A surveyor standing in the middle of a field turns her instrument to each corner of the plot in turn and records the angle between one corner and the next. When she has gone all the way round she has a list of angles, and before she does anything else she adds them together.
They must come to three hundred and sixty. She has turned a full circle and stopped where she began. There is no room for opinion about it.
If the total is three hundred and fifty-nine, or three hundred and sixty-one, she has made a mistake somewhere, and she knows it before she leaves the field. That is the whole value of the check: it does not tell her which angle is wrong, but it tells her that one of them is, while the equipment is still set up and the light is still good.
Her apprentice asked why she bothered when the instrument was accurate to a fraction of a degree. She said accuracy is not the point. Any single reading can be written down wrongly, or taken to the wrong corner, or recorded twice. The instrument cannot catch that. The total can.
Surveyors call this closing, and every trade has its own version. A carpenter measures a frame's two diagonals; an accountant balances two columns. In each case a quantity that is fixed in advance is compared with what the work produced.
"Do the arithmetic that must come out," she told him. "It is the only kind that can tell you you are wrong."