Four-dimensional space is a difficult concept but this idea is driving a new revolution in programming today. Individuals familiar with August Ferdinand Möbius’ research know that an additional dimension allows a three-dimensional form to be rotated over on top of its mirror image. This gives us the so-called Möbius strip. While computer algorithms that really simulate scalable four-dimensional space are still in their infancy, they’re already making a big splash.
Mobius Strip. Credit: http://paulbourke.net/geometry/mobius/
It’s important to remember that abstract mathematical concepts have no real bearing on the actual universe. Texts on theoretical physics use four-dimensional space as a term to describe the phenomenon caused by three-dimensional objects moving through time. Naturally, this concept of a fourth dimension is far different from that defined by computer scientists. While additional dimensions are valid mathematical constructs, they have little to do with the world around us. Software is merely producing two-dimensional output anyway, so its safe to assume that nothing a TV screen produces is going to break the space-time continuum.
Image Credit: John Hopkins
Computers provide mathematicians with the opportunity to produce very complex geometrical forms. In three dimensions, polyhedra are made up of distinct two-dimensional polygons. Four-dimensional space grants engineers the freedom to create polychora made up of three-dimensional polyhedra. While this might be complicated, it’s actually useful outside of the world of mathematical research.
Mapping Euclidean space gives scientists the opportunity to produce stereographic projection diagrams of theoretical objects like the Clifford torus. This could be useful in the construction of space colonies, for instance. Puzzles based around 120-cell hecatonicosachoron objects became popular for a time, and illustrate the advantages of constructing objects in a virtual world.
Average computer users probably aren’t too interested in this type of research either. They might be more pleased to hear that four-dimensional simulations are revolutionizing video games. While virtual reality might not actually be the future, a simulation of it very well could be.
Edwin A. Abbot popularized the concept of different dimensions in fiction, and Marc Ten Bosch’s new independent video game is taking it to the next level. Miegakure is a platform that is essentially set in a three-dimensional environment, but players can go through walls and inspect them by entering into an additional dimension. The game has yet to be released to the general public, but it illustrates the possibilities programmers have when they leave the confines of our limited universe. Just as an author isn’t limited when writing a novel, computer programmers can create simulations that aren’t defined by what real individuals can and cannot do.
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