jinydu wrote:GARD1, it seems that you do not understand the definition of a dimension. A capability is not a dimension. Here is the real definition of a dimenion:

More generally you'd want to be looking at the covers of a manifold to get its covering dimension rather than its vector space dimension (which is what jinydu has provided). It just so happens that Euclidean n-space (or Minkowski n+1-space, to taste) is a vector space and its covering dimension is equal to its vector space dimension.

To be frank, 'dimension' is, at the very least, a word in the lexicon of mathematics. To remove it from such is to change (read: butcher, from the point of view of a purist) its definition to suit a need. Of course one can say that the 'dimensions of velocity are LT^-1' but this is a completely different use of the word. To give credit to the argument that a capacity is a 'dimension' is akin to what I just did above - use the word in a non-similar, disjoint fashion. Sure, capacity could be a 'dimension', but it wouldn't be a "spatial dimension" like length, width, and time in the mathematical (topological) sense of the word.