Exploring Hyperobjects: A Metaphor of Higher Dimensions

Michael Mahan
Bridges: Mathematical Connections in Art, Music, and Science (2004)
Pages 243–250


The idea that 3-D projections of 4-D objects are analogous to 2-D projections of 3-D objects is an old one, but the ability to represent and explore these 3-D images in detail was impossible before the advent of computers and 3-D modeling programs. This paper will define "hyperobjects" as a loose 3-D analogy of the 2-D images. It will explain how these hyperobjects must be viewed from the inside and how reflective materials provide a simulation of fourth dimensionality. It will describe how images produced by various classes of hyperobjects differ and how they can generate some very sophisticated images that can certainly be taken as representing recursive mathematical concepts as well as higher spatial dimensions.