It looks like you're using an Ad Blocker.
Please white-list or disable AboveTopSecret.com in your ad-blocking tool.
Thank you.
Some features of ATS will be disabled while you continue to use an ad-blocker.
Fourth Dimension - Wikipedia
The fourth dimension as time Main article: Spacetime Often, when a reference is made to the fourth dimension, it is the temporal interpretation which is meant. In this case, the four coordinates are understood to represent 3 dimensions of space plus 1 dimension of time. Such a space is called a Minkowski space or "(3 + 1)-space",[2] and is the space used in Einstein's theories of special relativity and general relativity. Bertrand Russell explains that in Relativity it is more relevant to speak of "space-time" than to discourse on "space and time". He goes on, "... because that is, from a philosophical and imaginative point of view, perhaps the most important of all the novelties that Einstein introduced."[3] [edit] The fourth dimension as space The fourth dimension may also be interpreted in the spatial sense: a space with literally 4 spatial dimensions, 4 mutually orthogonal directions of movement. This space, known as 4-dimensional Euclidean space, is the space used by mathematicians when studying geometric objects such as 4-dimensional polytopes. It is not to be confused with the Einsteinian notion of time being the fourth dimension. Regarding this, Coxeter writes: Little, if anything, is gained by representing the fourth Euclidean dimension as time. In fact, this idea, so attractively developed by H. G. Wells in The Time Machine, has led such authors as J. W. Dunne (An Experiment with Time) into a serious misconception of the theory of Relativity. Minkowski's geometry of space-time is not Euclidean, and consequently has no connection with the present investigation. —H. S. M. Coxeter, Regular Polytopes[4] Mathematically, the 4-dimensional spatial equivalent of conventional 3-dimensional geometry is the Euclidean 4-space, a 4-dimensional normed vector space with the Euclidean norm. The "length" of a vector \mathbf[x] = (p, q, r, s) expressed in the standard basis is given by \| \mathbf[x] \| = \sqrt[p^[2] + q^[2] + r^[2] + s^[2]] which is the natural generalization of the Pythagorean Theorem to 4 dimensions. This allows for the definition of distance between two points and the angle between two vectors (see Euclidean space for more information).