The provocative subtitle contains the fallacy. This is the fallacy of looking for an ultimate reality apart from human experience. Tegmark, and authors like him, are using mathematics as a substitute for the religious need to be in touch with ultimate reality or absolute truth. We need to outgrow such childish needs. Truth is what works to advance human knowledge, understanding, wellbeing and flourishing. A pragmatic secular society is morally superior to one still tied to religious fundamentalism or the search for ultimate reality and absolute truth. These are not available to us. Everything decision we make or action we undertake is in the face on uncertainty and contingency accompanied by unintended consequences. How many ways and how many times do we have to ask ourselves if we are in touch with reality? Reality is our environment and the problems and opportunities it presents to us. The search for ultimate reality is just a substitute for the search for God. Both are a waste of time and effort.
In terms of truth and the nature of reality, we are just organisms trying to cope with our environment, the idea of a truth corresponding with reality is a meaningless question in that what we face is reality at our level of existence. This is by definition the truth of reality. When people speak of the correspondence theory of truth, I must ask, correspondence to what? Something non-human? A universal moral law, God, mathematical structure etc.? We already have scientific and other types of tests for adopting beliefs that work in our environment.
The author holds an unredeemed Platonic conception of mathematics and I will state at the outset of this review that I have a Kantian conception of mathematics. For Max Tegmark, the physical world is not only described mathematically, “…but that it is mathematics.” This is to claim too much. I will concede that mathematics occupies a privileged intermediate space between physical science and metaphysical speculation but I cannot conceded that existence is mathematical. To do so actually reaches back to the Pythagorean perspective of reality upon which Plato built. The mathematical structure that Tegmark sees as the instantiation of the physical world is one that has been found to be riddled with paradoxes and proven to be incomplete. I do not think that mathematics can be regarded as an a explanation in itself of anything. Physical theories are not what they are because of mathematics. Mathematics are the language in which we state our theories about the physical universe. That is, nothing is the way it is because of a mathematical principle. However, even if reality can be described mathematically, it does not follow that the final or ultimate ontology of realty is mathematical. If the ultimate nature of reality is mathematical it follows that mathematics is the cause of ultimate reality. This is, I am sorry, prima facie absurd. For example, we can describe everything we take to be reality with words, but it does not follow that the final or ultimate ontology of realty is linguistic. What is most interesting is that, from either or any philosophical perspective, paradoxes and incompleteness notwithstanding, the practical application mathematics proceeds and works as the author more than adequately demonstrates in this book. Mathematics still provides the most precise manner in which to express our theories, but it is also possible that we have a cognitive bias to seek theories to explain the universe that can be expressed mathematically. My concern here is more philosophical than practical.
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. I am suggesting that reality cannot simply be equated to mathematics or language. The social and cultural unities of mathematics and linguistics are well known, but their referents are from fixed. I argue that they have no definitive referents, no reality beyond which these discourses are constituted. This does not mean that they have no existence or that they are only exist discursively, but that there is no ultimate (extra-discursive) reality that these discourses simply reflect. Rather, what we know as mathematics or language is constituted through discursive relations within which our thoughts and theories about any possible extra-discursive aspects of reality are expressed. But these thoughts and theories are always subject to interpretation and a range meanings or as a corollary to a range of different meanings. I question the assumption and the possibility of knowing ultimate reality by any means and prefer to reflect upon the possibilities of reality explained in several different ways.
All knowledge cannot ultimately be squeezed into a form of pure mathematics. Knowledge cannot be narrowly reduced to necessary truths.
Other Sellers on Amazon
$16.46
+ $3.99 shipping
+ $3.99 shipping
Sold by:
allnewbooks
Sold by:
allnewbooks
(267932 ratings)
92% positive over last 12 months
92% positive over last 12 months
In stock.
Usually ships within 4 to 5 days.
Shipping rates
and
Return policy
Usually ships within 4 to 5 days.
$20.72
& FREE Shipping
& FREE Shipping
Sold by:
Book Depository US
Sold by:
Book Depository US
(911334 ratings)
89% positive over last 12 months
89% positive over last 12 months
In stock.
Usually ships within 3 to 4 days.
Shipping rates
and
Return policy
Usually ships within 3 to 4 days.
$17.53
+ $3.99 shipping
+ $3.99 shipping
Sold by:
Blackwell's U.K. *dispatched from UK*
Sold by:
Blackwell's U.K. *dispatched from UK*
(9387 ratings)
92% positive over last 12 months
92% positive over last 12 months
In stock.
Usually ships within 4 to 5 days.
Shipping rates
and
Return policy
Usually ships within 4 to 5 days.
Add to book club
Loading your book clubs
There was a problem loading your book clubs. Please try again.
Not in a club?
Learn more
Join or create book clubs
Choose books together
Track your books
Bring your club to Amazon Book Clubs, start a new book club and invite your friends to join, or find a club that’s right for you for free.
Flip to back
Flip to front
Follow the Author
Something went wrong. Please try your request again later.
OK
Our Mathematical Universe: My Quest for the Ultimate Nature of Reality Paperback – February 3, 2015
by
Max Tegmark
(Author)
|
Max Tegmark
(Author)
Find all the books, read about the author, and more.
See search results for this author
|
|
Price
|
New from | Used from |
|
Audible Audiobook, Unabridged
"Please retry"
|
$0.00
|
Free with your Audible trial | |
|
Hardcover, Deckle Edge
"Please retry"
|
$49.97 | $17.45 |
Enhance your purchase
-
Print length432 pages
-
LanguageEnglish
-
PublisherVintage
-
Publication dateFebruary 3, 2015
-
Dimensions6.1 x 0.9 x 9.2 inches
-
ISBN-100307744256
-
ISBN-13978-0307744258
The Amazon Book Review
Book recommendations, author interviews, editors' picks, and more. Read it now.
Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.
-
Apple
-
Android
-
Windows Phone
-
Android
|
Download to your computer
|
Kindle Cloud Reader
|
Frequently bought together
Customers who viewed this item also viewed
Page 1 of 1 Start overPage 1 of 1
Our Mathematical Universe & Life 3.0 Being Human in the Age of Artificial Intelligence By Max Tegmark 2 Books Collection SetMax TegmarkPaperback$54.99$54.99FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16Only 1 left in stock - order soon.
Something Deeply Hidden: Quantum Worlds and the Emergence of SpacetimeSean CarrollHardcover$16.73$16.73FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
The StrangerPaperback$6.39$6.39FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
The PlaguePaperback$9.29$9.29FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
Inferno (The Divine Comedy)DantePaperback$13.50$13.50FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
Siddhartha (Penguin Classics Deluxe Edition)Paperback$14.40$14.40FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
What other items do customers buy after viewing this item?
Page 1 of 1 Start overPage 1 of 1
The StrangerPaperback$6.39$6.39FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
Dante's InfernoPaperback$5.95$5.95FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Friday, Sep 17
Siddhartha: A NovelMass Market Paperback$6.24$6.24FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
Life 3.0: Being Human in the Age of Artificial IntelligencePaperback$14.99$14.99FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
The Inferno (Signet Classics)Dante AlighieriMass Market Paperback$5.95$5.95FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
Siddhartha (Penguin Classics Deluxe Edition)Paperback$14.40$14.40FREE Shipping on orders over $25 shipped by AmazonGet it as soon as Thursday, Sep 16
Editorial Reviews
Review
“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.” —Amir Alexander, The New York Times
“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.” —Andrew Liddle, Nature
“Our Mathematical Universe is a fascinating and well-executed dramatic argument from a talented expositor.” —Peter Woit, The Wall Street Journal
"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” —Edward Frenkel, The New York Times Sunday Book Review
“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.” —Mark Buchanan, New Scientist
“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.” —Brian Greene, physicist, author of The Elegant Universe and The Hidden Reality
“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.” —Michio Kaku, author of Physics of the Future
“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.” —Ray Kurzweil, author of The Singularity is Near
"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." —Stephen Hirtle, The Pittsburg Post-Gazette
“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. Edward Witten, physicist, Fields Medalist & Milner Laureate
“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. Andrei Linde, physicist, Gruber & Milner Laureate for development of inflationary cosmology
“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. Mario Livio, astrophysicist, author of Brilliant Blunders and Is God a Mathematician?
“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. Julian Barbour, physicist, author of The End of Time
“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. Seth Lloyd, Professor of quantum mechanical engineering, MIT, author of Programming the Universe
“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.” —Prof. David Deutsch, physicist, Dirac Laureate for pioneering quantum computing
“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.” —Publishers Weekly (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.” —Bryce Cristensen, Booklist (starred review)
“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.” —Robert Matthews, BBC Focus magazine
“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.” —Nathan Gelgud, Biographile Nathan Gelgud, Biographile
“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.” —Clive Cookson, Financial Times
"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.'" —Peter Forbes, The Independent
“[M]ind-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." —Giles Whittell, The Times
"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." —Brian Rotman, The Guardian
“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.” —Andrew Liddle, Nature
“Our Mathematical Universe is a fascinating and well-executed dramatic argument from a talented expositor.” —Peter Woit, The Wall Street Journal
"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” —Edward Frenkel, The New York Times Sunday Book Review
“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.” —Mark Buchanan, New Scientist
“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.” —Brian Greene, physicist, author of The Elegant Universe and The Hidden Reality
“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.” —Michio Kaku, author of Physics of the Future
“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.” —Ray Kurzweil, author of The Singularity is Near
"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." —Stephen Hirtle, The Pittsburg Post-Gazette
“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. Edward Witten, physicist, Fields Medalist & Milner Laureate
“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. Andrei Linde, physicist, Gruber & Milner Laureate for development of inflationary cosmology
“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. Mario Livio, astrophysicist, author of Brilliant Blunders and Is God a Mathematician?
“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. Julian Barbour, physicist, author of The End of Time
“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. Seth Lloyd, Professor of quantum mechanical engineering, MIT, author of Programming the Universe
“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.” —Prof. David Deutsch, physicist, Dirac Laureate for pioneering quantum computing
“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.” —Publishers Weekly (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.” —Bryce Cristensen, Booklist (starred review)
“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.” —Robert Matthews, BBC Focus magazine
“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.” —Nathan Gelgud, Biographile Nathan Gelgud, Biographile
“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.” —Clive Cookson, Financial Times
"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.'" —Peter Forbes, The Independent
“[M]ind-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." —Giles Whittell, The Times
"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." —Brian Rotman, The Guardian
About the Author
Max Tegmark is author or coauthor of more than two hundred technical papers, twelve of which have been cited more than five hundred times. He holds a Ph.D. from the University of California, Berkeley, and is a physics professor at MIT.
Excerpt. © Reprinted by permission. All rights reserved.
Chapter 9
Internal Reality, External Reality and Consensus Reality
Sweet exists by convention, bitter by convention, color by convention; atoms and void [alone] exist in reality.
—Democritus, ca. 400 B.C.
“Nooooo! My suitcase!”
They were already boarding my flight from Boston to Philadelphia,
where I was supposed to help with a BBC documentary about Hugh Everett, when I realized that my hand wasn’t holding a suitcase. I ran back to the security checkpoint.
“Did someone just forget a black roll-on bag here?”
“No,” said the guard.
“But there it is—that’s my suitcase, right there!”
“That’s not a black suitcase,” said the guard. “That’s a teal suitcase.”
Until then, I’d never realized how color-blind I was, and it was quite
humbling to realize that many assumptions I’d previously made about reality—and my wardrobe—were dead wrong. How could I ever trust what my senses told me about the outside world? And if I couldn’t, then how could I hope to ever know anything with certainty about the external reality? After all, everything I know about the outside world and my untrustworthy senses, I’ve learned from my senses. This puts me on the same shaky epistemological footing as a prisoner who’s spent his whole life in solitary confinement, whose only information about the outside world and his untrustworthy prison guard is what his prison guard has told him. More generally, how can I trust what my conscious perceptions tell me about the world if I don’t understand how my mind works?
This basic dilemma has been eloquently explored by philosophers throughout the ages, including titans such as Plato, René Descartes, David Hume and Immanuel Kant. Socrates said: “The only true wisdom is in knowing you know nothing.” So how can we make further progress in our quest to understand reality?
So far in this book, we’ve taken a physics approach to exploring our external physical reality, zooming out to the transgalactic macrocosm and zooming in to the subatomic microcosm, attempting to understand things in terms of their basic building blocks such as elementary particles. However, all we have direct knowledge of are instead qualia, the basic building blocks of our conscious perception,* (* For introductions to the vast literature on consciousness by psychologists, neuroscientists, philosophers and others, I recommend the books about the mind in the “Suggestions for Further Reading” section.) exemplified by the redness of a rose, the sound of a cymbal, the smell of a steak, the taste of a tangerine or the pain of a pinprick. So don’t we also need to understand consciousness before we can fully understand physics? I used to answer “yes,” thinking that we could never figure out the elusive “theory of everything” for our external physical reality without first understanding the distorting mental lens through which we perceive it. But I’ve changed my mind, and in this brief interlude chapter, I want to tell you why.
External Reality and Internal Reality
Perhaps you’re thinking, Okay, Max, but I’m not color-blind. And I’m looking at the external reality right now with my own eyes, and I’d have to be paranoid to think it’s not the way it looks. But please try these simple experiments:
Experiment 1: Turn your head from left to right a few times. Experiment 2: Move your eyes from left to right a few times, without moving your head.
Did you notice how the first time, the external reality appeared to rotate, and the second time, it appeared to stay still, even though your eyeballs rotated both times? This proves that what your mind’s eye is looking at isn’t the external reality, but a reality model stored in your brain! If you looked at the image recorded by a rotating video camera, you’d clearly see it move as it did in Experiment 1. But your eyes are a form of biological video camera, so Experiment 2 shows that your consciousness isn’t directly perceiving the images formed on their retinas. Rather, as neuroscientists have now studied in great detail, the information recorded by your retinas gets processed in highly complex ways and is used to continually update an elaborate model of the outside world that’s stored in your brain. Take another look in front of you, and you’ll see that, thanks to this advanced information processing, your reality model is three-dimensional even though the raw images from your retinas are two-dimensional.
I don’t have a light switch near my bed, so I’ll often take a good look at my bedroom and all the obstacles littering the floor, then turn off the light and walk to my bed. Try it yourself: put down this book, stand up, look around, and then walk a few steps with your eyes closed. Can you “see”/”feel” the objects in the room moving relative to you? That’s your reality model being updated, this time using information from your leg movements rather than from your eyes. Your brain continuously updates its reality model using any useful information it can get hold of, including sound, touch, smell and taste.
Let’s call this reality model your internal reality, because it’s the way you subjectively perceive the external reality from the internal vantage point of your mind. This reality is internal also in the sense that it exists only internally to you: your mind feels as if it’s looking at the outside world, while it’s actually looking only at a reality model inside your head—which in turn is continually tracking what’s outside your brain via elaborate but automatic processes that you’re not consciously aware of.
It’s absolutely crucial that we don’t conflate this internal reality with the external reality that it’s tracking, because the two are very different. My brain’s internal reality is like the dashboard of my car: a convenient summary of the most useful information. Just as my car’s dashboard tells me my speed, fuel level, motor temperature, and other things useful for a driver to be aware of, my brain’s dashboard/reality model tells me my speed and position, my hunger level, the air temperature, highlights of my surroundings and other things useful for the operator of a human body to be aware of.
The Truth, the Whole Truth and Nothing but the Truth
Once my car’s dashboard malfunctioned and sent me to the garage with its “CHECK ENGINE” indicator illuminated even though nothing was wrong. Similarly, there are many ways in which a person’s reality model can malfunction and differ from the true external reality, giving rise to illusions (incorrect perceptions of things that do exist in the external reality), omissions (nonperception of things that do exist in the external reality) and hallucinations (perceptions of things that don’t exist in the external reality). If we swear under oath to tell the truth, the whole truth and nothing but the truth, we should be aware that our perceptions might violate all three with illusions, omissions and hallucinations, respectively.
So metaphorically speaking, the “CHECK ENGINE” incident was my car hallucinating—or experiencing phantom pain. I recently discovered that my car also suffers from an illusion: based on its speedometer reading, it thinks it’s always driving two miles per hour faster than it really is. That’s not bad compared to the vast list of human illusions that cognitive scientists have discovered, which afflict all our senses and distort our internal reality. If your version of this figure is in color rather than black and white, you’ll probably see the lower dot in the left panel as orange and the upper dot as somewhat brown. Figure 9.1 (in the book) shows two examples of optical illusions, where our visual system creates an internal reality different from the external reality. In the external reality, the light from both of them has identical properties, with a wavelength around 600 nanometers. If a spotlight beamed out such light, it would be orange light. What about brown? Have you ever seen a spotlight or a laser pointer produce a brown beam? Well, you never will, because there’s no such thing as brown light! The color brown doesn’t exist in the external reality, but only in your internal reality: it’s simply what you perceive when seeing dim orange light against a darker background.
For fun, I sometimes compare how the same news story is reported online by MSNBC, FOX News, the BBC, Al Jazeera, Pravda and elsewhere. I find that when it comes to telling the truth, the whole truth, and nothing but the truth, it’s the second part that accounts for most of the differences in how they portray reality: what they omit. I think the same holds for our senses: although they can produce hallucinations and illusions, it’s their omissions that account for most of the discrepancy between the internal and external realities. My visual system omitted the information that distinguishes between black and teal suitcases, but even if you’re not color-blind, you’re missing out on the vast majority of the information that light carries. When I was taught in elementary school that all colors of light can be made up by mixing three primary colors red, green, and blue, I thought that this number three told us something fundamental about the external reality. But I was wrong: it teaches us only about the omissions of our visual system. Specifically, it tells us that our retina has three kinds of cone cells, which take the thousands of numbers that can be measured in a spectrum of light (see Figure 2.5 in Chapter 2) and keeps only three numbers, corresponding to the average light intensity across three broad ranges of wavelengths.
Moreover, wavelengths of light outside of the narrow range 400–700 nanometers go completely undetected by our visual system, and it came as quite a shock when human-built detectors revealed that our external reality was vastly richer than we’d realized, teeming with radio waves, microwaves, x-rays, and gamma rays. And vision isn’t the only one of our senses that’s guilty of omissions: we can’t hear the ultrasound chirping of mice, bats and dolphins; we’re oblivious to most faint scents that dominate the olfactory inner reality of dogs, and so on. Although some animal species capture more visual, auditory, olfactory, gustatory or other sensory information than we humans do, they’re all unaware of the sub-atomic realm, the galaxy-spangled cosmos, and the dark energy and dark matter that, as we saw in Chapter 4, makes up 96% of our external reality.
Consensus Reality
In the first two parts of this book, we’ve seen how our physical world can be remarkably well described by mathematical equations, fueling the hope that one day equations can be found for a “theory of everything,” perfectly describing our external reality on all scales. The ultimate triumph of physics would be to start with the external reality from the “bird perspective” of a mathematician studying these equations (which are ideally simple enough to fit on her T-shirt) and to derive from them her internal reality, the way she subjectively perceives it from her “frog perspective” inside the external reality. To accomplish this would clearly require a detailed understanding of how consciousness works, including illusions, omissions, hallucinations and other complications.
However, between the external reality and the internal reality, there’s also a third and intermediate consensus reality, as illustrated in Figure 9.2 (in the book). This is the version of reality that we life-forms here on Earth all agree on: the 3-D positions and motions of macroscopic objects, and other everyday attributes of the world for which we have a shared description in terms of familiar concepts from classical physics. Table 9.1 summarizes these reality descriptions and perspectives and how they’re interrelated.
Each of us has our own personal inner reality, perceived from the subjective perspective of our own position, orientation and state of mind, and distorted by our personal cognitive biases: in your inner reality, dreams are real and the world turns upside down when you stand on your head. In contrast, the consensus reality is shared. When you give your friend driving directions to your place, you do your best to trans- form your description from one involving subjective concepts from your inner reality (such as “here” and “in the direction I’m facing”) to shared concepts from the consensus reality (such as “on 70 Vassar Street” and “north”). Since we scientists need to be precise and quantitative when we refer to our shared consensus reality, we try extra-hard to be objective: we say that light has a “600-nanometer wavelength” instead of “orange color” and that something has “CH3COOC5H11 molecules” instead of “banana flavor.” The consensus reality isn’t free from some shared illusions relative to the external reality, as we’ll elaborate on below: for example, cats, bats and robots also experience the same quantum randomness and relativistic time dilation. However, it’s by definition free from illusions that are unique to biological minds, and therefore decouples from the issue of how our human consciousness works. The internal reality may feel teal deficient to me, black and white to a seal, iridescent to a bird seeing four primary colors, and still more different to a bee seeing polarized light, a bat using sonar, a blind person with keener touch and hearing, or the latest robotic vacuum cleaner, but we all agree on whether the door is open.
This is why I’ve changed my mind: although understanding the detailed nature of human consciousness is a fascinating challenge in its own right, it’s not necessary for a fundamental theory of physics, which need “only” derive the consensus reality from its equations. In other words, what Douglas Adams called “the ultimate question of life, the universe and everything” splits cleanly into two parts that can be tackled separately: the challenge for physics is deriving the consensus reality from the external reality, and the challenge for cognitive science is to derive the internal reality from the consensus reality. These are two great challenges for the third millennium. They’re each daunting in their own right, and I’m relieved that we need not solve them simultaneously.
Chapter 9 is continued in the book…
Internal Reality, External Reality and Consensus Reality
Sweet exists by convention, bitter by convention, color by convention; atoms and void [alone] exist in reality.
—Democritus, ca. 400 B.C.
“Nooooo! My suitcase!”
They were already boarding my flight from Boston to Philadelphia,
where I was supposed to help with a BBC documentary about Hugh Everett, when I realized that my hand wasn’t holding a suitcase. I ran back to the security checkpoint.
“Did someone just forget a black roll-on bag here?”
“No,” said the guard.
“But there it is—that’s my suitcase, right there!”
“That’s not a black suitcase,” said the guard. “That’s a teal suitcase.”
Until then, I’d never realized how color-blind I was, and it was quite
humbling to realize that many assumptions I’d previously made about reality—and my wardrobe—were dead wrong. How could I ever trust what my senses told me about the outside world? And if I couldn’t, then how could I hope to ever know anything with certainty about the external reality? After all, everything I know about the outside world and my untrustworthy senses, I’ve learned from my senses. This puts me on the same shaky epistemological footing as a prisoner who’s spent his whole life in solitary confinement, whose only information about the outside world and his untrustworthy prison guard is what his prison guard has told him. More generally, how can I trust what my conscious perceptions tell me about the world if I don’t understand how my mind works?
This basic dilemma has been eloquently explored by philosophers throughout the ages, including titans such as Plato, René Descartes, David Hume and Immanuel Kant. Socrates said: “The only true wisdom is in knowing you know nothing.” So how can we make further progress in our quest to understand reality?
So far in this book, we’ve taken a physics approach to exploring our external physical reality, zooming out to the transgalactic macrocosm and zooming in to the subatomic microcosm, attempting to understand things in terms of their basic building blocks such as elementary particles. However, all we have direct knowledge of are instead qualia, the basic building blocks of our conscious perception,* (* For introductions to the vast literature on consciousness by psychologists, neuroscientists, philosophers and others, I recommend the books about the mind in the “Suggestions for Further Reading” section.) exemplified by the redness of a rose, the sound of a cymbal, the smell of a steak, the taste of a tangerine or the pain of a pinprick. So don’t we also need to understand consciousness before we can fully understand physics? I used to answer “yes,” thinking that we could never figure out the elusive “theory of everything” for our external physical reality without first understanding the distorting mental lens through which we perceive it. But I’ve changed my mind, and in this brief interlude chapter, I want to tell you why.
External Reality and Internal Reality
Perhaps you’re thinking, Okay, Max, but I’m not color-blind. And I’m looking at the external reality right now with my own eyes, and I’d have to be paranoid to think it’s not the way it looks. But please try these simple experiments:
Experiment 1: Turn your head from left to right a few times. Experiment 2: Move your eyes from left to right a few times, without moving your head.
Did you notice how the first time, the external reality appeared to rotate, and the second time, it appeared to stay still, even though your eyeballs rotated both times? This proves that what your mind’s eye is looking at isn’t the external reality, but a reality model stored in your brain! If you looked at the image recorded by a rotating video camera, you’d clearly see it move as it did in Experiment 1. But your eyes are a form of biological video camera, so Experiment 2 shows that your consciousness isn’t directly perceiving the images formed on their retinas. Rather, as neuroscientists have now studied in great detail, the information recorded by your retinas gets processed in highly complex ways and is used to continually update an elaborate model of the outside world that’s stored in your brain. Take another look in front of you, and you’ll see that, thanks to this advanced information processing, your reality model is three-dimensional even though the raw images from your retinas are two-dimensional.
I don’t have a light switch near my bed, so I’ll often take a good look at my bedroom and all the obstacles littering the floor, then turn off the light and walk to my bed. Try it yourself: put down this book, stand up, look around, and then walk a few steps with your eyes closed. Can you “see”/”feel” the objects in the room moving relative to you? That’s your reality model being updated, this time using information from your leg movements rather than from your eyes. Your brain continuously updates its reality model using any useful information it can get hold of, including sound, touch, smell and taste.
Let’s call this reality model your internal reality, because it’s the way you subjectively perceive the external reality from the internal vantage point of your mind. This reality is internal also in the sense that it exists only internally to you: your mind feels as if it’s looking at the outside world, while it’s actually looking only at a reality model inside your head—which in turn is continually tracking what’s outside your brain via elaborate but automatic processes that you’re not consciously aware of.
It’s absolutely crucial that we don’t conflate this internal reality with the external reality that it’s tracking, because the two are very different. My brain’s internal reality is like the dashboard of my car: a convenient summary of the most useful information. Just as my car’s dashboard tells me my speed, fuel level, motor temperature, and other things useful for a driver to be aware of, my brain’s dashboard/reality model tells me my speed and position, my hunger level, the air temperature, highlights of my surroundings and other things useful for the operator of a human body to be aware of.
The Truth, the Whole Truth and Nothing but the Truth
Once my car’s dashboard malfunctioned and sent me to the garage with its “CHECK ENGINE” indicator illuminated even though nothing was wrong. Similarly, there are many ways in which a person’s reality model can malfunction and differ from the true external reality, giving rise to illusions (incorrect perceptions of things that do exist in the external reality), omissions (nonperception of things that do exist in the external reality) and hallucinations (perceptions of things that don’t exist in the external reality). If we swear under oath to tell the truth, the whole truth and nothing but the truth, we should be aware that our perceptions might violate all three with illusions, omissions and hallucinations, respectively.
So metaphorically speaking, the “CHECK ENGINE” incident was my car hallucinating—or experiencing phantom pain. I recently discovered that my car also suffers from an illusion: based on its speedometer reading, it thinks it’s always driving two miles per hour faster than it really is. That’s not bad compared to the vast list of human illusions that cognitive scientists have discovered, which afflict all our senses and distort our internal reality. If your version of this figure is in color rather than black and white, you’ll probably see the lower dot in the left panel as orange and the upper dot as somewhat brown. Figure 9.1 (in the book) shows two examples of optical illusions, where our visual system creates an internal reality different from the external reality. In the external reality, the light from both of them has identical properties, with a wavelength around 600 nanometers. If a spotlight beamed out such light, it would be orange light. What about brown? Have you ever seen a spotlight or a laser pointer produce a brown beam? Well, you never will, because there’s no such thing as brown light! The color brown doesn’t exist in the external reality, but only in your internal reality: it’s simply what you perceive when seeing dim orange light against a darker background.
For fun, I sometimes compare how the same news story is reported online by MSNBC, FOX News, the BBC, Al Jazeera, Pravda and elsewhere. I find that when it comes to telling the truth, the whole truth, and nothing but the truth, it’s the second part that accounts for most of the differences in how they portray reality: what they omit. I think the same holds for our senses: although they can produce hallucinations and illusions, it’s their omissions that account for most of the discrepancy between the internal and external realities. My visual system omitted the information that distinguishes between black and teal suitcases, but even if you’re not color-blind, you’re missing out on the vast majority of the information that light carries. When I was taught in elementary school that all colors of light can be made up by mixing three primary colors red, green, and blue, I thought that this number three told us something fundamental about the external reality. But I was wrong: it teaches us only about the omissions of our visual system. Specifically, it tells us that our retina has three kinds of cone cells, which take the thousands of numbers that can be measured in a spectrum of light (see Figure 2.5 in Chapter 2) and keeps only three numbers, corresponding to the average light intensity across three broad ranges of wavelengths.
Moreover, wavelengths of light outside of the narrow range 400–700 nanometers go completely undetected by our visual system, and it came as quite a shock when human-built detectors revealed that our external reality was vastly richer than we’d realized, teeming with radio waves, microwaves, x-rays, and gamma rays. And vision isn’t the only one of our senses that’s guilty of omissions: we can’t hear the ultrasound chirping of mice, bats and dolphins; we’re oblivious to most faint scents that dominate the olfactory inner reality of dogs, and so on. Although some animal species capture more visual, auditory, olfactory, gustatory or other sensory information than we humans do, they’re all unaware of the sub-atomic realm, the galaxy-spangled cosmos, and the dark energy and dark matter that, as we saw in Chapter 4, makes up 96% of our external reality.
Consensus Reality
In the first two parts of this book, we’ve seen how our physical world can be remarkably well described by mathematical equations, fueling the hope that one day equations can be found for a “theory of everything,” perfectly describing our external reality on all scales. The ultimate triumph of physics would be to start with the external reality from the “bird perspective” of a mathematician studying these equations (which are ideally simple enough to fit on her T-shirt) and to derive from them her internal reality, the way she subjectively perceives it from her “frog perspective” inside the external reality. To accomplish this would clearly require a detailed understanding of how consciousness works, including illusions, omissions, hallucinations and other complications.
However, between the external reality and the internal reality, there’s also a third and intermediate consensus reality, as illustrated in Figure 9.2 (in the book). This is the version of reality that we life-forms here on Earth all agree on: the 3-D positions and motions of macroscopic objects, and other everyday attributes of the world for which we have a shared description in terms of familiar concepts from classical physics. Table 9.1 summarizes these reality descriptions and perspectives and how they’re interrelated.
Each of us has our own personal inner reality, perceived from the subjective perspective of our own position, orientation and state of mind, and distorted by our personal cognitive biases: in your inner reality, dreams are real and the world turns upside down when you stand on your head. In contrast, the consensus reality is shared. When you give your friend driving directions to your place, you do your best to trans- form your description from one involving subjective concepts from your inner reality (such as “here” and “in the direction I’m facing”) to shared concepts from the consensus reality (such as “on 70 Vassar Street” and “north”). Since we scientists need to be precise and quantitative when we refer to our shared consensus reality, we try extra-hard to be objective: we say that light has a “600-nanometer wavelength” instead of “orange color” and that something has “CH3COOC5H11 molecules” instead of “banana flavor.” The consensus reality isn’t free from some shared illusions relative to the external reality, as we’ll elaborate on below: for example, cats, bats and robots also experience the same quantum randomness and relativistic time dilation. However, it’s by definition free from illusions that are unique to biological minds, and therefore decouples from the issue of how our human consciousness works. The internal reality may feel teal deficient to me, black and white to a seal, iridescent to a bird seeing four primary colors, and still more different to a bee seeing polarized light, a bat using sonar, a blind person with keener touch and hearing, or the latest robotic vacuum cleaner, but we all agree on whether the door is open.
This is why I’ve changed my mind: although understanding the detailed nature of human consciousness is a fascinating challenge in its own right, it’s not necessary for a fundamental theory of physics, which need “only” derive the consensus reality from its equations. In other words, what Douglas Adams called “the ultimate question of life, the universe and everything” splits cleanly into two parts that can be tackled separately: the challenge for physics is deriving the consensus reality from the external reality, and the challenge for cognitive science is to derive the internal reality from the consensus reality. These are two great challenges for the third millennium. They’re each daunting in their own right, and I’m relieved that we need not solve them simultaneously.
Chapter 9 is continued in the book…
Start reading Our Mathematical Universe on your Kindle in under a minute.
Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.
Don't have a Kindle? Get your Kindle here, or download a FREE Kindle Reading App.
Product details
- Publisher : Vintage; Reprint edition (February 3, 2015)
- Language : English
- Paperback : 432 pages
- ISBN-10 : 0307744256
- ISBN-13 : 978-0307744258
- Item Weight : 1.2 pounds
- Dimensions : 6.1 x 0.9 x 9.2 inches
-
Best Sellers Rank:
#36,869 in Books (See Top 100 in Books)
- #37 in Mathematics History
- #71 in Cosmology (Books)
- #220 in History & Philosophy of Science (Books)
- Customer Reviews:
Customer reviews
4.4 out of 5 stars
4.4 out of 5
980 global ratings
How are ratings calculated?
To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. It also analyzes reviews to verify trustworthiness.
Top reviews
Top reviews from the United States
There was a problem filtering reviews right now. Please try again later.
Reviewed in the United States on September 22, 2018
Verified Purchase
90 people found this helpful
Report abuse
4.0 out of 5 stars
A hypothesis of the universe as a mathematical structure, with a bit of scientific memoir interspersed.
Reviewed in the United States on September 6, 2017Verified Purchase
In this book, physicist Max Tegmark makes an argument for the possibility of a reality in which the universe is a mathematical structure a theory that predicts a Level IV multiverse (i.e. one in which various universes all have different physical laws and aren’t spread out across one infinite space [i.e. not “side-by-side.”]) Nobel Laureate Eugene Wigner wrote a famous paper entitled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” The article describes one of the great mysteries of science, namely, how come mathematics describes our universe so well and with such high precision. Tegmark’s answer is because the universe is fundamentally mathematical—or at least he suspects it could be.
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.
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.
47 people found this helpful
Report abuse
Top reviews from other countries
View from nowhere
5.0 out of 5 stars
The unreasonable effectiveness of mathmatics
Reviewed in the United Kingdom on December 29, 2020Verified Purchase
Having recently read an introduction to the philosophy of Mathmatics, I wanted to follow up by hearing about someone who tackles head on, one of the ancient questions, why a field of abstraction such as numbers, works so incredibly well at explaining the real world. Why have mathmatical patters developed by a single person with his pen, later have independent applications in the real world?
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.
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.
4 people found this helpful
Report abuse
SimpleSimon
5.0 out of 5 stars
Wonderful Book
Reviewed in the United Kingdom on January 4, 2021Verified Purchase
I join the consensus reality that this is a well written account of a couple of decades of exploring the big questions facing Physics and Philosophy and of a personal journey developing a coherent explanation for what we observe.
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.”
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.”
3 people found this helpful
Report abuse
nicholas hargreaves
5.0 out of 5 stars
Top Rate
Reviewed in the United Kingdom on September 4, 2014Verified Purchase
The first part is an excellent summary of cosmology and quantum physics that's the most readable and informative I've read to date.Or maybe that's an effect of having read too many books in the same genre. Either way the author makes light work of issues other authors struggle with, and each chapter concludes with a helpful brief outline to ease the process.
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.
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.
19 people found this helpful
Report abuse
dunxd
4.0 out of 5 stars
and how we need to protect our future from existential threats (with the techie favourite AI enslaving us all as the favourite t
Reviewed in the United Kingdom on February 21, 2016Verified Purchase
I fascinating tour of Tegmark's physics and mathematics view of the ultimate nature of reality, which touches on some mind blowing concepts, such as: an infinite physical universe, where everything may occur, including infinite versions of yourself separated by unsurmountable distance; and quantum suicide where you may in fact experience immortality (but everyone else sees you die). This book is definitely worth reading through for all these existential challenges. On the downside, these are all thought experiments that are probably impossible to prove as right or wrong (how can you verify if two possibilities both happen, since you can only experience one?) and perhaps the mathematical basis for reality is actually rooted in a socially constructed mathematical basis for understanding reality. Also Tegmark doesn't point us towards any practical outcomes of the theories described, apart from a final chapter on how unique and fragile we may be in the multiverse, and how we need to protect our future from existential threats (with the techie favourite AI enslaving us all as the favourite threat). I'd really like to have read some more predictions about where current experiments around gravity waves and Higgs bosons might lead.
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.
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.
3 people found this helpful
Report abuse
C. Johnson
4.0 out of 5 stars
Loved the first half.
Reviewed in the United Kingdom on May 6, 2019Verified Purchase
Well thought out and very readable and believable, as a scientist. Lots of great ideas to think about, many that I cannot disagree with. However, and it's only a personal feeling, when we got to the 4 parallel universes, i was not persuaded enough to want to read the detail to the end, so speed-read so I didn't miss anything. However, of all the books on the theory of everything that I have read, this was the most compelling.
2 people found this helpful
Report abuse
Deals related to this item
Page 1 of 1 Start overPage 1 of 1
Pages with related products.
See and discover other items: history of physics, mathematics history, complex numbers, nonfiction essays, the universe of physics books





