In Trans. Am. Math. Soc. 295, 325-346 (1986; Zbl 0625.54047) R. D. Mauldin and S. C. Williams proved a theorem which at first sight may seem slightly paradoxical but we perceive as exceedingly interesting. This theorem states that the Hausdorff dimension \(d_ c^{(0)}\) of a randomly constructed Cantor set is \(d_ c^{(0)} = \phi\), where \(\phi = (\sqrt{5} - 1)/2\) is the Golden Mean. That such disordered indeterministic construction which actually epitomize dissonance should single out the Golden Mean, an epitomy of perfect order and internal harmony, as a Hausdorff dimension strikes us at least in the first instance as surprising. Now if we could extrapolate the random construction of the said Cantor set to \(n\) dimensions, then one could utilize some of the results of our recent work on \(n\) dimensional Cantor sets [the author, Complex dynamics in 4D Peano-Hilbert space, Il Nuovo Cimento 107B, 589 (1992) and On dimensions of Cantor set related systems, Chaos Solitons Fractals 3, No. 675-685 (1993)] and claim that the Hausdorff dimension of a four-dimensional version is \(d_ c^{(4)} = (1/\phi)^ 3\). This is a direct application of the bijection formula \(d_ c^{(4)} = (1/d_ c^{(0)})^{n-1}\) introduced by L. Nottale [Int. J. mod. Phys. A 4, 5047-5117 (1989)]and the author [loc. cit. and Chaos Solitons Fractals 1, No. 5, 485-487 (1991; Zbl 0758.58015)]. In other words, by lifting \(d_ c^{(0)} = \phi\) to four dimensions one finds that \[ d^ 4_ c = (1/\phi)^ 3 = 4.236067977 = \sqrt{5} + 2 = 4 + \phi^ 3 = 4 + d_ c^{(-2)}. \] It is the aim of this short note to glance at the implications of the preceeding construction to the geometry of micro space-time of quantum mechanics.