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Our Mathematical Universe: My Quest for the Ultimate Nature of Reality Hardcover – Deckle Edge, January 7, 2014
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*Starred Review* Nobel-laureate physicist Eugene Wigner regarded the power of mathematics to explain the cosmos as a baffling mystery. Tegmark offers a resolution of that mystery, arguing that mathematics describes the universe so well because the universe ultimately is mathematics. The rare intellectual daring in this claim emerges as Tegmark teases out its stunning implications not only for the visible universe but also for countless, unseen, parallel universes (on four levels!) in which all conceivable possibilities become realities. Aware of the skeptics, Tegmark demonstrates that his theorizing harmonizes with concepts now central to cosmology, particularly the astrophysical formulas for the post–Big Bang inflation that gave space its geometry. Tegmark’s mathematical paradigm also accounts for the strange fine-tuning of the universe’s fundamental constants and dispels the paradoxes surrounding quantum measurement. Lively and lucid, the narrative invites general readers into debates over computer models for brain function, over scientific explanations of consciousness, and over prospects for finding advanced life in other galaxies. Though he reflects soberly on the perils of nuclear war and of hostile artificial intelligence, Tegmark concludes with a bracingly upbeat call for scientifically minded activists who recognize a rare opportunity to make our special planet a force for cosmic progress. An exhilarating adventure for bold readers. --Bryce Christensen
Brian Greene, physicist, author of The Elegant Universe and The Hidden Reality
“Our Mathematical Universe boldly confronts one of the deepest questions at the fertile interface of physics and philosophy: why is mathematics so spectacularly successful at describing the cosmos? Through lively writing and wonderfully accessible explanations, Max Tegmark—one of the world’s leading theoretical physicists—guides the reader to a possible answer, and reveals how, if it’s right, our understanding of reality itself would be radically altered.”
Michio Kaku, author of Physics of the Future
“Daring, Radical. Innovative. A game changer. If Dr. Tegmark is correct, this represents a paradigm shift in the relationship between physics and mathematics, forcing us to rewrite our textbooks. A must read for anyone deeply concerned about our universe.”
Ray Kurzweil, author of The Singularity is Near
“Tegmark offers a fresh and fascinating perspective on the fabric of physical reality and life itself. He helps us see ourselves in a cosmic context that highlights the grand opportunities for the future of life in our universe.”
Prof. Edward Witten, physicist, Fields Medalist & Milner Laureate
“Readers of varied backgrounds will enjoy this book. Almost anyone will find something to learn here, much to ponder, and perhaps something to disagree with.”
Prof. Andrei Linde, physicist, Gruber & Milner Laureate for development of inflationary cosmology
“This inspirational book written by a true expert presents an explosive mixture of physics, mathematics and philosophy which may alter your views on reality.”
Prof. Mario Livio, astrophysicist, author of Brilliant Blunders and Is God a Mathematician?
“Galileo famously said that the universe is written in the language of mathematics. Now Max Tegmark says that the universe IS mathematics. You don’t have to necessarily agree, to enjoy this fascinating journey into the nature of reality.”
Prof. Julian Barbour, physicist, author of The End of Time
“Scientists and lay aficionados alike will find Tegmark’s book packed with information and very thought provoking. You may recoil from his thesis, but nearly every page will make you wish you could debate the issues face-to-face with him.”
Prof. Seth Lloyd, Professor of quantum mechanical engineering, MIT, author of Programming the Universe
“In Our Mathematical Universe, renowned cosmologist Max Tegmark takes us on a whirlwind tour of the universe, past, present—and other. With lucid language and clear examples, Tegmark provides us with the master measure of not only of our cosmos, but of all possible universes. The universe may be lonely, but it is not alone.”
Prof. David Deutsch, physicist, Dirac Laureate for pioneering quantum computing
“A lucid, engaging account of the various many-universes theories of fundamental physics that are currently being considered, from the multiverse of quantum theory to Tegmark’s own grand vision.”
Amir Alexander, The New York Times
“This is science writing at its best — dynamic, dramatic and accessible. […] ‘Our Mathematical Universe’ is nothing if not impressive. Brilliantly argued and beautifully written, it is never less than thought-provoking about the greatest mysteries of our existence.”
Publishers Weekly (starred review)
“Tegmark offers a fascinating exploration of multiverse theories, each one offering new ways to explain ‘quantum weirdness’ and other mysteries that have plagued physicists, culminating in the idea that our physical world is ‘a giant mathematical object’ shaped by geometry and symmetry. Tegmark’s writing is lucid, enthusiastic, and outright entertaining, a thoroughly accessible discussion leavened with anecdotes and the pure joy of a scientist at work.”
Bryce Cristensen, Booklist (starred review)
“Lively and lucid, the narrative invites general readers into debates over computer models for brain function, over scientific explanations of consciousness, and over prospects for finding advanced life in other galaxies. Though he reflects soberly on the perils of nuclear war and of hostile artificial intelligence, Tegmark concludes with a bracingly upbeat call for scientifically minded activists who recognize a rare opportunity to make our special planet a force for cosmic progress. An exhilarating adventure for bold readers.”
Robert Matthews, BBC Focus magazine
“Max Tegmark is a professor of physics at MIT and a leading expert on theories of the Universe. But he’s also arguably the nearest we have to a successor to Richard Feynman, the bongo-playing, wise-cracking physicist who proved it is possible to be smart, savvy and subversive at the same time. […] now `Mad Max’ has been given the freedom of an entire book. And he hasn't wasted it. Around half of it is a lucid tour d'horizon of what we know about the Universe. The rest is an exhilarating expedition far beyond conventional thinking, in search of the true meaning of reality. Don't be fooled: Tegmark is a very smart physicist, not a hand-waving philosopher, so the going gets tough in parts. But his insights and conclusions are staggering—and perhaps even crazy enough to be true.”
Andrew Liddle, Nature
“Cosmologist Max Tegmark has written an engaging and accessible book, Our Mathematical Universe, that grapples with this multiverse scenario. He aims initially at the scientifically literate public, but seeks to take us to—and, indeed, beyond—the frontiers of accepted knowledge. […] This is a valuable book, written in a deceptively simple style but not afraid to make significant demands on its readers, especially once the multiverse level gets turned up to four. It is impressive how far Tegmark can carry you until, like a cartoon character running off a cliff, you wonder whether there is anything holding you up.”
Peter Woit, The Wall Street Journal
“Our Mathematical Universe is a fascinating and well-executed dramatic argument from a talented expositor.”
Edward Frenkel, The New York Times Sunday Book Review
"An informative survey of exciting recent developments in astrophysics and quantum theory [...] Tegmark participated in some of these pioneering developments, and he enlivens his story with personal anecdotes. [...] Tegmark does an excellent job explaining this and other puzzles in a way accessible to nonspecialists. Packed with clever metaphors”
Nathan Gelgud, Biographile Nathan Gelgud, Biographile
“Just a few years ago, the idea of multiple universes was seen as a crackpot idea, not even on the margins of respectability. […] But now, thanks in large part to Tegmark and his pursuit of controversial ideas, the concept of multiple universes (or a multiverse) is considered likely by many experts in the field.[…] Tegmark's clear, engaging prose style can take you down these exciting and unexpected pathways of thought without making you feel lost. [...] in Our Mathematical Universe, we meet a revolutionary cosmology physicist who is hell bent on figuring out if that theory is true, how to prove it, how to use it, and what it means for the world as we know it.”
Clive Cookson, Financial Times
“Today multiple universes are scientifically respectable, thanks to the work of Tegmark as much as anyone. [...] Physics could do with more characters like Tegmark. He combines an imaginative intellect and a charismatic presence with a determination to promote his subject [...] enough will be comprehensible for non-scientific readers to enjoy an amazing ride through the rich landscape of contemporary cosmology. There are many interesting diversions from the main argument, from an assessment of threats to human civilisation (such as a 30 per cent risk of nuclear war) to the chance of intelligent life elsewhere in our galaxy (lower than astrobiologists like to think). Written in a lively and slightly quirky style, it should engage any reader interested in the infinite variety of nature.”
Mark Buchanan, New Scientist
“The book is an excellent guide to recent developments in quantum cosmology and the ongoing debate over theories of parallel universes....Perhaps this book is proof that the two personalities needed for science—the speculative and sceptic—can readily exist in one individual.”
Peter Forbes, The Independent
"In Our Mathematical Universe, Max Tegmark—a distinguished cosmologist—gives a lucid rundown of the current state of knowledge on the origin, present state, and fate of the universe(s). [...] It is immensely illuminating on the reach of current cosmological theories. [...] From time to time, Tegmark engagingly admits that such ideas sound like nonsense, but he makes the crucial point that if a theory makes good predictions you have to follow all of the consequences. [...] His concluding chapter on the risks humanity faces is wise and bracing: he believes we "are alone in our Universe" but are capable of tackling terrible threats from cosmic accidents, or self-induced nuclear or climatic catastrophes. He doesn’t cite poets but his philosophy adds up to an updated 21st-century version of Thomas Hardy's 'If way to the better there be, it exacts a full look at the worst.'"
Giles Whittell, The Times
"mind-bending book about the cosmos" [...] "Tegmark's achievement is to explain what on earth he is talking about in language any reasonably attentive reader will understand. He is a professor at MIT, and clearly a fine teacher as well as thinker. He tackles the big, interrelated questions of cosmology and subatomic physics much more intelligibly than, say, Stephen Hawking."
Brian Rotman, The Guardian
"Max Tegmark's doorstopper of a book takes aim at three great puzzles: how large is reality? What is everything made of? Why is our universe the way it is? Tegmark, a professor of physics at MIT, writes at the cutting edge of cosmology and quantum theory in friendly and relaxed prose, full of entertaining anecdotes and down-to-earth analogies."
Stephen Hirtle, The Pittsburg Post-Gazette
"Our Mathematical Universe is a delightful book in which the Swedish-born author, now at MIT, takes readers on a roller coaster ride through cosmology, quantum mechanics, parallel universes, sub-atomic particles and the future of humanity. It is quite an adventure with many time-outs along the way.... Our Mathematical Universe gives keen insight into someone who asks questions for the pure joy of answering them."
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The first chapter serves as an introduction, setting the stage by considering the core question with which the book is concerned, “What is reality?” The book then proceeds in three parts. The first, Chapters 2 through 6, discuss the universe at the scale of the cosmos. Chapters two and three consider space and time and answer such questions as how big is the universe and where did everything come from. Chapter 4 explores many examples of mathematics’ “unreasonable effectiveness” in explaining our universe with respect to expansion and background radiation and the like (a more extensive discussion is in Ch. 10.) The fifth chapter investigates the big bang and our universe’s inflation. The last chapter in part one introduces the idea of multiverses and how the idea of multiple universes acts as an alternative explanation to prevailing notions in quantum physics (e.g. collapsing wave functions)—and, specifically, Tegmark describes the details of the first two of four models of the multiverse (i.e. the ones in which parallel universes are out there spread out across and infinite space), leaving the other two for the latter parts of the book.
Part two takes readers from the cosmological scale to the quantum scale, reflecting upon the nature of reality at the smallest scales—i.e. where the world gets weird. Chapter 7 is entitled “Cosmic Legos” and, as such, it describes the building blocks of our world as well as the oddities, anomalies, and counter-intuitive characteristics of the quantum realm. Chapter 8 brings in the Level III approach to multiverses and explains how it negates the need for waveform collapse that mainstream physics requires we accept (i.e. instead of a random outcome upon observation, both [or multiple] outcomes transpire as universes split.)
The final part is where Tegmark dives into his own theory. The first two parts having outlined what we know about the universe, and some of the major remaining mysteries left unexplained or unsubstantiated by current theories, Tegmark now makes his argument for why the Mathematical Universe Hypothesis (MUH) is at least as effective at explaining reality as any out there, and how it might eliminate some daunting mysteries.
Chapter 9 goes back to the topic of the first chapter, namely the nature of reality and the differences between our subjective internal reality, objective external reality, and a middling consensus reality. Chapter 10 also elaborates on the nature of reality, but this time by exploring mathematical and physical reality. Here he elaborates on how the universe behaves mathematically and explains the nature of mathematical structures—which is important as he is arguing the universe and everything in it may be one. Chapter 11 is entitled, “Is Time and Illusion?” and it proposes there is a block of space-time and our experience of time is an artifact of how we ride our world lines through it—in this view we are braids in space-time of the most complex kind observed. A lot of this chapter is about what we are and are not. Chapter 12 explains the Level IV multiverse (different laws for each universe) and what it does for us that the others do not. Chapter 13 is a bit different. It describes how we might destroy ourselves or die out, but that, it seems, is mostly a set up for a pep talk. You see, Tegmark has hypothesized a universe in which one might feel random and inconsequential, and so he wants to ensure the reader that that isn’t the case so that we don’t decide to plop down and watch the world burn.
While this book is about 4/5ths pop science physics book, the other 1/5th is a memoir of Tegmark’s trials and tribulations in coloring outside the lines with his science. All and all, I think this serves the book. The author avoids coming off as whiny in the way that scientists often do when writing about their challenges in obtaining funding and / or navigating a path to tenure that is sufficiently novel but not so heterodox as to be scandalous. There’s just enough to give you the feeling that he’s suffered for his science without making him seem ungrateful or like he has a martyr complex.
Graphics are presented throughout (photos, computer renderings, graphs, diagrams, etc.), and are essential because the book deals in complex concepts that aren’t easily translated from mathematics through text description and into a layman’s visualization. The book has endnotes to expand and clarify on points, some of which are mathematical—though not all. It also has recommended reading section to help the reader expand their understanding of the subject.
I enjoyed this book and found it to be loaded with food-for-thought. If Tegmark’s vision of the universe does prove to be meritorious, it will change our approach to the world. And, if not, it will make good fodder for sci-fi.
Combining the information with personal and world events that were occurring while various discoveries were made, kept the reading more lively. Not a textbook, more like an adventure. I seldom recommend a book this highly.
I have heard for a long time that the math for relativity or the very large and the math for quantum mechanics or the very small each work very well in their own settings, but try to put them together and they produce non-sense. The math that puts the two together predicts strings or loops that exist in many more than our usual four dimensions.
So we go from atoms to sub-atomic particles like protons to sub-sub-atomic fuzzy particles like up and down quarks to sub-sub-sub atomic vibrations – or equations. Things get fuzzier as we go down. Quarks are pretty fuzzy things. They are not building blocks. Stings or loops are not things at all. It is not that something is vibrating, it is the vibrations themselves that make up reality. There is no “thing” or building block of reality. There is no uncuttable thing like Democrates' atom that is at the basis of it all. There is only an abstraction or a number, according to Tegmark. Reality is based on numbers, math – a Platonic world of forms in a way.
I can say those words, just like I can say that a singularity is a point of infinite density and temperature without mass or space, but I really don’t know what that means.
But reality is not just independently existing vibrations. Reality comes from their relationships. Mathematical structures are about the relationships between units, in these cases vibrations. (“A mathematical structure is as set of abstract entities with relations between them.” p. 259) I have no idea why they relate at all to each other in certain ways to produce things like quarks, etc. But they do, or we would not be here. Beyond that, I can say things like gluons mediating the strong force that relates up and down quarks to each other in defined ways that lead to protons and neutrons. Relationships between particles are maybe even more real than the the particles themselves.
Why should the various forces, from the strong to weak to electromagnetic to gravity etc etc have the values they do? There is no reason for it. It is just that in our universe they do, or we would not be here. There are many other possible mathematical values for these and other possible forces, and all of those universes exist too, Tegmark argues. Most of them won’t lead to anything that we could recognize as structured reality since their values and math don’t go there. But out of an infinite number of possible values, there is at least one that has the ones that permit us to have evolved. Without all the many goldilocks conditions that have to exist for us to be here, we would not be here to be aware of our own universe and that others must exist as well.
Tegmark argues for four levels of multiverses and how each realizes a different mathematical structure.
Just a century ago, we thought that the Milky Way galaxy was the universe. We wondered if there were any other habitable planets. We now know there are billions of other galaxies and planets. Why shouldn't there be that many other universes? And math does have an uncanny ability to describe a reality that is more remarkable than we can grasp yet. Does math create universes? Do universes keep breaking off to form new ones every time we act in different ways at the same time? It's worth the time to read Tegmark's arguments for all this.
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