In Fourth Dimension, Be a Monster or Solve Sudokus

John Gray, ‘The Immortalization Commission: Science and the Strange Quest to Cheat Death’, 2011:

“....Lenin's tomb was designed by AV Shchusev, an architect involved in the constructivist movement and influenced by Kazimir Malevich, the founder of suprematism. Malevich viewed abstract geometrical forms as the embodiment of a higher reality. Believing that Lenin's cube-shaped mausoleum represented a "fourth dimension" where death did not exist, he suggested that Lenin's followers keep a cube in their homes. The proposal was adopted by the party, and cubic shrines to the dead leader were set up in "Lenin corners" in offices and factories. Shchusev's design reflected Malevich's belief in the occult properties of the cube. At a meeting of the funeral commission in January 1924, Shchusev declared: "Vladimir Ilyich is eternal . . . In architecture the cube is eternal. Let the mausoleum derive from a cube." He then sketched a design made of three cubes, which the commission accepted....”

 Matt Parker, ‘Things to Make and Do in the Fourth Dimension: A Mathematician's Journey Through Narcissistic Numbers, Optimal Dating Algorithms, at Least Two Kinds of Infinity, and More’, 2014:

 “....As humans, we live in a three-dimensional world. We are 3D creatures, and as a 3D creature I find no concept as terrifying as the notion of encountering a 4D creature. Such an organism would be god-like to us and, were it the slightest bit malicious, it could torment and destroy us at will. Humans are not equipped physically or mentally to deal with a fourth dimension, so any higher-dimensional being would have the ultimate tactical advantage.

There’s a reasonably accurate description of an interdimensional fight in the comic 1963 – Tales of the Uncanny (published in 1993). The story ‘It Came from … Higher Space!’ features a 4D protagonist attacking a 3D victim. It was written by comic-book legend Alan Moore (author of Watchmen, V for Vendetta, The League of Extraordinary Gentlemen, and many others) and the monster appears as a collection of hovering, disjointed body parts which move and morph around in the air. It starts as a series of wisps in mid-air which balloon out into 3D and are described as being almost like doughnuts made of meat. Not appealing.

We can explain the disjointed nature of the 4D monster by looking at what would happen if we, as 3D creatures, attacked a 2D creature. Being 3D means that the space we operate in extends in three different directions: side to side, backwards and forwards, and up and down. A 2D creature can move only in two directions: it’s constrained to a flat surface. Let’s imagine a hypothetical creature who is completely flat – a hypoflatical, say – living in a completely thin universe, so thin that it would appear as a piece of paper does to us. We could loom as close to it in an up or down direction as we want and, because the hypoflatical has no concept of a third dimension, it would have no idea we were there. The third dimension provides perfect cover. Time to mount our own terrifying attack on a lesser-dimensional being – and all it takes is a move in the third direction into its two-dimensional world....”

"Time passes more slowly in that dimension, so take these sudokus."  

Artist: Edward Steed, The New Yorker, June 2016