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Summary
Summary
Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last--this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
Author Notes
Max Tegmark is a professor at Massachusetts Institute of Technology. He is the author of numerous technical papers on such topics as cosmology to artificial intelligence. He is the author of Our Mathematical Universe, and Life 3.0: Being Human in the Age of Artificial Intelligence.
(Bowker Author Biography)
Reviews (5)
Publisher's Weekly Review
Theoretical physicist Tegmark takes readers on an illuminating trip through cutting edge cosmology to one of the strangest ideas in a field overflowing with them: that our universe isn't just described by math, it may actually be made out of it. Since Galileo first proclaimed nature to be "a book written in the language of mathematics," physicists have used math to describe everything from motion to the shape of space-time itself. Tegmark explains how the discovery that the universe was expanding supported the concept of a "Big Bang" origin. Subsequent news that the expansion of our universe is actually accelerating led cosmologists to the idea that it may be just one of many universes within a vast multiverse. Tegmark offers a fascinating exploration of multiverse theories, each one offering new ways to explain "quantum weirdness" and other mysteries that have plagued physicists, culminating in the idea that our physical world is "a giant mathematical object" shaped by geometry and symmetry. Tegmark's writing is lucid, enthusiastic, and outright entertaining, a thoroughly accessible discussion leavened with anecdotes and the pure joy of a scientist at work. Agents: John and Max Brockman, Brockman Inc. (Jan.) (c) Copyright PWxyz, LLC. All rights reserved.
Booklist Review
*Starred Review* Nobel-laureate physicist Eugene Wigner regarded the power of mathematics to explain the cosmos as a baffling mystery. Tegmark offers a resolution of that mystery, arguing that mathematics describes the universe so well because the universe ultimately is mathematics. The rare intellectual daring in this claim emerges as Tegmark teases out its stunning implications not only for the visible universe but also for countless, unseen, parallel universes (on four levels!) in which all conceivable possibilities become realities. Aware of the skeptics, Tegmark demonstrates that his theorizing harmonizes with concepts now central to cosmology, particularly the astrophysical formulas for the post-Big Bang inflation that gave space its geometry. Tegmark's mathematical paradigm also accounts for the strange fine-tuning of the universe's fundamental constants and dispels the paradoxes surrounding quantum measurement. Lively and lucid, the narrative invites general readers into debates over computer models for brain function, over scientific explanations of consciousness, and over prospects for finding advanced life in other galaxies. Though he reflects soberly on the perils of nuclear war and of hostile artificial intelligence, Tegmark concludes with a bracingly upbeat call for scientifically minded activists who recognize a rare opportunity to make our special planet a force for cosmic progress. An exhilarating adventure for bold readers.--Christensen, Bryce Copyright 2010 Booklist
New York Review of Books Review
HALFWAY INTO HIS new book, "Our Mathematical Universe," the M.I.T. physicist Max Tegmark describes his "Dr. Jekyll/Mr. Hyde Strategy": During the day he would do respectable work on mainstream topics in cosmology, but at night he would "transform into the evil Mr. Hyde" and indulge in writing "wacky" papers on "the ultimate nature of reality." This strategy is employed in the book itself, which can be divided into two parts, different as day and night. One, by Dr. Tegmark, is an informative survey of exciting recent developments in astrophysics and quantum theory. The other, by Mr. Tegmark, is a discussion of his controversial idea that reality itself is a mathematical structure. The first part starts with a list of fundamental questions, such as: Is space infinite? Is the Milky Way expanding? What caused the Big Bang? What are dark matter and dark energy? After lucidly educating us about stars and galaxies, Dr. Tegmark quickly gets to the main points. He tells us of cosmic microwave radiation, "the faint afterglow" of the Big Bang, and other discoveries in cosmology in the past 50 years that yielded "baby pictures of when our universe was 'only' 400,000 years old" and "crucial clues to our cosmic origins." Tegmark participated in some of these pioneering developments, and he enlivens his story with personal anecdotes. However, the Big Bang and the expansion of the universe still elude our understanding. An important step toward unraveling the mystery was the theory of inflation initiated in the 1980s by Alan Guth and others. The "radical insight" was that if once upon a time there was "a tiny uniform blob of a substance whose density was very hard to dilute," then it could "inflate," exponentially increasing its size. But if so, how could mass be created from nothing: "Who paid for the ultimate free lunch?" Tegmark does an excellent job explaining this and other puzzles in a way accessible to nonspecialists. Packed with clever metaphors, this section illuminates an important area on the cutting edge of modern physics. Then Tegmark's professed alter ego takes over. He asks a question that philosophers and scientists have debated for centuries: Why is mathematics so effective in describing the world? The answer is not as simple as it might seem. A great body of math has been developed without any reference to physical reality, motivated by problems within the narrative of mathematics itself. Some of these theories subsequently found real-world applications (for example, 60 years after Riemannian geometry was developed, Einstein used it to describe gravity), but most modern math does not currently manifest itself in the world around us. An argument can also be made that mathematical ideas are objective and exist independently from the human mind - many mathematicians adhere to this view, called mathematical Platonism. Yet Tegmark's take is quite different from - and in some ways inconsistent with - Platonism. Math is so effective in describing the world, he says, because physical reality is a mathematical structure. He calls it the Mathematical Universe Hypothesis (M.U.H.). What exactly this means is a big question, which is never fully answered. Mr. Tegmark's argument is that all physical properties of an electron, say, can be described mathematically; therefore, to him, an electron is itself a mathematical structure - as is everything else, including us. "You're a pattern in space-time," Tegmark says, and he is not just speaking metaphorically. Well, it's true that the trajectory of a human is a pattern in space-time, but does it mean that a human is this pattern? What accounts for consciousness, for example? "I think that consciousness is the way information feels when being processed in certain complex ways," Tegmark says. I tried to process this information, but didn't feel much. Let's go back to the notion of "mathematical structure." We read in the book that it is a "set of abstract elements with relations between them," like the set of whole numbers with operations of addition and multiplication. However, there is a lot more to math than such mathematical structures. Objects other than sets are necessary, and they have now become widespread. Moreover, there is an effort underway to overhaul the foundations of math in which set theory is no longer central. So mathematical structures constitute but a small island of modern mathematics. Why would someone who believes that math is at the core of reality try to reduce all of reality to just this island? Where would the rest of math then reside? Unfortunately, these questions are not addressed. A bigger problem is that M.U.H, appears to contradict Gödel's incompleteness theorem, which states that in any sufficiently sophisticated, consistent mathematical theory there will be true statements that cannot be decided within that theory. Conceding this point, Tegmark replaces Mathematical Universe Hypothesis with Computable Universe Hypothesis: Only "computable" mathematical structures should be allowed. But this rules out all structures that contain infinity! In fact, he admits that "our current standard model (and virtually all historically successful theories) violate the C.U.H.," which does not bode well for the whole idea, to say the least. Ironically, Mr. Tegmark has no qualms about telling us that there are infinitely many parallel universes out there. Actually, he believes that any mathematical structure spawns its own universe, and that all of these universes exist in parallel and on equal footing (further, he claims that if you accept M.U.H, or C.U.H., you are forced to also accept this proposal). According to him, a simple square, for example, should be viewed as just as legitimate a universe as the world around us. Tegmark's "Level IV Multiverse" is therefore much like Borges's Library of Babel, containing all possible books that can be written with a given alphabet. Any question is answered in one of them, but no one knows which one. In what sense is having all these books (or universes) different from nothing at all? In fact we do know that mathematical structures are not created equal. The development of mathematics was never random - there was always a sense of direction and purpose. Besides, how could one possibly prove or disprove the existence of this mathematical multiverse? Mr. Tegmark claims he can: "One of the key testable predictions of the Mathematical Universe Hypothesis is that physics research will uncover further mathematical regularities in nature." But such regularities can mean anything, so this "prediction" is as far from the scientific method as the purported universes are from one another. This does not stop the author from entertaining various situations involving multiple copies of "you" living in those universes, such as: "When the number of yous increases, you perceive subjective randomness. When the number of yous decreases, you perceive subjective immortality." (The real question, however, might be, What is the number of yous who can understand what this means?) There is nothing wrong with contemplating speculative ideas, but the problem is that while pretending to stay in the realm of science, the "Mr. Hyde" part of the book crosses over to what I must consider science fiction and mysticism. It raises provocative questions that will make you ponder the essence of reality, but readers expecting the discussion to be as coherent and intellectually fulfilling as it is in the scientific sections will be disappointed. Max Tegmark's controversial idea is that reality itself is a mathematical structure. EDWARD FRENKEL is a professor of mathematics at the University of California, Berkeley, and the author of "Love and Math: The Heart of Hidden Reality."
Choice Review
Based on some of the blurbs for this book, this reviewer expected a philosophical argument for a particular relationship between mathematics and reality; that is not what this is. This book is clearly intended for nonscientists and nonmathematicians who want an introduction to how to think about the relationship between physical theories, mathematics, and reality. Written much like a memoir, the book first looks at the large-scale structure of the universe and discusses the important conclusions of modern cosmology. Tegmark (physics, MIT) then "zoom[s] in" to look at the atomic world and introduces modern physics. The difference between this book and others is the author's next approach, which is to consider these two scales as a whole and ask what they tell people about reality. He introduces questions, and a survey of answers, about the nature of reality and its connection to physics and mathematics. Again, this is not a text that addresses the modern philosophical questions surrounding these topics. It is, however, a well-written introduction on how to think about these serious philosophical questions and introduces some ways they might be answered. Summing Up: Recommended. General readers and undergraduate students. E. Kincanon Gonzaga University
Guardian Review
Max Tegmark's doorstopper of a book takes aim at three great puzzles: how large is reality? What is everything made of? Why is our universe the way it is? Tegmark, a professor of physics at MIT, writes at the cutting edge of cosmology and quantum theory in friendly and relaxed prose, full of entertaining anecdotes and down-to-earth analogies. His book seeks to induct the reader into a wildly speculative cosmic vision of infinite time and space and infinite parallel universes. Close to his heart is an extreme Pythagorean/Platonic thesis: physical reality is ultimately nothing other than a giant mathematical totality. The story goes as follows. Our observable universe is the result of an explosion, the big bang, some 13.7bn years ago. The explosion, now called inflation, is a solution to Einstein's theory of gravity in which a subatomic blob of non-diluting substance (dark matter might have this property) can double its size at regular time intervals while keeping its density constant. After inflation ends the expansion of space slows to roughly the present rate, gravity having coalesced matter into the familiar stars and planets we observe in space. The inflation solution explains many puzzles but includes a shocker: the process doesn't terminate - inflation is eternal. This means that just as our universe inflated and coalesced an infinite number of others, remote from us in space and time (but in principle accessible), were doing the same. And since, in an infinite space "everything that can happen according to the laws of physics does happen", some of these would contain planets and inhabitants virtually indistinguishable from ours. The assemblage of all these "Level 1 parallel universes" containing our observable universe is called the multiverse - that is, the Level 1 multiverse. But there is more. Inflation, the "gift that keeps on giving", Tegmark quips, contains a second shocker. Starting from something smaller than an atom, inflation "can create an infinite space inside of it, containing infinitely many galaxies, without affecting the exterior space". This allows him - through an argument that involves the so-called fine-tuning of the fundamental constants of physics - to posit the existence of a multiverse Level 2, composed of an infinite number of Level 1 multiverses, each of which is inaccessible to us or any of the other universes in our Level 1 multiverse. What's more, unlike the situation with Level 1 parallel universes, many physical laws and fundamental constants may vary across a Level 2 multiverse, though little is known. Indeed, Tegmark admits that parallel universes themselves remain "highly controversial" and that by no means all physicists are convinced by inflation. This cosmic "zooming out" makes up part one of the book. Part two zooms in to the ultimate building blocks of matter, from electrons to mesons, gluons and so on. The interpretation of quantum physics is notoriously contentious, with many competing versions. Dominant in most textbooks is the Copenhagen interpretation. According to this, Schrodinger's wave equation, which deterministically describes an electron as being in superposed states and spread out in space, breaks down under observation: the electron is found to be in a definite, but random position and state. Tegmark is made uneasy by physics' recourse to the intervention of an "observer" to explain experiments and opts for the so-called many-worlds interpretation of quantum phenomena, introduced by Hugh Everett in 1957. Dismissed at the time as bonkers, it now apparently has a sizable following. According to Everett, the wave equation never collapses: it always applies. But not just to the particle; it applies to the combined system of particle and observing apparatus. This means an experimental observation "puts your mind into two states at once . . . so that at the end of it, there will be two different versions of you. Each subjectively feeling just as real as the other, but completely unaware of each other's existence." It's as if the universe repeatedly splits in two, resulting in innumerable copies of you in parallel worlds. As a bonus, the randomness of the universe that so troubled Einstein disappears, being simply "how it feels when you're cloned". Tegmark calls these parallel worlds Level 3 universes that together make up the Level 3 multiverse. He plays with the consequences of this mind-splitting picture of multiple realities, exploring such topics as quantum suicide and the possibility of quantum immortality, and demonstrating why your brain and its consciousness can't be a quantum computer. So far, in parts one and two mathematics appears as no more than physics' indispensible tool kit for describing the world. The final part ups the ante: "Our reality isn't just described by mathematics - it is mathematics . . . Not just aspects of it, but all of it, including you." In other words, "our external physical reality is a mathematical structure". He calls this the Mathematical Universe Hypothesis (MUH). Admitting that the idea sounds far-fetched, he proposes to demonstrate it in the time-honoured manner of Euclid by logically proving it from a self-evident truth, namely the External Reality Hypothesis (ERH): "There exists an external physical reality completely independent of us humans." Tegmark's demonstration that ERH implies MUH is complicated, difficult to follow, and resists summary. It requires, among other things, a certain (disputable) characterisation of mathematics; an insistence that a "complete" description of external reality must be defined in a form "devoid of any human baggage like 'particle', 'observation'" or other words; and it is obliged to argue - given that mathematical structures are static objects - that time and physical motion are illusory. Thus everything physical is ultimately mathematical, including you and me, "making us self-aware parts of a giant mathematical object". He calls this vast nebulous entity the Level 4 multiverse, an omnium eternally "there" stacked above or beyond or behind the other multiverses than contain us. To the objection we don't feel such a truth, Tegmark counters that we don't feel like we're travelling in space at thousands of kilometres a second, but we are. Perhaps physicists really do understand themselves to be part of a giant mathematical object. For them Tegmark's conclusion that we are living inside a Platonic, Level 4 all-encompassing mathematical multiverse will be appealing: the ultimate guarantor and resting place of their quest for a theory of everything. (After all, physics excludes, in principle, anything in physical reality not measurable or describable in mathematical language, so what other ultimate truth can it think.) But as a mathematician, convinced that mathematics is a human construction, that numbers don't exist in the world before humans put them there, I don't buy it. And the claim that our minds are ultimately self-aware mathemes - insofar as that assertion makes sense - seems like saying that Shakespeare's plays are ultimately patterns of words: it tells you next to nothing about its object. Brian Rotman's books include Ad Infinitum: The Ghost in Turing's Machine. To order Our Mathematical Universe for pounds 17.99 with free UK p&p call Guardian book service on 0330 333 6846 or go to guardianbookshop.co.uk. - Brian Rotman So far, in parts one and two mathematics appears as no more than physics' indispensible tool kit for describing the world. The final part ups the ante: "Our reality isn't just described by mathematics - it is mathematics . . . Not just aspects of it, but all of it, including you." In other words, "our external physical reality is a mathematical structure". He calls this the Mathematical Universe Hypothesis (MUH). Admitting that the idea sounds far-fetched, he proposes to demonstrate it in the time-honoured manner of Euclid by logically proving it from a self-evident truth, namely the External Reality Hypothesis (ERH): "There exists an external physical reality completely independent of us humans." Tegmark's demonstration that ERH implies MUH is complicated, difficult to follow, and resists summary. It requires, among other things, a certain (disputable) characterisation of mathematics; an insistence that a "complete" description of external reality must be defined in a form "devoid of any human baggage like 'particle', 'observation'" or other words; and it is obliged to argue - given that mathematical structures are static objects - that time and physical motion are illusory. Thus everything physical is ultimately mathematical, including you and me, "making us self-aware parts of a giant mathematical object". He calls this vast nebulous entity the Level 4 multiverse, an omnium eternally "there" stacked above or beyond or behind the other multiverses than contain us. To the objection we don't feel such a truth, Tegmark counters that we don't feel like we're travelling in space at thousands of kilometres a second, but we are. - Brian Rotman.
Excerpts
Excerpts
Chapter 9 Internal Reality, External Reality and Consensus Reality Sweet exists by convention, bitter by convention, color by convention; atoms and void [alone] exist in reality. --Democritus, ca. 400 B.C. "Nooooo! My suitcase!" They were already boarding my flight from Boston to Philadelphia, where I was supposed to help with a BBC documentary about Hugh Everett, when I realized that my hand wasn't holding a suitcase. I ran back to the security checkpoint. "Did someone just forget a black roll-on bag here?" "No," said the guard. "But there it is--that's my suitcase, right there!" "That's not a black suitcase," said the guard. "That's a teal suitcase." Until then, I'd never realized how color-blind I was, and it was quite humbling to realize that many assumptions I'd previously made about reality--and my wardrobe--were dead wrong. How could I ever trust what my senses told me about the outside world? And if I couldn't, then how could I hope to ever know anything with certainty about the external reality? After all, everything I know about the outside world and my untrustworthy senses, I've learned from my senses. This puts me on the same shaky epistemological footing as a prisoner who's spent his whole life in solitary confinement, whose only information about the outside world and his untrustworthy prison guard is what his prison guard has told him. More generally, how can I trust what my conscious perceptions tell me about the world if I don't understand how my mind works? This basic dilemma has been eloquently explored by philosophers throughout the ages, including titans such as Plato, René Descartes, David Hume and Immanuel Kant. Socrates said: "The only true wisdom is in knowing you know nothing." So how can we make further progress in our quest to understand reality? So far in this book, we've taken a physics approach to exploring our external physical reality, zooming out to the transgalactic macrocosm and zooming in to the subatomic microcosm, attempting to understand things in terms of their basic building blocks such as elementary particles. However, all we have direct knowledge of are instead qualia, the basic building blocks of our conscious perception,* (* For introductions to the vast literature on consciousness by psychologists, neuroscientists, philosophers and others, I recommend the books about the mind in the "Suggestions for Further Reading" section.) exemplified by the redness of a rose, the sound of a cymbal, the smell of a steak, the taste of a tangerine or the pain of a pinprick. So don't we also need to understand consciousness before we can fully understand physics? I used to answer "yes," thinking that we could never figure out the elusive "theory of everything" for our external physical reality without first understanding the distorting mental lens through which we perceive it. But I've changed my mind, and in this brief interlude chapter, I want to tell you why. External Reality and Internal Reality Perhaps you're thinking, Okay, Max, but I'm not color-blind. And I'm looking at the external reality right now with my own eyes, and I'd have to be paranoid to think it's not the way it looks. But please try these simple experiments: Experiment 1: Turn your head from left to right a few times. Experiment 2: Move your eyes from left to right a few times, with- out moving your head. Did you notice how the first time, the external reality appeared to rotate, and the second time, it appeared to stay still, even though your eyeballs rotated both times? This proves that what your mind's eye is looking at isn't the external reality, but a reality model stored in your brain! If you looked at the image recorded by a rotating video camera, you'd clearly see it move as it did in Experiment 1. But your eyes are a form of biological video camera, so Experiment 2 shows that your consciousness isn't directly perceiving the images formed on their retinas. Rather, as neuroscientists have now studied in great detail, the information recorded by your retinas gets processed in highly complex ways and is used to continually update an elaborate model of the outside world that's stored in your brain. Take another look in front of you, and you'll see that, thanks to this advanced information processing, your reality model is three-dimensional even though the raw images from your retinas are two-dimensional. I don't have a light switch near my bed, so I'll often take a good look at my bedroom and all the obstacles littering the floor, then turn off the light and walk to my bed. Try it yourself: put down this book, stand up, look around, and then walk a few steps with your eyes closed. Can you "see"/"feel" the objects in the room moving relative to you? That's your reality model being updated, this time using information from your leg movements rather than from your eyes. Your brain continuously updates its reality model using any useful information it can get hold of, including sound, touch, smell and taste. Let's call this reality model your internal reality, because it's the way you subjectively perceive the external reality from the internal vantage point of your mind. This reality is internal also in the sense that it exists only internally to you: your mind feels as if it's looking at the outside world, while it's actually looking only at a reality model inside your head--which in turn is continually tracking what's outside your brain via elaborate but automatic processes that you're not consciously aware of. It's absolutely crucial that we don't conflate this internal reality with the external reality that it's tracking, because the two are very different. My brain's internal reality is like the dashboard of my car: a convenient summary of the most useful information. Just as my car's dashboard tells me my speed, fuel level, motor temperature, and other things useful for a driver to be aware of, my brain's dashboard/reality model tells me my speed and position, my hunger level, the air temperature, high- lights of my surroundings and other things useful for the operator of a human body to be aware of. The Truth, the Whole Truth and Nothing but the Truth Once my car's dashboard malfunctioned and sent me to the garage with its "CHECK ENGINE" indicator illuminated even though nothing was wrong. Similarly, there are many ways in which a person's reality model can malfunction and differ from the true external reality, giving rise to illusions (incorrect perceptions of things that do exist in the external reality), omissions (nonperception of things that do exist in the external reality) and hallucinations (perceptions of things that don't exist in the external reality). If we swear under oath to tell the truth, the whole truth and nothing but the truth, we should be aware that our perceptions might violate all three with illusions, omissions and hallucinations, respectively. So metaphorically speaking, the "CHECK ENGINE" incident was my car hallucinating--or experiencing phantom pain. I recently discovered that my car also suffers from an illusion: based on its speedometer reading, it thinks it's always driving two miles per hour faster than it really is. That's not bad compared to the vast list of human illusions that cognitive scientists have discovered, which afflict all our senses and dis- tort our internal reality. If your version of this figure is in color rather than black and white, you'll probably see the lower dot in the left panel as orange and the upper dot as somewhat brown. Figure 9.1 (in the book) shows two examples of optical illusions, where our visual system creates an internal reality different from the external reality. In the external reality, the light from both of them has identical properties, with a wavelength around 600 nanometers. If a spotlight beamed out such light, it would be orange light. What about brown? Have you ever seen a spotlight or a laser pointer produce a brown beam? Well, you never will, because there's no such thing as brown light! The color brown doesn't exist in the external reality, but only in your internal reality: it's simply what you perceive when seeing dim orange light against a darker background. For fun, I sometimes compare how the same news story is reported online by MSNBC, FOX News, the BBC, Al Jazeera, Pravda and else- where. I find that when it comes to telling the truth, the whole truth, and nothing but the truth, it's the second part that accounts for most of the differences in how they portray reality: what they omit. I think the same holds for our senses: although they can produce hallucinations and illusions, it's their omissions that account for most of the discrepancy between the internal and external realities. My visual system omitted the information that distinguishes between black and teal suitcases, but even if you're not color-blind, you're missing out on the vast majority of the information that light carries. When I was taught in elementary school that all colors of light can be made up by mixing three primary colors red, green, and blue, I thought that this number three told us something fundamental about the external reality. But I was wrong: it teaches us only about the omissions of our visual system. Specifically, it tells us that our retina has three kinds of cone cells, which take the thousands of numbers that can be measured in a spectrum of light (see Figure 2.5 in Chapter 2) and keeps only three numbers, corresponding to the average light intensity across three broad ranges of wavelengths. Moreover, wavelengths of light outside of the narrow range 400-700 nanometers go completely undetected by our visual system, and it came as quite a shock when human-built detectors revealed that our external reality was vastly richer than we'd realized, teeming with radio waves, microwaves, x-rays, and gamma rays. And vision isn't the only one of our senses that's guilty of omissions: we can't hear the ultrasound chirping of mice, bats and dolphins; we're oblivious to most faint scents that dominate the olfactory inner reality of dogs, and so on. Although some animal species capture more visual, auditory, olfactory, gustatory or other sensory information than we humans do, they're all unaware of the sub- atomic realm, the galaxy-spangled cosmos, and the dark energy and dark matter that, as we saw in Chapter 4, makes up 96% of our external reality. Consensus Reality In the first two parts of this book, we've seen how our physical world can be remarkably well described by mathematical equations, fueling the hope that one day equations can be found for a "theory of everything," perfectly describing our external reality on all scales. The ultimate triumph of physics would be to start with the external reality from the "bird perspective" of a mathematician studying these equations (which are ideally simple enough to fit on her T-shirt) and to derive from them her internal reality, the way she subjectively perceives it from her "frog perspective" inside the external reality. To accomplish this would clearly require a detailed understanding of how consciousness works, including illusions, omissions, hallucinations and other complications. However, between the external reality and the internal reality, there's also a third and intermediate consensus reality, as illustrated in Figure 9.2 (in the book). This is the version of reality that we life-forms here on Earth all agree on: the 3-D positions and motions of macroscopic objects, and other everyday attributes of the world for which we have a shared description in terms of familiar concepts from classical physics. Table 9.1 summarizes these reality descriptions and perspectives and how they're interrelated. Each of us has our own personal inner reality, perceived from the subjective perspective of our own position, orientation and state of mind, and distorted by our personal cognitive biases: in your inner reality, dreams are real and the world turns upside down when you stand on your head. In contrast, the consensus reality is shared. When you give your friend driving directions to your place, you do your best to trans- form your description from one involving subjective concepts from your inner reality (such as "here" and "in the direction I'm facing") to shared concepts from the consensus reality (such as "on 70 Vassar Street" and "north"). Since we scientists need to be precise and quantitative when we refer to our shared consensus reality, we try extra-hard to be objective: we say that light has a "600-nanometer wavelength" instead of "orange color" and that something has "CH3COOC5H11 molecules" instead of "banana flavor." The consensus reality isn't free from some shared illusions relative to the external reality, as we'll elaborate on below: for example, cats, bats and robots also experience the same quantum randomness and relativistic time dilation. However, it's by definition free from illusions that are unique to biological minds, and therefore decouples from the issue of how our human conscious- ness works. The internal reality may feel teal deficient to me, black and white to a seal, iridescent to a bird seeing four primary colors, and still more different to a bee seeing polarized light, a bat using sonar, a blind person with keener touch and hearing, or the latest robotic vacuum cleaner, but we all agree on whether the door is open. This is why I've changed my mind: although understanding the detailed nature of human consciousness is a fascinating challenge in its own right, it's not necessary for a fundamental theory of physics, which need "only" derive the consensus reality from its equations. In other words, what Douglas Adams called "the ultimate question of life, the universe and everything" splits cleanly into two parts that can be tackled separately: the challenge for physics is deriving the consensus reality from the external reality, and the challenge for cognitive science is to derive the internal reality from the consensus reality. These are two great challenges for the third millennium. They're each daunting in their own right, and I'm relieved that we need not solve them simultaneously. Chapter 9 is continued in the book... Excerpted from Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark All rights reserved by the original copyright owners. Excerpts are provided for display purposes only and may not be reproduced, reprinted or distributed without the written permission of the publisher.
Table of Contents
| Preface | p. ix |
| 1 What Is Reality? | p. 3 |
| Not What It Seems | |
| What's the Ultimate Question? | |
| The Journey Begins | |
| Part 1 Zooming Out | |
| 2 Our Place in Space | p. 17 |
| Cosmic Questions | |
| How Big Is Space? | |
| The Size of Earth | |
| Distance to the Moon | |
| Distance to the Sun and the Planets | |
| Distance to the Stars | |
| Distance to the Galaxies | |
| What Is Space? | |
| 3 Our Place in Time | p. 34 |
| Where Did Our Solar System Come From? | |
| Where Did the Galaxies Come From? | |
| Where Did the Mysterious Microwaves Come From? | |
| Where Did the Atoms Come From? | |
| 4 Our Universe by Numbers | p. 68 |
| Wanted: Precision Cosmology | |
| Precision Microwave-Background Fluctuations | |
| Precision Galaxy Clustering | |
| The Ultimate Map of Our Universe | |
| Where Did Our Big Bang Come From? | |
| 5 Our Cosmic Origins | p. 95 |
| What's Wrong with Our Big Bang? | |
| How Inflation Works | |
| The Gift That Keeps on Giving | |
| Eternal Inflation | |
| 6 Welcome to the Multiverse | p. 119 |
| The Level I Multiverse | |
| The Level II Multiverse | |
| Multiverse Halftime Roundup | |
| Part 2 Zooming In | |
| 7 Cosmic Legos | p. 157 |
| Atomic Legos | |
| Nuclear Legos | |
| Particle-Physics Legos | |
| Mathematical Legos | |
| Photon Legos | |
| Above the Law? | |
| Quanta and Rainbows | |
| Making Waves | |
| Quantum Weirdness | |
| The Collapse of Consensus | |
| The Weirdness Can't Be Confined | |
| Quantum Confusion | |
| 8 The Level III Multiverse | p. 184 |
| The Level III Multiverse | |
| The Illusion of Randomness | |
| Quantum Censorship | |
| The Joys of Getting Scooped | |
| Why Your Brain Isn't a Quantum Computer | |
| Subject, Object and Environment | |
| Quantum Suicide | |
| Quantum Immortality? | |
| Multiverses Unified | |
| Shifting Views: Many Worlds or Many Words? | |
| Part 3 Stepping Back | |
| 9 Internal Reality, External Reality and Consensus Reality | p. 233 |
| External Reality and Internal Reality | |
| The Truth, the Whole | |
| Truth and Nothing but the Truth | |
| Consensus Reality | |
| Physics: Linking External to Consensus Reality | |
| 10 Physical Reality and Mathematical Reality | p. 243 |
| Math, Math Everywhere! | |
| The Mathematical Universe | |
| Hypothesis | |
| What Is a Mathematical Structure? | |
| 11 Is Time an Illusion? | p. 272 |
| How Can Physical Reality Be Mathematical? | |
| What Are You? | |
| Where Are You? (And What Do You Perceive?) | |
| When Are You? | |
| 12 The Level IV Multiverse | p. 319 |
| Why I Believe in the Level IV Multiverse | |
| Exploring the Level IV Multiverse: What's Out There? | |
| Implications of the Level IV Multiverse | |
| Are We Living in a Simulation? | |
| Relation Between the MUH, the Level IV Multiverse and Other Hypotheses | |
| Testing the Level IV Multiverse | |
| 13 Life, Our Universe and Everything | p. 358 |
| How Big Is Our Physical Reality? | |
| The Future of Physics | |
| The Future of Our Universe-How Will It End? | |
| The Future of Life | |
| The Future of You-Are You Insignificant? | |
| Acknowledgments | p. 399 |
| Suggestions for Further Reading | p. 401 |
| Index | p. 407 |