Himmel und Hölle
It is telling that the imagery drawn upon in Cora Cummin’s exhibition ‘Himmel und Holle’ contrasts are of sites and locations of serious thought reflection and research – against locales of commodified leisure and hedonism.
Cummin’s depictions of weather stations, hermit’s huts, writer’s retreats are suggestive of cultural resistance and opposition to an imperfect world. In contrast, Golf courses and hotel complexes – epitomizing a culture of shallow consumption and mindless leisure; are depicted as under threat, cast under the shadow of looming clouds – suggestive of ecological, economic and moral doom.
Fleeing the Flexagon World
The works in Cora Cummins exhibition ‘Himmel und Hölle’ ponder the various significances of sites of escape and isolation, be they volutary or forced; conscious or unconscious. As such the works touch on notions of a tactical withdrawal; regrouping and re-gathering resources; as well as temporary or permanent ‘time outs’ from worldly concerns.
The specific imagery and subject matter addressed by the works in the show relate to the relative merits of a range of contrived spaces and topologies. These include picturesque landscapes, golf courses, islands, chalets, castles, and other retreats including the slick digital spaces of computer games. These various types of ‘bolt holes’ can be either places of serious contemplation, growth, renewal and development; or be sites of hedonism, self-denial, mindless consumption and stagnation.
Looming cloud forms are a key image and metaphor in this show – suggesting ‘trouble in paradise’. In relation to this, the exhibition can be understood as both acknowledging the need to escape to ideal spaces – imaginary or actual – along with a wry critique of how sometimes the notion of retreats from the world can be tied up with self-delusion and pretention.
After all, while withdrawal from the everyday world can be an opportunity for grand and serious imaginings of ideal worlds; there is also an ever-present risk of decending into self-indulgance and sulky posturing. Of course a critical view of the concept of retreat and flight, is not an entirely negative sentiment – it reminds us that our shared human fallibility is a very endearing trait.
Returning to the motif of clouds and weather systems, this exhibition can be read in overall terms as concerned with the concept of the potential of in-between states and the ultimate impossibility of completely retreating from the flux and cyclical change of the world.
Pinching the Nose of Fortune
The fortune-teller game is a popular children’s pastime. The focus of the game is a simple folded paper contraption, which serves as a fortune telling device. It is a unique toy in our commidified world, in that can be easily made, customized and decorated by children themselves.
There are numerous intriguing titles for the simple paper plaything – including ‘scrunchie’ or ‘chatterbox’; but it is arguably the German names that are most evocative ¬– Himmel und Hölle (Heaven and Hell), Nasenkneifer (nose pincher), Pfeffer und Salz (pepper and salt) and Salznäpfchen (salt pot).
The folded paper form can be technically described, using the dry terminology of geometry as a ‘flexagon’. In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front.
Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A prefix can be added to the name to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a hexaflexagon with a total of six faces is called a hexahexaflexagon.
The Device
The origami fortuneteller game was featured in ‘Marjorine’ – episode 134 of Comedy Central's South Park. First aired 26 Oct 2005. The story begins with the character Cartman gathering the boys together in his basement to show them a video tape of the girls of South Park Elementary apparently using a time machine, a high-tech gadget which gives them the ability to see into the future (in reality a paper fortune teller). Amongst other antics, the boys build a containment center with hazardous material suits and a quarantine shower with which to study ‘the device’, and come up with a plan to steal it.
The Game
For a simple thing of child’s play, the game is quite complex to explain. In the fortune telling game a player asks a question, and the operator of the paper flexagon fortune teller, answers using an ‘algorithm’ (often as simple as spelling out the letters in the names of a colour or number represented on the device in order to determine the number of folding and unfoldings of the paper form) to manipulate the fortune teller's shape. Questions, answers, colors or numbers may be written on the folded paper fortune-teller. The player asks a question of the person holding the fortuneteller; this question will be ‘answered’ by the device. The holder then asks for a number or colour. Once the number or colour is chosen, the holder uses their fingers to switch between the two groups of colours and numbers inside the fortuneteller.
The holder switches these positions a number of times: which may be determined by the number of letters in the color selected, the number originally chosen, or the sum of both. Once the holder has finished switching the positions of the fortuneteller, the player chooses one of the flaps revealed. These flaps often have colors or numbers on them. The holder then lifts the flap and reveals the fortune underneath. Steps may be repeated to suit the users …
Origins
The first mention of similar fortune-teller games in Europe is in the early 17th century. It is not known if a European learned the game in Asia first, or if the game developed on it's own in Europe. By the early 20th century, the game was firmly established and well known amongst children throughout Asia, Europe, and North America.
Discovery of the Flexagon
Flexagons were ‘discovered’ in 1939 by Arthur Stone, then a graduate student at Princeton University who later became a lecturer in mathematics at the University of Manchester. An Englishman, Stone was trimming American notebook sheets to fit in his English binder when it occurred to him to fold the strips of paper to make figures, one of which was the trihexaflexagon (so called because it has six sides and three faces). He elaborated on this model to create the hexahexaflexagon (six sides, six faces).
Stone showed his models to his friends: Bryant Tuckerman, a graduate student in mathematics who became a mathematician at IBM’s research center; Richard Feynman, a graduate student in physics who went on to win the Nobel Prize in 1965; and John W. Tukey, a math student and later a professor of mathematics at Princeton who made significant contributions to topology and statistical theory. They formed the Flexagon Committee, and were later joined by Tuckerman’s father, the physicist Louis B. Tuckerman.
The Committee devised ways to make flexagons with 9, 12, 15 or 48 faces, as well as square flexagons. Tukey and Feynman worked out a complete mathematical theory of hexaflexagons in 1940; however, it was never published. Feynman also did diagrams of flexagons which were precursors of his Feynman Diagrams describing the behavior of subatomic particles.
Flexagons began catching on with the general public in 1956, when author and Renaissance man Martin Gardner wrote an article on them that was published in Scientific American magazine (the article became the first of Gardner’s regular columns on recreational mathematics).
Flexagon fans have devised variations, created new flexagons with various shapes and properties, and even contemplated flexahedra, which are four-dimensional analogues of flexagons.
Patenting Fortune
In 1955, Russell Rogers and Leonard D'Andrea of Homestead Park, Pennsylvania applied for, and in 1959 were granted, U.S. Patent #2,883,185 for the hexahexaflexagon, under the title "Changeable Amusement Devices and the Like." The patent imagined possible applications of the device "as a toy, as an advertising display device, or as an educational geometric device." A few such novelties were produced by the Pittsburgh printing firm of Herbick and Held, where Rogers worked, but the device, marketed as the "Hexmo", failed to catch on commercially.
Varient Forms
Tritetraflexagon; Cyclic hexa-tetraflexagon; Hexaflexagons; Trihexaflexagon; Hexahexaflexagon; Other hexaflexagons; Higher order flexagons; Right octaflexagon and right dodecaflexagon; Pentaflexagon and right decaflexagon; Generalized isosceles n-flexagon; Nonplanar pentaflexagon and nonplanar heptaflexagon.
Limits of the Flexagon
These clusters and nuggets of factoids where gathered during a set of fingers perambulations across a keyboard. They represent the fruits of ambling along the hedgerows of the ISDN slip roads and information dual carriageways …
The range of numerous, but ultimately finite, possible combinations and configurations of content afforded by the flexagon fortune telling folded paper games; is actually quite a good cautionary metaphor for certain processes of research and knowledge acquisition.
The Curse of the Flexagon
The web is often touted as a free and limitless source of knowledge. But of course the information paths and repositories of the Internet are no less regulated than their real world equivalents. As well as this, whether we are immediately aware of it or not, all our web meanderings and inquiry’s are not only directed, but monitored and anticipated as well.
It thus has to be conceded that much of the material gathered on this page can be thought of as only a kind of quasi-enquiry – in other words ‘flexagon research’.
The web can be thought of as a kind of digital origami flexagon –that gives the illustion of omnipent knowledge. The sites and pages such as wikipedia function as the various folds and faces of a flexagon form …
Flexagon Times
‘Flexagon thinking’, epitomizes the mind set the post-modern late capitalist culture we live in today. It is typified by an almost un- thinking zombie like, endless re-combination of what has already gone. In contemporary culture retro-gardism prevails over the avant-garde.
“Contemporary culture has eliminated both the concept of the public and the figure of the intellectual. Former public spaces – both physical and cultural – are now either derelict or colonized by advertising. A cretinous anti-intellectualism presides, cheerled by expensively educated hacks in the pay of multinational corporations who reassure their bored readers that there is no need to rouse themselves from their interpassive stupor. The informal censorship internalized and propagated by the cultural workers of late capitalism generates a banal conformity that the propaganda chiefs of Stalinism could only ever have dreamt of imposing.”
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Cora Cummins Bio
Cora Cummins was born in Carlow 1973. Solo exhibitions have included ‘Retreat’ (December 2009) Dunamaise Arts Centre, Laois; 'Means of Escape' (April 2008) The Lab, Dublin; 'A Thousand Islands in the Sea', The Dock, Carrick-on-Shannon (July 2006); 'Someplace Somewhere' (2004);'Halved Hill' (2002); 'Various Fields' (2000) Kevin Kavanagh Gallery, Dublin. Graduated from DIT in 1995. 2003 MA Fine Art NCAD. 2002 IMMA Work Programme Studio Residency. Co-founder of Workroom Elsewhere with Alison Pilkington. Curation projects include 'Elsewhere from Here' (2004) Workroom, Dublin; 'All Yesterday's Partys' (2005) along with the Workroom Elsewhere publication project The Fold (2007).
