In his most ambitious book yet, Clifford Pickover bridges the gulf between logic, spirit, science, and religion. While exploring the concept of omniscience, Pickover explains the kinds of relationships limited beings can have with an all-knowing God. Pickover's thought exercises, controversial experiments, and practical analogies help us transcend our ordinary lives while challenging us to better understand our place in the cosmos and our dreams of a supernatural God. Through an inventive blend of science, history, philosophy, science fiction, and mind-stretching brainteasers, Pickover unfolds the paradoxes of God like no other writer. He provides glimpses into the infinite, allowing us to think big, and to have daring, limitless dreams.
|Publisher:||St. Martin's Press|
|Edition description:||First Edition|
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About the Author
The author of over 20 highly-acclaimed books, including Computers, Patterns, Chaos, Beauty, Clifford A. Pickover writes on diverse topics ranging from computers and creativity, art, mathematics, and astronomy to human behavior and intelligence, time travel, alien life, and science fiction.
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The Paradox of God and the Science of Omniscience
By Clifford A. Pickover
St. Martin's PressCopyright © 2001 Clifford A. Pickover
All rights reserved.
The Paradox of Omniscience
God created the world for His own glory. This is an indisputable fact and one, moreover, that is quite understandable. A greatness that nobody can see is bound to feel ill at ease.
— Leszek Kolakowski, The Keys to Heaven
Truly Thou are a hidden God.
— Blaise Pascal, Pensées, 1670
You are captain of a large starship drifting in interstellar space. On your viewscreen is a ship of the Nephilim, a race of tentacled beings to whom you wish to demonstrate your courage. Showing weakness may one day give them the idea that they can take over the Earth and its solar system.
You are racing toward the Nephilim on a collision course. If neither of you veers from your course, your two ships will crash and all crew members will die. You certainly don't want that. Neither does the captain of the other ship, the huge Dr. Eck. But you do want to show the Nephilim your stamina and unbridled courage by staying your course and having Dr. Eck swerve to prevent a catastrophic collision.
However, if you have to chicken out, you wouldn't be too disappointed if both you and Dr. Eck lost nerve and swerved. At least you would be alive and wouldn't be embarrassed by your loss of nerve in front of the Nephilim and your adoring crew mates. Of course, even if you swerved and Dr. Eck didn't, you'd prefer to survive and be humiliated rather than die with your crew. Here, then are some possible outcomes.
You know several things about the Nephilim. You've met with Dr. Eck before. You know he and his race are rational creatures. They want to survive the encounter.
You only have a few seconds to think about what to do. Think fast! If you have had many such encounters with the Nephilim, it seems like the best you can do is to chicken out, in the hope that the Nephilim will be sufficiently wise and do the same. If either you or the Nephilim does not veer to the side, one of you will be very angry and may not swerve during another encounter. Neither humans nor Nephilim will live long and prosper unless they are cowards.
There's just one problem with this logic. A big problem. The Nephilim are omniscient, just like God is supposed to be. They are telepathic and can read your mind. They always anticipate your moves with perfect accuracy. (In fact, some people believe that the Nephilim are gods, because of their omniscience.)
One of your initial thoughts is that the Nephilim have a big advantage over you in this dangerous form of brinkmanship. After all, they know for sure what you will do. They have more knowledge of you than you of them.
You think back to 1962, when American president John F. Kennedy and Soviet premier Nikita Khrushchev played a similar dangerous game of "chicken" during the Cuban Missile Crisis. Nikita Khrushchev had secretly supplied Cuba with missiles that could deliver nuclear bombs to the United States. Kennedy told Khrushchev to get the missiles out of Cuba or risk nuclear war. Luckily, Khrushchev decided to remove the missiles rather than risk such a catastrophe.
In 1964, Khrushchev was deposed as leader of the USSR, in part because his people considered him weak in his dealing with Kennedy. During the crisis, both sides were far from omniscient. In fact, unknown to President Kennedy, Soviet forces in Cuba had been equipped with nuclear weapons that could be used in the battlefield, and America had no idea that there were as many as 40,000 Soviet soldiers in Cuba.
You ponder the Cuban Missile Crisis as Dr. Eck's ship comes closer. Would the nation with the most knowledge have been better off in the Cuban Missile Crisis?
You look out the ship's window. It doesn't look good, as the ships are only miles apart:
A deep, stentorian voice comes over your radio. "Turn away!" screams Dr. Eck. His voice has a vague metallic echo.
"I cannot!" you yell back to Dr. Eck.
"This is madness!" Dr. Eck says. "Don't be a fool. For God's sake, change your course."
You slam your fist down onto your captain's chair. "Who are you trying to scare? It is you who must turn."
Hurry! The ships are drawing closer to each other! Only seconds remain. What should you do?
The answer is clear. It is actually you who have the advantage over an omniscient being. You must stay the course. You should not swerve. Because Dr. Eck is omniscient, if you were to swerve he would have predicted it and thus stayed his course. Humanity would have been humiliated, and Dr. Eck might have descended to Earth and devoured most forms of mammalian life — not to mention wreaking havoc with Earth's delicate geopolitical balance.
Here's what happens if you do not swerve. Dr. Eck knows he has only two choices:
Table 1.2 The Fate of Dr. Eck
What Dr. Eck Does
Dr. Eck swerves.
Dr. Eck survives
Dr. Eck stays his course.
Dr. Eck dies
This means that Dr. Eck's only choice is to swerve. Because he knows you will stay your course, he must swerve. You already know he is rational and does not want himself and his crew to die in a conflagration in the depths of interstellar space. Thus, you have beaten an omniscient being and won the gambit.
This paradox of omniscience demonstrates the limits of common sense when considering the actions of omniscient beings and gods. In this scenario, you can see that omniscience is a disadvantage for "gods" playing risky games. No amount of thinking can help Dr. Eck out of his dilemma. Even though he is omniscient, he cannot gain the advantage over you.
MUSINGS AND SPECULATIONS
God is something less than absolutely omnipotent. He is actually engaged in a conflict with his creatures, in which he may very well lose the game. ... Can God play a significant game with his own creatures?
— Norbert Wiener, God & Golem, Inc., 1964
What makes the paradox of omniscience so amazing to contemplate is that it is precisely the alien's omniscience, and your awareness of it, that ensures you obtain the best possible outcome and that the alien does not. This is the paradox — most people would never expect the superior ability of a godlike creature to diminish his position in a conflict. Do you think that there are instances in the Bible or in history where humans were on a collision course with God and where neither wants to swerve? Of course, the situation with Dr. Eck can be made more complicated. For example, an omniscient being may know much more than your thoughts. He may know that you or he will die of a heart attack in 45 seconds.
The God of the Bible appears to be frustrated and surprised at times, which itself seems paradoxical for an omniscient being. For example, God frequently asks questions throughout the Bible before passing judgment. After Adam and Eve eat the forbidden fruit and hide themselves in the Garden of Eden, they are bombarded with a series of questions: "Where are you?" "Who told you that you were naked?" "Have you eaten of the tree, whereof I commanded you that you should not eat?" "What is this you have done?" (Genesis 3:9, 11, 13).
Later in Genesis, God asks questions of Adam's son Cain: "Why are you angry? And why is your countenance fallen? If you do well, shall it not be lifted up?" "Where is Abel, your brother?" "What have you done?" In the Book of Job, God asks Satan, "Where do you come from?" (Satan answers God, "From roaming through the earth and going back and forth in it") (Genesis 4:6–7, 9, 10; Job 1:7).
Of course, we might argue that these questions are largely rhetorical and only asked for the sake of the humans. Liberal theologians who do not take the Bible as the literal word of God might say that these are simply examples of anthropopatheia, ascribing human attributes to God. However, even when God is not asking us questions, God continually tests. He tests Abraham by suggesting he sacrifice his son. Satan persuades God to test Job's devotion through a series of emotional and physical tortures.
One of the best examples in which God's words might be taken as implying His nonomniscience occurs during the test of Abraham. A literal interpretation of the Bible could suggest God did not know how Abraham would react:
Abraham reached out his hand and took the knife to slay his son. But the angel of the Lord called out to him from heaven, "Abraham! Abraham!" "Here I am," he replied. "Do not lay a hand on the boy," he said. "Do not do anything to him. Now I know that you fear God, seeing that you have not withheld from me your son, your only son." (Genesis 22:10–12)
Even if God asks all His questions rhetorically, or if they are meant as mere allegory, or if God knows the answers to His tests, it is notable that God's reaction upon hearing many answers is one of anger and frustration, an almost explosive fury that must be quenched. When God learns of Eve's disobedience, He tells Eve, "I will make most severe your pangs in childbearing. In pain shall you bear children." He tells Adam, "Cursed be the ground because of you. By toil shall you eat of it all the days of your life: thorns and thistles shall it sprout for you. ... For dust you are and to dust you shall return" (Genesis 3:16–19). The Old Testament God surely sounds like an angry and jealous God, and He describes himself as such throughout.
Although a metaphorical interpretation of the Bible provides an escape hatch for some of the paradoxes described in this book, I nevertheless ask the reader to consider what lessons these metaphors are intended to teach humanity, and what paradoxes may still persist as a result of following these lessons. As just one example, recall the many instances in the Bible where God appears to sanction the torture and killing of children for the sins of their parents. Even if we do not take the Bible literally, we can still wonder at, or try to resolve, the logical paradoxes or incongruities that arise when we juxtapose these stories with God's edict that sons should not share the guilt of the fathers. (Appendices C and D give numerous similar examples.)
* * *
The paradox of omniscience need not apply only to God. One can imagine similar scenarios with nations, one of which has thousands of spies and is, in effect, omniscient. The other nation, if it knows that there are thousands of spies, can have an advantage over the "omniscient" nation — just like you did over Dr. Eck. Perhaps the paradox of omniscience will someday enter our daily lives if computers with numerous sensors monitor our movements and thoughts.
Another way to play this collision-course game would be to convince your opponent that you are crazy and will keep going no matter what. If he is rational, he will swerve. The challenge would be to convince your opponent that you are crazy. After all, if he is rational, he will realize that it is to your advantage to appear insane. So your supposed insanity could actually be a sign of your sharp intelligence. Perhaps you will have the best advantage if you are truly insane. Perhaps someone who really wanted to win could make himself temporarily nuts by eating a hallucinogenic mushroom. Would you risk this in a life-and-death situation? Paradoxically, you will have transformed yourself into someone who can act in your best interest. Your actual insanity might manifest itself in many ways — drooling, cursing, self-mutilation, shouting words from the Bible at random intervals while jumping around like a chicken with its head cut off, and so on. If the Russians had convinced us they were insane during Kennedy's administration, the Cuban Missile Crisis might have ended with a different outcome. If true psychics existed, you could always win when playing such games with them. The psychic is at a disadvantage. The true psychic has the dangerous disadvantage of omniscience.
* * *
Despite the seemingly secular atmosphere of much of modern Western society, the idea of a biblical God still affects millions of people. Surveys indicate that 95 percent of Americans believe in God. A recent Newsweek survey found that 87 percent of adults believe God sometimes answers their prayers. Of course, most of these individuals would have only a very limited knowledge or understanding of the Bible. For example, how many would have heard of the great Nephilim?
Yes, the term "Nephilim" is from the Old Testament. One of the most enigmatic stories of the Bible occurs in Genesis 6:1–4. Here we find that the "sons of God saw that daughters of men were beautiful, and they married any of them they chose." Kenneth Davis, author of Don't Know Much About the Bible, speculates that the "sons of god" might have been angels who took wives from the daughters of humans. The offspring of these angel-human marriages were the Nephilim, the ancient heroes and warriors:
The Nephilim were on the earth in those days — and also afterward — when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown. (Genesis 6:4)
The word "Nephilim" also literally translates to the "fallen ones." The Nephilim had superhuman powers. Notice that they should have been destroyed in the great Flood, but we do find them later in Canaan during the time of Moses, according to the Book of Numbers.
Some have speculated that the strange biblical reference to Nephilim may represent a deep collective memory of the time when Neanderthals coexisted with Homo sapiens. We know that Neanderthals inhabited Europe and the Middle East during the late Pleistocene Epoch, about 100,000 to 30,000 years ago. The Neanderthals were the first hominids to intentionally bury their dead, and they had larger brain cases than modern humans. Examination of skeletal remains indicates that Neanderthals were a physically powerful and war-scarred race. Not without controversy, some researchers suggest that the Nephilim might refer to either Neanderthals or strongly muscled but possibly sterile hybrids produced by the mating of Neanderthals and Homo sapiens. Even today, scientists do not fully understand the Neanderthal's evolutionary origin and final fading from the world scene.
Perhaps God might isolate sectors within himself and simulate limited knowledge in order to overcome the paradox of knowing everything yetnot knowing what it would be like to learn or be surprised. This challenge gives God a very good reason to divide himself into pieces, to become incarnate as a human being, at which point He can experience the essence of being a limited mind containing a shard of infinity within.
— Luke Dunn, personal communication
If, on the other hand, he went to pay his respects to the Door, and it wasn't there ... what then? The answer, of course, was very simple. He had a whole board of circuits for dealing with exactly this problem, in fact this was the very heart of his function. He would continue to believe in it whatever the facts turned out to be, what else was the meaning of Belief? The Door would still be there, even if the door was not.
— Douglas Adams, Dirk Gently's Holistic Detective Agency
My life has been remarkably happy, perhaps in the upper 99.99 percentile of human happiness, but even so, I have seen a mother die painfully of cancer, a father's personality destroyed by Alzheimer's disease, and scores of second and third cousins murdered in the Holocaust. Signs of a benevolent designer are pretty well hidden.
— Steven Weinberg, Skeptical InquirerCHAPTER 2
God and Evil
If [God] is omnipotent, then every occurrence, including every human action, every human thought, and every human feeling and aspiration is also His work; how is it possible to think of holding men responsible for their deeds and thoughts before such an almighty Being? In giving out punishment and rewards He would to a certain extent be passing judgment on Himself. How can this be combined with the goodness and righteousness ascribed to Him? The main source of the present-day conflicts between the spheres of religion and of science lies in this concept of a personal God.
— Albert Einstein, Out of My Later Years
You are with an extraterrestrial artist named Miss Muxdröözol. Muxdröözol, a trochophore with two huge teardrop-shaped eyes, has painted a biblical scene of the Tower of Babel using the blood of several ancestors.
You sometimes wonder about Miss Muxdröözol. Her skin is exceptionally smooth but her shape is somewhat disconcerting. She essentially has no body — just a large head connected to arms and legs. Sometimes the arms seem to retract behind the folds of her cloak.
You are telling her your ideas about God. "Miss Muxdröözol, moral truth is God's will. Something is good because God desires it. Think of the Ten Commandments."
She shakes her head. "No. That's backwards. God desires it because it's good. I can prove it."
"No way!" You frown and then after a few seconds grin, although the smile doesn't reach your eyes. "I thought I saw something." But now you think the snakelike movement within the depths of her hair must be just a trick of the light.
"This?" Miss Muxdröözol asks as she moves her arm and a tangle of emerald light reflects against her face. Several gems are inlaid in her wrist.
Excerpted from The Paradox of God and the Science of Omniscience by Clifford A. Pickover. Copyright © 2001 Clifford A. Pickover. Excerpted by permission of St. Martin's Press.
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Table of Contents
Introduction * The Paradox of Omniscience * God and Evil * Cain's Dilemma * The Parable of Algae * Newcomb's Paradox and Divine Foreknowledge * The Devil's Offer * The Revelation Gambit * The Paradox of Eden * The Brain and God: Who's in Charge? * The Bodhisattva Paradox * The Paradox of Pascal's Wager * Two Universes * Gödel's Proof of God * The Paradox of Uzzah * The Paradox of Dr. Eck * The Paradox of Led Zeppelin * A Few Quick Puzzles and Surveys * Some Final Thoughts * Appendices * A. Can God Change His Mind? * B. Biblical Suggestions that God is Omniscient * C. 30 Examples of God Entering the Time Stream and Aiding Mass Killing * D. Can a Just God support Cannibalism and Child Sacrifice? * E. Aquinas's God and Maxwell's Demon * F. Can an Omniscient Being Lose His Temper? * G. The Paradox of the Flood * H. St. Augustine and The City of God * I. Does God Makes Mistakes and Learn? * J. God Wants Fear * K. Two Proofs That God is not All Knowing? * L. Sixty Way-out Questions to Ponder