Ellery Queen's Mystery Magazine, Vol. 86, No. 6. Whole No. 511, December 1985

Straight lines by Isaac Asimov[10]

I stretched out luxuriously in my armchair in the library of the Union Club and said, “When I was young, I had a memory like blotting paper. Without actually trying to, I memorized all the maps in my geography books and to this day I retain them in detail. I know all the boundaries, all the capitals, rivers, mountain ranges, and so on, but they’re all pre-World War II. I can’t do Africa and parts of Asia for that reason.”

Baranov said, “If that’s your only problem in life, you’re not suffering much.”

I ignored that. “I used to win bets that I could write down the names of all forty-eight states — forty-eight then — in five minutes, or that I could write down every state capital with its state in ten.”

“Can you still do it?” said Jennings, sounding only faintly interested.

“Of course,” I said, “and I can add Juneau, Alaska, and Honolulu, Hawaii.” A bit more cautiously, I added, “I haven’t tried it in thirty years or so. I suppose it’s conceivable I might miss one or two.” Then, my courage reviving: “But I doubt it.”

“Did you make much money that way?” asked Jennings.

“I never bet more than a nickel,” I said virtuously, “and I was betting on a sure thing.”

“You must have been an insufferable prig when you were young,” said Jennings.

“Why not?” said Baranov. “He’s insufferable now.”

It was at this point that Griswold stirred. He grunted, sipped at his drink, and said, “I think I can match that performance, at least as far as the United States is concerned, and even outdo it.”

I said, “Come, come, Griswold, if you think you’re going to trap me into one of your bets—”

“Not at all,” said Griswold freezingly, “I was merely going to say that an interesting espionage puzzle once rested on just such a point, and I see now that I will be forced to explain.”

The matter [said Griswold] came up during the Second World War, when I was a young man on the fringes of the world of spy and counterspy. I was under the wing of one of the grand old hands of that world — Wingate, his name was. He’s long since dead, though he died in bed and in comfort, which was not true of many of us.

He told me the story one evening when we were taking a break from our efforts to work out just what the Germans knew, if anything, about our forthcoming landing at Salerno. It was a relief to turn to the simpler days before our entry into the First World War.

In 1916, as it is just possible one or another of you might know, the United States was having trouble with a Mexican revolutionary — well, we called him a bandit — named Pancho Villa. He gambled for popular support in Mexico against his Mexican opponents by trying to force the United States to intervene on the side of those opponents.

He did this by killing Americans. In January of that year, he stopped a train in northern Mexico, took off seventeen American engineers, and shot sixteen of them without even bothering to make up a reason. When that didn’t do the trick he actually sent four hundred raiders across the American line into the border town of Columbus, New Mexico. They burned the town and killed nineteen Americans.

That got him what he wanted. The United States could under no conditions sit still for that. We forced the Mexican government to grant permission, and a week after Villa’s raid we sent six thousand American troops under Black Jack Pershing into Mexico. They penetrated hundreds of miles into the country and kept up the case for nearly a year. The one thing they didn’t do, however, was catch Villa.

Villa, after all, was on his home turf and was swimming through a sea of sympathetic peasants. As week after week and month after month passed without a capture, the United States looked more and more like a paper tiger. Villa grew more and more popular with the Mexican people, and the Mexican government was forced to take on a more and more anti-American stance or it would lose all support. It was a fiasco for the U.S. that ended in February 1917 when a stubborn President Wilson was forced to bow to the inevitable because it was clear to him that we would soon be at war with Germany and have far more important problems on our hands. He recalled Pershing and Villa lived on until 1923 when he was assassinated by a Mexican enemy.

And yet Villa might have been caught fairly early on and things would have worked out well for the American forces because they had an ace operative on their side. He was a young man from across the border who had been an American citizen for the last decade. He was well tanned, he carefully cultivated a Mexican-style moustache, he could speak Mexican Spanish perfectly, and in the proper clothes no one could possibly doubt he was anything but Mexican.

He was a crackerjack scout. If anyone could have found Villa in the jumble of semi-desert hills and ravines in which the American division was trying to find its way, it was this man. He had joined the expedition under the name of Mackenzie Clifford, but few people knew that. To almost everyone, he was only Pedro.

He was a man of amazing skill. He managed to find peasants who for one reason or another were sufficiently anti-Villa to be willing to drop messages in places where they could be found by the proper people. He worked up a chain of helpers, and American soldiers saw him only in apparent accidental encounters during which he spoke only in Spanish and behaved like an ignorant peasant who dared not show openly the hostility he clearly felt. That was necessary. One never knew what eyes were watching, what ears were listening.

Generally he was heard from only by way of messages in cipher. They were mere substitution ciphers — those were simple days and whatever skills Villa and his men might have had, they did not include sophistication in deciphering coded messages. There was one complication, to be sure. There were twenty-six different systems of substitution, each one in itself simple. Each was tied to a letter of the alphabet and the variations for each letter had to be memorized, both by Pedro and by several men in the camp. That was better than risking the equivalent of a dictionary on a scrap of paper, which might be lost.

If you began with a key word, and used each letter of the word in turn as representing a particular variety of substitution, you might have a message consisting of, let us say, seven or eight t’s in a row that would yet be deciphered into a meaningful word. Naturally, the identity of the key word was all-important and it was periodically changed. Pedro chose them, and in the accidental meetings with him or with some of his Mexican allies there was always some reference to it that seemed innocent.

“I have a brother who lives in Mobile. Senor,” someone might say. That would seem to any unauthorized ear to be a natural attempt to curry favor with an armed and possibly dangerous foreign soldier, but it made Alabama the key word.

The key word was always the name of a state. There were forty-eight of them, which made sufficient variety, and they could be referred to with relative innocence and ease. Of course, against any sophisticated enemy the constant use of the name of a state would have been dangerous, but those were simple days.

Pedro managed to slip into camp one night — always a very risky thing. He was hot on the trail of Villa and had pinned him down, he thought, to a particular region. This region he intended to penetrate, and if he could — and stay alive — he might be able to send back a message by a trusted ally, provided he stayed alive. The few American soldiers who worked with Pedro — and my friend Wingate was the youngest of them — discussed possible ways of trapping Villa, if he were where Pedro thought he was, but it was clear that everything depended on just which valley he was in at the moment, and this was what Pedro had to find out.

It was only after Pedro had slipped out of camp as dawn was approaching that the soldiers realized he had not given them the key word for his next, all-important message. He might be able to send them the usual roundabout indication, but he might not. He should have told them while he was right there. After some agonized recrimination, it fell to Wingate, as junior man, to take out in pursuit of Pedro and get the information without blowing his cover.

Wingate took off with two enlisted men and, choosing the one decent path in the direction in which Pedro was going, they overtook him on his burro. Pedro looked at them in the dim light with considerable hostility. That hostility probably did not have to be assumed. Any contact with the Yanquis would give grounds for suspicion to anyone who might witness the event from the surrounding hills.

Wingate realized this and asked his questions brusquely, as a soldier might of a peon. In his broken Spanish he asked as to the neighboring villages and if there were armed men in the vicinity and if government armies had passed through and whether some key route might exist through the mountains. Some key route, he said, and the word “key” was scarcely emphasized.

Pedro answered sullenly, professing ignorance of even the simplest matters, as a peon might when addressing soldiers. Shrugging, he said, “I do not know how best to go through the mountains. There are many paths, and I stay at home, you understand. I have been told the paths are all straight on every side. I have heard the northernmost of these might be what you want, but I do not know for myself.”

Wingate, satisfied, wheeled about and returned to camp. There, he repeated the elliptical utterance.

What Pedro said made no sense, of course, unless you knew what Wingate was after. Pedro spoke in that way with the clear intention of keeping any significance away from any unauthorized eavesdropper. To Wingate and his colleagues, however, it was clear. The key that Pedro intended to use was a state whose boundaries were all straight lines. That meant that any state that was bounded even in part by an ocean or a river or the ridge of a mountain chain was eliminated. When a map was consulted, it was at once clear that forty-five states were thus eliminated. There were only three states all of whose boundaries were straight lines: Colorado, Utah, and Wyoming. Of these three states, Wyoming was the northernmost, and so they all agreed that was the key.

Eventually a message arrived from Pedro — a longer one than usual. Everyone was certain that it must contain explicit details on Villa’s whereabouts and on the best route to take in order to block his retreat and to trap him.

Pedro himself never returned, nor was his body ever found. The natural assumption was that he had trusted one Mexican too many, had been betrayed, and shot.

At the time the message arrived, however, Wingate and the others didn’t know Pedro would never return. If they had had some presentiment of this, moreover, they would have shrugged it off, human nature being what it is. Pedro had known the risks; he was running them for his country; and it was the message that was all-important and that had been delivered. A life was a regrettable but not too high price to pay for it.

That is, if the message had been of use. As you’ve probably guessed, since you know the Americans never caught Villa, it proved of no use. Wyoming had been taken as the key, but it was quickly obvious that all it delivered was gibberish.

There was enormous dismay, as you can imagine. Naturally, there was a strong suspicion that Wingate’s Spanish did not enable him to tell “northernmost” from “easternmost” or “westernmost.” Colorado was the easternmost of the three and Utah was westernmost. They were both tried and both failed. All three gave different decipherings, but they were only three varieties of gibberish.

Then some pointed out that Arizona and New Mexico were new states that had entered the Union only four years earlier. Pedro might not be quite certain of their boundaries. Both had mostly straight lines as boundaries. Arizona was bounded on the west by the Colorado River, and New Mexico, the better bet, was almost entirely straight lines except for one tiny stretch of the Rio Grande.

Both were tried. Nothing. Nevada was mostly straight lines, too, except for a bit of the Colorado in the southeast, so that was tried. Again nothing.

Wingate, feeling his career hung in the balance, was the only one who didn’t give up after that. He made up a written dictionary of the various ciphers keyed in to each letter of the alphabet. That was against the rules, but he didn’t want to lose out by making a mistake in that respect. He then tried the six states already tested and went on to try all the remaining states as well. Nothing in every case.

That was Wingate’s story that hot summer evening in 1943, and when he concluded he said, “I won’t say that ended my career, because it obviously didn’t, but it certainly slowed my advance. Someone had to be blamed and I was the obvious candidate. It took me several years to live down that blot on what proved to be an otherwise distinguished career. I did live it down and I am doing well, so I can’t really complain. Still, I wish I knew what went wrong. Could Pedro have made a mistake in the ciphering? He never had at any other time. Could the message have been intercepted and a false message substituted? Somehow I don’t see Villa possessing that subtle a sense of humor. His methods might have been effective, but they were always crude.

“But what went wrong, then? I tried every state. In fact, I felt that for the final climactic message he would choose a very unusual key, just to make sure it wouldn’t be broken if intercepted. Once that occurred to me in later years, I even tried some U.S. territories — Alaska, Hawaii, Puerto Rico, Samoa, Guam, the Canal Zone. Nothing worked. I expect that until I die I’ll wake up at night still worrying about it.”

I had listened to the story attentively. I was only an apprentice in my mid-twenties and Wingate was one of the great men in the field. When he finished, I said diffidently, Do you still have the message? And the list of substitutions for each letter?”

“Oh, yes,” said Wingate bitterly. “I’ve kept it on hand as a grim reminder of the fact that disasters wait around every comer. And every once in a while I gaze at it in the hope that illumination will suddenly blaze up within me. — It never has.”

“In that case,” I said even more diffidently, “I might be able to read it for you.”

“What!” he said. “Are you mad?”

“I hope not, sir,” I said.

“Are you trying to tell me that I’ve been worrying over this for over a quarter of a century and you’ve got the answer after hearing the story once?”

“It’s possible, sir. Let me tell you something about Pedro that you haven’t told me, and if I’m right I’ll tell you what I think is the key to the message.”

“You do that, son,” he said, “and I shall take the greatest interest possible in your future advancement.”

Well, it worked out, of course. The message was a straightforward description of where Villa was and how to trap him, and he would have been trapped in a week but for a natural and unfortunate failure of communication between Wingate and Pedro. The correct translation of the message is now buried in some government pigeonhole and I doubt that it will ever be released for public consumption, but at least it meant that Wingate had his private misery lifted from his heart.

Wingate did take an interest in my advance and I moved rapidly up the ranks until my unfortunate habit of being right when my superiors were wrong, and reminding them of the fact whenever I thought it would do them good, made it more comfortable for them to see to it that I underwent early retirement.

Griswold returned to his whiskey and soda and I said, “Hold on! You did say that this man Wingate tried all forty-eight states, didn’t you?”

“Yes, I did.”

“He didn’t inadvertently leave out one?”

“No, he didn’t.”

“Or make a mistake in the deciphering?”

“No, he didn’t.”

“Well, then, how could you work out an answer? It’s impossible.”

Jennings and Baranov made indignant sounds of agreement with me.

Griswold said, “Impossible only to inferior minds. I told you the story exactly as Wingate told it to me and Wingate said nothing of Pedro’s origin except that he was from ‘across the border.’ Combine that with the fact that he could speak perfect Mexican Spanish and it might seem that he was originally from Mexico. You three probably took it for granted he was.

“However, his real name was Mackenzie Clifford, as Wingate told me and as I told you, and that is not a name that sounds Mexican. There is another border, after all, and William Lyon Mackenzie was the nearest thing to a George Washington that Canada had. Anyone with a first name of Mackenzie is very likely to be Canadian.”

“Oh!” I said, feeling enlightenment begin to creep in on me.

“Yes, oh!” said Griswold. “Americans think of American states and then their minds close. Canadians think of American states, yes, but of Canadian provinces as well, and they can’t help giving the latter at least equal prominence. Wingate had speculated that Pedro, or Mackenzie Clifford, wanted something unusual as his key for this particular message and I imagine he did — so he automatically thought of a province.

“There were nine Canadian provinces in 1916, Newfoundland not being included at the time. Since I, too, have maps in my mind as our friend here has, I could see the answer at once. Of the nine provinces, six border on the Atlantic Ocean or Hudson Bay and one on the Pacific Ocean. That leaves two provinces without a waterfront: Alberta and Saskatchewan. Of these two, Alberta’s southwestern border follows the irregular line of a ridge of the Rocky Mountains. Saskatchewan is therefore the only Canadian province whose boundaries are all straight lines.

“Saskatchewan was farther north than any American state at the time. When Pedro said the key was the northernmost with all straight boundaries, he very naturally was thinking of Saskatchewan, and Wingate and his colleagues just as naturally thought of Wyoming.

“To begin with, I guessed that Pedro was born in Saskatchewan and that local pride was showing. I said as much to Wingate, and, with great surprise, he confirmed it. I knew I was right then, and went ahead in full confidence.”

And with what I imagine he felt to be a modest smirk, Griswold took another sip at his drink.