“Said the man who would really like to have sex with Ingrid Bergman,” she said, smiling. “I’m pretty tired. Hold the thought for another night?”
“Sure.”
By the time we got up on Sunday, it was past noon. Iphwin’s people had supplied us with the English-language version of the Batavia paper, plus the LA Times in Exile from Auckland. We sat around, read, ate, and talked. Late in the afternoon we went out on one of the Big Sapphire’s many observation decks and watched the big waves roll by, messengers from some storm a thousand miles away. For the whole of Sunday, nothing unusual happened. That was beginning to seem strange.
PART TWO
The Bureau of Missing Nations
On Monday morning we made and ate a quick breakfast in the room’s kitchenette, then got dressed, stepped out the door into the corridors of the Big Sapphire, and headed for the office that we had been assigned. Iphwin was waiting for us there, to my surprise; I couldn’t help wondering how a man who ran so much of the planet’s economy had time to meet with us so often and at such length, without even any interruptions.
“Well,” Iphwin said. “Glad to have you here at last. I’ve decided to take charge of this matter personally, at least for a while. Now, Helen, let’s start with a reconciliation problem. Let me suppose the existence of two documents of equally good provenance, containing statements absolutely contrary to each other. Suppose, say, that one of them specifies that General Grant died at the battle of Cold Harbor, and the other that he was killed while holding Little Round Top at Gettysburg.”
“But he wasn’t,” I said. “He lived to be the president of the United States, for two terms I think, after Johnson?”
“After Johnson?” Helen said, gaping at me. “Where I grew up, Lyndon Johnson was the president of the Republic of Texas, the last one before they voted to go communist, and shot him. And after I came to Enzy, I learned he was the first Secretary of the Treasury for the government in exile. Either way, U.S. Grant couldn’t have been president after him—”
“Andrew Johnson,” I said. “The Vice President who succeeded Abe Lincoln after his assassination in 1865.”
She shook her head slowly. “Hannibal Hamlin succeeded Lincoln,” she said. “In 1863. After the impeachment.”
None of this perturbed Iphwin one bit that I could see; he listened with great interest but didn’t seem to feel any need to intervene.
After a long pause, just to break the silence, I finally asked, “Can I ask what provenance is?”
“Provenance is what you have when you have established that a document actually originated where and when it was supposed to have,” Helen said. “As Iphwin has set up this problem, the documents have equally good provenance, which means the case is equally strong that either one really does date from the American Civil War.”
“Oh,” I said. “I was hoping that I was just misunderstanding one idea somewhere, but it doesn’t seem likely, now.”
The pause dragged on, broken only by Iphwin’s moving between three chairs. When he finally found one he liked, at least for the moment, Iphwin sat tugging at his lower lip and said, “All right, now, imagining you have those two documents, of equally good provenance, what is your next move?”
“Well,” Helen said, “speaking as a historian I guess it’s pretty obvious. I need to find some way to challenge the accuracy or the provenance of at least one of them, preferably both.”
“What would you do, Lyle?”
“I’m not a historian.”
“Answer as the developer of abductive statistics.”
“Hmmm. But if you can do the things Helen just outlined, that would be the thing to do.”
“Assume for the moment that it proves impossible; you cannot show that either document is from anything other than that period, and both appear to be absolutely authentic. Furthermore, in your case, anyway, you have a large body of evidence that tells you that neither of the documents can possibly be right.”
“In abductive math, we don’t. We leave them unreconciled until something turns up to settle the question.”
“All right,” Iphwin said, with seemingly infinite patience, though I felt like a complete idiot who had wandered into a Socratic dialogue while looking for the bathroom. “Suppose now it is absolutely dreadfully important to reconcile the two documents and the known facts.”
“Well, then, at that point I try to identify how many things the documents do agree on. For example, they agree that there really was a General Grant in the Civil War.”
“Why do you want to know that?” Iphwin demanded. For one moment he had an expression of keen interest, before he resumed his usual bland composure.
“Because what I’m finding out are the implicit constraints on the solution. It can’t be one that denies the shared material.”
“All right, go on.”
“Then at the next higher level, you get more abstract points of agreement, like that the Civil War had battles and that General Grant died in one of them. And then you try to figure out whether the two messages are different enough. That is, do they require reconciliation? How much does your world change if they can or can’t be reconciled? For example, we are more likely to have hypotheses in which General Grant died once; till then we know he’s dead and that it’s probably associated with battle during the war.
“Thus the abductive process would say that we suspend conclusions and not apply induction or deduction yet—and would then work on the conditions that allow us to form hypotheses, because if all your hypotheses were just random noise, you’d never find anything that worked in the real world.
“There has to be an abductive process, a process of generating hypotheses more likely to be right than not—and so what you’re doing is taking the shared elements in the evidence and identifying a family of hypotheses—all the possible hypotheses in which Grant served in the Civil War, all of those hypotheses in which he was killed in battle, and so forth—down to where you have to suspend judgment and get more evidence. Abduction isn’t a process of finding answers—ordinary induction and deduction do that—but of allocating scarce time to questions. And of course from that standpoint, only having two pieces of evidence, the question is trivial; it gets more complex when some of the hypotheses are about which pieces of evidence are relevant, and how.”
Iphwin nodded. “Now let’s try something bigger. This time you have two documents from the American Civil War, and each contains a list of ten battles. There are only two battles that overlap between the two lists.”
“Well,” Helen said, “the usual thing a historian would do is figure that the two lists were made for different purposes by different people, and what’s important for one may not be important for the other.”
“Suppose each list purports to be a list of the ten battles with the highest death tolls.”
“The two sides may have called them by different names, or they may disagree about what a battle is,” she said. “Like the way that the first three days of the Battle of Wheeling is often called the Battle of Deer Run, and the last four days are counted separately as the Battle of Steubenville.” She seemed to be gaining morale every moment as her specialty was called on; her green eyes were keen with interest and she sat up with her old athletic energy.