The general manager was none too gracious about Tupelo’s offer of help. He indicated that the System would solve this little problem without any help from harebrained professors who thought that whole subway trains could jump off into the fourth dimension. Tupelo submitted to Whyte’s unkindness, then went to bed. At about 4:00 A.M. the telephone awakened him. His caller was a contrite Kelvin Whyte.

  “Perhaps I was a bit hasty last night, professor,” he stammered. “You may be able to help us after all. Could you come down to the Milk Street Cross-Over?”

  Tupelo agreed readily. He felt none of the satisfaction he had anticipated. He called a taxi, and in less than half an hour was at the prescribed station. At the foot of the stairs, on the upper level, he saw that the tunnel was brightly lighted, as during normal operation of the System. But the platforms were deserted except for a tight little knot of seven men near the far end. As he walked towards the group, he noticed that two were policemen. He observed a one-car train on the track beside the platform. The forward door was open, the car brightly lit, and empty. Whyte heard his footsteps and greeted him sheepishly.

  “Thanks for coming down, professor,” he said, extending his hand. “Gentlemen, Dr. Roger Tupelo, of Harvard. Dr. Tupelo, Mr. Kennedy, our chief engineer; Mr. Wilson, representing the Mayor; Dr. Gannot, of Mercy Hospital.” Whyte did not bother to introduce the motorman and the two policemen.

  “How do you do,” said Tupelo. “Any results, Mr. Whyte?”

  The general manager exchanged embarrassed glances with his companions. “Well… yes, Dr. Tupelo,” he finally answered. “I think we do have some results, of a kind.”

  “Has the train been seen?”

  “Yes,” said Whyte. “That is, practically seen. At least, we know it’s somewhere in the tunnels.” The six others nodded their agreement.

  Tupelo was not surprised to learn that the train was still on the System. After all, the System was closed.

  “Would you mind telling me just what happened?” Tupelo insisted.

  “I hit a red signal,” the motorman volunteered. “Just outside the Copley junction.”

  “The tracks have been completely cleared of all trains,” Whyte explained, “except for this one. We’ve been riding it, all over the System, for four hours now. When Edmunds, here, hit a red light at the Copley junction, he stopped, of course. I thought the light must be defective, and told him to go ahead. But then we heard another train pass the junction.”

  “Did you see it?” Tupelo asked.

  “We couldn’t see it. The light is placed just behind a curve. But we all heard it. There’s no doubt the train went through the junction. And it must be Number 86, because our car was the only other one on the tracks.”

  “What happened then?”

  “Well, then the light changed to yellow, and Edmunds went ahead.”

  “Did he follow the other train?”

  “No. We couldn’t be sure which way it was going. We must have guessed wrong.”

  “How long ago did this happen?”

  “At 1:38, the first time—”

  “Oh,” said Tupelo, “then it happened again later?”

  “Yes. But not at the same spot, of course. We hit another red signal near South Station at 2:15. And then at 3:28—”

  Tupelo interrupted the general manager. “Did you see the train at 2:15?”

  “We didn’t even hear it, that time. Edmunds tried to catch it, but it must have turned off onto the Boylston shuttle.”

  “What happened at 3.28?”

  “Another red light. Near Park Street. We heard it up ahead of us.”

  “But you didn’t see it?”

  “No. There is a little slope beyond the light. But we all heard it. The only thing I don’t understand, Dr. Tupelo, is how that train could run the tracks for nearly five days without anybody seeing—”

  Whyte’s words trailed off into silence, and his right hand went up in a peremptory gesture for quiet. In the distance, the low metallic thunder of a fast-rolling train swelled up suddenly into a sharp, shrill roar of wheels below. The platform vibrated perceptibly as the train passed.

  “Now we’ve got it!” Whyte exclaimed. “Right past the men on the platform below!” He broke into a run towards the stairs to the lower level. All the others followed him, except Tupelo. He thought he knew what was going to happen. It did. Before Whyte reached the stairs, a policeman bounded up to the top.

  “Did you see it, now?” he shouted.

  Whyte stopped in his tracks, and the others with him.

  “Did you see that train?” the policeman from the lower level asked again, as two more men came running up the stairs.

  “What happened?” Wilson wanted to know.

  “Didn’t you see it?” snapped Kennedy.

  “Sure not,” the policeman replied. “It passed through up here.”

  “It did not,” roared Whyte. “Down there!”

  The six men with Whyte glowered at the three from the lower level. Tupelo walked to Whyte’s elbow. “The train can’t be seen, Mr. Whyte,” he said quietly.

  Whyte looked down at him in utter disbelief. “You heard it yourself. It passed right below—”

  “Can we go to the car, Mr. Whyte?” Tupelo asked. “I think we ought to talk a little.”

  Whyte nodded dumbly, then turned to the policemen and the others who had been watching at the lower level. “You really didn’t see it?” he begged them.

  “We heard it,” the policemen answered. “It passed up here, going that way, I think,” and he gestured with his thumb.

  “Get back downstairs, Maloney,” one of the policemen with Whyte commanded. Maloney scratched his head, turned, and disappeared below. The two other men followed him. Tupelo led the original group to the car beside the station platform. They went in and took seats, silently. Then they all watched the mathematician and waited.

  “You didn’t call me down here tonight just to tell me you’d found the missing train,” Tupelo began, looking at Whyte. “Has this sort of thing happened before?”

  Whyte squirmed in his seat and exchanged glances with the chief engineer. “Not exactly like this,” he said, evasively, “but there have been some funny things.”

  “Like what?” Tupelo snapped.

  “Well, like the red lights. The watchers near Kendall found a red light at the same time we hit the one near South Station.”

  “Go on.”

  “Mr. Sweeney called me from Forest Hills at Park Street Under. He heard the train there just two minutes after we heard it at the Copley junction. Twenty-eight track miles away.”

  “As a matter of fact, Dr. Tupelo,” Wilson broke in, “several dozen men have seen lights go red, or have heard the train, or both, inside of the last four hours. The thing acts as though it can be in several places at once.”

  “It can,” Tupelo said,

  “We keep getting reports of watchers seeing the thing,” the engineer added. “Well, not exactly seeing it, either, but everything except that. Sometimes at two or even three places, far apart, at the same time. It’s sure to be on the tracks. Maybe the cars are uncoupled.”

  “Are you really sure it’s on the tracks, Mr. Kennedy?” Tupelo asked.

  “Positive,” the engineer said. “The dynamometers at the power house show that it’s drawing power. It’s been drawing power all night. So at 3:30 we broke the circuits. Cut the power.”

  “What happened?”

  “Nothing,” Whyte answered. “Nothing at all. The power was off for twenty minutes. During that time, not one of the two hundred fifty men in the tunnels saw a red light or heard a train. But the power wasn’t on for five minutes before we had two reports again—one from Arlington, the other from Egleston.”

  There was a long silence after Whyte finished speaking. In the tunnel below, one man could be heard calling something to another. Tupelo looked at his watch. The time was 5:20.

  “In short, Dr. Tupelo,” the general manager finally said, “we are compelled to admit that there may be something in your theory.” The others nodded agreement.

  “Thank you, gentlemen,” Tupelo said.

  The physician cleared his throat. “Now about the passengers,” he began. “Have you any idea what—?”

  “None,” Tupelo interrupted.

  “What should we do, Dr. Tupelo?” the mayor’s representative asked.

  “I don’t know. What can you do?”

  “As I understand it from Mr. Whyte,” Wilson continued, “the train has… well, it has jumped into another dimension. It isn’t really on the System at all. It’s just gone. Is that right?”

  “In a manner of speaking.”

  “And this… er… peculiar behavior has resulted from certain mathematical properties associated with the new Boylston shuttle?”

  “Correct.”

  “And there is nothing we can do to bring the train back to… uh… this dimension?”

  “I know of nothing.”

  Wilson took the hit in his teeth. “In this case, gentlemen,” he said, “our course is clear. First, we must close off the new shuttle, so this fantastic thing can never happen again. Then, since the missing train is really gone, in spite of all these red lights and noises, we can resume normal operation of the System. At least there will be no danger of collision—which has worried you so much, Whyte. As for the missing train and the people on it—” He gestured them into infinity. “Do you agree, Dr. Tupelo?” he asked the mathematician.

  Tupelo shook his head slowly. “Not entirely, Mr. Wilson,” he responded. “Now, please keep in mind that I don’t fully comprehend what has happened. It’s unfortunate that you won’t find anybody who can give a good explanation. The one man who might have done so is Professor Turnbull, of Tech, and he was on the train. But in any case, you will want to check my conclusions against those of some competent topologists. I can put you in touch with several.

  “Now, with regard to the recovery of the missing train, I can say that I think this is not hopeless. There is a finite probability, as I see it, that the train will eventually pass from the nonspatial part of the network, which it now occupies, back to the spatial part. Since the nonspatial part is wholly inaccessible, there is unfortunately nothing we can do to bring about this transition, or even to predict when or how it will occur. But the possibility of the transition will vanish if the Boylston shuttle is taken out. It is just this section of track that gives the network its essential singularities. If the singularities are removed, the train can never reappear. Is this clear?”

  It was not clear, of course, but the seven listening men nodded agreement. Tupelo continued.

  “As for the continued operation of the System while the missing train is in the nonspatial part of the network, I can only give you the facts as I see them and leave to your judgment the difficult decision to be drawn from them. The transition back to the spatial part is unpredictable, as I have already told you. There is no way to know when it will occur, or where. In particular, there is a fifty percent probability that, if and when the train reappears, it will be running on the wrong track. Then there will be a collision, of course.”

  The engineer asked: “To rule out this possibility, Dr. Tupelo, couldn’t we leave the Boylston shuttle open, but send no trains through it? Then, when the missing train reappears on the shuttle, it cannot meet another train.”

  “That precaution would be ineffective, Mr. Kennedy,” Tupelo answered. “You see, the train can reappear anywhere on the System. It is true that the System owes its topological complexity to the new shuttle. But, with the shuttle in the System, it is now the whole System that possesses infinite connectivity. In other words, the relevant topological property is a property derived from the shuttle, but belonging to the whole System. Remember that the train made its first transition at a point between Park and Kendall, more than three miles away from the shuttle.

  “There is one question more you will want answered. If you decide to go on operating the System, with the Boylston shuttle left in until the train reappears, can this happen again, to another train? I am not certain of the answer, but I think it is: No. I believe an exclusion principle operates here, such that only one train at a time can occupy the nonspatial network.”

  The physician rose from his seat. “Dr. Tupelo,” he began, timorously, “when the train does reappear, will the passengers—?”

  “I don’t know about the people on the train,” Tupelo cut in. “The topological theory does not consider such matters.” He looked quickly at each of the seven tired, querulous faces before him. “I am sorry, gentlemen,” he added, somewhat more gently. “I simply do not know.” To Whyte, he added: “I think I can be of no more help tonight. You know where to reach me.” And, turning on his heel, he left the car and climbed the stairs. He found dawn spilling over the street, dissolving the shadows of night.

  That impromptu conference in a lonely subway car was never reported in the papers. Nor were the full results of the night-long vigil over the dark and twisted tunnels. During the week that followed, Tupelo participated in four more formal conferences with Kelvin Whyte and certain city officials. At two of these, other topologists were present. Ornstein was imported to Boston from Philadelphia, Kashta from Chicago, and Michaelis from Los Angeles. The mathematicians were unable to reach a consensus. None of the three would fully endorse Tupelo’s conclusions, although Kashta indicated that there might be something to them. Ornstein averred that a finite network could not possess infinite connectivity, although he could not prove this proposition and could not actually calculate the connectivity of the System. Michaelis expressed his opinion that the affair was a hoax and had nothing whatever to do with the topology of the System. He insisted that if the train could not be found on the System then the System must be open, or at least must once have been open.

  But the more deeply Tupelo analyzed the problem, the more fully he was convinced of the essential correctness of his first analysis. From the point of view of topology, the System soon suggested whole families of multiple-valued networks, each with an infinite number of infinite discontinuities. But a definitive discussion of these new spatio-hyperspatial networks somehow eluded him. He gave the subject his full attention for only a week. Then his other duties compelled him to lay the analysis aside. He resolved to go back to the problem later in the spring, after courses were over.

  Meanwhile, the System was operated as though nothing untoward had happened. The general manager and the mayor’s representative had somehow managed to forget the night of the search, or at least to reinterpret what they had seen and not seen. The newspapers and the public at large speculated wildly, and they kept continuing pressure on Whyte. A number of suits were filed against the System on behalf of persons who had lost a relative. The State stepped into the affair and prepared its own thorough investigation. Recriminations were sounded in the halls of Congress. A garbled version of Tupelo’s theory eventually found its way into the press. He ignored it, and it was soon forgotten.

  The weeks passed, and then a month. The State’s investigation was completed. The newspaper stories moved from the first page to the second; to the twenty-third; and then stopped. The missing persons did not return. In the large, they were no longer missed.

  One day in mid-April, Tupelo traveled by subway again, from Charles Street to Harvard. He sat stiffly in the front of the first car, and watched the tracks and gray tunnel walls hurl themselves at the train. Twice the train stopped for a red light, and Tupelo found himself wondering whether the other train was really just ahead, or just beyond space. He half-hoped, out of curiosity, that his exclusion principle was wrong, that the train might make the transition. But he arrived at Harvard on time. Only he among the passengers had found the trip exciting.

  The next week he made another trip by subway, and again the next. As experiments, they were unsuccessful, and much less tense than the first ride in mid-April. Tupelo began to doubt his own analysis. Sometime in May, he reverted to the practice of commuting by subway between his Beacon Hill apartment and his office at Harvard. His mind stopped racing down the knotted gray caverns ahead of the train. He read the morning newspaper, or the abstracts in Reviews of Modern Mathematics,

  Then there was one morning when he looked up from the newspaper and sensed something. He pushed panic back on its stiff, quivering spring, and looked quickly out the window at his right. The lights of the car showed the black and gray lines of wall-spots streaking by. The tracks ground out their familiar steely dissonance. The train rounded a curve and crossed a junction that he remembered. Swiftly, he recalled boarding the train at Charles, noting the girl on the ice-carnival poster at Kendall, meeting the southbound train going into Central.

  He looked at the man sitting beside him, with a lunch pail on his lap. The other seats were filled, and there were a dozen or so straphangers. A mealy-faced youth near the front door smoked a cigarette, in violation of the rules. Two girls behind him across the aisle were discussing a club meeting. In the seat ahead, a young woman was scolding her little son. The man on the aisle, in the seat ahead of that, was reading the paper. The Transit-Ad above him extolled Florida oranges.

  He looked again at the man two seats ahead and fought down the terror within. He studied that man. What was it? Brunette, graying hair; a roundish head; wan complexion; rather flat features; a thick neck, with the hairline a little low, a little ragged; a gray, pin-stripe suit. While Tupelo watched, the man waved a fly away from his left ear. He swayed a little with the train. His newspaper was folded vertically down the middle. His newspaper! It was last March’s!

  Tupelo’s eyes swiveled to the man beside him. Below his lunch pail was a paper. Today’s. He turned in his seat and looked behind him. A young man held the Transcript open to the sports pages. The date was March 4th. Tupelo’s eyes raced up and down the aisle. There were a dozen passengers carrying papers ten weeks old.

  Tupelo lunged out of his seat. The man on the aisle muttered a curse as the mathematician crowded in front of him. He crossed the aisle in a bound and pulled the cord above the windows. The brakes sawed and screeched at the tracks, and the train ground to a stop. The startled passengers eyed Tupelo with hostility.

 

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