In the space of a single year, a cautious German professor who disapproved of revolutions produced two numbers that would shape the century after him. One of them was measured. The other was manufactured. Nobody, including him, ever wrote the difference down.

The first was the quantum of action, squeezed out of infrared readings taken by instrument builders in a Berlin laboratory founded to help the lamp industry sell brighter lamps. It was a real quantity, extracted from real dials, and it has survived every revision physics has thrown at it since. Today it does not merely describe the kilogram. It defines it.

The second was the Planck length. It was not measured, and it could not have been. It was assembled out of three constants by dimensional bookkeeping, in a short paper written a year before its author had any quantum theory at all. It sits roughly twenty orders of magnitude below anything any instrument has ever touched, which is a polite way of saying that the gap between it and our best microscope is larger than the gap between our best microscope and a continent. Over the following century it hardened into something else entirely: a wall, a grain, a floor, a foam, the place where space and time were said to give out. Whole research programs were built on the assumption that something happens there. Nobody has ever explained how that assumption was arrived at, because it was never argued for. It was inherited.

This book follows both numbers from the same desk in Berlin to their opposite fates, and uses them to ask a question that reaches well past physics: how do we tell the part of a result that the instruments recorded from the part we supplied ourselves so that the recording would mean something? Max Planck faced that question more sharply than almost anyone alive. He answered it brilliantly in one case and never thought to ask it in the other.