In this paper it is proposed that the
Conservation of Hartley-Shannon Information (hereafter contracted to H-S Information)
plays the same role in discrete systems as the Conservation of Energy does in
physical systems. In particular, using a variation approach, it is shown that
the symmetry of scale-invariance, power-laws and the Conservation of H-S
Information are intimately related and lead to the prediction that the
component sizes of any software system assembled from components made from
discrete tokens always asymptote to a scale-free power-law distribution in the
unique alphabet of tokens used to construct each component. This is then
validated to a very high degree of significance on some 100 million lines of
software in seven different programming languages independently of how the
software was produced, what it does, who produced it or what stage of maturity
it has reached. A further implication of the theory presented here is that the
average size of components depends only on their unique alphabet, independently
of the package they appear in. This too is demonstrated on the main dataset and
also on 24 additional Fortran 90 packages
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