Our Mathematical Universe

by Max Tegmark

  To teach people what a scientific concept is and how a scientific lifestyle will improve their lives, we need to go about it scientifically: we need new science-advocacy organizations that use all the same scientific marketing and fund-raising tools as the anti-scientific coalition employ. We’ll need to use many of the tools that make scientists cringe, from ads and lobbying to focus groups that identify the most effective sound bites. We won’t need to stoop all the way down to intellectual dishonesty, however. Because in this battle, we have the most powerful weapon of all on our side: the facts.

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  1Most instabilities involve some form of runaway self-reproduction/chain reaction: for example, burning trees in a forest produce more burning trees, free neutrons in a nuclear bomb produce more free neutrons, a carrier of the bubonic plague produces more carriers, and one buyer of a disruptively successful product produces more buyers.

  The Future of You—Are You Insignificant?

  After spending most of this book heading away to explore the most distant and abstract levels of our physical reality, we’ve devoted this last chapter to gradually returning homeward, discussing the future of our own Universe and the future of our human civilization. Let’s finish by returning all the way home, to explore what this means for us personally—for you and me.

  The Meaning of Life

  As we’ve seen, the fundamental mathematical equations that appear to govern our physical reality make no reference to meaning, so a universe devoid of life would arguably have no meaning at all. Through us humans and perhaps additional life-forms, our Universe has gained an awareness of itself, and we humans have created the concept of meaning. So in this sense, our Universe doesn’t give life meaning, but life gives our Universe meaning.

  Although “What’s the meaning of life?” can be interpreted in many different ways, some of which may be too vague to have a well-defined answer, one interpretation is very practical and down-to-Earth: “Why should I want to go on living?” The people I know who feel that their lives are meaningful usually feel happy to wake up in the morning and look forward to the day ahead. When I think about these people, it strikes me that they split into two broad groups based on where they find their happiness and meaning. In other words, the problem of meaning seems to have two separate solutions, each of which works quite well for at least some people. I think of these solutions as “top-down” and “bottom-up.”

  In the top-down approach, the fulfillment comes from the top, from the big picture. Although life here and now may be unfulfilling, it has meaning by virtue of being part of something greater and more meaningful. Many religions embody such a message, as do families, organizations and societies where individuals are made to feel part of something grander and more meaningful that transcends individuality.

  In the bottom-up approach, the fulfillment comes from the little things here and now. If we seize the moment and get the fulfillment we need from the beauty of those little flowers by the roadside, from helping a friend or from meeting the gaze of a newborn child, then we can feel grateful to be alive even if the big picture involves less-cheerful elements such as Earth getting vaporized by our dying Sun and our Universe ultimately getting destroyed.

  For me personally, the bottom-up approach provides more than enough of a raison d’être, and the top-down elements I’m about to argue for simply feel like an additional bonus. For starters, I find it utterly remarkable that it’s possible for a bunch of particles to be self-aware, and that this particular bunch that’s Max Tegmark has had the fortune to get the food, shelter and leisure time to marvel at the surrounding universe leaves me grateful beyond words.

  Why We Should Care About Our Own Universe

  In addition, I feel motivation and inspiration from top-down thinking, about the potential future of life in our Universe that we discussed at length earlier in this chapter. But if there are parallel universes where all physically possible futures play out, why should we care about our own Universe? If all outcomes will happen, why should we care about what choices we make? Indeed, why should we lift a finger or care about anything at all if the Level IV multiverse exists and even change itself is an illusion? We face a choice between two rational alternatives:

  1. We care about at least something, and therefore go ahead and live life, making logical decisions reflecting the things we care about.

  2. We care about nothing, and therefore do nothing at all or act completely randomly.

  Both you and I have already made our choices, selecting option 1. It seems like the smart choice to me.

  But this choice has logical consequences. When I think about people I care about, it feels logical to also care about the civilization, the planet, and the universe that they belong to. In contrast, it feels logical to care less about other universes, because my decisions here in our Universe by definition can’t have any effect on them—they’re therefore unaffected by what I care about. With this logic, let’s limit our remaining discussion to our own Universe, and explore our role in it.

  Are We Insignificant?

  When gazing up on a clear night, it’s easy to feel insignificant. For most of my life, the more I learned about the vastness of our cosmos and our place in it, the more insignificant I felt. But not anymore!

  Since our earliest ancestors admired the stars, our human egos have suffered a series of blows. For starters, we’re smaller than we thought. As we saw in Part I of the book, Eratosthenes showed that Earth was larger than millions of humans, and his Hellenic compatriots realized that the Solar System was thousands of times larger still. Yet for all its grandeur, our Sun turned out to be merely one rather ordinary star among hundreds of billions in a galaxy that in turn is merely one of hundreds of billions in our observable Universe, the spherical region from which light has had time to reach us during the 14 billion years since our Big Bang. Our lives are small temporally as well as spatially: if this 14-billion-year cosmic history were scaled to one year, then 100,000 years of human history would be 4 minutes and a 100-year life would be 0.2 seconds. Further deflating our hubris, we’ve learned that we’re not that special either. Darwin taught us that we’re animals; Freud taught us that we’re irrational; machines now outpower us and outsmart us in chess and on the Jeopardy! quiz show. Adding insult to injury, cosmologists have found that we’re not even made of the majority substance.

  The more I learned about this, the less significant I felt. But I’ve suddenly changed my mind and turned more optimistic about our cosmic significance. Why? Because I’ve come to believe that advanced evolved life is very rare, yet has huge future potential, making our place in space and time remarkably significant.

  Are We Alone?

  When I give lectures about cosmology, I often ask the audience to raise their hands if they think there’s intelligent life elsewhere in our Universe. Infallibly, almost everyone does, from kindergartners to college students. When I ask why, the basic answer I tend to get is that space is so huge that there’s got to be life somewhere, at least statistically speaking. But is this argument really correct? I think it’s wrong—let me explain why.

  As the American astronomer Francis Drake pointed out, the probability of there being intelligent life in a given place can be calculated by multiplying together the probability of there being a habitable environment there (say an appropriate planet), the probability that life will evolve there, and the probability that this life will evolve to become intelligent. When I was a grad student, we had no clue about any of these three probabilities. After the past decade’s dramatic discoveries of planets orbiting other stars, it now seems likely that habitable planets are abundant, with billions in our own Galaxy alone. The probability of evolving life and intelligence, however, remains extremely uncertain: some experts think that one or both are rather inevitable and occur on most habitable planets, whereas others think that one or both are extremely rare because of one or more evolutionary bottlenecks that require a wild stroke of luck to pass through. Some
proposed bottlenecks involve chicken-or-the-egg problems at the earliest stages of self-reproducing life: for example, for a modern cell to build a ribosome, the highly complex molecular machine that reads our genetic code and builds our proteins, it needs another ribosome, and it’s not obvious that the very first ribosome could evolve gradually from something simpler. Other proposed bottlenecks involve the development of higher intelligence. For example, although dinosaurs ruled Earth for over 100 million years, a thousand times longer than we modern humans have been around, evolution didn’t seem to inevitably push them toward higher intelligence and inventing telescopes or computers.

  In other words, I think it’s fair to say that we still have no clue what fraction of all planets harbor intelligent life: a priori, before actually observing any other planets to check, any order-of-magnitude guess is about as good as any other. This is a standard way of modeling such extreme uncertainty in science, and goes by the geeky-sounding name uniform logarithmic prior; in plain English, it means that the fraction of planets with intelligent life is roughly equally likely to be one in a thousand, one in a million, one in a billion, one in a trillion, one in a quadrillion, and so on.

  Given this, how far from us is our nearest-neighbor intelligent civilization? From our assumption, it follows that this distance also has a uniform logarithmic prior, so a priori, before looking, the answer is roughly equally likely to be 1010 meters, 1020 meters, 1030 meters, 1040 meters, and so on, as illustrated in Figure 13.7.

  Now let’s turn to what we know from observation. So far, direct astronomical searches have turned up no evidence for extraterrestrial intelligence, and there’s no widely accepted evidence that aliens have visited Earth. My personal interpretation of this is that the fraction of planets harboring intelligence is minuscule, and that there’s probably no highly intelligent life within about 1021meters of us, i.e., in our own Galaxy or its immediate vicinity. I’m basing this conclusion on several assumptions:

  Figure 13.7: Are we alone? The huge uncertainties about how life and intelligence evolved suggest that our nearest neighbor civilization in space is roughly equally likely to be anywhere along the horizontal axis above, making it quite unlikely that it’s between the edge of our Galaxy (about 1021 meters away) and the edge of our Universe (about 1026 meters away). If it were much closer than this range, there should be so many other advanced civilizations in our Galaxy that we’d probably have noticed, which suggests that we’re in fact alone in our Universe.

  Click here to see a larger image.

  1. Interstellar colonization is physically possible and can easily be accomplished if a civilization as advanced as ours has a million years to develop the required technology.

  2. There are billions of habitable planets in our Galaxy, many of which formed not only millions but billions of years before Earth.

  3. A non-negligible fraction of civilizations that can colonize space would choose to do so.

  For assumption 1, I’m keeping an open mind about what technologies may be used. For example, rather than physically sending large human-sized organisms through space, it may be more efficient to send swarms of small self-assembling nanoprobes that build factories on landing and assemble any larger life-forms using “emailed” instructions transmitted at the speed of light via electromagnetic radiation.1 Common objections to assumption 3 include the supposition of advanced civilizations being intrinsically kind or otherwise uninterested in colonization, perhaps because their advanced technology allows them to accomplish all their goals using the resources they already have. Alternatively, perhaps they keep a low profile for self-protection or other reasons, or colonize only in a way that we don’t notice: this has been called the zoo hypothesis by the U.S. astronomer John A. Ball, and features in sci-fi classics such as Olaf Stapledon’s Star Maker. Personally, I think we shouldn’t underestimate the diversity of advanced civilizations by assuming that they all share the same goals: all it takes is one civilization deciding to overtly colonize all it can, and it will engulf our Galaxy and beyond. Faced with this risk, even civilizations otherwise uninterested in colonization may feel pressured to expand for self-protection.

  If my interpretation is correct, then the closest civilization is about 1,000,…000 meters away, where the total number of zeros is roughly equally likely to be 21, 22, 23,…100, 101, 102, etc.—but not much smaller than 21. However, for this civilization to be in our own Universe, whose radius is about 1026 meters, the number of zeros can’t exceed 26, and the probability of the number of zeros falling in the narrow range between 22 and 26 is quite small. This is why I think we’re alone in our Universe.

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  1The economist Robin Hanson has made an interesting point about assumption 1. The apparent incompatibility between the abundance of habitable planets in our Galaxy and the lack of extraterrestrial visitors, known as the Fermi paradox, suggests the existence of what Hanson calls a “Great Filter,” an evolutionary/technological roadblock somewhere along the developmental path from nonliving matter to space-colonizing life. If we discover independently evolved primitive life in our Solar System, this would suggest that primitive life is not rare, and that the roadblock lies after our current human stage of development—perhaps because assumption 1 is false, or because almost all advanced civilizations self-destruct before they are able to colonize. I’m therefore crossing my fingers that all searches for life on Mars and elsewhere find nothing: this is consistent with the scenario where primitive life is rare but we humans got lucky, so that we have the roadblock behind us and have extraordinary future potential.

  Are We Really Insignificant?

  I’ve just argued that we’re probably the most intelligent life-form in our entire Universe. This is a minority view,1 and I may well be wrong, but it’s at the very least a possibility that we can’t currently dismiss. Let’s therefore explore the implications of its being true and us being the only civilization in our Universe that has advanced to the point of building telescopes.

  It was the cosmic vastness that made me feel insignificant to start with. Yet those grand galaxies are visible and beautiful to us—and only to us. It’s only we who give them any meaning, making our small planet the most significant place in our entire observable Universe. If we didn’t exist, all those galaxies would be just a meaningless and gigantic waste of space.

  I also felt that my short lifespan appeared insignificant when compared with the vastness of cosmic time. However, this brief century of ours is arguably the most significant one in the history of our Universe: the one when its meaningful future gets decided. We’ll have the technology to either self-destruct or seed our cosmos with life. The situation is so unstable that I doubt that we can dwell at this fork in the road for more than another century. If we end up going the life route rather than the death route, then in a distant future, our cosmos will be teeming with life that all traces back to what we do here and now. I have no idea how we’ll be thought of, but I’m sure that we won’t be remembered as insignificant.

  In this book, we’ve explored our physical reality, seeing through the eyes of science a breathtakingly beautiful universe, which through us humans has come alive and started becoming aware of itself. We’ve seen that life’s future potential in our Universe is grander than the wildest dreams of our ancestors, tempered by an equally real potential for intelligent life to go permanently extinct. Will life in our Universe fulfill its potential or squander it? I think this will be decided in our lifetime here on Spaceship Earth, by you, me and our fellow passengers. Let’s make a difference!

  THE BOTTOM LINE

  • Even though our two intellectual expeditions set off in opposite directions, toward the large and the small, they ended up in the same place: in the realm of mathematical structures.

  • On the largest and smallest scales, the mathematical fabric of reality becomes evident, while it remains easy to miss on the intermediate scales that we humans are usually aware of.

  • If the ultim
ate fabric of reality really is mathematical, then everything is in principle understandable to us, and we’ll be limited only by our own imagination.

  • Although the Level IV multiverse is eternal, our particular Universe might end in a Big Chill, Big Crunch, Big Rip, Big Snap or with death bubbles.

  • Evidence suggests that there’s no other life-form as advanced as us humans in our entire Universe.

  • From a cosmic perspective, the future potential of life in our Universe is vastly greater than anything we’ve seen so far.

  • Yet we humans devote only meager attention and resources to existential risks that threaten life as we know it, including accidental nuclear war and unfriendly artificial intelligence.

  • Although it’s easy to feel insignificant in our vast cosmos, the entire future of life in our Universe will arguably be decided on our planet in our lifetime—by you, me and our fellow passengers on Spaceship Earth. Let’s make a difference!

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  1However, John Gribbin comes to a similar conclusion in his 2011 book Alone in the Universe. For a spectrum of intriguing perspectives on this question, I also recommend Paul Davies’s 2011 book The Eerie Silence.

  Acknowledgments

  In addition to the people mentioned in the preface, I’m grateful to the organizations whose research grants have helped enable the research described in this book: NASA, the National Science Foundation, the Packard Foundation, the Research Corporation for Science Advancement, the Kavli Foundation, the John Templeton Foundation, the University of Pennsylvania and the Massachusetts Institute of Technology. I also wish to thank Jonathan Rothberg and an anonymous donor for their generous support of the Omniscope project.