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The Vindicator pushes up from TrueSpace into HyperSpace.

TrueSpace refers to ordinary space-time, the dimension in which, as far as we know, all sentient life developed, and is used to contrast ordinary space-time with the exotic dimensions of HyperSpace, QuasiSpace and the theorized origin dimension of the Orz ("PrettySpace"), as well as the little-understood "spirit world" with which the Pkunk are able to communicate. It encompasses the three traditional spatial dimensions and fourth time dimension, and contains the complex structures of matter and energy that make up stars and galaxies; this complex, material structure appears to be absent in the chaotic permeating mediums that fill HyperSpace and QuasiSpace. It is expansive; TrueSpace travel to even the closest of stars would take thousands of years, as opposed to HyperSpace and QuasiSpace where the vast swathes of emptiness that make up most of TrueSpace appear to be strongly compressed. Because of this, travel through TrueSpace is strongly limited by relativity and the speed-of-light barrier; relativistic effects make it impossible to, for instance, establish any absolute time scale for TrueSpace chronology for a space larger than a single star system. Hence, HyperSpace-based astronomy, astrogation and chronology have overtaken TrueSpace-based systems for all purposes among the starfaring races.

It is assumed that all known races evolved in TrueSpace (including the Arilou, who maintain an enormous TrueSpace bubble in QuasiSpace to house Falayalaralfali), since ordinary matter and energy do not exist in the other known dimensions. However, events surrounding the disappearance of the Androsynth and the discovery of the Orz as well as the bizarre abilities of the Pkunk throw that into doubt, and create the possibility that intelligences, if not true material life forms, exist in other dimensions -- lending credence to theories that the sentient races' superstitions, religions, and other belief systems about the supernatural may hold true in other dimensions.