Everyone by nature desires to know.
—Aristotle, Metaphysics
EVERY WEEK, headlines announce new breakthroughs in our understanding of the universe, new technologies that will transform our environment, new medical advances that will extend our lives. Science is giving us unprecedented insights into some of the big questions that have challenged humanity ever since we’ve been able to formulate them. Where did we come from? What is the ultimate destiny of the universe? What are the building blocks of the physical world? How does a collection of cells become conscious?
In the last ten years alone we’ve landed a spaceship on a comet, built robots that can create their own language, used stem cells to repair the pancreas of diabetic patients, discovered how to use the power of thought to manipulate a robotic arm, and sequenced the DNA of a 50,000-year-old cave girl. Science magazines are bursting with the latest breakthroughs emerging from the world’s laboratories. We know so much.
Science is our best weapon in our fight against fate. Instead of giving in to the ravages of disease and natural disaster, we have created vaccines to combat deadly viruses like polio and Ebola. As the world’s population continues to escalate, scientific advances provide the best hope of feeding the 9.6 billion people who are projected to be alive in 2050. Science warns us about the deadly impact we are having on our environment and gives us the chance to do something about it before it is too late. An asteroid might have wiped out the dinosaurs, but science is our best shield against any future direct hits. In the human race’s constant battle with death, science is its best ally.
Science is king not only when it comes to our fight for survival but also in improving our quality of life. We are able to communicate with friends and family across vast distances. We have created virtual worlds to which we can escape in our leisure time and we can re-create in our living rooms the great performances of Mozart, Miles, and Metallica at the press of a button.
The desire to know is programmed into the human psyche. Early humans with a thirst for knowledge were the ones who survived to transform their environment. Those not driven by that craving were left behind. Evolution has favored the mind that wants to know the secrets of how the universe works. The adrenaline rush that accompanies the discovery of new knowledge is nature’s way of telling us that the desire to know is as important as the drive to reproduce. As Aristotle suggested in the opening line of Metaphysics, understanding how the world works is a basic human need.
When I was a schoolkid, science very quickly captivated me. I fell in love with its extraordinary power to reveal the workings of the universe. The fantastic stories that my science teachers told me seemed even more fanciful than the fiction I’d been reading at home. I persuaded my parents to buy me a subscription to New Scientist and devoured Scientific American in our local library. I hogged the television each week to watch episodes of Horizon and Tomorrow’s World. I was enthralled by Jacob Bronowski’s Ascent of Man, Carl Sagan’s Cosmos, and Jonathan Miller’s Body in Question. Every Christmas, the Royal Institution Christmas Lectures provided a dollop of science alongside our family turkey. My stocking was stuffed with books by George Gamow and Richard Feynman. It was a heady time, with new breakthroughs announced each week.
Alongside these stories of discovery, I began to get fired up by the untold tales. What we knew lay in the past but we didn’t yet know the future, my future. I became obsessed with the puzzle books of Martin Gardner that my math teacher gave me. The excitement of wrestling with a conundrum and the sudden release of euphoria as I cracked each puzzle got me addicted to the drug of discovery. Those puzzles were my training ground for the greater challenge of tackling questions that didn’t have an answer in the back of the book. It was the unanswered questions, the mathematical mysteries and scientific puzzles that no one had cracked, that would become the fuel for my life as a scientist.
It is quite extraordinary how much more we have understood about the universe even in the half century that I’ve been alive. Technology has extended our senses so we can see things that were beyond the conception of the scientists who excited me as a kid. A new range of telescopes that look out at the night sky enabled us to discover planets like Earth that could be home to intelligent life. They have revealed the amazing fact that three quarters of the way into the lifetime of our universe, its expansion started to accelerate. I remember reading as a kid that we were in for a big crunch, but now it seems that we have a completely different future awaiting us.
Particle colliders like the Large Hadron Collider at CERN have allowed us to penetrate the inner workings of matter itself, revealing new particles—like the top quark discovered in 1994 and the Higgs boson discovered in 2012—that were bits of speculative mathematics when I was reading my New Scientist at school. And since the early ’90s the fMRI scanner has allowed us to look inside the brain and discover things that were not even considered part of the remit of science when I was a kid back in the ’70s. The brain was the preserve of philosophers and theologians, but today technology can reveal when you are thinking about Jennifer Aniston or predict what you are going to do next even before you know it yourself.
Biology has seen an explosion of breakthroughs. In 2003 it was announced that scientists had mapped an entire human DNA sequence consisting of 3 billion letters of genetic code. In 2011 the complete neuronal network of the C. elegans worm was published, providing a complete picture of how the 302 neurons in the worm are connected. Chemists, too, have been breaking new territory. A totally new form of carbon was discovered in 1985, which binds together like a football; and chemists surprised us again in 2003 by creating the first examples of graphene, showing how carbon can form a honeycomb lattice one atom thick.
In my lifetime the subject to which I would eventually dedicate myself, mathematics, has seen some of the great enigmas finally resolved: Fermat’s Last Theorem and the Poincaré conjecture, two challenges that had outfoxed generations of mathematicians. New mathematical tools and insights have opened up hidden pathways to navigate the mathematical universe. Keeping up with all these new advances, let alone making your own contribution, is a challenge in its own right.
A few years ago I got a new job title to add to my role as a professor of mathematics at Oxford: the Simonyi Professor for the Public Understanding of Science. There seems to be a belief that with such a title I should know it all. People ring me up expecting me to know the answer to every scientific question. Shortly after I’d accepted the job, the Nobel Prize for medicine was announced. A journalist called, hoping for an explanation of the breakthrough that was being rewarded: the importance of telomeres.
Biology has never been my strong point, but I was sitting in front of my computer screen and so I’m embarrassed to admit I got the Wikipedia page up on telomeres and, after a quick scan, proceeded to explain authoritatively that they are the bit of genetic code at the end of our chromosomes that controls aging, among other things. The technology we have at our fingertips has increased that sense that we have the potential to know anything. Tap any question into a search engine and the device seems to predict, even before you finish typing, what you want to know and provides a list of places to find the answer.
But understanding is different from a list of facts. Is it possible for any scientist to know it all? To know how to solve nonlinear partial differential equations? To know how SU(3) governs the connection between fundamental particles? To know how cosmological inflation gives rise to the state of the universe? To know how to solve Einstein’s equations of general relativity or Schrödinger’s wave equation? To know how neurons and synapses trigger thought? Newton, Leibniz, and Galileo were perhaps the last scientists to know all that was known.
I must admit that the arrogance of youth infused me with the belief that I could understand anything that was known. With enough time, I thought, I could crack the mysteries of mathematics and the universe, or at least master the current lay of the land. But increasingly, I am beginning to question that belief, to worry that some things will forever remain beyond my reach. Often my brain struggles to navigate the science we currently know. Time is running out to know it all.
My own mathematical research is already pushing the limits of what my human brain feels capable of understanding. I have been working for more than ten years on a conjecture that remains stubbornly resistant to my attempts to crack it. My new role as the Professor for the Public Understanding of Science has pushed me outside the comfort zone of mathematics into the messy concepts of neuroscience, the slippery ideas of philosophy, the unfounded theories of physics. It has required a way of thinking that is alien to my mathematical mode of thought, which deals in certainties, proofs, and precision. My attempts to understand everything currently regarded as scientific knowledge have severely tested the limits of my own ability to understand.
We stand on the shoulders of giants, as Newton famously declared. And so my own journey to the frontiers of knowledge has pushed me to explore how others have articulated their work, to listen to lectures and seminars by those immersed in the fields I’m trying to understand, and to talk to those pushing the boundaries of what is known, questioning contradictory stories and consulting the evidence recorded in scientific journals. How much can you trust any of these stories? Just because the scientific community accepts a story as the current best fit doesn’t mean it is true. Time and again, history reveals the opposite to be the case, and this must always act as a warning that current scientific knowledge is provisional. Mathematics has a slightly different quality, as a proof provides the chance to establish a more permanent state of knowledge. But even when I am creating a new proof, I will often quote results by fellow mathematicians whose proofs I haven’t checked myself. To do so would mean running in order to keep still.
For any scientist the real challenge is not to stay within the secure garden of the known but to venture out into the wilds of the unknown. That is the challenge at the heart of this book.
Despite all the breakthroughs made over the last centuries, there are still lots of deep mysteries waiting out there for us to solve. Things we don’t know. The knowledge of what we don’t know seems to expand faster than our catalog of breakthroughs. The known unknowns outstrip the known knowns. And it is those unknowns that drive science. A scientist is more interested in the things he or she can’t understand than in telling all the stories we already know the answers to. Science is a living, breathing subject because of all those questions we can’t answer.
For example, the stuff that makes up the physical universe we interact with seems to account for only 4.9 percent of the total matter content of our universe. So what is the other 95.1 percent of so-called dark matter and dark energy made up of? If our universe’s expansion is accelerating, where is all the energy coming from that fuels that acceleration?
Is our universe infinite? Are there infinitely many other infinite universes parallel to our own? If there are, do they have different laws of physics? Were there other universes before our universe emerged from the Big Bang? Did time exist before the Big Bang? Does time exist at all, or does it emerge as a consequence of more fundamental concepts?
How can we unify Einstein’s theory of general relativity, the physics of the very large, with quantum physics, the physics of the very small? This is the search for something called quantum gravity, an absolute necessity if we are ever going to understand the Big Bang.
And what of the understanding of our human body, something so complex that it makes quantum physics look like a high school exercise? We are still trying to come to grips with the complex interaction between gene expression and our environment. Can we find a cure for cancer? Is it possible to beat aging? Could there be someone alive today who will live to be a thousand years old?
And what about where humans came from? Evolution is a process of random mutations, so would a different roll of the evolutionary dice still produce organisms with eyes? If we rewound evolution and pressed “play,” would we still get intelligent life, or are we the result of a lucky roll of the dice? Is there intelligent life elsewhere in our universe? And what of the technology we are creating? Can a computer ever attain consciousness? Will I eventually be able to download my consciousness so that my mind can survive the death of my body?
Mathematics, too, is far from finished. Despite popular belief, Fermat’s Last Theorem was not the last theorem. Mathematical unknowns abound. Are there any patterns in prime numbers, or are they outwardly random? Will we be able to solve the mathematical equations for turbulence? Will we ever understand how to factorize large numbers efficiently?
Despite so much that is still unknown, scientists are optimistic that these questions won’t remain unanswered forever. The last few decades give us reason to believe that we are in a golden age of science. The rate of discoveries in science appears to grow exponentially. In 2014 the science journal Nature reported that the number of scientific papers has been doubling every nine years since the end of World War II. Computers are also developing at an extraordinary rate. Moore’s Law has it that computer processing power will double every two years. Ray Kurzweil believes that the same applies to technological progress: that the rate of change over the next hundred years will be comparable to what we’ve experienced in the last 20,000 years.
Can scientific discovery really sustain this growth? Kurzweil talks about the Singularity, a moment when the intelligence of our technology will exceed human intelligence. Is scientific progress destined for its own singularity, a moment when we know it all? Surely at some point we might actually discover the underlying equations that explain how the universe works. We will discover the final particles that make up the building blocks of the physical universe and how they interact with each other. Some scientists believe that the current rate of scientific progress will lead to a moment when we might discover a theory of everything. They even give it a name: ToE.
As Stephen Hawking declared in A Brief History of Time, “I believe there are grounds for cautious optimism that we may be near the end of the search for the ultimate laws of nature.” He concludes dramatically with the provocative statement that then “we would know the mind of God.”
Is such a thing possible? To know everything? Would we want to know everything? Scientists have a strangely ambivalent relationship with the unknown. On the one hand, what we don’t know is what intrigues and fascinates us, and yet the mark of success as a scientist is resolution and knowledge, to make the unknown known.
Are there limits to what we can discover? Are there quests that will never be resolved? Are some regions beyond the predictive powers of science and mathematics—like time before the Big Bang? Are there ideas so complex that they exceed the conception of our finite human brains? Can brains really investigate themselves, or does the analysis enter an infinite loop from which it is impossible to rescue itself? Are there mathematical conjectures that can never be proved true?
It seems defeatist, even dangerous, to acknowledge such questions. While the unknown is the driving force for doing science, the unknowable is science’s nemesis. As a fully signed-up member of the scientific community, I hope that we can ultimately answer the big open questions. So it seems important to know whether the expedition I’ve joined will hit boundaries beyond which we cannot proceed. Are there in fact any questions that won’t ever get closure?
That is the challenge I’ve set myself in this book. I want to know whether there are things that, by their very nature, we will never know. Are there things that will always be beyond the limits of knowledge? Despite the marauding pace of scientific advances, are there things that will remain beyond the reach of even the greatest scientists? Mysteries that will forever remain part of the great unknown?
It is, of course, very risky at any point in history to try to articulate the Things We Cannot Know. How can you know what new insights will suddenly pull the unknown into the knowable? This is partly why it is useful to look at the history of how we came to know the things we know, because it reveals how often we’ve been at a point where we think we have reached the frontier, only to find a greater landscape beyond.
Take the statement made by French philosopher Auguste Comte in 1835 about the stars: “We shall never be able to study, by any method, their chemical composition or their mineralogical structure.” An absolutely fair statement given that this knowledge seemed to depend on our visiting the star. What Comte hadn’t considered was the possibility that the star could visit us, or at least that photons of light emitted by the star could reveal its chemical makeup.
A few decades after Comte’s prophecy, scientists had determined the chemical composition of our own star, the sun, by analyzing the spectrum of light emitted. As the nineteenth-century British astronomer Warren de la Rue declared: “If we were to go to the Sun, and to bring some portions of it and analyze them in our laboratories, we could not examine them more accurately than we can by this new mode of spectrum analysis.”
Scientists went on to determine the chemical composition of stars we are unlikely ever to visit. As science in the nineteenth century continued to give us an ever greater understanding of the mysteries of the universe, there began to emerge a feeling that we might eventually have a complete picture.
In 1900 Lord Kelvin, regarded by many as one of the greatest scientists of his age, believed that moment had come. He declared to the meeting of the British Association of Science: “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” American physicist Albert Abraham Michelson concurred. He too thought that the future of science would simply consist of adding a few decimal places to the results already obtained. “The more important fundamental laws and facts of physical science have all been discovered . . . our future discoveries must be looked for in the sixth place of decimals.”
Five years later, Einstein announced his extraordinary new conception of time and space, followed shortly by the revelations of quantum physics. Kelvin and Michelson couldn’t have been more wrong.
What I want to try to explore is whether there are problems that we can prove will forever remain beyond our knowledge. Perhaps there are none. As a scientist, that is my hope. One of the dangers when faced with currently unanswerable problems is to give in too early to their unknowability. But if there are unanswerables, what status do they have? Can you choose from the possible answers and it won’t really matter which one you opt for?
Talk of known unknowns is not reserved to the world of science. Secretary of Defense Donald Rumsfeld strayed into the philosophy of knowledge with the famous declaration:
There are known knowns; there are things that we know that we know. We also know there are known unknowns; that is to say, we know there are some things we do not know. But there are also unknown unknowns, the ones we don’t know we don’t know.
Rumsfeld received a lot of flack for this cryptic response to a question fired at him during a briefing at the Department of Defense about the lack of evidence connecting the government of Iraq with weapons of mass destruction. Journalists and bloggers had a field day, culminating in Rumsfeld being given the Foot in Mouth award by the Plain English Campaign. And yet if one unpacks the statement, Rumsfeld very concisely summed up different types of knowledge. He perhaps missed one interesting category: the unknown knowns, the things that you know yet dare not admit to knowing. As the philosopher Slavoj Zizek argues, these are possibly the most dangerous, especially when held by those with political power. This is the domain of delusion. Repressed thoughts. The Freudian unconscious.
I would love to tell you about the unknown unknowns, but then they’d be known! Nassim Taleb, author of The Black Swan, believes that the emergence of unknowns is responsible for the biggest changes in society. For Kelvin, relativity and quantum physics turned out to be the great unknown unknown that he was unable to imagine. My hope in this book is to articulate the known unknowns and ask whether any will remain forever unknown.
I have called these unknowns “Edges.” There are seven of them, and each one represents the horizon beyond which we cannot see. My journey to the Seven Edges of knowledge will pass through the known knowns, to demonstrate how we have traveled beyond what we previously thought were the limits of knowledge. This journey will also test my own ability to grasp what is known, because it’s becoming increasingly challenging as a scientist to know even the knowns.
As much as this book is about what we cannot know, it is also important to understand what we do know and how we know it. My journey to the frontiers of knowledge will take me through the terrain that scientists have already mapped, to the very limits of today’s breakthroughs. On the way I will stop to consider those moments when scientists thought they had hit a wall beyond which progress was no longer possible, only for the next generation to find a way. This will give us an important perspective on those problems that we might think are unknowable today. By the end of our journey, I hope this book will provide a comprehensive survey not just of what we cannot know but also of the things we do know.
To help me through these areas of science that are outside my comfort zone, I have enlisted the help of experts to guide me as I reach each science’s Edge and to test whether it is my own limitations or limitations inherent in the questions I am tackling that make these questions unknowable.
What happens then if we encounter a question that cannot be answered? How does one cope with not knowing? Dare I admit to myself that some things will forever remain beyond my reach? How do we cope with not knowing? That challenge has elicited some interesting responses from humans across the millennia, not least the creation of an idea called God.
There is another reason why I have been driven to investigate the unknowable, which is also related to my new job. The previous incumbent of the chair for the Public Understanding of Science was a certain Richard Dawkins. When I took over the position from Dawkins I braced myself for the onslaught of questions that I would get, not about science, but about religion. The publication of The God Delusion and his feisty debates with creationists resulted in Dawkins spending the later years of his tenure debating questions of religion and God.
So it was inevitable that when I took up the chair people would be interested in my stance on religion. My initial reaction was to distance myself from the debate about God. My job was to promote scientific progress and to engage the public in the breakthroughs happening around them. I was keen to move the debate back to questions of science rather than religion.
In an urban environment like London, football has taken over the role that religion played in society of binding a community together, providing rituals that they can share. For me, the science that I began to learn as a teenager did a pretty good job of pushing out any vaguely religious thoughts I had as a kid. I sang in my local church choir, which exposed me to the ideas that Christianity had to offer for understanding the universe. School education in the 1970s in the United Kingdom was infused with mildly religious overtones: renditions of “All Things Bright and Beautiful” and the Lord’s Prayer in assemblies. Religion was dished up as something too simplistic to survive the sophisticated and powerful stories that I would learn in the science labs at my secondary school. Religion was quickly pushed out. Science . . . and football . . . were much more attractive.
Inevitably the questions about my stance on religion would not be fobbed off with such a flippant answer. I remember that during one radio interview on a Sunday morning on BBC Northern Ireland I was gradually sucked into considering the question of the existence of God. I guess I should have seen the warning signs. On a Sunday morning in Northern Ireland, God isn’t far from the minds of many listeners.
As a mathematician I am often faced with the challenge of proving the existence of new structures or coming up with arguments to show why such structures cannot exist. The power of the mathematical language to produce logical arguments has led a number of philosophers throughout the ages to resort to mathematics as a way of proving the existence of God. But I always have a problem with such an approach. If you are going to prove existence or otherwise in mathematics, you need a very clear definition of what it is that you are trying to prove exists.
So after some badgering by the interviewer about my stance on the existence of God, I pushed him to try to define what God meant for him so that I could engage my mathematical mind. “It is something which transcends human understanding.” At first I thought: what a cop-out. You have just defined it as something that by its very nature I can’t get a handle on. But I became intrigued by this definition. Perhaps it wasn’t such a cop-out after all.
What if you define God as the things we cannot know. The gods in many ancient cultures were often placeholders for the things people couldn’t explain or understand. Our ancestors found volcanic eruptions or eclipses so mysterious that they became acts of gods. As science has explained such phenomena, these gods have retreated.
This definition has some things in common with a God commonly called the “God of the gaps.” This phrase was generally used as a derogatory term by religious thinkers who could see that this God was shrinking in the face of the onslaught of scientific knowledge, and a call went out to reject this kind of God. The phrase “God of the gaps” was coined by the Oxford mathematician and Methodist church leader Charles Coulson, when he declared: “There is no ‘God of the gaps’ to take over at those strategic places where science fails.”
But the phrase is also associated with a fallacious argument for the existence of God, one that Richard Dawkins spends some time shooting down in The God Delusion: if there are things that we can’t explain or know, there must be a God at work filling the gap. I am more interested not in the existence of a God to fill the gap, but in equating God with the abstract idea of the things we cannot know. Not in the things we currently don’t know, but the things that by their nature we can never know—the things that will always remain transcendent.
Religion is more complex than the simple stereotype often offered up by modern society. For many ancient cultures in India, China, and the Middle East, religion was not about worshiping a supernatural intelligence so much as it was an attempt to appreciate the limits of our understanding and of language. As the theologian Herbert McCabe declared, “To assert the existence of God is to claim that there is an unanswered question about the universe.” Science has pushed hard at those limits. So is there anything left? Will anything always be beyond the limit? Does McCabe’s God exist?
This is the quest at the heart of this book. But first we need to know if, in fact, anything will remain unanswered about the universe. Is there really anything we cannot know?