She fed us until we refused another morsel of food, then ushered us out. “Go and get on with it,” she said cheerfully. “You’ll sort it out. I know you will.”
It was good to have the confidence of at least one person in the world. Stuffed with food, we trudged back up the hill. I felt good, and optimistic. But I think that was because the materials were so new to me. Bill must have stared at them already until his eyes popped out.
Up at Little House once more, the real work started. We went over the letters and diary again, page by page, date by date, phrase by phrase. Nothing new there, although now that we had seen it once, we could see the evidence again and again of the brother-sister/husband-wife ambivalence.
The drawings came next. The Heteromorphs were so alien in appearance that we were often guessing as to the functions of organs or the small objects that on close inspection appeared to be slung around their bodies or held in one of the numerous claws, but at the end of our analysis we had seen nothing to change our opinions, or add to our knowledge.
We were left with one more item: the ledger of tables of numbers, written in the hand of Louisa Derwent. Bill opened it at random and we stared at the page in silence.
“It’s dated October, 1855, like all the others,” I said at last, “That’s when they left.”
“Right. And Luke wrote ‘Louisa has completed the necessary calculations.’” Bill was scowling down at a list of numbers, accusing it of failing to reveal to us its secrets. “Necessary for what?”
I leaned over his shoulder. There were twenty-odd entries in the table, each a two or three digit number. “Nothing obvious. But it’s reasonable to assume that this has something to do with the journey, because of the date. What else would Louisa have been working on in the last few weeks?”
“It doesn’t look anything like a navigation guide. But it could be intermediate results. Worksheets.” Bill went back to the first page of the ledger, and the first table. “These could be distances to places they would reach on the way.”
“They could. Or they could be times, or weights, or angles, or a hundred other things. Even if they are distances, we have no idea what units they are in. They could be miles, or nautical miles, or kilometers, or anything.”
It sounds as though I was offering destructive criticism, but Bill knew better. Each of us had to play devil’s advocate, cross-checking the other every step of the way, if we were to avoid sloppy thinking and unwarranted assumptions.
“I’ll accept all that,” he said calmly. “We may have to try and abandon a dozen hypotheses before we’re done. But let’s start making them, and see where they lead. There’s one main assumption, though, that we’ll have to make: these tables were somehow used by Luke and Louisa Derwent, to decide how to reach the Heteromorphs. Let’s take it from there, and let’s not lose sight of the only goal we have: We want to find the location of the Heteromorph base.”
He didn’t need to spell out to me the implications. If we could find the base, maybe the Analytical Engine would still be there. And I didn’t need to spell out to him the other, overwhelming probability: chances were, the Derwents had perished on the journey, and their long-dead bodies lay somewhere on the ocean floor.
We began to work on the tables, proposing and rejecting interpretations for each one. The work was tedious, time-consuming, and full of blind alleys, but we did not consider giving up. From our point of view, progress of sorts was being made as long as we could think of and test new working assumptions. Real failure came only if we ran out of ideas.
We stopped for just two things: sleep, and meals at Big House. I think it was the walk up and down the hill, and the hours spent with Jim and Annie Trevelyan, that kept us relatively sane and balanced.
Five days fled by. We did not have a solution; the information in the ledger was not enough for that. But we finally, about noon on the sixth day, had a problem.
A mathematical problem. We had managed, with a frighteningly long list of assumptions and a great deal of work, to reduce our thoughts and calculations to a very unpleasant-looking nonlinear optimization. If it possessed a global maximum, and could be solved for that maximum, it might yield, at least in principle, the location on Earth whose probability of being a destination for the Derwents was maximized.
Lots of “ifs.” But worse than that, having come this far neither Bill nor I could see a systematic approach to finding a solution. Trial-and-error, even with the fastest computer, would take the rest of our lives. We had been hoping that modern computing skills and vastly increased raw computational power could somehow compensate for all the extra information that Louisa Derwent had available to her and we were lacking. So far, the contest wasn’t even close.
We finally admitted that, and sat in the kitchen staring at each other.
“Where’s the nearest phone?” I asked.
“Dunedin, probably. Why?”
“We’ve gone as far as we can alone. Now we need expert help.”
“I hate to agree with you.” Bill stood up. “But I have to. We’re out of our depth. We need the best numerical analyst we can find.”
“That’s who I’m going to call.”
“But what will you tell him? What do we tell anyone?”
“Bits and pieces. As little as I can get away with.” I was pulling on my coat, and picking up the results of our labors. “For the moment, they’ll have to trust us.”
“They’ll have to be as crazy as we are,” he said.
The good news was that the people we needed tended to be just that. Bill followed me out.
* * *
We didn’t stop at Dunedin. We went all the way to Christchurch, where Bill could hitch a free ride on the university phone system.
We found a quiet room, and I called Stanford’s computer science department. I had an old extension, but I reached the man I wanted after a couple of hops—I was a little surprised at that, because as a peripatetic and sociable bachelor he was as often as not in some other continent.
“Where are you?” Gene said, as soon as he knew who was on the line.
That may sound like an odd opening for a conversation with someone you have not spoken to for a year, but usually when one of us called the other, it meant that we were within dinner-eating distance. Then we would have a meal together, discuss life, death, and mathematics, and go our separate ways oddly comforted.
“I’m in Christchurch. Christchurch, New Zealand.”
“Right.” There was a barely perceptible pause at the other end of the line, then he said, “Well, you’ve got my attention. Are you all right?”
“I’m fine, But I need an algorithm.”
I sketched out the nature of the problem, and after I was finished he said, “It sounds a bit like an under-determined version of the Traveling Salesman problem, where you have incomplete information about the nodes.”
“That’s pretty much what we decided. We know a number of distances, and we know that some of the locations and the endpoint have to be on land. Also, the land boundaries place other constraints on the paths that can be taken. Trouble is, we’ve no idea how to solve the whole thing.”
“This is really great,” Gene said—and meant it. I could almost hear him rubbing his hands at the prospect of a neat new problem. “The way you describe it, it’s definitely non-polynomial unless you can provide more information. I don’t know how to solve it, either, but I do have ideas. You have to give me all the details.”
“I was planning to. This was just to get you started thinking. I’ll be on a midnight flight out of here, and I’ll land at San Francisco about eight in the morning. I can be at your place by eleven-thirty. I’ll have the written details.”
“That urgent?”
“It feels that way. Maybe you can talk me out of it over dinner.”
After I rang off, Bill Rigley gave me a worried shake of his head. “Are you sure you know what you’re doing? You’ll have to tell him quite a bit.”
“Less than
you think. Gene will help, I promise.” I had just realized what I was doing. I was cashing intellectual chips that I had been collecting for a quarter of a century.
“Come on,” I said. “Let’s go over everything one more time. Then I have to get out of here.”
* * *
The final division of labor had been an easy one to perform. Bill had to go back to Little House, and make absolutely sure that we had not missed one scrap of information that might help us. I must head for the United States, and try to crack our computational problem. Bill’s preliminary estimate, of 2,000 hours on a Cray-YMP, was not encouraging.
I arrived in San Francisco one hour behind schedule, jet lagged to the gills. But I made up for lost time on the way to Palo Alto, and was sitting in the living room of Gene’s house on Constanza by midday.
True to form, he had not waited for my arrival. He had already been in touch with half a dozen people scattered around the United States and Canada, to see if there was anything new and exciting in the problem area we were working. I gave him a restricted version of the story of Louisa Derwent and the vanished Analytical Engine, omitting all suggestion of aliens, and then showed him my copy of our analyses and the raw data from which we had drawn it. While he started work on that, I borrowed his telephone and wearily tackled the next phase.
Gene would give us an algorithm, I was sure of that, and it would be the best that today’s numerical analysis could provide. But even with that best, I was convinced that we would face a most formidable computational problem.
I did not wait to learn just how formidable. Assuming that Bill and I were right, there would be other certainties. We would need a digital data base of the whole world, or at least the southern hemisphere, with the land/sea boundaries defined. This time my phone call gave a less satisfactory answer. The Defense Mapping Agency might have what I needed, but it was almost certainly not generally available. My friend (with a guarantee of anonymity) promised to do some digging, and either finagle me a loaner data set or point me to the best commercial sources.
I had one more call to make, to Marvin Minsky at the MIT Media Lab. I looked at the clock as I dialed. One forty-five. On the East Coast it was approaching quitting time for the day. Personally, I felt long past quitting time.
I was lucky again. He came to the phone sounding slightly surprised. We knew each other, but not all that well—not the way that I knew Bill, or Gene.
“Do you still have a good working relationship with Thinking Machines Corporation?” I asked.
“Yes.” If a declarative word can also be a question, that was it.
“And Danny Hillis is still chief scientist, right?”
“He is.”
“Good. Do you remember in Pasadena a few years ago you introduced us?”
“At the Voyager Neptune flyby. I remember it very well.” Now his voice sounded more and more puzzled. No wonder. I was tired beyond belief, and struggling to stop my thoughts spinning off into non-sequiturs.
“I think I’m going to need a couple of hundred hours of time,” I said, “on the fastest Connection Machine there is.”
“You’re talking to the wrong person.”
“I may need some high priority access.” I continued as though I had not heard him. “Do you have a few minutes while I tell you why I need it?”
“It’s your nickel.” Now the voice sounded a little bit skeptical, but I could tell he was intrigued.
“This has to be done in person. Maybe tomorrow morning?”
“Friday? Hold on a moment.”
“Anywhere you like,” I said, while a muttered conversation took place at the other end of the line. “It won’t take long. Did you say tomorrow is Friday?”
I seemed to have lost a day somewhere. But that didn’t matter. By tomorrow afternoon I would be ready and able to sleep for the whole weekend.
* * *
Everything had been rushing along, faster and faster, towards an inevitable conclusion. And at that point, just where Bill and I wanted the speed to be at a maximum, events slowed to a crawl.
In retrospect, the change of pace was only in our minds. By any normal standards, progress was spectacularly fast.
For example, Gene produced an algorithm in less than a week. He still wanted to do final polishing, especially to make it optimal for parallel processing, but there was no point in waiting before programming began. Bill had by this time flown in from New Zealand, and we were both up in Massachusetts. In ten days we had a working program and the geographic data base was on-line.
Our first Connection Machine run was performed that same evening. It was a success, if by “success” you mean that it did not bomb. But it failed to produce a well-defined maximum of any kind.
So then the tedious time began. The input parameters that we judged to be uncertain had to be run over their full permitted ranges, in every possible variation. Naturally, we had set up the program to perform that parametric variation automatically, and to proceed to the next case whenever the form of solution was not satisfactory. And just as naturally, we could hardly bear to leave the computer. We wanted to see the results of each run, to be there when—or if—the result we wanted finally popped out.
For four whole days, nothing emerged that was even encouraging. Any computed maxima were hopelessly broad and unacceptably poorly-defined. We went on haunting the machine room, disappearing only for naps and hurried meals. It resembled the time of our youth, when hands-on program debugging was the only sort known. In the late night hours I felt a strange confluence of computer generations. Here we were, working as we had worked many years ago, but now we were employing today’s most advanced machine in a strange quest for its own earliest ancestor.
We must have been a terrible nuisance to the operators, as we brooded over input and fretted over output, but no one said an unkind word. They must have sensed, from vague rumors, or from the more direct evidence of our behavior, that something very important to us was involved in these computations. They encouraged us to eat and rest; and it seemed almost inevitable that when at last the result that Bill and I had been waiting for so long emerged from the electronic blizzard of activity within the Connection Machine, neither of us would be there to see it.
The call came at eight-thirty in the morning. We had left an hour earlier, and were eating a weary breakfast in the Royal Sonesta motel, not far from the installation.
“I have something I think you should see,” said the hesitant voice of the shift operator. He had watched us sit dejected over a thousand outputs, and he was reluctant now to raise our hopes. “One of the runs shows a sharp peak. Really narrow and tight.”
They had deduced what we were looking for. “We’re on our way,” said Bill. Breakfast was left half-eaten—a rare event for either of us—and in the car neither of us could think of anything to say.
The run results were everything that the operator had suggested. The two-dimensional probability density function was a set of beautiful concentric ellipses, surrounding a single land location. We could have checked coordinates with the geographic data base, but we were in too much of a hurry. Bill had lugged a Times atlas with him all the way from Auckland, and parked it in the computer room. Now he riffled through it, seeking the latitude and longitude defined by the run output.
“My God!” he said after a few seconds. “It’s South Georgia.”
After my first bizarre reaction—South Georgia! How could the Derwents have undertaken a journey to so preposterous a destination, in the southeastern United States?—I saw where Bill’s finger lay.
South Georgia Island. I had hardly heard of it, but it was a lonely smear of land in the far south of the Atlantic Ocean.
Bill, of course, knew a good deal about the place. I have noticed this odd fact before, people who live south of the equator seem to know far more about the geography of their hemisphere than we do about ours. Bill’s explanation, that there is a lot less southern land to know about, is true but not completely c
onvincing.
It did not matter, however, because within forty-eight hours I too knew almost all there was to know about South Georgia. It was not very much. The Holy Grail that Bill and I had been seeking so hard was a desolate island, about a hundred miles long and twenty miles wide. The highest mountains were substantial, rising almost to ten thousand feet, and their fall to the sea was a dreadful chaos of rocks and glaciers. It would not be fair to say that the interior held nothing of interest, because no one had ever bothered to explore it.
South Georgia had enjoyed its brief moment of glory at the end of the last century, when it had been a base for Antarctic whalers, and even then only the coastal area had been inhabited. In 1916, Shackleton and a handful of his men made a desperate and successful crossing of the island’s mountains, to obtain help for the rest of his stranded trans-Antarctic expedition. The next interior crossing was not until 1955, by a British survey team.
That is the end of South Georgia history. Whaling was the only industry. With its decline, the towns of Husvik and Grytviken dwindled and died. The island returned to its former role, as an outpost beyond civilization.
None of these facts was the reason, though, for Bill Rigley’s shocked “My God!” when his finger came to rest on South Georgia. He was amazed by the location. The island lies in the Atlantic ocean, at 54 degrees south. It is six thousand miles away from New Zealand, or from the Heteromorph winter outpost on Macquarie Island.
And those are no ordinary six thousand miles, of mild winds and easy trade routes.
“Look at the choice Derwent had to make,” said Bill. “Either he went west, south of Africa and the Cape of Good Hope. That’s the long way, nine or ten thousand miles, and all the way against the prevailing winds. Or he could sail east. That way would be shorter, maybe six thousand miles, and mostly with the winds. But he would have to go across the South Pacific, and then through the Drake Passage between Cape Horn and the Antarctic Peninsula.”
His words meant more to me after I had done some reading. The southern seas of the Roaring Forties cause no shivers today, but a hundred years ago they were a legend to all sailing men, a region of cruel storms, monstrous waves, and deadly winds. They were worst of all in the Drake Passage, but that wild easterly route had been Luke Derwent’s choice. It was quicker, and he was a man for whom time was running out.
The Year's Best SF 11 # 1993 Page 58
