Nigh

Nigh's given name was Corin, but he had been called Nigh since he was ten, when a bargeman asked him how much a stacked wagon weighed and Corin answered, without pausing, "Nigh to nine hundred," and was proven right within a sack.

He learned nearness the way other children learn their letters — early, and without noticing. A number was never just itself; it was always closest to some friendly landmark. Forty-seven leaned toward fifty. Forty-two leaned toward forty. A number sat between two landmarks and belonged, for the ferry's purposes, to whichever it was nearer.

The hard cases were the ones that sat exactly between. Forty-five — was it forty or fifty? Nigh's mother had a rule, and it was the same rule the academy would later teach: when a number sits at the halfway mark, round it up, to the higher landmark, so that everyone uses the same rule and no two ferrymen ever disagree about the same load.

A travelling proctor from the academy crossed on Nigh's ferry one autumn and watched the boy — grown now — call out load-weights all morning without a scale.

"You are estimating," the proctor said.

"I am judging the nigh weight," said Nigh.

"That is the same thing," said the proctor. "In the academy we round numbers to the nearest ten or hundred and reason with those. It is faster than the exact number and, for most questions, exactly as useful. We could use a mind like yours."

Nigh had never left the river. He thought about it for a season. Then he 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 painted number line along one wall, with the tens marked bold and the numbers between them marked faint. He begins the same way each year. He points at sixty-three and asks, "Which bold mark is it nearest?"

The children look. Sixty-three sits just past sixty, far from seventy. They say sixty.

"Yes," says Nigh. "Sixty-three rounds to sixty, because it is nigh to sixty. Now — sixty-eight?" The children see it lean the other way, toward seventy, and say seventy. "Yes. And sixty-five, sitting square in the middle?" The children hesitate. Nigh gives them the ferryman's rule: "At the halfway mark, we agree to round up. Sixty-five rounds to seventy. Not because it is truly closer — it is exactly between — but because we all keep the same rule, so we all get the same answer."

Then he shows them why it is worth doing. He writes a hard sum — 312 + 289 — and before anyone reaches for a slate he says, "Round first. Three hundred and nigh three hundred. That is six hundred. The true answer is near six hundred. Now if a friend tells you the answer is nine hundred, you already know they are wrong, because you knew the nigh answer before you knew the true one." The children realize they can catch mistakes with an estimate — that the round guess is a lantern held up before the exact number arrives.