“Ah,” Myra said, because she knew what the answer would have to be, too, and knew that hearing it would have hurt Surash. They had discussed the matter of religion long since, she and Ranjit, and they were of the same mind. If Ranjit quoted one obscure twentieth-century philosopher’s “All religions were invented by the devil to hide God from mankind,” she might retort with, “The greatest tragedy in mankind’s entire history may be the hijacking of morality by the church. The church doesn’t know what to do with morality. It thinks morality is defined by the will of a nonexistent person.”
Still, Myra knew how fond her husband was of the old monk. Lacking any ideas that would satisfy them all, she changed the subject. “Did you see what Robert was doing for Surash when you were coming in?”
He blinked at her. “No—oh, wait a minute. He was doing one of his little jigsaws, wasn’t he?”
“Not so little, Ranjit. That was a five-hundred-piecer he did in the kitchen. And there’s something else he’s been doing.”
She stopped there, smiling. Ranjit took the bait. “Are you going to tell me what that is?” he demanded.
“I’d rather show you. Let’s go up to his room.” She wouldn’t say anything more until they were there. Robert, sitting before his screen and its pictures of animals, looked up with a big smile on his face. “Robert, dear,” his mother said, “why don’t you show your dad your pentominoes?”
The news that his son was interested in pentominoes wasn’t entirely a shock to Ranjit. He had been fascinated by them himself, at the age of five or six, and he was the one who had first tried to interest the boy in them. He had patiently explained the little tiles to Robert: “You know what a domino looks like, two squares stuck together. Well, if you stick three squares together, you call it a trimino, and it can take two shapes—one that looks like a capital I, the other a capital L. Do you see what I mean?”
Robert had peered gravely at his father’s demonstration but wouldn’t commit himself about understanding. Nevertheless Ranjit had plunged on. “If you go to four squares, together it’s called a tetromino, and it can take four shapes—”
He drew swiftly:
“Rotations and reflections don’t count,” he added, and then had to explain what rotations and reflections were. “None of the tetromino shapes is particularly exciting, but when you go to five squares stuck together, things start to happen!” Because, he said, there were twelve of the five-squared pentominoes. When you put them all together, you had a tiled surface of sixty squares.
Which immediately raised the question: Could you tile a surface of sixty squares—say, a five-by-twelve rectangle, or a long, skinny two-by-thirty rectangle—using all twelve pentominoes, so that the whole surface was covered and no squares were left over?
The answer—which had fascinated five-year-old Ranjit—was not only that you could but that you could do it in no less than 3,719 ways! The six-by-ten rectangles had 2,339 ways of tiling, the five-by-twelves had 1,010 ways, and so on.
How much of what he’d been saying had gotten past Robert’s cheerfully affectionate mask Ranjit could not have said. Then Robert had obligingly switched the program on his learning computer. At once it had begun to roll off images of different pentomino tilings—all of the tilings for the five-by-twelves, then the six-by-tens, and so on to the very end.
Ranjit was now startled and delighted in almost equal amounts. The “handicapped” Robert had identified and displayed every last one of the pentomino tilings—a task that Ranjit himself had given up on all those years ago! “I—I—I think that’s grand, Robert,” he began, reaching out to his son for a hug.
And then he stopped, staring at the screen.
It had completed the display of pentomino patterns. What Ranjit expected it to do then was to turn itself off. It didn’t do that. It took the next step and went on to seek hexomino patterns.
Ranjit had never mentioned hexominoes to his son. It was too complicated a subject for Robert to have any hope of grasping it, Ranjit was sure. Why, there were thirty-five different hexominoes, and if you spread them all out, they covered a surface of two hundred ten units. And that was where young Ranjit had found them unwelcomely disappointing in those long-ago days of his childhood. Any rational person would think that a truly astronomical number of those two-hundred-ten-unit rectangles could be exactly covered by the thirty-five hexominoes. That person would be wrong. Not a single rectangle, whatever the ratio of its sides, could be tiled by the hexominoes in any pattern at all. Always, irreparably, there would be at least four empty spaces left over.
Obviously, that would have been too hard, and too frustrating, for the handicapped little Robert.
But evidently the real-world little Robert hadn’t been deterred at all! His computer screen was rolling off hexomino pattern after hexomino pattern. Robert wasn’t satisfied to just give up. He was going to check every one off for himself.
When Ranjit hugged his son, it was with almost bone-bending force; young Robert wriggled and grunted, though mostly with pleasure.
For years the people who were supposed to be helping Myra and Ranjit with “the Robert problem” had offered the same, unsatisfying consolation: Don’t think of him as disabled. Think of him as “differently abled.”
But that had never made sense to Ranjit. Not until today, when he found something that his son not only could do, but could do better than almost anyone else Ranjit knew.
He found his cheeks damp—with tears of joy—as the family finally went downstairs to their postponed daily chores, and to the real world. And for the first time in his life, Ranjit Subramanian almost wished that there really had been a God—any kind of a God—that he could have believed in, so that there would have been someone he could thank.
It was at this point that “Bill,” on his journey homeward, stopped for a brief period in the vicinity of that mildly troublesome planet whose inhabitants called it Earth. Though it was not a long stop, it was ample for him to be deluged with many billions of billions of bits of information concerning what the condemned inhabitants of Earth were currently doing and, more important by far, what egregious action the local representatives of the Grand Galactics, the Nine-Limbeds, had taken it upon themselves to commit.
One could not say that what the Nine-Limbeds had done was of a caliber to worry the Grand Galactics. The Grand Galactics had nothing to fear from a few billion ragtag mammalian humans, with their pitiful weaponry—the nuclear kind of weapons that exploded and knocked things around, or that other nuclear kind of weapon that generated electromagnetic pulses that interfered destructively with an opponent’s own electromagnetic pulses. Such rudimentary matters were insignificant to the Grand Galactics. They would fear them about as much as some H-bomb-wielding human general might fear a gypsy woman’s curse.
Nevertheless, in letting the humans know of their existence, the Nine-Limbeds had done something that, if not strictly prohibited for them, was not specifically allowed, either.
Actions would have to be taken. Decisions would have to be made.
For the first time ever Bill wondered whether he alone should make such decisions, or whether he needed to rejoin with the other Grand Galactics to meditate these decisions’ implications.
35
THE USES OF VACCINATION