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

Although the four levels of infinities can nicely fit in our local universe ... even per person/instant, and thus make our eigenvector of constants just one of infinitelt many ... it somehow forgets to ponder that, of these infinities within infinities, there are likely to be constructs which utilize their universe in total, as a quantum-like computational system. Hard to imagine that neither Tegmark nor Hawking thought this through.

Math knowledge can be very helpful but it is not necessary to grasp the concepts.
I have read other books about cosmology and quantum physics but found this book to be much more clear and simple in explaining complex ideas.
Additionally, for me, this book offered ideas and theories that I had not seen before.

This book needs to be required reading for anyone interested in the reality we live in. Its an easy read, I read it in one day, and yet I am sure the ideas it contains will stay with me forever. Every page is a joy to read even though I was already familiar with many of its topics. If you buy one book in the next year this should be the one.

Tegmark throws around a lot of very large numbers and, of course, the vastness of just our observable universe dictates large descriptive numbers but . . . in Chapter 6, for example, Tegmark refers to 500 knobs each with 10 settings giving rise to 10 to the 500 power possibilities. This is, of course, absurd. The correct number is 10 x 500 = 5,000 possibilities. When a book which has presumably undergone an editing process of some rigors, contains an obviously absurd calculation such as this, the overall accuracy of the author's exposition is called seriously into doubt.

Although I agree with the author's general hypothesis, the numerical absurdities leave me cold.

I think Tegmark has it backward. Mathematics is the science of patterns. We observe patterns in the world around us and record them in our mathematical notations (language). Sometimes we slice and dice the patterns we've seen and recombine the pieces producing a mathematics of patterns that don't exist in the real world. (Like combining horses and horns to get unicorns.) But it should come as no surprise that much of mathematics DOES describe the real world. That's where it came from.

I'm fine with the science. It's a very nice sketch of modern cosmology. And, while not convinced, I'm even entertained by the speculation. But how many readers really care about the incidental personal stuff? Okay, so working for years on tons of data can get very boring. But does the author need to bore us by telling us how bored he was?

Knopf has a wonderful staff of editors. Couldn't the gee whiz style have been toned down a little? (Hum. maybe the printed book _is_ the toned down version...)

All those planning to write a book for the general public are urged to go back and re-read George Gamow's wonderful popular works. As far as I know, Gamow never once mentioned his career, marriage, children, habits, etc.

Tegmark's books starts with the usual run down of contemporary research in physics and astronomy. He starts by telling us about the age of the universe and its size while telling us a little about his personal journey in researching these things. Later chapters however take us into areas of physics which, by Tegmark's own admission, are much more speculative. Tegmark suggests that our universe is really a multiverse and that this multiverse is really four levels of different multiverses. The first level of multiverse is the physical universe we cannot currently observe. The second level of multiverse is the physical universe we cannot currently observe and never will be able to observe due to cosmic inflation. The third level of multiverse is the creation of parallel universes by the quantum wave function. In this multiverse observers break off into different worlds describable mathematically by an infinite dimensional Hilbert space. The final multiverse is determined by all the mathematical structures that define the many different fundamental laws of physics that are theoretically possible. It is this final multiverse, postulated by Tegmark, that gives us the title of the book. As the book progresses one starts to feel that Tegmark is no longer talking physics but metaphysics. For example, Tegmark suggests that the mathematical multiverse is premised on the notion that this multiverse describes a reality independent of our minds. Tegmark suggests that we discover rather then create this mathematical reality but how come the mind can use math to discover this reality? Is the square root of 2 something that exists independent of the human mind? If so, what does it really mean to say that the square root of 2 exists independent of the mind? Interestingly, another physicist, Saul Paul Sirag, when talking about a higher dimensional mathematical structure as the ontological structure underlying all reality, came to the conclusion that this mathematical structure was consciousness or mind itself. Sadly, I think no lab experiment is going to settle these issues. Tegmark's book helps one think about the bigger questions that physics may pose and is worth checking out.

Possibly. You can't get much further out there than Tegmark does in this hugely engaging and thought-provoking book. The object of Tegmark's interest is, well, everything -- from the littlest things (assuming both stuff and space itself reduce to infinitesimal indivisibles) to the largest things (4 different types of nested spacial infinities). Tegmark's answer to the ultimate question: it's all math. Literally.

Whether anything Tegmark writes about (once he slips the surly bonds of standard cosmological theory and goes rogue) is true is unknown and -- alas -- almost certainly unknowable. But it's brilliant stuff to contemplate. Early on, Tegmark crushes the line between physics and metaphysics. But he does so with writerly aplomb and with a logical rigor that defy casual dismissal.

Some readers will roll their eyes through much of this book. Others will take inspiration from it. I have no idea whether Tegmark is onto something (several somethings, in fact), but this very fine book compels me to the view that his ideas merit further study. Aside from a very weak closing chapter, I thought this book was first-rate.

Late to review but oh boy will blow your mind. Max has more credentials than Albert Einstein lol Reading this book will be the equivalent of taking the 'red pill' so get ready for a wet and wild ride. title of book is a little bit of a hint what the bomb drop is going to be but I won't 'ruin' the final surprise.

This is not meant to be a technical book by any means but I suspect that lazy thinkers or the non curious will have a bit of a tough slog. It challenges the reader to think and evaluate the various propositions and string of logic that, for Max anyway, leads to a profound insight and the 'truth' of all reality. And folks it's a barn burner!

I could not put this book down! Purchased it after hearing him talk with Sam Harris and wow did this live up to all my expexcatins.

I've studied physics and hold a PhD in philosophy. So I was delighted to see someone take up the challenge of bringing both together.

From a scientific standpoint the book issues a profound argument for the theory of a multiverse. Sadly, most of the book isn't about science but about philosophy and that's where Tegmark seems to be not so well versed in.

Tegmark ends up constantly mixing two distinct arguments:

* Epistemological view: Everything in the cosmos can be DESCRIBED using mathematics.
* Ontological view: Everything in the cosmos IS mathematics.

It seems to me, Tegmark doesn’t even know both disciplines do exist. As a result, he doesn’t deliver a reason, why it is legitimated to derive the ontological from the epistemological standpoint: From the fact that we can describe everything using mathematics doesn’t follow that everything is mathematics.

As a logical result of this misconception Tegmark also ends up with a superficial notion of what philosophers call reductionism.

What does this mean? Well, it means we don’t need sociology, because everything can be explained by biology. We even don’t need biology, because itself can be explained by chemistry. And, you guessed it, we don’t need chemistry, because we can explain chemistry by physics.

Philosophically speaking this discussion has a long history, dating back centuries. Sadly, Tegmark doesn’t have the academic background to locate his own view within the history of philosophy or even within the history of natural sciences. (There have been physicists and philosophers before him, holding this view, he’d just have to check an encyclopedia of philosophy/science.)

As a result, the books ends up being a great science book and a boring monologue of a hobby philosopher.

"In the sunset of dissolution, everything is illuminated by the aura of nostalgia, even the guillotine" - Milan Kundera

Have you ever regretted anything deeply, some life's important milestones not achieved, some unrecoverable mistakes made, some dear loved ones lost. Have you ever experienced unspeakable joy, the sudden epiphany of understanding, the sparkling connection of two hearts, the soothing satisfaction being in a shadow of a banyan tree in a mid-summer afternoon.Have you ever thought to yourself, only if i can live one more time... But you can, and you did, and you will, forever and ever in this universe and beyond, to the infinitum. And all these, as Max Tegmark articulated in his intriguing new book, is because that we are, as part of our universe, mathematics, not by, not of, not due to, but are, mathematics.

Parallel universes is not a new idea, it is usually presented as a by-product of the quantum physics. So what I described above might have already crossed your mind before. Tegmark, though, put everything is a very new and interesting perspective. He introduced 4 different levels of multiverses and progressed into the overall MUH (Multi Universe Hypothesis). Ultimately, he argued, we are all mathematical structures and each mathematical structure is a universe on the highest level. Along the shore of the beautiful mathematical universe ocean, physics creates this and that reality that represent the true essence of mathematics in every possible way. We, as part of the representation, are both so pointless and inevitable.

Here we are back to the eternal return, your mistakes and achievement will be made over and over again, your sorrow and joy ever so fresh each time you experience it. There is no future and no past, there is only sequences of events, just like every combination of numbers can be found in Pi, every sequence of events can be found in the MUH.

... So, guillotine will be guillotine times infinitum, but it is neither unbearable lightness nor weight, for in MUH everything is pardoned in advance and therefore everything cynically permitted.

With my undergrad level understanding of math, but a high level of interest in science and physics, I thought Tegmark did a very nice job of providing an engaging and non-patronizing look into some relatively advanced ideas in modern physics. That is not an easy thing to do, I don't think.

I can't say I find his conclusions convicning - but of course I am grossly unqualified to actually have an opinion about who is or is not "correct" on matters of quantum mechanics and cosmology.

But that isn't really the point, or at least it isn't really the point to me. I don't read something like this so I can form an opinion about how many levels (if any) of multiverse there are out there. It isn't like anything anyone could say would be particularly convincing to me, or rather, anyone with the necessary level of expertise to have an opinion can easily fool me. It's like listening to two brain surgeons argue about the best way to dig a tumor out of someone's skull. I might find the debate incredibly interesting, but there is no way I can form any kind of reasonable opinion about which of them is actually correct.

So for me, a book like this is about the process, the story, and the history. And Tegmark does an outstanding job of taking me along with him as he looks into this stuff. It was a great read, and I was continually intrigued and interested in the "next level" of the story.

However, in another universe where I am way smarter, I might be writing a review about how ridiculous his theories are and how completely wrong he is - actually, if he is right, it is certainly the case that I am doing so... :)

I just finished listening to the audio book version of this work by Dr. Tegmark. I come away with mixed feelings. First, the books title is a bit misleading. The bulk of it is an explanation into the physics of cosmology and quantum mechanics... not necessarily a discussion of the mathematics. If, like me, you were expecting more of an explanation of the underlying mathematics of universal and scientific phenomena, then you will likely be disappointed at some level. Granted, the math and physics are so interrelated that they cannot be discussed independently. However, my going in expectation was that the book was to be an explanation to the layman about the mathematics.

Secondly, this is really not a book for the lay person at all anyway. To give you a sense of my background, I have an engineering degree from an ivy league university (and have taken advanced math courses, quantum mechanics and physics) and I found myself completely over my head for much of the book. Some of this might be chalked up to listening to book versus reading it, but I would say that the best most of the lay readership will do is come away with some familiarity with the lexicon of the subject matter and little more about the fundamental understanding about the processes themselves. This is not a knock against the book or the author, just some guidance on what to expect as a reader. I'd rather read / listen to a book that is over my head than far too 'dumbed down' to gain anything useful.

The third comment I have is that in the last quarter or so of the book, the author veers into a policy discussion. I am always skeptical when the advice seems to be more oversight from the state or some other benevolently described institution. I think we often forget that it is almost always the state's actions and its unintended consequences that are the root of many of our problems in the first instance. While I don't discount the possibility (or probabilities frankly) that Dr. Tegmark places on the occurrence of such things as nuclear war, catastrophic asteroid strikes, the singularity, etc., I frankly remain a skeptic that these issues can be mitigated with just the right person or people running the ship.

In conclusion, I would state that the author clearly is a brilliant physicist, and possesses a writing style that is generally quite readable - despite the complexity of the subject matter. It is an ambtitious book in both the scope it attempts to cover and the underlying subject matter. If you come away with an understanding of 10% of the informational content of the book, it will have been very much worth reading.

This is a book on cosmology, but in many ways it borders on metaphysical speculation with political undertones -- and that is probably why it has stirred up so much controversy. Tegmark makes some extravagant claims in the book, and perhaps the biggest of all is his statement that if he's wrong, then physics is doomed. By that he means that if the multiverse is not essentially mathematics, then physics can never hope to understand it fully, and will at some point encounter a brick wall beyond which it cannot go. Without knowing more about Tegmark, one might question whether he is an opportunist or just someone who loves to rock the boat. I suspect the later, and that's probably why despite all the extravagant claims, I like him as a person; he is not afraid of making waves, even though it might cost him somewhat academically. The Level III multiverse is certainly the most controversial hypothesis in the book. And while it's extremely hard for the average individual to wrap his or her head around, it should not be ruled out solely for that reason. To simply state that it is way too far-fetched and absurd is not sufficient grounds for discounting it. The chapters dealing with the Level III multiverse are what make this book, in my opinion, so extraordinary and frankly unforgettable. The initial response is bound to be skepticism, but after some reflection perhaps an open mind is the best way of handling it. In refusing to dismiss it out of hand, one's whole view of life may change dramatically. That's the power of this book: you will come to view reality as a much grander, stupendous realm than you ever imagined. In the final pages of the book, Tegmark makes another extravagant claim: that our planet Earth is the only planet in our part of the Level I multiverse that has intelligent life. This, to my mind, seems almost harder to accept than Everett's Many Worlds Interpretation. Furthermore, insufficient arguments are presented to back up this contention. He also does not define what he considers intelligent life. It seems abundantly clear, based upon what we know about the lifeforms on our own planet, that there are various species that exhibit some forms of intelligence. Intelligence is not binary, all or nothing; there are gradations. Where do you draw the line?

This last claim, that our planet alone has intelligent life, has made me question the entire book more deeply and wonder whether there are underlying political motivations for arguing along these lines. Frankly, I have had to recycle the book as a result and say that that it is fatally flawed in its thinking. Tegmark seems to be implying that our portion of the universe is ours for the taking, for us to exploit as we see fit. He says in so many words that mankind is the very crown of creation, and that it is our destiny to rule over our portion of the visible universe. Isn't this the same kind of thinking that has lead to the current environmental catastrophe, and the vanishing of so many species on our own little planet? I'm sure Ayn Rand would approve of such ideas, but personally I find the book's ending a bit too jingoistic. We are not the center of the universe, metaphorically or otherwise, and we need some humility in respecting the vast multitude of lifeforms that make up this cosmos, intelligent and otherwise.

This is the best book I have ever read. Ever.
Fiction or non-fiction. And I have read thousands of books, in multiple languages.
It is as gripping as fiction but the (very complex) non-fiction topics are explained so clearly that - I am not kidding - I cried with joy. I CRIED OVER A MATH BOOK. This book helped me see things that somehow I always knew but could not explain. I didn't have the language to explain them; Max Tegmark gave me the language of math. I only took one math course in college, and that one reluctantly - oh how I wish I could go back in time and have Tegmark for my teacher. And perhaps in some parallel universe, I did - ha!
I could go on and on, but - JUST READ IT. Slowly. With a pencil to underline all the juicy bits (and there are dozens).

This book began as a very excellent introduction to physics concepts through the lens of Max Tegmark's education - his life was used in a very basic way to structure the order in which we encounter these concepts. I've read a lot of these physics books, and the way in which this was handled was, I thought, very good. It was interesting to hear his journey from not understanding the value of physics to having his interest in it rekindled by reading a work of Richard Feynman. Mostly, though, it was interesting hearing about the physics concepts themselves. Tegmark has a very lucid style and his writing is able to explain these ideas to the layperson in a coherent manner without talking down or resorting to quasi-insulting metaphors like 'Mr. Up and Down and Mr. Back and Forth live in an apartment building' as some popularizers of physics (*cough* Greene *cough*) are wont to do. It was a pleasure to read.

By the end of the book, Tegmark begins to explain his personal view on a theory of existence he has been working on that posits that relational mathematics constitute the essential nature of everything, understood down to its depths. Apparently, he has been warned by some editors of prominent scientific journals that this is crazy, but he managed to present this in a way that made me, a layperson, not worry that he was insane. It sounded very interesting.

The book ends up discussing truly astonishing, very "out there" concepts that are suggested by our modern understanding of physics, such that you realize that the borderlands of modern physical science suggest oddities much more wild than anything advocated by religion or 'trippy guru' types.

This was one of the most interesting books I've read. Highly recommended.

This book in not short in surprises, as author Max Tegmark (Professor at MIT), delves into the fascinating subject of cosmology, and discusses how the field has advanced since Friedmann’s theory - “Big Bang”- came into fruition in the early 20th Century. The book progresses from the non-controversial to controversial (or most debated) topics in Cosmology. Tegmark not only makes cosmology understandable to his audience, but he makes it interesting and fun as well – two traits of a master teacher.

This book was ok, but disappointing. The first half of the book is a nice romp through the past in astronomy, on how measurements were made they way they were, how people discovered the size of the earth, the moon, and the sun, etc. All of that is written well and enjoyable to read, though it was mostly things I already knew. Through all of that, while he does show that math was important in all those areas of astronomy, and continue to be today, TEgmark doesn't make an argument for how the universe IS math as opposed to math being the language that describes the universe well.

So, I was ready for the remainder of the book to dive into why he feels the universe IS math. He ever does. Instead he brings up multiverse universes, which he claims math implies, but I still see no reason to believe the theories or that the universe is math.

When I read Is God a Mathematician?, I found it fascinating how this idea of math being an inherent part of the universe versus a descriptive language fascinating. In Is God a Mathematician? The author did a fantastic job of explaining both sides of the argument throughout history to current day. BTW, it's not about god at all:-)

I thought this book would be similar, just with different arguments. But while this author does a good job of explaining how math is used to measure in astronomy and physics and a bit on how it's used to "predict" a multiverse, I'm still unconvinced of his claim or the multiverse. I found myself skimming the last few chapters, as it read to me like a lot of speculation.

Overall I was disappointed, given the title of the book.

The first half of Professor Tegmark's book is about as good as they come for popular physics books. The book's organisation (with a FAQ on what you can miss depending on your degree of knowledge) is a big plus, however, I did not for an instant regret reading everything despite being reasonably familiar with both cosmology and particle physics at the popular level. His 'do you know the answers to these 16 questions ?' , the deepest questions about our universe(s), bring you brutally back to earth, whatever your level of pretension, and he goes on to give the sort of answers which convince you that the deep can also be clear.
In the second half, the author has three flagpoles to run his flags up. : (1) That the wave equation never collapses (Everett's 'many worlds'), except that (2) sometimes it seems to, through 'decoherence', and (3) everything that is, is just a mathematical function.
You can get fascinated and convinced by (1). As for (2), the author is too busy staking out his bragging rights with respect to the theory to explain either what coherence is and why it was import ant in the first place (must be, if decoherence is the answer, no ?), or how the fact that any particle in the real world decoheres within (10^- a lot) seconds is compatible with either Everett's non-collapsing wave, or with a double split experiment which requires the photons or other particles to remain in quantum superpoosition for a lot longer than that.. or indeed (my pet hate in QM popularisation books) What Happens Next ? Do the decohered (or waveform collapsed) particles skulk around naked without superposition for the rest of eternity ?
As for the last 150pp, on the mathematical universe hypothesis, well, it might please the already converted. I just found that 150pp trying to explain that road maps and roads are really the same thing, and that it's the maps that are the most important (that's my metaphor for his arguments) a little tedious. He starts by claiming that physics does not need to explain the representations of the world in subjective reality, the domain of cognitive science, and then positions mathematical theory as more fundamental than external reality. Nowhere does he address the fact that mathematical theory is a creation of our poor little wetware brains and thus automatically conforms to our subjective representations of reality. They are created by the same neural and logical mechanisms. He takes the identity between two mathematical objects created by complete equivalence, and blithely claims that that 'proves' that reality is just mathematical. Never trust a physicist who quotes a philosopher to clinch his argument (p.280 in hardback). Never trust a physicist who uses probabilites to draw conclusions about particular instances (the 'anthropic principle' argument etc.).
But, apart from that, a lively, highly informative, and (annoyingly) stimulating book.

I had read Tegmark's paper on parallel universes in Scientific American and I was curious to know how the author can justify such an apparently crazy theory. The book is an e"xpansion iof the paper, very well written. The first half is devoted to a general theory of inflation and is a preparation to the second part, the theory of parallel universes. What is really fascinating and very exciting is the defense of the platonist thesis saying that universe is purely mathematical. It is not to say that we can admit completely by this thesis, but Tegmark's discussion is clear, informative and gives a new light on many topics. A marvelous reading for anybody interested in the deep structure of universe and reality.

There is no question that Max Tegmark has some unique things to say about the nature of the "universe." His tone is conversational and he is adept at making complex topics understandable. That said, there are a number of areas of misattribution, especially in the area of Darwinian Evolution, which he continually cites as being the basis for many phenomena that it is incapable of predicting or extrapolating towards. The inner workings of cells, biochemistry, etc were not developed in Darwin's time, and as in so many texts, too much is assigned to Darwin's theory, and to Darwin himself . To attribute the nature of the universe to mathematical description is a phenomenon of the chauvinistic, arrogant, anthropomorphic human mindset. Whatever direction current technology is headed towards at a given time becomes the metaphor for the true nature of the universe. Currently, information in the form of quantum computing is regarded as the ultimate dynamic, and so the universe is a very large quantum computer. Prior to that it was viewed as energy. In earlier times, a mechanistic/clockwork view was favored. Max knows a lot of math. But Max really doesn't know any more of the true nature of the universe than the average man on the street who's read some sci-fi novels.

I enjoyed very much this book and I warmly recommend it. I did not find all parts equally interesting but overall an extremely captivating and stimulating reading. I liked more the last chapters (the ones that might ruin Max's career) where there is an abundance of challenging ideas: "is time flow real?", "did cosmic inflation really happen?", "why there is such amazing fine tuning for universal physical constants?", "are there multiple copies of you?"...
It is one in a series of books concluding that Multiple Universes are an obvious choice for contemporary physics "status", but personally I don't find any of the "proves" very convincing.
More concrete related to my "multiverse" skepticism: So while writing this review, there are an infinite copies of me, writing an infinite reviews to "the store-like" infinite number of sites, in an infinite number of languages, using all possible combinations of words, making all possible spelling mistakes ... Besides the obvious incredible waste, which is the determining factor for "quantum decoherence"moment?

Considering this book concerns mathematical structure, the book lacks some. The first few chapters were a real struggle. The style annoying and poorly drafted. I wonder if it bypassed editing and I almost didn't continue as it was so frustrating. Continuing on, I felt I deserved some reward which never materialized. Excessively wordy, some tightening up of the prose would have benefited the reader. As far as the content, it was just enough to keep me reading, but lacked a conclusion which I was led to believe was forthcoming.

Our Mathematical Universe by Max Tegmark is written in a far-reaching style. It grabs the reader, twists his mind and then reflects it back on the author’s—providing an insight seldom encountered in a book. While mathematics alone offers a window into the workings of nature Tegmark takes a mathematical stand preferring to view the vast cosmos as a gargantuan mathematical puzzle. He claims that mathematics is everywhere, from the parabola’s path that objects follow under the force of gravity to the dynamics of orbiting bodies it is plain to see the mathematical observations Tegmark observes.

Mathematics is a way to observe nature, according to Tegmark. The book emerges as a breath-taking vista of which we are unable to comprehend its bounds—like gazing into Yosemite Canyon for the umteenth time.

By zooming out, zooming in and stepping back, we can claim a unique perspective. All the great minds of the world, from Archimedes to Copernicus to Einstein, have tended these views. That’s why we have awakened as a species. Now, Max Tegmark joins this elite society with an attempt under his belt to shed light on what reality really means.

We are surprised by the way the author imports subtle meaning by considering a variation of facts that appear to fit the nature scheme of things. Hence, Tegmark has won the grand prize for composing a work of monumental inspiration. Tegmark is on a quest for the ultimate nature of reality—and he’s well on his way.

Our Mathematical Universe
By Max Tegmark

Every long while, there comes along a book explaining science in layman’s terms that are outstanding. I remember George Gamow’s One, Two, Three…Infinity, which I read in the early sixties was one of these. It explained cutting edge physics and math as of 1947. Well, Max Tegmark has done it again. He updates the fields of cosmology, particle physics, and philosophy in a easy to understand four hundred page book. He eschews the difficult, but vital, higher mathematics by using well thought up word pictures to describe the Big Bang, Inflation, and his cutting edge ideas. The book came out a few weeks prior to the announcement that the observatories in Antarctica had discovered direct evidence of cosmic inflation in the form of gravity waves imprinted on the cosmic background radiation. Cosmology is in its Golden Era and it is hard to keep such a book as this current.

The book is well laid out. The author doesn’t wander. He summarizes the main points at the end of each chapter. He uses his own illustrations to illustrate difficult ideas. The book is somewhat of a autobiography which tells his work in the field of cosmology. He describes the continuous collaborative effort among scientists to work out problems. He gives credit to the great minds that have forged ahead with current thinking on the origin of the Universe and the nature of reality. Yes, he does bring his kids in which humanizes his work.

Two of the several ideas he brings out is that he says there are four levels of parallel universes: the Universe that lies beyond our vision, that is beyond the glow of the cosmic background; the second level is the universes where the cosmic constants are different but the laws of physics are the same; the universe created when the Universe splits as a result of a random even (the Schrödinger's cat thought experiment); and the parallel universes where the mathematics are different, (e.g., quantum mechanics doesn’t exist).

The other idea is that reality is based on, not simply described by, mathematics. This lays him open to criticism that he’s pushing Platonism. That is matter and reality is, ultimately composed of abstract forms. The last third of the book expounds on this theme. He also believes, but can’t prove, that there are no intelligent species, besides ourselves, in “our” universe. He differentiates “our” universe as the universe we can see with our telescopes and the infinitely bigger Universe which we can never see. He says that there are a vast number of intelligences out there, some nearly exactly our own, but we’ll never have any communication with them. No Star Trek universe for us.

This is an outstanding book, I recommend it highly.

I love the science aspect and it definitely explains some concepts in interesting ways. But, I especially love Max's personal anecdotes and humor he brings to the table. I do enjoy reading about math and physics but I often get lost around 25% through a book. His writing style made me want to keep reading on. (but the science and philosophy is great too!)

At some time in our lives, we all are mesmerized about the secrets of life and the universe. What is the nature of physical laws that govern our existence, and what is physical reality? Physics tries to answer these questions in terms of the laws of physics operating on matter (or energy) in spacetime. MIT Professor Max Tegmark, a well-respected theoretical physicist, says that only mathematical formulas are real; they create physical reality and all else including the laws of physics are an illusion. According to his theory, there are billions of parallel universes (multiverse) which have four levels of existence. Three of them have been proposed by other physicists, and Max Tegmark suggests a fourth level which he calls a mathematical universe.

The first level of multiverse is an infinite space, and our space is only 13.72 billion years old (starting with the Big Bang.) In an infinite space scenario, billions of parallel universes are possible (which share the same space as ours). The second level is created by the application of physics equations on this universe, after the big bang. At level three, the parallel universes exist in an abstract mathematical structure called Hilbert space, which can have infinite spatial dimensions. Each universe is real, but exists in different dimensions of this Hilbert space. The fourth level which is entirely due to the author, which he calls an external reality. This theory proposes that there is a reality out there that is independent of us or our physics; this is created by mathematics. Essentially a mathematical structure is a universe by itself, says the author. This is not entirely a new idea since physicist Galileo said that the nature of reality is written in the language of mathematics.

The ideas of the author are interesting but physicists are not racing to buy his theory. Einstein spent much of his life thinking that there is such a thing as physical reality out there, but he was thinking in terms of unifying the laws of quantum physics with the laws of classical physics. The author goes beyond this frame of spacetime by considering all possible universes out there.

The book does not involve any mathematical equations or "hard" physics, but assumes knowledge of undergraduate level physics to fully appreciate the subject matter.

1. Many Worlds in One: The Search for Other Universes
2. The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos
3. In Search of the Multiverse: Parallel Worlds, Hidden Dimensions, and the Ultimate Quest for the Frontiers of Reality

There is no question that Max Tegmark has some unique things to say about the nature of the "universe." His tone is conversational and he is adept at making complex topics understandable. That said, there are a number of areas of misattribution, especially in the area of Darwinian Evolution, which he continually cites as being the basis for many phenomena that it is incapable of predicting or extrapolating towards. The inner workings of cells, biochemistry, etc were not developed in Darwin's time, and as in so many texts, too much is assigned to Darwin's theory, and to Darwin himself . To attribute the nature of the universe to mathematical description is a phenomenon of the chauvinistic, arrogant, anthropomorphic human mindset. Whatever direction current technology is headed towards at a given time becomes the metaphor for the true nature of the universe. Currently, information in the form of quantum computing is regarded as the ultimate dynamic, and so the universe is a very large quantum computer. Prior to that it was viewed as energy. In earlier times, a mechanistic/clockwork view was favored. Max knows a lot of math. But Max really doesn't know any more of the true nature of the universe than the average man on the street who's read some sci-fi novels.

I enjoyed very much this book and I warmly recommend it. I did not find all parts equally interesting but overall an extremely captivating and stimulating reading. I liked more the last chapters (the ones that might ruin Max's career) where there is an abundance of challenging ideas: "is time flow real?", "did cosmic inflation really happen?", "why there is such amazing fine tuning for universal physical constants?", "are there multiple copies of you?"...
It is one in a series of books concluding that Multiple Universes are an obvious choice for contemporary physics "status", but personally I don't find any of the "proves" very convincing.
More concrete related to my "multiverse" skepticism: So while writing this review, there are an infinite copies of me, writing an infinite reviews to "the store-like" infinite number of sites, in an infinite number of languages, using all possible combinations of words, making all possible spelling mistakes ... Besides the obvious incredible waste, which is the determining factor for "quantum decoherence"moment?

Considering this book concerns mathematical structure, the book lacks some. The first few chapters were a real struggle. The style annoying and poorly drafted. I wonder if it bypassed editing and I almost didn't continue as it was so frustrating. Continuing on, I felt I deserved some reward which never materialized. Excessively wordy, some tightening up of the prose would have benefited the reader. As far as the content, it was just enough to keep me reading, but lacked a conclusion which I was led to believe was forthcoming.

Our Mathematical Universe by Max Tegmark is written in a far-reaching style. It grabs the reader, twists his mind and then reflects it back on the author’s—providing an insight seldom encountered in a book. While mathematics alone offers a window into the workings of nature Tegmark takes a mathematical stand preferring to view the vast cosmos as a gargantuan mathematical puzzle. He claims that mathematics is everywhere, from the parabola’s path that objects follow under the force of gravity to the dynamics of orbiting bodies it is plain to see the mathematical observations Tegmark observes.

Mathematics is a way to observe nature, according to Tegmark. The book emerges as a breath-taking vista of which we are unable to comprehend its bounds—like gazing into Yosemite Canyon for the umteenth time.

By zooming out, zooming in and stepping back, we can claim a unique perspective. All the great minds of the world, from Archimedes to Copernicus to Einstein, have tended these views. That’s why we have awakened as a species. Now, Max Tegmark joins this elite society with an attempt under his belt to shed light on what reality really means.

We are surprised by the way the author imports subtle meaning by considering a variation of facts that appear to fit the nature scheme of things. Hence, Tegmark has won the grand prize for composing a work of monumental inspiration. Tegmark is on a quest for the ultimate nature of reality—and he’s well on his way.

Our Mathematical Universe
By Max Tegmark

Every long while, there comes along a book explaining science in layman’s terms that are outstanding. I remember George Gamow’s One, Two, Three…Infinity, which I read in the early sixties was one of these. It explained cutting edge physics and math as of 1947. Well, Max Tegmark has done it again. He updates the fields of cosmology, particle physics, and philosophy in a easy to understand four hundred page book. He eschews the difficult, but vital, higher mathematics by using well thought up word pictures to describe the Big Bang, Inflation, and his cutting edge ideas. The book came out a few weeks prior to the announcement that the observatories in Antarctica had discovered direct evidence of cosmic inflation in the form of gravity waves imprinted on the cosmic background radiation. Cosmology is in its Golden Era and it is hard to keep such a book as this current.

The book is well laid out. The author doesn’t wander. He summarizes the main points at the end of each chapter. He uses his own illustrations to illustrate difficult ideas. The book is somewhat of a autobiography which tells his work in the field of cosmology. He describes the continuous collaborative effort among scientists to work out problems. He gives credit to the great minds that have forged ahead with current thinking on the origin of the Universe and the nature of reality. Yes, he does bring his kids in which humanizes his work.

Two of the several ideas he brings out is that he says there are four levels of parallel universes: the Universe that lies beyond our vision, that is beyond the glow of the cosmic background; the second level is the universes where the cosmic constants are different but the laws of physics are the same; the universe created when the Universe splits as a result of a random even (the Schrödinger's cat thought experiment); and the parallel universes where the mathematics are different, (e.g., quantum mechanics doesn’t exist).

The other idea is that reality is based on, not simply described by, mathematics. This lays him open to criticism that he’s pushing Platonism. That is matter and reality is, ultimately composed of abstract forms. The last third of the book expounds on this theme. He also believes, but can’t prove, that there are no intelligent species, besides ourselves, in “our” universe. He differentiates “our” universe as the universe we can see with our telescopes and the infinitely bigger Universe which we can never see. He says that there are a vast number of intelligences out there, some nearly exactly our own, but we’ll never have any communication with them. No Star Trek universe for us.

This is an outstanding book, I recommend it highly.

I love the science aspect and it definitely explains some concepts in interesting ways. But, I especially love Max's personal anecdotes and humor he brings to the table. I do enjoy reading about math and physics but I often get lost around 25% through a book. His writing style made me want to keep reading on. (but the science and philosophy is great too!)

At some time in our lives, we all are mesmerized about the secrets of life and the universe. What is the nature of physical laws that govern our existence, and what is physical reality? Physics tries to answer these questions in terms of the laws of physics operating on matter (or energy) in spacetime. MIT Professor Max Tegmark, a well-respected theoretical physicist, says that only mathematical formulas are real; they create physical reality and all else including the laws of physics are an illusion. According to his theory, there are billions of parallel universes (multiverse) which have four levels of existence. Three of them have been proposed by other physicists, and Max Tegmark suggests a fourth level which he calls a mathematical universe.

The first level of multiverse is an infinite space, and our space is only 13.72 billion years old (starting with the Big Bang.) In an infinite space scenario, billions of parallel universes are possible (which share the same space as ours). The second level is created by the application of physics equations on this universe, after the big bang. At level three, the parallel universes exist in an abstract mathematical structure called Hilbert space, which can have infinite spatial dimensions. Each universe is real, but exists in different dimensions of this Hilbert space. The fourth level which is entirely due to the author, which he calls an external reality. This theory proposes that there is a reality out there that is independent of us or our physics; this is created by mathematics. Essentially a mathematical structure is a universe by itself, says the author. This is not entirely a new idea since physicist Galileo said that the nature of reality is written in the language of mathematics.

The ideas of the author are interesting but physicists are not racing to buy his theory. Einstein spent much of his life thinking that there is such a thing as physical reality out there, but he was thinking in terms of unifying the laws of quantum physics with the laws of classical physics. The author goes beyond this frame of spacetime by considering all possible universes out there.

The book does not involve any mathematical equations or "hard" physics, but assumes knowledge of undergraduate level physics to fully appreciate the subject matter.

1. Many Worlds in One: The Search for Other Universes
2. The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos
3. In Search of the Multiverse: Parallel Worlds, Hidden Dimensions, and the Ultimate Quest for the Frontiers of Reality

I did take the author's suggestion and skip ahead as I am familiar with much of the physics. For that reason, my judgement could
flawed because I missed some passages that deal with the main problem that I see with this volume. I find the central thesis of the
book to be totally implausible. I think it absurd to contend that reality and mathematics are identical. In physics, we use mathematics
to describe reality. It is a language. Saying that the mathematics is the reality is rather like saying that a love poem or a description of sexual
relations is the essential reality of those relations. In a less politically correct environment people would say that Professor Tegmark has lost
a sane sense of the real world. He can of course say what he likes and he is clearly professionally very able but I find it disturbing that
a reputable publisher has released this volume and that a large number of people who are not technically able physicists are reading it. That is for two reasons: First, though he writes well and describes much current physics accurately, the picture which emerges of contemporary
physics is highly misleading and gives the impression that the field is currently dominated by wild speculation. That is bad for both
the profession and society, which needs the insights which physics can provide. Secondly it is disturbing because it encourages a
trend even among the more moderate of the more speculative theorists in recent years, to take their mathematics too seriously and to confuse it
with reality itself. For example supersymmetric models were taken much too seriously for many years despite the implausibility of
a theory which doubled the number of fundamental paritcles at a stroke without a shred of experimental evidence. The shock waves
which I have observed among my colleagues when the LHC's recent run revealed no evidence of supersymmetric partners indicates
to me that this tendency is quite real and dangerous for the future health of physics.

The success of popular books of this sort in the
marketplace has been taken to be a blessing by most of the physics community because it popularizes physics and paints it in
a positive light.. However that success provides motivation for more and more physicists to make wild speculations and write
popular books about them before the speculations have been properly vetted by the physics community and, even more importantly,
by experimental test. In the long run, the damage done to the discipline by this spiral into wild speculation will outrun the
short term benefits of the popularity it engenders. People will catch on and the reputation of physics will suffer damage from which
it will take a long time to recover.

Don't waste your money. You would expect a book that claims that our reality is a mathematical structure would engage with questions like "What does it mean to say something exists?" and "What are the possibilities and limits of our knowledge?" In other words, a bit of ontology and epistemology. I'm not asking for much: the sort of thing you could get by taking a Philosophy grad student out to dinner and running your ideas past them. Tegmark seems to be innocent of any awareness that other people might have thought about some of the things he is so eager to assert.

The book is entirely without discipline. There are points where you can see someone has said, "You really ought to think about <argument>," and Tegmark has put in half a para saying "Some people might think <argument> is relevant, but it's not." You can imagine how impossibly annoying he would have been to have as a student.

While he's at it, he reveals some deeply distasteful game-playing in the publishing priority racket, which really calls into question the integrity of the structures of science that exist at the moment.

I gave it two stars rather than one because the first part is a fairly useful summary of where cosmology is at the moment, but nothing that came as a great revelation to a reader of pop science.

Apparently Tegmark is a serious cosmologist, but he should stick to his day job. This is a bad book, I regret buying it, and I even more regret buying it as a Kindle edition because I can't even sell it on.

This is an extremely well written book which introduces the reader to the concept of parallel universes based on the latest scientific research from astronomy and modern physics. While the reader may remain skeptical about such ideas, he will realize that they are the subject of very serious and competent academic research and should be taken seriously.

a mind-altering trip through the foundations of reality. For the layperson (like myself), it provides more more than a casual glimpse at the staggering questions that theoretical physics ponders, yet manages to keep the material accessible enough for understanding.
The chapters describing the forces behind the Big Bang, and the formation of the elements that make up (our version) the Universe resonated most with me, as they are never taught in such a holistic format. Admittedly, the sections describing Quantum Mechanics seems like utter heresy until you understand that the (provable) mathematical substrate of it simply requires heretical thinking. Truly fascinating. I highly recommend it to anyone who wonders where it all came from and why.

I was first introduced to Max Tegmark's ideas through popular science shows such as 'Through the Wormhole' with Morgan Freeman. Just the little bits I heard him say there piqued my interest, so when I saw this book, it immediately went to the top of my 'must read' list.

The basic idea, that our universe (and perhaps many others) is essentially a mathematical structure, should hit the reader like a ton of bricks. Whether or not you subscribe to the MUH (mathematical universe hypothesis) proposed in this book, it must be accepted that at the bottom rung of reality (the quantum level), subatomic particles cannot be described as anything but mathematical entities. What Tegmark is saying here is that 'reality', at its most basic level, cannot be anything other than math, which in turn can be defined as information. The author recounts his friendship with John Wheeler, perhaps the foremost physicist to hold this 'reality IS information' idea, and gives his own argument for why he also believes this to be the case.

This basic premise, and the reason it should make the reader jump out of her chair, is that reality is nothing more nor less than a meta-physical (i.e. platonic mathematical) structure. The author gives compelling scientific reasons why he agrees with the ancient view held by Plato that there exists a realm of pure mathematical forms, but to hear a mainstream scientist propose this is verging on scientific heresy. To say that the universe is not only describable by math, but IS math, is pure platonism. The author is saying that the ultimate reality is not atoms and the void, but information.

I must confess that, along with the author, I am also philosophically a Platonist at heart, but this is beside the point in approaching the subject of this book. Reality is what it is, and, as Tegmark says, it is not our job as thinking beings to tell it what to be or how it should behave. It is our job to pursue it in as unbiased a manner as possible. Whether or not there are multiple universes, or whether we will ever know, is also beside the point. Unless you're a solopsist, you must acknowledge that at least the universe we inhabit exists, and so far as we can tell, it is, at the most fundamental level, nothing but math.

I like Max Tegmark, and I did enjoy this book. It was a fun intellectual exercise, even though I don't totally agree with all the conclusions Tegmark draws. It was hard to understand how the last chapter related to the rest of the book. It came across somewhat preachy and just seemed appended to the end of the book although it didn't really relate to the rest of the book.

Max Tegmark, the author, gives the reader the option of skipping certain chapters in "Our Mathematical Universe" based upon the reader's prior knowledge of the material. Good idea, but I decided to read it all anyway and to have my grandson read the book with me. So you were going to get a double-review here.
As we read along together, my grandson sometimes became confused (briefly) by such statements as "he (Aristarchos) estimated that the angle between the moon and the sun was about 87 degrees at this time. (The time of the quarter-moon.) The angle between the moon and the sun? Michael could envision a straight line between the moon and the sun but he had to cogitate a bit to realize the author was referring to the angle that would be formed between the positions of the moon at each end of the hemisphere at quarter-moon, in relation to the sun.
Not a big problem. Michael worked out the author's meaning and we continued reading along.
Michael is a sharp kid, and he pointed out that one of the diagrams earlier in the book ran in reverse to the explanatory description given beneath the diagram. He was correct, of course, but I explained that we were reading a "reviewers' copy" and that the diagram would likely be corrected in the final print edition of the book...(although I knew from past experience that this is not necessarily the case.)
Shortly thereafter I had to explain to Michael why the Catholic church had burned Giordano Bruno at the stake. Luckily, I knew much more about Giordano Bruno than what was mentioned in the book and I was able to handle Michael's curiosity. But at this point, Mike decided he didn't want to continue reading "Our Mathematical Universe" with his grandpa, and I completely understood. So from here on in what you get will be from me alone.
"Our Mathematical Universe" is easily a 5 star book. I have tried to keep abreast of developments in Cosmology and I thought I was doing okay. Tegmark showed me that I was mistaken. I had believed that the Big Bang part of the Standard Theory was that there was this "singularity" that was so tiny and so highly pressurized that it exploded and produced our universe. It turns out that this isn't really what happened at all...or rather, that it kind of happened but only as the beginning of the end of our universe; and it probably didn't involve that singularity at all. It all has to do with the process of "eternal inflation."
I am not an expert. Far from it. Just a lifelong student; so I don't wish to get into scientific details here. I have heavily marked up Tegmark's book, and I intend to re-read it after a reasonable pause to let the new information seep into this old brain.
Tegmark talks of corollaries to the Standard Theory which predict other universes quite similar (if not identical) to our own; with other people who are pretty much replicas of ourselves walking about their earths doing pretty much what we are doing. I now reach out to each of my millions of "other selves" night and wish them well before I fall asleep, believing that my "other selves" are possibly also reaching out to me. These other selves may be a bit different from us...(e.g.., the sounds they utter may be different etc.;) and the whole idea may not really be true at all, but it is fascinating to consider. And I'm an old guy, and I somehow find it all a bit comforting.
I cannot recommend this book highly enough. If I have misstated ideas from the book or if I have misunderstood them I apologize, and I hope Max will forgive me.

This book is absolutely a wonderful read for the layperson!   I can't recommend it highly enough!

My only worry is that the title will scare people away (because readers might assume that the book is full of mathematical formulas). On the contrary, the author has managed to clearly explain a great variety of physical concepts without having to resort to mathematical formulas.  The author achieves this by the use of analogies.   For example, he explains how increasing the size of a sphere flattens it out by drawing an analogy to an ant on a small ball.  The ant easily sees its curvature.  However, if the size of the ball expands to that of the earth, then everything around the ant will appear to be completely flat.  He explains negative pressure by analogy to stretching a rubber band (versus positive pressure, in which you have to compress something in order to add energy to it).  For every interesting concept and new discovery in physics over the last century, Tegmark has an extremely clear explanation for it.  There is an occasional equation here and there but even those equations are explained by reasoning (rather than by mathematical manipulation).  He will say something like:  "Given this equation, if we increase this, then we will end up doubling that." and so the reader does not have to actually understand the mathematics of the equation (when one is given).  

This gift of explanation, which Tegmark possesses, makes him a writer of physics to be cherished by the layperson. He gives the reader the clearest explanation of the theory cosmological inflation (in terms of both why/how it was conceived, what it accomplishes, and its current status) of any physics-for-the-layperson book I have read.   I now see why some of my favorite physics authors (e.g., Kaku, Deutsch, Barbour) give positive reviews.  Finally, Tegmark seems to be at the center of many of the breakthroughs occurring in modern cosmology and he appears to have been a member, throughout his career, of many key physics teams.  

As he describes it, Tegmark's area of research involves developing methods (and corresponding computer programs) to analyze the voluminous amounts of data returned by various advanced, multi-million dollar instruments.  Therefore he is in a unique position to understand that point at which experimental and theoretical physics meet.  Even if you have already read other, popular physics books (e.g., about different types of multi-verses and quantum realities) you will still want to get your hands on Tegmark's book.  Do not let the word "mathematical" in the title scare you away!

Max Tegmark, a prominent Cosmology researcher at MIT provides a description of his personal journey of discovery and hypothesizing about the ultimate nature of reality. It is unlike many popular science books written for the non-scientists in that while describing things that are already known (such as measures that can be made of the size and properties of the earth, sun and other stars) it shares the basis for the reader to intelligently examine many problems that are not yet definitively solved, including the ultimate nature of physical reality, and the nature of consciousness. In the unsolved/exploratory areas of this journey Tegmark endorses and describes certain theories shared by many prominent scientists such as Cosmological Inflation, and others prominently his Mathematical Universe Hypothesis ones shared by a few leading researchers (such as Konrad Zuse, Edward Fredkin, Steven Wolfram giving his justification for each (as well as a means for refutation). Interestingly, he also theorizes on the nature of a conscious entity (what he calls a Self-Aware Substructure [SAS]), explores the notion of whether we might be living in a simulation, and the likelihood and character of a Technological Singularity. I am slightly unclear (my limitations rather than the book) about what is the exact nature of the "Mathematical Structure" on which he claims physical reality is based, whether is is the same or differs from the Algebraic Structures referred to in modern Abstract Algebra. I find his theorizing about subjects which might be outside of a physicist's expertise refreshing and interesting rather than ill-informed. I highly recommend this book for a challenging and enlightening intellectual journey.

This book offers a detailed approach to questions like the origin of the universe, explaining the many possible answers and clearly discussing the many areas where there is yet no agreement.

As a non-specialist who's very curious about cosmology, I was very pleased to find that the book was written clearly enough to help me understand imponderables like four-dimensional space-time and the possible role of quantum mechanics in celestial mechanics.

There's also a lot of discussion of multiverses, a huge, maybe endless set of parallel universes. You don't have to buy into the author's own view here in order to learn immensely from the explanations.

Bet he wishes he had waited about 6 months to publish it, to rewrite the sections related to microwaves, inflationary multiverse and mathematical proofs of that and more info about dark matter/dark energy!

Fantastically interesting, inspiring, and almost comprehensible to this non-physicist, non-advanced-mathematician! Recommended highly if these topics interest you!

My favorite parts, quoted or summarized, are on Goodreads and some will be tweeted. LOVED this book! Thanks, Max!

Some years ago, when the discovery of the accelerating expansion of the universe was new, I emailed Dr. Tegmark, who I didn’t know then or now, and asked him some questions about dark energy. He took time out of his busy day, replied and explained matters in a way that a child might understand. This left me with the impression that he was a nice guy and good at explanations. So I decided to read his book, even though it has a scary title.

After an opening in which he is killed by an oncoming truck Dr. Tegmark tells us about his career as a physicist. His writing does a fine job of conveying the fun, excitement and hard work of being involved in frontier scientific research.

He moves on to discuss the study of (1) the cosmic background radiation, which he can deal with in a you-are-there fashion since he was involved in the work, and (2) cosmic inflation. He presents both topics with admirable clarity. Oh, that there were someone with the talent of Dr. Tegmark to rewrite the brief Wikipedia entry titled “Introduction to Gauge Theory.”

The going gets a bit rougher when Dr. Tegmark turns to the subject of the multiverse. He is a passionate, very enthusiastic advocate of the multiverse idea. Here he is selling hard, and he may leave some readers feeling hammered rather than simply informed and possibly persuaded. More sensitive souls might want to pop a valium or do some breathing exercises before diving in.

Then on to the gnarly subject of the interpretation of quantum mechanics. Dr. Tegmark views the Copenhagen interpretation with utter scorn, describing it with Shakespeare’s phrase “Something is rotten in Denmark.” He embraces Everett’s Many Worlds interpretation, making it perfectly clear that, for the thinking man, it is the only interpretation that makes any sense whatsoever, although it does, ahem, need a little work, which Dr. Tegmark himself is happy to do right before our eyes.

While he presents his arguments here as clearly as he presented all the previous topics, I’m afraid that in this case the effect on me was the opposite of what he intended. The Tegmark extension of the Everett interpretation fairly screamed for an application of Occam’s razor, which, for this occasion I will restate as “If you find yourself actually needing an infinity of multiverses just to scratch your mathematical backside, that should tell you something.” After Dr. Tegmark’s pitch for Everett, rather than being ready to join the Many Worlds fan club, I felt that I, for the first time, actually understood the reason for the “shut up and calculate” approach to interpreting quantum mechanics, and the Copenhagen interpretation never looked so good, on grounds of its sheer practicality. If Schrödinger’s wave equation is considered as a map of an aspect of reality, was it so wrong of the Copenhagen plant to install a simple feature (“collapse of the wave function”) that neatly folds the map the moment you are done with it?

That pretty much finished the fun part of the book. Now it was time for Dr. Tegmark to talk about

Please allow me to interrupt myself. In his book Dr. Tegmark describes himself as a Dr. Jekyll and Mr. Hyde. Jekyll does the every-day cosmology, where the universe blows itself up like bubble gum, while Hyde works on the controversial “mathematical universe” concept. It has been demonstrated that this can produce a Jekyll/Hyde effect in a reader of the book. Physicist Peter Woit has published two separate, dueling, reviews of the book, one reasonable, balanced, elegant, while in the other he makes a startling transformation into a no-kidding, way over the line Mr. Hyde.

I considered writing this book review as no big deal. Read the book, report events that occurred in my central nervous system while I was reading, done. The way I responded to the book might turn out to be unique, or, much more likely, my experience might have been shared by other readers.

Doing things this way seemed to work well enough while dealing with the first, Jekyll, half of the book, but there was some question about this approach while reading the second, Hyde, half. As I read this part, events in my nervous system were getting out of control. I was left to decide whether to continue reporting events as they occurred, or to wait for a moment of tranquility and reflection and write something different. I decided to continue as I began and describe what I was actually experiencing while I was reading. Thankfully, my own Mr. Hyde seems to be just a doofus who can only be accused of doing himself no credit, failing to provide any real insight, lacking any understanding of the true nature of the ideas in the book, being utterly unable to grasp the grave implications that Dr. Tegmark’s work has for the science of physics as we know it today, and blah, blah, blah

Back to the review:

That pretty much finished the fun part of the book. Now it was time for Dr. Tegmark to talk about his hobby, the idea - (the possibility suggested in the next few words is so horrifying that the reader may wish to consider stopping here, rather than learning of it) - that the physical universe is literally made out of MATH, the kind of math that turns up its nose at things like “numbers,” math about entities that have no properties except the relations that hold between them, relations that have no properties except which elements they relate, structures that correspond to all equivalent descriptions of the structure. It’s worse than it sounds. I slogged through it in a soldierly fashion, considering it a test of manhood, keeping my mind open of course, alert for any signs that a seed of conversion had been planted, but no, I kept questioning, “Tegmark seems to think that when the Theory Of Everything is found, the math of the TOE will be what the universe is made of. In Ptolemy’s day, was the universe made of Ptolemy’s math?”

On I went, through a beyond-nightmare world where (cue creepy music) there is no light, no color, no sound, no music, only waveforms. I imagined a child’s typical school day consisting of period one, Math, period two, Math, what’s for lunch today in the cafeteria: Math, period three, Math Appreciation, period four, Math, math homework, math for dinner, math TV, and what will I dream about tonight?

Was I near the end? I looked. No, there were chapters to go yet. Well, the word “mathematical” was right there in the title of the book, the warning was clear. Now I knew (creepy music getting louder) what becomes of those who do not heed the warning.

And in math-world there is no change. This is because of the math. This math is not ordinary math, it is Platonic Ideal math, perfect, eternal, unchanging. This math does not admit of change, so change is false, illusory, unnecessary. Even changing your underwear. There is no change. I would be reading this chapter forever, I realized, at the rate I was going.

I imagined young people who were considering a career in science reading about this world and deciding to become drop-outs, anarchists, tattoo artists, creationists.

There was a brief interlude where we touched on comparatively pleasant topics like planet-destroying strangelets and universe-destroying death bubbles (Up to now, being hit by a meteorite has been the first choice on my list of ways I would prefer to go, but a death bubble sounds pretty cool, too. Then again, I would be taking the entire universe with me, so maybe I shouldn’t be so self-centered). But then it was back to the universe being made of math. By now I was more or less getting used to it, symptoms such as hysterical blindness were diminishing.

With six pages left, Dr. Tegmark writes “the fundamental mathematical equations that appear to govern our physical reality make no reference to meaning.” This seemed kind of Zen, given the context. Further reading revealed that Tegmark is sure that life does have meaning, even though there doesn’t appear to be an equation for it.

At the end of the book I found myself holding a neurobiological point of view. One of the functions of our brain is to create what we perceive as reality out of the blip-blip electrochemical Morse code signals of the sensory nerves. No surprise then that a fellow who spends his days immersed in equations and computer code could find himself at home in a reality self-evidently made of math. Gautama Buddha saw a universe that was composed of delusion and desire. Shakespeare lived in a cosmos that was more complicated and perplexing.

What crossed my mind as I was closing the cover was the “ultraviolet catastrophe.” In that puzzling case the math was perfectly good, many agreed, but the black body radiation wouldn’t cooperate. In the end it was the math that had to change, quite a bit. This might suggest that math is different from, and in a way, superior to reality. When the math doesn’t work, you can change it.

With rare exception, I have found most books I've received through the the store Vine program to be a disappointment. This is one of those rare exceptions. I have an advanced degree; my background is in biology and chemistry, but have always been fascinated by physics. My bookshelf is filled with physics books and math books. I find I generally have to read a physics book every month or so, either to keep up or to refresh what I've forgotten (which is usually a lot).

This complements Louisa Gilder's "Age of Entanglement" and Ray Monk's "Robert Oppenheimer."

I don't think there's actually "any" math in it; it's all narrative, and very, very good narrative. The author points out which chapters "hard-core readers of popular science" might skip; and which chapters "physicists" might skip, but the writing is so entertaining it would be hard to skip any of it.

Inside the front cover the publisher suggests that this book will fascinate readers of Brian Greene, Roger Penrose, and Ray Kurzweil. I found this book more interesting than Brian Greenes' and that's saying a lot, but to some extent that's like comparing apples and oranges. Max Tegmark's "Quest" is his personal journal trying to answer the "big questions."

He writes so nicely, it's almost as if he's narrating to middle school students; in fact there's an anecdote early on in which he is taking questions from kindergarten students, where his son attends an after-school program. The child asks "Does space go on forever" and although I'm not sure how he answered the 5 y/o, he did a great job expanding the question (what the question was really asking) and then providing an answer.

I love to read a chapter slowly and then impart some basic concepts from that chapter with my 10 y/o granddaughter. It's a great book to read for pleasure, but it will also bring you up to speed -- where physics stands in 2014. [And just possibly, it will help you understand the CBS sitcom, "The Big Bang Theory" a little bit better.)

This book is an exceptionally eye-opening read containing new, fresh concepts and unbelievable {sometimes shocking} insights. `Our Mathematical universe' covers topics such as cosmology,unique philosophy and the nature of reality. It delves into scientific topics such as `the Big Bang' and the beginning of creation and life itself, to our future and the existence of parallel worlds {both sub-atomic and intergalactic}. This supremely singular study could be classed as a science-fiction sub-genre if it were not for the use of mathematics which the author relies heavily on; for explanation of theories and a deeper understanding. So many of our deepest questions are attempted to be answered, with Max Tegmark using mathematics such as for instance; the scope of reality, what everything is made of and why our universe is the way it is.

Including many charts/ graphs and diagrams alongside facts to back up the hypothesis, this truly is an in-depth look into our world written by such a visionary masterful author. Anyone who is interested in finding out more about our world and the unexplained will be dazzled by this engaging, credible book as too will those sceptics who seek answers to all the riddles. If you like books by Professor Brian Cox then this is an ideal read for you! I am so pleased to have won a copy of `Our Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark' through a Goodreads, first-read giveaway.

An illuminating read @ 3.5 stars!

Disclaimer: I am reviewing an advance unproofread copy that I received for free through the Vine program. Also I have met the author, many years ago, and my wife used to collaborate with him on research in cosmology.

I really loved reading this book! I had such a good time while reading it. Many wonderful "observer moments" were had by "me" AKA this copy of my observer existence in this Level 4/3/2/1 universe. (that will make more sense after you've read the book)

It's really like 3 different books in one; maybe one could argue that it's not focused enough on a single topic, but I think it's literally like having 3 good books all come packaged together, and flowing one into another pretty smoothly.

The "first book" (early chapters) has some good technical but accessible stuff, very clear and coherent explanations of some otherwise difficult ideas, about recent discoveries in cosmology, especially dark matter and dark energy (that's the stuff my wife used to collaborate with the author on). Now I know a little more about what they were working on! including things with funny names like "the Great Wall" and "the Axis of Evil" (again, will make sense after you read the book; the names really are just whimsical, not intended to actually depict or portray any actual characteristics of the phenomena, but they're still lots of fun).

Woven together with the accessible explanations of technical material are a lot of emjoyable personal anecdotes from the author's colorful life. (this is what I'd call the "second book") This distinguishes this book from some others in related areas that have come out in recent years; they don't usually get into the personal life, hopes, dreams, fears etc. of the author as much as Tegmark does. And this works very well here; so there's a kind of partial sketch of an autobiography woven in here. Apparently it was a gambit (to go personal, whenever possible) suggested by his editor or publisher, and I think it worked out very well.

Later on in the book comes the presentation of the author's own controversial pet theory, about the Mathematical Universe Hypothesis, AKA restricted versions like the Computable Universe Hypothesis, or the "Level 4 Multiverse", or "everything literally IS mathematics, is not just REPRESENTED BY mathematics" etc. (this is what I'd call the "third" book)

There is some overlap in material with some other recent (also very good) pop science books like those of Brian Greene. But Tegmark comes from the background & starting perspective of theoretical astrophysics and cosmology, based on observational data. That's a very different perspective than Greene's who comes from the world of "string theory". In fact the book I'm reviewing here will stand regardless of whether string theory is valid or not, and clarifies some things I was still confused about after reading a few of Greene's books.

Tegmark's overall classification of existential schemas for parallel worlds into "Level 1/2/3/4" multiverses is very helpful in getting me to understand and visualize at least some tiny bit of what they're talking about. (again, you'll understand after you've read the book). Randomness is "just a side-effect of cloning", apparently (that's the Level 3 multiverse where really ever possible outcome of a measurement DOES occur, but in different parallel multiverses, and "you" as a single consciousness are just in one of them, though you can't tell which one and you can never communicate with any of your clones in the other ones).

Even if you discard his own personal "Mathematical Universe Hypothesis" (hey it's fun to read about; I don't know if it's plausible or whacky, I'm just an armchair reader and "faculty spouse"), that only means his "Level 4 Multiverse" is dropped out of the game; the other 3 stand on their own, regardless of that last hypothesis.

Too much discussion by the author about himself and not enough on the theories. I found myself jumping ahead to read the summary pages. I also ordered the Kindle version and it was a pain to link to find diagrams referenced then going back to the page you left reading. The author would starting talking about a chart but you had to move forward pages to find it.

The short summary:
Max Tegmark's new book, "Our Mathematical Universe", is amazing. It's easily highly readable by ordinary laymen, and makes the reader present to the joy and wonder of discovery. It describes the amazing history of our understanding of reality (the world, space, universe, multiverse) and our place in it. It addresses existential risks: [...], [...], and points out areas where your funds and efforts could make the biggest difference in improving humanity's chance to get out of this century alive, and eventually later bring life out into the universe. Highly recommended reading.

In detail:

Max Tegmark [...], highly respected professor and scientist in physics and cosmology, takes us on a wild tour of the universe (and more!), from the earliest moments to possible endings. He shows how mathematics has been critical as scientists have assembled an astonishingly precise picture of reality from various kinds of data and observations. And, he does it without showing any equations, so it is highly readable by everyone. The text is sprinkled liberally with pointers to his extensive Suggested Reading list, so the reader can learn more on any of the topics, and get as math-intensive as you like. It is also a story about people, with amusing anecdotes from Max's life and about the people who explored the universe.

Max shows us the various things that modern science has revealed that run counter to our intuitions. Our intuitions are grounded in our ordinary experiences on the surface of a planet and in society with our fellows. At the subatomic and the cosmic scales, reality just doesn't behave like that. We have had to learn to think beyond our intuitions, and mathematics has been our power tool. It has been so useful in building models that can predict the weird events in those counter-intuitive realms, that its very usefulness is puzzling. This has led some investigators, including Dr. Tegmark, to suspect that reality is not just described by mathematics, it is defined by mathematics, or even: it is mathematics.

This is the out-of-the-box thinking that Max is famous for. His explanation is so lucid that ideas which start out sounding insane become thinkable, ponderable. Even if you end up unconvinced, you will at least be conversant with ideas which are persuading an increasing number of reluctant scientists to include in their thinking. As you hear popular-press items on science, you will have some background, a framework by which to comprehend.

In the final chapter, Max addresses the various catastrophes predictable in the far future for our planet, our local space, our galaxy, and eventually our universe. However, there are catastrophes much closer in time that might terminate humanity early. These are called existential risks. Many of those catastrophes are created or magnified by our activities. We are doing a dismal job of reducing those risks. How often do you hear a politician run on a platform of reducing existential risks?

Making ourselves extinct is a disaster that takes real effort to even think about. It involves the fate of everybody alive today and of all their potential descendants. We have no good idea how many future people that is. Expanding into space is possible, once we get over some serious but temporary technological hurdles. Max makes strong, mathematically-based arguments that the Milky Way Galaxy, at least, is devoid of advanced life-forms capable of building a civilization. If this Galaxy is going to have intelligent life, it's probably up to us. Now, we're talking about a LOT of future people.

Further, Max makes a viable case that the entire "visible" universe (the part we could ever interact with) is empty in that sense. As we learn more, it is becoming more believable that it is really hard (unlikely) for life to get started and that there are many paths to extinction. We got really lucky getting this far. Now, we need to not blow it. Every year, we need to again not blow it. This why Max gives a grade of D- for our handling of existential risks, for our efforts at deliberately keeping ourselves alive.

Different risks have different numbers of people working on them, and bringing different amounts of resources to bear. The ones that are getting very little attention are the ones where one person could make a real difference. It could be you. And the clock is ticking.

This is one of the best popular science books of 2013. The writing style is easy to follow making the text a fast read. Much of the book is about the process of arriving at theories that involve the author Max Tegmark. Here Tegmark explains how we could be just one of multiple universes or maybe also a afterthought of some advanced civilization. There is not much math to speak of in the book which makes sense since this is in the "popular science" category. But I was hoping for some meat in the soup. However the mathematics behind multiple universes is so complex that even most mathematicians don't understand it. At least that is what I am told.

There is a definite teleological slant to the book. I don't know if the author intended to come across that way or not. But one certainly gets that feeling. This area is left vague and I suppose it's up to the reader to judge whether there is/was a grand designer who conjured up this thing we call our universe.

This is a pop-sci physics book (heavy on cosmology) with a smidgen of memoir added. Tegmark talks a bit about his life, schooling, and the various experiments he worked on. It never gets very personal or interesting, but it's less dry than the usual book, if you like that sort of thing.

I originally picked this book up, thinking it would be more math-heavy than the usual release, but instead the title refers to the author's belief that the universe is a mathematical construct.

My main recommendation is: if you're interested in this book, get the Kindle version and read it on a tablet or computer. There are loads of beautiful color illustrations and hyperlinks to footnotes. Even though I got a free paper version though Vine, I bought a Kindle copy, because I was just missing too much in black-and-white. It's much more enjoyable as an ebook.

Max Tegmark’s idea of a mathematical universe is admittedly a “radical extreme” idea that all matter is made up of particles that can be reduced to mathematical properties. Someday, there will be a mathematical function that will explain the universe and everything in it; the illusive grand unified theory perhaps. “Our Mathematical Universe” is much more than Mr. Tegmark’s pet theory. If you have an inquisitive mind like Mr. Tegmark’s, many of your lingering questions may be answered, and progressively, you will be immersed into universes that get wackier by the chapter. If there is even an ounce of truth to any of the ideas espoused by Mr. Tegmark, truth is indeed stranger than fiction.

I recall that Alain Badiou in his Being and Event uses mathematics as ontology. So this idea perhaps is not new. On the other side there is a different hypothesis that our Universe is just Memory. From Memory Dump Analysis Anthology, Volume 4, page 271:

EPOCH: Exception Processing Of Crash Hypothesis (or Memory Dump Universe Hypothesis). Our Universe is Unhandled Exception Processing saving one huge Memory Dump from a runaway HUC (Big Bang of Hyper-Universal Computation, or simply HUge Computation).

I don't see any problems in grand metaphysical speculations.

This Book is amazing not only for the Mathematicians, physicists but also for general readers who are curious to know about our universe. I am very deeply intrigued by everything Prof. Tegmark has written and I absolutely loved this book.

I first came across the author giving a lecture on the topics expanded on in this book and I am glad I pursued that interesting notion. Tegmark makes digestible what should be difficult material for a non-physicist to comprehend. I feel I have a much deeper appreciate understanding of reality and alternate perspectives. The call to action is inspiring.

Don't worry, it's not full of incomprehensible mathematical equations. This is a very different perspective written so that those with basic scientific knowledge, can understand it without being a math major. Max Tegmark is a scientist with a keen sense of humor who obviously loves sharing the wonder of science as it relates to everything from the universal to the personal. Although I got a little lost in some of his analogies near the end, he caught and held my attention throughout the book. If you like books in this genre, this is a must read!

This book was like a time machine that allowed me to go advance my 42 year old physics education to the present state of knowledge on the origin and nature of our universe. I'm also grateful to the author for his willingness to extrapolate/speculate on the true nature of the universe from his rare perspective as an accomplished theoretical physicist. Anyone with a strong curiosity as to the nature of the universe will enjoy this book (heavy math knowledge is not required).

Fascinating account of the author's involvement in physics, especially the development of cosmic background radiation maps. Since modern physics is indeed essentially a mathematical science, the book has 'Mathematical" in the title. But there is little math in the book, so don't be put off. There are pictures of equations, but no math. And when I saw pictures of equations, I mean literally framed pictures of Maxwell's Equations, Einstein's Equations for special and general relativity, Schrodinger's Equation, etc.

So much of modern physics is unintuitive, the premise of the book is that it can basically only be understood from its mathematical description. I tend to agree; the equations model the underlying concepts and the experiments confirm the equation's predictions.

The author describes the importance of the physics and modern experimental findings very well; a highly enjoyable read.

Brilliant Author. Since much of the material is difficult for a layman to comprehend, I especially appreciated his summaries at the end of each chapter. He believes in multiverses, a concept I find difficult to accept. If you understand uantum physics, you will especially enjoy this book.

this book was both educational and enjoyable. The mathematical thesis was well presented and certainly gives one much to ponder. The humorous tone and anecdotes keep the material from becoming too heavy. Finally his call to some form of logical, planet wide action for self preservation is well timed and worthy of sincere consideration. Scientists need to engage political figures in examining solutions but risk losing objective credibility if not very careful. This is a huge challenge.
the book was a very enjoyable read.

If you enjoy "Nova" on PBS, you will love this book. It is a walk through history of math and science with a brilliant companion, who sheds a new light and insightful comments on all of math, space, and science. Is he right? I did not care; the book was such a brainy tour de force that thrilled and made new connections in my brain; I enjoyed being swept of my feet,, with my brain cells in uproar.

I haven't been keeping up with the latest in physics for a couple of decades. Things have changed since I last cracked a book on "the latest" in physics. All those newly discovered subatomic particles, parallel universes, multiverses, and strings! Well, I started to become intrigued as I watched popular documentaries on these things. Then I started to read material by Michio Kaku. Wow, have I been missing out on a lot of stuff! I love to ponder reality, what is and what could be... For example, mathematically we can trace things back to the beginning of the big bang, but no one has any idea what came before, or even if there was a before. That's where I like to ponder the possibilities.

Tegmark is a ponderer in the same sense that I am, but of course his knowledge is vastly deeper and broader than mine. I am glad that he touches on all the things that I have been pondering, turning what were just buzzwords, into intellectually tangible objects. His writing style is casual, as is Kaku's. This is important for us lay people who use these books to open our eyes, not close them when we need some shuteye.

If you too are a ponderer, this book will reinforce material from other such books, clear up some foggy areas, and help to quench your thirst to know what's out there.

(Google Play Edition)

I'm MAT (my initials), a retired cleaning lady at MIT's building 37,
Office 626B, Professor Tegmark's, Cambridge, Massachusetts.

Professor Max Erik Tegmark (MET@MIT) is a Renaissance person,
a loving, warm human being with a terrific sense of humor, whom I
daydreamed marrying but who was 22.5 years my junior.

Our Mathematical Universe is a masterpiece of synthesis. The three
greatest scientific theories so far, passing ALL experimental tests with
flying colors, are evolution, special/general relativity, and quantum
mechanics; we venture beyond them at our own peril. MET boldly goes
where no scientist has gone before, knowing fairly well he will be proved
right or wrong in the next 40 years.
Superstition (and her daughter religion), mysticism, the paranormal,
and pseudoscience have no place in science, at least not in this out of the
possible 10^500 universes. Philosophy has a place (sorry, Dr Hawking,
it is in our genes just as math is!). Science fiction has a place--what was
science fiction in Leonardo da Vinci's time all the way to 40 years ago is
now science and technology.
The book has 13 chapters and 421 pages. Buy it and read it! If a cleaning
lady can wade through it so can you.

MET, your quest for the ultimate nature of reality is our quest. Moreover, why our
universe behaves the way it does? is there life in other galaxies, in other universes?
do all living things have a soul or a spirit? what is the purpose of life? what is the
meaning of existence? are we human beings "self-aware parts of a giant mathematical
object"? is "what is" just the outward manifestation of the Absolute (the ground of
being) or just a hologram or just a computer simulation? Are these meaningless questions
or the core of philosophy and having nothing to do with the basis of modern science,
scientific determinism? Or is Confucius right: "It's hard to find a black cat in a dark
room, especially if the cat does not exist"?

How wonderful would be to witness a meeting of minds among (in alphabetical order
by last name) François Englert, Brian Greene, Stephen Hawking, Peter Higgs,
Michio Kaku, Lisa Randall, MET, Gerardus 't Hooft, Neil de Grasse Tyson, Martinus
Veltman, and Edward Witten!

If you google the title of his book you'll find positive and negative reviews, as you will
here at the store.com. Personal attacks (argumenta ad hominem) have no place
in science--let's zero in on ideas, not on the person. Please!

So...if you can't stand the heat don't tickle the Stockholm Dragon.

MAT, MET, MIT, MOT, MUT, MUH....?

The beginning of the book is easy and fun to read although it goes over familiar terrain for people who might be interested in such topics. However, as the author himself says, at one point the book diverges. I read it to the end, only to see where he would end up. The main argument hinges around eternal expansion, which is an ad-hoc assumption that seems to explain a lot of things but that I simply do not buy.because there is no test that it is true. Not falsifiable, hence not science, just an assumption.
On top of this, the idea that we must live not only in a multiverse but in a series of multiverses of different types, seem a bit too much. I feel closer to physicists that think that theories like string theory where at the start, you have to assume 11 or 12 dimensions of space just for the construction to be mathematically coherent is too far fetched to be real physics.
If you want to read an exactly opposite view, read Lee Smolin's latest book about Time. Smolin is the author of "The trouble with physics" in which he attacks string theory, that has occupied thousands of great minds for the last 30 years with not the single real result to justify all the effort..
There is no doubt that we are still far from understanding why quantum mechanics and general relativity do not match. Possibly, we are missing some great truth. I do not believe that making up extremely difficult mathematics will solve this issue. Maybe because we are part of the universe, there is something that will always evade our minds.

I found concepts and arguments in this book very subtle for my mind. In literary sense I felt this book was very well written and I truly enjoyed the personal stories that Max seeded through most of the chapters.

On the other hand, I admit, these were the only parts I truly understood. The remaining parts sailed so high over my head that the book could have been written in a foreign language.

To me the argument that the universe is a Mathematical Structure is as incomprehensible as saying that it is made of Animal Crackers. Perhaps at a fundamental level there are no objects and no properties only relationships between something? I didn't quite grasp what that something is. Even allowing for this supposition, the explanation of how reality emerges from this number soup also evaded my understanding.

I had little less trouble following the multiverse arguments, at least at the beginning. I was wondering though... given current state of our knowledge can we really estimate the statistical distance to another, identical Type 1 universe? What if space is continuous and just one of those mathematical relationships that define it contains irrational number. Wouldn't that make our universe unique even if space is infinite?

Well maybe I am commenting more on myself than this book. Yes I am a moron if you still wonder. To summarize, my problem with the book is that every logical leap in these arguments seems questionable to the uninitiated and prompts one flood of unanswered questions after another. I guess Max would make a great next door neighbor. I would love siting on his porch listening to these ideas and asking questions. Until that happens this book is a poor substitute.

I appreciate the author's effort to make the far-reaching and complex science accessible to people who do not make the topics their work, though the topics and their implications touch most of us, if only as fleeting questions about our universes. Max's weaving of his personal experiences and personal ideas with scientific explanations of the Universe is fun as well as enlightening. I think that he does a good job distinguishing his personal thoughts from the accepted and controversial science. His explanations of the controversies in science are excellent and enlightening, as well. Most of us think that statements from scientists or branded as scientific are the end-all-be-all of them, those people, the scientists and their industry. Max explains various understandings of major scientific theories and some of their history. Not so easy to read even for someone with a technical background, but fun to work through.

My brain hurts. This was an excruciating ride but one well worth taking. In the end, I have to admit that I feel that I've only skimmed the surface of this book, only gained a better feel for the state of everything from quantum mechanics to cosmology today. I can't say I've understood it but I've come to appreciate it just the same. That great minds can think along these lines and outline their thoughts for the rest of us is reassuring.

I'm enjoying this book and am looking forward to the conclusions.

But what's up with the illustrations? The book has important illustrations and photographs scattered throughout the text, but they are so small that they're confounding to try and decipher. Whoever made the decision to include thumbnail-sized illustrations instead of the full-page sized ones needs to go back to editing school. It really cheapens this book.

"They laughed at Columbus, they laughed at Fulton, they laughed at the Wright brothers. But they also laughed at Bozo the Clown." -Sagan

The 9 first chapters constitute 50% of the book and provide no new information and no new insights. None. Chapter one was the best in writing style and the least boring. This first half of the book is basically a review of parts of physics (classical and quantum) but the author seems to think he is making important points where I could not find them for example in describing Everett's interpretation of quantum mechanics he uses exclamation points too frequently when what is being stated is already common knowledge (parallel universe and non collapse of wave functions). I found myself saying, yes, come on already what is your point? Give me some insight or even a new reference or some humor for gods sake! But no. The author instead spends too much time describing how he spent nights doing this or that calculation and repeatedly talking about scribbling numbers on napkins over lunch.... I mean what do I care?! Please deliver!

I picked up this book with an open mind knowing what it is about and fully willing to accept radical thoughts and ideas. I think I even forced myself to read all the first 9 chapters just to allow myself to experience any numbing the author may have intentionally engineered to induce acceptance of his subsequent thesis. After 9 painfully boring chapters we finally reach chapter 10 where the author is ready to present his theory that the universe *is* a mathematical structure. His arguments:

1- A complete description of our external reality has no baggage (by baggage the author explains that he means unnecessary human abstractions and concepts)
2- Something that is "baggage free" is therefore a mathematical structure

By baggage the author means human-made concepts and abstractions. He gives the example of a basketball (the concept) as baggage, the less-baggage is the collection of atoms making up the ball and even an atom is a concept of more elemental mathematical properties and constants. He is correct these are human-made abstractions and concepts but I wonder: Won't we always only be able to observe fewer (initially only "mathematical") properties about the most distant (both smallest and biggest) parts of our reality and at the frontiers of our knowledge? Does that mean what we can observe today at the most distant scale is all that exists? Today's "concepts" were yesterdays measurement. When we learn more about quarks and eventually develop their concepts and abstractions, will they (quarks) still *be* just numbers? The "highest resolution" of observation at a given point in time given our technological capability is a moving target so even today's "math truths" will get "baggage" tacked onto them as we learn more. Why is the least useful resolution where we cannot measure well or map correctly or use predictions, why is that supposedly the true nature of reality?

The core book thesis is since the smallest building blocks of reality (quarks inside atoms for example) -according to the author- have only number properties (no smell, or color) then they *are* numbers. AND since we can (the author claims but does not show) describe (all?) higher abstractions and concepts of our reality by those numbers (only?), then our reality with its "baggage" also *is only* numbers!
What a leap! If you think you can buy this, then buy the book.

The author mentions a harsh letter from a reviewer warning him the papers he is submitting are not making sense and the author's reaction is along the lines of "all great minds were ridiculed so I will march on", hence the title of my review.

Abstractions are useful and at some level biology is just chemistry and chemistry is just physics but physics is not math (is physics language?). Additionally even if it were, if you cannot measure reliably at the smallest (quantum) scale, why reduce the bigger scale where we can measure, predict, and make some sense of things to that smaller scale in the first place? If you cannot show me that you can map from that smaller scale to the bigger scale why are we discussing this zoomed-in useless resolution? Why are we confusing math with "least abstract"? Math is a language and can be used to describe any abstraction (I can talk about either proteins or atoms with either math or English). The author seems to think that everything is math but says math is not arithmetic! Dude, if you claim some ratios and equations are fundamental go ahead and claim it is all just addition for a ratio is really division and division is repeated subtraction and subtraction is addition with negative signs. He is not just claiming his select ratios are fundamental, he is claiming reality *is* a "mathematical structure" and the universe (including us) is just a sort of computer simulation!

The author seems to think that if you divide a number such as the mass of the proton by another such as the mass of the electron then that is a fundamental quantity but he also lists 31 other quantities in a table and claims but does not show that everything is reducible to these numbers and thus -he reasons- reality *is* math. One of the constants he lists in that table is "dark energy density". Well, dark energy and dark matter are just fudge factors we invented to explain what we do not know. We observed that the outer galaxies are moving faster than they should (if our laws held true) so instead of saying those laws do not apply everywhere, we invented something called dark matter and dark energy. Something we cannot observe (dark) but supposedly is out there so it can "cause" those stars to move the way we observe! I ask: How can you consider -as the author does- dark energy density to be a core fundamental math number when it is a human abstraction, concept, and invention? Worse, it is a wastebasket made to contain and "explain" discrepancies between reality and our limited present laws. We lobbed all errors of observation inside a fudge factor and the author is claiming it as fundamental!

In summary: The author needs to justify this leap between "a few essential numbers can describe the world", which I am even willing to accept, and the thesis that "reality *is* a mathematical structure". The book promises but does not deliver. I not only feel cheated out of the time and money I spent on this, text, but also am now concerned for my tax dollars that could be funding this or similar work.

OUR MATHEMATICAL UNIVERSE is certain to be an instant classic. I liken it to A Brief History of Time - like that seminal work, I wonder how many people will buy it but not read it, or read it and not understand it. Regardless, it is a significant book, on the cutting edge of our current scientific understanding and thus deserving of a place in every library.

My only criticism of the work is the introduction - it starts rather clumsily, almost as if the editor told the author "before all the science stuff, open with a story". Thankfully, this portion is brief, and one is immersed in absolutely fascinating discussions of astronomy, cosmology, and multiverse theory shortly thereafter.

Four stars.

What makes ‘Our Mathematical Universe’ different is the personal flavor author Max Tegmark injects: the constant thread of ‘this is my life in academic cosmology’ - complete with accounts of last-minute preparation and tweaking of papers, computer models, conference talks to be delivered, the quirks and eccentricities of his fellow research travelers; their sense of shared camaraderie (and competition).

I found this to be both a strength and a weakness: While the book engages on a personal level far more than I expected, it was often disconcerting to be lulled at one moment into contemplating the Big Questions cosmology addresses, only to be jarred the next by the relative banality of the author’s everyday life. All too often I felt Tagmark was speaking to fellow academics and, rightly or wrongly, only they would fully appreciate his arguments and perspective.

Content-wise, ‘Our Mathematical Universe’ was rough sledding for me and I wouldn’t recommend it as a first book on cosmology for readers without a scientific background and even fluency in the language and math of quantum physics. Tegmark does his best to tailor his prose to popular science readers whose interest may trump their ability to drill deep. But unfortunately, from my perspective, he takes far too much for granted: casually describing in prose complex calculations and experimental processes that I would struggle to follow were they diagrammed simply on a whiteboard.

As best I could follow, the first part of the book broadly details the evolution of cosmology from a largely philosophical pursuit, owing to limitations in data gathering and analysis, into its present incarnation as ‘precision cosmology’ incorporating techniques from information theory to mine the tremendous volumes of data made available through advances in radio astronomy.
The longstanding Big Bang hypothesis of the universe’s likely origins has been seriously challenged by the theory of Inflation that suggests infinite continuous exponential growth. This accounts for both the perceived limits of what we can detect as ‘our universe’ as well as the implied existence of multiple – in fact countless – other universes comprising a ‘multiverse’ of infinite possibilities.

Among the more intriguing possibilities Tegmark asks us to consider is that our own lives are but a single instance of many such ‘identical-yet-alternate’ lives playing themselves out in parallel universes. While by the author’s own admission, his multiverse theory is both speculative and controversial he nonetheless comes across as a serious, peer-reviewed scientist who can’t easily be brushed off as a crank.

For myself as a reader, Tegmark’s passion is infectious and his writing colloquial and unpretentious - even humorous at times – but he ultimately comes up short in that elusive ability to describe complex matters in clear and simple language that engages as well as informs.

Well somebody needs to rain on this parade of fanboy reviews, so here goes. The only reason I’m giving this book any stars at all is because it is worth the read to see just how daft and disconnected from physical reality modern cosmological views have become.

The author claims to be a scientist but he is not, he is only a mathematician and a delusional one that. Not all mathematicians are delusional but plenty of them are and Max Tegmark is a shining example of the breed. How can you tell a delusional mathematician when you encounter one? It’s simple, if he/she claims that math underlies reality and is, in fact, the very basis of physical reality, they are delusional.

This claim, that math underlies reality, is as simple-minded and unsophisticated as the tired old philosophical view that things only come into existence when we humans have given them names. No, the matter is straightforward, mathematics is a human invention. It is a powerful and useful tool for modeling physical reality. Models however are only models and as such they are no more equivalent to the reality they describe than a map is equivalent to the territory it describes. People who believe otherwise are delusional.

The whole thrust of Our Mathematical Universe is to stake a claim for the primacy of math over physical reality and as such it should at best be considered a kind of freak show curiosity. If you want a close up look at what has become of the once noble endeavor of science this is the book for you. All the hubris, the vacuous intellectual posturing, and the incestuous back-scratching of the academically walled-off guild that is the modern scientific community is fully on display.

This psychological and sociological nightmare that has evolved in the academy over the last hundred years or so might be forgivable if it had brought forth a scientifically viable cosmological model. Unfortunately, the results, known variously as the Big Bang, Lambda-CDM, or the Standard Model of Cosmology no more resembles the physical reality we actually observe than does the ancient earth centered cosmology of Ptolemy.

Like the Ptolemaic model, the Big Bang can, by clever mathematical finagling, be made to ‘predict’ mundane events, but you cannot ask if the model itself structurally resembles physical reality. If you do ask, you will find the answer is no. The Big Bang model no more resembles physical reality than does the Ptolemaic model. Both require a belief in events that defy scientific credulity.

According to Ptolemy the sun, moon, planets and stars all whirl about the stationary earth on a daily basis. It is hard to account for a physical mechanism which might permit such behavior of course. The Big Bang model is far worse. It tells us that at one point in time, approximately 13.8 billion years ago, all of the vast universe that we observe and even parts of it we cannot observe, were all co-located at a single infinitessimally small point. Except of course, as you will read in Tegmark’s account, mathematician’s would rather not discuss this inexplicable moment of origin but prefer to take up the tale a few millionths of a second after so they don’t have to account for a physically impossible condition and can instead proceed to discuss with great confidence a merely implausible one.

An impossible initial condition isn’t the Big Bang model's only problem unfortunately. The model starts with the assumption that the cosmological redshift discovered by the astronomer Edwin Hubble is caused by a recessional velocity; the farther away a galaxy is from us the faster it is receding. (It should be noted that Hubble himself did not fully accept that interpretation but it nevertheless became the orthodox belief.) Mathematicians then arrived at the Big Bang’s impossible initial condition by ‘running the film of expansion backwards’. But a funny thing happened when they reran the expansion forward; it didn’t produce the universe we observe.

Not to worry though, a clever mathematical theorist named Alan Guth cooked up a scenario whereby some negative vacuum pressure in the early moments of the expansion blew up the whole cosmos at a rate far exceeding the speed of light, thereby imprinting quantum fluctuations and producing just the universe we observe. Truly amazing, no? You can call it ad hoc and implausible also if you want to but the end result is, this so-called Inflation Theory saved the Big Bang’s bacon.

But then, there are still other problems, The Big Bang model doesn’t seem to work on larger scales without invoking some invisible and ill-defined ‘stuff’, with the descriptively blunt names dark matter and dark energy. This invisible ‘stuff’ we are told comprises 95% of the universe while the real stuff we actually observe comprises the remaining 5%. To make matters clear, in order to agree with the results of actual physical observations the Big Bang model requires that the universe be composed of large amounts of invisible ‘stuff’ despite the fact there is no empirical evidence whatsoever for the existence of any such hypothetical ‘stuff’.

Having said all this you may be surprised to hear that the Big Bang model is considered a triumph by mathematical theorists like Max Tegmark. Well that’s why I gave the book 3 stars - don’t take my word for it - read it for yourself. It’s all there in black and white. But do the memory of once noble Science a favor - borrow, don’t buy the book. You really shouldn’t provide funding and encouragement for this kind of blithering mathematical nonsense.

If the author toned down the autobiography, it could be a good book. Who wants to know what you did with whom and when or what papers you published and how long it took you? Just give the reader what you promised - why our universe is mathematical and what the mathematics is. Perhaps you talk about it later in thd book, but i can't get past chapter 4 because of autobiography overload.

This book may satisfy the personal quest of its author and many readers, who search for what they consider the Ultimate Nature of Reality. It does, however, not come close to the much profounder quest that the - until now severely misinterpreted - ancient Greeks sages, Thales, Pythagoras, Parmenides, Empedocles, Socrates, Plato, etc., pursued.

They truly experienced, as I show in The Socrates Code (For an introduction see: “Man, the measure of all things?” in The Philosopher, V. 102 No. 2, 2014), parallel worlds of the psychic kósmos by unquestionable self-observation and not by speculation as Tegmark employs. These worlds are part of the description of the Greek kosmología (kosmogonía), which is epistemologically much more revealing than Tegmark’s Mathematical Universe.

The reality behind the Greek notion of NATURE (phýsis) is far more comprehensive than Tegmark’s speculatively searched-for Ultimate Nature of Reality, which for the Greek sages is the lowest of all worlds. This NATURE (phýsis) is accessed by the Greek sages with reawakened extraordinary senses by what Parmenides calls the PATH TO TRUTH. It is a path (ascent of the psyche) that transcends the nature perceived by the familiar senses by what he calls the path of opinion.

Who desires to grasp the difference between both paths and get in touch with the QUEST for the Ultimate NATURE OF REALITY of the ancient Greek and other sages, may want to look at my critical reviews of

Plato: Timaeus and Critias (Penguin Classics), translated by Desmond Lee,
Plato: Republic (Hackett Classics), translated by C. D. C. Reeve,
Plato: Symposium (Hackett Classics), translated by Alexander Nehamas and Paul Woodruff,
Theology of Arithmetic, by Robin Butterfield,
The Essence of Truth: On Plato's Cave Allegory and Theaetetus (Bloomsbury Revelations), by Martin Heidegger.
The Gnostic Gospels; by Elaine Pagels.
Divine Matrix, by Gregg Bradan

Who understands Plato's kosmología (kosmogonía) in the way I beautifully match it in THE SOCRATES CODE to that of the Chinese sage Laotse (LAO TZU), will accept that Mark Tegmark also only follows the PATH OF OPINION.

For futher details see my Youtube presentation. TAO: PATH TO DISCOVER THE PSYCHO-COSMIC ORIGIN OF THE WESTERN CULTURE.

Max Tegmark's new book purports to be lively and accessible, although I would say it often lives up to the first adjective, but rarely shows itself to be accessible. While one can't fault Tegmark's enthusiasm for his subject and the knowledge he displays about physics, the work will be a tough read for those not versed in mathematics or the basics of physics. Additionally, one thing that distracted me from the book's contents was the author's continual reminders about personal events in his life: his accomplishments, and the positions or awards obtained by his close buddies. Maybe I'm being a little resentful here (in the Nietzschean way) since Tegmark has authored (or coauthored) more than 200 technical papers, and these papers have been cited more than 500 times, and he has a Ph.D. from Berkeley and teaches physics at MIT. He's a leading expert and researcher--so what is there not to envy if one is an academic?

But despite these achievements, I'd like to think that my review is based on the book's merits as far as I can judge. Firstly, the good points are that Tegmark does make learning physics fun, for the most part; he's creative, enthusiastic and clearly adept at his field. There are numerous figures (illustrations) that elucidate his subject matter and he's even knows a little Plato.

On the other hand, Tegmark is supposed to be advocating a new theory, but does not seem to realize that he was preceded in time not only by Plato, but also by Pythagoras, who considered ultimate reality to be mathematical. Granted, Pythagoras did not have the advantage of living in the 21st century after all of these scientific achievements had been made which seem to validate that reality is mathematical in some sense of the word. But Tegmark appears to be piggybacking on the ideas of his ancient soul-mate without greatly acknowledging his debt to the one of Pythagorean fame. Granted, he does mention the Pythagoreans on page 247. That is not nearly enough credit though.

Furthermore, other modern writers have tried what Tegmark is attempting to do; and they have maybe done it even more effectively (i.e. Brian Greene, Paul Davies, and Roger Penrose). To say that there are no fresh ideas in the book "Our Mathematical Universe" would be an overstatement. Yet I have read books of this kind that explain the subject on a popular-level with more adeptness and finesse.

If I seem overly critical, I guess it's because of the writer's tendency to remind us of all the famous folks he knows and because I've read books of this caliber that I liked better. This book could also have used an index and maybe a different version will provide one. But, on a positive note, I liked the author's explanation of Eratosthenes' feat(measuring the earth's circumference with rudimentary instruments) and his narrative of the Big Bang theory. The chapters on the multiverse are perforce highly speculative. Despite my critical comments, the book is worth perusing.

Max Tegmark has written a book based on today's assumption on expansion, Big Bang, particle theory and of course parallel worlds. The author tells readers it is is own thought process and applying mathematics for his hypothesis that our physical reality is a mathematical structure. Author takes each section of learned sciences on the subject of How big is Space? To the subatomic Particle Physics and waves. After building of a base of understanding he second half of the book takes a leap of faith with quantum and reality discussions. Very interesting to read and absorbing to try to comprehen all the author's points. Look forward to more from the author.

I had the pleasure of discovering Professor Tegmark on television and subsequently interviewed him on my radio show. I must admit I am still reading the book but I absolutely love it. It is for both the science enthusiast or anyone interested in the workings of our existence. The graphics are tremendous in illustrating the ideas and make this the all more approachable. I recommend it highly and thank him for being an amazingly gracious guest for "This is Diana"!

The author of this book, Max Tegmark has a very friendly writing style and his ability to explain physics to the lay person is excellent. You have to have an interest in physics and math or you aren't going to get much out of this book.

I don't think I really understand the whole mathematical universe idea the way someone more sophisticated in math and physics might, but it was still an enjoyable and very informative read.

Recommended.

It's fascinating ... but much of it was WAY over my head. Still, getting the general concept and knowing that there is this kind of detail to back it up was worth the slog. Methinks Prof Tegmark is mighty fond of himself ... but then he's good a very, very interesting view of the world. I do wish he'd written down a tad; that would have helped.

If the author toned down the autobiography, it could be a good book. Who wants to know what you did with whom and when or what papers you published and how long it took you? Just give the reader what you promised - why our universe is mathematical and what the mathematics is. Perhaps you talk about it later in thd book, but i can't get past chapter 4 because of autobiography overload.

This book may satisfy the personal quest of its author and many readers, who search for what they consider the Ultimate Nature of Reality. It does, however, not come close to the much profounder quest that the - until now severely misinterpreted - ancient Greeks sages, Thales, Pythagoras, Parmenides, Empedocles, Socrates, Plato, etc., pursued.

They truly experienced, as I show in The Socrates Code (For an introduction see: “Man, the measure of all things?” in The Philosopher, V. 102 No. 2, 2014), parallel worlds of the psychic kósmos by unquestionable self-observation and not by speculation as Tegmark employs. These worlds are part of the description of the Greek kosmología (kosmogonía), which is epistemologically much more revealing than Tegmark’s Mathematical Universe.

The reality behind the Greek notion of NATURE (phýsis) is far more comprehensive than Tegmark’s speculatively searched-for Ultimate Nature of Reality, which for the Greek sages is the lowest of all worlds. This NATURE (phýsis) is accessed by the Greek sages with reawakened extraordinary senses by what Parmenides calls the PATH TO TRUTH. It is a path (ascent of the psyche) that transcends the nature perceived by the familiar senses by what he calls the path of opinion.

Who desires to grasp the difference between both paths and get in touch with the QUEST for the Ultimate NATURE OF REALITY of the ancient Greek and other sages, may want to look at my critical reviews of

Plato: Timaeus and Critias (Penguin Classics), translated by Desmond Lee,
Plato: Republic (Hackett Classics), translated by C. D. C. Reeve,
Plato: Symposium (Hackett Classics), translated by Alexander Nehamas and Paul Woodruff,
Theology of Arithmetic, by Robin Butterfield,
The Essence of Truth: On Plato's Cave Allegory and Theaetetus (Bloomsbury Revelations), by Martin Heidegger.
The Gnostic Gospels; by Elaine Pagels.
Divine Matrix, by Gregg Bradan

Who understands Plato's kosmología (kosmogonía) in the way I beautifully match it in THE SOCRATES CODE to that of the Chinese sage Laotse (LAO TZU), will accept that Mark Tegmark also only follows the PATH OF OPINION.

For futher details see my Youtube presentation. TAO: PATH TO DISCOVER THE PSYCHO-COSMIC ORIGIN OF THE WESTERN CULTURE.

Max Tegmark's new book purports to be lively and accessible, although I would say it often lives up to the first adjective, but rarely shows itself to be accessible. While one can't fault Tegmark's enthusiasm for his subject and the knowledge he displays about physics, the work will be a tough read for those not versed in mathematics or the basics of physics. Additionally, one thing that distracted me from the book's contents was the author's continual reminders about personal events in his life: his accomplishments, and the positions or awards obtained by his close buddies. Maybe I'm being a little resentful here (in the Nietzschean way) since Tegmark has authored (or coauthored) more than 200 technical papers, and these papers have been cited more than 500 times, and he has a Ph.D. from Berkeley and teaches physics at MIT. He's a leading expert and researcher--so what is there not to envy if one is an academic?

But despite these achievements, I'd like to think that my review is based on the book's merits as far as I can judge. Firstly, the good points are that Tegmark does make learning physics fun, for the most part; he's creative, enthusiastic and clearly adept at his field. There are numerous figures (illustrations) that elucidate his subject matter and he's even knows a little Plato.

On the other hand, Tegmark is supposed to be advocating a new theory, but does not seem to realize that he was preceded in time not only by Plato, but also by Pythagoras, who considered ultimate reality to be mathematical. Granted, Pythagoras did not have the advantage of living in the 21st century after all of these scientific achievements had been made which seem to validate that reality is mathematical in some sense of the word. But Tegmark appears to be piggybacking on the ideas of his ancient soul-mate without greatly acknowledging his debt to the one of Pythagorean fame. Granted, he does mention the Pythagoreans on page 247. That is not nearly enough credit though.

Furthermore, other modern writers have tried what Tegmark is attempting to do; and they have maybe done it even more effectively (i.e. Brian Greene, Paul Davies, and Roger Penrose). To say that there are no fresh ideas in the book "Our Mathematical Universe" would be an overstatement. Yet I have read books of this kind that explain the subject on a popular-level with more adeptness and finesse.

If I seem overly critical, I guess it's because of the writer's tendency to remind us of all the famous folks he knows and because I've read books of this caliber that I liked better. This book could also have used an index and maybe a different version will provide one. But, on a positive note, I liked the author's explanation of Eratosthenes' feat(measuring the earth's circumference with rudimentary instruments) and his narrative of the Big Bang theory. The chapters on the multiverse are perforce highly speculative. Despite my critical comments, the book is worth perusing.

Max Tegmark has written a book based on today's assumption on expansion, Big Bang, particle theory and of course parallel worlds. The author tells readers it is is own thought process and applying mathematics for his hypothesis that our physical reality is a mathematical structure. Author takes each section of learned sciences on the subject of How big is Space? To the subatomic Particle Physics and waves. After building of a base of understanding he second half of the book takes a leap of faith with quantum and reality discussions. Very interesting to read and absorbing to try to comprehen all the author's points. Look forward to more from the author.

I had the pleasure of discovering Professor Tegmark on television and subsequently interviewed him on my radio show. I must admit I am still reading the book but I absolutely love it. It is for both the science enthusiast or anyone interested in the workings of our existence. The graphics are tremendous in illustrating the ideas and make this the all more approachable. I recommend it highly and thank him for being an amazingly gracious guest for "This is Diana"!

Having just written a review noting that scientist authors often fail miserably when trying to author a book as opposed to a academic paper, I found Max Tegmark to be an exception. Tegmark's writing style makes the difficult topic of theoretical physics easy to understand and without a doubt I'll be looking for future works from this author.

The author of this book, Max Tegmark has a very friendly writing style and his ability to explain physics to the lay person is excellent. You have to have an interest in physics and math or you aren't going to get much out of this book.

I don't think I really understand the whole mathematical universe idea the way someone more sophisticated in math and physics might, but it was still an enjoyable and very informative read.

Recommended.

It's fascinating ... but much of it was WAY over my head. Still, getting the general concept and knowing that there is this kind of detail to back it up was worth the slog. Methinks Prof Tegmark is mighty fond of himself ... but then he's good a very, very interesting view of the world. I do wish he'd written down a tad; that would have helped.

This review relates to the part of Prof. Tegmark's book covering cosmic blackbody radiation. Other sections on the interpretation of quantum theory and multiverses will be reviewed later.

When the history of our age is written, the unique achievement of mankind in the 20th and 21st centuries will surely be our success in beginning to understand the dynamics of the universe. The development of quantum mechanics, gravitation, atomic, nuclear and molecular physics together with precise astronomical observations enabled by spacecraft and giant telescopes have combined to allow remarkable progress in figuring out something about the early history of the cosmos. This great adventure is far from complete of course, but what an intellectual drama. There is a natural hunger among the educated but non-technical public to know more about this, but unfortunately few sources exist to satisfy the need. The reason for this - and in some cases the excuse given as to why professional scientists don't try harder to teach to a broader audience - has to do with the specialized mathematical language of physics and the approximately eight years of full time study which is ordinarily invested to fully understand it. It is important that the general public be helped to understand the cutting edge of physics, but few working scientists have the motivation to make a real effort to fill this gap. This is particularly regrettable in that the US public pays for and supports this research from tax dollars; Prof. Tegmark's work is supported by the US Dept of Energy, NSF, and NASA.

Most often, when scientists offer 'popular' books on their life work, they tend to believe they should humanize the subject rather than take on the challenge of communicating the principles. This is misguided. Professor Tegmark's personal memoir of his professional life as a contributor to cosmology is lively, fascinating, energetic, and highly entertaining - but begs off the hard work of teaching cosmology. I will give just one example. Tegmark was closely involved in the story how high precision measurements of the fluctuation maps of the cosmic blackbody radiation contained many implications about the early universe. He tells this exciting story in Chapter 4; what he relates however is heavy on tales of pulling all-nighters to finish big papers before conference deadlines and light on clear explanations of the fundamentals which are the real heart of the subject. Figure 4.2 shows that the power spectrum of temperature variations seen by space probes and telescopes clearly support the predictions of the so-called standard Big Bang model - and definitively rule out alternative cosmologies. This graph and this conclusion represent an enormous achievement. But Tegmark makes little attempt to explain in detail why or precisely how the different theories predict the various curves, no doubt considering this 'too technical' to be conveyed. Likewise his explanations of dark energy are sketchy and do not lay out clearly the evidence for it. Ultimately this cop-out talks down to lay readers and leaves them with a possibly false sense of having understood something. The TV program NOVA is an example how an entire hour can be filled with flashy animations which communicate virtually nothing of real science. "I saw a great Nova show last night," someone will say at the water cooler, "Something about the Big Bang I guess .. pretty cool stuff!" This is the "entertainment" theory of popular science, which in the case of the present book might also be called the "All About Me" approach. (A much worse example of egotism in pop science - apparently a disease for which theorists are particularly at risk - is Steven Gubser of Princeton's recent book on string theory, in which he rambles about his mountain climbing and piano playing, and makes analogies to Fred Astaire dancing in place of any serious effort to explain string theory.)

There is another way, one which requires more effort from the scientist and more discipline in choosing material - but it is not impossible, even without relying on a mathematical background. Consider the online iTunes U course on cosmology developed by Prof. Charles Bailyn of Yale, Frontiers and Controversies in Astrophysics, aimed at non-science track Yale undergrads. He assumed only high school algebra, but instead of surveying the entire field in a superficial overview, selected just three topics - exoplanets, black holes, and dark energy - going into each one in depth including how the experimental data was obtained. It is a real course tried out on real students, with readings, lectures and problem sets, and is impressive in communicating something of the principles as they are understood by practitioners; science, not pop fluff. By the end, a non-scientist who has followed it will understand not everything about astrophysics but certain key ideas - including the meaning of dark energy - genuinely enough to perhaps explain to others. Another gem of physics for the layperson is Feynman's short book QED, The Strange Theory of Light and Matter, which explains quantum interference using only vector diagrams - but communicating the essence in an intuitive way that advanced mathematics could not improve on. And neither Bailyn nor Feynman waste the reader's time with excessive personal anecdotes.

Tegmark's book is gossip about science rather than science itself. Yes, readers will hear about dark energy, but also about cocktail parties, the author's children, the many talks he has given around the world, his marriage and divorce, and that he prefers muesli to granola for breakfast - as if he were Lindsay Lohan and there was a fanbase eager to know what he eats for breakfast. The whole value of science is that it goes beyond the Lindsay Lohan level of human existence. What we really care about Professor Tegmark, is for you to communicate to us the real meaning of dark energy in an extremely clear and step-by-step manner. That's what you have to offer, and not just that you're a cool guy. And please keep in mind that we - the taxpayers - have already paid you for this service; you're not really doing us a favor.

I don't mean to be too critical of Tegmark's book, which is valuable documentation of a brilliant period in the history of science, and conveys his enthusiasm and personal excitement for a life in science. But much more is needed before science professionals can be said to have fulfilled their responsibility to report back from the cutting edge.

On initial read I was a bit disappointed in this book. Too wordy, I thought, and a little too conversational. And too long. Then I realized I was unfairly comparing Tegmark to Feynman and Gamow — not so much as a scientist but as a writer. And that's really not fair. I still prefer those other scientists' styles to Tegmark's — this is a bit of a slog — but the content is fascinating. I am on a board that recommends books for purchase as awards to high school students and I may very well nominate this next year. Recommended.

I'm through the first chapter,and I am enjoying the personal style this is written in. You definitely feel the author's enthusiam for the subject matter, which makes the information he is conveying interesting as well.

Part physics book, part manifesto, part ego-trip, Max Tegmark's "Our Mathematical Universe" is a lumpy mess. Parts of it are engaging, to be sure. But precious little time is spent on the supposed subject of the book, with, instead, much meandering to revisit the history of physics, and much repetition to make sure we "get it". He spends a lot of time telling us what he's going to tell us, then telling us what he told us, instead of just getting to the point.

And when he finally does get to the point, it's rather underwhelming. The Universe (or level 4 multiverse, as he puts it) must be made of math because - drumroll, please! - it can (maybe, hopefully) be described as a pure "mathematical structure". He hasn't quite worked out those pesky details, but - hey! - he's written some computer programs that churn out "possible universes" (i.e., "mathematical objects" obeying who-knows-what kind of arbitrary rules - he never really explains), so sooner or later he's bound to hit upon it.

Um. OK.

So. Because I can describe all my thoughts (maybe, hopefully) in English - my first language - does that mean my *mind* is made of English? It must be. What else could it be made of? My wife's mind is made of Chinese. Our daughter's must be made of both languages, which is, perhaps, analogous to the wave/particle duality of quantum physics. Or to the supposition that universes can be made of different "mathematical structures" or combinations thereof in the same way that different minds can be made of different languages.

His reasoning (and I'm simplifying, but not by much) goes like this: first, because we cannot probe the quantum "stuff" that comprises reality at the smallest scales (it gets all fuzzy and spread out), it must ONLY consist of those numbers we assign to their various properties and the relationships between those numbers. This means that they are perfectly abstract, hence, mathematical. Second, any two systems that are perfectly isomorphic (in the mathematical sense of producing sets that map one-to-one with each other) are indistinguishable. So...since quantum objects only have abstract mathematical properties, and since math so perfectly describes them, then they must be made of math! And since those little quantum entities are made of math, that means EVERYTHING is made of math! Of course, scientists have not discovered perfect mathematical isomorphs of every single aspect of our universe, but that's just a matter of time. As I write this, Dr. Tegmark's computer might well have spit out that elusive Theory Of Everything!

Do you see the problem here? Allow me to illustrate with an example:

"All Llamas eat. Dr. Tegmark eats, too. Therefore Dr. Tegmark is a Llama."

It's the same error, in a more obviously absurd context: a hasty syllogism in the absence of complete understanding that leads to a silly conclusion.

"All physical things can be represented with mathematical structures. Mathematical structures can, themselves, be generated with mathematical procedures. Therefore all physical things must be made of math."

All that's left is to find the mathematical thingamahoochie that generated our Universe(s).

Now, to be fair, he could be right. He says, correctly, that weirdness alone should not disqualify a theory. He could also be a Llama in a man suit. Who knows?

I would not feel the need to pour such derision out on this book, but for the unforgivably *smug* tone he nurtures throughout, culminating in a final chapter of such self-righteous arrogance that I wanted to smash my iPhone on the ground to make him shut up. (I listened to it as an audio book on my commute). We'd all be better off, and might just Save The Planet, he claims (over and over again, for what seems like an eternity), if we just adopted the same kind of "scientific" lifestyle that he and his "colleagues" are so careful to practice.

Of course! He and his colleagues have it all figured out! They know exactly how we should all live! Somebody better tell those well-dressed kids on the bikes that keep knocking on my door and asking me if I know Jesus...

Wonderful panorama of first standard modern cosmology and then, a stupendous tour of fascinating speculations on life,mind, the universe and everything and all of that with a very good sense of humor.

This book belongs on the list with Schneider's Beginner's Guide to Constructing the Universe, Dunham's Mathematical Universe (the alphabetical journey is fantastical!). Turns math haters into fascinators, and lovers into scholars.

1) Max Tegmark writes on page 398 (last the bottom line):
"Even though our two intellectual expeditions set off in opposite directions, toward the large and the small, they ended up in the same place: in the realm of mathematical structures."

Lot nations have proverbs in different forms, but with the same meaning:
We cannot take diner by mantra: "I'm fed up. I'm fed up. I'm fed up...."
Real diner is assimilation of biological substances like meat, fish, and vegetables and so on. Abstract diner like mantra "I'm fed up" does not exist because it is abstract.
Ideal abstract notion as Euclid's point without parts does not exist because it is abstract and it has inside contradiction: no parts. Euclid's point exists in man imagination only.
If we call not-existed imagination as "internal reality" then we trick ourselves and other:
again - mantra "I'm fed up" does not work, the "internal reality" is not real.

2) On page 316 he write:
"In fact, I have two suspects: `infinitely big' and `infinitely small.' "
On website http://edge.org/responses/what-scientific-idea-is-ready-for-retirement Max Tegmark proposed to retire notion of infinity.
Per Weyl, mathematics is science about infinity, and if so then per Tegmark should be retired mathematics, his theory and his book.

3) "Our Mathematical Universe" is another illustration of main problem of theoretical physics: the revival of abstract notions.
Steven Weinberg has "working philosophy" as "a belief in the objective reality of the ingredients of our scientific theories".
Follower of Plato - Roger Penrose built "Road to Reality" and on page 1027 Penrose feels that it is "pipe dream" and road from reality.
Lee Smolin makes the revival of the man-made notion of time and call it as "more scientific notion".
Last "discovery" of Higgs boson is the revival of abstract notion of mass. It looks like if we spend 10 billion dollars to print menu, then we can take diner by reading this menu only.

More points, but not all, I have considered in my book "The Search For Physics. Infinity." http://www.the store.com/Search-Physics-Infinity-Viktor-Moroz/dp/1496919904/ref=sr_1_1?s=books&ie=UTF8&qid=1409016801&sr=1-1&keywords=Viktor+Moroz

4) Lot positive reviews of Tegmark's book can be explained by several reasons:
a) Habit to follow traditions and authorities which were created by believers.
b) Education per approach "Shut up and calculate".
c) Public money for pseudoscientific fictions about mathematical singularity.
Good fact for taxpayers is: USA did not participate in financing of LAC project in Europe.
Bad fact for taxpayers is financing of project(s) for dark matter and dark energy.

The faith in the inconsistent abstract notions and authorities is not science, math or physics.
It is a religion, a religious activity.

If you can believe that in millions of universes everyone in those universes has superglued a banana to their head and have rushed outside shouting "OINK OINK BOINK" whilst in a equal number of different universes they have rushed outside, also suitably attired with banana, but shouting "OINK OINK HOINK" then multiverse theory is for you.

It seems to me that multiverses, like God, have been invented to answer two so called fundamental questions - of Origin, why does something rather than nothing exist and of tuning, why are the constants of reality just right for life. Multiverses reduce Origin to a commonplace happening at all places and times, fine tuning is explained away by positing there is a infinite variety of tuning and it is merely contingent we live in a Universe with this tuning. You could in fact say pseudo scientists need to invent multiverses in order to stop God jumping into a perceived logical hole.
Both God and multiverses involve infinite regress, a infinity of multiverses and the who created God? God2? regress.

There is however a much simpler solution involving no regress whatever. If one keenly applies Ockhams razor then one just accepts Reality as a given, THE given in fact. This given is the object of scientific investigation. There is no why. Science and maths can describe how but "why?" is not a meaningful scientific question. It is an expression of most of humankinds psychological need to feel there is a "higher meaning" to life.

As for Mr T's Vision of ultimate reality as mathematical !! Well, it is neither scientific or philosophically sound.

To say reality IS mathematical is none sense. There is no formal identity. Dr Johnson, in a similar context, never kicked an equation. (Although interestingly Bishop B was claiming the Real was virtual whilst Mr T is claiming the virtual is real ). Maths is a human activity not something Reality does.

To say that if something can be described mathematically then it itself is mathematical is meaningless, it is a simple conceptual category error, a nonsensical pseudo tautology.If something is described by its colour as green it does not mean its nature is "greenness".

Being mathematical is not an attribute of Reality. Attributes of Reality are atoms, forces, stars etc.
Even "being able to be modelled mathematically" is not a attribute of Reality, it is a function of mathematics.

If one is speaking in a ordinary day to day discourse it is however perfectly feasible to say, as a METAPHOR or simile, that reality is mathematical. E.g both reality and maths are ordered having constituent parts which follow rules, elementary particles are equivalent to numbers, fundamental forces are equivalent to axioms etc. But that usage is purely metaphorical and cannot be used in a scientific discourse as a basis for theory building. In a similar way in day to day discourse it can be used as a reasonable circumlocution For the long winded "reality can be described mathematically".

The Universe exhibits observable order. ( the hows whys and degrees of order etc are not pertinent to the question at hand). The point is the universe exhibits order, what kind of order is irrelevant to the current question. It is also pertinent that there are very few ways of a system being ordered compared to a infinity of ways of it being disordered, entropy. There are a limited number of models needed to model reality, not a infinite number.

Mathematics, devised by sentient intelligences,uses axioms and rules to elaborate models/systems. Mathematics has a infinite toolset to construct these models so it can in theory, as Bertrand Russell has mathematically (sic) shown, MODEL ANY AND EVERY ORDERLY SYSTEM.

So it is no surprise that it can model reality. If reality was ordered in a different way mathematics would still be able to model it. ALL orderly systems conform to mathmatically modelling - in fact that could be a definition of "order". You cannot thus visualise a orderly system/universe which does not conform to mathematical modeling.

So The effectiveness of maths in modelling reality is not a random accident, nor does it imply in any way that what is being described mathematically must be itself be mathematical ( whatever that is supposed to mean), nor does it imply anything suggestive of any more deeper "correlation" or hidden truths about the Universe and Maths etc. It is simply a example of the great explanatory power of maths. It is what Maths , a human construct, does.

I have a accurate map of Hackney, when I go to Hackney I am not amazed the topography of Hackney agrees with the map, nor do I think Hackney has a mapematical nature, nor do I think is is mere luck Hackney is mappable, nor do I think that if the topography of Hackney was different it would be unmappable, nor do I think there is any hidden correlation between map making and the topography of Hackney, nor do I think Hackney is in itself a map, nor do I think "out there" in different mapverses there are infinite slightly different maps of this Hackney and it is just because i am a human in this mapverse that I happen to have the correct map

Mr T's "theory" of MUH is not any kind of science it is just a example of circular speculative thinking exactly akin to medieval speculations as to how many angels can dance on the head of a pin.

Personally as I do not concede it is a scientific theory I do not think it can be proved or disproved. However if I remember correctly, as i have dekindled the book in disgust, Mr T in a token Popperian gesture posits that his theory can be falsified if it can be shown that there are aspects of reality that cannot be modelled mathematically.

Well, as far as I am aware, there are chaotic systems that you could argue Maths cannot model effectively, if at all e.g., in describing turbulent flows or the laminar to turbulent transition from first principles and the chaotic nature of fluid dynamics in general. Also I know of no mathematical modelling of consciousness, the appreciation of a Bach fugue, the experience of a sunset etc. Thus according to Mr T's own posited test of his theory it is not valid.

Finally, if we were to convene the court of poetic justice and summon a Mr Godol as witness he would testify that any mathematical system , in a formal logical sense, is incomplete and cannot fully and adequately prove or describe ITSELF (sic). This, aside from showing Mr T's falsebility criteria is in fact invalid and thus again showing his theory not to be scientific, also amusingly implies that if Reality itself was a mathematical structure then Mr T would never be able to fully prove it.

My cat, Salem, in one of those infinite multiverses is at this moment exclaiming, " Hah! Since it cannot be proved to be true, and Mr T has not proved it to be true, then it must be true." Such is the logic of multiverses.

Whenever a physicist, a discipline allegedly committed to examining only physical realities, not only accepts but lobbies for the existence of an INFINITE multi-verse, then it's time for anyone other than mental masturbatory, abstract-loving mathematicians to tune out.

I ask you, what, Mr. Tegmark, is NOT possible in an INFINITE multi-verse?

Like, for example, how 'bout an over-arching, overweening super- conscious intelligence which, even if not omniscient, omnipotent, omnipresent and eternal, nonetheless may be an intelligence which is 'niscient, potent, present and 'ternal enough to have designed and created US. In other words, (ohmigod) a god!!?? At least as much a god as any of us mere earth-bound mortals are concerned.

In fact, in an INFINITE multi-verse, not only is such an intelligence a given, an INFINITE number of such intelligences is a given. Such is the bizzaro, almost mystical nature of the concept of an infinite number of ANY physical thing, be they infinite sub-atomic particles or infinite universes.

Nonetheless, some of you physicists toss around INFINITITES of physical things with an appalling, solipsistic, self-absorbed, unimaginative arrogance matched only by the appalling arrogance which renders you guys constitutionally incapable of conceiving that, in an INIFINITE multi-verse, not only are there infinite clones of you (as you acknowledge), there are, BELEIVE IT OR NOT, infinite clones of creatures with minds so much vastly superior to the one which inhabits your skull that (ohmigod) yep, your meta-physical mind-wandering meanderings lead to the inescapable conclusion that we are created by gods.

btw, Paul Davies, a much humbler and more self-reflective physicist noted this really rueful paradox back when the INFINITE multi-verse first became the "answer" of choice promulgated by certain physicists for so many of those really problematic, really fundamental remaining physics conundrums (or, to put it in the straightforward language of math: no designer(god) = an infinite multi-verse = a designer; or in the straightforward language of us humans, uh-oh) .

To compare, Brian Greene, in his "Fabric of the Cosmos," at least recognizes the possibility that an infinite multi-verse likely gives rise to multiple superior intelligences which could have created us. But, once again, subject to that physicists' hubris, he imagines those superior intelligences to be ... well, just like him except with really, really good computers. And, thus, we become ... computer simulations!---"The Matrix" revisited except that our creators are doing ... what else? ... an experiment, of course. Me, I prefer Andre Linde's musings that, eventually, even we humans will be able not only to create our own "Big Bang" but will be able to seed it with the fundamental constants which now give physicists such agita viz our own universe.

Ultimately, though, I would argue (and I think Kurt Gödel and even Stephen Hawking in humbler moments would also argue)that to seek a "Theory of Everything" when we are part of that everything is a fool's errand.

Mr. Tegmark's math was pretty impressive though. I suggest he sticks with it and stays away from physics. For, to paraphrase Einstein, measurement without math is lame, but math without measurement is blind. Like string theory with its infinite solutions (see Ed Witten's sotto voce admission to Larry Krause), your math, however impressive, betrays just how blind it is.

Mr. Tegmark states that he believes in a Level 4 Multiverse. I go him one better. I believe in Level 5 - that's the one where all the lunatics who believe in Levels 1-4 are returned to their padded cells in the Hospital for the Criminally Insane.

It's ironic that so many mathematicians and physicists, a fair number of whom are atheists, deride religious folks for holding to beliefs which have no basis in reality and yet do exactly the same thing by subscribing to the string theory/multiverse concept, for which there is not a scintilla of evidence. Karl Popper said that the hallmark of science is falsifiability, but the advocates of the multiverse cannot provide any method by which their theory can be falsified. Therefore, it is not science.

Several of these so-called scientists are shameless self-promoters - Michio Kaku, Ray Kurzweil and Brian Greene come to mind. The rest are just sheep, following along with the herd.

There is one aspect of the multiverse idea which appeals to me - in at least one of those alternate universes, I must certainly be married to a Sports Illustrated swimsuit model.

Oh boy...Title should be simply; My Quest for the Ultimate Nature of Reality. First chapter has little about Our Mathematical Universe:and is more personal philosophy. When ever a science book drops right in defending Darwinism I know it's going to be more one sided that any fundamentalist religion, especially when bold statements are made and no facts presented.

Unfortunately this is the state of the art of modern science writing. For some reason a frontal attack on any faith is paramount and questioning such is prohibited. Scientific fascism.

Generally when I make such comments I am quickly branded as a young earth creationist wacko. But I am about to complete a Masters of Science degree at University of Texas and have gone through 6+ years of formal science education without having to encounter this argument in a lecture. Yet most books feel the need to weigh in.

Seems to me most science writers have hugely inflated egos and believe that having a grasp on science and makes them authorities of philosophy. The most humorous part is they will use the weakest arguments to make a point. Never do you see them take on the likes of Thomas Aquinas to name one and resort to true fringe thinkers like Ken Ham.... Of course this is counter to the scientific method, their dogma. Pointing this out is generally not acceptable....

Perhaps the book evens out... I'll never know. I have gained a sense when not to waste my time. Perhaps if he started with more facts and figures and eased into the discussion or simply named the book as I suggested and did not try to create some personal scientific manifesto....

Anyway...hopefully one day these Dawkins et al will mellow out and stick to what they are actually good at.

Yea right huh!

I wonder why people don't speak that out. Science is testable, multiverses, at whatever level, are not.
To quote the philosopher Ludwig Wittgenstein: Whereof one cannot speak, thereof one must be silent.
The only interesting thing to note is how many celebrities have endorsed the book.

Max Tegmark's personal theory is grounded in very solid science. It is the interpretation of current knowledge as it makes the most sense to him. The question of "What is Reality" is one that scientists and philosophers have sought an answer from the dawn of civilization. Quantum Mechanics itself forces us to alter our understanding of 'reality'. It's become very popular for well-spoken scientists to write books detailing their own conclusions about what the facts as we know them actually mean to us. Tegmark is to be congratulated on his superb ability to explain both the facts of particle physics and QM and clearly show how he reaches his conclusion to that favorite debate question: "Is mathematics simply a tool to explain reality or is it the inherent property that is reality?" This is a fun topic to ponder and Tegmark's book will very likely affect how you think about it... you may agree, or you may strongly disagree, but you will learn a lot about the science involved.

The first few chapters appealed to me -- carefully written, consistent with much of what I already had read elsewhere, educational.

But later chapters just became incomprehensible. I've read many of the reviews here as well in more general publications, and I can't really decide whether Tegmark is onto something or not. Only my indecision and lack of serious mathematical and physics training forces me to give the book the second star. In terms of new certainty, one star for sure.

We have been donating our libraries to the New York Public Library on York and 78th Street, which has a book store in the basement and which raises a million dollars a year for the system. This book will sell for a buck and for a true believer in Tegmark's approach, a great bargain. For guys like me, pass it by.

Robert C. Ross
September 2018

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 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. 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 adequality demonstrates in this book. My concern here is more philosophical than practical.

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. 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. 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.

Interesting theory but unrealistic. Mixes speculation with hard science. Toward the end he ends up in a pseudo-psychological rant that seems to make a near religion of science with men like himself as its priests and prophets. I expected a more rational volume from someone with his credentials.
Because he strays from science you're better off reading someone like Jordan Peterson if that floats your boat.

Disciplined pursuits such as cosmology or small particle physics are bound to lead practitioners into paradoxes and anomalies. Some practitioners revel in them as very features of the universe, or possibly of human consciousness; others try simply to solve them. Max Tegmark tries to solve them. In so doing he necessarily transcends the terms of his immediate training and professional research pursuits. He needs remedial help from the world outside his authoritative vision, from the everyday categories of logical implication, consistency, the cogency of rational argument, and informed imagination. Not surprisingly he draws for these categories from the unexamined commonsense culture we all share yet manages to make the products of his arguments appear as natural extensions of professional empirical science born in the manner of "hypothesis."

Tegmark draws two distinctions in his book, one between scientific consensus about recent cosmic discoveries versus controversial/competing schools of scientific thought about what it all suggests (theory) and where science is moving, the other between the latter versus where Tegmark takes off into his own conjecture, which he allows many of his colleagues regard as bordering on fantasy. Somewhere transcending these distinctions is Tegmark's thesis that the universe itself is nothing more than mathematical relations—not an extreme stance for a discipline that promises to find equivalences between every empirical observation and mathematical calculation. But then he gets into consciousness, randomness of personal identity, infinite parallel universes of a unique sort, and doppelgangers.

When it comes to research science, Tegmark is an uncontestable authority and full participant in cutting edge discovery. You will delight in his lucid, reader-friendly accounts of consensus and controversy about what research is turning up about our universe, inflation, Big Bang, quantum physics, string theory, even multiple universes as conventionally understood. The great strength of this book is Tegmark's ability to make so much of this material intelligible to the general reader. Even if we do have to take some of this technical material on faith, we see where the author is coming from via his careful reviews of familiar territory and its links to marvelously unfamiliar territory. The conventional and consensus science in this book is very heady stuff.

Perhaps it should be enough to say that this book is thoroughly enjoyable on every level, including some lively social commentary at the end. But when Tegmark leaves the domain of scientific expertise, while nevertheless straining to show his speculations as informed by that expertise, he makes some startlingly naïve assertions about the nature of objectivity, consciousness, and humanity, offering them up as almost a priori axioms, as givens too obvious to investigate as topics in their own right. Some of the terms he coins are, without acknowledgement, similar to those in the humanities and social sciences that have been investigated for generations—"consensus reality" is a lot like culture, "internal reality" is a lot like individual subjectivity, and a third category, "external reality," seems to be the reality that only physical sciences can reveal as "the real thing," i.e. real reality. Social scientists of all stripes, especially social phenomenologists, have shown such concepts to be way too problematic to be simply hawked, as in "there are" these realities (such an assertion would have to be make from outside these realities in any case), and while Tegmark seems relatively up to date on certain developments in philosophy (mostly the philosophy of science in an advocacy mode; otherwise he seems content to treat philosophy as a proto-science, a pre-scientific science that scientists invoke as a foil when criticizing one another for being "too" philosophical or "just" philosophical), the philosophies and research programs specifically devoted to the matters he takes up in the last third of his book (especially phenomenology) are nowhere to be seen.

Hence Tegmark can spell out a "logical framework" and enclose it in a rectangle much as postulates are rectangled in geometry textbooks: "There exists an external physical reality completely independent of human beings." This is an odd assumption on its face, since human beings would have to be part of that reality in the first place and therefore not independent of it. Not to mention that there are people on our planet for whom such a postulate is not simply false but utterly unintelligible. Nevertheless I see Tegmark's reasoning and try to follow where he is leading us. He seems to be leading us in the direction of consciousness as a topic for physical science and cosmology, a hopeful sign since whatever else is true of consciousness, it, too, came out of Big Bang (or as Tegmark informs earlier, ongoing inflation) the same as everything else. What is there about Big Bang that would provide for this, and what is consciousness as a thing-in-the-world? Tegmark flirts with such questions, but in the end he does not go there. Instead he treats consciousness as a given and tries to explain what we are conscious of in light of principles he has laid out earlier about the nature of mathematical reality. This is similar to showing why we, situated as we are on a planet this size and shape, experience the earth as flat. Since we are ourselves mathematical, there are ways to derive how we would necessarily experience the mathematical universe that surrounds us, including our mathematical selves, our sense of time, our sense of embodiment, and each person's sense of self as unique and as having come to life once and only once in space-time—even though all of these experiences render false impressions similar to our impressions of a flat earth.

The alternative to falseness would be, once again, the real reality that science has revealed or will reveal. As a strong advocate for science, I am happy to go along with this with certain caveats and qualifications. (In what sense can two plus two equal four independently of addition?) But when speculating creatively in an endeavor to solve revealed paradoxes or apparent incoherence (e.g. the way small particles spin in and out of existence according to whether or not they are "observed"), it is possible to arrive at new incoherence more troubling, perhaps, than the incoherence one is trying to resolve (e.g. what is true about small particles must be true about big ones as well, including our bodies).

When incoherence proliferates that way, we might just as easily see a reductio ad absurdum as see a demonstration of "what the numbers show." Take the idea that your individual biography is being lived by an infinite number of yous in parallel universes, i.e. you are just one of them. Add to that the notion that you and your numberless doppelgangers are constantly splitting off from one another into separate parallel universes by the second (or the microsecond; it's unclear what the unit of time is) to go their merry ways in an infinite branching contexture of alternative futures from the life you've lived so far. Tegmark doesn't exactly say this is true or that science can demonstrate it, but he comes awfully close. He does say he believes it's true, that "there are" these parallel universes inhabited with identical-yet-divergent people with identical-yet-divergent biographies to ours, including identical-yet-divergent histories—U.S. history without our Civil War comes to mind. Any imaginable alternative to the way things are happening here has to be happening somewhere; in fact, it has to happening in an infinity of somewheres.

I have a hard time imagining what it would be like for Tegmark believing his theory, and I wonder if he is being completely truthful. Of course "belief" is a mutable concept, so I qualify my doubt by saying I can't imagine Tegmark believing in doppelganger universes with the same kind of conviction that he (probably) believes that the Civil War happened (this time) or that India exists whether or not he has ever been there. To believe in doppelganger universes the same way one believes in India (or photons) would seem, to me, to be routinely troubling—wondering, for example, whether it is proper to be jealous of all the yous that got the job you were hoping for but didn't get this go-around. Why did I get stuck being this one instead of that one? (And who, specifically, is stuck?) Integrating doppelganger belief into everyday belief would result in chronic entanglements concerning which one I am and what difference it makes.

But belief might be professed belief to press a professional point, or an obstinate belief to declare one's confidence in "where the numbers lead no matter how ridiculous it sounds," or a challenging belief as in "show me where I went wrong," or it could be a hypothesis, or it could be a literary device. It also goes without saying that "belief" also includes religious belief. To that I say that it's easier for me to believe that Earth is six thousand years old and that God arranged false appearances to fool all the scientists than to believe in doppelganger universes. The "talking snake" (Bill Maher's foil) is easier for me to accept than an infinite number of Max Tegmarks, all discovering alternative universes in 2017, some proving them next week beyond a shadow of a doubt, others going down in flames because of poor choices about which graduate school to attend, still others never publishing anything at all, still others becoming sociologists, still others dying young on impact with a forty ton truck, and others never being born in the first place because their parents never met.

It is of course gratifying to see a research scientist of Tegmark's caliber willing to go out on a limb and share his ruminations about life, the universe, and everything, especially when he is so eager to share how is colleagues tell him he is going off the deep end. But could Tegmark be right? On that note, we must not forget the many scientific initiatives launched from ruminations that in their infancy seemed quite insane. Einstein comes easily to mind. But we also must not forget Stanley Moon's rejoinder to George Spiggot's response to his calling George a "nutcase" for claiming to be the Devil. George says, "They said the same of Jesus Christ, Freud, and Galileo." Stanley replies: "They said it of a lot of nutcases too!" (The fact that George turns out to really be the Devil should not influence us in either direction.)