P.D. Ouspensky was my first foray into non-euclidean geometry. His book, The Tertium Organon, is not only a grandiosely titled treatise, but an interesting look at the limits of geometry (or the lack thereof). The book lays out a foundation for a paradigm shift in thinking about the world around us. In essence the shift is from a three dimensional world view to a view of nth dimensional space. Other writing I have read on the subject of non-euclidean space and extra spatial dimensions tend to limit the number of dimensions of space that they are willing to conceive.
As my reading has bumped into the world of physics, Ouspensky's limitless conception of dimensionality has increasingly appeared to be the target that other researchers have flirted with, but ultimately missed.
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