Demon at the partition has been at his ledger all afternoon

The demon at the partition has been at his ledger all afternoon, and the ledger is the trouble. Give him a gate and a swift finger and he sorts the fast molecules from the slow, but the sorting is not free: every molecule must be observed before it is judged, and the observation must be recorded somewhere, and the record must be erased before the next observation takes its place. The information is the currency. Spend it on measuring the molecule and you have less to spend on moving the piston. Count the gas and you have already warmed it a little.

The same difficulty appeared in smaller form at Glenlair last week, with the colour top. The disc carries sectors of red, green, and blue, and the eye reports a single blended grey when the disc spins fast enough. But the blend depends on how the sectors are measured. Weigh the painted card before painting and after; the pigments sit at different depths, scatter differently at the rim, and the sector angles I read off with the dividers are not the angles the eye receives. The act of partitioning the circle into countable sectors introduces boundaries the continuous sensation never had. The grey of the spinning disc is not the average of three colours; it is the average of three colours as divided, and the division is visible in the result.

Map the propagation generally: an observer couples to the observed system, the coupling carries a finite speed, and during the propagation the system moves on. No measurement is instantaneous, so no measurement reports the system unaccompanied by the measuring. The phase relationship between the observation and the thing observed is part of every reading. Two experiments on the same subject, differing only in how finely they count, are not the same experiment; their results interfere, and the fringes belong to the counting, not the counted.

The remedy, if there is one, is to write the cost of observation into the equation alongside the quantity observed, as the demon writes his erasures into his ledger. The gas at the partition this evening held 447 molecules on the fast side.

The ledger recorded 447.