Torrent - Dimensions - A walk through mathematics. Exotic spheres, or why 4-dimensional space is a crazy place. The world we live in is strictly 3-dimensional: up/down, left/right, and forwards/backwards, these are the only ways to move. For years, scientists and science fiction writers have contemplated the possibilities of higher dimensional spaces. What would a 4- or 5-dimensional universe look like? Or might it even be true, as some have suggested, that we already inhabit such a space, that our 3-dimensional home is no more than a slice through a higher dimensional realm, just as a slice through a 3-dimensional cube produces a 2-dimensional square? Just as a 3-dimensional object can be projected onto a 2-dimensional plane, so a 4-dimensional object can be projected onto 3-dimensional space. According to the early 20th century horror writer H.P. Lovecraft had some interest in mathematics, and indeed used ideas such as hyperbolic geometry to lend extra strangeness to his stories (as Thomas Hull has discussed in Math Horizons).
Higher dimensions and hyperspheres Do higher dimensions exist? TFBCON2003: TFBCON2003 Home Page. Plus, Minus: A Gentle Introduction to the Physics of Orthogonal. F or the past year or so I've been spending most of my waking hours in a place where light, matter, energy and time obey different laws of physics than those that rule our own universe. Studying the way things move and interact under these alternative laws reveals some familiar behaviour, some strange and eerily beautiful phenomena, and some terrifying risks. To reach what I will call the Riemannian universe involves nothing more than changing a minus sign to a plus sign in a simple equation that governs the geometry of space-time.
And curiously enough, although the consequences sometimes seem bizarre, the basic laws here can be understood more easily and intuitively than those that apply in the real world. We have known for more than a hundred years that the best way to understand time in our universe is to think of it as combining with the familiar three dimensions of space to form a four-dimensional space-time, which obeys its own distinctive geometrical laws. The Ontology And Cosmology Of Non-Euclidean Geometry.