Georgia on My Mind and Other Places (52 page)

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 underdetermined 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, your time. 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 Y-MP, 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 database 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, toward 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 database was on-line.

Our first Connection Machine run was performed that same evening. It was a success, if by “success” you mean by 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 database, 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 convincing.

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.”