he said, thrashing his arms and legs a little, just loosening up after a long day, “it’s worth it, if it keeps my patients calm. But of course you’re not a patient.”
“To tell you the truth,” I said, “I wasn’t quite sure. The Master was—a little vague.”
“He was very vague with me.” Euglane said. “He told me he wanted me to form my own impressions—a good idea generally, but I’m pretty much a blank at the moment; anything you tell me is going to be news.”
I nodded. “What do you know about dimensions?” I said.
“Dimensions?”
I explained, as briefly as possible—which was not very. I finished: “What I ran into recently—not anywhere near here, though I am not at all sure ‘near’ has any meaning in this context—is, then, and among other things, a claim to live in terms of ‘other dimensions’. I am damned if I know what that means.”
He shut his eyes. His arms began to twine around each other, not tightly. I waited for a long minute.
“I assume,” he said without opening his eyes, “you heard this claim as something literal. Not some sort of figurative, poetic statement.”
“The speaker didn’t strike me as the poetic type,” I said.
He hummed for a second. Not an unpleasant sound—a little distant. Then his eyes opened. “A dimension is a mathematical convenience,” he said. “N-dimensional space is a common enough theoretical concept. But to speak of living in some— other set of dimensions—well, we can define a dimension in terms of right angles.”
“Go ahead.” The easiest way to consult an expert is to let him explain to you, even if you know most of what he’s going to tell you.
“Take a line—one-dimensional, assume it’s a mathematical line, without width. Erect another line at right angles to it and you have a two-dimensional structure. Erect still another at right angles to both of those, and you have an object in three dimensions.”
I nodded. “Clear so far,” I said. “And a fourth line, at right angles to all the other three, defines a fourth spatial dimension—space-four, in fact.”
“That’s the theory,” he said, “and since we do travel in terms of space-four, we can accept the theory as having some sort of practical existence.”
“Line, square, cube, tesseract,” I said. “So far I’m with you.”
“Now, if we continue to erect lines, each at right angles to all of the previous lines, we will be creating objects of more and more dimensions.”
“We can deal with the objects mathematically,” I said. “We can’t picture them. Not that picturing them is a final test of anything.”
“It is some sort of test in this case, though,” he said. “This being—Folla?”
“Folla.”
“Folla was able to interact—massively, he moved your ship—in terms of our four spatial dimensions. While he was doing that, he must have been—in a way—picturable. If you see what I mean.”
“He must have existed in this space.”
“At least in part,” Euglane said. His arms twined again. “The question is: does he exist in terms of more than our dimensions—three spatial dimensions, we can travel by means of space-four, but we can’t do anything in it, so to speak, or with it, we just pass through—or merely a different three?”
He had said something I hadn’t expected, for the first time. And I had only one reply, though I seemed to have been saying it a lot lately. “I am damned if I know.”
“It must be one or the other,” he said, and as he said it I held up a hand. Something had occurred to me, something interesting. Just perhaps…
“He said he was now existing in these spaces, and implied he’d been existing in different ones, or a different combination,” I said. “But does this involve a different set of dimensions?”
Euglane raised an arm over his head, and turned it. A shrug?. “What else can it mean, after all? It sounds like science-fiction, as I understand such stuff—it sounds, even, like very bad science-fiction—but there it is.”
“Maybe,” I said, “just maybe, there it isn’t.”
He left his chair. I’d been right; he didn’t stand upright. He eased himself to the carpet, which was expensive-looking but thin and comparatively stiff, and got around in a sort of combination crawl and all-fours. He went over to another table, where there was a small pile of papers. He levered himself up to a chair next to the table, picked a paper off the top of the pile, and said: “I’ve been thinking about this general subject for some time.”
What a psychological-statics expert had been doing thinking about other dimensions I couldn’t really imagine, and, as politely as possible, I said so.
“A few of my patients report contact with alien intelligences from other dimensions,” he said.
I blinked. “But—”
“But they’re mad,” he said. “Crazy. Mentally many degrees out of true. Yes. And I do not for a second believe that any report I’ve heard has any foundation in objective fact.”
“Well, then—”
“But my habit is to look everywhere,” he said. “Let me give you an example.”
I took a swallow of fruit juice. “Go ahead.”
“A few years ago,” he said, “a patient of mine reported that she was being spied on by aliens. From some ‘other dimension’, I don’t doubt. They patrolled her building, she said. They had a set of signals that told them which room of her little apartment she was in—she lived at the top floor of a small building—so they could train their spy-rays on her at any time.”
“And you found the aliens?” I said.
He laughed. He had a musical sort of laugh, with an undertone of the gruffness that was in his voice. “I did not,” he said. “I never expected to. But I looked. I hired some people to look.”
“And?”
“There were no aliens,” he said. “Of course there weren’t, and never had been. But—on the roof of a building near hers, with a good view of three of her windows—there was a human. A peeping tom.”
I nodded. “Everybody needs a hobby.”
“I suppose so,” he said. “A little talk with him stopped the practice, at least as far as my patient was concerned—and perhaps altogether, I can’t be sure.”
“And that relieved your patient?” I said.
“Not by itself, though it certainly helped,” he said. “Humans do tend to feel that they’re being watched—when they’re being watched. Sometimes, as well, when they’re not—but the feeling diminished greatly for my patient when the practice stopped. Some further work with her helped
