Our Mathematical Universe: My Quest for the Ultimate Nature of Reality Hardcover – Deckle Edge, January 7, 2014
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“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."
- Publisher : Knopf; 1st edition (January 7, 2014)
- Language : English
- Hardcover : 432 pages
- ISBN-10 : 0307599809
- ISBN-13 : 978-0307599803
- Item Weight : 1.8 pounds
- Dimensions : 6.6 x 1.6 x 9.52 inches
- Best Sellers Rank: #707,671 in Books (See Top 100 in Books)
- Customer Reviews:
"A timely novel highlighting the worth and delicate nature of Nature itself." -Delia Owens Learn more
Top reviews from the United States
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Thinkers working in the philosophy of mathematics since the time of Plato are traditionally separated between those who say that mathematical statements are true about the physical world (empiricists view), those who feel that this does not do justice to the inexorability of mathematics and claim an eternal truth status for mathematics (Platonic view) and a third view offered by Kant which is that mathematical statements are true for the 'form of our intuition'; that we bring them to the world to organize our experience of exigence to better navigate the world (intuitionist view). For Wittgenstein (twentieth-century), the whole idea that mathematics is concerned with the discovery of truth is a mistake. This mistake arose from the treatment of pure mathematics as an area of study apart from application to the physical sciences. When mathematics is treated as a tool, or a series of techniques for calculating, measuring, analyzing etc, philosophical questions about the nature mathematics simply do not arise. The philosophical nature of mathematics is so mush resolved as it dissolved by Wittgenstein.
From a purely utilitarian point of view, what matters most is that mathematics works and produces results. But since all mathematical models of the physical world break down at some point, combined with many inconstancies, paradoxes and unproven assumptions found at the heart of mathematics, I come down on the side of it being a human invention like chess, but a great invention it is!!!! Mathematics is not the language in which the universe is written, it is a selective tool which we use to explore the universe. Both chess and mathematics are highly useful systems, but constitutive of their rules, rules that are subjectively imposed by humans. In this frame of mind, we can take the “shackles” off our thinking – we need not wait around for a new discovery. Instead, we can be creative and free to invent more, better and new mathematics as needed. What the author does not see is that mathematics is a human creation, a tool that we use to explain physical reality to ourselves, not a feature of nature to be discovered.
In author’s defense, this book is not intended purely as a history of mathematics, but I think Russell’s paradox (shockingly not mentioned in this book) demonstrates that mathematics is a human invention. Russell’s paradox shows that mathematics is not rooted in logic as both Russell and Frege had originally set out to demonstrate. It is not objective. Mathematics is not the product of logic and objectivity separate or apart from the sensible subjective world. Mathematics, and logic, is more as Kant described it after all, its origins lie not in objective knowledge but in our own a priori subjective intuitions about space and time. Mathematics is not fundamentally an objective science - the product our discoveries about reality. Instead, at its foundations, it is a synthetic enterprise and its findings are based on our ability to use our imagination and harness our intuition. Mathematics is not a body of immutable absolute truth as Pythagoras, and later Plato, tells us and with which the author agrees. Rather, it is a collection of useful problem-solving techniques constructed upon, and built up from, the most banal tautologies.
The fact that we constantly fall into paradoxes combined with our ability to construct logical contradictions and traps demonstrates that the basis of logic itself is flawed or contains fundamental contradictions, e.g., again Russell’s paradox which is the result of a logical contradiction in the use of classifications to explain numbers and organize reality, number is a mathematical notion and class is a logical notion. The relationship between the internal reality of the human mind and external physical reality is a cacophony of concatenated asymmetrical subjective approximations that we invent and impose. Mathematics is the human way of imposing organization and determination onto an underlying reality of randomness and indeterminacy. To know mathematics, to know something about math & logic shows more about how human beings think, perceive and reason; not an objective truth about reality. Tegmark recognizes the subjectivism in a field such as economics, but not in mathematics, the only difference is the degree of subjectivity. Mathematics is not a body of metaphysical truths out there to be found. This is to succumb to a seductive ontological temptation. There is nothing there to be found that we did not put there ourselves. The author tells us that mathematical equations offer us a window into the working of nature. Maybe he is correct for reasons he does not realize, nature as we describe it with our mathematics is our subjective imposition so of course nature is full paradox and contraction because we put them there. Nature does not create paradoxes and contractions, humans do this. We then make the mistake of looking back on our subjective impositions upon the physical world and please ourselves by calling them objective.
Mathematics is an abstraction of the human mind, it does not have a separate existence to be discovered. There is no unified origin of everything, call it truth, math, science or God. The meaning is not in the mathematics, we do the mathematics and create the meaning. Mathematics is a discursive exercise. Instead, the author treats us to a curious mathematical fantasy whereby the path to ultimate knowledge is opened.
All knowledge cannot ultimately be squeezed into a form of pure mathematics. Knowledge cannot be narrowly reduced to necessary truths.
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.
Top reviews from other countries
This is perhaps best expressed in the title of one of Eugene Wigner's papers, 'the unreasonable effectiveness of Mathmatics in the natural sciences'. Why do a few simple formulas explain the fundemental structures of the universe?
Since as far back as Pythagoras, one proposal is that Mathmatics in the fundemental substance of the universe. This is a bold and controversial thesis. There are many that try to defend Mathmatical platonism, that in some sense the realm of Mathmatics really exists. However few go as far as Max Tegmark and postulate that the Universe simple is one elaborate mathmatical structure. Whilst hard to accept, I find this an interesting and exciting idea, which is worth exploring. It would certainly explain why our physical theories are so full of equations that are simple and work so well.
This subject alone could be elaborated across many books, however this hardly scratches the surface of all the topics that the author takes on. He throws out opinions on space, time, multiple universes, consciousness, the end of time, the meaning of life, the possibility of reality being a computer generation. This is a whistle stop tour of all the mind bending physical and metaphysical subjects you can think of.
Of course much of this is wild speculation, however I love to hear about the crazy big ideas and he might just be right about one of two things. Why should physicists stick to number crunching, they're as informed as anyone and entitled to take on the big philosophical questions. However it's up to the philosophers to check for inconsistentcies and perhaps breath a little more restraint into the picture. These questions will live on as long as humans are alive and it's always exciting to hear another radical voice. This is well worth reading.
I particularly like the anecdotes, illustrations, tables, summaries (in bullet points) and general handholding. He’s what I call a generous author.
Consequently while I started as a sceptic, I finished accepting and feeling I understood the logic of his ‘crazy’ hypothesis.
Like other reviewers, I wasn’t so impressed by the more skimmable last chapter, which seemed far less well constructed and less grounded, with a lot of ‘I think’ opinions about our fragile position in the universe. He probably feels he’s earned the right to bend our ears a bit, and indeed I think he has.
However I felt his strongest conclusion came in the previous chapter where he declares, “We’ve found ourselves inhabiting a reality far grander than our ancestors ever dreamed of, and this means that our future potential for life is much grander than we thought.”
The second part of the book deals with more esoteric subject matters,which is more challenging for the lay reader and requires more abstract imaginative processing to comprehend.
Overall I found the book is readable and I rarely counted the pages or became over taxed intellectually,which to me, is the sign of an excellent author.
But nonetheless this is the most enjoyable popular science book I have read in some years, and kept me hooked till the last page. Highly recommended.