A. Square is the name of a square who lives in a land of two dimensions, Flatland. One day he has a strange encounter a being from a three-dimensional place, Spaceland. Being from a world of width and breadth but no depth, A. Square cannot perceive this foreign body, but none the less they have a long chat about two dimensionality and three dimensionality, before taking off together and making brief stops at Lineland, a place of one dimension and Pointland, where there is no dimension. A. Square soon comes upon the radical idea that if there is a third dimension that he can come to imagine but never fully comprehend, then there must conceivably be a fourth dimension that those from Spaceland could think about, but not perceive. It’s all in Flatland: A Romance of Many Dimensions, a most excellent short novel written by an English schoolmaster called Edwin Abbott Abbott in 1884 that remains surely the single best description of the dimensions and the possible relations between them.
Part of Yokohama-based artist Yusuke Shigeta’s examination of the ways three-dimensional space might conceivably interact with two-dimensional space if such a thing existed, an animation series called narrative kinetics will be presented next week in the video art program at Big In Japan in Sydney and Melbourne. In Euclidean geometry a square is both a rhombus (meaning it has equal sides) and a rectangle (meaning it has equal angles). Thanks to this uncommon equality in the square’s form it boasts quadruple symmetry, meaning it can be rotated four times while appear exactly as itself. It can also be divided or multiplied by four infinitely without ever altering its form, a property that is beautifully exploited in these thoughtful works.
Yusuke’s fascination with flat geometry in relation to physical space has also led the artist several times to experiments with cartography, and he recently released an app. based on antique maps of Edo (the old city of Tokyo) that allows users to go back in time as they navigate the modern city. If you are in Tokyo or planning on being there it’s available here.