Such an argument may or may not be true, but there are potential flaws. Professional mathematicians for the most part ignore the incompleteness theorem in their work. This is because the incompleteness theorem begins by a.n.a.lyzing statements that refer to themselves; that is, they are self-referential. For example, statements like the following are paradoxical: This sentence is false.
I am a liar.
This statement cannot be proven.
In the first case, if the sentence is true, it means it is false. If the sentence is false, then the statement is true. Likewise, if I am telling the truth, then I am telling a lie; and if I am telling a lie, then I am telling the truth. In the last case, if the sentence is true, then it cannot be proven to be true.
(The second statement is the famous liar"s paradox. The Cretan philosopher Epimenides used to ill.u.s.trate this paradox by saying, "All Cretans are liars." However, Saint Paul missed the point entirely and wrote, in his epistle to t.i.tus, "One of Crete"s own prophets has said it, "Cretans are always liars, evil brutes, lazy gluttons." He has surely told the truth.") The incompleteness theorem builds on statements such as "This sentence cannot be proven using the axioms of arithmetic" and creates a sophisticated web of these self-referential paradoxes.
Hawking, however, uses the incompleteness theorem to show that a theory of everything cannot exist. He claims that the key to G.o.del"s incompleteness theorem is that mathematics is self-referential, and physics suffers from this disease as well. Since the observer cannot be separated from the observation process, it means that physics will always refer to itself, since we cannot leave the universe. In the final a.n.a.lysis, the observer is also made of atoms and molecules, and hence must be an integral part of the experiment he is performing.
But there is a way to avoid Hawking"s criticism. To avoid the paradoxes inherent in G.o.del"s theorem, professional mathematicians today simply state that their work excludes all self-referential statements. They can then circ.u.mvent the incompleteness theorem. To a large degree, the explosive development of mathematics since G.o.del"s time has been accomplished simply by ignoring the incompleteness theorem, that is, by postulating that recent work makes no self-referential statements.
In the same way it may be possible to construct a theory of everything that can explain every known experiment independent of the observer/observed dichotomy. If such a theory of everything can explain everything from the origin of the big bang to the visible universe that we see around us, then it becomes academic how we describe the interaction between the observer and observed. In fact, one criterion for a theory of everything should be that its conclusions are totally independent of how we make the split between the observer and the observed.
Furthermore, nature may be inexhaustible and limitless, even if it is based on a handful of principles. Consider a chess game. Ask an alien from another planet to figure out the rules of chess simply by watching the game. After a while the alien can figure out how p.a.w.ns, bishops, and kings move. The rules of the game are finite and simple. But the number of possible games is truly astronomical. In the same way the rules of nature may also be finite and simple, but the applications of those rules may be inexhaustible. Our goal is to find the rules of physics.
In some sense we already have a complete theory of many phenomena. No one has ever seen a defect in Maxwell"s equations for light. The Standard Model is often called a "theory of almost everything." a.s.sume for the moment that we can shut off gravity. Then the Standard Model becomes a perfectly sound theory of all phenomena besides gravity. The theory may be ugly, but it works. Even in the presence of the incompleteness theorem, we have a perfectly reasonable theory of everything (besides gravity).
To me it is truly remarkable that on a single sheet of paper one can write down the laws that govern all known physical phenomena, covering forty-three orders of magnitude, from the farthest reaches of the cosmos over 10 billion light-years away to the microworld of quarks and neutrinos. On that sheet of paper would be just two equations, Einstein"s theory of gravity and the Standard Model. To me this reveals the ultimate simplicity and harmony of nature at the fundamental level. The universe could have been perverse, random, or capricious. And yet it appears to us to be whole, coherent, and beautiful.
n.o.bel laureate Steve Weinberg compares our search for a theory of everything to the search for the North Pole. For centuries the ancient mariners worked with maps in which the North Pole was missing. All compa.s.s needles and charts pointed to this missing piece of the map, yet no one had actually visited it. In the same way, all our data and theories point to a theory of everything. It is the missing piece of our equations.
There will always be things that are beyond our grasp, that are impossible to explore (such as the precise position of an electron, or the world existing beyond the reach of the speed of light). But the fundamental laws, I believe, are knowable and finite. And the coming years in physics could be the most exciting of all, as we explore the universe with a new generation of particle accelerators, s.p.a.ce-based gravity wave detectors, and other technologies. We are not at the end, but at the beginning of a new physics. But whatever we find, there will always be new horizons continually awaiting us.
NOTES.
PREFACE.
This has happened several times... The reason that this is true is because of the quantum theory. When we add all possible quantum corrections to a theory (a tedious process called "renormalization") we find that phenomena that were previously forbidden, at the cla.s.sical level, reenter the calculation. This means that unless something is explicitly forbidden (by a conservation law, for example) then it reenters into the theory when quantum corrections are added.
2: INVISIBILITY.
Invisibility played a central part in Plato"s theory... Plato wrote, "No man would keep his hands off what was not his own when he could safely take what he liked out of the market, or go into houses and lie with anyone at his pleasure, or kill or release from prison whom he would, and in all respects be like a G.o.d among men...If you could imagine anyone obtaining this power of becoming invisible, and never doing any wrong or touching what was another"s, he would be thought by the lookers-on to be the most wretched idiot..."
Nathan Myhrvold, former chief technology officer at Microsoft... Nathan Myhrvold, New Scientist Magazine, November 18, 2006, p. 69.
That"s why he now declines... Josie Glausiusz, Discover Magazine, November 2006.
"Such a lens would offer..." "Metamaterials found to work for visible light," Eurekalert, www.eurekalert.org/pub_releases/2007-01, 2007. Also, New Scientist Magazine, December 18, 2006.
3: PHASERS AND DEATH STARS.
During World War II, the n.a.z.is... The n.a.z.is also sent a team to India to investigate some ancient mythological claims of the Hindus (similar to the plot line in Raiders of the Lost Ark ) . The n.a.z.is were interested in the writings of the Mahabharata, which described strange, powerful weapons, including flying craft.
Weapons created from focused light beams... Movies like this have also spread a number of misconceptions about lasers. Laser beams are actually invisible unless they are scattered by particles in the air. So when Tom Cruise had to navigate through a maze of laser beams in Mission Impossible, the lattice of laser beams should have been invisible, not red. Also in many ray gun battles in the movies you can actually see the laser pulses zip across a room, which is impossible, since laser light travels at the speed of light, 186,000 miles per second.
Writing about Einstein, Planck said, "That he may sometimes have missed the target..." Asimov and Schulman, p. 124.
4: TELEPORTATION.
The earliest mention of teleportation can be found... The best recorded example of teleportation is dated October 24, 1593, when Gil Perez, a palace guard in the Philippine military guarding the governor in Manila, suddenly appeared in the Plaza Mayor of Mexico City. Dazed and confused, he was arrested by the Mexican authorities who thought he was in league with Satan. When he was brought before the Most Holy Tribunal of the Inquisition, all he could say in his defense was that he had disappeared from Manila to Mexico "in less time than it takes a c.o.c.k to crow." (As incredible as the historic accounts of this incident may be, historian Mike Dash has noted that the earliest records of Perez"s disappearance date from a century after his disappearance, and hence cannot be fully trusted.) Sir Arthur Conan Doyle, best known for his Sherlock Holmes novels... Doyle"s early work was renowned for the methodical, logical thinking typical of the medical profession, as seen in the superb deductions of Sherlock Holmes. So why did Doyle decide to shift sharply away from the cold, rational logic of Mr. Holmes to the seat-of-your-pants, harrowing adventures of Professor Challenger, who delved into the forbidden worlds of mysticism, the occult, and the fringes of science? The author was profoundly changed by the sudden, unexpected deaths of several close relatives in World War I, including his beloved son Kingsley, his brother, two brothers-in-law, and two nephews. These losses would leave a deep, lasting emotional scar on him.
Depressed by their tragic deaths, Doyle embarked on a lifelong fascination with the world of the occult, believing perhaps that he might be able to communicate with the dead via spiritualism. He abruptly shifted from the world of rational, forensic science into mysticism, and went on to give famous lectures around the world about unexplained psychic phenomena.
This uncertainty was finally codified by Heisenberg... More precisely, the Heisenberg uncertainty principle says that the uncertainty in the position of a particle, multiplied by the uncertainty in its momentum, must be greater than or equal to Planck"s constant divided by 2p. Or the product of the uncertain in a particle"s energy times the uncertainty in its time must also be greater than or equal to Planck"s constant divided by 2 p. If we let Planck"s constant go to zero, then this reduces to ordinary Newtonian theory, in which all uncertainties are zero.
The fact that you cannot know the position, momentum, energy, or time of an electron prompted Tryggvi Emilsson to wisecrack, "Historians have concluded that Heisenberg must have been contemplating his love life when he discovered the Uncertainty Principle:-When he had the time, he didn"t have the energy and,-when the moment was right, he couldn"t figure out the position.") Barrow, Between Inner s.p.a.ce and Outer s.p.a.ce, p. 187.
"For my part, at least, I am convinced that He doesn"t throw dice." Kaku, Einstein"s Cosmos, p. 127.
Bemoaning the undeniable experimental successes of the quantum theory, Einstein wrote,... Asimov and Schulman, p. 211.
Everything changed in 1993, when scientists at IBM... a.s.sume for the moment that macroscopic objects, including people, can be teleported. This raises subtle philosophical and theological questions about the existence of a "soul" if a person"s body is teleported. If you are teleported to a new location, does your soul also move with you?
Some of these ethical questions were explored in James Patrick Kelley"s novel Think Like a Dinosaur. In this tale a woman is teleported to another planet, but there is a problem with the transmission. Instead of the original body being destroyed, the original remains untouched, with all her emotions intact. Suddenly, there are two copies of her. Naturally, when the copy is told to enter the teleportation machine to be disintegrated she refuses. This creates a crisis, because the cold-blooded aliens, who provided the technology in the first place, view this as a purely practical matter to "balance the equation," while emotion-p.r.o.ne humans are more sympathetic to her cause.
In most stories teleportation is viewed as a G.o.dsend. But in Stephen King"s "The Jaunt" the author explores the implications of what happens if there are dangerous side effects to teleportation. In the future, teleportation is commonplace and fondly called "The Jaunt." Just before teleporting to Mars, a father explains to his children the curious history behind the Jaunt, that it was first discovered by a scientist who used it to teleport mice, but the only mice that survived teleportation were ones that had been anesthetized. Mice that were awake while being teleported died horribly. So humans are routinely put to sleep before they are teleported. The only man who was ever teleported while awake was a convicted criminal who was promised a full pardon if he submitted to this experiment. But after being teleported, he suffered a ma.s.sive heart attack, uttering the last words, "It"s eternity in there."
Unfortunately, the son, hearing this fascinating tale, decides to hold his breath so that he won"t be anesthetized. The results are tragic. After being teleported he suddenly goes insane. His hair turns white, his eyes are yellowed with age, and he tries to claw out his eyes. The secret is now revealed. Physical matter is teleported instantly, but to the mind the trip takes an eternity, time appears endless, and the person is driven totally insane.
"For the first time," said Eugene Polzik, one of the researchers... Curt Suplee, "Top 100 Science Stories of 2006," Discover Magazine, December 2006, p. 35.
"We"re talking about a beam of about 5,000 particles..." Zeeya Merali, New Scientist Magazine, June 13, 2007.
"With luck, and with the help of recent theoretical advances,..." David Deutsch, New Scientist Magazine, November 18, 2006, p. 69.
5: TELEPATHY.
The careers of several magicians and mentalists, in fact, have been based... At dinner parties one can also perform amazing feats of telepathy. Ask everyone at a party to write down a name on a slip of paper and put the slips in a hat. One by one you pick out a sealed slip of paper and, before opening it, read aloud the name written on it. The audience will be stunned. Telepathy has been demonstrated right before their eyes. Some magicians, in fact, have risen to fame and fortune primarily because of this trick.
(The secret to this amazing feat of mind reading is the following. Pull out the first slip of paper and read it silently to yourself, but announce that you are having difficulty reading it because the "psychic ether" is clouded. Pull out a second slip of paper but don"t open it yet. Now recite the name you read on the first slip of paper. The person who wrote that first name will be amazed, thinking you have read the sealed, second slip of paper. Now open up the second slip of paper and silently read it to yourself. Pull out the third sealed slip of paper, and read aloud the name on the second slip of paper. Repeat this process. Each time you say aloud the name on a slip of paper, you are reading the contents of the previous slip of paper.) Gamblers also are able to read people"s minds... A person"s mental state can be roughly determined by tracing the precise path taken by a roving eye as it scans a photograph. By shining a thin light beam onto the eyeball, a reflected image of the beam can be cast onto the wall. By tracing out the path taken by this reflected beam of light on the wall one can then reconstruct precisely where the eye is roving as it scans a picture. (When scanning a person"s face in a picture, for example, the observer"s eye usually moves rapidly back and forth between the person"s eyes in the picture, and then wanders to the mouth, and back to the eyes, before it scans the entire picture.) As a person scans a picture, one can calculate the size of his pupils and hence whether he experiences pleasurable or unpleasurable thoughts, as it scans particular parts of a picture. In this way, one can read a person"s emotional state. (A murderer, for example, would experience strong emotions as he looks at a picture of a murder scene and scans the precise location of the body. Only the murderer and the police would know the location.) The first scientific studies of telepathy... The Society for Psychical Research included Lord Rayleigh (n.o.bel laureate), Sir William Crookes (inventor of the Crookes tube used in electronics), Charles Richet (n.o.bel laureate), American psychologist William James, and Prime Minister Arthur Balfour. Its supporters have included such luminaries as Mark Twain, Arthur Conan Doyle, Alfred Lord Tennyson, Lewis Carroll, and Carl Jung.
One researcher connected with the society... Rhine originally planned to become a minister, but then switched to botany while attending the University of Chicago. After attending a talk in 1922 given by Sir Arthur Conan Coyle, who was giving lectures around the country about communicating with the dead, Rhine became fascinated with psychic phenomena. Later he read the book The Survival of Man, by Sir Oliver Lodge, about purported communications with the deceased during seances, which further cemented Rhine"s interest. He was, however, dissatisfied with the current state of spiritualism; its reputation was often tarred with unsavory tales of frauds and trickery. In fact, Rhine"s own investigations exposed a certain spiritualist, Margery Crandon, as a fraud, earning him the scorn of many spiritualists, including Conan Doyle.
"There is left then, only the telepathic explanation..." Randi, p. 51 Further tests showed that the mice possessed no telepathic power... Randi, p. 143.
In particular, he noticed unusual activity...San Francisco Chronicle, November 26, 2001.
Some critics also claim... Lastly, there are also legal and moral questions if limited forms of telepathy become commonplace in the future. In many states it is illegal to tape-record a person"s phone conversation without his or her permission, so in the future it might be illegal to record one"s thought patterns without his or her permission as well. Also civil libertarians may object to reading a person"s thought patterns without his or her permission, in any context. Given the slippery nature of a person"s thoughts, it may never be legal to enter thought patterns in a court of law. In Minority Report, starring Tom Cruise, there was the ethical question of whether you can arrest someone for a crime that the person hasn"t committed yet. In the future there might be the question of whether a person"s intention to commit a crime, as evidenced by thought patterns, const.i.tutes incriminating evidence against that person. If a person makes threats verbally, would that count as heavily as if a person made these threats mentally?
There will also be the question of governments and security agencies that do not care about any laws whatsoever and subject people involuntarily to brain scans. Would this const.i.tute proper legal behavior? Would it be legal to read the mind of a terrorist to find out his or her plans? Would it be legal to implant false memories in order to deceive individuals? In Total Recall, starring Arnold Schwarzenegger, the question arose continually whether a person"s memories were real, or implanted, which affects the very nature of who we are.
These questions are likely to remain purely hypothetical for decades to come, but as the technology slowly advances, inevitably the technology will raise moral, legal, and societal issues. Fortunately, we have plenty of time to sort them out.
"But if that"s the device you want to build..." Douglas Fox, New Scientist Magazine, May 4, 2006.
In this sense, an fMRI mental translator may make it possible... Philip Ross, Scientific American, September 2003.
Such a device would never be as sophisticated...Science Daily, www.sciencedaily.com, April 9, 2005.
This process is difficult and tedious, since you have to carefully process out spurious waves... Cavelos, p. 184.
6: PSYCHOKINESIS.
Before Geller"s appearance, Carson consulted with Randi... The Amazing Randi, disgusted that professional magicians skilled at fooling gullible individuals could claim psychic powers and hence defraud the unsuspecting public, began a career of exposing fakes. In particular he took delight in duplicating every feat performed by the psychics. The Amazing Randi is in the tradition of the Great Houdini, a magician who also began a second career exposing fakes and charlatans who would use their magical skills to defraud others for private gain. In particular, Randi boasts that he can even deceive scientists with his tricks. He says, "I can go into a lab and fool the rear ends off any group of scientists." Cavelos, p. 220.
The National Research Council"s report studied creating a hypothetical "First Earth battalion"... Cavelos, p. 240.
The report concluded that there was "no scientific justification..." Cavelos, p. 240.
By training them to vary their brain waves... Philip Ross, Scientific American, September 2003.
These monkeys were then able to control... Miguel Nicolelis and John Chapin, Scientific American, October 2002.
"Then I knew that everything could go forward..." Kyla Dunn, Discover Magazine, December 2006, p. 39.
But, he admits, "it still takes the best groups in the world..." Aristides A. G. Requicha, "Nanorobots," ~lmr/publications/nanorobotics.
7: ROBOTS.
even renowned physicist Roger Penrose of Oxford... Professor Penrose argues that quantum effects must be present in the brain that make possible human thought. Most computer scientists would say that each neuron in the brain can be duplicated by a complex series of transistors; hence the brain can be reduced to a cla.s.sical device. The brain is supremely complicated but in essence consists of a bunch of neurons whose behavior can be duplicated by transistors. Penrose disagrees. He claims that there are structures in a cell, called microtubules, that exhibit quantum behavior, so the brain can never be reduced to a simple collection of electronic components.
Colin McGinn of Rutgers University says that artificial intelligence... Kaku, Visions, p. 95.
Steve Grand, director of the Cyberlife Inst.i.tute, says... Cavelos, p. 90.
"He failed, and I failed on the same problem in my 1981 Ph.D. thesis." Rodney Brooks, New Scientist Magazine, November 18, 2006, p. 60.
"It doesn"t mean Kasparov isn"t a deep thinker..." Kaku, Visions, p. 61.
Not surprisingly, Lenat"s motto is, Intelligence is 10 million rules. Kaku, Visions, p. 65.
"We were killing ourselves trying to create a pale shadow..." Bill Gates, Skeptic Magazine, vol. 12, no. 12, 2006, p. 35.
"Even something as simple as telling the difference between an open door and a window can be devilishly tricky for a robot." Bill Gates, Scientific American, January 2007, p. 63.
"No one can say with any certainty when-or if-this industry..." Scientific American, January 2007, p. 58.
"There"s no machine today that can do that." Susan Kruglinski, "The Top 100 Science Stories of 2006," Discover Magazine, p. 16.
Hans Moravec says, "Fully intelligent machines will result..." Kaku, Visions, p. 76.
""Please! Please! I need this! It"s so important..."" Kaku, Visions, p. 92.
Neurologist Dr. Antonio Damasio of the University of Iowa... Cavelos, p. 98.
"Computers just don"t get it." Cavelos, p. 101.
As Russian novelist Fyodor Dostoevsky wrote... Barrow, Theories of Everything, p. 149.
"Our successors will be amazed by the amount of scientific rubbish..." Sydney Brenner, New Scientist Magazine, November 18, 2006, p. 35.
"It is possible that we may become pets of the computers..." Kaku, Visions, p. 135.
"When that happens, our DNA will find itself out of a job,..." Kaku, Visions, p. 188.
So in the long term some have advocated a merging of carbon and silicon technology... So our mechanical creations may ultimately be the key to our long-term survival. As Marvin Minsky says, "We humans are not the end of evolution, so if we can make a machine that"s as smart as a person, we can probably also make one that"s much smarter. There"s no point in making just another person. You want to make one that can do things we can"t." Kruglinski, "The 100 Top Science Stories of 2006," p. 18.
In the far future, robots or humanlike cyborgs... Immortality, of course, is something that people have desired ever since humans, alone in the animal kingdom, began to contemplate our own mortality. Commenting on immortality, Woody Allen once said, "I don"t want to achieve immortality through my work. I want to achieve it through not dying. I don"t want to live on in the hearts of my countrymen. I would rather live on in my apartment." Moravec, in particular, believes that in the far future we will merge with our creations to create a higher order of intelligence. This would require duplicating the 100 billion neurons that are in our brain, each of which in turn is connected to perhaps several thousand other neurons. As we sit on the operating room table, there is a robot sh.e.l.l lying next to us. Surgery is performed such that as we remove a single neuron a duplicate silicon neuron is created in the robot sh.e.l.l. As time goes by every single neuron in our body is replaced by a silicon neuron in the robot, so that we are conscious throughout the operation. At the end, our entire brain has been continuously transferred into the robot sh.e.l.l while we witnessed the entire event. One day we are dying in our decrepit, decaying body. The next day we find ourselves inside immortal bodies, with the same memories and personality, without losing consciousness.
8: EXTRATERRESTRIALS AND UFOS.
Nevertheless, Seth Shostak, senior astronomer at SETI, optimistically believes... Jason Stahl, Discover Magazine, "Top 100 Stores of 2006," December 2006, p. 80.
"It"s hard to imagine how life could survive that extreme onslaught," he says. Cavelos, p. 13.
French astronomer Dr. Jacques Lasker estimates that... Cavelos, p. 12.
"We believe that life in the form of microbes..." Ward and Brownlee, p. xiv.
"We"re the first generation that has a realistic chance of discovering life on another planet." Cavelos, p. 26.
As I"ve discussed in my previous books... In general, although local languages and cultures will continue to thrive in different regions of the Earth, there will emerge a planetary language and culture that spans the continents. This global and local culture will exist simultaneously. This situation already exists with regards to the elites of all societies.
There are also forces that oppose this march to a planetary system. These are the terrorists who unconsciously, instinctively, realize that the progression to a planetary civilization is one that will make tolerance and secular pluralism a centerpiece of their emerging culture, and this prospect is a threat to people who feel more comfortable living in the last millennium.
9: STARSHIPS.
Mathematician and philosopher Bertrand Russell once lamented... Kaku, Hypers.p.a.ce, p. 302.
Nordley says, "With a constellation of pinhead-sized s.p.a.cecraft..." Gilster, p. 242.
10: ANTIMATTER AND ANTI-UNIVERSES.
Dr. Steven Howe, of Synergistics Technologies in Los Alamos... NASA, April 12, 1999.