“How do you know this?”
“I watched a program about it on the Discovery Channel.”
“All right. But how was this originally determined?”
“With tests to see how fast humans could count objects. If you are shown one, two, three, four, or five objects, you can answer the question about how many objects are present in roughly the same amount of time. Only for six or more objects does it take more time, and the amount of time it takes to report the tally goes up by an equal increment for every additional item present.”
“I never knew that,” I said.
“Live and learn,” said Hollus. “Members of my species can usually perceive cardinality up to six—a slight improvement over what you can do. But the Wreeds shunt us completely away from the center; the typical Wreed can perceive cardinality up to forty-six, although some individuals can do it as high as sixty-nine.”
“Really? But what happens when there are more items? Do they have to count them all, starting with item one?”
“No. Wreeds cannot count. They literally do not know how. Either they perceive the cardinality, or they do not. They have separate words for the numerals one to forty-six, and then they simply have a word that means ‘many.’”
“But you said some of them can perceive higher numbers?”
“Yes, but they cannot articulate the total; they literally do not have the vocabulary for it. Those Wreeds who can perceive larger cardinalities obviously have a competitive advantage. One might offer to swap fifty-two domesticated animals for sixty-eight domesticated animals, and the other, less-gifted Wreed, knowing only that they are both large quantities would have no way to evaluate the fairness of the trade. Wreed priests almost always have a higher-than-normal ability to do this.”
“Real cardinals of the church,” I said.
Hollus got the pun. His eyestalks rippled as he said, “Exactly.”
“Why do you suppose they never developed counting?”
“Our brains have only those abilities that evolution gave them. For the ancestors of your kind and mine, there were real-world, survival-oriented advantages to knowing how to determine quantities greater than five or six: if there are seven angry members of your species blocking your way on the left, and eight on the right, your chances, although slim, are still better with going to the left. If you have ten members of your tribe including yourself, and your job has been to gather fruit for dinner, you better come back with ten pieces, or you will make an enemy. Indeed, fetching just nine pieces will likely mean you yourself will have to forgo your fruit in order to placate the others, resulting in your having expended effort with no personal benefit.
“But Wreeds never form permanent groups larger than twenty or so individuals—a quantity they can perceive as a gestalt. And if there are forty-nine enemies to your left and fifty on your right, the difference is immaterial; you are doomed either way.” He paused. “Indeed, to use a human metaphor, one could say that nature dealt the Wreeds a lousy hand—or, actually, four lousy hands. You have ten fingers, which is a fine number: it lends itself to math, since it is an even number and can be divided into halves, fifths, and tenths; it is also the sum of the first four whole numbers: one plus two plus three plus four equals ten. We Forhilnors did well, too. We count by stomping our feet, and we have six of those—also an even number, and one that suggests halves, thirds, and sixths. And it is the sum of the first three whole numbers: one plus two plus three equals six. Again, a mental basis for mathematics.
“But the Wreeds have twenty-three fingers, and twenty-three is a prime number; it does not suggest any fractions other than twenty-thirds, a divisor too large for most real-world applications. And it is not the sum of any continuous sequence of whole numbers. Twenty-one and twenty-eight are the sums of the first six and first seven whole numbers, respectively; twenty-three has no such significance. With the arrangement of digits they have, they simply never developed counting or the kind of math we perform.”
“Fascinating,” I said.
“It is indeed,” said Hollus. “More: you must have noticed T’kna’s eye.”
That surprised me. “Actually, no. He didn’t seem to have any eyes.”
“He has precisely one—that moist, black strip around the top of his torso. It is one long eye that perceives a complete 360-degree circle. A fascinating structure: the Wreed retina is layered with photoreceptive sheets that rapidly alternate in a staggered sequence between transparency and opacity. These sheets are stacked to a depth of more than a centimeter, providing sharp images at all focal lengths simultaneously.”
“Eyes have evolved dozens of times in Earth’s history,” I said. “Insects and cephalopods and oysters and vertebrates and many others all developed eyes independently of each other. But I’ve never heard of an arrangement like that.”
“Nor had we until we met the Wreeds,” said Hollus. “But the structure of their eye also has an impact on the way they think. To stick with mathematics a moment longer, consider the basic model for all digital computers, whether made by humans or Forhilnors; it is the model, according to a documentary I saw on PBS, that you call the Turing machine.”
The Turing machine is simply an infinitely long strip of paper tape divided into squares, coupled with a print/erase head that can move left, right, or remain motionless and can either print a symbol in a square or erase the symbol already there. By programming movements and actions for the print/erase head, any computable problem can be solved. I nodded for Hollus to go on.
“The Wreed eye sees a complete, all-around panorama, and it requires no focusing—all objects are perceived with equal clarity at all times. You humans and we Forhilnors use the words concentrate and focus to describe both setting one’s attention and the act of thinking; you concentrate on an issue, you focus on a problem. Wreeds do neither; they perceive the world holistically, for they are physiologically incapable of focusing on one thing. Oh, they can prioritize in an intuitive sense: the predator up close is more important than the blade of grass far away. But the Turing machine is based on a kind of thought that is foreign to them: the print head is where all attention is concentrated; it is the focus of the operation. Wreeds never developed digital computers. They do, however, have analog computers and are adept at empirically modeling phenomenons, as well as understanding what factors go into producing them—but they cannot put forward a mathematical model. To put it another way, they can predict without explaining—their logic is intuitive, not deductive.”
“Amazing,” I said. “I’d have been inclined to think that mathematics would be the one thing we’d share with any other intelligent lifeform.”
“That was our assumption, too. And, of course, the Wreeds have been disadvantaged in some ways by their lack of math. Radio eluded them—which is why despite all the listening your SETI projects have done to Delta Pavonis, they were never detected. My race was monumentally surprised to find a technological civilization when our first starship arrived there.”
“Well, maybe Wreeds aren’t really intelligent,” I said.
“They are. They build the most beautiful cities out of the clay that covers most of their world. Urban planning is an art form for them; they see the whole metropolis as one cohesive entity. In fact, in many ways, they are more intelligent than we are. Well, perhaps that is an overstatement; let us say they are differently intelligent. The closest we come to having a common ground is in our use of aesthetics to evaluate scientific theories. You and I agree that the most beautiful theory is probably the correct one; we look for elegance in the way nature works. Wreeds share that, but understanding what constitutes beauty is much more innate in them; it lets them discern which of several theories is correct without testing them mathematically. Their sense of beauty also seems to have something to do with why they are so good at matters that perplex us.”
“Such as?”
“Such as ethics and morality. There is no crime in Wreed society, and they seem able to solve the m
ost vexing moral quandaries with ease.”
“For example? What insights do they have on moral issues?”
“Well,” said Hollus, “one of the simplest is that honor does not have to be defended.”
“A lot of humans would disagree with that.”
“None that are at peace with themselves, I suspect.”
I thought about that, then shrugged. Maybe he was right. “What else?”
“You tell me. Present an example of a moral quandary, and I will try to tell you how a Wreed would resolve it.”
I scratched my head. “Well, okay—okay, how about this? My brother Bill got married recently for the second time. Now, his new wife Marilyn is quite lovely, I think—”
“The Wreeds would say you should not attempt to mate with your brother’s spouse.”
I laughed. “Oh, I know that. But that’s not the question. I think Marilyn is lovely, but, well, she’s quite curvy—zaftig, even. And she doesn’t exercise. Now, Bill keeps bugging Marilyn to go to the gym. Meanwhile, Marilyn wants him to stop picking on her, saying he should accept her the way she is. And Bill says, ‘Well, you know, if I should accept your not exercising, then you should accept my wanting to change you—since wanting to change people is a fundamental part of my character.’ Get it? And, of course, Bill says his comments are selfless, motivated by genuine concern for Marilyn’s health.” I paused. The whole thing gives me a headache whenever I think about it; I always end up wanting to say, “Norman, coordinate!” I looked at Hollus. “So who is right?”
“Neither,” said Hollus, at once.
“Neither?” I repeated.
“Exactly. That is an easy one, from a Wreed point of view; because they do not do math, they never treat moral questions as a zero-sum game in which someone must win and someone else must lose. God, the Wreeds would say, wants us to love others as they are and also to struggle to help them fulfill their potential—both should happen simultaneously. Indeed, a core Wreed belief is that our individual purpose in life is to help others become great. Your brother should not vocalize his displeasure at his wife’s weight, but, until he attains that ideal of silence, his wife should ignore the comments; learning to ignore things is one of the great paths to inner peace, say the Wreeds. Meanwhile, though, if you are in a loving relationship, and your partner has grown dependent on you, you have an obligation to protect your own health by wearing safety belts in vehicles, by eating well, by exercising, and so on—that is Marilyn’s moral obligation to Bill.”
I frowned, digesting this. “Well, I guess that does make sense.” Not that I could think of any way to communicate it to either Bill or Marilyn. “Still, what about something controversial. You saw that newspaper article about the bombed abortion clinic.”
“The Wreeds would say that violence is not a solution.”
“I agree. But there are lots of nonviolent people on both sides of the abortion issue.”
“What are the two sides?” asked Hollus.
“They call themselves ‘pro-life’ and ‘pro-choice.’ The pro-lifers believe every conception has a right to fulfillment. The pro-choicers believe that women should have the right to control their reproductive processes. So who is correct?”
Hollus’s eyestalks weaved with unusual speed. “Again, it is neither.” He paused. “I hope I am not giving offense—it has never been my desire to be critical of your race. But it does astound me that you have both tattoo parlors and abortion clinics. The former—businesses devoted to permanently altering one’s appearance—imply that humans can predict what they will want decades in the future. The latter—facilities to terminate pregnancies—imply that humans often change their minds over timeframes as short as a few months.”
“Well, many pregnancies are unintentional. People have sex because it’s fun; they do it even when they don’t wish to procreate.”
“Do you not have methods of contraception? If you do not, I am sure Lablok could devise some for you.”
“No, no. We have many methods of birth control.”
“Are they effective?” asked Hollus.
“Yes.”
“Are they painful?”
“Painful? No.”
“The Wreeds would say that abortion, then, should simply not be a moral issue because simple precautions would obviate the need to discuss it at all, except in a handful of unusual cases. If one can easily choose not to get pregnant, then surely that is the proper exercising of choice. If you can avoid a difficult moral problem, such as when life begins, then why not simply do so?”
“But there are cases of rape and incest.”
“Incest?”
“Mating within one’s own family.”
“Ah. But surely these are exceptional occurrences. And possibly the best moral lesson my own people have learned during our association with the Wreeds is that general principles should not be based on exceptional cases. That one insight has enormously simplified our legal system.”
“Well, then, what do you do in exceptional cases? What should you do in the case of a rape resulting in pregnancy?”
“Obviously, the woman had no chance to proactively exercise her reproductive rights via contraception; therefore, clearly she should be permitted to regain control of her own biology as fully and completely as she desires. In such cases, abortion is obviously an acceptable option; in others, birth control is clearly the preferred route.”
“But there are humans who believe artificial birth control is immoral.”
Hollus’s eyes looked briefly at each other, then they resumed their normal oscillating. “You humans do seem to go out of your way to manufacture moral issues. There is nothing immoral about contraception.” He paused. “But these are easy examples of Wreed thinking. When we get into more complex areas, I am afraid their responses do not make much sense to us; they sound like gibberish—our brains apparently are not wired to appreciate what they are saying. Philosophy departments at the Forhilnor equivalents of what you call universities had little status until we met the Wreeds; they are now extremely busy, trying to decipher complex Wreed thought.”
I considered all of this. “And with minds geared for ethics and for discerning underlying beauty, the Wreeds have decided that God really does exist?”
Hollus flexed his six legs at both their upper and lower knees. “Yes.”
I’m not an overly arrogant man. I don’t insist that people refer to me as Doctor Jericho, and I try to keep my opinions to myself. But, still, I always felt I had a good grip on reality, an accurate view of the world.
And my world, even before I was stricken with cancer, did not include a god.
But I’d now met not one but two different alien lifeforms, two different beings from worlds more advanced than my own. And both of these advanced creatures believed the universe was created, believed it showed clear evidence of intelligent design. Why did this surprise me so much? Why had I assumed that such thoughts would be, well, alien to any advanced being?
Since ancient times, the philosophers’ secret has always been this: we know that God does not exist, or, at least, if he does, he’s utterly indifferent to our individual affairs—but we can’t let the rabble know that; it’s the fear of God, the threat of divine punishment and the promise of divine reward, that keeps in line those too unsophisticated to work out questions of morality on their own.
But in an advanced race, with universal literacy and material desires fulfilled through the power of technology, surely everyone is a philosopher—everyone is privy to the ancient, once-guarded truth, everyone knows that God is just a story, just a myth, and we can drop the pretense, dispensing with religion.
Of course, it’s possible to enjoy the traditions of a religion—the ceremonies, the ties with the past—without believing in God. After all, as one of my Jewish friends has been known to observe, the only Jews who survived World War II were either now atheists or hadn’t been paying attention.
But, in fact, there are millions of Jews who b
elieve—really believe—in God (or G-d); indeed, secular Zionist Judaism was on the wane while formal observance was rising. And there are millions of Christians who believe in the holy threefer of, as one of my Catholic friends occasionally quipped, Big Daddy, Junior, and the Spook. And there are millions of Muslims who embraced the Qur’an as the revealed word of God.
Indeed, even here, at the dawn of the century following the one in which we’d discovered DNA and quantum physics and nuclear fission and in which we’d invented computers and spaceships and lasers, ninety-six percent of the world’s population still really believed in a supreme being—and the percentage was rising, not falling.
So, again, why was I so surprised that Hollus believed in God? That an alien from a culture a century or two more advanced than my own hadn’t shucked off the last vestiges of the supernatural? Even if he hadn’t had a grand unified theory to justify his beliefs, why should it be so outlandish that he wasn’t an atheist?
I’d never questioned whether I was right or wrong when confronted by obviously deluded creationists. I’d never doubted my convictions when assailed by fundamentalists. But here I was, meeting with creatures from other stars, and the fact that they had been able to come to me while I had no way of going to see them made blindingly obvious which of us was intellectually superior.
And these aliens believed what I hadn’t since childhood.
They believed an intelligent designer had made the universe.
* * *
15
T
here are two reasons why a patient might wish to undergo chemotherapy,” Katarina Kohl had said to Susan and me, shortly after my diagnosis. “The first is in hopes of eliminating the cancer.” She looked at me, then at Susan, then back again at me. “But I will tell you the truth: the chances of eliminating your cancer are small, Tom. Lung cancer is only rarely cured.”
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