Is Quantum Space a Random Cantor Set with a Golden Mean Dimension at the Core?

In ref. [l], Mauldin et al. proved a theorem which at first sight may seem slightly paradoxical but we perceive as exceedingly interesting. This theorem states that the Hausdorff dimension dy’ of a randomly constructed Cantor set is d:’ = @, where $ = (d5 1)/2 is the G o Id en 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 suprising. Now if we could extrapolate the random construction of the said Cantor set to y1 dimensions, then one could utilize some of the results of our recent work on II dimensional Cantor sets [2,3] and claim that the Hausdorff dimension of a four-dimensional version is dy’ = formula dp’ = (l/d:‘)“-l (l/G)“. This is a direct application of the bijection introduced in refs [2-51. In other words, by lifting dL”’ = @ to four dimensions one finds that