Bits from it. Mathematical Clarification. (FQXI 2013 )

. R.V.L. Hartley in 1928 and C.E. Shannon in 1948 have formulated a fundamental assumption that the most natural choice for any future information theory is the logarithmic function. This assumption became common heuristic in contemporary physics, computer science and quantum information theory. Nevertheless, mathematically speaking, we may suppose that Hartley-Shannon Assumption [HSA] needs taking justification seriously. Our note represents the first attempt of re-examination of such sort of popular assumption and we show how an innocent number-theoretical finding by Shannon became “ unreasonably effective “ abstraction in contemporary theoretical physics, experimental quantum mechanics and cosmology.