Hello. :) This is my first post. I'm an amateur astronomer with a interest in cosmology. My understanding of cosmology is entirely derived from reading Hawking's 'A Brief History of Time', Guth's 'The Inflationary Universe' and relevant articles in Scientific American, Sky & Telescope and Astronomy magazines. So, please be gentle with me! In the above books and magazines I've read about the concepts of a gravitational singularity and of the Big Bang singularity. Up until now I'd (naively?) thought that diagrams like the one below were similar to the contour lines of an ordinary topographical map. That is, they represented what physical reality was doing in a way that the mind could easily grasp. But now this paper... http://ja-schweitz.se/onewebmedia/BIG BANG METRIC2.pdf ...has confused me. It seems to be saying that such a diagram of the Big Bang singularity is not so much representation as an artifact. (Or artefact.) Could somebody please explain what's going on here? (Preferably in terms that an enthusiastic amateur can grasp.) Thank you. Cerenkov.