(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.)(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Fractal dimension of the universe = 2?

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