Pinned to the wall of a schoolroom at Greenwich was a pale disc with a scatter of irregular smudges and dots on it, and the boys seated near the front copied it that way. The ones too far back to resolve the smudges joined them up, into a fine web of straight lines running clean across the face of the disc.

Edward Maunder and Joseph Evans ran that experiment in 1903 and published it in the Monthly Notices of the Royal Astronomical Society. Nobody had told the boys to look for lines. They'd been told to draw what they saw, which is where the trouble lives. Hand an eye a pattern slightly finer than it can resolve, then ask for a faithful record, and the eye supplies the joins.

Percival Lowell had spent nine years by then betting on the lines. In 1894 he put an observatory on a mesa above Flagstaff, picked for its steady air, and aimed it at one planet. He mapped Mars until he died. Hundreds of canals, named and catalogued and redrawn each opposition, and three books arguing that what he was tracing was engineering: an old civilization on a drying world, running meltwater down from the poles to the equator.

He was not careless. He had the better viewing site, a fine refractor, and more hours at the eyepiece than most of the men who doubted him. He had a method, and the method delivered. Each season returned more canals than the one before. Sharper technique, more of them. There was never a season when the careful looking came back holding nothing.

Thirteen points of light. Tap them in order and trace the figure you see. Tap the last one again to take it back.

The same year, at the University of Nancy in eastern France, René Blondlot announced a new radiation, N-rays, detectable as a faint brightening of a spark held at the edge of vision in a darkened room. Something like three hundred papers followed over the next three years, from a hundred-odd scientists across France.

In September 1904 the American physicist Robert Wood came to watch a demonstration, and in the dark he reached into the spectroscope and put the aluminium prism in his pocket. The prism was the instrument. Without it there was nothing to disperse and nothing to read. Blondlot's assistant read out the same spectrum he had read out before.

Nobody at Nancy was lying. The signal sat at the limit of what an eye in a dark room can judge, the expectation was strong, and the reading was being made somewhere behind the retina rather than in front of it.

Eighteen detection dog units were walked through a set of clean rooms at UC Davis in 2011. Nothing was hidden anywhere. The handlers had been told that a slip of red paper might mark the spot where drugs and explosives were hidden. Across 164 searches the dogs alerted 225 times, and the alerts gathered where the paper was. The dog was reading the handler. The handler was reacting to the paper.

What finished the canals wasn't scepticism. It was aperture. At the 1909 opposition, Eugène Antoniadi turned the 83-centimetre refractor at Meudon on Mars through a night of unusually steady air, and the canals did not resolve into finer canals. They came apart. Irregular patches and blots of shading, with nothing joining anything to anything. The lines had been an eye's best guess at detail it couldn't quite hold, and better seeing dissolved them.

The question is what would have counted as nothing. Answered in advance it gives you a method: describe the empty result before you look in enough detail that you'd know it if it turned up. Run the same question backwards over your own methods. Take the last ten times you used a particular method, the audits, the reviews, the diagnoses, the research rounds, and count how many came back with nothing. No empties can read like a good record, but it's the symptom.

Lowell's count, across twenty-two years, was zero. You don't get out of the canals by looking harder. Looking harder is how you get in.