared. Over twenty years later, Schnakenberg was one of a few special guest speakers, along with famed photographer Edward Steichen (1879-1973) and prominent author James Michener (1907-1997), at a celebration of the fiftieth anniversary of the Whitney.
Schnakenberg also remained associated with his old school, the Art Students League. He taught classes there on still life—a genre for which he became particularly known—during the 1923-1924 and 1924-1925 academic years, and in 1930 he was elected as President of the League’s Board of Control, at a difficult time when factional struggles at the school had led to the resignation from the Presidency by artist John Sloan (1871-1951), with whom Schnakenberg continued to maintain a friendship despite the political infighting.
Interests and Generosity of an Artist
He was interested in all kinds of art, not just his own and that of like-minded contemporaries. He experimented for a time with abstract art and, while he appreciated it, he recognized that it was not the right choice for him. In the memorial tribute cited above, Louis Untermeyer noted about Schnakenberg that, “Although he admired certain abstract artists, he was fully aware that it wasn’t part of his makeup to join the movement. He remained always honest to himself.”
Schnakenberg was an art collector, of work from different periods and cultures, including Asian art, Pre-Columbian sculpture, paintings by important French artists, and works by contemporaries—the purchase of which allowed him to support fellow artists. He was a frequent donor of art to several museums, including the Yale University Art Gallery, the Wadsworth Atheneum, and the Staten Island Museum. And he wrote on a variety of kinds of art, in articles published in The Arts in the mid 1920s that included critiques of the American mystical romantic artist Albert Pinkham Ryder (1847-1917) and of the eighteenth-century French genre artist Jean-Baptiste-Siméon Chardin (1699-1779). In another article, titled “Art at the Museum of Natural History,” he sought to point out that, in addition to being a showcase of the wonders of the natural world, the New York museum was also “a great storehouse of the art of vanished peoples.” Schnakenberg was also a generous donor to the Museum of Natural History, of both art and natural objects such as a large cut smoky quartz of over 2000 carats he gave in 1937 in memory of his father.
His generosity extended to using his time for causes in support of other artists. In 1938, Schnakenberg was awarded an honorary doctorate from the University of Vermont, Burlington, in part for his “helpful attitude toward young artists,” and he was involved in efforts to convince museums like the Metropolitan Museum of Art and the Pennsylvania Academy of the Fine Arts, Philadelphia, to do more to support emerging American artists. One of these efforts was a campaign to eliminate cash prize awards—which he thought were always misleading and often arbitrary—and instead have host museums use the money to purchase artwork from young artists. And Schnakenberg was generous with his own money as well: he donated five thousand dollars to the Wadsworth Atheneum in 1955 to establish a fund for the purchase of contemporary American painting and sculpture.
The next year was when Schnakenberg painted the Hillstrom still life of Dominoes. It was exhibited numerous times prior to its acquisition in 1969 by Reverend Hillstrom, including in an exhibit titled Sports and Recreation Panorama, held at the Davenport (Iowa) Municipal Art Gallery (now the Figge Art Museum) in 1959. And it was lent in 1964 to 1965 to the New York City Board of Education for exhibition at their premises.
The painting was featured in a solo exhibition of the artist’s works at New York’s Kraushaar Galleries, which represented Schnakenberg for many years and which held eighteen exhibitions of his work between 1927 and 1969, plus a memorial exhibit in 1976. Dominoes was in the fifteenth of Kraushaar’s lifetime exhibits, on view in January, 1960. It was mentioned in a New York Times review of January 15, 1960, which noted that Schnakenberg had recorded in the exhibited works many of his “visual pleasures,” citing specifically “still-lifes of chess pieces and dominos.”
The Hillstrom painting was shown the following month as well, at a solo exhibition held at the Stamford (Connecticut) Museum. A review of that exhibit in the March 11, 1960 Newtown Bee said of Schnakenberg, “He maintains a straight-forward descriptive style, ignoring the popular abstractionist mode.” It stated further that the works on view were “records of the artist’s pleasure and appreciation of his immediate surroundings,” including “the small things we have about which we do not think of as material for paintings,” specifically mentioning dominoes in a list that followed.
The New York Times review of the earlier Kraushaar exhibition also mentioned a still life of Chessmen, a work of the same dimensions as Dominoes that was painted a year later, in 1957. Interestingly, in June, 1960, a few months after the Kraushaar exhibition, Schnakenberg received a letter, preserved in the Archives of American Art, from Marcel Duchamp, who apparently had seen or read about the depiction of chess pieces and wrote to Schnakenberg as part of an effort on behalf of the American Chess Foundation. Duchamp indicated that he had a lifelong interest in chess and its cultural and intellectual value, and that as chairman of the Foundation’s “Arts Committee for American Chess,” he was enlisting the support of people in the art world to make gifts of paintings that could be sold to raise funds to support American participation in international chess events. It seems likely that Duchamp hoped that Schnakenberg might donate his painting Chessmen for the cause.
The Game of Dominoes
Perhaps Duchamp assumed Schnakenberg was also a chess aficionado, though there is no indication that the artist had particular interest in the game. Similarly, the Hillstrom painting could be just a carefully considered arrangement of dominoes the artist depicted in a visually compelling still life, although it’s possible Schnakenberg may have enjoyed playing dominoes, and the reviewer of the Stamford Museum exhibition referred to the painting as “an interrupted game….” The 1950s saw a strong interest in the game. According to a 1959 publication, there was a craze for dominoes around that time in San Francisco, where the book was published, and perhaps this was also the case on the east coast, since the game has always had a certain popularity. Domino tournaments are still held today, especially in the southern United States where the initial appeal of the game was related to prohibitions regarding playing card games, since dominoes can be played in a similar manner.
Games of dominoes begin with shuffling, in which the pieces are placed face down on a flat surface and mixed around. Each player then selects, or draws, dominoes to create a hand. There are two main types of domino play, blocking games and bidding games. In the first, contestants take turns playing from their hand a domino that matches one of the halves of a domino already played. Bidding games are played similar to card games such as bridge or spades, and involve winning tricks.
The physical form of the domino is somewhat a hybrid of a playing card and an ordinary six-sided die. Domino tiles have a rectangular face that is twice as long as it is wide. Each face is divided into two square halves by a line, and in a standard double-six set, each half has zero to six dots or pips, which are arranged in patterns identical to those on dice. The double-six set consists of a deck of twenty-eight dominoes, which represents all the possible face combinations of zero through six pips. Dominoes were traditionally made from ivory or bone, with more modern versions typically of plastic or wood. Their origin is uncertain, although there is some evidence that they were known in China, and they became widespread and common in Europe during the eighteenth century.
Despite the suggestion in print that the Hillstrom painting represents a game of dominoes in progress, this is clearly not the case, because in play the pieces lie flat or are held in hands, and none are left in their storage box, unlike some of the pieces in Schnakenberg’s still life. The box depicted in Dominoes appears to be an appropriate size for a double-six set if packed on end in seven rows of four pieces each. A lid partially covers the box, further indication that a game is not occurring.
Dominoes in Still Lifes
Given that play is not in progress in the Hillstrom painting, it seems likely that Schnakenberg may have chosen to depict the dominoes (and perhaps also the chess pieces of the related painting) in a still life simply because of their visual appeal and not for any particular ardor for the game. In arranging dominoes into a visually significant pattern, one approach that an artist might take would be to explore what mathematicians call tiling a plane. In planar tiling problems, an attempt is made to completely cover a two-dimensional area with planar tiles so that the entire area is covered by tiles and there are no overlaps or gaps. A domino can be considered a rectangular planar tile with dimensions of one unit by two units. Assuming the use of a double-six set of dominoes, the problem would be to cover a grid with the same number of units as all the planar tiles or dominoes, a total of fifty-six units (since there are twenty-eight dominoes in the standard set and each domino has two square units). This strictly two-dimensional mode of composing dominoes is the one used by contemporary printmaker Susan Gillette (born 1960) in her 2004 lithographs Domino Theory I and Domino Theory II, which are related to planar tiling questions.
However, for Schnakenberg, who is known for his depiction of three-dimensional space in the classic manner of Renaissance art, such an approach would have had little appeal. Certainly the Hillstrom painting of Dominoes shows the artist’s interest in creating carefully constructed compositions, in three dimensions, of ordinary objects, a method frequently encountered in his still lifes.
Comments made in a 1931 monographic study titled H. E. Schnakenberg, by art critic and museum curator Lloyd Goodrich (later director of the Whitney Museum of American Art) apply to this painting. Noting that still life was a favorite genre for Schnakenberg, Goodrich described his painstaking manner of arranging objects in still lifes, pointing out what he termed Schnakenberg’s “fine austerity and purity of style” in selecting his subject matter. The artist gave priority to three-dimensional values and was highly “interested in the reality of solid forms in space.” An earlier critic of Schnakenberg’s work, Margaret Bruening, wrote in a 1926 article titled “The Realism of H. E. Schnakenberg” (International Studio) that, “The seriousness and solidity of this spatial composition are apparent in the slightest of these still lifes, however amusing their trivial objects may appear or how apparently casual their arrangement.”
Still lifes are fundamentally different than other types of painting such as portraiture or landscape, since the artist has a great deal of leeway to physically manipulate and arrange the inanimate objects in order to convey pictorial qualities such as balance, color, or shape. Especially given that Schnakenberg taught classes in still life, it is interesting to speculate on what his strategy, or that of one of his students, might have been in an assignment to paint an image of dominoes. A likely starting point would be a box of double-six dominoes, and it’s probable that in arranging a still life from these, Schnakenberg would have imposed on himself or his student certain restrictions, including requirements such as having about half of the dominoes placed in the composition, and avoiding having the dominoes arranged in any symmetrical or predictable pattern, but instead making their arrangement appear somewhat random. The latter has natural appeal given that in the game of dominoes there is an element of randomness. While some games such as chess or checkers are strictly strategic in nature, and others such as the card game war are based purely on chance, dominoes is a hybrid involving both strategy and chance. In strictly mathematical terms, the word random refers to outcomes that are uncertain or unpredictable. In drawing dominoes for a hand, for example, assuming sufficient shuffling has occurred, the dominoes selected cannot be anticipated. But there is a concept of expectation in random processes, which is basically the average in the long run, and which gives some sense of how the end result of, for instance, choosing dominoes will appear.
Assuming a concern for the appearance of randomness, it can be asked what a teacher like Schnakenberg would expect to see in a still life assignment based on dominoes. He or his student would probably use a typical size of canvas, on which the dominoes would be depicted in a seemingly random configuration. Although the possible arrangements of dominoes are limitless, a student likely would show around half of the set, fourteen out of twenty-eight, probably with about half of the total squares visible, twenty-eight out of fifty-six, and with about half of the total number of pips visible, eighty-four out of 168, and about half of the doubles dominoes shown, three or four out of seven. Further, a student would probably choose the squares to be distributed fairly equally throughout the seven possible pip pairings. The dominoes themselves would be posed in a variety of ways, some lying flat, some standing horizontally or vertically, and some stacked, again, in relatively equal proportions.
Schnakenberg’s own arrangement of dominoes is in many ways as might be anticipated in such an assignment, although there are some subtle and surprising departures from the expected. He shows fifteen dominoes, with twenty-nine squares fully or partially visible, seventy-six pips in view, and three double dominoes displayed, varying only slightly from what might be expected. Further, the groupings of pips on the twenty-nine visible or partially visible squares are distributed in roughly equal proportions throughout the possible configurations, with a few more sixes and a few less threes than average. Schnakenberg stands a couple more dominoes horizontally than one might expect. But in general, any deviations from the anticipated are slight and fall well within the range of statistical sampling variability.
Schnakenberg departs significantly from the expected in two notable ways, however. In most standard or typical rectangular canvases, the shorter edge measures at least half of the longer edge, but Schnakenberg’s canvas measures approximately nine by twenty inches. Although he did a number of paintings of this size in the mid 1950s (including the still life of Chessmen described above), in this case it seems particularly significant and appropriate, because its horizontality suggests and amplifies the domino shape, especially since the proportions of the canvas are approximately one to two, the same as a domino.
But Schnakenberg’s subtlest departure from the expected can only be detected by close inspection of his domino configurations. The domino with six pips on one half and four pips on the other appears twice in the painting! While this may have been an oversight on the part of the artist, his deliberative nature suggests that he intentionally repeated that particular domino, perhaps as some sort of significant or symbolic gesture.
Whatever might have been Schnakenberg’s specific intentions with regard to the arrangement and details of the dominoes in the Hillstrom still life, he was interested in not only the physical reality of his subject, but more besides. In a 1961 Whitney Museum of American Art publication titled American Art of Our Century, by Lloyd Goodrich and John I. H. Baur, it was noted about the artist that “He is interested in many aspects of the world for their aesthetic possibilities: their offering of things pleasurable in themselves, and from which design can be created. His aim is less to express subjective emotion than to build images of reality which are satisfying for both their associations and forms. He is a solid constructor, not an improviser; and his style is characteristically lucid and free from mannerisms.” And although form in his work was clearly of high importance to Schnakenberg, he was not a cold or completely detached painter, as indicated by self-analysis in a letter he sent in 1949 to a curator at the Montclair (New Jersey) Art Museum, preserved in the holdings of the Archives of American Art. There the artist wrote “Taken all-in-all I suppose I could say that my major concern in painting is to render what I feel about what I see so that the viewer of my pictures may, consciously or not, get some of the emotional reaction that was mine.”
Schnakenberg’s emotional reaction in connection with the Hillstrom painting of Dominoes is difficult to discern with certainty. Perhaps it was something to do with the randomness of life, and to carry speculation into an even more fanciful realm, perhaps the repeat of the 6-4 domino was self referential: the artist was 64 years old when he painted this still life, assuming that an inscription of “11-56” on the back of the painting indicates an execution date of November, 1956. It’s possible, too, that the artist, who was socially conscious—as evidenced, for instance, by his June 29, 1953 letter in the New York Times decrying the death penalty—was alluding to world politics by his choice of subject matter. The Cold War was in full force when Schnakenberg painted Dominoes in 1956, two years after President Eisenhower made his famous speech warning of the “domino effect” in allowing communism to establish itself in Southeast Asia. The artist’s choice of subject for the Hillstrom still life might have been made with that context in mind. Regardless, however, of what reason Schnakenberg may have had for depicting dominoes in the Hillstrom oil—and this evidently was the sole time he essayed them as a subject—the end result was a painting that is visually very satisfying, and that is typical of the carefully calculating approach of the artist to his imagery.
Carolyn Pillers Dobler, Professor and Chair, Department of Mathematics and Computer Science
Donald Myers, Director, Hillstrom Museum of Art, and Instructor, Department of Art and Art History