What Relativity Means
First posited by Einstein in a 1913, the General Theory of Relativity shattered this absolutist view of the world. Relativity, as described by the British astronomer Eddington, was really the idea that,
"distance and duration, and all the physical quantities derived from them, do not as hitherto supposed refer to anything absolute in the external world, but are relative quantities which alter when we pass from one observer to another with different motion," (Clark, 125).
Relativity stated that even the quantified rules of our physical universe were not enough to completely describe existence. Instead, distance and duration, previously seen as set quantities, were dictated by their relationship to velocity. Thus, different, relative, physical and mathematical systems were equally valid, if differently structured. A yard did not have to be a yard, but rather could be eight yards at another point in the universe.
EinsteinŐs understanding of this phenomenon was one necessarily reliant on dimensional interactions. For example, his new theory of gravity posited that the mass of a three dimensional object in effect "bent" two-dimensional space so that matter or energy passing along a two-dimensional path would "curve" around the space bent by other matter. The classical description is that if two dimensional paths are represented by plane, such as a piece of paper, than matterŐs impact on it is the effect of a bowling ball impacting on the paper, causing a rolling marble to fall down, into its "orbit," (Clark, 254-5).
Eventually, the principles of relativity were extended to validate the existences of non-Euclidean, non-Newtonian worlds. Phenomena such a the effect of gravity on earth, while reliant on velocity for its relative "truth," were not only radically changed at higher velocities, but were, even at lower speeds, subtly different than the constructed truths that humanity had been brought to believe. The relative nature of velocity had never been taken into account before , and basic mathematical "truths," such as the Pythagorean theorem, were not necessarily true in other, relative, systems--a frighteningly different conclusion.
Links for more information about Relativity:
General Relativity tutorial at the University of St. Andrews in England
NOVA - Resources for Einstein and Relativity