Robert Silverberg - The Face of the Waters

“I’ve changed my mind,” said Quillan. “You remember I told you before that I thought the Face had to be Paradise and God Himself walked there, the First Cause, the actual Creator, He to whom we address all our prayers. Well, I don’t feel that way any more.”

“All right,” Lawler said, indifferently. The Face isn’t God’s vaargh, then. If you say so. You know more about these things than I do.”

“Not God’s vaargh, no. But definitely some god’s vaargh. This is the exact reverse of my original notion about the island, you see. And of everything I have ever believed about the nature of the Divine. I begin to drop into the greatest heresy. I become a polytheist at this late stage in my life. A pagan! It seems absurd even to me. And yet I embrace it with all my heart.”

“I don’t understand. A god, the god—what’s the difference? If you can believe in one god, you can believe in any number of them, as far as I can see. The trick is to believe in as many as one, and I can’t even get that far.”

Quillan gave him a loving smile. “You really don’t understand, do you? The classical Christian tradition, which derives from Judaism and for all we know from something out of ancient Egypt, holds that God is a single indivisible entity. I’ve never questioned that. I’ve never even thought of questioning that. We Christians speak of Him as a Trinity, but we are aware that the Trinity is One. That may seem confusing to an unbeliever, but we know what it means. No dispute about it: one God, only one. Just in the past few days, though—the last few hours, even—” The priest paused. “Let me make use of a mathematical analogy. Do you know what Godel’s Theorem is?”

“No.”

“Well, neither do I, not exactly. But I can give you an approximation of it. It’s a twentieth-century idea, I think. What Godel’s Theorem asserts, and nobody has ever been able to disprove it, is that there’s a fundamental limit to the rational reach of mathematics. We can prove all the assumptions of mathematical reasoning down to a certain bed-rock point, and then we hit a level where we simply can’t go any farther. Ultimately we find that we’ve descended beyond the process of mathematical proof to a realm of unprovable axioms, things that simply have to be taken on faith if we’re to make any sense out of the universe. What we reach is the boundary of reason. In order to go beyond it—in order to go on thinking at all, really—we are compelled to accept our defining axioms as true, even though we can’t prove them. Are you following me?”

“I think so.”

“All right. What I propose is that Godel’s Theorem marks the dividing line between gods and mortals.”

“Really,” Lawler said.

“This is what I mean,” said Quillan. “It sets a boundary for human reasoning. The gods occupy the far side of that boundary. Gods, by definition, are creatures who aren’t bound by the Godel limits. We humans live in a world where reality ultimately breaks down into irrational assumptions, or at least assumptions that are non-rational because they’re unprovable. Gods live in a realm of absolutes where realities are not only fixed and knowable down beyond the level of our axiomatic floor, but can be redefined and reshaped by divine control.”

For the first time in this discussion Lawler felt a flicker of interest. “The galaxy is full of beings which aren’t human, but their maths isn’t any better than ours, is it? Where do they fit your scheme?”

“Let’s define all intelligent beings who are subject to the Godel limitations as human, regardless of their actual species. And any beings that are capable of functioning in an ultra-Godelian realm of logic are gods.”

Lawler nodded. “Go on.”

“Now let me introduce the concept that came to me this morning when I was sitting up there thinking about the Face of the Waters. This actually is the blackest heresy, I admit. But I’ve been heretical before, and survived it. Though not this heretical.” Again Quillan smiled beatifically. “Let us suppose that the gods themselves at some point must reach a Godel limit, a place where their own reasoning powers—that is, their powers of creation and recreation—run up against some kind of barrier. Like us, but on a qualitatively different plane, they eventually come to a point at which they can go thus far, and no farther.”

“The ultimate limit of the universe,” Lawler said.

“No. Just their ultimate limit. It may well be that there are greater gods beyond them. The gods we’re talking about are encapsulated just as we mortals are within a larger reality defined by a different mathematics to which they have no access. They look upward to the next reality and the next level of gods. And those gods—that is, the inhabitants of that larger reality—also have a Godel wall around them, with even greater gods outside it. And so on and so on and so on.”

Lawler felt dizzy. “To infinity?”

“Yes.”

“But don’t you define a god as something that’s infinite? How can an infinite thing be smaller than infinity?”

“An infinite set may be contained within an infinite set. An infinite set may contain an infinity of infinite subsets.”

“If you say so,” replied Lawler, a little restless now. “But what does this have to do with the Face?”

“If the Face is a true Paradise, unspoiled and virgin—a domain of the holy spirit—then it may very well be occupied by superior entities, beings of great purity and power. What we of the Church once called angels. Or gods, as those of older faiths might have said.”

Be patient, Lawler thought. The man takes these things seriously.

He said, “And these superior beings, angels, gods, whatever term we choose to use—these are the local post-Godelian geniuses, do I have it right? Gods, to us. Gods to the Gillies, too, since the Face seems to be a holy place for them. But not God Himself, God Almighty, your god, the one that your church worships, the prime creator of the Gillies and us and everything else in the universe. You won’t find Him around here, at least not very often. That god is higher up along the scale of things. He doesn’t live on any one particular planet. He’s up above somewhere in a higher realm, a larger universe, looking down, checking up occasionally on how things are going here.”

“Exactly.”

“But even He isn’t all the way at the top?”

“There is no top,” Quillan said. “There’s only an ever-retreating ladder of Godhood, ranging from the hardly-more-than-mortal to the utterly unfathomable. I don’t know where the inhabitants of the Face are located on the ladder, but very likely it’s somewhere at a point higher than the one we occupy. It’s the whole ladder that is God Almighty. Because God is infinite, there can be no one level of godhood, but only an eternally ascending chain; there is no Highest, merely Higher and Higher and Even Higher, ad infinitum . The Face is some intermediate level on that chain.”

“I see,” said Lawler uncertainly.

“And by meditating on these things, one can begin to perceive the higher infinities, even though by definition we can never perceive the Highest of all, since to do that we’d have to be greater than the greatest of infinities.” Quillan looked toward the heavens and spread his arms wide in a gesture that was almost self-mocking. But then he turned to Lawler and said in an entirely different tone of voice from the one he had used a moment before, “At last, doc, I’ve come to an understanding of why I failed in the priesthood. I must have been aware all along that the God I was looking for, the One Supreme Entity who watches over us, is utterly unattainable. So far as we’re concerned He doesn’t in fact exist. Or if He does. He exists in a region so far removed from our existence that He might just as well not exist at all. Now finally I understand that I need to go looking for a lesser god, one who’s closer to our own level of awareness. For the first time, Lawler, I see the possibility that I can find some comfort in this life.”