A reply to 'Definitions of the units radian, neper, bel and decibel' by I. M. Mills et al.

摘要

The concept of units for dimensionless quantities, whether they be the number one or other numbers, lacks convincing supporting logic. In proposing various "units" for a dimensionless quantity called logarithmic decay, with a single definition, the authors seek to avoid recognition by the SI that there is more than one quantity associated with that term. They propose that the least commonly used quantity and its definition be adopted, with "units" that may be other than unity, as the only recognized quantity of that name. I propose, on the contrary, that both naperian logarithmic decay and decadic logarithmic decay be recognized in the SI as normal and different dimensionless quantities, with different names and having different applications, and be expressed as pure numbers in the commonly accepted sense.In defining angle as a dimensionless quantity, the ratio of the length of an arc of a circle to that of its radius, the CIPM has adopted a term that has long been used for another, well-established concept that is defined independently of circular geometry and of any other quantity, and is of a different dimension. That decision leads to all the complications and distortions, including non-unitary dimensionless "units" for numbers, with names already widely used for other, real units, proposed in the paper. It is recommended that the CCU, in its duty to a community wider than that of theoretical scientists, and in consultation with ISO TC12, should adopt another term for the concept that it currently calls angle. Angle should instead be adopted formally as a base quantity with a definition that is consistent with the general, universal view of lexicographers and of the majority who understand and use the term in its classical sense.