Power-laws and the Conservation of Information in discrete token systems: Part 2 The role of defect

摘要

In a matching paper (arXiv:1207.5027), I proved that Conservation of Size andInformation in a discrete token based system is overwhelmingly likely to leadto a power-law component size distribution with respect to the size of itsunique alphabet. This was substantiated to a very high level of significanceusing some 55 million lines of source code of mixed provenance. The principlewas also applied to show that average gene length should be constant in ananimal kingdom where the same constraints appear to hold, the implication beingthat Conservation of Information plays a similar role in discrete token-basedsystems as the Conservation of Energy does in physical systems. In this part 2, the role of defect will be explored and a functionalbehaviour for defect derived to be consistent with the power-law behavioursubstantiated above. This will be supported by further experimental data and the implicationsexplored.