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I removed the comments on the page, stating that the interpretation of dimensional regularization may not be profound and that the geometrical intepretation of partial dimensions is hard. While i may sympathise with those feelings, the first one should be backed up by references, and the second one should not be in an encyclopedia. Siebren 09:58, 14 November 2005 (UTC)
- The geometrical interpretation of partial or fractional dimensions (see Felix Hausdorff, Hausdorff dimension, and List of fractals by Hausdorff dimension) is not at all difficult and is fully a part of mathematics and physics, such as in Fractal theory, where it is also called a fractal dimension. Informally, this concept encodes the "jaggedness" of an (n-1) dimensional boundary. For example, a coastline bounding sea and land can naively be thought of as one-dimensional, and yet cannot be measured, as the measurement method depends strongly on its resolution and because the microscopic definition of such a boundary is both undefined and ever-changing. Since it cannot be measured, its true dimension in terms of measurement must be considered as somewhere between one and two. This concept is also related to other self-similar concepts such as Space-filling curves, which are also of dimension between one and two. In summary, fractional dimensions are already in Wikipedia, and are not "hard" to interpret. Fractional dimensions (along with dimensions higher than 4) are an important concept in String theory, in Quantum mechanics, and in Group Theory, Meromorphic functions, and Numerical analysis, although for some strange reason they are not mentioned in those articles. David Spector (talk) 15:45, 24 May 2019 (UTC)
There must be a mistake in the hypersurface formula given as there is no mention of r, the radius, while the formula is clearly stated to be the hypersurface of a sphere of radius r. --128.139.226.37 11:21, 11 August 2007 (UTC)
It would be better if the final integral was evaluated and given an expression in terms of \epsilon. —Preceding unsigned comment added by Lathrop (talk • contribs) 01:29, 25 October 2008 (UTC)