“Ambassador, what is your purpose?”

The Ghosts, the Ambassador said, had two objectives. The first was to use the Planck boundary conditions to build a perfect reflective surface, an age-old goal of the energy-hoarding Ghosts.

The second objective was more interesting.

“The capacity of any computing machine is limited by the Uncertainty Principle,” the Ambassador said. “The exploration of, say, high-value prime numbers has always been constrained by the fact that energy changes within a device must remain above the uncertainty level.

“With the reduction in Planck’s constant we can go further. Much further. For example, we have already managed to find a disproof of an ancient human hypothesis known as Goldbach’s conjecture.”

Goldbach, it seems, speculated that any even number can be expressed as the sum of two primes. Twelve equals five plus seven; forty equals seventeen plus twenty-three. Centuries of endeavor had neither proved nor disproved the hypothesis.

The Planck machine had found a counterexample, a number in the region of ten raised to the power eighty.

“I guess I’m impressed,” I said.

The Ghost rolled gently. “My friend, age-old problems melt before our Planck machine; already several NP-type problems have—”

I told the Ambassador I believed it, and to dump down the details later.

The science platforms were pulling away now, leaving the gold-silver sphere exposed and alone.

The Sink Ambassador continued its lecture. “But we want to go further. We see this Planck-adjustment technique as a means of probing — not just the very large — but the infinite. Our device will verify some of the most important theorems of our, and your, mathematics, simply by a direct inspection of cases, all the way to infinity.”

I stared at the bobbing Ghost. “I think you’re losing me. Won’t an infinite number of cases still take an infinite amount of time? — and energy?”

“Not if the time and energy is allocated in decreasing amounts, so that the total converges to some finite value. And — if the Uncertainty Principle is removed completely — there is no limit to the smallness of energy allocations.”

“Right. So you’re going to take Planck’s constant all the way to zero.”

“That’s right. And, Jack, mathematical conjectures are just the start. A training exercise. The artificial mind is heuristic — it is flexible; it can learn. With its infinite capacity at our disposal we anticipate the dawn of a new era of—”

There was a spark, dazzling bright, at the heart of the silvered Planck sac. The mind-device thrashed like some grotesque fetus.

I knotted my fingers in a length of silvered rope. “Ambassador, ‘space could shatter.’ ”

“What?”

“What does that mean to you?”

“…Nothing. Jack, are you—”

The flame filled the sac, overwhelming the machine. For an instant the sac glowed brighter than the star core.

Then the sac turned silver. It looked like some huge Ghost. Images of the crowding science platforms, of the slotted walls of the city-world cavity, shivered over its flanks.

“Ambassador, what’s happening?”

“…I’m not certain.”

“Have you achieved Planck Zero?”

“Yes. But the device should be signaling to us—”

The walls of the sac contracted by a few hundred feet, trembling; it was as if the sac were a living creature, breathing in.

My ship lurched away from the sac and towards the walls of the chamber. One crewman was left tumbling in space, like a drop of mercury in freefall. I clung grimly to my rope.

The walls were still miles away.

The sac’s surface billowed out and overwhelmed us.

I was utterly alone.

Lonely.

Darkness.

…Dark because photons could carry no energy, here at Planck Zero; nothing to excite my optic sensors…

Cold. How could I be cold? I rubbed my hands together. I could feel my fingers break up like ancient, crumbled paper.

Electron orbits in an atom are proportional to Planck’s constant. At Planck Zero the orbits must collapse… right? So, no more chemistry. How long before the crumbling process reached my brain pan?

How would it feel?

And quantum wave functions, linking me to the rest of the Universe, had all turned to dust at Planck Zero.

I could feel it. I was alone in this shattered space.

What about the ship? Was it still heading for the wall?… Something else, in here with me. The Ghosts? No; something larger, more powerful.

Infinite.

The mind-device was without limit. It was stranded in this discontinuous space, and it was enraged.

Enraged by a pain I recognized.

Now I made out other minds. Ghosts. They were like tiny stars, shining out, falling away from each other.

The Planck mind lashed out. Ghosts were overwhelmed, insects in fire.

…The ship burst out of the sac; quantum functions rushed over me (for a precious moment visible, like prismatic waves lapping around me) and I was bound into the Universe once more.

The ship hurtled through a city-world passage, trailing ragged fragments. Ghosts lay dying all around me, their proud bodies deflated.

I looked back down the passage. A silver half-dome peered after us like some vast eye.

“…Sink Ambassador?”

“I’m still here, Jack.”

We emerged from the city-world. Ghost paramedics floated onto our ship and tended the wounded.

The city-world was changing.

A light, clear and white, shone out of the hundreds of portals, illuminating the murky giant star material. The massive drive assemblies at the poles had been damaged; I saw sparks fizzing across the surface of the nearer. A flotilla of heavy Ghost ships approached the drive units.

“Ambassador, what are they doing?”

“We must endeavor to repair the drive units, or the moon will fall into the core… Jack, the growth of the Planck sac in that cavity was not controlled. We are afraid.”

“I bet you are.”

“We are going to try to move the moon out of the giant star.”

“And then what?”

“We must find some way to restrain the sac.”

I stared down at the core of the giant. “Ambassador, it will overwhelm you. What are the limits to its growth?”

“There are no limits. Perhaps the Xeelee will intervene.”

“The Xeelee aren’t gods.” I thought fast. “Sink Ambassador, listen to me. Do you have any influence over operations here?”

“Why?”

“Stop the efforts to repair the drives.”

“…I do not have the authority.”

“Then find someone who does. As acting human ambassador here, I formally request this. Sink Ambassador, have you recorded that?”

“Yes, Jack. Why do you want this?”

“Because I’m frightened, too. But I think there is a way out.”

The Ghosts cut the drive assemblies loose from the city-world. Within an hour the Planck sac had overwhelmed the battered moon; it hung in the giant star glow, perfectly silver. They got us out of there. I could see reflections in the sac’s surface, chains of ropy Ghost ships heading for safety. It took about a day for the Planck sac to impact the star core. By that time it was ten thousand miles wide and still growing. Huge ripples crossed its monstrous surface. It slid inside the star core, fusing hydrogen closing smoothly over the shining ovoid, vacuoles flaring.

An hour later the core started to implode.

Disembodied, the Sink Ambassador and I floated over Virtual images of the collapsing core. I said, “I wish Eve could see this.”

“Yes.”

By now, of course, the Ghosts had figured it out for themselves; but I couldn’t resist rubbing it in. “It was your chance comment about electron degeneracy pressure that gave me the key. Suppose Planck were reduced to zero in the star core. The higher quantum states would collapse — spin values, for instance, would fall from Planck multiples to zero.”