Nigh

"You cannot know the true weight," his mother said, coiling rope. "You can know the nigh weight. And the nigh weight, held against the limit, tells you whether to launch before you could ever weigh a soul."

That is the move the academy would later call estimation for a bound: replace the exact with the nearest landmark, and use the rounded figure not as the answer but as a check on whether the exact answer is even plausible.

Nigh's given name was Corin, but he was called Nigh from the day a bargeman asked the weight of a stacked wagon and he said "nigh to nine hundred" and was proven right within a sack. He came to see every number as leaning toward a landmark. Forty-seven leans to fifty; forty-two leans to forty. A number sits between two round marks and belongs, for the ferry's purposes, to whichever it is nearer — and the whole skill is knowing which place you are rounding to. Nigh to the nearest ten, forty-seven is fifty. Nigh to the nearest hundred, it is zero — vanishing beside a hundred. The landmark you choose sets how coarse your estimate is, and a good estimator chooses the coarseness that fits the question.

The hard cases sat exactly on the halfway mark. Forty-five — forty or fifty? Nigh's mother had a rule, the same one the academy taught: at the halfway mark, round up, to the higher landmark, so that every ferryman uses one convention and no two ever disagree about the same load. "It isn't that forty-five is truly nearer fifty," Nigh tells his students. "It sits square between. We round it up by agreement — a shared rule so our estimates match. A convention isn't a truth; it's a promise we keep together so the numbers stay comparable."

A travelling proctor crossed on Nigh's ferry one autumn and watched him call load-weights all morning without a scale. "You are estimating," the proctor said. "We round to the nearest ten or hundred and reason with those — faster than the exact number, and for most questions just as useful." Nigh thought about it for a season, handed the ferry-pole to his cousin, and walked to the academy, where he has taught rounding for nine years.

In his classroom Nigh keeps a long number line along one wall, tens marked bold, the numbers between them faint. He points at sixty-three and asks which bold mark it is nearest; the children say sixty. Sixty-eight leans to seventy. Sixty-five, square in the middle, gets the ferryman's rule: round up, by agreement. Then he shows them why it earns its keep. He writes 312 + 289 and says, "Round first. Three hundred, and nigh three hundred — that is six hundred. So the true answer lives near six hundred. Now if a slate says nine hundred, you already know it is wrong, because you knew the nigh answer before the true one arrived." The children realise the estimate is a lantern: it lights up a wrong exact answer before they can trust it. This is estimation's real job in the academy — not to replace the calculation, but to bound it and catch the blunder.