by Isaac Asimov
James Drake, who had been quietly listening from the other side of Mason, said, “I know what you mean. I once met a Holmes fan—he may even have been a Baker Street Irregular—who told me he was working on a paper that would prove that both Sherlock Holmes and Dr. Watson were fervent Catholics and I said, 'Well, wasn't Doyle himself a Catholic?* which he was, of course. My friend turned a very cold eye on me and said, 'What has that to do with it?'“
“Exactly,” said Mason, “exactly. The most highly regarded of all Sherlockian activities is to prove your point by quotations from the stories and by careful reasoning. People have written articles, for instance, that are supposed to prove that Watson was a woman, or that Sherlock Holmes had an affair with his landlady. Or else they try to work out details concerning Holmes's early life, or exactly where Watson received his war wound, and so on.
“Ideally, every member of the Baker Street Irregulars should write a Sherlockian article as a condition of membership, but that's clung to in only a slipshod fashion. I haven't written such an article yet, though I'd like to.” Mason looked a bit wistful. “I can't really consider myself a true Irregular till I do.”
Trumbull leaned over from across the table. He said, “I've been trying to catch what you've been saying over Rubin's monologue here. You mentioned 221b Baker Street”
“Yes,” said Mason, “that's where Holmes lived.”
“And is that why the club is the Baker Street Irregulars?'*
Mason said, “That was the name Holmes gave to a group of street urchins who acted as spies and sources of information. They were his irregular troops as distinguished from the police.”
“Oh well,” said Trumbull, “I suppose it's all harmless.”
“And it gives us great pleasure,” said Mason seriously. “Except that right now it's inflicting agony on me.”
It was at this point, shortly after Henry had brought in the veal cordon bleu, that Rubin's voice rose a notch. “Of course,” he said, “there's no way of denying that Sherlock Holmes was derivative. The whole Holmesian technique of detection was invented by Edgar Allen Poe; and his detective, Auguste Dupin, is the original Sherlock. However, Poe only wrote three stories about Dupin and it was Holmes who really caught the imagination of the world.
“In fact, my own feeling is that Sherlock Holmes performed the remarkable feat of being the first human being, either real or fictional, ever to become a world idol entirely because of his character as a reasoning being. It was not his military victories, his political charisma, his spiritual leadership—but simply his cold brain power. There was nothing mystical about Holmes. He gathered facts and deduced from them. His deductions weren't always fair; Doyle consistently stacked the deck in his favor, but every mystery writer does that. I do it myself.”
Trumbull said, “What you do proves nothing.”
Rubin was not to be distracted. “He was also the first believable super-hero in modern literature. He was always described as thin and aesthetic, but the fact that he achieved his triumphs through the use of brain power mustn't mask the fact that he is also described as being of virtually superhuman strength. When a visitor, in an implicit threat to Holmes, bends a poker to demonstrate his strength, Holmes casually straightens it again—the more difficult task. Then, too—”
Mason nodded his head in Rubin's direction and said to Gonzalo, “Mr. Rubin sounds like a Baker Street Irregular himself—”
Gonzalo said, “I don't think so. He just knows everything —but don't tell him I said so.”
“Maybe he can give me some Sherlockian pointers, then.”
“Maybe, but if you're in trouble, the real person to help you is Henry.”
“Henry?” Mason's eye wandered around the table as though trying to recall first names.
“Our waiter,” said Gonzalo. “He's our Sherlock Holmes.”
“I don't think—” began Mason doubtfully.
“Wait till dinner is over. You'll see.”
Halsted tapped his water glass and said, “Gentlemen, we're going to try something different this evening. Mr. Mason has a problem that involves the preparation of a Sherlockian article, and that means he would like to present us with a purely literary puzzle, one that has no connection with real life at all. —Ron, explain.”
Mason scooped up some of the melted ice cream in his dessert plate with his teaspoon, put it in his mouth as though in a final farewell to the dinner, then said, “I've got to prepare this paper because it's a matter of self-respect. I love being a Baker Street Irregular, but it's difficult to hold my head up when every person there knows more about the canon than I do and when thirteen-year-old boys write papers that meet with applause for their ingenuity.
“The trouble is that I don't have much in the way of imagination, or the kind of whimsy needed for the task. But I know what I want to do. I want to do a paper on Dr. Moriarty.”
“Ah, yes,” said Avalon. “The villain in the case.”
Mason nodded. “He doesn't appear in many of the tales, but he is the counterpart of Holmes. He is the Napoleon of crime, the intellectual rival of Holmes and the great detective's most dangerous antagonist. Just as Holmes is the popular prototype of the fictional detective, so is Moriarty the popular prototype of the master villain. In fact, it was Moriarty who killed Holmes, and was killed himself, in the final struggle in The Final Problem.' Moriarty was not brought back to life.”
Avalon said, “And on what aspect of Moriarty did you wish to do a paper?” He sipped thoughtfully at his brandy.
Mason waited for Henry to refill his cup and said, “Well, it's his role as a mathematician that intrigues me. You see, it is only Moriarty's diseased moral sense that makes him a master criminal. He delights in manipulating human lives and in serving as the agent for destruction. If he wished to bend his great talent to legitimate issues, however, he could be world famous—indeed, he was world famous, in the Sherlockian world—as a mathematician.
“Only two of his mathematical feats are specifically mentioned in the canon. He was the author of an extension of the binomial theorem, for one thing. Then, in the novel, The Valley of Fear, Holmes mentions that Moriarty had written a thesis entitled The Dynamics of an Asteroid, which was filled with mathematics so rarefied that there wasn't a scientist in Europe capable of debating the matter.”
“As it happened,” said Rubin, “one of the greatest mathematicians alive at the time was an American, Josiah Willard Gibbs, who—”
“That doesn't matter,” said Mason hastily. “In the Sherlockian world only Europe counts when it comes to matters of science. The point is this, nothing is said about the contents of The Dynamics of an Asteroid', nothing at all; and no Sherlockian has ever written an article taking up the matter. I've checked into it and I know that.”
Drake said, “And you want to do such an article?”
“I want to very much,” said Mason, “but I'm not up to it. I have a layman's knowledge of astronomy. I know what an asteroid is. It's one of the small bodies that circles the Sun between the orbits of Mars and Jupiter. I know what dynamics is; it's the study of the motion of a body and of the changes in its motion when forces are applied. But that doesn't get me anywhere. What is The Dynamics of an Asteroid about?”
Drake said thoughtfully, “Is that all you have to go by, Mason? Just the title? Isn't there any passing reference to anything that is in the paper itself?”
“Not one reference anywhere. There's just the title, plus the indication that it is a matter of a highly advanced mathematics.”
Gonzalo put his sketch of a jolly, smiling Mason—with the face drawn as a geometrically perfect circle—on the wall next to the others and said, “If you're going to write about how planets move, you need a lot of fancy math, I should think.”
“No, you don't,” said Drake abruptly. “Let me handle this, Mario. I may be only a lowly organic chemist, but I know something about astronomy too. The fact of the matter is that all the mathematics needed to handle the dynam
ics of the asteroids was worked out in the 1680s by Isaac Newton.
“An asteroid's motion depends entirely upon the gravitational influences to which it is subjected and Newton's equation makes it possible to calculate the strength of that influence between any two bodies if the mass of each body is known and if the distance between them is also known. Of course, when many bodies are involved and when the distances among them are constantly changing, then the mathematics gets tedious—not difficult, just tedious.
'The chief gravitational influence on any asteroid is that originating in the Sun, of course. Each asteroid moves around the Sun in an elliptical orbit, and if the Sun and asteroids were all that existed, the orbit could be calculated, exactly by Newton's equation. Since other bodies also exist, the gravitational influences, much smaller than that of the Sun, must be taken into account as producing much smaller effects. In general, we get very close to the truth if we just consider the Sun.”
Avalon said, “I think you're oversimplifying, Jim. To duplicate your humility, I may be only a lowly patent lawyer, and I won't pretend to know any astronomy at all, but haven't I heard that there's no way of solving the gravitational equation for more than two bodies?”
“That's right,*” said Drake, “if you mean by that, a general solution for all cases involving more than two bodies. There just isn't one. Newton worked out the general solution for the two-body problem but no one, to this day, has succeeded in working out one for the three-body problem, let alone for more bodies than that. The point is, though, that only theoreticians are interested in the three-body problem. Astronomers work out the motion of a body by first calculating the dominant gravitational influence, then correcting it one step at a time with the introduction of other lesser gravitational influences. It works well enough.” He sat back and looked smug.
Gonzalo said, “Well, if only theoreticians are interested in the three-body problem and if Moriarty was a high-powered mathematician, then that must be just what the treatise is about.”
Drake lit a new cigarette and paused to cough over it. Then he said, “It could have been about the love life of giraffes, if you like, but we've got to go by the title. If Moriarty had solved the three-body problem, he would have called the treatise something like, An Analysis of the Three-Body Problem, or The Generalization of the Law of Universal Gravitation. He would not have called it The Dynamics of an Asteroid.”
Halsted said, “What about the planetary effects? I've heard something about that. Aren't there gaps in space where there aren't any asteroids?”
“Oh, sure,” said Drake. “We can find the dates in the Columbia Encyclopedia, if Henry will bring it over.”
“Never mind,” said Halsted. “You just tell us what you know about it and we can check the dates later, if we have to.”
Drake said, “Let's see now.” He was visibly enjoying his domination of the proceedings. His insignificant gray mustache twitched and his eyes, nested in finely wrinkled skin, seemed to sparkle.
He said, “There was an American astronomer named. Kirkwood and I think Daniel was his first name. Sometime around the middle 1800s he pointed out that the asteroids' orbits seemed to cluster in groups. There were a couple of dozen known by then, all between the orbits of Mars and Jupiter, but they weren't spread out evenly, as Kirkwood pointed out. He showed there were gaps in which no asteroids circled.
“By 1866 or thereabouts—I'm pretty sure it was 1866— he worked out the reason. Any asteroid that would have had its orbit in those gaps would have circled the Sun in a period equal to a simple fraction of that of Jupiter.”
“If there's no asteroid there,” said Gonzalo, “how can you tell how long it would take it to go around the Sun?”
“Actually, it's very simple. Kepler worked that out in 1619 and it's called Kepler's Third Law. May I continue?”
“That's just syllables,” said Gonzalo. “What's Kepler's Third Law?”
But Avalon said, “Let's take Jim's word for it, Mario. I can't quote it either, but I'm sure astronomers have it down cold. Go ahead, Jim.”
Drake said, “An asteroid in a gap might have an orbital period of six years or four years, let us say, where Jupiter has a period of twelve years. That means an asteroid, every two or three revolutions, passes Jupiter under the same relative conditions of position. Jupiter's pull is in some particular direction each time, always the same, either forward or backward, and the effect mounts up.
“If the pull is backward, the asteroidal motion is gradually slowed so that the asteroid drops in closer toward the Sun and moves out of the gap. If the pull is forward, the asteroidal motion is quickened and the asteroid swings away from the Sun, again moving out of the gap. Either way nothing stays in the gaps, which are now called 'Kirkwood gaps.' You get the same effect in Saturn's rings. There are gaps there too.”
Trumbull said, “You say Kirkwood did this in 1866?” “Yes.”
“And when did Moriarty write his thesis, supposedly?” Mason interposed. “About 1875, if we work out the internal consistency of the Sherlockian canon.”
Trumbull said, “Maybe Doyle was inspired by the new: of the Kirkwood gaps, and thought of the title because of it. In which case, we can imagine Moriarty playing the role of Kirkwood and you can write an article on the Moriarty gaps.”
Mason said uneasily, “Would that be enough? How important was Kirkwood's work? How difficult?”
Drake shrugged. “It was a respectable contribution, but it was just an application of Newtonian physics. Good second-class work; not first class.”
Mason shook his head. “For Moriarty, it would have to be first class.”
“Wait, wait!” Rubin's sparse beard quivered with growing excitement. “Maybe Moriarty got away from Newton altogether. Maybe he got onto Einstein. Einstein revised the theory of gravity.”
“He extended it,” said Drake, “in the General Theory of Relativity in 1916.”
“Right. Forty years after Moriarty's paper. That's got to be it. Suppose Moriarty had anticipated Einstein—”
Drake said, “In 1875? That would be before the Michel-son-Morley experiment. I don't think it could have been done.”
“Sure it could,” said Rubin, “if Moriarty were bright enough—and he was.”
Mason said, “Oh yes. In the Sherlockian universe, Professor Moriarty was brilliant enough for anything. Sure he would anticipate Einstein. The only thing is that, if he had done so, would he not have changed scientific history all around?”
“Not if the paper were suppressed,” said Rubin, almost chattering with excitement. “It all fits in. The paper was suppressed and the great advance was lost till Einstein rediscovered it.”
“What makes you say the paper was suppressed?” demanded Gonzalo.
“It doesn't exist, does it?” said Rubin. “If we go along with the Baker Street Irregular view of the universe, then Professor Moriarty did exist and the treatise was written, and it did anticipate General Relativity. Yet we can't find it anywhere in the scientific literature and there is no sign of the relativistic view penetrating scientific thought prior to Einstein's time. The only explanation is that the treatise was suppressed because of Moriarty's evil character.”
Drake snickered. “There'd be a lot of scientific papers suppressed if evil character were cause enough. But your suggestion is out anyway, Manny. The treatise couldn't possibly involve General Relativity; not with that title.”
“Why not?” demanded Rubin.
“Because revising the gravitational calculations in order to take relativity into account wouldn't do much as far as as-teroidal dynamics are concerned,” said Drake. “In fact, there was only one item known to astronomers in 1875 that could be considered, in any way, a gravitational puzzle.”
“Uh-oh,” said Rubin, “I'm beginning to see your point.”
“Well, I don't,” said Avalon. “Keep on going, Jim. What was the puzzle?”
Drake said, “It involved the planet Mercury, which revolves about the
Sun in a pretty lopsided orbit At one point in its orbit it is at its closest to the Sun (closer than any other planet, of course, since it is nearer to the Sun in general than the others are) and that point is the 'perihelion.' Each time Mercury completes a revolution about the Sun, that perihelion has shifted very slightly forward.
“The reason for the shift is to be found in the small gravitational effects, or perturbations, of the other planets on Mercury. But after all the known gravitational effects are taken into account, the perihelion shift isn't completely explained. This was discovered in 1843. There is a very tiny residual shift forward that can't be explained by gravitational theory. It isn't much—only about 43 seconds of arc per century, which means the perihelion would move an unexplained distance equal to the diameter of the full Moon in about forty-two hundred years, or make a complete circle of the sky”—he did some mental calculations—”in about three million years.
“It's not much of a motion, but it was enough to threaten Newton's theory. Some astronomers felt that there must be an unknown planet on the other side of Mercury, very close to the Sun. Its pull was not taken into account, since it was unknown, but it was possible to calculate how large a planet would have to exist, and what kind of an orbit it must have, to account for the anomalous motion of Mercury's perihelion. The only trouble was that they could never find that planet.
“Then Einstein modified Newton's theory of gravitation, made it more general, and showed that when the new, modified equations were used the motion of Mercury's perihelion was exactly accounted for. It also did a few other things, but never mind that.”
Gonzalo said, “Why couldn't Moriarty have figured that out?”