The same ghost played through hers. She rubbed her neck with one finger. Her nails were short and chrome-colored. Her lips were full and brown. “I’m a cybralogist,” she said. “As far as I know, there’s no such thing as a cybralogician.”
Bron laughed. “Oh. Well, I’ll be honest with you. I’ve never even heard of a ‘cybralog.’”
“I’ve heard of metalogics ... ?”
While Bron laughed, inside the ghost momentarily became real. “Look,” he said. “I can either tell you about metalogics and, by tomorrow, we can probably have you doing something that isn’t too dull, if not useful.” He turned his hands up. “Or we can have some coffee and just ...” He shrugged—“talk about other things. I mean I know how exhausting these hurry-up-and-wait mornings can be. I had to go through my share before ending up here.”
Her smile became a short (but with that sullen ghost still playing through) laugh. “Why don’t we have the coffee and you can tell me about metalogics.”
Bron nodded. “Fine. I’ll just get—” getting up.
“May I sit in this—?”
“Sure. Make yourself comfortable. How do you take your—?”
“Black,” she said from the sling chair, “as my old lady,” and laughed again (while he reached into the drawer at his knee and dialed. One plastic bulb, sliding out, hit his knuckles and burned). “That’s what my father always used to say.” She put her hands on her knees. “My mother was from Earth—Kenya, actually; and I’ve been trying to live it down ever since.”
Bron smiled back, put one coffee bulb on the desk, reached down for the other and thought: Typical u-1 ... always talking about where they come from, where their families started. His own parents had been large, blond, diligent, and (after years of working as computer operators on Mars, when their training on Earth, outmoded almost before their Martian emigration, had promised them glorious careers in design) fairly sullen. They were in their midforties when he’d come along, a final child of five. (He was pretty sure he was a final child.) Was that, he wondered again, why he liked sullen-looking women? His parents had been, like so many others it was embarrassing, laborers in a new world that needed such labor less and less. He had not lived with them since he was fifteen, had not seen them since he was twenty, thought about them (usually when someone was talking about theirs) seldom, talked about them (in concession to a code of politeness almost universal outside the u-1 that, once he had realized it existed, he’d found immensely reassuring) never.
Bron handed Miriamne the second bulb. “All right. Metalogics ...” Back behind the desk? No, better prop himself on the front again, for effect. “People—” He settled back on crumpling flimsies—“when they go about solving any real problem, don’t use strict, formal logic, but some form of metalogic, for which the rules of formal logic can be considered—on off Thursdays—the generating parameters. You know the old one: If a hen-and-a-half lays an egg-and-a-half in a day-and-a-half ... ?” He raised an eyebrow (the real one) and waited for her to sip:
Her plastic bulb wrinkled in miniscule collapse. She looked up.
“The question is: Then how many eggs does one hen lay in one day?”
“One?” she suggested.
“—is the quote logical unquote answer people have been giving off the top of their heads for over a hundred years. A little thought, however, will show you it’s really two-thirds of an egg—”
Miriamne frowned. “Cybralogs are speech/thought representation components—I’m a hardware engineer: I don’t know too much about logic, meta or otherwise. So go slow.”
“If a hen-and-a-half lays an egg-and-a-half in a day-and-a-half, then three hens would lay three eggs in the same day-and-a-half, right? Therefore one hen would lay one egg in that day and a half. Therefore one hen lays—”
“Two thirds of an tgg—” She nodded, sipped. The bubble collapsed more—“in one day.”
“We got into metalogic,” Bron explained (thinking: With the sullen, intelligent ones, that look of attention means we’re getting further than we would if they were smiling), “when we ask why we called ‘one’ a ‘logical’ answer in the first place. You know the beginning tenet of practically every formal logic text ever written, ‘To deny P is true is to affirm P is false’?”
“I vaguely remember something about denying the Taj Mahal is white—” Miriamne’s bubble was all wrinkled plastic between bright nails—“is to affirm that it’s not white ... an idea that, just intuitively, I’ve never felt very comfortable with.”
“You have good reason.” Bron sipped his own and heard the plastic crackle. “The significance of ‘white,’
like the significance of any other word, is a range of possibilities. Like the color itself, the significance fades quite imperceptibly on one side through gray toward black, and on another through pink toward red, and so on, all the way around, toward every other color; and even toward some things that aren’t colors at all. What the logician who says ‘To deny the Taj Mahal is white is to affirm that it is not white’ is really saying is: 7/ I put a boundary around part of the range of significance space whose center we all agree to call white, and // we then proceed to call everything within this artificial boundary “white” and everything outside this boundary “not white” (in the sense of “nonwhite”—now notice we’ve already introduced a distortion of what we said was really there), then any point in the total range of significance space must either be inside or outside this boundary—already a risky idea; because if this boundary is anything in the real universe, from a stone wall to a single wave pulse, there has to be something underneath it, so to speak, that’s neither on one side nor the other. And it’s also risky because if the Taj Mahal happens to be made of white tiles held to brown granite by tan grotte, there is nothing to prevent you from affirming that the Taj Mahal is white and the Taj Mahal is brown and the Taj Mahal is tan, and claiming both tan and brown to lie in the area of significance space we’ve marked as ‘nonwhite’—”
“Wait a second: Part of the Taj Mahal is white, and part of the Taj Mahal is brown, and part of the Taj Mahal is—”
“The solution’s even simpler than that. You see, just like ‘white,’ the words ‘Taj Mahal’ have a range of significance that extends, on one side, at least as far as the gates around the grounds, so that once you enter them you can say, truthfully, ‘I am at the Taj Mahal,’ and extend, on another side, at least down to the individual tiles on the wall, and even further to the grotte between them, so that, as you go through the Taj’s door and touch only your fingernail to the strip of no-colored plaster between two tiles, you can say, equally truthfully, T have touched the Taj Mahal.’ But notice also that the grounds of the Taj Mahal have faded
(until they are one with) the area of significance of the ‘surface of India,’ much of which is not the grounds of the Taj at all. And the grotte between the tiles has faded into (until it is one with) Vriamin Grotte—grotte mined from the Vriamin Clay-pits thirty miles to the south, some of which went into the Taj and some of which went into other buildings entirely. Language is parametal, not perimetal. Areas of significance space intermesh and fade into one another like color-clouds in a three-dimensional spectrum. They don’t fit together like hard-edged bricks in a box. What makes ‘logical’ bounding so risky is that the assertion of the formal logician that a boundary can be placed around an area of significance space gives you, in such a cloudy situation, no way to say where to set the boundary, how to set it, or if, once set, it will turn out in the least useful. Nor does it allow any way for two people to be sure they have set their boundaries around the same area. Treating soft-edged interpenetrating clouds as though they were hard-edged bricks does not offer much help if you want to build a real discussion of how to build a real house. Ordinary, informal, nonrigorous language overcomes all these problems, however, with a bravura, panache and elegance that leave the formal logician panting and applauding.” Bron rocked on his desk once. “Visualize an area of significance space—which is hard to do at the best of times, because the simplest model we’ve come up with has to represent it in seven coordinates (one for each sense organ): and the one we use currently employs twenty-one, some of which are fractional—which isn’t any harder than working with fractional exponents, really—and several of which are polar, because the resultant, nondefinable lines between bipolar coordinates nicely model some significance discontinuities we haven’t yet been able to bridge coherently: things like the slippage between the denotative and the connotative, or the metonymic and the metaphoric. They take a smidge of catastrophe theory to get through—incidentally, did you know catastrophe theory was invented back in the twentieth century by the same twentieth-century topologist, Rene Thorn, the neo-Thomists are always going on about?—but not as much as you might think ...”