The Beginning of Infinity is a counterargument to the belief that there is a finite amount of knowledge in the universe. People ranging from theoretical physicists to a former Commissioner of the US Patent Office have said that, sooner or later, humanity will stop learning because we know everything there is to know. Physicist David Deutsch wrote this book as a rebuttal to his peers, to explain to them why humanity will never stop learning and why we must never stop learning.
Deutsch rejects the idea of finite knowledge as both wrong and harmful. He believes it leads to complacency at best (there’s no need to learn because we already know everything), and pessimism at worst (we can’t advance any further; this is as good as civilization gets). Deutsch argues instead that there’s no limit to knowledge.
His reasoning is that people actively create knowledge through questions, studies, and calculations, rather than merely “finding” it by experiencing the world around them. Furthermore, Deutsch believes that because there’s no limit to how much knowledge we can create, there’s no limit to how much we can improve the world.
Deutsch is a physicist who specializes in quantum mechanics. He’s also a visiting professor of physics at several prominent universities, including Oxford. His first book, The Fabric of Reality, explains his ideas of how quantum physics, evolutionary science, information science, and epistemology (the study of knowledge) work together to create a cohesive and coherent model of reality. In The Beginning of Infinity, published in 2011, he narrows his focus to explore epistemology much more deeply—in particular, how people create knowledge, and the significance of that process.
Despite its finer focus, this book and The Fabric of Reality are notable for their scope: In both books, Deutsch attempts to combine numerous fields of study and schools of thought into universal explanations of reality—one might call them “theories of everything.” Deutsch’s peers and critics sometimes laud him for his bold, compelling ideas, and sometimes assert that he lacks the knowledge to effectively argue his points on topics other than physics.
In The Beginning of Infinity, Deutsch makes five key arguments:
To help you fully understand these arguments, our guide will discuss how physicists and mathematicians understand infinity and what it means for there to be infinite knowledge. We’ll also explore theories of how people create knowledge, and how we as a species increase our knowledge over time.
With that foundation in place, we’ll move on to how people use knowledge, with special attention to how knowledge influences culture and vice versa. Finally, we’ll conclude with Deutsch’s argument for an optimistic outlook on the future: While problems are inevitable, we’ll always be able to solve them because we can always create new knowledge.
Our commentary will focus on providing background information to help you understand Deutsch’s more complicated ideas, as well as how some of his theories have been put into practice in real life.
Before we can understand infinite knowledge, we must first comprehend the idea of infinity. Infinity is a hard concept to grasp logically—in fact, Deutsch believes that the human mind has a natural aversion to it. Many people find it easier to think of infinity as some arbitrarily large number, but that’s a poor approximation. Instead, we can illustrate the concept of infinity with a simple thought experiment:
Imagine a person standing in an endless hallway. He walks an endless distance down that hallway. Once he’s done so, there’s still an endless distance ahead of him. He repeats this process countless times, but there is still an immeasurable distance between him and the end of the hallway. This is why Deutsch says, no matter how much knowledge we create, we’ll never know everything—in other words, no matter how far we travel, we’ll never reach the end of the hallway.
It’s also why imagining infinity as a really big number doesn’t work: Infinity doesn’t obey the same rules as finite numbers do. Instead, it may help to picture infinity as an unreachable destination; no matter how long we travel, we never get closer to it.
All Infinities Aren’t the Same
It will be easier to understand the endless hallway thought experiment if you recognize that there are many different sizes of infinity. That’s counterintuitive—surely infinity should equal infinity—but we can prove it with an easy example:
Consider the set of all positive integers (0, 1, 2, 3…∞). Clearly, that’s an infinite string of numbers.
Now consider the set of all integers greater than or equal to -1 (-1, 0, 1, 2…∞). This is also an infinite string of numbers, but there’s one more number than in the previous set.
As you can see, infinity isn’t a fixed value. That’s why traveling an infinite distance down an infinitely long hall won’t get you to the end of that hall.
Another way Deutsch explains how we could possibly have “more” than infinite knowledge is that we live in a multiverse: A web of interconnected universes that each stretch infinitely (like our hallway). Every one of those infinite universes is unique; any given universe could be almost identical to our own, or completely different from anything we’ve seen.
This suggests one way in which infinite knowledge creation wouldn’t lead to the endpoint of knowledge—even if we create all possible knowledge in our own universe, there would still be an infinite number of other universes to learn about.
(Shortform note: Various theories over the last 70 years or so have predicted different numbers of universes in the multiverse. The Many-Worlds Theory of the 1950s proposed an infinite multiverse like Deutsch describes here. More recently, String Theory predicted 10500 different universes (that’s a one followed by 500 zeroes)—which is an enormous number, but not infinite. Stephen Hawking’s final paper before his death also predicted a finite number of universes, though he did not say exactly how many.)
Now that we’ve discussed the concept of infinity, we’ll move on to what Deutsch means by “creating infinite knowledge.” Specifically, we’ll discuss how people create knowledge, and why it’s crucial that they continue to do so.
Empiricism is the belief that all knowledge comes from observation and extrapolation. A related philosophy, Positivism, says that the only true knowledge is scientific knowledge, and all scientific knowledge can be proven or verified through experimentation. In other words, Positivism argues that knowledge doesn’t have to originate with experience, but it must be confirmed by it.
Deutsch rejects both of these philosophies. He says that it’s impossible to gain true knowledge just from observation, because we also have to interpret whatever we observe. In Deutsch’s definition, “true” knowledge is free from subjectivity, but observation is run through the filter of our past experiences, beliefs, and assumptions. Therefore, observation is not a reliable way to learn new information.
Instead, Deutsch argues that knowledge comes from conjecture and testing—in other words, we come up with new ideas based on what we already know, then experiment to see if those ideas hold up under scrutiny. Note that this differs from Positivism because much of what we know can’t be directly observed or experienced. For example, people believed that the sun rotated around the Earth based on what they saw and felt: The Earth seemed to be holding still while the sun, stars, and other planets moved around it. However, careful observations and mathematical calculations eventually proved that theory wrong.
(Shortform note: Empiricism and Positivism both reject the idea of objective reality. Both schools of thought say we can only know what we personally experience or observe, and that knowledge must be filtered through our biases and assumptions. Therefore, it’s not surprising that Deutsch—a scientist whose entire career is dedicated to discovering truths that we can’t observe empirically—would begin by dismissing those theories. Generally speaking, however, experts take a more moderate approach. For example, Professor of Philosophy Peter Kosso writes that empirical evidence is crucial to natural sciences like biology and most types of physics, but useless in fields like math and quantum physics where the subjects aren’t observable.)
Several times throughout The Beginning of Infinity, Deutsch warns against what he calls parochialism: That is, mistaking one’s own experiences for universal truth. Parochial refers to a church parish, but in more general terms it means having a narrow or shortsighted outlook. Deutsch uses it to evoke the image of a priest dictating “truth” to his congregation—the exact opposite of the endless search for knowledge that Deutsch wants. (Shortform note: The opposite can also be true: the “Argument from Incredulity” is a logical fallacy in which a person dismisses an idea as crazy or illogical because it contradicts their own experiences or belief system.)
The author urges us to remember that science can’t prove something is true; instead, it disproves what is false. In other words, we gain new knowledge by correcting our mistakes. He calls this fallibilism: remembering that there’s no such thing as perfect knowledge, and that nobody should be considered the absolute authority on any subject. In fact, Deutsch humorously suggests that we replace the word theory with misconception (as in, “the misconception of gravity”) to make the point that theories will never be completely right; they can only become less wrong.
In short, there’s always the chance that what we “know” could be proven wrong. Even something as fundamental as the theory of gravity could still be disproven if a scientist could demonstrate a phenomenon science can’t explain; say, a rock falling sideways instead of toward the earth. So far, nobody has managed to disprove gravity, but it’s still possible that someone could.
On a related note, Deutsche defines a “good” or “bad” explanation of a phenomenon based on how hard it would be to change the details of that explanation without destroying it. To continue with the theory of gravity, it would be very hard to change the details—that mass attracts mass with a particular amount of force—without making the whole explanation useless. If we proposed instead that mass repels mass, or we changed the theorized amount of force, then the theory would no longer explain what we observe in the universe. Therefore, gravity is a good explanation of those phenomena.
How Science Advances Through Mistakes
Deutsche claims that science progresses by becoming less and less wrong. In The Structure of Scientific Revolutions, physicist and philosopher Thomas Kuhn explains that science makes its biggest advancements (scientific revolutions) by recognizing and correcting mistakes. For example, the shift from the geocentric (Earth-centered) model of the solar system to the heliocentric (sun-centered) model required just such a revolution.
Kuhn’s proposed steps of a scientific revolution are:
Normal science. This is what most people imagine as “science”: incremental improvements to existing knowledge through study and experimentation.
Anomaly. Scientists observe a phenomenon that current scientific theories can’t explain. New theories arise to explain it. For example, astronomers noticed that planetary movements didn’t line up with their predictions based on the geocentric model.
Crisis. Two or more theories compete to be accepted as the new “correct” theory. Famously, Copernicus proposed the heliocentric model of the solar system. He met fierce resistance, even though his theory explained the anomalies that astronomers had found.
Revolution. Through continued experimentation and debate, one of the new theories overturns the existing theory as the dominant idea in the scientific community. Now, of course, nearly everyone accepts the heliocentric model as correct—and will continue to do so until or unless scientists find more anomalies that this theory can’t explain.
One of Deutsch’s main problems with empiricism—the idea that we acquire knowledge through experience—is that it implies we’re essentially blank slates waiting for the universe to imprint knowledge on us through our experiences. In contrast, Deutsch believes that the ability to actively create knowledge through reasoning, extrapolation, and experimentation is what makes us people.
Similar to the “blank slate” belief, some people think the entire world was created for our benefit; in other words, that all life on Earth exists simply to support humanity. Deutsch rejects this idea as well, saying we support ourselves by creating knowledge. In other words, people create knowledge in order to solve problems—ranging from how to support an ever-growing population to how we can explore other planets.
What Is a Person?
In everyday conversation, most people use “person” interchangeably with “human.” However, in law and the social sciences, exactly what defines a person is an ongoing discussion with far-reaching implications.
Deutsch’s proposed definition of a person being a knowledge-creating entity is open to interpretation, and potentially problematic no matter how it’s interpreted. For example, if we take it to mean that a person is any individual who’s capable of learning, then many nonhuman beings (and even some advanced computers) could be considered people.
If, instead, we interpret it to mean that only someone who can add to humanity’s overall knowledge is a person, that would leave out people who lack the skills or education to make new discoveries.
Overall, it would be best to remember that Deutsch is neither a legal expert nor a sociologist, and to take his definition of “person” with a grain of salt.
Interestingly, although people create knowledge intentionally while evolution happens naturally, Deutsch says that the two processes have a number of things in common:
(Shortform note: In biology, a “successful” gene is one that helps its host organism survive and reproduce, thereby passing itself on to the next generation. Deutsch is echoing that definition in his discussion of successful ideas—they’re ideas that survive and pass from person to person through conversation, media, and imitation.)
(Shortform note: Both organisms and ideas have to compete for limited resources—however, in the case of ideas, the resources are people’s time and attention. Just like animals die if they don’t get enough food, ideas die if nobody talks about them.)
(Shortform note: For an example of how changing an evolutionary adaptation can prevent it from working properly, consider the genetic disease cystic fibrosis (CF). In CF, a mutation to a single gene makes it so the body can’t properly regulate flows of salt and fluids throughout your body. This leads to the buildup of thick, sticky mucus in the lungs, which (if not treated) eventually proves fatal. In other words, slightly changing a bodily process makes it not work correctly, thereby killing the person.)
How Did Religion Evolve?
Evolutionary biologist Richard Dawkins first discussed the similarities between genes and ideas in his book The Selfish Gene. In fact, that book is where the word “meme” originated, though the definition was quite different from the modern one: Dawkins defined a meme as a piece of information that spreads from one organism to another through imitation—for instance, some birds’ songs spread because nearby birds mimic the songs they hear.
As an example of a successful meme, Dawkins discusses the idea of gods. Belief in a higher power has existed in some form throughout almost all of human history, making it one of the most successful memes ever—though, admittedly, a lot of the time people imitated others’ beliefs under threat of violence. As a biologist, Dawkins says that it’s tempting to talk about memes in evolutionary terms; to ask, “How does believing in God help one to survive and reproduce?” Perhaps simply because it’s comforting to think something more powerful than ourselves is in control of the universe.
However, Dawkins also says that belief in God might just be a side effect of how our brains developed: As we look for patterns and explanations in what we observe, “God did it” presents an easy and satisfying answer. Remember, as Deutsch says, neither genes nor memes create perfect solutions, only solutions that are good enough for the present circumstances.
Deutsch adds that cultures consist of ideas that people share—in other words, cultures are built on successful memes (using the original meaning of “meme,” as Dawkins defined it). Deutsch identifies two different types of memes, and the cultures that come from them:
Rational memes are beneficial, based in knowledge, and encourage people to continue building knowledge. For example, the theory of gravity is a rational meme: It’s based on our current best understanding of reality, and it replicates because we keep teaching new generations about gravity. Rational memes create dynamic cultures, which change and evolve as the memes within them do.
Anti-rational memes suppress thought and creativity. They replicate via blind devotion and intolerance for questions or doubts. Anti-rational memes lead to static cultures, which maintain stability by never allowing anything to change. For example, many orthodox religious sects are static cultures: All members must believe the same things and perform the same rituals, generation after generation. Deutsch adds that static cultures are doomed to collapse sooner or later; their inability to create new knowledge means that they can’t respond to unforeseen dangers, and eventually one such danger or another will destroy them.
Why Static Cultures Are Fragile
In Antifragile, mathematician Nassim Nicholas Taleb explains why some things break after being damaged while other things become stronger:
Fragile systems are rigid and unable to change. As a result, no matter how strong those systems are, sooner or later they’ll break. Almost any nonliving object is fragile, whether it’s as easily broken as a pane of glass or as durable as a car engine.
Antifragile systems can change and adapt, not just recovering from damage but actually becoming stronger from it. The classic example of an antifragile system is a muscle: Exercise damages the muscle, which becomes stronger after repairing itself.
In the case of static versus dynamic cultures, we’d say that static cultures (born from unchanging anti-rational memes) are fragile. They refuse to adapt to change, and thus they’re bound to break eventually. For example, a culture that tried to continue as normal in the face of a deadly plague might end up being destroyed by it.
However, dynamic cultures (born from evolving rational memes) are antifragile. They adapt to stressors and become stronger from learning how to cope with them. If faced with that same deadly plague, a dynamic culture would learn how to avoid and treat that disease; then, going forward, that culture would have improved hygienic and medical techniques to keep its people healthy.
On the topic of static versus dynamic cultures—and specifically, how those cultures are run—Deutsch says that many people have a flawed view of how to make a good decision. In short, it’s a mistake to think about choosing the “best” option from a preset list of choices by weighing the pros and cons of each. Instead, truly effective decision-making requires creating new options that didn’t exist before.
Furthermore, since making good decisions requires new and creative solutions, Deutsch adds that group decision-making is fatally flawed by nature. That’s because, when a group of people must make a decision, it inevitably starts with arguments about “pros and cons,” of existing ideas, and ends with the group choosing one option off of a short list. Generally, it’s the option that the most people in that group can be convinced to accept. It’s an inefficient, irrational, and imprecise process.
(Shortform note: What Deutsch is getting at in this section is that group intelligence often seems to be less than the sum of its parts—that no matter how many brilliant and creative people are in a group, they work against each other and can’t bring out their full potential. One of the reasons why groups that are made up of creative individuals struggle to be creative collectively is due to a lack of friction. For new ideas to emerge, there needs to be differing viewpoints and passions that butt up against one another and spark, so to speak. Once a group begins working “collaboratively,” agreeing with one another, the sparks subside.)
Deutsch’s solution is that decision-making bodies—for example, governments—should be primarily concerned with two things:
A group that can easily fix its mistakes with new ideas, and easily replace people who make bad decisions, is as good as group decision-making is going to get. A group that adheres to those two principles will be able to constantly evolve as ideas and culture do, and to make decisions reflecting that evolution.
Deutsch proposes that humans evolved the ability to be creative so that we could share memes (again, in the original sense of “meme”). Essentially, he says that we need creativity to solve problems, and to share what we’ve learned with others. Remember that Deutsch’s definition of a person is a being who creates knowledge. Therefore, in a very real sense, we need creativity in order to be people.
The Impact of Creativity
Whether creativity is necessary for personhood depends on whether you agree with Deutsch’s definition of “person.” However, there’s little doubt that creativity is a crucial part of learning and decision making, and plays a key role in humanity’s development on the individual and societal levels:
Individual: Researchers believe that childhood games, imagination, and “playing pretend” play a key role in learning and in developing skills that will be useful later in life. This is especially evident in how children tend to imitate their parents or other nearby adults.
Societal: We can track how societies developed by examining their tools, art, and what remains of their architecture—all products of creativity. Remember, the main purpose of creativity is to solve problems, and an evolving society faces numerous new problems ranging from how to house and feed everyone, to how to maintain order among so many people.
Just as evolution involves competition between various biological adaptations, knowledge creation involves competition between different ideas and ways of thinking. Deutsch discusses two such schools of thought—reductionism and holism—in order to point out the fatal flaws in each:
1) Reductionism means discussing a phenomenon in terms of each individual part that composes it—in other words, it focuses on the smallest and most fundamental levels possible. For example, a strict reductionist might try to understand a rainstorm by calculating the behavior of each individual water molecule (an impossible task).
(Shortform note: Deutsch is using the scientific definition of reductionism, meaning the belief that any event can be explained in terms of physics. For example, in chemistry, a reductionist approach would mean describing a chemical reaction by explaining the physics that cause the chemicals to combine in certain ways.)
2) Holism is the opposite: It’s the belief that understanding a small piece of something is useless except in terms of what it can tell you about the whole. For example, a strict holist wouldn’t be interested in learning about one type of tree, except in terms of how that species contributes to the forest it’s in.
(Shortform note: Scientific holism emerged in the 1920s, and was originally a theory stating that simple parts will naturally come together to form complex wholes—individual atoms forming molecules, individual thoughts forming a person’s psyche, and so on. Holism, by this definition, never found much traction in the scientific community, but the term itself survived and took on the meaning that Deutsch uses here.)
Deutsch talks about these two opposite extremes in order to make the point that knowledge can’t be ranked. In other words, detailed knowledge of the parts isn’t “better” than broad knowledge of the whole, or vice versa. Any type of knowledge is valuable, and—perhaps even more importantly—any type of knowledge could turn out to be the basis for further discoveries.
(Shortform note: Deutsch isn’t arguing against reductionism or holism, only against strict reductionism and holism; both schools of thought provide us with valuable knowledge. For example, one microbiologist wrote that molecular biology (reductionism) and systems biology (holism) depend upon each other and complement one another. We need both types of knowledge in order to understand complex events, like how an organism grows or how a wound heals.)
Deutsch adds that, while knowledge usually grows incrementally (new discoveries building step-by-step on those that came before), sometimes one of those discoveries has far-reaching, even universal, implications.
For example, as scientists studied what matter is made of, breaking it down into smaller and smaller parts, they eventually discovered the elements of the periodic table and the atoms that compose them. We now know that everything—from sand to stars to our own bodies—is made of those atoms in various combinations.
In theory, by finding the right ways to combine the elements of the periodic table, we could create anything we can imagine. Deutsch says we can’t do that yet because we don’t fully understand the universality of the atom. In other words, we know (to some extent) what atoms are and how they behave, but we don’t know why everything is made of atoms, and why certain combinations of atoms create certain things.
Think of atoms as the alphabet of the universe: Once we fully understand the rules that gave rise to it, we’ll be able to arrange the letters into any words we want. Once we have that breakthrough, our understanding of atoms and elements will become universal.
The Search for Universal Truth
According to theoretical physicist Stephen Hawking, the search for these pieces of universal knowledge is the ultimate purpose of science. In A Brief History of Time, Hawking explains that science currently has two prevailing theories that explain how the universe works:
General relativity accurately explains and predicts how large objects behave (in physics terms, “large” generally means “big enough to see with the naked eye”). However, it cannot explain how subatomic particles such as electrons behave.
Quantum mechanics can somewhat explain the behavior of those subatomic particles, but it operates with completely different rules than general relativity. Furthermore, quantum mechanics is still imprecise, only offering results in terms of probability rather than certain outcomes.
Hawking says that the final goal of physics is to combine these two theories into a Grand Unified Theory that applies to any type of physics problem—what Deutsch would call a piece of “universal knowledge.” However, so far the two theories have proven incompatible, meaning that we need more incremental advancements before we can achieve Hawking’s dream of a universal theory of everything.
We’ve discussed various ways in which humans create knowledge, and how we could continue creating knowledge forever. However, all of that begs the question: So what? For Deutsch, the potential to create infinite knowledge is grounds for infinite optimism about the future.
First of all, there have been—and continue to be—many pessimistic predictions about the future. For example, there have been numerous projections about how many human beings Earth can support, some of which estimated under a billion people; clearly, we’ve far surpassed those predictions. Today, many scientists predict that climate change will devastate much of the world, perhaps within our lifetimes, but there’s hope that we can overturn those predictions as well.
Such predictions were—and are—based on current knowledge. We’ve exceeded expectations many times before, and that’s because there’s no way of knowing what we’ll know in the future. Therefore, Deutsch rejects such pessimism and instead offers a knowledge-based argument for embracing optimism.
First, he starts with the assumption that knowledge alleviates suffering. Basically, because we develop new knowledge in order to answer questions and solve problems, every bit of knowledge we acquire reduces suffering in the world by a tiny bit. Second, he reiterates that knowledge is infinite.
In short: There’s no limit to what we can learn, and therefore there’s no limit to how much we can reduce suffering in the world.
We Don’t Know What We’ll Know
Perhaps one of the most optimistic visions of the future comes from Lifespan, written by geneticist David Sinclair. Sinclair predicts that Earth can support a theoretically infinite number of people, that our quality of life will improve endlessly, and that someday people will be able to live forever.
Some of these predictions—especially about overcoming aging and living forever—are based on Sinclair’s own work as a scientist, but others are rooted in the same optimism that Deutsch has: That knowledge can increase endlessly, and that there’s no way of knowing what we’ll know in the future.
As a proof of concept, Sinclair points out that the last two centuries have seen the biggest population boom in the history of the world, driven in large part by increased life expectancy; at the same time, the average quality of life has increased drastically. He doesn’t see any reason why those trends should suddenly reverse.
Everyone has the capacity to create new knowledge. Think about what knowledge you might have already created and what you hope to create in the future.
What’s one piece of knowledge you’ve created in your lifetime? This doesn’t have to be some great scientific discovery—a piece of hard-learned advice, a new recipe, or a good trick of your trade are equally valid.
What knowledge would you like to create in the future? Perhaps you want to contribute something to your favorite hobby, or advance your professional field. How do you see yourself improving the world in some small way?
How might you begin to do that? Bear in mind that, as Deutsch says, it’s impossible to know what we’ll know in the future, but you might start by considering your current area of expertise and any exceptional skills you have. What is your first step toward creating new knowledge?