Our Mathematical Universe: My Quest for the Ultimate Nature of Reality

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality

Our Mathematical Universe is a journey to explore the mysteries uncovered by cosmology and to discover the nature of reality. Our Big Bang, our distant future, parallel worlds, the sub-atomic and intergalactic - none of them are what they seem. But there is a way to understand this immense strangeness - mathematics. Seeking an answer to the fundamental puzzle of why our universe s...

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Title:Our Mathematical Universe: My Quest for the Ultimate Nature of Reality
Author:Max Tegmark
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Edition Language:English

Our Mathematical Universe: My Quest for the Ultimate Nature of Reality Reviews

  • Emma Sea

    I have three things I'd like to say about this book.

    1) I accidentally left it behind at a cafe. When I went back it was gone :(

    Imagine my surprise when I discovered some nice person had found the book and returned it to the library for me. Thank you, kind human!

    2) Tegmark writes fantastically. Wisely, he doesn't try to make the reader *cough me cough* follow his maths, but instead offers URLs for papers offering the mathematical proofs for the concepts he discusses as ad

    I have three things I'd like to say about this book.

    1) I accidentally left it behind at a cafe. When I went back it was gone :(

    Imagine my surprise when I discovered some nice person had found the book and returned it to the library for me. Thank you, kind human!

    2) Tegmark writes fantastically. Wisely, he doesn't try to make the reader *cough me cough* follow his maths, but instead offers URLs for papers offering the mathematical proofs for the concepts he discusses as additional reading, for those so inclined. Tegmark walks us through the information gradually, and interspersing the heavy concepts with light personal anecdotes. His analogies are so clear and this makes the book gripping, understandable, and illuminating.

    3) Tegmark's writing is in fact

    clear that I had a moment of the most exquisite understanding while reading it. I was lying in bed, and I started crying, because for a split second I had an clear conceptualization of the beauty of the mathematical universe, and it was vast and overwhelming and fucking gorgeous. I was weeping with a sublime bliss. It was a very special moment. I doubt I'll ever have another like it, and I'm ok with that. I feel privileged to have had that glimpse.

    Recommended.

  • ☘Misericordia☘ ~ The Serendipity Aegis ~  ⚡ϟ⚡ϟ⚡⛈ ✺❂❤❣

    An unexpectedly deep perusal of the mathematial nature of this baffling world we find ourselces in. Well-written and rich in ideas to ponder on.

    Q:

    ... to me, an electron colliding with a positron and turning into a Z-boson feels about as intuitive as two colliding cars turning into a cruise ship. On microscopic scales, particles schizophrenically appear in two places at once, leading to the quantum conundrums mentioned above. On astronomically large scales —surprise!—weirdness strikes

    An unexpectedly deep perusal of the mathematial nature of this baffling world we find ourselces in. Well-written and rich in ideas to ponder on.

    Q:

    ... to me, an electron colliding with a positron and turning into a Z-boson feels about as intuitive as two colliding cars turning into a cruise ship. On microscopic scales, particles schizophrenically appear in two places at once, leading to the quantum conundrums mentioned above. On astronomically large scales —surprise!—weirdness strikes again:

    (c)

    Q:

    we’ll explore the fascinating relations between computation, mathematics, physics and mind, and explore a crazysounding belief of mine that

    , making us self-aware parts of a giant mathematical object. We’ll see that this leads to a new and ultimate collection of parallel universes so vast and exotic that all the above-mentioned bizarreness pales in comparison, forcing us to relinquish many of our most deeply ingrained notions of reality (с)

    Q:

    I wanted to do my small part to make our planet a better place, and felt that the main problem wasn’t that we lacked technical solutions, but that we didn’t properly use the technology we had. I figured that the best way to affect people’s behavior was through their wallets, and was intrigued by the idea of creating economic incentives that aligned individual egoism with the common good. Alas, I soon grew disillusioned, concluding that

    where you got rewarded for saying what the powers that be wanted to hear. Whatever a politician wanted to do, he or she could find an economist as advisor who had argued for doing precisely that. Franklin D. Roosevelt wanted to increase government spending, so he listened to John Maynard Keynes, whereas Ronald Reagan wanted to decrease government spending, so he listened to Milton Friedman.(c)

    Q:

    Although the book wasn’t really about physics, dwelling more on topics such as how to pick locks and how to pick up women, I could read between the lines that this guy just loved physics. Which really intrigued me. (c)

    Q:

    physics is the ultimate intellectual adventure, the quest to understand the deepest mysteries of our Universe... Physics doesn’t take something fascinating and make it boring. Rather, it helps us see more clearly, adding to the beauty and wonder of the world around us. When I bike to work in the fall, I see beauty in the trees tinged with red, orange and gold. But seeing these trees through the lens of physics reveals even more beauty, captured by the Feynman quote that opens this chapter. And the deeper I look, the more elegance I glimpse: ...

    (c)

    Q:

    I love questions. Especially big ones. I feel so fortunate to be able to spend much of my time tackling interesting questions. That I can call this activity work and make a living from it is just luck beyond my wildest expectations.(c)

    Q:

    There’s no better guarantee of failure than convincing yourself that success is impossible,

    and therefore never even trying. (с)

    Q:

    Read as Макс Тегмарк. Наша математическая вселенная. В поисках фундаментальной природы реальности.

  • Manny

    "

    "

    That's my girlfriend, who's just been unwise enough to let me read her a paragraph of this book. But our guest K, a local nuclear physicist, is more tolerant. "Well," she smiles, "it doesn't sound so bad. A bit exciting, a bit populistic..." Blah blah blah. On the other hand, she isn't a native speaker of English.

    Okay, let's start by getting the bad news out of the way. Max Tegmark's chatty, informal, slightly manic style is on the irritating side, and if you kn"Aaargh!

    "

    "

    That's my girlfriend, who's just been unwise enough to let me read her a paragraph of this book. But our guest K, a local nuclear physicist, is more tolerant. "Well," she smiles, "it doesn't sound so bad. A bit exciting, a bit populistic..." Blah blah blah. On the other hand, she isn't a native speaker of English.

    Okay, let's start by getting the bad news out of the way. Max Tegmark's chatty, informal, slightly manic style is on the irritating side, and if you know some physics it may also give you the impression that you're not going to learn anything from

    . Unless you're working at the cutting edge of the subject, that impression is almost certainly false. When I briefly explained the content to K, I soon found that it wasn't just a question of a few interesting details that she hadn't previously come across. Isolated like most working scientists in her own specialty, the dating of rocks using radioactive isotopes, she hadn't even heard that a major paradigm shift was under way in the theoretical basis of her field. I hope I managed to convince her that the book was well worth looking at.

    Yes, the style is annoying at first, but after a couple of chapters I stopped noticing it. I was in the bar, I'd had a few beers, and my new buddy Max ("Mad Max", he'd said, with an ironic smile) was telling me about his research, life in the charmed inner circle of theoretical physics, and his ideas about the ultimate nature of reality. Every now and then, I managed to get a word in edgeways and complain about some of the more outrageous claims. Max had evidently heard it all before, and deftly batted back my objections. I wasn't exactly convinced, but he made it sound a whole lot more plausible than I'd expected.

    Max's central idea is the Multiverse, where he has been one of a small number of people who's played an evangelical role. More or less considered as science-fiction fifteen years ago, it's now almost respectable; it's astonishing how quickly the change has happened. Max has a cunning scheme in which the Multiverse is presented in four increasingly bolder versions, from Level I to Level IV. I'd seen a fair amount of his material already, particularly in Brian Greene's

    , but Max's presentation is much better. He's worked directly on several of the key ideas, and his hands-on experience makes the stories considerably more believable. He starts off with Level I, which at first sounds innocuous.

    What is there in the universe? he asks. A naive answer might be that it's everything we can see through our telescopes. But even a moment's thought will prompt some revision. Sometimes there are things in the way - clouds of dust and gas along the galactic plane, for example. Surely there's something behind those clouds. Well then, the universe consists of all the things we can see, plus all the similar things we can infer must also be there.

    But what are those other things? Objects getting in the way is just one problem. There are also things that are very distant - so distant that light from them hasn't had time to reach us yet. How far away could these other objects be? That's a complicated question which has to do with the structure of space. Max has done a lot of work with the Cosmic Background Radiation, the light from the Big Bang, to see what it can tell us about that structure. It was fascinating to see him quickly sketching graphs on paper napkins, explaining how he'd analyzed the data and what the results told us. One key finding, as I'd heard before, is that space turns out to be flat. That means it goes on forever, so there are infinitely many more galaxies over the horizon of visibility. In that infinite expanse, every possible history has played out, including histories arbitrarily close to our own. It's sort of Nietzsche's Eternal Recurrence, but in space instead of time. At some unfathomable distance (he makes a rough estimate), there are doppelgangers of Max and me, sitting in the same bar and having the same conversation. An extremely weird conclusion... but, oddly enough, it seems to follow from entirely reasonable premises.

    And this is only Level I. So

    is the universe flat? asks Max rhetorically. Inflation? I say, as I order another round. I've seen many explanations of inflation, but it's hard to decide how seriously I should take them. Max knows all the ins and out, and argues both sides of the case. He collects some beer mats and arranges peanuts on them to demonstrate a simple argument, due to his buddy Alexander Vilenkin, that shows why inflation has to be "eternal". If it happened at all, it more or less had to generate an infinite number of Level I multiverses, all with different physical laws; that's Level II. But did it happen? I ask. What's the evidence? Max scribbles down more pictures of the power spectrum from the CBR, and explains how they fit the inflation scenario while ruling out a bunch of other theories. He really has that talent for showing you what the mathematics means in intuitive terms. I have to admit it: the case looks better than I'd realized.

    Level III is the quantum multiverse: everything that can happen, does happen. I've read several books about this and am more or less convinced already, but Max's version of it is very nice. He describes how he invented the quantum suicide thought experiment and tells me about some clever details that I should have thought of but hadn't. It's even weirder than I'd realized. And now, we need to proceed to Level IV before closing time. But surely we should get some more beer first? I mumble something about how I've maybe had enough, but Max isn't taking no for an answer.

    he says, and before I know what's happened there's a bottle of akvavit on the table between us. He pours out a couple of generous glasses.

    Level IV, it turns out, makes all the others look modest in comparison. Think about the fundamental particles, urges Max. We can see that they are entirely specified by their mathematical properties. So what's the simplest explanation? Reality just

    mathematical structure. Every mathematical structure specifies a reality! But what breathes fire into the equations? I ask. Nothing does! says Max.

    I empty my glass, which is magically full again a moment later. The room seems to be revolving slowly. It's... uh... interesting, I say. But surely there's no way to investigate the idea empirically? Maybe! replies Max, and sketches out yet another graph, this time showing constraints on the Higgs VEV. His explanation is fiendishly clever, unless that's just the effect of the akvavit.

    But surely there are problems with all this? I say weakly, ashamed that I can't immediately come up with half a dozen objections. Max suddenly looks thoughtful and almost sober. The measure problem is very serious, he says. It's a crisis in physics. He and his identical twin, who's just appeared next to him, proceed to explain it. I nod every now and then and try to put my hand over my glass, but he's too quick for me.

    The next morning, I have no memory at all of how I got back to my hotel room, though I dimly recall Max saying something about the dangers of nuclear war, meteorites and evil AI entities. Or was that a dream? I do at any rate have a pile of paper napkins, covered in illegible scrawls and smelling strongly of akvavit.

    Read this book. It's fun.

  • David Katzman

    Before I begin, a brief word about physics

    This is a book of speculative physics. At the same time it is a mostly lucid walkthrough of the latest theories in physics. It's important to distinguish between theories and speculation. Theories are directly testable. Results of the theories are repeatable. Special and General Relativity are examples of theories that have been demonstrated over and over again. A result is calculated from the theory, an experiment is performed...the res

    Before I begin, a brief word about physics

    This is a book of speculative physics. At the same time it is a mostly lucid walkthrough of the latest theories in physics. It's important to distinguish between theories and speculation. Theories are directly testable. Results of the theories are repeatable. Special and General Relativity are examples of theories that have been demonstrated over and over again. A result is calculated from the theory, an experiment is performed...the results match. Where the speculative part of the book comes in to play is where Tegmark attempts to project what he sees as the natural outcome, the logical result of these theories or the "real world" ramifications. That is to say, if the mathematical theories are accurate representations of the real world, then what must this real world look like? Really. He describes these hypotheses as "predictions" of theories.

    As an overview of the current state of physics, this is highly digestible. It's exciting to get a window into the latest thinking in cosmology and subatomic space. I'm going to focus on his speculations. According to Tegmark, the latest theories result in their being a possibility of four different types of multiverses. At the core of these propositions are two contentious suppositions.

    Inflation

    The Schrodinger Equation.

    I think most of us have heard that the universe is "expanding" although I think few of us can really envision what this means. Space is getting larger...like a balloon. However, inflation is different. Imagine taking an object and then duplicating it. Duplicate it exponential times. Then duplicate each of those duplicates exponential times. This is inflation and apparently the hypothesis that inflation occurred immediately after the Big Bang explains several big puzzles of cosmology. (At least for now.) Such as, why the background radiation is

    distributed throughout the universe. With inflation, you get your matter for nothing and the matter comes from Energy (E=MC2) being converted. And inflation can propagate faster than the speed of light. Not all scientist are in agreement; inflation is still a hypothesis, but Tegmark points out that it neatly answers many conundrums. I did see this article recently about

    .

    A lot of "could bes." More on inflation in a bit.

    The Schrodinger Equation is the mathematical formula that captures the state of a quantum particle. What it has always shown is a range of probabilities and never a defined location. When a particle is captured, it is always found in one of the positions defined by the Schrodinger Equation, and the probability of finding it in any given position can be calculated with this formula before you locate it. The Schrodinger Equation has been demonstrated to be accurate over and over again through experimentation.

    The mind-bending issue arises because physicists haven't been able to explain why the equation "collapses" when a particle is observed. That is, before observation, a particle exists only in a state of probability, it does not have an exact position (or velocity). But the moment it is observed, it assumes instantly a location. You've likely have heard of the Schrodinger Cat thought experiment (the cat being both alive and dead until observed) that demonstrates the absurdity and mind-bending nature of this result. If not,

    .

    How is it that the act of observation (or measurement) causes the quantum particle to assume a state? The common solution called the Copenhagan Interpretation simple says

    but not

    . Observation closes the loop, end of story. What is the mechanism that causes an interaction with a probability sphere to collapse into actuality? There are now quite a few other interpretations. Such as that it never collapses, only seems to. Tegmark sees the most coherent solution to this to be the Everett Many-World's Interpretation. More on that in a bit.

    As a result of both the concept of inflation and the difficulty in explaining how the Schrodinger Equation relates to reality, Tegmark suggests that there are four possible conditions that may describe the universe(s). But all are preceded by the idea that if inflation is correct then space must be infinite. This an important assumption and one that there is really zero proof of, but it makes for interesting conceptual thinking. These are his "Universe Levels."

    ONE: Given space as infinite there are infinitely many "universe islands" like our own. That would mean there are infinite beings just like us but different in some small or large aspects. These beings are beyond the distance that light could even travel to us since the Big Bang. In some universes, our "duplicates" don't exist at all. In others, our species doesn't exist or our planet. In others, everything exists exactly as it does except your eyes are purple. He claims this is the natural outcome of having infinite space along with fairly similar starting conditions. This reminds me a lot of Nietzche's Eternal Recurrence hypothesis.

    TWO: Same as one except that in these universe islands, the laws or constants of physics might be different. He uses the "fine-tuning argument" as some justification for this view. More on fine-tuning in a bit. And...each universe island may have had it's own Big Bang moment.

    THREE: Multiverse time....Tegmark's preferred explanation of the Schrodinger Equation is that at each moment in time when a particle can exist in different states, the universe splits into a unique universe for each potential state. All states occur and then due to "decoherence" they separate and cannot interact with each other. There is no state vector/equation collapse...all states occur and split us into multiple universes. These universe all exist "simultaneously" (doesn't really mean anything because all time exists at the same time) in an infinite Hilbert Space. The Hilbert Space is basically the uber-universe. All time and space as an unmoving object.

    FOUR: The Universe is a mathematical object. This is his pet preferred hypothesis. My interpretation of it is something like this: Particles can be fully described mathematically. The universe can be thought of as a collection of particles in a particular arrangement. Therefore, the universe is much like a computer program, an arrangement of numbers. The matrix. An individual life form is a complex mathematical object traveling within this mathematical universe. Kind of like a parenthesis in a larger formula Universe = (being 1) + (being 2) + etc. He essentially says that consciousness (and free will) is an illusion and is merely the sensation of experiencing the split into multiverses (I'm given the impression that he believes in Levels 2, 3, and 4 combined). And here's where it gets really weird (abstract/abstruse/absurd), he suggests that all that exists

    math. A sort of reverse Platonism. Somehow when mathematical formulas are complex enough, they become self-aware and perceive the mathematical universe as a reality. Even basic mathematical systems exist in their own universe, albeit one not complex enough for life. He gives the example of how videos are constructed from ones and zeros but give us the impression that they are real images. The universe is kind of like that. A self-contained mathematical formula that simulates reality. Although he actually doesn't believe in the simulated universe hypothesis, it seems to me to be the same thing. Math formulas take on a life of their own. Jeff Noon wrote a book called

    that was about math formulas coming to life as I recall.

    Unfortunately, although Tegmark presents this model, he really can't explain it. It is certainly intriguing and unanswered what reality is and how we perceive it as such...and how we could (if we do) have free will. However, it is even harder to explain how an abstract structure (a "computationally valid" mathematical formula) could somehow form a reality. Math is pure abstraction. So how could an abstraction perceive? How could an abstraction create a form? Saying something is "emergent" doesn't explain it, it's just saying that you can't explain it.

    The universe may be imaginary, but it sure damn feels real. How could a mathematical formula feel real? How could math develop the ability to "feel." His hypothesis doesn't really explain anything. He says the theory doesn't need to explain consciousness...that's someone else's job.

    One justification he has for level 2 universe is the "fine-tuning" argument. I'm no mathematician and Tegmark is one of the top in the world apparently. So I say this with humbleness that I may be wrong...but I see a profound gulf in one simple area. It is a misunderstanding of the relationship between probability and "real" life. If something has actually happened, i.e., exists, then the probability of it happening is 100%. There is no probability. Before it occurs, there is a probability. Therefore, when the so-called "fine-tuning argument" is used as a factor to sell a theory, my back gets up. The fine tuning argument states that some constants are so "finely tuned" to support life, that either God tuned them (Tegmark doesn't say this but creationists do)...or there is a significant theory missing to explain why the quantities are such as they are so specifically. For example, if dark energy energy was minimally less dense then the universe would have flown apart already. If dark energy was slightly denser then it would have collapsed. Of course, dark energy hasn't even been proven to exist yet...although...

    Tegmark believes all these constants will be justified mathematically at some point. Lot of belief there. But regardless of why the constants are in the state they are, they

    . There is no "chance" or probability that they could be anything else. So regardless of how you explain them, there is no proof that they could anything other than what they are, which means the probability of them being what they are is 1. It's not amazing that the odds turned up life. Life is. The constants are. It wasn't god who made them, nature did. I'm not saying we won't necessarily learn more which will explain why some values are what they are. I'm saying that the fine-tuning argument falls apart because probability is not relevant to the outcome. There are no "other states."

    In the end, this book is both lucid and whimsical. It's quite entertaining and rather farfetched at the same time. After I had completed most of this review I went and read a few professional reviews on the NYTimes website, The Guardian, etc. All of these reviewers find the multiverse theory to still be bunk and unprovable and/or the mathematical universe idea to be absurd. So take it all with a grain of salt. Still, a fun read.

  • WarpDrive

    This is a complex and very interesting book, addressing many important questions about the fundamental nature of reality.

    The author adopts (and convincingly explains) a particular version of mathematical Neo-Platonism stating that reality is essentially nothing but mathematical structures. His position might be classified as a form of mathematical “monism” (as it essentially denies ontological reality to anything except mathematical objects). From a philosophical perspective, the author can be

    This is a complex and very interesting book, addressing many important questions about the fundamental nature of reality.

    The author adopts (and convincingly explains) a particular version of mathematical Neo-Platonism stating that reality is essentially nothing but mathematical structures. His position might be classified as a form of mathematical “monism” (as it essentially denies ontological reality to anything except mathematical objects). From a philosophical perspective, the author can be allocated to what is termed "Ontological Structural Realism", whose main statement (crudely expressed) is the claim that there are no ‘things’ as such, and that “structure” is all there is. This approach has proved quite attractive to a few philosophers of physics, philosophers of mathematics (such as Stewart Shapiro) and physicists, and I personally find it quite compelling (my Neo-Platonism was (at least, until I finished reading this book) more of the Heisenberg or Roger Penrose flavour – the latter famously positing the existence of three worlds – the world of conscious perception, the physical world and the Platonic world of mathematical forms, interconnected in a complex fashion).

    The author starts his argument by observing, in a convincing way, that the very fabric of our physical world appears to be fully describable in a mathematical way. Look at "space" itself, for example, whose only intrinsic properties are "mathematical" (such as dimensionality, curvature and topology); and this equally applies to the “stuff” our physical world is made of – the only intrinsic properties of elementary particles are mathematical (charge, spin and lepton number, for example).

    I think that the author here is correct, and I must add that this debunks the myth of the Kantian “thing in itself” (das Ding an sich), this mysterious “essence” which Kant confusingly opposed to the phenomenological behaviour of the object. The most fundamental entity in classical quantum mechanics, the wave function, can be considered, after all, a mathematical object which "lives" in the infinite-dimensional place called Hilbert space. Fields can be considered mathematical objects, or at least spatially defined clusters of information.

    Just as a side note, I would have expected the author to also explore the concept of entropy, which is a fundamental, emergent phenomenon ultimately driving the time arrow evolution of the Universe, and which again is nothing but a “mathematical”/statistical concept based on the measure of the number of specific ways in which a system may be arranged (commonly understood as a measure of “disorder”). This would have further confirmed his theory.

    I tend to share the author's views here: the more I have studied quantum mechanics and relativity, the more I have started to feel that the deeper you dig, the more this physical “stuff” starts looking like an illusion, as its fundamental core nature appears to be nothing but information and structure... “mathematics”, if you wish.

    After all, particles are excitations of the corresponding quantum fields (which are not “physical” in the traditional meaning of the term), or they can be defined, in modern particle physics, as "elements of an irreducible representation of the corresponding symmetry group".

    And, after all, what does the word “physical” mean ? Is it what it can be perceived by our limited sensory organs ? Well, I think that this old-fashioned concept of "physical world" has been made obsolete for quite some time.

    Moreover, the author compellingly and beautifully explains that we DISCOVER such structures fully describing reality, we do NOT invent them – all we invent is the NOTATION for describing such structures. A structure is defined as a set of abstract entities with a set of relations between them, whereby the only properties of these entities are those embodied by the relations between them: and it is clear to the author, from the latest developments in science in the last 90 years, that the properties of nature stem not from properties of its ultimate building blocks, but from the RELATIONS between such building blocks - and I find myself in substantial agreement with this view.

    The author, after discussing the point that the fundamental properties of reality appear to be mathematical, addresses the relationship between such mathematical structures describing reality, and reality itself. What is such relationship ? Is such relationship an isomorphism, or is it an identity? In other words, is mathematics the language of nature, or IS IT nature itself ? Here, the author thesis is that, if two structures are “equivalent” (where equivalence is defined as the existence of a one-to-one relationship between the two structures, preserving all relations), they are the same and they describe the one and the same thing. The author's conclusion is: “this means that if some mathematical equations completely describe both our external physical reality and a mathematical structure, then our external physical reality and the mathematical structure are one and the same”. Here the author, disappointingly, does not really develop this crucial point in any satisfactory detail: he refers to the work (a master thesis) done by a certain Marius Cohen (page 280 of the book), and this is all we have. Not enough, and I was left profoundly dissatisfied here - I will try and retrieve Marius Cohen's work, but that such a crucial point was not developed in more detail remain a weakness of this book, in my opinion.

    But overall his points are very compelling, beautifully addressed and explained, and fascinating – a real intellectual challenge to our everyday perspective of reality.

    There is so much to discuss here in relation to this book - I feel I could write a book on this book, as there are so many different interesting themes and fascinating points discussed by the author.

    Just as an example, the author beautifully highlights how fundamental the property of “symmetry” is in the characterisation of mathematical structures and of reality. Also, the author addresses the issues raised by the concept of “infinity” and by incompleteness (as raised by Godel), elaborating, as a response to such issues, his initial “Mathematic Universe Hypothesis” into a "Computable Universe Hypothesis" (CUH), which posits that all COMPUTABLE mathematical structures exist. Fascinating, I must say.

    Where I disagree with him however is in his own enthusiasm for the Multiverse interpretation of Quantum Mechanics (Level III Multiverse in his book) - I found his treatment of this specific issue quite weak, and the author also makes the mistake (unfortunately still common) of interpreting Bell's inequality experimental results as ruling out hidden variables – this is not correct – what has been ruled out is the existence of hidden LOCAL variables, so alternative interpretations (in particular, the de Broglie-Bohm theory, which I personally find quite attractive, and which elegantly tries to address the measurement problem), are still not ruled out. I realize though that this particular interpretation sits in a minority position, and many do not agree with it at all.

    Overall, it is a great book, challenging, rich and fascinating. It even explores, with fascinating insights, hard problems such as the nature of consciousness, the issue of the potential future "singularity", and our place and our meaning in the Universe.

    To finish, I would have loved a more quantitative treatment of some of the items discussed in the book (at least in areas such as quantum mechanics and symmetry) but I guess this is part of the current commercially-driven trend of dumbing down the maths in order to enlarge the potential audience (and therefore the potential customer base) - this is (together with the couple of other shortcomings I highlighted above) why I could not give this otherwise great book a full 5 star rating.

  • Tara

    This book covers quite a bit of material, topics ranging from astronomy, cosmology, and quantum physics, to far more precarious stuff such as the level IV multiverse and the “Mathematical Universe Hypothesis,” which Tegmark champions rather emphatically. In the beginning of the book (page 13), he includes a helpful diagram that clearly states which chapters are considered “mainstream,” “controversial” and even “extremely controversial.” He’s very upfront about which parts of his book fall into w

    This book covers quite a bit of material, topics ranging from astronomy, cosmology, and quantum physics, to far more precarious stuff such as the level IV multiverse and the “Mathematical Universe Hypothesis,” which Tegmark champions rather emphatically. In the beginning of the book (page 13), he includes a helpful diagram that clearly states which chapters are considered “mainstream,” “controversial” and even “extremely controversial.” He’s very upfront about which parts of his book fall into which category, so I don’t believe we should fault him overmuch for being too speculative. I mean, in order for science to

    , for it to explore radical new territory and discover equally radical new truths, radical new hypotheses are absolutely essential. Even, or perhaps especially, the ones that seem a little bananas. As Tegmark points out, it is

    After all, we don’t want to be like Mac on

    (best show ever!), slam science for barking up the wrong tree sometimes, and end up hating all the “stupid science bitches,” now do we?

  • BlackOxford

    It starts with Plato, this idea that the universe is a mathematical expression, populated by objects which are (often imperfect) copies of abstract ‘forms’ (the most perfect of which are numbers), which in turn interact according to strict rules of geometry and aesthetic necessity.* More importantly it was Plato who suggested that things are not what they seem. What we are able to perceive are distorted manifestations of eternal truths which are permanently beyond our grasp,

    It starts with Plato, this idea that the universe is a mathematical expression, populated by objects which are (often imperfect) copies of abstract ‘forms’ (the most perfect of which are numbers), which in turn interact according to strict rules of geometry and aesthetic necessity.* More importantly it was Plato who suggested that things are not what they seem. What we are able to perceive are distorted manifestations of eternal truths which are permanently beyond our grasp, leaving open, therefore, the meaning of what we glibly call reality. In a sense he was the first post-modernist in pointing out that reality isn’t even verifiable much less obvious through our observation and experience.**

    Hence the general preference of ‘hard’ scientists, like physicists, for Aristotle rather than Plato. Aristotelians like to rely on their senses; they crave observational data, facts. They look down on Platonists, including mathematicians, just as Freudians look down on Jungians, and for the same reason. They simply can’t abide the idea that eternal laws could generate facts - whether those laws are of the Collective Unconscious or the Eternal Forms. For science, facts precede laws both logically and ontologically. Facts are real. Laws are inferred regularities, evolving theories. As such they can only be considered as expedient hypotheses.

    So the conflict of fact and law has been fought for two and a half millennia with no victory for either side in sight. Tegmark‘s book is a chronicle of a recent skirmish in which the Platonic standard is held high. Tegmark is a bit coy but he puts forth the historical Platonist party line clearly as:

    This particular battle is part of a much larger war, in a sense a cosmic war, called metaphysics. Metaphysics is the discipline of thinking about ‘what’s really there.’ The main difficulty in the metaphysical war from an intellectual point of view is the same as in any other war, namely that the cause one is fighting for justifies its own arguments. Each side has an implicit criterion of validity which,

    , produces precisely the results to show success by that criterion and failure by the opposing view. All wars in metaphysics are, therefore, ‘just’ - for both sides.

    To oversimplify, but not by much, mathematicians really appreciate patterns. They search for them constantly and revel in the thought that they are already there waiting to be discovered. While scientists are also attuned to patterns, however, they know that scientific progress is most often generated not by taking patterns at face value but by concentrating on the apparent exceptions to patterns which are the source of new theoretical patterns. The standards of evidence in the two disciplines are very different.

    So for the scientist, the weirdness of quantum physics and black holes is a spur to create a new theory, to confront a resistant universe with observational challenges. For the mathematician the challenge is to coax out the already existing pattern within the structure of his mathematical representations and techniques. One man’s Mede is another man’s Persian, to coin a phrase. Each considers the other to be somewhat Gnostic in their reliance on esoteric knowledge and their distinctive forms of mistrust of the universe - the scientific hesitation about generalization, and the mathematical disdain for the particular.

    It makes no sense trying to reconcile the two views because, as an observant philosopher might point out, each already contains a presumption about what reality is and these presumptions are validated by there very use not by their results, which are fundamentally incomparable. This incomparability is not rational; it is aesthetic, that is, pre-rational. The aesthetic is the foundation upon which each constructs his own edifice of Reason.

    The bottom line then is that while

    is an entertaining as well as informative read, its real value is probably to confirm the views already held by the Platonist choir. It is only likely to irritate the Aristotelians who already think that mathematics has ruined real science by its entirely abstract reasoning. To the latter, Tegmark will not seem merely “crazy-sounding” but crazy

    *It turns out that Plato was more correct than even he could have thought according to the latest science:

    **For a rather wonderful tale of the Platonic view of mathematics, see:

  • David

    The first half of this book is a review of modern physics on the macro and micro scales. The second half of this book is a discussion of the author's speculation, that the universe is a mathematical structure. Max Tegmark is quite clear--he is not saying that the universe is

    by mathematics, but that the universe

    mathematics. He calls this the "Mathematical Universe Hypothesis", or "MUH" for short.

    Tegmark asserts that this idea is a testable, falsifiable hypothesis. I did not find t

    The first half of this book is a review of modern physics on the macro and micro scales. The second half of this book is a discussion of the author's speculation, that the universe is a mathematical structure. Max Tegmark is quite clear--he is not saying that the universe is

    by mathematics, but that the universe

    mathematics. He calls this the "Mathematical Universe Hypothesis", or "MUH" for short.

    Tegmark asserts that this idea is a testable, falsifiable hypothesis. I did not find the experimental test, but perhaps I simply missed it. To be perfectly frank, I don't even understand his reasoning.

    The last chapter of the book switches gears entirely, and discusses the existential threats to human survival. Things like asteroid collisions, eventual expansion of the sun, and so on. Then the book describes the two most immediate threats to human existence. The first is a nuclear war. And the second is--are you sitting down for this?--the singularity, where artificial intelligence takes over the world.

    I didn't read this book--I listened to the audiobook, read by Rob Shapiro. He did an excellent job, giving the narration an aura of authenticity. It's just too bad that the content of the book is not as good as the narration.

  • Manuel Antão

    If you're into stuff like this,

    The Stages of Truth: "Our Mathematical Universe - My Quest for the Ultimate Nature of Reality" by Max Tegmark

    Forget about Tegmark’s 4 levels. The stages of truth I can remember are:

    • Old Greeks saying "We only see a faint reflection of reality", i.e. we have observation, and that's flawed.

    • Old Chinese saying "All we have is observation. Reality is observation, and observation is a function of the

    If you're into stuff like this,

    The Stages of Truth: "Our Mathematical Universe - My Quest for the Ultimate Nature of Reality" by Max Tegmark

    Forget about Tegmark’s 4 levels. The stages of truth I can remember are:

    • Old Greeks saying "We only see a faint reflection of reality", i.e. we have observation, and that's flawed.

    • Old Chinese saying "All we have is observation. Reality is observation, and observation is a function of the human form" which is a most interesting thing. They state that sense is inherently limited by our being. Excellent.

    • Descartes saying "to know stuff, you must have doubt. Knowledge is developed by doubt" which means testing: the scientific method. Which he didn't invent, but put on a logical footing. And also founding it all on "I think, therefore I exist".

    • Karl Popper saying that the essential property of what's knowable is what can be tested, questioned. This continues from Descartes and quite a few more in between including Kant obviously who's really cool but illegible.

  • Gendou

    The thesis of this book is nothing but a giant exercise in circular reasoning.

    Max Tegmark calls his idea the Mathematical Universe Hypothesis, that the external physical reality described by the Theory of Everything is a mathematical structure. He starts off by, I kid you not, assuming that the external physical reality is a mathematical structure.

    This radical idea, that reality is "made of math" is embodied in the title of the book, but nowhere within the pages is there

    The thesis of this book is nothing but a giant exercise in circular reasoning.

    Max Tegmark calls his idea the Mathematical Universe Hypothesis, that the external physical reality described by the Theory of Everything is a mathematical structure. He starts off by, I kid you not, assuming that the external physical reality is a mathematical structure.

    This radical idea, that reality is "made of math" is embodied in the title of the book, but nowhere within the pages is there any logical argument in for the idea. It's merely assumed.

    This assumption is necessary to apply the rule of isomorphism to the external physical reality and the Theory of Everything, an undertaking which is supposed to provide support for the Mathematical Universe Hypothesis. But you can't start out assuming the thing you're trying to prove!

    Mad Max, as he's known in the physics community, has the gall to let this glaring logical error stand uncorrected. On his Facebook page, I asked him about this circular reasoning, and he dodged the question but admitted the starting assumption.

    It's infuriating that someone can publish a book claiming the universe is "made of math" and have no argument inside the book to support this outrageous claim. This isn't speculative. It's unscientific.

    Aside from his own pet theory, he presents an out-of-date picture of the Everett's Many Worlds interpretation as thought it were a unique theory from other interpretations of quantum mechanics. This is wrong.

    There's also a whole chapter full of bogus Anthropic arguments, like quantum suicide, etc. Max has got to be the sloppiest thinker who's eyes I've ever had the displeasure of being forced to see the world through.

    The first half of the book does contain some half-way decent introduction to cosmology, but you're better off reading a real author like Stephen Hawking or even Brian Greene.

    See also

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