(Maybe this should go under General Math or maybe even Topology but since it's about the dimension of the universe I'll put it here. Feel free to move it.) I've had too much coffee and on one my frequent wiki binges - reading about life, the universe and everything - I've come up with a question, the answer to which I'm probably not going to understand. Here goes anyway: Various sources lists the fractal dimension of the universe to be "about 2" (e.g.: http://en.wikipedia.org/wiki/Fractal_cosmology). What is meant by "about 2" and which definition of dimension is used here? Does "about 2" mean above or below 2? From reading a little about fractal dimensions I realize that there seems to be different definitions as to what a fractal dimension is, but the one I'm (vaguely) familiar with seems to be Hausdorff's (http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension). Using this definition a coastline for example, can be said to be one dimensional object "aspiring" to fill out the second dimension which would give it a Hausdorff dimension somewhere between 1 and 2. Similarly, A "menger sponge" can be seen as a 2 dimensional object "apsiring" to fill out the third making it somewhere between 2D and 3D. Following this logic I'm not entirely sure if I would expect the universe to have a dimension between 3 and 4 or 4 and 5 (?), but definitely not 2. What gives? I'm not asking for a mathematical treatise mind you. It just puzzles me... Regards.