Hyperspatial Interlace - Grasping Four-dimensional Geometry through Crafted Models
type: CreativeWork
description: Although our everyday perception of space tells us that it is composed of three spatial dimensions of length, height and width, it is possible to imagine a space having four spatial directions that are exactly identical with respect to each other, and meet at right angles. This concept of a four-dimensional space has had a profound and lasting effect not only on philosophy, mysticism, mathematics, and theoretical physics, but also on fiction and visual arts. Because the mathematically described four-dimensional structures are difficult to grasp visually, it is instructive to observe spaces of lower and higher dimensionality in their hierarchical relation. In this context we can see that our challenges to understand and visualize four-dimensional objects are analogous to the difficulties a two-dimensional being, confined to a plane, would have with respect to our three-dimensional space and its shapes. Consequently, just as three-dimensional structures can be drawn, unfolded, sliced, photographed or otherwise projected onto a two-dimensional medium like paper or a computer screen, these graphical techniques can be generalized to acquire the three-dimensional appearances of the four-dimensional hypersolids. The objective of the artistic research reported here was to craft physical, three-dimensional models that illustrate regular hyperspatial structures through novel visualization methods. I considered kinetic models of the four-dimensional polytopes in particular to be beneficial for understanding these structures. As a research method I employed experimental crafting with traditional materials and techniques, and the theory guiding these constructions came from the field of descriptive geometry. The cultural references in the history of hyperspace, such as interpretations in spiritualism and science fiction, served as a poetic inspiration in designing the models. As the results of my research, I present five concepts for physical models, each of which illustrates a …
abstract: Although our everyday perception of space tells us that it is composed of three spatial dimensions of length, height and width, it is possible to imagine a space having four spatial directions that are exactly identical with respect to each other, and meet at right angles. This concept of a four-dimensional space has had a profound and lasting effect not only on philosophy, mysticism, mathematics, and theoretical physics, but also on fiction and visual arts. Because the mathematically described four-dimensional structures are difficult to grasp visually, it is instructive to observe spaces of lower and higher dimensionality in their hierarchical relation. In this context we can see that our challenges to understand and visualize four-dimensional objects are analogous to the difficulties a two-dimensional being, confined to a plane, would have with respect to our three-dimensional space and its shapes. Consequently, just as three-dimensional structures can be drawn, unfolded, sliced, photographed or otherwise projected onto a two-dimensional medium like paper or a computer screen, these graphical techniques can be generalized to acquire the three-dimensional appearances of the four-dimensional hypersolids. The objective of the artistic research reported here was to craft physical, three-dimensional models that illustrate regular hyperspatial structures through novel visualization methods. I considered kinetic models of the four-dimensional polytopes in particular to be beneficial for understanding these structures. As a research method I employed experimental crafting with traditional materials and techniques, and the theory guiding these constructions came from the field of descriptive geometry. The cultural references in the history of hyperspace, such as interpretations in spiritualism and science fiction, served as a poetic inspiration in designing the models. As the results of my research, I present five concepts for physical models, each of which illustrates a …
author: Luotoniemi, Taneli
language: en
date published: 2019
date modified: 2026-07-27T18:39:42Z
provider: Aalto University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Aalto University