A superconducting junction lit by microwaves does something odd: the voltage across it will not vary smoothly. It climbs in steps, and the size of those steps is set by the driving frequency. Since frequency is the quantity humanity measures best, that turns a clock into a voltage.

Cool a thin sheet of electrons in a strong magnetic field and something equally strange happens to its resistance, which stops depending on the material, the shape or the history of the sample and settles onto values built from two constants of nature.

Julian Ashworth explains how those two effects, put together by Ohm's law, now produce the ampere.

They had to. The old definition, retired in 2019, described a current flowing in two conductors of infinite length and no thickness, suspended in vacuum a metre apart. It was a thought experiment presented as a specification, and no laboratory could carry it out. Its replacement declares the charge on the electron to be an exact number and says nothing whatever about equipment — which relocates the difficulty rather than removing it.

An honest objection follows, and the book takes it seriously: this route delivers a current without ever counting a single electron. Hence the pumps that shift charge one particle per cycle. Hence, too, the triangle: three devices of quite different physics, obliged to return the same answer if any of them is to be believed. Closing that triangle remains unfinished work, and is described here as unfinished.

The final chapters descend from the cryostat to the calibration bench and the meter on a wall, ending with a published instance of an error in high-resistance traceability being caught and put right — which is the argument in miniature, since a system that cannot be checked is not a measurement system at all.