South Africa, Aug. 4 -- The arithmetic only worked because Day had understood something his competitors had not. His readers were not his customers. As Tim Wu records in The Attention Merchants, they "were in fact his product."

Day was reselling attention in bulk to advertisers who had no way of knowing which readers had noticed their notices. So the trade settled on the one number anyone could count, which was how many copies left the building. Circulation became the currency of advertising because it was countable, not because it was accurate.

Nearly two hundred years later we are still trading that proxy. We have renamed it Reach.

The problem was never that reach is useless. The problem is that we treat a measure of opportunity as a...