by Seth Lloyd
A more parsimonious strategy for eternal life is to make do with a finite amount of energy, as proposed by Freeman Dyson, of the Institute for Advanced Study.17 After all, the total number of ops that can be performed is proportional to the amount of energy available times the amount of time for which it is available. If time goes on forever, a finite amount of energy should suffice to compute forever. Unfortunately, whenever an op is performed, some of the energy will be wasted due to errors and inefficiency. Eventually the supply of energy will dwindle and approach zero. Dyson points out that despite the dwindling of stores of energy, life could still go on as long as it is willing to slow down.
Suppose that each time this future life-form performs an op, all the energy that was used to perform it is dissipated. This is the worst-case scenario. So the next time the being performs an op, there is less energy available. That’s OK—the next op is just performed more slowly, using a smaller amount of energy. The available energy is gradually decreasing, but at a slower and slower rate. Similarly, the time taken to perform each op gets longer and longer. But as long as you keep on performing ops more and more slowly, you can still perform an infinite number of ops in an infinite time, using a finite amount of energy.
How about memory space? As the amount of available energy dwindles, the total memory space available in a given volume also drops. So to keep on increasing the amount of memory space available, our deathless life-form must spread its energy out over a larger and larger volume. In other words, if you want to live forever, you have to slow down and get fat (a strategy many people have already adopted).
The biggest potential problem with this slow-down/get-fat strategy is waste. You have to get rid of that used-up energy somehow. Fortunately, slowing down and getting fat also helps here: the slower you are, the less energy you have to dissipate, and the larger you are, the greater the surface area you have through which to dissipate it. You have to be careful, however, to expand slowly enough so that your average energy per bit (that is, your temperature) remains above the temperature of the surrounding universe. If the universe has an intrinsic minimum temperature, as suggested by some cosmological observations, then you’re sunk. At some point, you’ll just be swamped by the surrounding radiation. However, if the temperature of the universe keeps decreasing forever at a sufficiently rapid rate, as suggested by other cosmological observations, then you’re cool: you can keep on processing information and increasing your memory space.
Supposing it can exist, what would such an ultimate life-form look like? It would expand to encompass first stars, then galaxies, then clusters of galaxies, and eventually, it would take billions of years to have a single thought. Attractive? It depends on your taste. But if you want to live forever, you have to expect to make a few sacrifices.
Being Human
We’ve looked at the hot past; we’ve looked at the dim and distant future. To conclude our discussion of complexity, let’s return to the present. Where do human beings fit in the computational universe? The innate information-processing capacity of the universe at the fundamental level gives rise to all possible forms of information processing. After the Big Bang, as different pieces of the universe tried out all possible ways of processing information, sooner or later, seeded by a quantum accident, some piece of the universe managed to find an algorithm to reproduce itself. That accident led to life. Life evolved by processing genetic information to try out new strategies for survival and reproduction. After trying out billions of strategies, some living systems eventually discovered sex, a technique that vastly increases the rate at which new evolutionary strategies and algorithms can be explored, because it speeds up the rate of genetic information processing. After billions of years of sex, living creatures had evolved all sorts of methods for getting and processing information—eyes, ears, and brains, to name a few.
Somewhere in the last 100,000 years or so, human beings hit upon language. Human language must have seemed an odd-sounding innovation to the other animals around. But by allowing the expression of arbitrarily complicated concepts, human language allowed people to process information in a highly distributed fashion. The distributed nature of human information processing in turn allowed people to cooperate in new ways, forming groups, associations, societies, companies, and so on. Some of these new forms of cooperation proved strikingly effective, as various forms of distributed information processing, such as democracy, communism, capitalism, religion, and science, took on a life of their own, propagating themselves and evolving over time.
It is the richness and complexity of our shared information processing that has brought us this far. The invention of human language, coupled with diverse social development, was a true information-processing revolution that has substantially changed the face of the Earth. It has been argued that the human brain sets us apart from other animals. We human beings are very attached to our brains. Without them, we would have no thought or perception (the same holds true for other animals with brains). Language allows us to connect the workings of our brains to the workings of other people’s brains. Communication allows us to collaborate and compete in ever more complex ways. To paraphrase John Donne, no one is an island. Every human being on Earth is part of a shared computation.
It is the joint computation shared by all of human society that makes us special—if indeed we are special, that is. Human beings are not the only physical systems to participate in a complex, rich computation. As I’ve tried to show, every atom, every elementary particle participates in the huge computation that is the universe. At bottom, each bit of the universe is just a bit. In their ability to register and process information, all bits are equal.
Science has an uncomfortable way of pushing human beings from center stage. In our prescientific stories, humans began as the focal point of Nature, living on an Earth that was the center of the universe. As the origins of the Earth and of mankind were investigated more carefully, it became clear that Nature had other interests beyond people, and the Earth was less central than previously hoped. Humankind is just one branch of the great family of life, and the Earth is a smallish planet orbiting an unexceptional sun quite far out on one arm of a run-of-the-mill spiral galaxy.
We are, nonetheless, unique (as are bacteria; as are elm trees). What makes us unique is information—the bits of DNA that join us to monkeys, and the habits of language and thought that separate us from them. There is no separate substance, no vis vitae or vital force, that makes us living, breathing human beings. We are made of atoms, like everything else. It is the way that those atoms process information and compute in concert that makes us what we are. We are clay, but we are computational clay.
Universal Thoughts
Now that we are aware of the computational nature of the universe as a whole, it is tempting to ascribe to it a kind of cosmic intelligence, like Laplace’s divine “demon.” There is nothing wrong with thinking of the universe itself as some kind of gigantic intelligent organism, any more than it is wrong to think of the Earth itself as a single living being (an idea known as the “Gaia hypothesis”). Note, however, that if you assert the intelligence of the universe, you cannot deny the brilliance of one of its greatest “ideas”—natural selection.18 For billions of years, the universe has painstakingly designed new structures by a slow process of trial and error. Each “Aha” in this design process is a tiny quantum accident, whose consequences are elaborated by the laws of physics. Some accidents work out, others don’t. After billions of years, the result is us, and everything else.
In the final analysis, to say that the world is alive, or that the universe thinks, is only a metaphor. After all, what are these thoughts of the universe? Some of the information processing the universe performs is indeed thought—human thought. Some of that information processing, like digital computation, can resemble thought. But the vast majority of the information processing in the universe lies in the collision of atoms, in the slight motions of matter and light.
Compared with what is normally called thought, such universal “thoughts” are humble: they consist of elementary particles just minding their own business. But humility is not the same as weakness. Quantum chaos can amplify slight motions until they become a hurricane. The microscopic dance of matter and light had the power to produce not just human beings, but every being. The collision of two atoms can—and does—change the future of the universe.
Personal Note: The Consolation of Information
My road to the concept of effective complexity has been a long and complex one. It began with my work with Heinz Pagels at Rockefeller, and it continued as my Ph.D. moved into view and I was offered a postdoctoral position with Rolf Landauer at IBM. Landauer was one of the founders of the field of physics of information. His motto, “Information is physical,” is an underlying principle of this book: all information that exists is registered by physical systems, and all physical systems register information.
I was somewhat surprised by the job offer. I had gone up to IBM’s Watson Laboratories in Yorktown Heights that fall to deliver a talk on Maxwell’s demon. As part of my Ph.D. thesis (“Black Holes, Demons, and the Loss of Coherence: How Complex Systems Get Information and What They Do with It”), I had made a quantum-mechanical model of how one quantum system gets information about another and showed how such apparent violations of the second law of thermodynamics do not cause any actual violations. My talk had not gone too well. Landauer had been crusty. Charles Bennett had just published a definitive article on Maxwell’s demon that year, articulating far better than I had the trade-off between information and entropy. Perhaps worse, I inadvertently insulted Gregory Chaitin at lunch by making a joke about people who believe in the healing power of crystals, unaware that he kept a large crystal in his living room because it helped him concentrate.
Nevertheless, here was the impressive job offer, and I made preparations to go. Shortly after Landauer’s call, the head of my laboratory at Rockefeller walked into my office. “Murray Gell-Mann wants to talk with you on the phone immediately,” he declared. By now I was wary of professors walking into my office and making pronouncements. Why on earth would Gell-Mann want to talk with me? I had never met him (the fistfight in the convent hadn’t happened yet), and I had no idea why the world’s best-known physicist would be interested in any of the peculiar stuff I was doing.
I picked up the phone. “Where is your application to Caltech?” Gell-Mann demanded. He was working on problems of complexity and on foundations of quantum mechanics and was having a hard time finding a postdoctoral fellow to work with him on these subjects. He’d been searching for months for someone who had done a Ph.D. in these fields and had finally come across me. He would piece together a postdoctoral position for me, if I was willing to accept. I had gone from no job to two job offers in the course of a week. It was a tough decision to make. Because I had missed the usual Caltech hiring process, the salary that Gell-Mann could offer me for the first year was half of what IBM was offering. On the other hand, I was excited by the prospect of going to Caltech. In the end, I decided to go west. It was the summer of 1988. I packed my belongings into my ten-year-old Datsun and started driving.
My first stop was Santa Fe, New Mexico, where I attended the first Santa Fe Institute Summer School and met Gell-Mann in person for the first time. We drove up to Los Alamos together and spent the afternoon debating the concept of complexity. Gell-Mann is a striking sight, with curly white hair and an electric smile. He is a remarkable person with whom to have a conversation, for the simple reason that he has about ten times the normal expected knowledge on virtually any subject you care to mention. He does not hesitate to let you know if your own speculations on the subject are mistaken. At one point in our three-hour discussion I hazarded an opinion about an aspect of quantum mechanics with which I was not sufficiently familiar. “No,” said Gell-Mann, his voice getting louder. “No!” Putting his forehead down on the table where we were sitting, he began pounding the table with his fists. “No! No! No! No!! No!!!” Here, I thought, was someone I could work with.
After a month in Santa Fe, I drove up to the Aspen Center for Physics to visit Heinz, who had a house outside Aspen, where he and Elaine and their two small children were spending the summer. Our work on thermodynamic depth had inspired debate in the scientific community and attention from science journalists. On a series of hikes in the Elk Mountains, we discussed our next work. Or rather, we spent a small fraction of the time discussing our next work; most of the time Heinz regaled me with wild stories about things other than physics. Atop Castle Peak, he spread his arms to the mountains around and declaimed, “I present to you all the wealth and all the beautiful women in the world.”
Two days later, disaster struck. Heinz and I had decided to climb Pyramid Peak, a 14,000-foot pile of rotten rock in the West Maroon wilderness about ten miles from Aspen. The day was fine; we started early and, taking care to avoid falling rock, we were at the top by noon. On the way down, we had to make a brief traverse with a lot of exposure; if you fell, you fell a long way. We edged along a crack in the rock, Heinz in front. At the end of the crack, he hopped onto a saddle between two crags. Heinz’s ankle had been weakened by polio when he was a child. When his foot hit the saddle, his ankle buckled. He fell and slid out of sight down an almost vertical gully.
I called. There was no response. Quickly, before I froze up, I jumped from the crack to the saddle. It was a small, slightly awkward hop. I called again and again to silence. The gully was too steep to descend on my own, and Heinz had had the rope in his backpack. I turned and ran down the trail to get help.
There is no happy ending. The sheriff took me to tell Elaine what had happened, while the mountain rescue crew went to look for Heinz in the hope that he might still be alive in a crevice. When they couldn’t find him, they took me back up the mountain in a helicopter. We rose slowly up into the great bowl of Pyramid Peak, the central part of it a cliff of sheer and rotten rock rising half a mile to the summit. We found where Heinz had fallen. There was no crevice. He had fallen 100 feet, hit hard, and died—a quick, clean death. After impact, his body had tumbled 2,000 feet farther down the mountain, where we found him on a shelf of rock. Slowly, we sank down out of the bowl. Then I went to give Elaine the bad news.
Over the following months, I tried to make sense of what happened. My loss was nothing compared with Elaine’s; still, between the shock and the sadness, I was nearly destroyed. After the funeral, I returned to Los Alamos, to work with Wojciech Zurek. I was living in a bed-and-breakfast overlooking a canyon. At night, Heinz’s voice would course through my head and wake me from sleep. I’d jump out of bed, thinking he was in the room. Guilty for having survived, I went on a long hiking trip by myself in the Pecos Wilderness. I lost myself in the woods; for several days of hiking I had no idea where I was. I did solo climbs I should not have done. I sought out cliffs and peered down them, terrified, from the top.
I looked for some kind of comfort in work, but physical law, while absorbing, is short on comfort. All chance occurrences have their roots in quantum mechanics. The Many Worlds interpretation of quantum mechanics holds that for every accident that happens, there are a lot of other worlds in which it doesn’t. Heinz’s death was a tragic accident. He was an experienced climber and could have jumped from the crack to the saddle a thousand times safely. Just this time, he landed at slightly the wrong angle, and his ankle failed him. Here, in our world, he fell. Other worlds gave me no comfort. Like the protagonist of Kenzaburo Oe’s novel A Personal Matter, I learned that “you can’t make the absoluteness of death relative, no matter what psychological tricks you use.”
But this world still affords a measure of consolation. In talking with Elaine, and with Heinz’s friends John Brockman and Sharon and David Olds, I have learned more about Heinz and his life. In working on ideas that stemmed from our brief collaboration, including some of the ideas in this book, I have gained satisfaction in imagining Heinz’s respon
ses and criticisms. Consolation has gradually come from information—from bits both real and imagined. Heinz’s body and brain are gone. The information his cells processed is wrapped up in the Earth’s slow processes. He has lost consciousness, thought, and action. But we have not entirely lost him. While he lived, Heinz programmed his own piece of the universe. The resulting computation unfolds in us and around us: the vivid thoughts and outrageous behavior he impressed on us still flourish in our thoughts and behavior and have their own vivid and outrageous consequences. Heinz’s piece of the universal computation goes on.
Acknowledgments
I would like to thank all my teachers, particularly my family and friends.
My wife, Eve, and daughters, Emma and Zoe, exhibited great tolerance during the writing of this book. My parents, Robert and Susan Lloyd, were the book’s first readers and editors. My brothers Ben and Tom both contributed valuable questions, as did my nieces, nephews, cousins, uncles, aunts, and in-laws.
My friends at MIT and elsewhere gave many useful comments and criticisms, in particular Charlie Bennett, Paul Davies, and the members of the Moses seminar: Joel Moses, Bob Berwick, Robert Fano, Gadi Geiger, Jay Keyser, Tom Knight, Sanjoy Mitter, Arthur Steinberg, and Gerry Sussman. Terry Orlando’s graduate reading group patiently read the manuscript and told me what they thought; I listened. JR Lucas, Janet Brown, and Aram Harrow helped me track down elusive typing monkeys. Murray Gell-Mann taught me quantum mechanics and complexity, and Doyne Farmer made me bicycle up and down high mountains while discussing the relation between the two topics. Shen Tsai helped me with Mencius.
All my colleagues in the field of quantum information and computation contributed greatly to this book via their own scientific work. Much of the research on which this book is based was funded by the Cambridge-MIT Initiative, the National Science Foundation, the Army Research Office, the Defense Advanced Research Projects Agency, the Advanced Research and Development Activity, the Naval Research Office, and the Air Force Office for Scientific Research.