The QUeST (256 dimensions and fermions) and UTMOST (1024 dimensions and fermions) theories are derived from a deep basis in 1 dimension spaces. These theories are then shown to have a series of subspaces. One remarkable subspace of QUeST gives our 4-dimension space and The Standard Model of Particles explicitly answering the question in the title! We provide rules for the extraction of subspaces and show there are relic 16 dimension and 64 dimension subspaces that poke their head up in fermion and other particle phenomena. We discuss whether there is a deeper level than the 1 dimension basis found for each theory. We believe not since the concept of dimension is a primitive. The evidence: dimension is only specified operationally. We give fractal dimensions as an example and raise the question, apparently for the first time, why are fractal dimensions always greater than or equal to one. We suggest fractal dimensions below 1 may be possible. The book gives a detailed description of all aspects of dimensions of spaces and subspaces, and their associated fundamental fermion spectrums. Many explanatory figures in this challenging subject area!