Comment on Dimensionless Units in the SI

The recent paper by Mohr and Phillips (arXiv:1409.2794) describes several problems relating to the treatment of angle measurement within SI, the unit hertz, and quantities that can be considered countable (rather than measureable). However, the proposals that they put forward bring new problems of their own. This paper proposes alternative suggestions that solve the problems less painfully. Specifically, clarifying the text on angle in the SI brochure; relegating the hertz to a “Non-SI unit accepted for use with the International System of Units”, with specific application only for “revolutions or cycles per second”; and encouraging countable quantities to be presented as pure numbers, while requiring that a sufficient description of the quantity being counted is given in the accompanying text.

💡 Research Summary

The paper provides a critical response to the proposals made by Mohr and Phillips (arXiv:1409.2794) concerning the treatment of dimensionless quantities in the International System of Units (SI). While Mohr and Phillips correctly identify ambiguities in the current SI handling of angles, the hertz, and countable quantities, their suggested reforms introduce new complications that would disrupt long‑standing conventions in physics, engineering, and data management. The author therefore offers three pragmatic alternatives that preserve the coherence of the SI while addressing the identified problems. First, the SI brochure’s description of angle should be clarified: the radian remains a dimensionless number, but it should be explicitly defined as a unit specialized for angular measurement, with the symbol “rad” permitted for clarity. This amendment separates the radian from generic dimensionless ratios and helps students and practitioners avoid confusion when converting between angular and linear quantities. Second, the hertz should be demoted from a base SI unit to a “non‑SI unit accepted for use with the SI,” with its application limited to rotations or cycles per second. By stating that 1 Hz equals one revolution per second (or one cycle per second) the proposal eliminates the current ambiguity between frequency (Hz) and the generic reciprocal second (s⁻¹), which is especially important in electronics and communications where both concepts coexist. Third, countable quantities such as particle numbers, event counts, or sequence lengths should be expressed as pure numbers, while the accompanying text must provide a clear description of what is being counted. This approach avoids the proliferation of ad‑hoc units for counts, prevents overlap with the mole, and simplifies database handling and unit conversion. The paper argues that these modest textual and usage clarifications can be implemented without major revisions to the SI structure, and that they would resolve the practical issues raised by Mohr and Phillips in a less disruptive manner. The author calls on the International Committee for Weights and Measures (CIPM) and related working groups to consider these suggestions in the next SI revision cycle, thereby achieving a more consistent and user‑friendly system for dimensionless units.