I said half aloud, half to myself, "A five-sphere would satisfy v2+H;2+Jc2+y2+z2=r2. The 'surface' would be a set of hypervolumes made of hyperspheres, all equidistant from a single center-point. The 'volume'
would be a su-perhypervolume, and…"
Something happened. Quietly, quickly, unexpectedly. Not what I was trying to do. But something amazing.
Under my finger, the sphere changed into a five-dimensional object. I saw it.
The ringing damped even more quickly when that happened, and I yanked my hand away even as red sparks began to tremble across the safe surface.
I said aloud, "Victor, you're good at math. What is the ratio of the surface area of a five-dimensional sphere to its volume?"
He said, "I am not good at that kind of math. But the ratio is higher than that of a hypersurface of a globe to its content, much higher than a normal sphere surface to its volume. Remember the pie plate and the goldfish bowl. The more dimensions you have, the more water you can fill in, within the same given radius."
I said, "The surface area for any number of dimensions is directly proportional to 2 pi raised to the power of nil, where n is the number of dimensions. It is inversely proportional to gamma times one-half n"
Colin said, "Oh my dear lord, she is talking in equations again. Quentin! Get your gag back out! The spirits are demanding Colin be spared!"
"I'll say it simply. This will sound odd, but the hypersurface area and content reach maxima and then decrease towards zero as n increases."
Colin shook his head. He spoke in a voice of lilting sarcasm: "Odd? No. That sounds 'normal.' Why would I think that sounded odd?"
I pointed at the safe. "If I raised the number of dimensions to six, and kept the same radius, the volume would decrease, and, for a seven-D sphere, it would get even lower. So I think I cannot make it any heavier than I just did…"
It sounded like an explosion. The bottom crashed out of the safe with a noise like battleship armor being holed. Compared to the safe bottom, the wooden floor was matchwood. Boards and splinters flew up in a fountain. Whatever was on the floor below also exploded with noise of cracking boards, breaking glass, and screaming metal. Shocking reports like gunshots, snapping even louder than the general cacophony, stunned our ears.
Victor had his hand up. There were holes like bullet holes in the wall above us, where metal shards had flown, but he had deflected the worst of it overhead. Quentin, behind the desk, was unhurt. Colin, once again moving faster than was possible, had thrown himself in front of Vanity, with his arms out, and was bleeding from two large splinters, which had cut his cheek and shoulder. I had flinched at the noise, moved half an inch in the "blue" direction, and let the matter pass "through" me without touching me.
Victor said, 'They must have heard that."
Vanity, who was looking scared, said, "I don't sense anything—"
Victor said, "Then they must be jamming your attention-detector. Leader… !" Victor turned to me. "I strongly urge we just grab the stuff from the safe and go. We can pause to examine it later. Which way?"
Vanity had her hankie out and was trying to wipe the blood off Colin's face. Colin was saying, "I'm fine, I'm fine. Ow, shit! These wounds are no more real than if someone painted ink on my face. Fuck! And I could get myself to believe that if it didn't hurt so damn much!"
Vanity said, "You are spouting gibberish. Hold still. You can't believe what you don't believe."
Colin muttered, "Not this me. The real me believes it. I wish he were here."
"Yeah," said Vanity. "Because he would not be spouting gibberish. He would also hold still."
I stepped over the wreckage of the safe, made it light, and pushed it over. There was a splintered hole in the floor. Below was a crater of what had once been a bookshelf. In the middle of the crater was a sphere. It gave off no light in three-space, but to my eyes, it was shining and pale.
I said, "Quentin, if you know any healing magic, cast a charm on Colin. If not, Victor, can you manipulate the atoms his body is made out of, and stitch up his face? Vanity, collect the stuff from the safe."
Victor said, "And you… ?"
"I am going down after my sphere. Everyone else start moving to the roof now. If we get split up, we meet…"
Damn it. I hated being leader. Leaders do not get to say things like, meet at the house of that tawdry, grasping Jezebel Lily Lilac.
"… we meet at the dock where Lily Lilac keeps her motorboat. Quentin says it will go badly for us if we steal it. If we tap on her window at—jeez, what time is it?—at four o'clock in the morning, is she a good enough… um… friend that she would lend it to you… V
Vanity stooped down at my feet and started looting the safe. There were no papers and no money, nothing but the four objects: a book, a necklace, a drug ampoule, a small brown card. Even in the dim light, the gold tracery on the cover of the book, the silver weave of the necklace, glittered and glinted.
Vanity's coat had many large pockets. She zippered them carefully inside.
Except for the necklace. After staring at its fine chain for a brief moment, she smiled an impish smile, reached under her hair to clasp it around her neck. It was studded with tiny emeralds, and there was a pendant, a green stone with silver wings. It looked nice on her.
Victor said, "She said I could borrow it any time I wished."
I looked at Quentin. "Would that count? I mean, I am sure no one means it literally when they say 'any time.'"
Victor said curtly, "If she intended to convey a more precise meaning, she would have spoken more precisely."
Quentin said to me, "I'm not sure. In fairy tales, though, it is the exact wording that counts, not the intent.
We can take the boat." Then he smiled and gave out a laugh.
Colin said, "I'm bleeding my face off here, and you're laughing. What's so funny?"
Victor, who had stepped over to peer at Colin's face, said over his shoulder to me, "Leader, I do not think his body is made of atoms. I cannot really do much."
Quentin was talking to Colin. He smiled a self-deprecating smile. "We should have checked the desk first… look here…"
Vanity's head jerked up. " Wait—"
"… I wonder if this goes to the safe…" Quentin picked a small metal key out of a drawer and held it up.
"—don't touch it!"
Quentin shouted in pain and threw the key from him. The key was covered with crawling sparks, and the metal surface was red-hot. It crossed the room like a coal from a stove, like a tiny meteor, and tinkled against the far wall.
Vanity said in the shrill voice, "Leader! I regret to report that my detection sense is not being jammed! It just went off! Several people just became aware of us."
Quentin was clutching his hand. There were tears of pain in his eyes. 'Tricky bloody bastards, aren't they?"
I said, "Roof, now! Run!"
Quentin said, "I should stay with you…"
I said, "No back-talk! Victor, you're second-in-command. Get everyone up."
Victor said, "How are you going to get out?"
I hesitated. I had no idea. But I was not going to leave my sphere.
Colin said, "Hey! Don't you have wings? Winged squid? Remember? I just remembered. Wings? Can't you hear me? Wings…"
I stared at him blankly.
He said, "Hello… ? Well… ? Do they work?"
I rotated part of my shoulder blade. Shimmering with higher-dimensional motes of music, glittering with thought-energies, pinions made of transparent blue, mingled with dapples of starlight and colors the human eye could not see, appeared around me, passing "through" the back of my coat, and yet not disturbing the fabric.
I said, "Roof. This is a direct order." I made the floor insubstantial in relation to me, and dropped from sight as if through a trapdoor.