Adam Pugh

The theory of a fourth dimension was pursued hungrily by artists in the early 20th century, with Marcel Duchamp, Theo van Doesburg and many of the cubists tackling the questions – geometrical, philosophical, epistemological – that it raised. Implicitly folding in this history, and guided by a beguiling Victorian text by Edwin Abbott Abbott, Flatland: A Romance of Many Dimensions from 1884, Dutch artist Melvin Moti’s intelligent, expansive moving-image commission The Eightfold Dot for Pavilion plots a journey from zero to four dimensions, stalking the four-dimensional hypercube as both form and symbol.

Lit by a spectral source, the vitreous faces of a fluorite crystal reveal and consume themselves as they rotate towards a black void. As the crystal fills the frame, referents of scale and depth are dissimulated until it is unclear whether the cube is three-dimensional or a planar surface which happens in some way to imitate depth. This perceptual problem, encountered by the two-dimensional narrator of Flatland upon encountering a sphere, offers two insights: one, that what we perceive is not necessarily all there is to see, and two, that if what we perceive is not necessarily all there is to see, then that which we perceive as impossible might not be so. And it is hard not to freight this conclusion with metaphorical potential.

Avoiding prosaic description of his subject, Moti instead summons the interstices between the spaces and anti-spaces described by form, light and motion. His patient, transcendent macro-photography recuperates the photographic image from the service of verisimilitude and returns it to its root: all is light-play. Indeed, the film shares the formal sensibilities of László Moholy-Nagy’s Ein Lichtspiel schwarz weiss grau, 1930. In both, the tool least likely to offer a route to abstraction, the camera lens – the objective – wrests worlds atomic and cosmic, imploding form and scale until the infinitesimally small resembles vast nebulae.

There is an auspicious reflexive relationship between the subject of The Eightfold Dot and its exhibition space, a semi-derelict former nightclub and cinema in which the skein of successive developments is unwound, a crosswise skeleton of steel joists forming a uterine interior within the larger building. So too are there many parallels between the geometry of projected film and that of film-as-material, with images of instants arranged temporally on a curved surface, coiled together – a model of non-Euclidean space-time. But Moti’s film speaks also, if quietly, of potential, of alternatives, of a more ‘spacious Space’, as the narrator of Flatland dreams: a means of combating the tendency of the status quo towards the reductive, homogenising, entropic.

If, as the 18th-century philosopher David Hume argued, causation is necessarily but an inference based on the observable relationships between known phenomena, we cannot rule out unknown causes influencing known effects (this is not to say that they are not physical, but that they are governed by physical rules not yet understood). This allows for a discourse around belief and theism, selfhood and agency, and rather than dismiss it as the newest product of a godless science, the theosophists of the early 20th century saw it as an opportunity to claim the fourth dimension as a higher mental, mystical or spiritual state, as Abbott himself appears to have done, limning it ‘Thoughtland’. It also plots a trajectory on which enlightenment is proportionate to dimensionality.

From the solipsism of zero dimensions to the relative superiority of three, in which the limits of the laws of motion and form in the two-dimensional world of Flatland are comprehensively breached, we can project the benefits to a three-dimensional order of the wisdom of four. What The Eightfold Dot implies is that rather than an accretion or extension, the progression from three to four dimensions demands a dissolution, a reformation, where all is in flux (indeed, the root of the word ‘fluorite’ refers to this fluidity). This is no mere revolution, no turning-again, but an insurrection.

As Flatland satirises, the extent of our perception dictates the degree to which we depart from brutishness, our petty stratification a product of our benighted worldview: if we rely upon faulty induction and do not try to conceive an alternative, or to deny it even in the face of plausible paradigms, we are condemned to live in the ‘dull level wilderness’ experienced by the narrator on his return from three to two dimensions; a specious space. We accept our current model as logical or natural because it is expedient to do so – but this does not preclude the existence of other, more equable models, nor should it prevent their institution.