Shannon's Formula and Hartley's Rule: A Mathematical Coincidence?

Shannon's formula C = 1/2log(1+P/N) is the emblematic expression for the information capacity of a communication channel. Hartley's name is often associated with it, owing to Hartley's rule: counting the highest possible number of distinguishable values for a given amplitude Δ and precision ±Δ yields a similar expression C' = log(1+A/Δ). In the information theory community, the following "historical" statements are generally well accepted: (1) Hartley put forth his rule twenty years before Shannon; (2) Shannon's formula as a fundamental tradeoff between transmission rate, bandwidth, and signal-to-noise ratio came unexpected in 1948; (3) Hartley's rule is an imprecise relation while Shannon's formula is exact; (4) Hartley's expression is not an appropriate formula for the capacity of a communication channel. We show that all these four statements are questionable, if not wrong. [ABSTRACT FROM AUTHOR]