They all were smiling. “It’s hard to believe they’re exploding outward, those stars,” he said somewhat lamely. “Most of the ones you see aren’t,” Afra said. “They’re members of our own Milky Way galaxy, a comparatively steady unit. Even the other galaxies of our local group are maintaining their positions pretty well.”

Ivo realized that he had stepped from one inanity into a worse one. But Beatryx, coincidentally, came to his rescue. “Oh,” she inquired. “I thought every galaxy was flying away from every other one at terrible speed. Because of that big argument.”

“The so-called big bang,” Brad said, without smiling this time. “You are right, Tryx. Groups of galaxies are moving apart, or at least appear to be from our lookout. But this should be a temporary state, and the reversal may already be in process, since our universe is finite and falls within the calculated gravitational radius. A few more years of observation with the macroscope, and we’ll have a better idea. Assuming we can get around the galactic interference limitation.”

“Reversal?” Beatryx was worried. “Do you mean everything will start flying together?”

“Afraid so. It will be quite crowded, by and by.”

“Oh,” she said, distressed.

“Yes, five or six billion years from now things may really be hopping.”

Brad was teasing her, a little cruelly Ivo thought, and it was his own turn to come to the rescue. “What’s this galactic interference? You’re not talking about the—”

“No, not about the destroyer. This is less blatant. Within the galaxy the scope of the macroscope is absolute — but we can’t seem to get any meaningful images from other galaxies. No natural ones, that is. Nothing but a confused jumble that fades in and out. So our assorted telescopes are still superior for the million and billion light-year range.”

“The Big Eye and the Big Ear are better for long distance than the Big Nose,” Ivo observed.

“We’re confident that advances in the state-of-the-art will bring the macroscope up to snuff, however.”

“Meanwhile, I suppose you can make do with the local galaxy,” Ivo said. “With a hundred billion or more stars to sniff in three or four dimensions.”

“And every planet and speck of dust, given time,” Brad agreed. “We can see them all, virtually — assuming we get the scopes and manpower to look.”

“Four dimensions?” Beatryx again.

“Space-time continuum,” Brad said. “Or, in human terms, our old problem of travel-time. The farther away the star we’re looking at, the older it is, because of the time it takes our macrons to get here. This doesn’t matter much when we snoop Earth, because the delay is only five seconds. The entire diameter of our solar system is only a matter of light-hours. But Alpha Centauri is four years away, and an intriguing monster like Betelgeuse — ‘Beetle-juice’ to cognoscenti — is three hundred. That civilized species on Sung, the probs, that I showed Ivo today is ten thousand years away. So our galactic map, the moment we made it, would be out of date by a variable factor ranging up to seventy thousand years. Unless we recognize that added dimension of time, we’re hopelessly fouled up.”

“Oh.”

“If we had some form of instantaneous travel — and that isn’t in the cards, in this framework of reality — we’d still have the darndest time visiting that Sung civilization, presuming that it existed today,” Brad continued. “We’d have to assume that our instant system was posted on universal rest, and that’s trouble right there. Our galaxy is moving and spinning at a considerable rate. A star thirty thousand light-years distant would be nowhere near our mapped coordinates — even if they were entirely accurate by our present frame of reference.”

“Why not orient on the galaxy, then?” Ivo asked. “The stars are pretty stable relative to each other inside it, aren’t they?”

“Too easy, Ivo. That implies that the galactic rotation can be ignored, and it can’t. You jump thirty thousand light-years toward galactic center and you carry a sizable energy surplus with you. Angular momentum must be conserved. It’s like the Coriolis force, or Ferrel’s Law on Earth. You—”

“If I may,” Harold Groton said, interrupting him politely. “I have been this route myself. Ivo, did you ever whirl a noisemaker at the end of a string?”

“No, but I know what you mean.”

“And you know what happens when you pull it short?”

“Buzzes around twice as fast.”

“That’s what happens when you pull in toward the center of the whirling galaxy.”

“If we had instantaneous transport,” Brad said. “But the problem is academic, so I suppose it doesn’t matter if our maps are outdated before we can make them up.”

The meal was done, and Ivo realized that he had enjoyed it without paying any attention to what it was. Chocolate cake for dessert, and—

“Come on, Bradley,” Groton said. “Relax your top-heavy mind with a sprout.” And light wine, and—

Brad laughed. “You never give up. Why don’t you take on Ivo?”

Groton obligingly turned to Ivo. “Are you familiar with the game?”

“And mashed potatoes—” Ivo said, then blushed as they glanced at him in concert. He had to stop letting his thoughts run away with him! “Uh, the game. I guess not, since I don’t know what you’re talking about.”

Afra was looking restless again, and now Ivo was also beginning to wonder. Brad knew he wasn’t going to have Schön for the coming crisis with officialdom. Why did he persist in this party-game banter? It was costing crucial time. Brad should be setting things up to divert the senator and postpone disaster.

Still, what could any of them do, but play along? Brad’s mind operated far more subtly than most people suspected, and he never gave up on a problem.

Groton brought out a sheet of paper and two pencils. “Sprouts is an intellectual game that has had an underground popularity with scientists for a number of years. There are several variants, but we’ll stick to the original one this time; it’s still the best.” He put three dots on the paper. “The rules are simple. All you do is connect the dots. Here, I’ll take the first turn.” He drew a line between two dots, then added a new dot in the center of that line. “One new spot each time, you see. Now you connect any two, or loop around and join one to itself, and add a spot to your line. You can’t cross a line or a spot, or join a spot that already has three lines connected to it. The new ones formed on the lines actually have two connections already made, you see.”

“Seems pretty simple to me. How is the winner determined?”

“The winner is the one who moves last, before the spots run out. Since two are used up and only one added, each turn, there is a definite limit.”

Ivo studied the paper. “That’s no game,” he protested. “The first player has a forced win.”

Brad and Afra laughed together. “Nabbed you that time, Harold, you old conniver,” Brad said.

“I’ll be happy to play second,” Groton said mildly. “Suppose we start with a simple two-dot game, to get the feel of it?”

“That’s a win for the second player.”

Groton glanced at him speculatively. “You sure you never played this game before?”

“It’s not a game. There’s no element of chance or skill.”

“Very well. You open a three-spot game, and I’ll take my luck with that nonexistent chance or skill.”

Ivo shrugged. He marked a triangle of dots

and drew a line between the top and the left, adding a spot to the center.

Groton connected the center spot to the isolated one.