by Tom DeMarco
All of the defenses against approach from the south involved slipping behind the attacking fleet, and then coming down on it with the wind. But that was a maneuver that had to be carried out with great precision. And from the moment the attack was signaled, everything would depend on being able to outsail the opposition. It would be foolhardy to expect Paule to try again in tired old boats like the McMillan yawls. This time he would come in something faster and a lot more handy, probably multi-hulls. And against such boats, the Baracoa fleet would be seriously outclassed. Of course, eventually, Paule would be able to bring some steam powered ships into play. But Baracoa was working on that angle too. It would take a year or so, but they would soon have something to counter a steam threat from the north. Only in the interim did they have to worry about being outsailed. Paule had instant access to all the expensive toys that American yachtsmen had accumulated over the years, while Loren had only those vessels the group had arrived in plus a few catamarans from Guantanamo. The Revolutionary Republic of Cuba, unfortunately, had not been a great center of yachting.
What could he do to increase the advantage for the Baracoa fleet? How could he give his vessels better sailforms, lower drag, better hullspeed or a higher pointing angle? If they could sail even five degrees closer to the wind than the opposing fleet, he knew, that would be a huge advantage. A huge advantage.
From years of training as a physicist, he began to sketch a model, part physical and part mathematical, of the factors that affected a sail’s ability to pull when trimmed close to the wind. Within an hour he had reconstructed the equations from memory of the Bernouli Effect, the acceleration of the wind around the leading edge of a sail and its resultant force drawing the boat forward. He made a simple approximation of the resistance of the keel that kept the boat from sliding downwind. Each of his equations involved one use of differential calculus, a derivative with respect to time, and this caused his mind to wander back into the realm of t-prime, the elevated state of time brought on by the Layton Effect.
He divided time into its two components and re-did the equations. Since the boat and the sea it sailed through were governed by the same t-prime, the difference washed out and he was left with essentially the same results again. But suppose that weren’t true? Suppose t-prime could take on one value at the sail and another at the keel? He seemed to recall that there was something they had been grappling with during the previous spring in Ithaca that might have an application now to the problem of making their boats sail higher, even faster. Underneath his bed, he found the battered shoulder bag he had carried on the flight from Ithaca to Ft. Lauderdale. He hadn’t even thought of that bag for more than half a year. In preparation for their departure on that long-ago May evening, Homer had insisted that Loren bring along the laboratory daybook. Who knew, he had argued, that they wouldn’t find a few minutes one day by the pool to think about some aspect of the problems they were working on, and have need of the records they had been keeping in the daybook? Loren found the book now in the bottom of the shoulder bag.
Sitting on his bunk in the cottage he shared with Edward, Loren leafed through the dated entries in the book. At last he came to the Sunday afternoon of his presentation to the group about t-prime. The six now-familiar equations were laid out neatly in his handwriting. These were the equations that had enabled change to the very fabric of time in this world. He stared at them, thinking through again their significance. It was still stunning, how wrong they had been before in the way they thought about time. The old view seemed so simplistic and naive, now that they knew. Nothing was simple about time. It was baroque, convoluted, Peculiar, in the special sense that Homer had given to that word. Yet it was no more surprising than the baroqueness earlier generations of physicists had discovered in the inner workings of energy or gravity or light.
But all that had to do with Physics, the pure science. What Loren was interested in now was a gimmick to make boats sail faster, some way to turn the equations again to their advantage. He took the daybook and set out in search of Edward. He found him in the workshop.
“Look at this, Ed. Something from your past.” Loren laid the book down, open to the t-prime equations. He placed it directly on top of the telephone network diagrams that Edward had been going over with D.D. Pease. “I’m not interrupting, am I?”
“Goodness, no. Pease and I were just working on re-establishing the modern world. Nothing serious, mind you. Only that. We’re going to have phones working throughout the village within the next week.”
“Oh, good. Ed, do look at this equation for a minute and tell me if I’m off on a goose hunt…”
“A wild goose chase.”
“Uh huh. You see, there is an additional stable value of t-prime, beyond the one we have elevated ourselves to. There was the old original value, the one that I called t-prime-zero: that was the way the world was before we got involved. And then there is a t-prime-one: that is the reduced time flow that we have now, with time proceeding at something like a twentieth of a percent slower rate.”
“Yes, I remember.” Edward just looked distracted.
“But then, the equation predicts that there is a second stable state, considerably slower than the others. I’ll call that t-prime-two. It would slow time down to about one ten thousandth of what it is now.”
“Right.”
“Notice it would be too slow to propagate. I mean it would take thousands of years to inject itself onto the earth’s magnetic field. So it could only have local impact, just in the immediate surroundings of the Effector.
“Oh good. I just couldn’t bear to have the whole world slowed down by a factor of ten thousand. Think how it would set back our phone project.”
“Uh huh. But now suppose we built ourselves a t-prime-two Effector and attached it to the keel of a sailboat. When we turned it on, time would be slowed enormously in the direction of the beam. If we were to align the beam perpendicular to the keel, we would have a boat that was extremely stable in its plane. It simply could not heel over. And it couldn’t slip downwind. I mean it would be slipping, but ever so slowly, because time would be so sluggish in that direction. Don’t you see? It would be the ultimate keel. And it wouldn’t depend at all on water resistance. The boat could move directly forward or backward, but not sideways. And it couldn’t tilt. It would be locked in its plane.”
“A little inconvenient when it comes time to turn,” said Pease.
“We switch it off. And then when we’re established on the new course, we turn it on again. Think of the advantage it would give us to be able to sail without side-slip and without heeling. We could sail rings around whatever they sent down against us.”
“Cute,” said Edward.
“Cute?! This is more than cute. This is important, Ed. I think you guys ought to drop what you’re doing and work with me on this.”
Barodin shrugged, and then gave Loren an evil little grin. “Pease and I are reasonable men, Loren. We’re so impressed with the promise of your ultimate keel that we’re going to let you clear off one whole workbench, that one right over there under the window, to give yourself a place to build your invention. No, don’t thank us. The workbench is yours. Just pile all the cases on the floor and push the cat off and unload those light radios that are waiting to be tuned. And all you have to do is to keep as quiet as a little mouse as you go about your work, so as not to interrupt the Alexander Graham Bell project.”
“Edward! Aren’t you going to help me?”
“Of course we are, Loren. We’ve already put you on the list. You’ve got a number. What’s his number, D.D.?”
“One-eighty-six. He comes just after the new coil for the girls’ dorm water heater.”
“There you are. Number one-eighty-six. We’ll be all yours in just a month or two.”
Loren cleared off the bench, muttering. It took him an hour to build a new Effector from the parts around the shop. Once it was wired, he calculated the energy required to boost it up to t-prime-two an
d applied the corresponding charge from a jury-rigged power source. Nothing happened. He checked his math and tried once more. The beam would not sustain itself at that level; it wasn’t stable. The equation predicted that it would be stable, but it wasn’t.
After one more check over the calculations, he went looking for Sonia. He knew where she would be, where she always was at that hour in the early afternoon. He came upon her in the open-air dining hall, correcting papers.
“Hi, Sonia. Remember this?” Loren put the page from the daybook down across the paper she was grading.
Sonia looked down with distaste at the equations. “Barely.”
“Remember that Sunday when I first displayed these equations on the plasma board. Just after I made my presentation, we split up to work separately on different aspects of t-prime, and if I’m not mistaken, you elected to consider the significance of the second stable state, t-prime-two.”
“I don’t remember.”
“Sure you do, Sonia. You were the first one to notice that the equation predicted stability for a still more slowed down time. In fact you even calculated what the second stable value would be. Look, it’s in your handwriting right here.” He pointed to the notation on the same page, very fine writing in Sonia’s hand. “You said it would be stable at a time flow of 0.00013.”
“I don’t remember.”
“Anyway, I tried it. And it’s not stable at that value. The beam won’t stay on.”
“Loren, I’ve got forty papers to grade. And there are kids coming in in half an hour for special tutoring.”
“Come on, Sonia, this is important.”
She showed a flash of irritation. “Important! Let me tell you what’s important. I’ve got a little boy who wets his bed every night. He sleeps in a dorm with a dozen other boys and absolutely everyone knows. Even the girls have heard. Can you imagine how that feels? He’s eleven years old. He’s eleven and he’s tearing himself up inside. That’s important. These equations are irrelevant.”
“Oh,” said Loren. He felt a little foolish, staring down at his daybook. After a moment he looked up to her again. “Try giving him honey.”
“What?”
“Honey. We had the same thing with my little sister Sanchy when she was that age. And Assunción started giving her a teaspoon of honey each night before she went to bed. She told her that it would clear up the problem just fine. So of course it did.”
“Thank you. I’ll try that.”
“It couldn’t hurt.”
“Thank you. Now, I’ve got a lot to do.”
Within weeks of their arrival the previous spring in Baracoa, Homer had moved out of the faculty village cottage allocated to him by Chancellor Brill. He had found a little waterfront shack, half a mile down the beach. There wasn’t much to it, but then his needs were not great. Its door opened directly out onto the sand. The previous occupant of the shack had been a clam digger, and Homer took up that job as his own. He could be seen almost any morning, carrying clams and crabs and mussels and edible seaweed up toward the cookhouse. Loren found him in the shack a little after three in the afternoon. As he walked in, Homer was stretched out on his back on the floor, with a baby raccoon on his stomach. The scene was so gentle that Loren smiled. And of course, Homer saw that smile. It seemed to annoy him.
“Oh yes. This is how it is when you’re old. At least that’s what you’re thinking, isn’t it, my young friend?” He lifted himself up and sat down on the only chair. The raccoon jumped up into his lap. “You’re thinking that as you get old, you slow down, but it’s not too bad. You turn your attention to playing with little animals, and you take your rest in the afternoon on your back. That’s what old age is like, just a slowing down. Well forget it. Old age is not a slowing down. Old age is a shipwreck.” His yellow eyes were angry.
“No need to get mad, Homer. I just came by for some advice.”
“Here’s advice. Don’t get old. Old age is a shipwreck. If you see somebody that is shipwrecked, don’t smile that little smile, the condescension of the young. I was sharing my plight with this little guy, a fellow victim of the storm. He and I are both shipwrecked. I because I am old, and he because he is an orphan. Wait a minute! I guess I am an orphan too, since both my parents are dead. So we are two shipwrecked orphans. And you come in smiling your smile at us, as though it were perfectly all right. It is not all right. We don’t want to be shipwrecked. It’s lousy.”
Loren sat down on the edge of Homer’s bed. Under the pillow, he saw the edge of a folded nightgown. Homer noticed his glance at that, too. He didn’t miss much. “Well now you know all my secrets. I talk to animals during the day and I go to bed with Dean Sawyer at night. Don’t tell her that you know, though. She is very proper.”
“I won’t.”
Homer leaned back in the chair, scratching the little animal behind its ears. He let out a long sigh. “You don’t need too much sleep when you’re old. Maybe that’s the good part of being shipwrecked. An hour of sleep is plenty. I find I get all the sleep I need during Chandler’s council meeting every morning. That leaves plenty of time for Maria at night.”
“Sounds nice.”
“It is nice. This furry little fellow is named Bear-Bane, by the way, or maybe it’s Dragon-Killer. I am only just learning raccoon talk. Bear-Bane, this is Dr. Loren Martine, scientist and admiral of the high seas.”
Loren said, “Hello Bear-Bane.” The animal looked back intelligently at him.
“So what can I do for you? Not that I’m very inclined to do anything for anybody.”
“I was thinking about t-prime this morning.”
“Tea Prime, a beverage?”
Loren ignored him. “I got out the daybook, and went over the equations again. There ought to be another stable value of t-prime. The equation predicts that. But there isn’t. I built a t-prime-two Effector and it doesn’t work.”
“I don’t remember any of that stuff.”
“Be serious, Homer. T-prime is the most important work you ever did. Generations in the future won’t think of you for dark and luminous matter, but for the Layton Effect, for your solution to the riddle of Peculiar Motion. You are the man who changed the flow of time.”
“Not me. Not my sort of thing at all. That physics and math is much too dull. I’m amazed you can even think about it with so many other better things to do. Why aren’t you swimming, for example? The swimming here is superb. Or why not find some useful work, like gathering clams? Now that is satisfying work. In retrospect, it is my true calling. Too bad I used up so much of my life before I discovered it. First I enjoy the work, picking clams by the seaside, in the sun and with a cool breeze wafting down on me. And then I get to eat some of the results. What a good deal! Hey, why don’t I dig some clams right now?” He stood up, spilling the little raccoon onto the floor. There was a clam fork leaning against the side of the shack. Homer picked it up and headed toward the beach without another word.
Loren was left, exchanging bewildered looks with Bear-Bane. There was a short whistle from down the beach, and the raccoon leapt up to the sill of the open window. He paused there for a moment to stare back at Loren, then hurried off in pursuit of Homer.
Peter Chan was Loren’s last hope for constructive advice. The Princeton mathematician was an amateur physicist in addition to being at the top of his own field. It turned out he was also a pretty good carpenter. He had apprenticed himself to D.D. Pease to help out on woodworking projects. When Loren sought him out, the famous Dr. Chan was hard at work on the repair of Columbia’s bow. He was wielding a two-handled spokeshave to pare down the over-thick planking used to rebuild the damaged prow.
“Mr. Pease is an artist with a spokeshave,” he told Loren. “Look at the left side of the bow. He did that in only a few minutes. And I have been working for hours on the other side, not nearly so pretty.” He stared discouragedly at his handiwork, which looked perfect to Loren’s eye. The somewhat pudgy professor was dripping with sweat through his tee-shir
t. There were pine shavings stuck in the moisture on one side of his round face.
“I was hoping you might be able to give me some advice, Dr. Chan. I am having trouble with these equations.” He held the daybook page up alongside the freshly shaved bow section. They were kneeling together on the deck of the scaffolding erected around Cornell in the makeshift shipyard. Chan looked at the equations briefly, then turned back to his work.
“The famous t-prime equations,” he said.
“Yes.” It didn’t seem likely that even Peter Chan could have absorbed the six equations in such a short glance. Loren assumed he would turn back to them, if and when he managed to prick his interest. “Let me explain my problem. There ought to be a second stable value of t-prime at around 0.00013. But there isn’t. I can’t get it to happen. It seems not to exist at all, at least not in that range. But the equations predict it should be there.”
“The third equation is wrong,” Chan said. The tone of his voice flat, leaving no room for doubt. He put the spokeshave down and began feeling the two sides of the bow, comparing them with the tips of his fingers. His eyes were unfocused.
Loren stared at him. “How can you say that? It predicted where we would find the first stable elevated state, t-prime-one. And it was there, exactly where it ought to have been. If it weren’t, we never would have been able to build the Effectors and change the flow of time. ”
“Oh yes. It works fine for t-prime-one. But it doesn’t predict at all the way things were before you turned on the Effector, at what you call t-prime-zero. Your equation looks good for the past 18 months, but doesn’t explain at all what was going on for the 18 billion years before that.”
Loren looked down at the page, considering what the third equation implied about the zero state. It looked fine to him. “What’s wrong with it?”