The Numbers Game

22 June – 30 July 2000

Billy Apple, Liz Coats, Chiara Corbelletto, Neil Dawson, Robert Ellis, Dick Frizzell, Terrence Handscomb, Paul Hartigan, John Hurrell, Horst Kiechle, Colin McCahon, Julia Morison, Simon Morris, Simeon Nelson, Michael Norris, Michael Parekowhai, Richard Reddaway, Jacky Redgate, Peter Robinson, Peter James Smith, and Ruth Watson


A discipline of specialist notations and calculations based on numbers, maths is inherent in any quantification of shape, size and space. The ramifications of mathematics are intrusive and ubiquitous. Telecommunications, time keeping, clocking speed, mapping the landscape, budgeting – everyday our lives are shaped by numerical codes and networks. At the macro level, our understanding of the universe is based on systems, science reveals patterns in nature and we acquiesce unconsciously to notions of universal laws.

As a number of related sciences seemingly supporting order and finitude, mathematics is less frequently acknowledged as a determinant of our cultural lives. Early attempts to base mathematics on logic frequently assumed indisputable and absolute reasoning. Only later when different ‘logics’ were discovered by both anthropologists and mathematical logicians, did it become clear that logic was a cultural artefact, not a necessary component of every culture.

Theories used to explain our societies and cultures are apparently based on empirical evidence but social statistics are determined entirely by context and assumptions. In New Zealand the definition of Maori in the national Census has constantly altered as acknowledgement of racial mix has broadened. A number of works in this exhibition refer to interconnections between the operation and authority of symbolic languages and ways we understand such tools. Peter Robinson is conscious of the personal and cultural values assigned to measures. Institutional appraisals of identity, and personal evaluations of self as they may be judged against some standard of ‘otherness’, for Maori as well as many other indigenous and racial groups, is reflected in Robinson’s percentage paintings.

As both a statistician and an artist, Peter James Smith reflects on ways in which numerical data operate as information. Across history civilisations have developed sophisticated number systems in order to count and calculate. Symbols based on a range of number bases were formative in establishing Aztec, Babylonian, Chinese, Greek, Roman and Arab civilisations (Arabic numerals remain in use today). In Smith’s Random Numbers, chaotic and subjective qualities are apparent amidst the perfect and rational properties ascribed to numbers. His painting Orbital Elements of the comets known to Halley refers to an episode in humankind’s search for explanations of natural phenomena – Halley’s enlightenment quest to replace the supernatural features of astronomy with empirical understanding. Smith acknowledges the human urge to both explain and control the world around us, while accepting that we react to nature as romantic and sublime.

The development of the computer in the second half of last century opened up new potentialities for creativity as much as for business or learning. Composer Michael Norris has pursued his work with electroacoustics to a new level with Silence Lives in Blue Rooms. Each time the audience enters the soundscape the artificial intelligence of the programme will have developed within this audio world further. A reading of In den Nachmittag geflüstert by Georg Trakl undergoes the algorithmic operations of Norris’s programming and is influenced by chance happenings to result in seemingly free and natural sounds.


Today when computers operate on the binary logic of zeroes and ones and world markets trade enormous notional sums, zero is intrinsic not only to numerical representations but also to the fabric of life. Zero is historically interesting for its relatively late invention in around the sixth century AD, while numerically it is also an oddity – for example it is excluded from counting (beginning at one), and it has unique properties in arithmetic operations (multiplication, division etc).

Julia Morison’s work Amperzand II highlights the paradoxical nature of the zero. Invented to symbolise empty space in place-value notation, philosophically zero is associated with the void and absence. If as Morison has said, these works are almost like thought or speech bubbles, they contain nothing but our own mental construct. Conceptually, nought provides a symbol to document magnitudes beyond our comprehension, to count the inestimable.

Zero and zero and zero and zero ad infinitum remain zero, as Amperzand signifies. Infinity and zero come together most commonly in our endeavour to understand space—the galaxy, black holes, the Big Bang. While scientists would tell us there is no such thing as empty space, Paul Hartigan’s SKY 02 reinstates an imaginary wide blue yonder—immeasurable, indeterminable, unending.


Serious pursuits inevitably have a flip side, entertainment can also be intellectual or earnest. As long as maths is compulsory in our education system there will have to be sugar pills to make learning fun. Books such as The Man Who Counted by Brazilian mathematician Malba Tahan give peculiar insights into mathematical history, delivering messages of the ethical and economic rewards awaiting mathematical astuteness (thankfully leavened with humour). In the field of play, conventional games from sports to board games rely on players’ calculations and are in essence competitions for the highest score.

Ruth Watson has often used games in her work, transforming playing boards, chess sets and jigsaw puzzles, or re-contextualising scrabble pieces (from the exhibitions A E I O U and Among the Scrabble). Beyond the obvious associations of game playing, Scrabble denotes a hierarchical position for the English language. Those who through good fortune are given the tools to acquire a voice in the dominant language are placed in the superior position of determining how and with whom they communicate and what is said.

Michael Parekowhai also reflects on the acquisition and application of language, by employing a popular mathematical device. Ataarangi resembles a construction of enlarged Cuisinaire rods.

Through these objects and the title, the work refers to the changing use of Cuisinaire from a maths teaching aid teaching spoken Maori. Confronting written and oral languages, English (the sculpture reads ‘HE’ on its side) and Maori traditions, Parekowhai suggests the reinvigoration of systems and ideas as cultures and identities assert their own existence.


Until the nineteenth century and physiological advances in understanding the operations of the eye, a primary objective of artists was the reproduction of the real world. Theories of perception and optics dating from the time of Aristotle understood vision according to a Cartesian model of perspective organised around the idea of a disembodied, monocular eye. Visual languages of artmaking and design relied on drawing systems, from the simplest single point perspective to more developed orthographic projections based on projective geometry. Such systems gave spatial relationships a correspondence with their counterparts in the external world. The notion that visual rays from the eyes met at the centre of single point perspective allowed Alberti to define the picture plane as a window and Dürer to depict the use of drawing machines. With these devices the artist looked through a frame or sight vane, observing his subject matter in relation to the gridded squares within the frame.

Over the last two centuries geometry and description have given way to subjectivity and suggestion in art making. In his Rakaumangamanga paintings, Robert Ellis transforms the topology of a mountain site in the Bay of Islands into a conjunction of plan, elevation and sections. His seemingly cartographic images conceal the lived meanings and importance of this sacred area for Nga Puhi under European signs of charting and ownership. Ellis indicates that mapping systems, like numbers, do not have universal reference but are exclusive in their metaphorical transferral of understanding, knowledge and power.


The quest for understanding and appropriating symmetry and proportion has been evident since the Ancient Greeks assigned metaphysical properties to naturally occurring phenomena. Billy Apple often works with ratios and proportions, especially permutations of the Golden Section. For this exhibition, Apple utilised a central feature of the Adam Art Gallery building and worked with the relative qualities of that space. Painted in safety orange on the wall above its physical location, Mind the Gap replicated the dimensions of the void on the upper level of the Chartwell Galleries, bringing 22.32 percent of the unusable floor area of these Galleries into the exhibition area.

Cities, machines and other systems can abstractly be compared to forms and systems in nature. For example, the spiral created by the golden section is observed in many plants and shells, while golden section proportions have been observed in buildings since the Parthenon and Great Pyramid of Giza. Neil Dawson’s House Alteration works transform the iconic form of the residence into simplified models. Dawson uses simple mathematical processes (enlargement, rotation) to manipulate the schematic structure of the house, continually challenging our understanding of its form and function. Dawson makes tangible the allegorical possibilities of rigorous operations such as perspective and illusion.

Liz Coats employs geometry as a starting point in paintings made with liquid and transparent colours, arriving at images not entirely under her control. The images arise partly from Coats’s interest in symmetry/asymmetry in the natural environment and experienced world. Central to the work are also the processes of growth and movement that occur during both the creation and viewing of the works.

In creating an infinitely repeatable three-dimensional mosiac, like a sort of perfect crazing, Chiara Corbelletto is also reflecting on patterns appearing in the natural and biological worlds. Often based on tessellation and rotations of a unitary form, Corbelletto’s modular sculptural hangings highlight the potential for variety within unity, for shifts in scale and for the interaction of forms with the surrounding environment. Recent work by Simeon Nelson is based on manipulation of syntactical or numerical rules, rules that may be further warped or controlled by the artist. The ultimate results are mapped in three dimensions. Forms of works such as the Calculus series evoke macro and microstructures and the networks of living and man-made systems.


It is a truism to say that much abstract art that looks geometric and systematically proportioned has in reality been the result of intuitive or subjective considerations. By contrast, there is often little to belie the calculated or sequential systems of organisation of some art making. Systematic processes are applied as structuring devices in John Hurrell’s methodology. Geometric paintings from the late 1970s came about through an extensive process of positioning predetermined forms according to dice throws, followed by further intuitive shifts. In two-dimensional works from the 1980s and 1990s, printed maps comprised a ready-made symbolic and formal base material as the prime compositional ingredient. By choosing a singular aspect of the map or its indexical operation, Hurrell features selected attributes in each work and the blankness of black paint obliterates any other detail.

A set of wall paintings by Simon Morris spotlight the artist’s interest in the operation of minimalist abstraction as it is generated within a limited set of options. The compositional placement of colour bars depends on the flip of a coin enacted in the gallery space. Performing the same operations across wall paintings over time indicates possible permutations or may replicate positions. Apparent formal order arises out of the disorder of performance and chance.

Aberrant forms by Richard Reddaway also inhabited the gallery building. Mirrored sections appear in atomistic units that couple and congregate in larger fields or crystal growths. Reddaway’s concepts are more speculative than pseudo-scientific, delving into theories of complex behaviour such as Chaos Theory or growth forms and non-linear systems.

Engineer Horst Kiechle utilises complex concepts (such as intuitive irregularity, natural imperfection and marginalised geometries) in analogous ways to counter simplified and reductive understandings of society. In site specific and virtual architectonic projects, Kiechle inserts complex and irregular growths in spaces for residents to come to terms with. Basic mathematical logic is corrupted and bent by irregularity and intuition. Kiechle is conscious not to smooth out the details he believes are often lost in the abstractions of precise disciplines or in our search for concrete truths.


Academically a division has existed between the ‘hard’ sciences and ‘soft’ arts, both in terms of a physical versus a literary understanding of the world and in the relative values placed upon these disciplines. The distinction was most notably recognised in the late 1950s by C.P.Snow, who addressed the perceived separation of the ‘two cultures’ as distinguished by scientific conventions of observation, experiment and empirical measurement as opposed to the rhetoric, creativity and imagination of the arts.1 Of course these generalisations are simplistic. Both fields utilise languages and systems to visualise experience of the world and offer questions and parallels rather than answers. Both operate through acts of the imagination, are the result of inductive leaps or are directed by incorrect conjectures and prodded by criticism.

Dick Frizzell relies on the natural intrigue of signs and symbols to send a serious message. His double-sided comment ‘Faith’ points to the implicit trust we place in all things scientific. Frizzell simultaneously questions any meaning that might be ascribed to mathematical symbols and languages. Communication in a culture based on symbols relies on each of us to exercise a naming function on new symbols or to develop a vocabulary of signs. To communicate information signs must operate in a set of logical possibilities. Works produced by Terrence Handscomb in the late 1980s questioned the values and meanings assigned to symbolic codes and called attention to the weight of information carried by, and validity of, such conventions. Combinations of text and icon, formulae and grammar, in works such as Close the Canal, frustrate the viewer with brief passages of recognition and comprehension. Ultimately inaccessible as a whole unless Handscomb’s personal code can be broken, this work makes evident the problematic nature of representation. Colin McCahon, like Ralph Hotere, included numbers and segments of calendars in numerous works, often as a reference to the Stations of the Cross. McCahon produced sets of numerals from the late 1950s onwards, in which the conjunction of I, One accentuated the artist’s religious symbolism. Works employing groups of numbers emphasised the significance of progression, (Teaching Aids, Walk, Jump I – IV) but with varied rhythms and associations. The idea of broader academic connections – blackboards, calculating, measuring or computing – as well as metaphysical notions, appeared in the numerically saturated composition of Preliminary Study for University of Otago Library Mural 1966.

Early 1940’s landscape compositions by McCahon, such as Otago Peninsula, utilised the proportions of the golden mean and logarithmic spirals.2 The Song of the Shining Cuckoo links the panoramic progression and Stations of the Cross to Maori beliefs regarding the departing spirit. Based on a poem written by Ralph Hotere’s father, Tangirau Hotere, it depicts the flight of a cuckoo above the shifting sands of Muriwai beach, a symbol of the recently departed spirit making its way to Te Rerenga Wairua, from where it will begin the journey to ancestral Hawaiki.


Art and mathematics cross paths where the processes of cognition and intuition meet. In this space, order meets disorder and universal laws confront conjecture. Jacky Redgate worked from eighteenth century mathematical formulae derived form the discipline of Solid Geometry to create the six computer rendered solids of equal volume but differing shape in Equal Solids. Redgate unsettles experience and perception through the application of calculations dating back to Isaac Newton. Ideas reappear as computer lathed forms that defy comprehension.

While we imagine we can understand the world sufficiently from our personal perspective, we quickly flounder when thrown into aspects of fields beyond our own sphere. A reminder of why maths is compulsory learning and also of the encounters possible outside the square!

Zara Stanhope

1. C.P.Snow,The Two Cultures and the scientific revolution, Cambridge University Press, New York, 1959.
2. Gordon H. Brown,Colin McCahon: Artist, AH & AW Reed Ltd., Wellington, 1994, p.143.


Robert Caplan,The Nothing That Is, A Natural History of Zero, The Penguin Press, London, 1999

H.S.M. Coxeter, M. Emmer, P. Penrose and M.L. Teuber (eds.) M.C.Escher: Art and Science, North-Holland, Amsterdam, 1987

Apostolos Doxiadis, Uncle Petros and Goldbach’s Conjecture, Faber and Faber, London, 2000

Michele Emmer (ed.), The Visual Mind, Art and Mathematics, MIT Press, A Leonardo Book, Cambridge, Mass. USA, 1993

Douglas R. Hofstadter,Godel, Escher, Bach: an Eternal Golden Braid, Basic Books Inc., New York, 1979

Victor J. Katz, A History of Mathematics, An Introduction, Adison Wesley, Reading, Mass. USA, 1988

Jerry Ravetz, Ziauddin Sardar and Borin, Van Loon, Introducing Mathematics, Allen and Unwin, Sydney 1999

Malba Tahan, The Man Who Counted, Leslie Clark and Alistair Reid (trans.), Canongate, Edinburgh, 1993