Ratios Have No Units

What we actually know

Our units are conventions with a history: the metre has been defined by the size of the Earth, by a metal bar, by a wavelength of light, and now by the distance light travels in a fixed fraction of a second, where the second itself depends on a caesium transition. Useful, but chosen by committees with ten fingers. Dimensionless ratios survive all of that. The inverse fine-structure constant, roughly 137.036, and the proton-to-electron mass ratio, roughly 1836.15, are the same numbers for any observer with any ruler.

Where the extrapolation begins

This is the standard argument for how a first contact artefact would be built to be legible: encode nothing in your units, encode everything in ratios and in physical constants any technological species must eventually measure. The twenty-one-centimetre hydrogen line is the usual candidate reference, because hydrogen is the simplest and most abundant element there is.

What the novel invents

The object's short diameter divided by the hydrogen wavelength gives 512.000000 to the limit of measurement — two to the ninth power. Its long axis divided by its short axis gives 1.00137841946, the neutron-to-proton mass ratio. Its reflected waveforms yield 137.035999 and 1836.1527 as ratios of frequencies. Maseko's caution stands: given enough numbers, human beings can find meaning in spilled rice. What defeats that objection is a second relationship that does not depend on the first — and Mbane already had it on the display.

Where to read next

• — CODATA values for the fine-structure constant and particle mass ratios
• — The 21 cm hydrogen line and its use as a universal reference in interstellar message design