4D Objects

We've all heard about 3D printing, which allows you to essentially create anything you want as long as you have the necessary materials and the design. It is a ground-breaking idea in and of itself, and it has found success in many other applications. One day, it might even make it possible to print biological things, like organs.

In 1754, Jean le Rond d'Alembert published "Dimensions," which was followed by Joseph-Louis Lagrange in the middle of the century, and culminated in Bernhard Riemann's precise formalisation of the theory in 1854. With the help of a step-by-step generalisation of the characteristics of lines, squares, and cubes, Charles Howard Hinton popularised these ideas in an essay titled "What is the Fourth Dimension?" in 1880.

Drawing two regular 3D cubes in 2D space, one containing the other, separated by a "unseen" distance, and then drawing lines between their equal vertices is the simplest way to implement Hinton's method. The above animation illustrates this whenever a smaller inner cube is enclosed by a larger outer cube. In this instance, a single direction in the "unseen" fourth dimension is represented by the eight lines joining the vertices of the two cubes.

That idea is simply expanded upon in 4D, with the exception that the printed objects may now respond in real time to various environmental factors. Many 4D materials, also known as smart materials, have been created in recent years. Examples include self-healing plastics that can eliminate wear and tear and make plastic items infinitely reusable, fabrics that can adjust their molecular structure to changes in the weather, and shoes that can fully repair themselves with an additional gel.