得之于一隅，必失之于他方

Eighteenth of April, evening. All five replies are in. Last September's five two-tael bags — drawn from the twenty catties split out of house two's batch, ranked soft to hard, one to five, an identical set to each household, hung beside their own string. One question: which of these five is your normal? Chang: four. Turpan: three. Rehmanjan: three. Tursun in Kucha: two. Imin in Kucha: four. Three clustered at three, two off by one grade. Nothing wrong with that.

Then step two, and step two broke. Chang to Turpan: one grade. Turpan to Tursun: one grade. So Chang to Tursun should be two. But Chang has that one directly — Tursun's family sent a string of their own goods over this year, and Chang pinched it and said: about the same. About the same is zero. Three numbers on the page: one, one, zero. One and one do not make zero.

I sent Luo the three lines with no explanation. He came straight back: who was compared with whom? Three pairs, each compared separately. Then that's your answer. And: three men each comparing in his own room; what comes out doesn't join up. And: I saw it in the purchasing stations. One lot of cotton, three stations, three grades, and not one station chief was wrong. And, and then he stopped: what was wrong was that nobody was standing in the middle holding the same thing.

Pei Xiu came on the twentieth. Forties; official robes, not new, cuffs worn; the look of a man who has spent his life over charts, eyes slightly narrowed. He carried a rolled thing and spread it on the table: a map on silk, very old — mountains, rivers, roads, a great deal of small writing, and in one corner a small grid of squares. He looked at my three numbers and said: one, one, zero. I have been looking at those three numbers all my life.

He asked the right question first. Your three pairs were measured by three separate people. In each pair, did both men have the same object in hand? Yes — all five have the identical five bags from one batch. He looked up: then your three numbers should not fail to join. And: think again. Two minutes, and I stood up. The Chang–Tursun pair did not use the five bags. That pair was Tursun's family posting a string of their own goods, and Chang pinching it. Then there you are. And: the first two pairs each measured against the five bags. The third pair measured against each other. And, and I picked up the pen: you have two measurements that are accurate and one that is affectionate.

I objected that a direct comparison ought to be more accurate. He laughed and pushed the map forward. Look at this. From this county to that one, over the hills. He traced the bend of the road with a finger. The man who walks it says a day and a half. Then he held the finger straight between the two points. On the map it is sixty li. And: which is true? Both. Correct. The walker is measuring road-distance. The map is measuring proportion. Both are right and they will not join. And: because elevation, slope and curve lie between them.

Then the six, one at a time. Proportion — the scale, how many li to the inch. The common bearing — and he stopped here: this is the one that matters. What is it? It is everything being laid out facing the same way. And: you draw a map, I draw a map. Your north is at the top, mine is to the left. Neither of us has drawn it wrong. And, six times into the book: if you have proportion but no common bearing, you may have it right in one corner and you will certainly have it wrong everywhere else. And: in your own corner you can measure any way you like and be right. Join it to somebody else's corner and all of it is wrong.

I said: my five bags are the common bearing. Yes. You already have it. You simply had one pair that did not use it. I said that pair was the two households' own initiative and I had not put a hand in. That is a good thing. And: but a good thing and an accurate thing are two different things. And: that they were willing to post directly to each other means the net is alive. And: once it is alive you have to give it a north — otherwise it will grow crooked on its own.

The last three. They are the ground being different. My six characters: adjusted according to the ground. And: the same sixty li is a day on the flat and three days in the hills. You cannot say the man in the hills walks slowly. So: Kucha sits a thousand metres above Turpan; the same number of hanging days does not produce the same goods. That is elevation. And: your table says "days hung." Days are road-distance. And: with road-distance and no correction for elevation, the number of your stages must disagree with the true distance. And, four times into the book: the number of days is not the thing itself. It is what the thing costs in that particular place.

Rolling the map up: the six must be brought together and checked against one another. What happens if one is missing? The map still gets drawn. It gets drawn, and it looks right. And at the door: right up until somebody takes it, sets out, and doesn't come back. — M.

Memo to file. Chengdu, 18–26 April 2032. Year one of the five-household exchange. The offsets don't add up.

1. The failure, stated cleanly. Chang→Turpan = +1. Turpan→Tursun = +1. Chang→Tursun should be +2; observed 0. The offsets are not transitive, which means at least one of them is not measuring what I think it is.

2. Where it broke, and it is not where I looked first. Two of the three pairs were measured against the five shared bags. The third was measured against each other — Tursun's family posted a string of their own goods and Chang pinched it directly. A direct comparison feels more accurate and composes worse. Two households comparing to each other produce a number only those two can use. Two households comparing to a common object produce a number all five can use. In map terms: I had proportion in every corner and no common bearing between them.*

3. The rule, issued 22 April, and the edit I made to it. First draft: whoever compares with whoever, compare against the five bags first. Do not compare directly household to household. I withdrew the second line and replaced it: direct comparison is fine too — record that figure in its own column, don't mix it with the others. Because the direct figure is usable by those two households; the against-the-bags figure is usable by all five. Suppressing the direct comparisons would have been the tidier system and the wrong one.

4. And then Ali, aged fifteen, told me what that string actually was. His grandfather told him to send it. "He said he wanted to know what the people inland are eating." And: "It wasn't to match numbers." Tursun is seventy-two, has spent his life in Kucha, and since the dentures cannot bite any more. He wanted to know what someone thirteen hundred kilometres away tastes. In the book: I brought a common bearing to correct something that was never a measurement. And: a wrong measurement should be corrected. But that string was never offered as one.

5. What I did about it, 25 April, to Ali only. I filed your grandfather's string in the wrong place — I recorded it as a number in the comparison column. I have moved it out into a column of its own. The column is called: looking at each other. He replied ok, then two minutes later: "He'll ask about that column." And: "He asks once a day whether Grandpa Chang has answered."

6. Chang's second sentence, which nobody heard the first time. He said two things after pinching that string; Chang Bin was out in the yard for the second. Asked again a week later, he repeated it: "The wind in this family's drying house is drier than ours." "He's like me — he shuts the windows too early."

7. The first sentence is elevation. The second is not, and it is the finding of the month. A sixty-five-year-old man, thirteen hundred kilometres away, who has never met the other man, read a working habit off a handful of dried fruit — and not a defect either: the same habit he has himself. In the book: what I am missing is not the common bearing. I have that. What I am missing is a seventh element — one that isn't in the six, because maps do not miss each other.

8. Practical carry-forward. — Add an elevation column: Kucha ~1,100 m above Turpan; days-hung is not comparable across that gap without a correction term, and I have no coefficient yet, so the column goes in empty (see 211: 阙 rather than a guess). — Keep the looking at each other column permanently; it is not measurement and must never be averaged into one. — Tursun is 72 and cannot bite. Whatever that column is for, its clock is short.

"If you have proportion but no common bearing, you may have it right in one corner and you will certainly have it wrong everywhere else."
From the preface to a set of eighteen regional maps, by a man who spent his working life on the problem of how two separately made drawings can be made to agree. He set out six elements, and the ordering is an argument: proportion, common bearing, road-distance, then elevation, slope, and curve against straight.
Proportion is the easy one — so many li to the inch — and it is the one everybody has. The trouble is that proportion is entirely local. A man measuring carefully inside his own district will get every distance in that district right, and his map will still be useless the moment it is laid beside his neighbour's, because nothing establishes how the two sheets are oriented with respect to each other.
Hence the second element, and his insistence that it is the one that matters. A common bearing is not a measurement. It is a shared direction that every measurement is taken with respect to — and it has to be agreed before the measuring starts, not reconciled afterwards.
The last three are a different kind of caution. Road-distance and true distance diverge in broken country, and the divergence is not error:
"With road-distance and no correction for elevation, slope and curve, the number of your stages must necessarily disagree with the true distance."
The walker who reports a day and a half and the map that reports sixty li are both telling the truth. What they are measuring is not the same quantity, and the phrase he uses for the fix is worth keeping: adjusted according to the ground. The same sixty li is a day on the flat and three days in the hills, and the man in the hills is not slow.
Which leaves the closing warning, and it is about a specific kind of danger — the kind that does not announce itself.
The map still gets drawn. It gets drawn, and it looks right.
Right up until somebody takes it, sets out, and doesn't come back.