“All right, Robin,” he said, looking surprised.
“Talk to me some more. It’s been a long trip, and I’m getting kind of irritable, I guess.”
“Oh, are you?” he asked, arching his brows; it was as close to judgmental as Albert usually gets. Then he said, “You know, Robin, you don’t have to remain awake for all of it. Would you like to power down until we get there?”
“No!”
“But Robin, it’s nothing to worry about. When you’re in standby mode it’s just as though no time at all were passing. Ask your wife.”
“No!” I said again. I didn’t even want to discuss it; standby mode sounded very much like that other mode they call “dead.” “No, I just want to talk for a while. I think-I really think,” I said, full of the new idea that had just occurred to me, “that this would be a good time for me to let you tell me about nine-dimensional space.”
For the second time in a few milliseconds Albert gave me that look—not astonished, exactly, but at least skeptical
“You want me to explain nine-dimensional space to you,” he repeated.
“You bet, Albert.”
He studied me carefully through the pipe smoke. “Well,” he said, “I can see that just the idea perks you up a little. Probably you figure you’ll have some pleasure out of making fun of me—”
“Who, me, Albert?” I grinned.
“Oh, I don’t mind if you do. I’m just trying to understand what the ground rules will be.”
“The ground rules,” I said, “is that you tell me all about it. If I get tired of it, I’ll let you know. So start, please. ‘Nine-dimensional space is
??? and then you fill in the blanks.”
He looked pleased, if still skeptical. “We should take these long trips more often,” he commented. “Anyway, that’s not the way to start. This is the way: First we consider normal three-dimensional space, the kind you grew up in, or thought you were growing up in, when you were still meat-what, already?”
I had my hand up. I said, “I thought that was four-dimensional. What about the dimension of time?”
“That’s four-dimensional space-time, Robin. I’m trying to make it simple for you, so let’s stick to three dimensions at first. I’ll give you an illustration. Suppose, for instance, that when you were a young man sitting with your girlfriend watching a PV show, you just happened to put your arm around her. The first thing you do is stretch your arm across the back of the couch-that’s the first dimension, call it breadth. Then you crook your elbow at a right angle, so your forearm is pointing forward and resting on her shoulder-that’s the second dimension, which we will call length. Then you drop your hand onto her breast. That’s depth. The third dimension.”
“That’s depth, all right, because I’m getting in pretty deep by then.” I grinned.
He sighed and ignored the remark. “You comprehend the image. You have so far demonstrated the three spatial dimensions. There is also, as you pointed out, the dimension of time: Five minutes ago your hand was not there, now it is, at some time in the future it will be elsewhere again. So if you want to specify the coordinates of any familiar system, you must add that dimension in, too. The three-dimensional ‘where’ and the fourth-dimensional ‘when’; that’s space-time.”
I said patiently, “I’m waiting for you to get to the part where it turns out that all this stuff that I already know is wrong.”
“I will, Robin, but to get to the hard part I have to make sure you have the easy part under control. Now we get to the hard part. It involves supersymmetry.”
“Oh, good. Are my eyes beginning to glaze over?”
He peered inquiringly into my face, just as solemnly as though I really had eyes and he had something to peer at them with. He’s a good sport, Albert is. “Not yet,” he said, pleased. “I’ll try not to glaze them. ’supersymmetry’ sounds terrible, I know, but it is just the name given to a mathematical model which fairly satisfactorily describes the main features of the universe. It includes or is related to things like ’super-gravity’ and ’string theory’ and ‘archeocosmology. ‘” He peered at me again. “Still not glazed? All right. Now we start to understand the implications of those words. The implications are easier than the words are. These are pretty good fields of study. Taken together, they explain the behavior of both matter and energy in all their manifestations. More than that. They don’t just explain them. The laws of supersymmetry and the others actually drive the behavior of all things. By that I mean that, from these laws, the observed behavior of everything that makes up the universe follows logically. Even inevitably.”
“But—”
He was in full course; he waved me down. “Stay with it,” he commanded. “These are basic. If the early Greeks had understood supersymmetry and its related subjects, they could have deduced Newton’s laws of motion and universal gravitation, and Planck and Heisenberg’s quantum rules, and even—” he twinkled “—my own relativity theory, both special and general. They would not have had to experiment and observe. They could have known that all these other things must be true, because they followed, just as Euclid knew that his geometry must be true because everything followed from the general laws.”
“But it didn’t!” I cried, surprised. “Did it? I mean, you’ve told me about non-Eudidean geometry—”
He paused, looking thoughtful. “That’s the catch,” he admitted. He looked at his pipe and discovered that it was out, so methodically he began tapping it empty again while he talked. “Eudidean geometry is not untrue, it is simply true only in the special case of a flat, twodimensional surface. There aren’t any of those in the real world. There’s a catch in supersymmetry, too. The catch there is that it, too, is untrue in the real world-or at least the world of three-dimensional space we perceive. For supersymmetry to work, nine dimensions are required, and we can only observe three. What happened to the other six?”
I said with pleasure, “I don’t have the faintest idea, but you’re doing this a lot better than usual. I’m not lost yet.”
“I’ve had a lot a practice,” he said dryly. “I’ve got good news for you, too. I could demonstrate to you mathematically why nine dimensions are necessary—”
“Oh, no.”
“No, of course not,” he agreed. “The good news is that I don’t have to in order to let you understand the rest of it.”
“I’m grateful.”
“I’m sure.” He lit his pipe again. “Now, about the missing six dimensions . . .” He puffed for a while, thoughtfully. “If nine spatial dimensions had to exist in order for the universe to be formed as it is in the first place, why can we find only three now?”
“Does it have something to do with entropy?” I hazarded.
Albert looked aghast. “Entropy? Certainly not. How could it?”
“Well, with Mach’s Hypothesis, then? Or some of the other things you were talking about in Deep Time?”
He said reprovingly, “Don’t guess, Robin. You’re just making it harder than it is. What happened to the other dimensions? They just disappeared.”
Albert gazed at me happily, puffing his pipe with as much satisfaction as though he had explained something significant.
I waited for him to go on. When he didn’t, I began to feel nettled. “Albert, I know you like to tweak me every now and then just to keep my interest up, but what the hell is ‘they just disappeared’ supposed to mean?”
He chuckled. He was having a good time, I could see that. He said, “They disappeared from our perception, at least. That doesn’t mean they were extinguished. It probably just means that they got very small. They shriveled up to where they just weren’t visible anymore.”