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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 seems so mathematical, Tegmark proposes a radical idea: that our physical world not only is described by mathematics, but that it is mathematics. This may offer answers to our deepest questions: How large is reality? What is everything made of? Why is our universe the way it is?
Table of Contents
Preface
1 What Is Reality?
Not What It Seems • What’s the Ultimate Question? • The Journey Begins
Part One: Zooming Out
2 Our Place in Space
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
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
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
What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation
6 Welcome to the Multiverse
The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup
Part Two: Zooming In
7 Cosmic Legos
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
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 Three: Stepping Back
9 Internal Reality, External Reality and Consensus Reality
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
Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure?
11 Is Time an Illusion?
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
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
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
Suggestions for Further Reading
Index
Table of Contents
Preface
1 What Is Reality?
Not What It Seems • What’s the Ultimate Question? • The Journey Begins
Part One: Zooming Out
2 Our Place in Space
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
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
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
What’s Wrong with Our Big Bang? • How Inflation Works • The Gift That Keeps on Giving • Eternal Inflation
6 Welcome to the Multiverse
The Level I Multiverse • The Level II Multiverse • Multiverse Halftime Roundup
Part Two: Zooming In
7 Cosmic Legos
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
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 Three: Stepping Back
9 Internal Reality, External Reality and Consensus Reality
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
Math, Math Everywhere! • The Mathematical Universe Hypothesis • What Is a Mathematical Structure?
11 Is Time an Illusion?
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
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
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
Suggestions for Further Reading
Index
432 pages, Hardcover
First published January 7, 2012
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February 24, 2014
"Aaargh! No! Make it stop!"
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 Our Mathematical Universe. 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 The Hidden Reality, 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 why 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. Du sa nåt om att du bott in Sverige? 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 is mathematical structure. Every mathematical structure specifies a reality! But what breathes fire into the equations? I ask. Nothing does! says Max. Skål! 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.
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 Our Mathematical Universe. 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 The Hidden Reality, 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 why 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. Du sa nåt om att du bott in Sverige? 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 is mathematical structure. Every mathematical structure specifies a reality! But what breathes fire into the equations? I ask. Nothing does! says Max. Skål! 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.
March 23, 2014
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 so 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.
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 so 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.
August 29, 2023
The Mind of God
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: “a crazy-sounding belief of mine that our physical world not only is described by mathematics, but that it is mathematics, making us self-aware parts of a giant mathematical object... our physical world not only is described by mathematics, but that it is mathematics: a mathematical structure, to be precise.”
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, quelle surprise, 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 Our Mathematical Universe 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 tout court.
*It turns out that Plato was more correct than even he could have thought according to the latest science: https://www.sciencefocus.com/news/sci...
**For a rather wonderful tale of the Platonic view of mathematics, see: https://www.goodreads.com/review/show...
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: “a crazy-sounding belief of mine that our physical world not only is described by mathematics, but that it is mathematics, making us self-aware parts of a giant mathematical object... our physical world not only is described by mathematics, but that it is mathematics: a mathematical structure, to be precise.”
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, quelle surprise, 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 Our Mathematical Universe 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 tout court.
*It turns out that Plato was more correct than even he could have thought according to the latest science: https://www.sciencefocus.com/news/sci...
**For a rather wonderful tale of the Platonic view of mathematics, see: https://www.goodreads.com/review/show...
January 2, 2018
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: if you intuitively understand all aspects of black holes, I think you’re in a minority of one, and should immediately put down this book and publish your findings before someone scoops you on the Nobel Prize for quantum gravity.(c)
Q:
we’ll explore the fascinating relations between computation, mathematics, physics and mind, and explore a crazysounding belief of mine that our physical world not only is described by mathematics, but that it is mathematics, 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 economics was largely a form of intellectual prostitution 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: ... the trees ultimately come from stars, and ... studying their building blocks suggests their existence in parallel universes.(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 ��егмарк. Наша математическая вселенная. В поисках фундаментальной природы реальности.
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: if you intuitively understand all aspects of black holes, I think you’re in a minority of one, and should immediately put down this book and publish your findings before someone scoops you on the Nobel Prize for quantum gravity.(c)
Q:
we’ll explore the fascinating relations between computation, mathematics, physics and mind, and explore a crazysounding belief of mine that our physical world not only is described by mathematics, but that it is mathematics, 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 economics was largely a form of intellectual prostitution 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: ... the trees ultimately come from stars, and ... studying their building blocks suggests their existence in parallel universes.(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 ��егмарк. Наша математическая вселенная. В поисках фундаментальной природы реальности.
February 17, 2020
Before I begin, a brief word about physics from a ninja.
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 evenly 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 discovery that could be inflation.
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, here's a description of it.
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 it does but not why. 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 its 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 is 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 Nymphomation 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 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...there was this recently. 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 are. 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.
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 evenly 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 discovery that could be inflation.
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, here's a description of it.
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 it does but not why. 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 its 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 is 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 Nymphomation 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 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...there was this recently. 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 are. 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.
February 6, 2016
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.
February 4, 2021
3.5 stars. 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 work, 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 “amusing how strong the conformist herd mentality is among many physicists, given that we all pay lip service to thinking outside the box and challenging authority.”
After all, we don’t want to be like Mac on It’s Always Sunny in Philadelphia (best show ever!), slam science for barking up the wrong tree sometimes, and end up hating all the “stupid science bitches,” now do we?
After all, we don’t want to be like Mac on It’s Always Sunny in Philadelphia (best show ever!), slam science for barking up the wrong tree sometimes, and end up hating all the “stupid science bitches,” now do we?
November 23, 2014
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 described by mathematics, but that the universe is 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.
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.
December 16, 2021
I'm a braid in spacetime, woven intricately and composed of probably multidimensional, definitely complex sub-structure strands. And I want to take it apart, unfold it, let it loose. But I'm no God. So I can only do this in my imagination, and as colorful as my imagination otherwise is, this cosmic, multi-dimensional braid eludes it. Yet, I know there is something incomprehensibly fundamental about each strand.
Tegmark seems to believe that the most fundamental structure that all of spacetime is built upon is purely mathematical. Interestingly, he is a proponent of Everett's many worlds theory which he classifies as a level 3 multiverse. And this brings me to his classification of multiverse into four levels, and it's the level four multiverse that is most relevant to this book. What in the name of everything that is holy is a level four multiverse you ask? Behold:
The Mathematical Universe Hypothesis implies that mathematical existence equals physical existence.
This means that all structures that exist mathematically exist physically as well, forming the Level IV multiverse.
This is a radical claim to say the least. Tegmark here isn't saying that the physical world can be represented by a mathematical structure. He is stating that our physical reality is a mathematical structure. And that all structures that exist mathematically exist physically as well. I have enough reason to doubt that most physicists and mathematicians would say this is complete baloney. Tegmark himself confesses to having recieved several disapproving mails over the years, and apparently, a distinguished physicist even called this crackpot physics.
Tegmark believes even we are purely mathematical and calls any intelligent species Self-Aware-Substructures. I am not an egomaniac, if I am a mathematical self-aware sub-structure, so be it. Given my lower level of physics knowledge and humble qualification of just having completed a masters in physics, I decided to give this whole theory the benefit of doubt even though my instincts were screaming at me not to. As a physics student, I obviously have come across mathematical quantities associated with real world structures that we simply do not know how to define in a physical sense. Spin is a great example - it has no classical analogue. People more familiar with particle physics will also recognise isospin. Not only did isospin help in the discovery of more particles, it also exhibits general patterns of conservation when we examine allowed particle reactions. Yet, it is just a number and if asked to describe what it is in a physical sense, I am afraid nobody has the answer.
While it may seem that these examples lend to Tegmark's claims, I simply believe it is a problem of human incomprehension. I still cannot help but think of mathematics as a descriptive language. The claim that all of reality is purely mathematical is too far- fetched and unfathomable to my poor, mortal brain. Tegmark seems to echo the Pythagorean belief about the link between physical reality and mathematics, and while it may have held some weight from the the ancient to enlightenment times, it just seems absurd now. But it sure is a fun thing to think about and makes for a wacky and an extremely interesting read.
P.S. What's with physicists adding random pictures of their family and children in their books? Stop. Just put it on social media like normal people.
Tegmark seems to believe that the most fundamental structure that all of spacetime is built upon is purely mathematical. Interestingly, he is a proponent of Everett's many worlds theory which he classifies as a level 3 multiverse. And this brings me to his classification of multiverse into four levels, and it's the level four multiverse that is most relevant to this book. What in the name of everything that is holy is a level four multiverse you ask? Behold:
The Mathematical Universe Hypothesis implies that mathematical existence equals physical existence.
This means that all structures that exist mathematically exist physically as well, forming the Level IV multiverse.
This is a radical claim to say the least. Tegmark here isn't saying that the physical world can be represented by a mathematical structure. He is stating that our physical reality is a mathematical structure. And that all structures that exist mathematically exist physically as well. I have enough reason to doubt that most physicists and mathematicians would say this is complete baloney. Tegmark himself confesses to having recieved several disapproving mails over the years, and apparently, a distinguished physicist even called this crackpot physics.
Tegmark believes even we are purely mathematical and calls any intelligent species Self-Aware-Substructures. I am not an egomaniac, if I am a mathematical self-aware sub-structure, so be it. Given my lower level of physics knowledge and humble qualification of just having completed a masters in physics, I decided to give this whole theory the benefit of doubt even though my instincts were screaming at me not to. As a physics student, I obviously have come across mathematical quantities associated with real world structures that we simply do not know how to define in a physical sense. Spin is a great example - it has no classical analogue. People more familiar with particle physics will also recognise isospin. Not only did isospin help in the discovery of more particles, it also exhibits general patterns of conservation when we examine allowed particle reactions. Yet, it is just a number and if asked to describe what it is in a physical sense, I am afraid nobody has the answer.
While it may seem that these examples lend to Tegmark's claims, I simply believe it is a problem of human incomprehension. I still cannot help but think of mathematics as a descriptive language. The claim that all of reality is purely mathematical is too far- fetched and unfathomable to my poor, mortal brain. Tegmark seems to echo the Pythagorean belief about the link between physical reality and mathematics, and while it may have held some weight from the the ancient to enlightenment times, it just seems absurd now. But it sure is a fun thing to think about and makes for a wacky and an extremely interesting read.
P.S. What's with physicists adding random pictures of their family and children in their books? Stop. Just put it on social media like normal people.
May 28, 2014
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 http://thephysicspolice.blogspot.com/...
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 http://thephysicspolice.blogspot.com/...
June 7, 2017
The title makes one feel this will be a daunting read and at times it is, but Tegmark starts out in a clear concise fashion reviewing current cosmological concepts. He provides detail on mapping the cosmic microwave-background radiation including his own considerable involvement. He describes how it mirrors our present day universe which maintains the background radiation’s uniform temperatures and densities. This leads to Alan Guth’s theory of inflation which explains the uniformity, flatness and the enormous size of the universe.
Tegmark accepts inflation as entirely consistent with everything we know but he admits to having some qualms. If gravity waves were proven, he would be completely convinced. Still he is comfortable using inflation to build his model. From here on Tegmark begins departing from what he considers widely accepted ideas. He sees inflation coming before the big bang not after as it is usually presented. Thus the universe did not start out as some super dense super-hot entity. The heat was caused by inflation. The big bang occurred when inflation stopped.
Tegmark believes inflation is always occurring in some region of space, a controversial idea called eternal inflation. This creates an infinite but still expanding universe contained in a finite volume. Those areas outside of our observable universe Tegmark calls Level I parallel universes. There are an infinite number of these parallel universes, some still inflating. The nomenclature here is what is unusual. Many physicists believe the universe is infinite, but dividing the portions we can’t see into Level I parallel universes allows Tegmark to build his model. Level I parallel universes share our laws of physics and physical constants.
Tegmark next posits the Level II multiverse, his term for a concept popular with string theorists. These are other finite volumes containing their own infinite parallel universes with their own laws of physics, physical constants and particle relationships. The Level II multiverse addresses the anthropic principle which holds that our universe seems to be fine-tuned to support life. With infinite universes just as with infinite planets one is bound to be just right for us.
Next Tegmark explores the quantum world. Everything is made of particles (quarks, electrons, etc.) but all we know about them are the mathematical values of their attributes (charge, spin, etc.). These values arrayed in space are described by quantum field theory. Tegmark believes that there is an underlying layer of reality that we perceive as particles; perhaps strings, quantum loops or something not yet thought of. Coincidentally while reading this my January 2017 issue of Scientific American arrived with an article about a group of physicists working on quantum gravity who are collaborating with scientists involved in quantum computer development. They have formed a program called “It from Qubit” to look for an underlying structure of information bits held together by entanglement that would generate space and time as its emergent property.
Tegmark’s take on quantum mechanics eschews the Copenhagen interpretation. He is smitten with Schrodinger’s equation, but does not believe the wave function ever collapses which leads to the many-worlds theory of Hugh Everett III. This theory holds that all outcomes are real not just those that are observed. Thus reality splits. Tegmark calls these separate realities Level III parallel universes. He points to small surveys that show more physicists now believe in the many-worlds theory than in the formerly popular Copenhagen interpretation, although many don’t ascribe to either theory. Tegmark describes his discussions with the famous theoretical physicist John Wheeler who died at 96 in 2008. Wheeler who coined the term black hole postulated the one electron universe that inspired his student Richard Feynman even if Feynman did not completely accept the idea. Hugh Everett and Richard Feynman had been Wheeler’s doctoral students at Princeton. The many-worlds theory was Hugh Everett’s doctoral thesis which Wheeler championed.
From this point on, Tegmark leaves traditional thinking completely behind. He posits the Level IV multiverse which is comprised of mathematical structures. These are Tegmark’s ultimate reality. Each structure generates a different universe. The mathematical structures could be anything, say a cube where the corners are connected to each other. A structure that would yield our universe would be much more complicated. Tegmark’s mathematical reality is a relational reality. “… the properties of the world around us stem not from the properties of its ultimate building blocks, but from the relations between these building blocks”. He offers an analogy to the brain in which it is the connections between neurons that form ideas not the properties of the individual neurons. It is the relationship between the neurons that yield consciousness just as the relationships in the mathematical structure yield the universe we perceive.
Tegmark points to symmetries as an important way mathematical structures produce the physical properties we perceive. Tegmark references German mathematician Emmy Noether who proved that continuous symmetries of mathematical structures produce conservation laws of physics yielding the physical constants. For example energy corresponds to time translation symmetry, momentum to space-translation symmetry, angular momentum to rotation symmetry, electric charge to a particular symmetry of quantum mechanics. Nobel Prize winner Eugene Wigner showed these symmetries dictated all the quantum properties of particles such as spin and mass.
The Level IV multiverse would not just have different physical constants like Level II but different equations. This answers John Wheeler who wondered, “Why these particular equations, why not others.” Or as Eugene Wigner put it “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious…there is no rational explanation for it.” Or as Stephen Hawking asked, “What is it that breathes fire into the equations and makes a universe for them to describe?” Tegmark answers with the Level IV multiverse.
So what can we make of all this? I have no idea how valid Tegmark’s thesis is, but I thoroughly enjoyed his presentation in which I learned about new concepts and lines of thought. In the 1930’s John Wheeler studied under Niels Bohr and worked alongside Einstein, two men who led revolutionary thinking in physics 100 years ago. Wheeler encouraged Tegmark writing him, “...behind quantum mechanics lies some deep and wonderful principle to be discovered…The likelihood of such a discovery is surely proportional to our belief that there is something there to be discovered.” Before we dismiss Tegmark’s wild abandon in his search for a mathematical universe, we should keep in mind that the ideas of John Wheeler, his famous students Richard Feynman and Hugh Everett, his mentor Niels Bohr and associate Albert Einstein were all considered silly at one point.
Tegmark accepts inflation as entirely consistent with everything we know but he admits to having some qualms. If gravity waves were proven, he would be completely convinced. Still he is comfortable using inflation to build his model. From here on Tegmark begins departing from what he considers widely accepted ideas. He sees inflation coming before the big bang not after as it is usually presented. Thus the universe did not start out as some super dense super-hot entity. The heat was caused by inflation. The big bang occurred when inflation stopped.
Tegmark believes inflation is always occurring in some region of space, a controversial idea called eternal inflation. This creates an infinite but still expanding universe contained in a finite volume. Those areas outside of our observable universe Tegmark calls Level I parallel universes. There are an infinite number of these parallel universes, some still inflating. The nomenclature here is what is unusual. Many physicists believe the universe is infinite, but dividing the portions we can’t see into Level I parallel universes allows Tegmark to build his model. Level I parallel universes share our laws of physics and physical constants.
Tegmark next posits the Level II multiverse, his term for a concept popular with string theorists. These are other finite volumes containing their own infinite parallel universes with their own laws of physics, physical constants and particle relationships. The Level II multiverse addresses the anthropic principle which holds that our universe seems to be fine-tuned to support life. With infinite universes just as with infinite planets one is bound to be just right for us.
Next Tegmark explores the quantum world. Everything is made of particles (quarks, electrons, etc.) but all we know about them are the mathematical values of their attributes (charge, spin, etc.). These values arrayed in space are described by quantum field theory. Tegmark believes that there is an underlying layer of reality that we perceive as particles; perhaps strings, quantum loops or something not yet thought of. Coincidentally while reading this my January 2017 issue of Scientific American arrived with an article about a group of physicists working on quantum gravity who are collaborating with scientists involved in quantum computer development. They have formed a program called “It from Qubit” to look for an underlying structure of information bits held together by entanglement that would generate space and time as its emergent property.
Tegmark’s take on quantum mechanics eschews the Copenhagen interpretation. He is smitten with Schrodinger’s equation, but does not believe the wave function ever collapses which leads to the many-worlds theory of Hugh Everett III. This theory holds that all outcomes are real not just those that are observed. Thus reality splits. Tegmark calls these separate realities Level III parallel universes. He points to small surveys that show more physicists now believe in the many-worlds theory than in the formerly popular Copenhagen interpretation, although many don’t ascribe to either theory. Tegmark describes his discussions with the famous theoretical physicist John Wheeler who died at 96 in 2008. Wheeler who coined the term black hole postulated the one electron universe that inspired his student Richard Feynman even if Feynman did not completely accept the idea. Hugh Everett and Richard Feynman had been Wheeler’s doctoral students at Princeton. The many-worlds theory was Hugh Everett’s doctoral thesis which Wheeler championed.
From this point on, Tegmark leaves traditional thinking completely behind. He posits the Level IV multiverse which is comprised of mathematical structures. These are Tegmark’s ultimate reality. Each structure generates a different universe. The mathematical structures could be anything, say a cube where the corners are connected to each other. A structure that would yield our universe would be much more complicated. Tegmark’s mathematical reality is a relational reality. “… the properties of the world around us stem not from the properties of its ultimate building blocks, but from the relations between these building blocks”. He offers an analogy to the brain in which it is the connections between neurons that form ideas not the properties of the individual neurons. It is the relationship between the neurons that yield consciousness just as the relationships in the mathematical structure yield the universe we perceive.
Tegmark points to symmetries as an important way mathematical structures produce the physical properties we perceive. Tegmark references German mathematician Emmy Noether who proved that continuous symmetries of mathematical structures produce conservation laws of physics yielding the physical constants. For example energy corresponds to time translation symmetry, momentum to space-translation symmetry, angular momentum to rotation symmetry, electric charge to a particular symmetry of quantum mechanics. Nobel Prize winner Eugene Wigner showed these symmetries dictated all the quantum properties of particles such as spin and mass.
The Level IV multiverse would not just have different physical constants like Level II but different equations. This answers John Wheeler who wondered, “Why these particular equations, why not others.” Or as Eugene Wigner put it “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious…there is no rational explanation for it.” Or as Stephen Hawking asked, “What is it that breathes fire into the equations and makes a universe for them to describe?” Tegmark answers with the Level IV multiverse.
So what can we make of all this? I have no idea how valid Tegmark’s thesis is, but I thoroughly enjoyed his presentation in which I learned about new concepts and lines of thought. In the 1930’s John Wheeler studied under Niels Bohr and worked alongside Einstein, two men who led revolutionary thinking in physics 100 years ago. Wheeler encouraged Tegmark writing him, “...behind quantum mechanics lies some deep and wonderful principle to be discovered…The likelihood of such a discovery is surely proportional to our belief that there is something there to be discovered.” Before we dismiss Tegmark’s wild abandon in his search for a mathematical universe, we should keep in mind that the ideas of John Wheeler, his famous students Richard Feynman and Hugh Everett, his mentor Niels Bohr and associate Albert Einstein were all considered silly at one point.
October 10, 2015
The first half of the book is a basic overview of modern physics and i moved through it quickly. He explores the current multiverse scenario in here. He classifies the multiverse into four categories. Level I multiverse consists of all the objects that lie beyond our cosmological horizon. Level II multiverse apparently consists of infinite number of Level I multiverses produced by inflation with different physical constants. Level III multiverse comes from the Everett interpretation of quantum mechanics. Everett interpretation actually makes some intuitive sense to me.
The second metaphysical part of the book where he presents his thesis is what i was looking forward to. His thesis seems to be that "our universe is a mathematical structure". He isn't just suggesting that our universe is described by mathematics but that it is mathematics, including us. There is nothing out there but mathematical relations, time is an illusion and nothing in the universe actually changes. This is where Level IV multiverse comes. All the structures that exist mathematically exist in the fourth level multiverse. All the structures that exist mathematically have the same ontological status.I found Tegmark's monism, an all-encompassing mathematical multiverse to be very appealing.
He comes to his idea of mathematical universe by reducing an empirical physical model of universe to mathematics. So for example, from what i understand, there are no objects such as quarks and leptons, but there are groups and the properties of quarks are described by the group. From this and considering the explanatory power of mathematics, a mathematical universe does make some intuitive sense. Perhaps the reason why mathematics is so successful in explaining our universe is because they are one and the same. I’m not sure that he made a convincing argument if everything can be reduced to mathematics ontologically. What about an emergent property like consciousness? His suggestion of mathematical self-aware structures didn't tell me much and his conjecture that Consciousness is a state of matter didn't make much sense to me. I never really understood what he means when he talks about subjective randomness and subjective immortality either. To whom is it subjective?
A lot of criticism for this book, as it seems to me, is that his theory is not "scientific". While i agree with this, it doesn't bother me. While there is nothing new or radical about Tegmark's mathematical monism, I was actually hoping that this book would be more mathematically and philosophically enlightening. But unfortunately there isn't much discussion about mathematical structures in here and this isn't a very good metaphysical treatise either. But if you are interested in an overview of modern physics, this is a very lucid and clear account.
The second metaphysical part of the book where he presents his thesis is what i was looking forward to. His thesis seems to be that "our universe is a mathematical structure". He isn't just suggesting that our universe is described by mathematics but that it is mathematics, including us. There is nothing out there but mathematical relations, time is an illusion and nothing in the universe actually changes. This is where Level IV multiverse comes. All the structures that exist mathematically exist in the fourth level multiverse. All the structures that exist mathematically have the same ontological status.I found Tegmark's monism, an all-encompassing mathematical multiverse to be very appealing.
He comes to his idea of mathematical universe by reducing an empirical physical model of universe to mathematics. So for example, from what i understand, there are no objects such as quarks and leptons, but there are groups and the properties of quarks are described by the group. From this and considering the explanatory power of mathematics, a mathematical universe does make some intuitive sense. Perhaps the reason why mathematics is so successful in explaining our universe is because they are one and the same. I’m not sure that he made a convincing argument if everything can be reduced to mathematics ontologically. What about an emergent property like consciousness? His suggestion of mathematical self-aware structures didn't tell me much and his conjecture that Consciousness is a state of matter didn't make much sense to me. I never really understood what he means when he talks about subjective randomness and subjective immortality either. To whom is it subjective?
A lot of criticism for this book, as it seems to me, is that his theory is not "scientific". While i agree with this, it doesn't bother me. While there is nothing new or radical about Tegmark's mathematical monism, I was actually hoping that this book would be more mathematically and philosophically enlightening. But unfortunately there isn't much discussion about mathematical structures in here and this isn't a very good metaphysical treatise either. But if you are interested in an overview of modern physics, this is a very lucid and clear account.
January 24, 2015
I find myself in the strange position of awarding five stars to a book that has plenty of content with which I disagree. The detail of that will come up later, but the reason that I can still confidently give this book five stars is that it is a great read, covers some less controversial aspects of physics and cosmology very well and where Max Tegmark strays into concepts that many don't accept, he does so in a way that really makes you think, and analyse just why these concepts seem so unlikely - which is great.
The book is an exploration of the development of Tegmark's leading edge (or wacky, depending on your point of view) ideas - I should stress, though, whether or not he's right, Tegmark is a respected physicist, not a random person with no knowledge to back up his ideas. The book includes an excellent pass through the development of the current hot big bang with inflation theory that it would be worth buying for without the rest. In his introduction, Tegmark says that regular popular science readers might want to skip these first few chapters, but I really recommend that you don't - for instance, he gives the best explanation and exploration of the concept of inflation I've ever seen in a popular science book. It's superb.
From then on, though I don't necessarily accept what Tegmark has to say, he gives a very engaging picture of the way that the concept of eternal inflation could produce a multiverse with a infinite collection of big bangs, each producing their own universe, an impassioned plea for the many worlds interpretation of quantum theory and a really impressive attempt to persuade us that the universe isn't just described by mathematics, but is fundamentally mathematical at its heart.
To be honest, you can stop there and go and buy it if you like. But I do have to say why, personally, I'm not very convinced by anything Tegmark says once he leaves the mainstream. I also have a couple of niggles about the book, which I'll get out of the way first. I found the bits about his personal life more distracting than helpful (though I know publishers love this kind of thing). He several times refers to the detailed colour picture of the Cosmic Microwave Background radiation that is shown on the cover. As you can see from the image above, if this is correct, then the universe is a whole lot more interesting that I thought it was. It's a shame the text wasn't updated to reflect the new edition. Also, the BICEP2 results form quite a big piece of evidence in favour of his view of inflation - unfortunately the book seems to have been published just before these were effectively dismissed, which would put Tegmark's reflections on BICEP in a very different light.
I won't spend too much on what I wasn't convinced by in the content, but a few key points are that he makes several deductions from infinity which I don't think can be justified (you have to be very careful, deducing things from infinity), for all his enthusiasm I wasn't sold on the many worlds interpretation of quantum mechanics, and I think in the final part of the book he makes the common error of conflating models and reality.
However, as I mentioned up front, I didn't care - because even when I didn't agree with him, I found the book really made me think. Which surely is a mark of class.
The book is an exploration of the development of Tegmark's leading edge (or wacky, depending on your point of view) ideas - I should stress, though, whether or not he's right, Tegmark is a respected physicist, not a random person with no knowledge to back up his ideas. The book includes an excellent pass through the development of the current hot big bang with inflation theory that it would be worth buying for without the rest. In his introduction, Tegmark says that regular popular science readers might want to skip these first few chapters, but I really recommend that you don't - for instance, he gives the best explanation and exploration of the concept of inflation I've ever seen in a popular science book. It's superb.
From then on, though I don't necessarily accept what Tegmark has to say, he gives a very engaging picture of the way that the concept of eternal inflation could produce a multiverse with a infinite collection of big bangs, each producing their own universe, an impassioned plea for the many worlds interpretation of quantum theory and a really impressive attempt to persuade us that the universe isn't just described by mathematics, but is fundamentally mathematical at its heart.
To be honest, you can stop there and go and buy it if you like. But I do have to say why, personally, I'm not very convinced by anything Tegmark says once he leaves the mainstream. I also have a couple of niggles about the book, which I'll get out of the way first. I found the bits about his personal life more distracting than helpful (though I know publishers love this kind of thing). He several times refers to the detailed colour picture of the Cosmic Microwave Background radiation that is shown on the cover. As you can see from the image above, if this is correct, then the universe is a whole lot more interesting that I thought it was. It's a shame the text wasn't updated to reflect the new edition. Also, the BICEP2 results form quite a big piece of evidence in favour of his view of inflation - unfortunately the book seems to have been published just before these were effectively dismissed, which would put Tegmark's reflections on BICEP in a very different light.
I won't spend too much on what I wasn't convinced by in the content, but a few key points are that he makes several deductions from infinity which I don't think can be justified (you have to be very careful, deducing things from infinity), for all his enthusiasm I wasn't sold on the many worlds interpretation of quantum mechanics, and I think in the final part of the book he makes the common error of conflating models and reality.
However, as I mentioned up front, I didn't care - because even when I didn't agree with him, I found the book really made me think. Which surely is a mark of class.
April 22, 2014
Our Mathematical Universe
by
Max Tegmark
Max Tegmark, a physics professor at MIT, is a leading proponent of the idea of the multiverse, familiar to many as the “parallel worlds” of science fiction, but taken increasingly seriously by sober scientific theorists. Several variations on the theme tell us that there must be an infinite number of versions of our Universe (capital “U”), other universes (small “u”), some indistinguishable from our own, some with minor differences, many with significant differences. separated from us in space or time. But Tegmark is careful not to frighten his readers by making such seemingly outrageous claims at the start of his book. Instead, he leads us gently by the hand through the traditional story of our place in the Universe, from the Sun and Solar System outwards, before wading into deeper waters.
Even this familiar story is enlivened by the author’s personal touch, with anecdotes from his childhood and early life in research. So by the time he gets to the tricky bit, he feels like an old and trustworthy friend. This is just as well, because things get very tricky indeed.
The first step into deep water is the easiest. If space is infinite, our visible Universe can be regarded as a bubble within that infinite space, analogous to the bubble of visibility surrounding a person walking through a fog. It is possible to calculate the number of particles (neutrons, protons and the like) in that bubble, and to calculate the number of ways they could be arranged. This is an enormous number, but, crucially, it is not infinite. So in infinite space, there must be other bubbles -- other universes -- with exactly the same arrangement of particles as in our Universe. This is the Type I multiverse, and it is almost common sense.
The Type II multiverse is only slightly more complicated. It takes on board the currently-favoured idea of inflation, which explains the present appearance of our Universe as resulting from an epoch of very rapid expansion at the time of the Big Bang. Each universe is an inflating bubble within some kind of superspace. But it is the Type III multiverse that is familiar from science fiction.
This is where quantum physics comes in to the story, with Schrödinger’s famous “dead and alive cat” and the idea that every time the world is faced with a choice of possibilities at the quantum level it splits to allow all possible developments. In fact, no “splitting” is required, and it is equally valid, as Schrödinger himself pointed out, to think of all quantum possibilities existing alongside each other “all the time”, whatever that means in this context.
Let me spell that out. In the famous thought experiment, a (purely hypothetical) cat is trapped in a box with a quantum device that ensures that it has a 50:50 chance of being dead or alive. When the box is opened, one possibility is realised. The “splitting” idea says that at that moment the Universe divides in two, one universe with a dead cat and one with a live cat. The “parallel” idea says that there are always two universes, each initially with a cat in the same situation, in one of which the cat dies while in the other it lives, with no splitting involved. “Parallel universes,” says Tegmark, “are not a theory, but a prediction of certain theories.”
All of this is allowed -- some would say, required -- by the known law of physics, or as Tegmark prefers, the known laws of mathematics. As Galileo said, nature is “a book written in the language of mathematics”. But Tegmark isn’t finished yet, He goes on (farther than most physicists would) to consider the Type IV multiverse, in which different universes are governed by different laws of mathematics. This leads on to speculation about the nature of reality and our place in it, the future of life and the future of the Universe. All a far cry from early chapters on our place in the Universe, and discussion of the sizes of planets and stars, but somehow a natural development, thanks to Tegmark’s gift for storytelling, from those beginnings. As he says, “physics is the ultimate intellectual adventure”; this is a great place to join in that adventure.
John Gribbin is a Visiting Fellow in Astronomy
at the University of Sussex
and author of In Search of the Multiverse (Penguin)
by
Max Tegmark
Max Tegmark, a physics professor at MIT, is a leading proponent of the idea of the multiverse, familiar to many as the “parallel worlds” of science fiction, but taken increasingly seriously by sober scientific theorists. Several variations on the theme tell us that there must be an infinite number of versions of our Universe (capital “U”), other universes (small “u”), some indistinguishable from our own, some with minor differences, many with significant differences. separated from us in space or time. But Tegmark is careful not to frighten his readers by making such seemingly outrageous claims at the start of his book. Instead, he leads us gently by the hand through the traditional story of our place in the Universe, from the Sun and Solar System outwards, before wading into deeper waters.
Even this familiar story is enlivened by the author’s personal touch, with anecdotes from his childhood and early life in research. So by the time he gets to the tricky bit, he feels like an old and trustworthy friend. This is just as well, because things get very tricky indeed.
The first step into deep water is the easiest. If space is infinite, our visible Universe can be regarded as a bubble within that infinite space, analogous to the bubble of visibility surrounding a person walking through a fog. It is possible to calculate the number of particles (neutrons, protons and the like) in that bubble, and to calculate the number of ways they could be arranged. This is an enormous number, but, crucially, it is not infinite. So in infinite space, there must be other bubbles -- other universes -- with exactly the same arrangement of particles as in our Universe. This is the Type I multiverse, and it is almost common sense.
The Type II multiverse is only slightly more complicated. It takes on board the currently-favoured idea of inflation, which explains the present appearance of our Universe as resulting from an epoch of very rapid expansion at the time of the Big Bang. Each universe is an inflating bubble within some kind of superspace. But it is the Type III multiverse that is familiar from science fiction.
This is where quantum physics comes in to the story, with Schrödinger’s famous “dead and alive cat” and the idea that every time the world is faced with a choice of possibilities at the quantum level it splits to allow all possible developments. In fact, no “splitting” is required, and it is equally valid, as Schrödinger himself pointed out, to think of all quantum possibilities existing alongside each other “all the time”, whatever that means in this context.
Let me spell that out. In the famous thought experiment, a (purely hypothetical) cat is trapped in a box with a quantum device that ensures that it has a 50:50 chance of being dead or alive. When the box is opened, one possibility is realised. The “splitting” idea says that at that moment the Universe divides in two, one universe with a dead cat and one with a live cat. The “parallel” idea says that there are always two universes, each initially with a cat in the same situation, in one of which the cat dies while in the other it lives, with no splitting involved. “Parallel universes,” says Tegmark, “are not a theory, but a prediction of certain theories.”
All of this is allowed -- some would say, required -- by the known law of physics, or as Tegmark prefers, the known laws of mathematics. As Galileo said, nature is “a book written in the language of mathematics”. But Tegmark isn’t finished yet, He goes on (farther than most physicists would) to consider the Type IV multiverse, in which different universes are governed by different laws of mathematics. This leads on to speculation about the nature of reality and our place in it, the future of life and the future of the Universe. All a far cry from early chapters on our place in the Universe, and discussion of the sizes of planets and stars, but somehow a natural development, thanks to Tegmark’s gift for storytelling, from those beginnings. As he says, “physics is the ultimate intellectual adventure”; this is a great place to join in that adventure.
John Gribbin is a Visiting Fellow in Astronomy
at the University of Sussex
and author of In Search of the Multiverse (Penguin)
February 4, 2021
(3.5 rounded up). At first the style was a bit irrritating but the contents made up for it. See also this review, which goes into much more detail on this whole book.
Some extra considerations:
- In the first part, I especially liked the clear rationale for introducing inflation as "the gift that keeps on giving".
-I am puzzled by the "reality is a mathematical structure" story. What else would it be? Mathematically/logically speaking, if you have a theory describing reality it must be mathematical (what else?) and therefore, reality is a mathematical model of this theory, assuming the theory is correct. What is the big deal, I wonder. Maybe it's me. As a side note, I couldn't help wondering whether it should be the 'smallest' model (in some sense), i.e. there is nothing in reality that is not described by the theory.
- The last part should have been removed. The concept of 'scientific lifestyle' is undefined.
Some extra considerations:
- In the first part, I especially liked the clear rationale for introducing inflation as "the gift that keeps on giving".
-I am puzzled by the "reality is a mathematical structure" story. What else would it be? Mathematically/logically speaking, if you have a theory describing reality it must be mathematical (what else?) and therefore, reality is a mathematical model of this theory, assuming the theory is correct. What is the big deal, I wonder. Maybe it's me. As a side note, I couldn't help wondering whether it should be the 'smallest' model (in some sense), i.e. there is nothing in reality that is not described by the theory.
- The last part should have been removed. The concept of 'scientific lifestyle' is undefined.
August 6, 2016
I really wanted to like this book.
The promise of tying together concepts of modern physics with mathematics and a philosophy of what life and the universe are all about kept me going.
I did appreciate the enthusiasm and energy that Tegmark has for his field. Unfortunately, this came through a bit too often as being full of himself.
When it got to layman's term explanations of quantum physics and relativity, the wording was either too brief or too obscure. I recognized that a lot has been accomplished since I was first reading about these topics twenty five years ago.
In the later chapters, when Tegmark pushes the boundaries of what I think is experimentally provable, when he argues that all reality is just math, I think he has gone a little too far.
I found myself skimming through rather than diving in for more understanding. Perhaps you may like it. I found it in the end rather empty.
The promise of tying together concepts of modern physics with mathematics and a philosophy of what life and the universe are all about kept me going.
I did appreciate the enthusiasm and energy that Tegmark has for his field. Unfortunately, this came through a bit too often as being full of himself.
When it got to layman's term explanations of quantum physics and relativity, the wording was either too brief or too obscure. I recognized that a lot has been accomplished since I was first reading about these topics twenty five years ago.
In the later chapters, when Tegmark pushes the boundaries of what I think is experimentally provable, when he argues that all reality is just math, I think he has gone a little too far.
I found myself skimming through rather than diving in for more understanding. Perhaps you may like it. I found it in the end rather empty.
August 25, 2016
Pēdējā laikā mani sāk nomākt iekšējie pārmetumi. Ja paskatās uz izlasīto, sanāk, ka mani lasīšanas paradumi pēdējo piecu gadu laikā ir kardināli mainījušies. Esmu gandrīz pilnībā pārgājis uz fantastikas un fantāzijas žanru. Populārzinātniskās grāmatas tiek pamestas novārtā. No vienas puses – cik reizes vari lasīt vienu un to pašu. Beigās jau bija nonācis pie tā, ka par tematu (vismaz vēsturisko aspektu) es zinu labāk par autoru. Populārzinātniskās grāmatas es pērku joprojām, bet ar lasīšanu neveicas tik labi kā vēlētos. Šī ar gaidīja savu kārtu jau no maija.
Šīs grāmatas galvenais uzdevums ir ātri iepazīstināt lasītāju ar mūsdienu kosmoloģijas pamatiem, nedaudz apstāstīt svarīgāko kvantu fizikā un tad pierādīt, ka patiesībā mūsu visums ir matemātiska struktūra ar visām no tā izrietošajām sekām. Grāmatā izlasītais garantēti laiku pa laikam noraus jumtu un liks aizdomāties par mūsu vietu pasaulē, agrāk vai vēlāk piespiežot lasītāju padoties multiversu vilinājumam.
Nav jau tā, ka grāmatas par multiversiem būtu retums, bet tik skaidri un saprotami uzrakstīta gadās reti. Ja man kāds tagad prasītu grāmatu par zinātnes vēsturi un iespējamo nākotni, es bez šaubīšanās viņam dotu šo. Ja arī neko daudz vairāk, tad vismaz iemācīsies patstāvīgi noteikt Zemes diametru. Taču nevajag satraukties, autors savus secinājumus būvē uz stipriem pamatiem, un lasītājam tiek pavēstītas visas galvenās nianses. Ja esi baigais populārzinātnisko grāmatu lasītājs, tad vari pirmās sešas nodaļas izlaist. Es gan to nerekomendētu, jo tajās ir atrodama nozīmīga pievienotā vērtība. Proti, autors daudz nodarbojies ar eksperimentu datu apstrādi. Parasti autori pavēsta par teoriju nemaz neiedziļinoties, kā tika apstrādāti eksperimenta laikā iegūtie dati, un kādēļ tieši šī interpretācija ir vislabākā. Autors par šo bieži aizmirsto teoriju pierādīšanas aspektu raksta visai daudz un ar entuziasmu.
Vispār visa grāmatā jūtams arī pats autors – viņa karjera un dzīve. Viņš nekautrējas stāstīt par savu zinātnieka dzīvi, par to kā viņam dažreiz ir izdevies atklāt jau atklātas lietas. Par to cik vīlies viņš juties uzzinot, ka tas nav nekas jauns, un par to, cik šādas vilšanās ir vajadzīgas, ja vēlies kļūt par īstu zinātnieku. Domājams, ka viņa grāmatas pusaudžu lasītājus varētu nosvērt par labu fizikas studēšanai. Šajā grāmatā, lasot par dažādu problēmu matemātiskajiem modeļiem, tie tiek pasniegti tik saistošā veidā, ka šķiet, ka viss ir saprotams bez īpašas piepūles.
Centrālais temats ir multiversi. Vispār izšķir veselus četrus to veidus. Viņi visi izriet kā sekas no jau pierādītām fizikas teorijām. Un ar pierādījumiem ir tā, ka tu nevari izvēlēties tikai tās sekas, kuras tev ir pieņemamas. Vai nu ņem visu vai neko. Tad nu lasītājs var uzzināt, ka gadījumā, ja tu vienu brīdi attopies kā vecākais planētas iedzīvotājs, tad tev būtu prātīgi pieņemt, ka eksistē trešā līmeņa multiversi. Savukārt, ja pieņem, ka mūsu visuma inflācijas teorija atbilst patiesībai, tad ļoti, ļoti tālu, kaut kur eksistē identiska Zemes kopija ar visiem tās iedzīvotāju un tādu pašu vēsturi. Un visi iespējamie starpstāvokļi un katrs no tiem bezgalīgi daudzās kopijās. Ar bezgalības tiešām ir prātam neaptveramas.
Un pašās beigās autors izvirza savu teoriju, ka visu visumu pamatā ir matemātiskas struktūras, kas variē no vienkāršām līdz sarežģītām. Iespējams, ka Hilberta telpa ir piebāzta pilna ar visdažādākajām konfigurācijām. Un mūsu Visums ir tāds tikai tādēļ, ka tāda ir viena no bezgalīgi daudzajām matemātiskajām struktūrām ar visām savām simetrijām.
Lieku 10 no 10 ballēm. Noteikti iesaku izlasīt visiem, pat ja līdz šim neesi par fiziku un kosmoloģiju interesējies tik cik melns aiz naga. Izlasi, nenožēlosi, pavērs jaunus zināšanu apvāršņus un spriedumi kā būtu, ja būtu izskatīsies daudz saprotamāki. Galvenais uzzināsiet, ka pārbaudīt vai lasītājs patiesībā nav “Bolcmaņa smadzenes”.
Šīs grāmatas galvenais uzdevums ir ātri iepazīstināt lasītāju ar mūsdienu kosmoloģijas pamatiem, nedaudz apstāstīt svarīgāko kvantu fizikā un tad pierādīt, ka patiesībā mūsu visums ir matemātiska struktūra ar visām no tā izrietošajām sekām. Grāmatā izlasītais garantēti laiku pa laikam noraus jumtu un liks aizdomāties par mūsu vietu pasaulē, agrāk vai vēlāk piespiežot lasītāju padoties multiversu vilinājumam.
Nav jau tā, ka grāmatas par multiversiem būtu retums, bet tik skaidri un saprotami uzrakstīta gadās reti. Ja man kāds tagad prasītu grāmatu par zinātnes vēsturi un iespējamo nākotni, es bez šaubīšanās viņam dotu šo. Ja arī neko daudz vairāk, tad vismaz iemācīsies patstāvīgi noteikt Zemes diametru. Taču nevajag satraukties, autors savus secinājumus būvē uz stipriem pamatiem, un lasītājam tiek pavēstītas visas galvenās nianses. Ja esi baigais populārzinātnisko grāmatu lasītājs, tad vari pirmās sešas nodaļas izlaist. Es gan to nerekomendētu, jo tajās ir atrodama nozīmīga pievienotā vērtība. Proti, autors daudz nodarbojies ar eksperimentu datu apstrādi. Parasti autori pavēsta par teoriju nemaz neiedziļinoties, kā tika apstrādāti eksperimenta laikā iegūtie dati, un kādēļ tieši šī interpretācija ir vislabākā. Autors par šo bieži aizmirsto teoriju pierādīšanas aspektu raksta visai daudz un ar entuziasmu.
Vispār visa grāmatā jūtams arī pats autors – viņa karjera un dzīve. Viņš nekautrējas stāstīt par savu zinātnieka dzīvi, par to kā viņam dažreiz ir izdevies atklāt jau atklātas lietas. Par to cik vīlies viņš juties uzzinot, ka tas nav nekas jauns, un par to, cik šādas vilšanās ir vajadzīgas, ja vēlies kļūt par īstu zinātnieku. Domājams, ka viņa grāmatas pusaudžu lasītājus varētu nosvērt par labu fizikas studēšanai. Šajā grāmatā, lasot par dažādu problēmu matemātiskajiem modeļiem, tie tiek pasniegti tik saistošā veidā, ka šķiet, ka viss ir saprotams bez īpašas piepūles.
Centrālais temats ir multiversi. Vispār izšķir veselus četrus to veidus. Viņi visi izriet kā sekas no jau pierādītām fizikas teorijām. Un ar pierādījumiem ir tā, ka tu nevari izvēlēties tikai tās sekas, kuras tev ir pieņemamas. Vai nu ņem visu vai neko. Tad nu lasītājs var uzzināt, ka gadījumā, ja tu vienu brīdi attopies kā vecākais planētas iedzīvotājs, tad tev būtu prātīgi pieņemt, ka eksistē trešā līmeņa multiversi. Savukārt, ja pieņem, ka mūsu visuma inflācijas teorija atbilst patiesībai, tad ļoti, ļoti tālu, kaut kur eksistē identiska Zemes kopija ar visiem tās iedzīvotāju un tādu pašu vēsturi. Un visi iespējamie starpstāvokļi un katrs no tiem bezgalīgi daudzās kopijās. Ar bezgalības tiešām ir prātam neaptveramas.
Un pašās beigās autors izvirza savu teoriju, ka visu visumu pamatā ir matemātiskas struktūras, kas variē no vienkāršām līdz sarežģītām. Iespējams, ka Hilberta telpa ir piebāzta pilna ar visdažādākajām konfigurācijām. Un mūsu Visums ir tāds tikai tādēļ, ka tāda ir viena no bezgalīgi daudzajām matemātiskajām struktūrām ar visām savām simetrijām.
Lieku 10 no 10 ballēm. Noteikti iesaku izlasīt visiem, pat ja līdz šim neesi par fiziku un kosmoloģiju interesējies tik cik melns aiz naga. Izlasi, nenožēlosi, pavērs jaunus zināšanu apvāršņus un spriedumi kā būtu, ja būtu izskatīsies daudz saprotamāki. Galvenais uzzināsiet, ka pārbaudīt vai lasītājs patiesībā nav “Bolcmaņa smadzenes”.
January 11, 2023
For youngsters, learning a global language and typing should trump long division and writing cursive.
In the Internet age, my own role as a classroom teacher has changed.
I’m no longer needed as a conduit of information, which my students can simply download on their own.
Rather, my key role is inspiring a scientific lifestyle, curiosity and desire to learn more.
In the Internet age, my own role as a classroom teacher has changed.
I’m no longer needed as a conduit of information, which my students can simply download on their own.
Rather, my key role is inspiring a scientific lifestyle, curiosity and desire to learn more.
March 13, 2014
All bad books are alike , each good book is good in its way\s (I think Tolstoy will forgive me for stealing his most famous quote.As the rating indicates, we are in the second state, good book, or rather a fucking unbelievable amazing good and fresh book.
Max Tegmark is(as I see him) the Pythagorean of our era.Pythagoras and his students were interested in the mysticism of numbers, realizing that when odd numbers starting from one are added together, the sum is always a square number. From here, they got the idea that everything in the world can be measured and described by numbers, and that "all is number" In this book Tegmark using theoretical physics, he wanted to show us something similar, but in scientific way not mystic, in a journey from the vast infinite space to the tiniest particle inside our brains (which are part of the journey)
This book stands in three parts. Part one talked about space in general and our place in it, putting us in the most recent (sometimes most complex) problems of modern cosmology.He showed us how the Inflation Theory by Alan Guth solved these problems such as the horizon problem and the flatness problem.
The inflation theory says that our baby Universe grew much like a human baby, an accelerating growth phase where the size doubled at regular intervals was followed by a more leisurely decelerating growth phase.So where and when did this inflation end?! Indeed it ended 14 billion years ago, in the part of space that we now inhabit, This means that there must be some physical process which can get rid of the inflating substance, causing it to decay into ordinary non-inflating matter, which then keeps expanding, clustering, and ultimately forming galaxies, stars and planets.
Alex Vilenkin Professor of Physics and Director of the Institute of cosmology at Tufts University, found that the question of where and when inflation ends is quite subtle and interesting. We know that inflation ends in at least some places, since 14 billion years ago, it ended in the part of space that we now inhabit, No not our planet, neither our galaxy, but our universe. Inflation theory gave us the Level I and Level II Multiverse which occupy the first part of the book.
Part tow talked about the subatomic world, it gives us a new picture of the current Standard Model(new at least for me), and produced the level III of multiverse(The Quantum Multiverse).Tegmark used the analogy of Schrodungar's cat experiment and made what he called The Quantum Card thought experiment and showed how you can be in quantum superposition(in tow places at once)
Part Three is the heart core of the book in this part Tegmark showed how mathematics by means of numbers and symbols can describe out physical world precisely, I will quote the author to be more sincerely and to avoid falling in troubles:
"The fabric of our physical reality contains dozens of pure numbers which all measurement constants can in principle be calculated"
"Our reality isn't just described by mathematics ,it is mathematics not just aspects of it, but all of it, including you."
"our external physical reality is a mathematical structure"
Tegmark called this the Mathematical Universe Hypothesis(MUH) call it Hypothesis number one.The External Reality Hypothesis (ERH)(number tow) stands that "There exists an external physical reality completely independent of us humans."
Tegmark's argument is that our most successful theories such as general relativity and quantum mechanics describe only part of the reality, for a complete description of external reality must be defined in a form "devoid of any human baggage like 'particle', 'observation' or other words" in other words it have to be a Mathematical Structure .Thus everything physical is ultimately mathematical, including you and me, "making us self-aware parts of a giant mathematical object".
This means that all structures that exist mathematically exist physically as well, forming the Level IV multiverse (this is a mind blowing conclusion)"Exploring the Level IV multiverse doesn't require rockets or telescopes, merely computers and ideas". (reminds me of Berekley)
"Mathematical structures, formal systems and computations are closely related, suggesting that they’re all aspects of the same transcendent structure whose nature we still haven’t fully understood"
Now the question of whatever we have to believe in all of this or not, one simply can be narrow minded and reject all of it, ,another one influenced by Popper's thought, can say that this is unscientific non-sense and can't be tested or falsified, for my part I found this Level VI Multiverse a little bit strange (as another levels) but worth thinking .Tegmark as he said moved the thinking of Multiverse from " this is non-sense I hate it " to "I hate it"
The book was complex and hard to follow in some parts (and hard to remember in all parts), but it was "Fantastic" in every sense of the word.
Max Tegmark is(as I see him) the Pythagorean of our era.Pythagoras and his students were interested in the mysticism of numbers, realizing that when odd numbers starting from one are added together, the sum is always a square number. From here, they got the idea that everything in the world can be measured and described by numbers, and that "all is number" In this book Tegmark using theoretical physics, he wanted to show us something similar, but in scientific way not mystic, in a journey from the vast infinite space to the tiniest particle inside our brains (which are part of the journey)
This book stands in three parts. Part one talked about space in general and our place in it, putting us in the most recent (sometimes most complex) problems of modern cosmology.He showed us how the Inflation Theory by Alan Guth solved these problems such as the horizon problem and the flatness problem.
The inflation theory says that our baby Universe grew much like a human baby, an accelerating growth phase where the size doubled at regular intervals was followed by a more leisurely decelerating growth phase.So where and when did this inflation end?! Indeed it ended 14 billion years ago, in the part of space that we now inhabit, This means that there must be some physical process which can get rid of the inflating substance, causing it to decay into ordinary non-inflating matter, which then keeps expanding, clustering, and ultimately forming galaxies, stars and planets.
Alex Vilenkin Professor of Physics and Director of the Institute of cosmology at Tufts University, found that the question of where and when inflation ends is quite subtle and interesting. We know that inflation ends in at least some places, since 14 billion years ago, it ended in the part of space that we now inhabit, No not our planet, neither our galaxy, but our universe. Inflation theory gave us the Level I and Level II Multiverse which occupy the first part of the book.
Part tow talked about the subatomic world, it gives us a new picture of the current Standard Model(new at least for me), and produced the level III of multiverse(The Quantum Multiverse).Tegmark used the analogy of Schrodungar's cat experiment and made what he called The Quantum Card thought experiment and showed how you can be in quantum superposition(in tow places at once)
Part Three is the heart core of the book in this part Tegmark showed how mathematics by means of numbers and symbols can describe out physical world precisely, I will quote the author to be more sincerely and to avoid falling in troubles:
"The fabric of our physical reality contains dozens of pure numbers which all measurement constants can in principle be calculated"
"Our reality isn't just described by mathematics ,it is mathematics not just aspects of it, but all of it, including you."
"our external physical reality is a mathematical structure"
Tegmark called this the Mathematical Universe Hypothesis(MUH) call it Hypothesis number one.The External Reality Hypothesis (ERH)(number tow) stands that "There exists an external physical reality completely independent of us humans."
Tegmark's argument is that our most successful theories such as general relativity and quantum mechanics describe only part of the reality, for a complete description of external reality must be defined in a form "devoid of any human baggage like 'particle', 'observation' or other words" in other words it have to be a Mathematical Structure .Thus everything physical is ultimately mathematical, including you and me, "making us self-aware parts of a giant mathematical object".
This means that all structures that exist mathematically exist physically as well, forming the Level IV multiverse (this is a mind blowing conclusion)"Exploring the Level IV multiverse doesn't require rockets or telescopes, merely computers and ideas". (reminds me of Berekley)
"Mathematical structures, formal systems and computations are closely related, suggesting that they’re all aspects of the same transcendent structure whose nature we still haven’t fully understood"
Now the question of whatever we have to believe in all of this or not, one simply can be narrow minded and reject all of it, ,another one influenced by Popper's thought, can say that this is unscientific non-sense and can't be tested or falsified, for my part I found this Level VI Multiverse a little bit strange (as another levels) but worth thinking .Tegmark as he said moved the thinking of Multiverse from " this is non-sense I hate it " to "I hate it"
The book was complex and hard to follow in some parts (and hard to remember in all parts), but it was "Fantastic" in every sense of the word.
April 1, 2016
If you find the concept of multiverses interesting, wonder whether consciousness is a quantum computer and don't mind having your brain twisted in a pretzel, then you might find this book a fun read.
January 17, 2019
Excellent, philosophical, mind-blowing, high-flying, provocative. We and everything are just part of an "eternal" and "primary" equation.
September 16, 2015
The human mind has constantly underestimated the size of our world and universe, while, at the same time, the human mind has constantly underestimated the chances of understanding it. Max Tegmark, one of the leading physicists in the world, explains theories about the universe and offer alternative conclusions which are considered controversial, but gain more and more acceptance and respect. He doesn't think the universe can be described by mathematics, he thinks it is mathematics. The smallest parts of the atom that we know of, the quarks, have no other quality than being mathematic. In the same way, the universe on the great scale seems to be symmetrical and consist of equations. The big and the small scales come together, and in the end, everything is mathematics.
Max Tegmark is a very interesting person, obviously very intelligent, interested in mysteries and the unexplainable, and has a great deal of open-minded imagination. That makes him a machine of ideas and theories about our universe. His determination is impressive. When he finds an obstacle, he writes a new computer program to be able to analyze data, or builds a groundbreaking kind of telescope - an omniscope, involving a method called 21 cm cosmology - to be able to continue his research.
This book brings out the physicist in you. Tegmark mixes equations and explanations with the big, existential questions. Sometimes the book is on the verge of philosophy, which only makes physics more beautiful. What are we, really? What makes us aware of everything and ourselves? Do we exist or are we just Boltzmann brains? (A self aware entity, existing due to fluctuations in space, according to quantum mechanics). What is reality? Is time an illusion? In which universe do we live? What does the world really look like? How accurate is our view when we depend on photons? (In the dark, we see nothing. Different materials absorb different light waves and the colour we see seems to be the one not absorbed. Much of the reality is hidden from us, like other dimensions).
This is some of the themes discussed in the book.
* Time is a fascinating dimension, belonging to the four dimensions of our universe. The speed of time moves differently depending on the whereabouts of the observer. Near a black hole, it goes faster. We are able to see almost 14 billion years back in time, when viewing the cosmic radiation created 400 000 years after the Big Bang.
* Hydrogen gives off radio waves with a wavelength of 21 centimeters. Since the waves reaches earth are stretched out by the expending universe, the length of them reveals how far away they come from. Since distance is a factor of time, that also reveals how old they are. It's called 21 cm tomography. It's a current scientific activity and physicists around the world are trying to track the signal from the places farthest away.
* Without three dimensions and time, woven together in a cosmic fabric of spacetime, life wouldn't exist, but according to Tegmark, we are not unique. Because of his theory about multiple universes, everything that can happen, will happen somewhere.
* According to Tegmark, there are universes on four levels. Our universe is on the first level, and is represented by how far we are able to see, or the light that has reached us in 14 billion years. Beyond that, there are other universes that we can't see. The universes on level two are a consequence of a great expansion happening before Big Bang, called the inflation theory. These universes have different physical rules depending on inflation and early fluctuations. Universes on level three are coming from quantum physics. Universes on level four are made of every mathematical structure there is. Every equation happens somewhere, and imagination is the limit.
* According to quantum physics, there are endless copies of you that have your memories and think they are you. When you gamble, somewhere one of you win, and one of you loose. There are no luck, there are only different outcomes. When you feel immortal, it means the number of you have diminished. When you feel lucky, the number of you have increased.
In one chapter, the apocalypse is discussed and five alternatives for the universe apocalypse are introduced. They are called Big Chill, Big Crunch, Big Rip, Big Snap and Death Bubbels. The theories have to do with the expanding or eventual compressing of the universe. When considering an apocalypse within a billion years, Tegmark thinks the sun is the big threat. He almost dismisses the idea of an invasion from intelligent life in our galaxy, since the probability of a planet with intelligent life existing within our galaxy, considering the immense size of the rest of the universe, is almost non-existent. (In the same way, one could argue that mankind will not live for billion years. The probability of us being born so early in that kind of time-line is very small). Many planets are inhabitable, but are still not inhabited. Many planets are older than earth, and if there were intelligent life somewhere in our galaxy, some of them would probably already have colonized the universe. Or, perhaps they already have?
In the near future, however, the existential risks are the biggest threat, considering nuclear weapons and the fact that we eventually might build an intelligent computer, which earns some egoistical person much money and leaves the rest of the world in poverty. The artificial intelligence might be well beyond ourselves, and learn how to evolve without us, which makes us superfluous and ultimately might lead to our extinction. We should be grateful to what we have and not waste it. We should be able to save ourselves and our planet with knowledge. Tegmark thinks that scientists have failed to educate people and have to improve their information distribution. Many people still think that mankind is only 10000 years old, and in 2012, twelve people were burned to death for witchcraft in Haiti. The lack of knowledge is dangerous and certain companies strive to maintain ignorance to profit.
Despite his successful career, Max Tegmark seems to be a very modest and humble man, fully aware of the risks of theories, and that research has turned out to be wrong before. That is why he has an open mind. His attitude and love for his work, his collegues and previous scientists is admiring. Perhaps scientists have to really love their work, be their work, to succeed. Often, they work day and night, struggling with their thesis and experiments, to be able to finally reach a conclusion.
Tegmark's view of the world is fascinating and very inspiring. He mentions facts that are very romantic, almost like poetry. Gold is produced when a star dies in a supernova explosion so violent and rare that, during a fraction of a second, it releases about the same amount of energy as every other star in our observable universe, together. The world needs school teachers like that. The only criticism might be the sometimes fast deductions in his arguments. It would have been nice with a few more sentences with distinct explanations about the consistency in some of the chapters.
The gigant distances, mystery, beauty and elegance of the universe often make us feel small and insignificant. We are not. First, we have a big decision to make. During our lifetime, the future of our planet is most likely to be decided, according to the book, and we will be remembered for it in the future. Second, as Tegmark so delicately puts it, the universe – which is a true art - is only beautiful because a conscious being can perceive it. We are probably the only intelligent beings in our galaxy, and if we weren't here, the beauty of the universe would be a waste of space. Instead of thinking the universe is giving meaning to us, we should think that we are giving meaning to the universe.
Max Tegmark is a very interesting person, obviously very intelligent, interested in mysteries and the unexplainable, and has a great deal of open-minded imagination. That makes him a machine of ideas and theories about our universe. His determination is impressive. When he finds an obstacle, he writes a new computer program to be able to analyze data, or builds a groundbreaking kind of telescope - an omniscope, involving a method called 21 cm cosmology - to be able to continue his research.
This book brings out the physicist in you. Tegmark mixes equations and explanations with the big, existential questions. Sometimes the book is on the verge of philosophy, which only makes physics more beautiful. What are we, really? What makes us aware of everything and ourselves? Do we exist or are we just Boltzmann brains? (A self aware entity, existing due to fluctuations in space, according to quantum mechanics). What is reality? Is time an illusion? In which universe do we live? What does the world really look like? How accurate is our view when we depend on photons? (In the dark, we see nothing. Different materials absorb different light waves and the colour we see seems to be the one not absorbed. Much of the reality is hidden from us, like other dimensions).
This is some of the themes discussed in the book.
* Time is a fascinating dimension, belonging to the four dimensions of our universe. The speed of time moves differently depending on the whereabouts of the observer. Near a black hole, it goes faster. We are able to see almost 14 billion years back in time, when viewing the cosmic radiation created 400 000 years after the Big Bang.
* Hydrogen gives off radio waves with a wavelength of 21 centimeters. Since the waves reaches earth are stretched out by the expending universe, the length of them reveals how far away they come from. Since distance is a factor of time, that also reveals how old they are. It's called 21 cm tomography. It's a current scientific activity and physicists around the world are trying to track the signal from the places farthest away.
* Without three dimensions and time, woven together in a cosmic fabric of spacetime, life wouldn't exist, but according to Tegmark, we are not unique. Because of his theory about multiple universes, everything that can happen, will happen somewhere.
* According to Tegmark, there are universes on four levels. Our universe is on the first level, and is represented by how far we are able to see, or the light that has reached us in 14 billion years. Beyond that, there are other universes that we can't see. The universes on level two are a consequence of a great expansion happening before Big Bang, called the inflation theory. These universes have different physical rules depending on inflation and early fluctuations. Universes on level three are coming from quantum physics. Universes on level four are made of every mathematical structure there is. Every equation happens somewhere, and imagination is the limit.
* According to quantum physics, there are endless copies of you that have your memories and think they are you. When you gamble, somewhere one of you win, and one of you loose. There are no luck, there are only different outcomes. When you feel immortal, it means the number of you have diminished. When you feel lucky, the number of you have increased.
In one chapter, the apocalypse is discussed and five alternatives for the universe apocalypse are introduced. They are called Big Chill, Big Crunch, Big Rip, Big Snap and Death Bubbels. The theories have to do with the expanding or eventual compressing of the universe. When considering an apocalypse within a billion years, Tegmark thinks the sun is the big threat. He almost dismisses the idea of an invasion from intelligent life in our galaxy, since the probability of a planet with intelligent life existing within our galaxy, considering the immense size of the rest of the universe, is almost non-existent. (In the same way, one could argue that mankind will not live for billion years. The probability of us being born so early in that kind of time-line is very small). Many planets are inhabitable, but are still not inhabited. Many planets are older than earth, and if there were intelligent life somewhere in our galaxy, some of them would probably already have colonized the universe. Or, perhaps they already have?
In the near future, however, the existential risks are the biggest threat, considering nuclear weapons and the fact that we eventually might build an intelligent computer, which earns some egoistical person much money and leaves the rest of the world in poverty. The artificial intelligence might be well beyond ourselves, and learn how to evolve without us, which makes us superfluous and ultimately might lead to our extinction. We should be grateful to what we have and not waste it. We should be able to save ourselves and our planet with knowledge. Tegmark thinks that scientists have failed to educate people and have to improve their information distribution. Many people still think that mankind is only 10000 years old, and in 2012, twelve people were burned to death for witchcraft in Haiti. The lack of knowledge is dangerous and certain companies strive to maintain ignorance to profit.
Despite his successful career, Max Tegmark seems to be a very modest and humble man, fully aware of the risks of theories, and that research has turned out to be wrong before. That is why he has an open mind. His attitude and love for his work, his collegues and previous scientists is admiring. Perhaps scientists have to really love their work, be their work, to succeed. Often, they work day and night, struggling with their thesis and experiments, to be able to finally reach a conclusion.
Tegmark's view of the world is fascinating and very inspiring. He mentions facts that are very romantic, almost like poetry. Gold is produced when a star dies in a supernova explosion so violent and rare that, during a fraction of a second, it releases about the same amount of energy as every other star in our observable universe, together. The world needs school teachers like that. The only criticism might be the sometimes fast deductions in his arguments. It would have been nice with a few more sentences with distinct explanations about the consistency in some of the chapters.
The gigant distances, mystery, beauty and elegance of the universe often make us feel small and insignificant. We are not. First, we have a big decision to make. During our lifetime, the future of our planet is most likely to be decided, according to the book, and we will be remembered for it in the future. Second, as Tegmark so delicately puts it, the universe – which is a true art - is only beautiful because a conscious being can perceive it. We are probably the only intelligent beings in our galaxy, and if we weren't here, the beauty of the universe would be a waste of space. Instead of thinking the universe is giving meaning to us, we should think that we are giving meaning to the universe.
February 27, 2022
Although I found myself frustrated in parts, I continue to be thinking about this book days after finishing it so that to me is a good sign.
Tegmark definitely deepened my understanding of cosmology and shored up and/or corrected areas I now realize I didn't have a firm grasp of - especially inflation and the Cosmic Microwave Background. Both sent my brain spinning to the point that I found myself up in the middle of the night trying to wrap my head around these concepts and their implications. Such as the fact that the CMB is seen as a sphere all around us as we detect it in any direction we look, yet since we expanded from basically a very dense point it felt like we should sense the CMB at wherever the "center" of our universe might be. This was particularly disturbing for me as I couldn't quite intuitively grasp what it "meant" in reality until that middle of the night reverie when I suddenly intuited that I needed to separate the spatial dimensions of what a sphere implies from the time dimension of what that sphere was telling us. Yes, we are looking out spatially which is simultaneously back in time. If the CMB is supposed to represent an event that happened everywhere the reason we only detect it as a sphere away from us is because we are in the present, not 13.8 billion years ago. If I were to somehow be on the surface of that sphere out in space looking back to Earth's location then I would indeed detect the CMB as I would then be looking at our location 13.8 billion years in the past. Surely there are better ways to spend your middle of the night hours, but this particular night felt productive in an "ah ha!" sort of way.
The implications of inflation are another brain twister as the true meaning of an infinite space leads to Tegmark's Multiverses 1 and 2, which in a way that doesn't even touch on quantum phenomenon, already implies Many Worlds consequences. In at least some of those universes this review would not be rambling quite as much and would indeed be more eloquent. Oh well... Love the universe you're in, am I right?
I was already more familiar with Tegmark's Multiverse 3, related to the non-collapse of the quantum waveform, from recently reading Adam Becker's What is Real (https://www.goodreads.com/book/show/3...). And in fact, this is where I thought Tegmark was going with his Mathematical Universe Theory. But this was merely the third stop on his journey. I will say that Everett's Many Worlds Theory seems a whole lot less crazy and impossible once you've already had to swallow the infinite universes implied by Inflation.
What I'm finding is that thinking too hard and too long on the true implications of infinity in cosmology and the quantum world can bring on a case of the screaming meanies if one isn't careful!
Unfortunately I found his actual Mathematical Universe Theory harder to swallow. There are parts of it I can get behind, such as the possibility that rather than math only describing our universe, our universe might actually be math at heart and we just experience it as physically real. In fact, that is close to my prior belief about the relationship between consciousness and the waveform. Where I start to have problems with Tegmark's thinking is that I might disagree with how he thinks about what physical reality might be. And his jump from "our universe is math" to "all consistent mathematical structures are also physically real." I know I'm not quite getting this down super clearly, but I will find solace in the fact that in at least one universe I described my thoughts perfectly.
I will say that this particular sentence stopped me in my tracks and described something I had already been thinking about so eloquently that I was quite taken aback: I think that consciousness is the way information feels when being processed in certain complex ways.
In fact, consciousness is becoming a larger and larger sticking point with me in terms of how to think about all of this. I think it might be useful to remind ourselves that our experienced universe is only the part of existence that we have evolved to perceive (even if only through the "data" of a detector or mathematical structures). Do we discover math out there as an objective thing? Or is math a relationship between us as we have evolved as life forms and the universe (whatever it might actually be) around us? If we evolved differently in terms of how we perceive our reality might that math be "discovered" to be different. I know this starts to butt up against anthropic theories but whatever the case I'm becoming more convinced that consciousness and the many ways we have evolved to perceive (including our technology) determines a large part of what we might determine the objective state of our reality is.
Or maybe the puzzle can be as simple and maddening as this...
If we accept the idea of Block Spacetime where nothing changes, and everything already exists as these braids of information, then why do our consciousnesses experience time? Why do we as life forms experience ourselves moving slice by slice through Spacetime? What started that movement? Does all life experience time in some way? And if so, why?
I keep hoping Nobel prize winning theoretical physicist me would travel from another multiverse to answer these questions, but so far I seem to be ghosting myself...
Tegmark definitely deepened my understanding of cosmology and shored up and/or corrected areas I now realize I didn't have a firm grasp of - especially inflation and the Cosmic Microwave Background. Both sent my brain spinning to the point that I found myself up in the middle of the night trying to wrap my head around these concepts and their implications. Such as the fact that the CMB is seen as a sphere all around us as we detect it in any direction we look, yet since we expanded from basically a very dense point it felt like we should sense the CMB at wherever the "center" of our universe might be. This was particularly disturbing for me as I couldn't quite intuitively grasp what it "meant" in reality until that middle of the night reverie when I suddenly intuited that I needed to separate the spatial dimensions of what a sphere implies from the time dimension of what that sphere was telling us. Yes, we are looking out spatially which is simultaneously back in time. If the CMB is supposed to represent an event that happened everywhere the reason we only detect it as a sphere away from us is because we are in the present, not 13.8 billion years ago. If I were to somehow be on the surface of that sphere out in space looking back to Earth's location then I would indeed detect the CMB as I would then be looking at our location 13.8 billion years in the past. Surely there are better ways to spend your middle of the night hours, but this particular night felt productive in an "ah ha!" sort of way.
The implications of inflation are another brain twister as the true meaning of an infinite space leads to Tegmark's Multiverses 1 and 2, which in a way that doesn't even touch on quantum phenomenon, already implies Many Worlds consequences. In at least some of those universes this review would not be rambling quite as much and would indeed be more eloquent. Oh well... Love the universe you're in, am I right?
I was already more familiar with Tegmark's Multiverse 3, related to the non-collapse of the quantum waveform, from recently reading Adam Becker's What is Real (https://www.goodreads.com/book/show/3...). And in fact, this is where I thought Tegmark was going with his Mathematical Universe Theory. But this was merely the third stop on his journey. I will say that Everett's Many Worlds Theory seems a whole lot less crazy and impossible once you've already had to swallow the infinite universes implied by Inflation.
What I'm finding is that thinking too hard and too long on the true implications of infinity in cosmology and the quantum world can bring on a case of the screaming meanies if one isn't careful!
Unfortunately I found his actual Mathematical Universe Theory harder to swallow. There are parts of it I can get behind, such as the possibility that rather than math only describing our universe, our universe might actually be math at heart and we just experience it as physically real. In fact, that is close to my prior belief about the relationship between consciousness and the waveform. Where I start to have problems with Tegmark's thinking is that I might disagree with how he thinks about what physical reality might be. And his jump from "our universe is math" to "all consistent mathematical structures are also physically real." I know I'm not quite getting this down super clearly, but I will find solace in the fact that in at least one universe I described my thoughts perfectly.
I will say that this particular sentence stopped me in my tracks and described something I had already been thinking about so eloquently that I was quite taken aback: I think that consciousness is the way information feels when being processed in certain complex ways.
In fact, consciousness is becoming a larger and larger sticking point with me in terms of how to think about all of this. I think it might be useful to remind ourselves that our experienced universe is only the part of existence that we have evolved to perceive (even if only through the "data" of a detector or mathematical structures). Do we discover math out there as an objective thing? Or is math a relationship between us as we have evolved as life forms and the universe (whatever it might actually be) around us? If we evolved differently in terms of how we perceive our reality might that math be "discovered" to be different. I know this starts to butt up against anthropic theories but whatever the case I'm becoming more convinced that consciousness and the many ways we have evolved to perceive (including our technology) determines a large part of what we might determine the objective state of our reality is.
Or maybe the puzzle can be as simple and maddening as this...
If we accept the idea of Block Spacetime where nothing changes, and everything already exists as these braids of information, then why do our consciousnesses experience time? Why do we as life forms experience ourselves moving slice by slice through Spacetime? What started that movement? Does all life experience time in some way? And if so, why?
I keep hoping Nobel prize winning theoretical physicist me would travel from another multiverse to answer these questions, but so far I seem to be ghosting myself...
December 17, 2016
This is Max Tegmark's first and only book so far. In the book, Max who likes to be called Mad Max proposes a really "mad" theory of everything called the "mathematical universe hypothesis" in which he argues that the ultimate nature of reality is mathematics. He also argues strongly for the multiverse idea, making it somewhat plausible.
The book is written with a mostly smooth and easy to understand narrative style that is often combined with inspirational quotations. It is from books like this that I get the feeling to want to do physics instead of medicine, even though I'm few weeks/months away from final year examinations. The author takes us through his personal quest for the ultimate nature of reality in which you'll see Einstein and Darwin next to Plato and Pythagoras.
The book is divided into three parts: physics of the big and small, mathematics as reality and philosophical reflections. The first chapters are the most beautiful in the book; I got immersed in them just like I do in an Orwell novel.
We are told about the ancient Greek scientists Eratosthenes and Aristarchus and their scientific discoveries made form limited observations. How just looking at a specter of a star can tell us so much information about it. He also asks 16 deep questions such as what is space, what is the curvature of the universe, how can triangles be more or less than 180 degrees, how did galaxies, atoms and elements form and what we don't know yet. He then continues with the history of scientific discoveries, going through Copernicus, Galileo, Giordano Bruno, Kepler, Newton, Hubble, Freidman and others.
A recurring theme is that of not taking one's theory seriously and to its full consequences. We see multiple scientists making the same mistake through the ages. He explains the inflation theory, which is the current mainstream theory to explain the Bang in the Big Bang. Here he makes the same point made by Hawking and Krauss in their recent books, that from a quantum vacuum we can get so much mass without breaking the law of conservation of energy. He calls it a galactic Ponzi scheme in which we borrow indefinitely from gravity.
Then he moves from the mainstream to purse the multiverse idea, which is enjoying much more support by physicists than it did decades ago when it was in the realm of science fiction only. He divides the multiverse into four levels and explains them. He maintains that while the multiverse is not testable/falsifiable, it is still science, because it's not a theory in it self, but a prediction of a testable theory; infinite inflation and quantum physics. He is critical of the Copenhagen interpretation of quantum physics and supports a Cosmological interpretation that is similar to the Many-worlds interpretation.
After that he reaches the Mathematical Universe Hypothesis which supports a level four multiverse, in which there is an infinite number of universes with their own set of fundamental laws of physics. The hypothesis states that mathematical structures are eternal and unchanging. They don't exist in time and space, rather space and time exist in some of them. The flow of time, creation and destruction are illusions, since change is an illusion. Mathematical existence = physical existence. He states and argues that this hypothesis is very simple and is testable/falsifiable.
In the last chapter, Tegmark tackles the future of the universe and how it could end. He talks about the existential threats to life on Earth from outside and inside, nature and human. He spends some time talking about artificial intelligence, the importance of education, the meaning of life and extraterrestrial intelligence.
The first parts of the book are absolutely amazing. I'd have given it 5 stars if it didn't contain some boring and hard to understand parts in the middle. Nevertheless, the book is really good and I recommend it.
The book is written with a mostly smooth and easy to understand narrative style that is often combined with inspirational quotations. It is from books like this that I get the feeling to want to do physics instead of medicine, even though I'm few weeks/months away from final year examinations. The author takes us through his personal quest for the ultimate nature of reality in which you'll see Einstein and Darwin next to Plato and Pythagoras.
The book is divided into three parts: physics of the big and small, mathematics as reality and philosophical reflections. The first chapters are the most beautiful in the book; I got immersed in them just like I do in an Orwell novel.
We are told about the ancient Greek scientists Eratosthenes and Aristarchus and their scientific discoveries made form limited observations. How just looking at a specter of a star can tell us so much information about it. He also asks 16 deep questions such as what is space, what is the curvature of the universe, how can triangles be more or less than 180 degrees, how did galaxies, atoms and elements form and what we don't know yet. He then continues with the history of scientific discoveries, going through Copernicus, Galileo, Giordano Bruno, Kepler, Newton, Hubble, Freidman and others.
A recurring theme is that of not taking one's theory seriously and to its full consequences. We see multiple scientists making the same mistake through the ages. He explains the inflation theory, which is the current mainstream theory to explain the Bang in the Big Bang. Here he makes the same point made by Hawking and Krauss in their recent books, that from a quantum vacuum we can get so much mass without breaking the law of conservation of energy. He calls it a galactic Ponzi scheme in which we borrow indefinitely from gravity.
Then he moves from the mainstream to purse the multiverse idea, which is enjoying much more support by physicists than it did decades ago when it was in the realm of science fiction only. He divides the multiverse into four levels and explains them. He maintains that while the multiverse is not testable/falsifiable, it is still science, because it's not a theory in it self, but a prediction of a testable theory; infinite inflation and quantum physics. He is critical of the Copenhagen interpretation of quantum physics and supports a Cosmological interpretation that is similar to the Many-worlds interpretation.
After that he reaches the Mathematical Universe Hypothesis which supports a level four multiverse, in which there is an infinite number of universes with their own set of fundamental laws of physics. The hypothesis states that mathematical structures are eternal and unchanging. They don't exist in time and space, rather space and time exist in some of them. The flow of time, creation and destruction are illusions, since change is an illusion. Mathematical existence = physical existence. He states and argues that this hypothesis is very simple and is testable/falsifiable.
In the last chapter, Tegmark tackles the future of the universe and how it could end. He talks about the existential threats to life on Earth from outside and inside, nature and human. He spends some time talking about artificial intelligence, the importance of education, the meaning of life and extraterrestrial intelligence.
The first parts of the book are absolutely amazing. I'd have given it 5 stars if it didn't contain some boring and hard to understand parts in the middle. Nevertheless, the book is really good and I recommend it.
February 17, 2014
Tegmark is currently a physics professor at MIT. His undergraduate education was at KTH in Stockholm. He did graduate work in Cosmology at Berkley and spent some time at Princeton working with John Wheeler. In this book he reviews many of the extraordinary results, obtained in the last few decades, of research into the origins of the Universe. The later part of the book is much more speculative and even metaphysical. Many in the physics community may find some of his ideas out of the bounds of the scientifically provable. Still it makes for a roller coaster ride into the unknown and at least to this reader quite an exciting one at that. For me one of the highlights was one of the rare well done explanations of the so called many worlds interpretation of quantum mechanics. This is frequently misunderstood both in the popular science and even in the physics community. I would consider this a must read for anyone puzzled by the idea of "collapse" of the wave function. Aside from this, Tegmark provides a very personal and amusing account of his experiences as both a student and a working professional. He also reveals that he is the son of the well known Mathematician, Harold S. Shapiro. He tells us that he switched his last name to his Swedish mother's maiden name in order to escape being confused with the many Shapiros working in physics. For maximum benefit the book requires some effort on the part of the reader. Even if one is not happy about the more speculative latter parts the book is worth its price for the parts that clearly explain much of modern cosmology.
November 18, 2014
A disappointing book. It started out well with a good description of modern cosmology, in particular the background microwave radiation, and then turned into absolute fluff. Some of the fluff was a bit entertaining, such as Quantum Suicide, but most of it was tedious and boring. The tedious and boring fluff included the main thesis of the book, that our universe is composed of “mathematical structures”. Good grief!
March 14, 2018
A Wild Ride With Mad Max
Alfred North Whitehead famously said that philosophy is a series of footnotes to Plato. Welcome to yet another footnote, as the thesis of this book, in the author’s words, “can be viewed as a form of radical Platonism, asserting that all the mathematical structures in Plato’s ‘realm of ideas’ exist ‘out there’ in a physical sense.” In other words, there is no physical reality, just pure mathematics.
This book is a fun ride for those with a reasonable understanding of physics, as long as fun means to stimulate your thinking without taking it all too seriously. As for the rest of us, be warned that the author himself explicitly rates his own chapters as “mainstream”, “controversial” and “extremely controversial”. And some of the supposedly mainstream stuff should also be labeled controversial.
Objective Reality Requires Objective Mathematics
Let us start at the beginning, with the assumption makes it possible to do science: “There exists an external physical reality completely independent of us humans.” But then Tegmark follows this up with a consequence I had not really thought of:
“If we assume that reality exists independently of us humans, then for a description to be complete, it must also be well defined according to nonhuman entities – aliens or supercomputers, say – that lack any understanding of human concepts. Such a description must be expressible in a form that is devoid of any human baggage like ‘particle’, ‘observation’ or other human words.”
Mathematics is the only language we have that meets these requirements. The question of whether or not our mathematics is truly free of human baggage is not really addressed, but let us assume this kind of mathematics does exist somewhere. Thus the goal science should be to eliminate such subjective human baggage. So far, so good.
The Illusion of Equivalence
We learn that our current descriptions of reality at the most basic level are becoming ever more abstract and mathematical. Yes, but now the fun begins. We are told that the Equivalence Principle means that two descriptions are equivalent if there is a correspondence between them that preserves all relations. Therefore, if external reality can be described by mathematics, it must actually be a mathematical structure. And if the reality we know is nothing but mathematics, then all imaginable forms of mathematics are equally valid descriptions of other realities.
Here we have the arbitrary assumption that because there can be equivalent descriptions of reality, it follows that those descriptions are equivalent to reality itself. Next, we get that most basic logical fallacy that if one mathematical structure describes reality, then all such structures must define a reality. This logic leads us from a single objective reality to the conclusion that all possible realities are true, which means that reality is arbitrary and therefore subjective.
Slippery Subjectivity
The same kind of word game is used inject the concept of subjectivity into Hugh Everett’s theory of the quantum multiverse. Ironically, that theory was constructed to avoid the subjectivity of the standard Copenhagen Interpretation. The logic goes like this: When you flip a quantum coin, the result is heads in one universe, and tails in another. He then claims, “At the end of this experiment (any choice) 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.”
This is an abuse of the term “subjective”. Each version of you (assuming they exist) has every right to objectively feel real, as there is no possible interaction with the other supposed universe. He actually makes the absurd statement that, “Everett’s work has shown that understanding the process of observation requires us to include a third part of our Universe as well: your mental state as an observer.” Don’t take my word that this is wrong. Later in the book, when he is back to being a physicist again, he says,
“Do you need a human observer to collapse the wavefunction? Now I am convinced that consciousness has nothing to do with it, since even a single particle could do the trick. I realized that quantum observation is not about consciousness, but simply about the transfer of information.”
Turning Entropy into Subjective Mush
Now we move from bad philosophy to outright error involving the well-established scientific concept of Entropy. While I am a bit weak on its mathematical foundation, all I need to know is that it has a mathematical foundation to know the following is rubbish:
“Entropy is a quantitative measure of our lack of information about a system…. If the object interacts with you, then you get more information about it, and its entropy decreases. If the object interacts with the environment, you lose information about it, so its entropy increases… The traditional formulation of the law simply corresponds to ignoring the subject.”
The subject is ignored for the good reason that entropy is about the information content of the system, not the observer. Let me try this simple analogy: If you do not tidy your desk, it tends to get messy, meaning more disordered, thus having more entropy. Even if you think you know where everything is, the desk is still just as disordered. Your knowledge describes the entropy of your mind, not the desk. If you neatly stack the papers the desk is now more ordered, with less entropy, even if you no longer know where anything is anymore.
How can a prominent physicist take a standard concept like entropy and turn it into subjective mush?
The Nature of Reality
While we are talking about philosophy, let us address the question of how we can know anything, as Plato tried to do so long ago. There is a brilliant treatment of this in The Beginning of Infinity: Explanations That Transform the World. I have a simpler explanation. We are not philosophers living in Plato’s cave; we have to survive in the real world. If our subjective model does not match external reality, we become someone’s lunch.
But Max’s solution for the connection between our internal subjective perception and external reality is to insert a layer between them called “consensus reality”. This is a rather surprising move for someone who prides himself in defying consensus and decries its herd mentality, but we have to expect surprises. Here is how he puts it: “The challenge for physics is deriving the consensus reality form the external reality, and the challenge for cognitive science is to derive the internal reality from the consensus reality.”
While in practical terms consensus reality is important (but certainly not infallible), it is by no means fundamental.
The Inflationary Multiverse
Much of the book is taken up with the idea of a multiverse. But one is not enough; Mad Max’s innovation is to posit four layers of different kinds of multiverses.
It begins with the chapter about cosmic inflation, which should really have the “controversial” rather than the “mainstream” classification. The idea is that our observable universe is only part of an infinite space created by the inflationary force. Somehow, General Relativity creates an infinite space inside a finite space smaller than an atom. Because that space is infinitely big, it apparently follows that anything that can happen does happen somewhere, so there must be infinitely many other worlds exactly like this one. That is the Level I multiverse.
Not sure about all that? No problem, just skip to later on in the book:
“[Inflation] predicted infinitely many observers measuring different things with probabilities depending on a measure that we don’t know. Which, in turn means that inflation, strictly speaking, is not predicting anything at all about what typical observers should see. All predictions are revoked, including those whose predictions that made us take inflation seriously in the first place! Self-destruction is complete.”
In other words it amounts to a bait and switch operation. The original inflation theory supposedly explained several features of the early universe, but with more development it got turned into “eternal inflation” and now anything is possible. Therefore, as he says, all predictions are revoked.
I also had my suspicion about the use of infinity. So does Max:
“There is a fundamentally flawed assumption at the very foundation of modern physics. Here is my prime suspect: infinity. In fact, I have two suspects: ‘infinitely big’ and ‘infinitely small’. By infinitely big, I mean the idea that space can have infinite volume, that time can continue forever, and that there can be infinitely many physical objects. By infinitely small, I mean the continuum: the idea that even a liter of space contains an infinite number of points, that space can be stretched out indefinitely without anything bad happening, and that there are quantities in nature that can vary continuously. The two are closely related: inflation created an infinite volume by stretching continuous space indefinitely.”
All this blows away two of the four levels of multiverse. The third one is the quantum multiverse. Remember the principle of equivalence? It actually applies here. There is only one mathematical expression of quantum field theory therefore all interpretations are equivalent. So the quantum multiverse is a legitimate but unverifiable interpretation. The final level is the mathematical universe, in which anything we can imagine is equally true. I will leave the evaluation of this idea to the reader.
The Trouble with Physics
In The Trouble with Physics: The Rise of String Theory, the Fall of a Science and What Comes Next Lee Smolin points out that scientific theories tend to take on a life of their own, even if there is little evidence to support them. Max Tegmark elevates this “bug” into the ultimate “feature” of his hypothesis: any and every valid mathematical structure defines a physical universe. By this logic, all 10^500 variants of string theory are by definition true. In the old days, a theory that predicted anything and everything was seen to predict nothing. Now, that is taken as more evidence for a multiverse.
The thing is, I really enjoyed reading this book. A lot of the information is well presented, and there are plenty of ideas with which to stimulate the imagination. There are some curiosities. For example, Tegmark is an expert on decoherence of the quantum wavefunction, and debunks the possibility of quantum processes in the brain. But the deeply related concept of entanglement is never mentioned.
Perhaps the saving grace is that most of the many questionable ideas get contradicted somewhere else. Controversy takes precedence over consistency. Perhaps we should think of all these contradictions as a superposition of states, which are true in different universes. Just not this one.
How can I rate such a book? For those with some knowledge of the subject, I give it five stars for its entertainment value. But I suggest those with less knowledge stay away – there is too much misleading material.
Alfred North Whitehead famously said that philosophy is a series of footnotes to Plato. Welcome to yet another footnote, as the thesis of this book, in the author’s words, “can be viewed as a form of radical Platonism, asserting that all the mathematical structures in Plato’s ‘realm of ideas’ exist ‘out there’ in a physical sense.” In other words, there is no physical reality, just pure mathematics.
This book is a fun ride for those with a reasonable understanding of physics, as long as fun means to stimulate your thinking without taking it all too seriously. As for the rest of us, be warned that the author himself explicitly rates his own chapters as “mainstream”, “controversial” and “extremely controversial”. And some of the supposedly mainstream stuff should also be labeled controversial.
Objective Reality Requires Objective Mathematics
Let us start at the beginning, with the assumption makes it possible to do science: “There exists an external physical reality completely independent of us humans.” But then Tegmark follows this up with a consequence I had not really thought of:
“If we assume that reality exists independently of us humans, then for a description to be complete, it must also be well defined according to nonhuman entities – aliens or supercomputers, say – that lack any understanding of human concepts. Such a description must be expressible in a form that is devoid of any human baggage like ‘particle’, ‘observation’ or other human words.”
Mathematics is the only language we have that meets these requirements. The question of whether or not our mathematics is truly free of human baggage is not really addressed, but let us assume this kind of mathematics does exist somewhere. Thus the goal science should be to eliminate such subjective human baggage. So far, so good.
The Illusion of Equivalence
We learn that our current descriptions of reality at the most basic level are becoming ever more abstract and mathematical. Yes, but now the fun begins. We are told that the Equivalence Principle means that two descriptions are equivalent if there is a correspondence between them that preserves all relations. Therefore, if external reality can be described by mathematics, it must actually be a mathematical structure. And if the reality we know is nothing but mathematics, then all imaginable forms of mathematics are equally valid descriptions of other realities.
Here we have the arbitrary assumption that because there can be equivalent descriptions of reality, it follows that those descriptions are equivalent to reality itself. Next, we get that most basic logical fallacy that if one mathematical structure describes reality, then all such structures must define a reality. This logic leads us from a single objective reality to the conclusion that all possible realities are true, which means that reality is arbitrary and therefore subjective.
Slippery Subjectivity
The same kind of word game is used inject the concept of subjectivity into Hugh Everett’s theory of the quantum multiverse. Ironically, that theory was constructed to avoid the subjectivity of the standard Copenhagen Interpretation. The logic goes like this: When you flip a quantum coin, the result is heads in one universe, and tails in another. He then claims, “At the end of this experiment (any choice) 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.”
This is an abuse of the term “subjective”. Each version of you (assuming they exist) has every right to objectively feel real, as there is no possible interaction with the other supposed universe. He actually makes the absurd statement that, “Everett’s work has shown that understanding the process of observation requires us to include a third part of our Universe as well: your mental state as an observer.” Don’t take my word that this is wrong. Later in the book, when he is back to being a physicist again, he says,
“Do you need a human observer to collapse the wavefunction? Now I am convinced that consciousness has nothing to do with it, since even a single particle could do the trick. I realized that quantum observation is not about consciousness, but simply about the transfer of information.”
Turning Entropy into Subjective Mush
Now we move from bad philosophy to outright error involving the well-established scientific concept of Entropy. While I am a bit weak on its mathematical foundation, all I need to know is that it has a mathematical foundation to know the following is rubbish:
“Entropy is a quantitative measure of our lack of information about a system…. If the object interacts with you, then you get more information about it, and its entropy decreases. If the object interacts with the environment, you lose information about it, so its entropy increases… The traditional formulation of the law simply corresponds to ignoring the subject.”
The subject is ignored for the good reason that entropy is about the information content of the system, not the observer. Let me try this simple analogy: If you do not tidy your desk, it tends to get messy, meaning more disordered, thus having more entropy. Even if you think you know where everything is, the desk is still just as disordered. Your knowledge describes the entropy of your mind, not the desk. If you neatly stack the papers the desk is now more ordered, with less entropy, even if you no longer know where anything is anymore.
How can a prominent physicist take a standard concept like entropy and turn it into subjective mush?
The Nature of Reality
While we are talking about philosophy, let us address the question of how we can know anything, as Plato tried to do so long ago. There is a brilliant treatment of this in The Beginning of Infinity: Explanations That Transform the World. I have a simpler explanation. We are not philosophers living in Plato’s cave; we have to survive in the real world. If our subjective model does not match external reality, we become someone’s lunch.
But Max’s solution for the connection between our internal subjective perception and external reality is to insert a layer between them called “consensus reality”. This is a rather surprising move for someone who prides himself in defying consensus and decries its herd mentality, but we have to expect surprises. Here is how he puts it: “The challenge for physics is deriving the consensus reality form the external reality, and the challenge for cognitive science is to derive the internal reality from the consensus reality.”
While in practical terms consensus reality is important (but certainly not infallible), it is by no means fundamental.
The Inflationary Multiverse
Much of the book is taken up with the idea of a multiverse. But one is not enough; Mad Max’s innovation is to posit four layers of different kinds of multiverses.
It begins with the chapter about cosmic inflation, which should really have the “controversial” rather than the “mainstream” classification. The idea is that our observable universe is only part of an infinite space created by the inflationary force. Somehow, General Relativity creates an infinite space inside a finite space smaller than an atom. Because that space is infinitely big, it apparently follows that anything that can happen does happen somewhere, so there must be infinitely many other worlds exactly like this one. That is the Level I multiverse.
Not sure about all that? No problem, just skip to later on in the book:
“[Inflation] predicted infinitely many observers measuring different things with probabilities depending on a measure that we don’t know. Which, in turn means that inflation, strictly speaking, is not predicting anything at all about what typical observers should see. All predictions are revoked, including those whose predictions that made us take inflation seriously in the first place! Self-destruction is complete.”
In other words it amounts to a bait and switch operation. The original inflation theory supposedly explained several features of the early universe, but with more development it got turned into “eternal inflation” and now anything is possible. Therefore, as he says, all predictions are revoked.
I also had my suspicion about the use of infinity. So does Max:
“There is a fundamentally flawed assumption at the very foundation of modern physics. Here is my prime suspect: infinity. In fact, I have two suspects: ‘infinitely big’ and ‘infinitely small’. By infinitely big, I mean the idea that space can have infinite volume, that time can continue forever, and that there can be infinitely many physical objects. By infinitely small, I mean the continuum: the idea that even a liter of space contains an infinite number of points, that space can be stretched out indefinitely without anything bad happening, and that there are quantities in nature that can vary continuously. The two are closely related: inflation created an infinite volume by stretching continuous space indefinitely.”
All this blows away two of the four levels of multiverse. The third one is the quantum multiverse. Remember the principle of equivalence? It actually applies here. There is only one mathematical expression of quantum field theory therefore all interpretations are equivalent. So the quantum multiverse is a legitimate but unverifiable interpretation. The final level is the mathematical universe, in which anything we can imagine is equally true. I will leave the evaluation of this idea to the reader.
The Trouble with Physics
In The Trouble with Physics: The Rise of String Theory, the Fall of a Science and What Comes Next Lee Smolin points out that scientific theories tend to take on a life of their own, even if there is little evidence to support them. Max Tegmark elevates this “bug” into the ultimate “feature” of his hypothesis: any and every valid mathematical structure defines a physical universe. By this logic, all 10^500 variants of string theory are by definition true. In the old days, a theory that predicted anything and everything was seen to predict nothing. Now, that is taken as more evidence for a multiverse.
The thing is, I really enjoyed reading this book. A lot of the information is well presented, and there are plenty of ideas with which to stimulate the imagination. There are some curiosities. For example, Tegmark is an expert on decoherence of the quantum wavefunction, and debunks the possibility of quantum processes in the brain. But the deeply related concept of entanglement is never mentioned.
Perhaps the saving grace is that most of the many questionable ideas get contradicted somewhere else. Controversy takes precedence over consistency. Perhaps we should think of all these contradictions as a superposition of states, which are true in different universes. Just not this one.
How can I rate such a book? For those with some knowledge of the subject, I give it five stars for its entertainment value. But I suggest those with less knowledge stay away – there is too much misleading material.
February 6, 2017
Who doesn’t like a good controversy in their popular science books? What’s a philosophical theory about the nature of the universe if it doesn’t ruffle some feathers? No one wants to write a book and then have everyone turn around and shrug at you. That doesn’t sell! So it’s not really surprising that Our Mathematical Universe: My Quest for the Ultimate Nature of Reality is a controversial book by a somewhat controversial physicist. I received this as a Christmas gift a few years ago, and that was the first I’ve heard of Max Tegmark. Since then he has popped up a few times here or there, and now I’ve finally made time to read this long and detailed treatise on the current state of physics and Tegmark’s personal conception of, well, reality.
I don’t actually find it all that controversial, per se—though I should clarify that I’m a mathematician by training, and not a physicist, so maybe the way Tegmark presents these ideas is more insulting or seems more radical when one is a physicist. That being said, I’m also not saying I agree with Tegmark’s Mathematical Universe Hypothesis (MUH), because, despite probably being a mathematical realist, Platonism itself strangely makes me uncomfortable….
Oh boy, I think I’ve already used too many strange terms! This review is probably going to get pretty heady and philosophical at some point, much like Our Mathematical Universe does. So let me spend the first part here just discussing the book, its structure and writing, etc., in a more general way, to give you an idea of whether or not it is of interest to you before you read my whole review. I’ll get to my thoughts about Tegmark’s specific claims later.
Firstly, regardless of any reservations I might have, I still recommend this book. This is a really well-written and approachable popular science work. Tegmark’s style is really accessible—despite going heavy on scientific and mathematical terminology, he is careful to proceed in a systematic way. This is not a book you want to be reading just before bed, maybe, or during a busy commute—it took me pretty much a week, albeit a busy week, to work my way through it. Nevertheless, I think it is a worthwhile use of one’s time.
Tegmark first impressed me with a table at the end of Chapter 1 called “How to read this book”. He lists every chapter of the book, along with three columns: Science-curious reader, hard-core reader of popular science, and physicist. Each column lists the chapters that reader would be best to read/skip—i.e., the science-curious reader should read the entire book; the hard-core reader can skip several of the earlier chapters because they presumably will have seen these explanations before; and the physicist can skip all but the controversial chapters (Tegmark also labels each chapter as “mainstream”, “controversial”, or “extremely controversial”). I love this approach and hope more popular science authors use it. Now, I, of course, ignored these suggestions and read the whole book anyway, because I wanted to see how Tegmark explained the Big Bang, inflation, etc. Yet I confess I skimmed some parts and felt better about it because I knew it was sanctioned.
One reason I’ll recommend this book is simply because Tegmark’s explanations for the origins of our universe, as currently understood by “mainstream” cosmology, are really lucid. He clarified several aspects of the Big Bang and inflation that, until now, I not only did not understand but didn’t realize I didn’t understand. He didn’t just improve my comprehension: he actually showed me parts of my comprehension of these theories that were inaccurate. I am not a physicist by training by any stretch of the imagination (I only took physics up to Grade 12 in high school, and they don’t even get into relativity by then, let alone QM); all of this knowledge is entirely autodidactic, and hence it isn’t surprising a lot if it is inaccurately understood. But I think I’ve plateaued a lot lately because I was having trouble finding explanations that were calibrated for my knowledge level: either the explanations get too technical and lose me, or else I just end up reading the same ground-floor “hey have you heard of this thing called the double-slit experiment?” stories over and over again, which isn’t fun either.
In particular, I really enjoyed Chapter 5, in which Tegmark explains inflation and why it is necessary to account for problems with the Big Bang theory. The idea of the Big Bang itself is now probably within the realm of general public knowledge, assuming a half-decent education (and regardless of whether one “accepts” the theory or prefers creationist nonsense). Yet there are probably as many misconceptions about this theory as there are explanations of it in popular science books, and once any two non-cosmologists start talking about it, we inevitably run into quasi-philosophical walls. Tegmark very clearly presents what the theory actually says; why it is compelling given the evidence; the problems with the theory without inflation and why inflation itself solves those problems.
Tegmark refers a lot to data gathered by several satellites and ground-based microwave telescopes that have observed the Cosmic Background Microwave Radiation (CBMR). He himself worked quite a bit on many of these projects, or with the data from these projects, to help sharpen and analyze this evidence. And this is another reason I enjoyed and recommend Our Mathematical Universe: Tegmark provides a great perspective on how science is done. From conferences to international projects poring over satellite data to writing and publishing papers, Tegmark shows us the act of physics research as much as the end result. He shows us how individual physicists’ opinions of theories will evolve over time. He shows us how people have different specializations, which in turn lead to different predilections and levels of knowledge about parts of physics. It’s really fascinating, and it’s an aspect to the discourse around science that I wish more media would cover.
So the first 6 or 7 chapters of this book are excellent, and I recommend reading at least those. After Chapter 8, Tegmark introduces the more “controversial” content. As I said above, I don’t see it as controversial so much as a bundle of claims that are either uninteresting because they are obvious or unappealing because they are largely unintelligible. Now we arrive at the part of the review that gets technical.
Let me refer you to Scott Aaronson’s review. He is a computer scientist and much more well-versed in this stuff than I am, so his review goes into more depth behind the mathematical/physics claims that Tegmark makes. I found myself largely nodding along and agreeing with most of Aaronson’s opinions there.
You might think that I, as a mathematically-inclined person, might seize upon the idea presented here. Tegmark’s MUH says not only that we can describe the universe using mathematics (a notion almost axiomatic to our physics) but that all of our physical reality itself is literally mathematical. That is, our entire subjective human experiences are simply the consequence of certain facets of a certain mathematical structure within a superset of structures, the entirety of which comprise the Level IV multiverse, i.e., the sum total of all existence and anything that could ever possibly exist.
It’s tempting. And yet….
Years ago I read The Grand Design . This was back in my university days, mind, when I was high on philosophy classes of all kinds and armed much more to purpose for these kinds of throw-downs. Nowadays, my memory of the differences between ontological and epistemological arguments requiring jogging from Wikipedia, I’m not so sure I’m up to the task. Yet one idea has stayed with me from Hawking and Mlodinow’s book: that of model-dependent realism. They proposed that the reason we are having so much trouble finding a “theory of everything” to unify the physics of the big (relativity) and the physics of the small (QM) is because no such theory exists. Rather, different theories are required depending on the situation one is trying to model. It is an intriguing idea, one I hadn’t really encountered in a science book before. And I really liked how it short-circuited many anti-realist objections to scientific realism.
Tegmark appears to move in the opposite direction. He backs the ToE horse (which is fine) by insisting that the ToE is reality. And then he kind of dodges the question of whether that means we will ever actually find a ToE (because if we did, wouldn’t that mean we just have … reality?).
That’s what I mean about the MUH being uninteresting and unintelligible. He starts off by talking about how the movement of time is an illusion, all very much standard stuff depending on how you define spacetime, etc. Yawn. When we get into the more “controversial” material, his argument just sort of breaks down. He starts making a whole bunch of probabilistic paradox arguments, like quantum suicide, the doomsday argument, etc.—the kind of thought experiments that are fun to put into a first-year philosophy textbook but that have little connection to, you know, reality. These thought experiments rely explicitly on making assumptions to make up for our near-total lack of knowledge about a situation. The whole point is that, as we acquire more certain knowledge, we are in a better position to see if we are indeed a representative sample or if, perhaps however improbably, we are not.
Tegmark’s MUH is also, despite his claims to the contrary, completely untestable/unfalsifiable. He insists that we will uncover evidence and create theories which logically imply the MUH, and that’s just silly. The MUH is untestable because we currently have no alternative to mathematics as a way of describing physical theories of reality. It is unfalsifiable, because even if we can get past the testing problem, how will we know if we’ve discovered a physical law or property that violates the MUH? Almost by definition, the MUH can take nearly any observational evidence and somehow fit into its framework. Tegmark claims that if the MUH is false, then we will one day run up against an insurmountable “wall” in physics beyond which our knowledge of reality can progress no further, since our mathematics will no longer be able to express reality. I disagree. I think model-dependent realism would be an effective way to counteract such a wall: maybe to progress, all we need do is abandon the search for a ToE and instead create theories of everything.
The last half of Our Mathematical Universe is a wild ride of philosophy of mathematics and science. I loved reading it. I found parts of it very convincing, but I don’t think those parts (combined with the other parts) necessarily add up to the whole that Tegmark calls the Level IV multiverse, the Mathematical Universe Hypothesis. I think he is incredibly enthusiastic about this idea and has clearly spent a lot of time thinking on it—which is great. I loved that I got a chance to read it. But I don’t think his arguments are as sound as he thinks they are. I say this not from a physicist’s position (because I’m not one) nor even a mathematician/logician (because, let’s face it, my memory of higher math dims with each passing day) but as the target demographic for this book, the hard-core popular science reader who is looking for a new hit to bring on that theoretical physics high. It’s a nice try, Tegmark, and you almost had me going.
I don’t actually find it all that controversial, per se—though I should clarify that I’m a mathematician by training, and not a physicist, so maybe the way Tegmark presents these ideas is more insulting or seems more radical when one is a physicist. That being said, I’m also not saying I agree with Tegmark’s Mathematical Universe Hypothesis (MUH), because, despite probably being a mathematical realist, Platonism itself strangely makes me uncomfortable….
Oh boy, I think I’ve already used too many strange terms! This review is probably going to get pretty heady and philosophical at some point, much like Our Mathematical Universe does. So let me spend the first part here just discussing the book, its structure and writing, etc., in a more general way, to give you an idea of whether or not it is of interest to you before you read my whole review. I’ll get to my thoughts about Tegmark’s specific claims later.
Firstly, regardless of any reservations I might have, I still recommend this book. This is a really well-written and approachable popular science work. Tegmark’s style is really accessible—despite going heavy on scientific and mathematical terminology, he is careful to proceed in a systematic way. This is not a book you want to be reading just before bed, maybe, or during a busy commute—it took me pretty much a week, albeit a busy week, to work my way through it. Nevertheless, I think it is a worthwhile use of one’s time.
Tegmark first impressed me with a table at the end of Chapter 1 called “How to read this book”. He lists every chapter of the book, along with three columns: Science-curious reader, hard-core reader of popular science, and physicist. Each column lists the chapters that reader would be best to read/skip—i.e., the science-curious reader should read the entire book; the hard-core reader can skip several of the earlier chapters because they presumably will have seen these explanations before; and the physicist can skip all but the controversial chapters (Tegmark also labels each chapter as “mainstream”, “controversial”, or “extremely controversial”). I love this approach and hope more popular science authors use it. Now, I, of course, ignored these suggestions and read the whole book anyway, because I wanted to see how Tegmark explained the Big Bang, inflation, etc. Yet I confess I skimmed some parts and felt better about it because I knew it was sanctioned.
One reason I’ll recommend this book is simply because Tegmark’s explanations for the origins of our universe, as currently understood by “mainstream” cosmology, are really lucid. He clarified several aspects of the Big Bang and inflation that, until now, I not only did not understand but didn’t realize I didn’t understand. He didn’t just improve my comprehension: he actually showed me parts of my comprehension of these theories that were inaccurate. I am not a physicist by training by any stretch of the imagination (I only took physics up to Grade 12 in high school, and they don’t even get into relativity by then, let alone QM); all of this knowledge is entirely autodidactic, and hence it isn’t surprising a lot if it is inaccurately understood. But I think I’ve plateaued a lot lately because I was having trouble finding explanations that were calibrated for my knowledge level: either the explanations get too technical and lose me, or else I just end up reading the same ground-floor “hey have you heard of this thing called the double-slit experiment?” stories over and over again, which isn’t fun either.
In particular, I really enjoyed Chapter 5, in which Tegmark explains inflation and why it is necessary to account for problems with the Big Bang theory. The idea of the Big Bang itself is now probably within the realm of general public knowledge, assuming a half-decent education (and regardless of whether one “accepts” the theory or prefers creationist nonsense). Yet there are probably as many misconceptions about this theory as there are explanations of it in popular science books, and once any two non-cosmologists start talking about it, we inevitably run into quasi-philosophical walls. Tegmark very clearly presents what the theory actually says; why it is compelling given the evidence; the problems with the theory without inflation and why inflation itself solves those problems.
Tegmark refers a lot to data gathered by several satellites and ground-based microwave telescopes that have observed the Cosmic Background Microwave Radiation (CBMR). He himself worked quite a bit on many of these projects, or with the data from these projects, to help sharpen and analyze this evidence. And this is another reason I enjoyed and recommend Our Mathematical Universe: Tegmark provides a great perspective on how science is done. From conferences to international projects poring over satellite data to writing and publishing papers, Tegmark shows us the act of physics research as much as the end result. He shows us how individual physicists’ opinions of theories will evolve over time. He shows us how people have different specializations, which in turn lead to different predilections and levels of knowledge about parts of physics. It’s really fascinating, and it’s an aspect to the discourse around science that I wish more media would cover.
So the first 6 or 7 chapters of this book are excellent, and I recommend reading at least those. After Chapter 8, Tegmark introduces the more “controversial” content. As I said above, I don’t see it as controversial so much as a bundle of claims that are either uninteresting because they are obvious or unappealing because they are largely unintelligible. Now we arrive at the part of the review that gets technical.
Let me refer you to Scott Aaronson’s review. He is a computer scientist and much more well-versed in this stuff than I am, so his review goes into more depth behind the mathematical/physics claims that Tegmark makes. I found myself largely nodding along and agreeing with most of Aaronson’s opinions there.
You might think that I, as a mathematically-inclined person, might seize upon the idea presented here. Tegmark’s MUH says not only that we can describe the universe using mathematics (a notion almost axiomatic to our physics) but that all of our physical reality itself is literally mathematical. That is, our entire subjective human experiences are simply the consequence of certain facets of a certain mathematical structure within a superset of structures, the entirety of which comprise the Level IV multiverse, i.e., the sum total of all existence and anything that could ever possibly exist.
It’s tempting. And yet….
Years ago I read The Grand Design . This was back in my university days, mind, when I was high on philosophy classes of all kinds and armed much more to purpose for these kinds of throw-downs. Nowadays, my memory of the differences between ontological and epistemological arguments requiring jogging from Wikipedia, I’m not so sure I’m up to the task. Yet one idea has stayed with me from Hawking and Mlodinow’s book: that of model-dependent realism. They proposed that the reason we are having so much trouble finding a “theory of everything” to unify the physics of the big (relativity) and the physics of the small (QM) is because no such theory exists. Rather, different theories are required depending on the situation one is trying to model. It is an intriguing idea, one I hadn’t really encountered in a science book before. And I really liked how it short-circuited many anti-realist objections to scientific realism.
Tegmark appears to move in the opposite direction. He backs the ToE horse (which is fine) by insisting that the ToE is reality. And then he kind of dodges the question of whether that means we will ever actually find a ToE (because if we did, wouldn’t that mean we just have … reality?).
That’s what I mean about the MUH being uninteresting and unintelligible. He starts off by talking about how the movement of time is an illusion, all very much standard stuff depending on how you define spacetime, etc. Yawn. When we get into the more “controversial” material, his argument just sort of breaks down. He starts making a whole bunch of probabilistic paradox arguments, like quantum suicide, the doomsday argument, etc.—the kind of thought experiments that are fun to put into a first-year philosophy textbook but that have little connection to, you know, reality. These thought experiments rely explicitly on making assumptions to make up for our near-total lack of knowledge about a situation. The whole point is that, as we acquire more certain knowledge, we are in a better position to see if we are indeed a representative sample or if, perhaps however improbably, we are not.
Tegmark’s MUH is also, despite his claims to the contrary, completely untestable/unfalsifiable. He insists that we will uncover evidence and create theories which logically imply the MUH, and that’s just silly. The MUH is untestable because we currently have no alternative to mathematics as a way of describing physical theories of reality. It is unfalsifiable, because even if we can get past the testing problem, how will we know if we’ve discovered a physical law or property that violates the MUH? Almost by definition, the MUH can take nearly any observational evidence and somehow fit into its framework. Tegmark claims that if the MUH is false, then we will one day run up against an insurmountable “wall” in physics beyond which our knowledge of reality can progress no further, since our mathematics will no longer be able to express reality. I disagree. I think model-dependent realism would be an effective way to counteract such a wall: maybe to progress, all we need do is abandon the search for a ToE and instead create theories of everything.
The last half of Our Mathematical Universe is a wild ride of philosophy of mathematics and science. I loved reading it. I found parts of it very convincing, but I don’t think those parts (combined with the other parts) necessarily add up to the whole that Tegmark calls the Level IV multiverse, the Mathematical Universe Hypothesis. I think he is incredibly enthusiastic about this idea and has clearly spent a lot of time thinking on it—which is great. I loved that I got a chance to read it. But I don’t think his arguments are as sound as he thinks they are. I say this not from a physicist’s position (because I’m not one) nor even a mathematician/logician (because, let’s face it, my memory of higher math dims with each passing day) but as the target demographic for this book, the hard-core popular science reader who is looking for a new hit to bring on that theoretical physics high. It’s a nice try, Tegmark, and you almost had me going.
January 5, 2016
If Sean Carroll, Vlatko Vedral, and Richard Feynman morphed into one person and wrote a book, I think it might look something like this book. I loved every page. Without question, this was one of my favorite books about the universe.
Lately I have been interested in information theory. Reading multiple books on the same subject, there is always the danger of becoming bored. After reading other books on the subject, I read this book and Island of Knowledge by Gleiser at the same time. Both of these books were excellent. Both books had a good deal of overlap but were markedly different in important ways. Rather than being repetitive, they served more to reinforce important ideas. The time I spent getting familiar with these books (often reading chapters over and over again) was deeply, deeply enjoyable.
Tegmark's sprinkling of biographical information along side his tutorials on basic and complex concepts in physics reminded me a lot of Feynman, if Feynman had been humble. Tegmark's gift for making the complex accessible to non-physicists reminded me of Carroll's gift in relating to all types of audiences. The subject matter in this book reminded me of Vedral's decoding reality, but it delved in a bit more at times and provided a richer over all experience, which felt more satisfying.
Tegmark provides one of the simplest and most beautiful descriptions of how each thing (be it atom, star, person, etc) is merely a compilation of smaller things that can ultimately be thought about ( and indeed do exist) as tiny bits of information. For sure, this argument has been made many times before, but I enjoyed Tegmark's argument to a surprising degree.
This was one of the most satisfying reading experiences I have had in a long time. When Tegmark related his Jekyll and Hyde story and then got into the meat of his argument, my brain was in a constant state of euphoria. Braingasm, braingasm, braingasm! I could feel the dopamine rush as he flooded my brain with idea after idea. While at university, I used to sit and talk with two of my best friends, and intellectual soulmates, about the ultimate nature of the universe. These times are some of my most treasured memories in life. Reading this book was like being back in those conversations.
Lately I have been interested in information theory. Reading multiple books on the same subject, there is always the danger of becoming bored. After reading other books on the subject, I read this book and Island of Knowledge by Gleiser at the same time. Both of these books were excellent. Both books had a good deal of overlap but were markedly different in important ways. Rather than being repetitive, they served more to reinforce important ideas. The time I spent getting familiar with these books (often reading chapters over and over again) was deeply, deeply enjoyable.
Tegmark's sprinkling of biographical information along side his tutorials on basic and complex concepts in physics reminded me a lot of Feynman, if Feynman had been humble. Tegmark's gift for making the complex accessible to non-physicists reminded me of Carroll's gift in relating to all types of audiences. The subject matter in this book reminded me of Vedral's decoding reality, but it delved in a bit more at times and provided a richer over all experience, which felt more satisfying.
Tegmark provides one of the simplest and most beautiful descriptions of how each thing (be it atom, star, person, etc) is merely a compilation of smaller things that can ultimately be thought about ( and indeed do exist) as tiny bits of information. For sure, this argument has been made many times before, but I enjoyed Tegmark's argument to a surprising degree.
This was one of the most satisfying reading experiences I have had in a long time. When Tegmark related his Jekyll and Hyde story and then got into the meat of his argument, my brain was in a constant state of euphoria. Braingasm, braingasm, braingasm! I could feel the dopamine rush as he flooded my brain with idea after idea. While at university, I used to sit and talk with two of my best friends, and intellectual soulmates, about the ultimate nature of the universe. These times are some of my most treasured memories in life. Reading this book was like being back in those conversations.
January 9, 2014
A fascinating exploration into our vast Universe that transcends all boundaries, by transporting you to remarkable heights!
This book is an exceptionally eye-opening read containing new, fresh concepts and unbelievable {sometimes shocking} insights. ‘Our Mathematical universe’ covers topics such as cosmology,unique philosophy and the nature of reality. It delves into scientific topics such as ‘the Big Bang’ and the beginning of creation and life itself, to our future and the existence of parallel worlds {both sub-atomic and intergalactic}. This supremely singular study could be classed as a science-fiction sub-genre if it were not for the use of mathematics which the author relies heavily on; for explanation of theories and a deeper understanding. So many of our deepest questions are attempted to be answered, with Max Tegmark using mathematics such as for instance; the scope of reality, what everything is made of and why our universe is the way it is.
Including many charts/ graphs and diagrams alongside facts to back up the hypothesis, this truly is an in-depth look into our world written by such a visionary masterful author. Anyone who is interested in finding out more about our world and the unexplained will be dazzled by this engaging, credible book as too will those sceptics who seek answers to all the riddles. If you like books by Professor Brian Cox then this is an ideal read for you! I am so pleased to have won a copy of ‘Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark’ through a Goodreads, first-read giveaway.
An illuminating read @ 3.5 stars!
This book is an exceptionally eye-opening read containing new, fresh concepts and unbelievable {sometimes shocking} insights. ‘Our Mathematical universe’ covers topics such as cosmology,unique philosophy and the nature of reality. It delves into scientific topics such as ‘the Big Bang’ and the beginning of creation and life itself, to our future and the existence of parallel worlds {both sub-atomic and intergalactic}. This supremely singular study could be classed as a science-fiction sub-genre if it were not for the use of mathematics which the author relies heavily on; for explanation of theories and a deeper understanding. So many of our deepest questions are attempted to be answered, with Max Tegmark using mathematics such as for instance; the scope of reality, what everything is made of and why our universe is the way it is.
Including many charts/ graphs and diagrams alongside facts to back up the hypothesis, this truly is an in-depth look into our world written by such a visionary masterful author. Anyone who is interested in finding out more about our world and the unexplained will be dazzled by this engaging, credible book as too will those sceptics who seek answers to all the riddles. If you like books by Professor Brian Cox then this is an ideal read for you! I am so pleased to have won a copy of ‘Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark’ through a Goodreads, first-read giveaway.
An illuminating read @ 3.5 stars!
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