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TOP 500 REVIEWERon 24 January 2015
I find myself in the strange position of awarding five stars to a book that has plenty of content with which I disagree. The detail of that will come up later, but the reason that I can still confidently give this book five stars is that it is a great read, covers some less controversial aspects of physics and cosmology very well and where Max Tegmark strays into concepts that many don't accept, he does so in a way that really makes you think, and analyse just why these concepts seem so unlikely - which is great.

The book is an exploration of the development of Tegmark's leading edge (or wacky, depending on your point of view) ideas - I should stress, though, whether or not he's right, Tegmark is a respected physicist, not a random person with no knowledge to back up his ideas. The book includes an excellent pass through the development of the current hot big bang with inflation theory that it would be worth buying for without the rest. In his introduction, Tegmark says that regular popular science readers might want to skip these first few chapters, but I really recommend that you don't - for instance, he gives the best explanation and exploration of the concept of inflation I've ever seen in a popular science book. It's superb.

From then on, though I don't necessarily accept what Tegmark has to say, he gives a very engaging picture of the way that the concept of eternal inflation could produce a multiverse with a infinite collection of big bangs, each producing their own universe, an impassioned plea for the many worlds interpretation of quantum theory and a really impressive attempt to persuade us that the universe isn't just described by mathematics, but is fundamentally mathematical at its heart.

To be honest, you can stop there and go and buy it if you like. But I do have to say why, personally, I'm not very convinced by anything Tegmark says once he leaves the mainstream. I also have a couple of niggles about the book, which I'll get out of the way first. I found the bits about his personal life more distracting than helpful (though I know publishers love this kind of thing). He several times refers to the detailed colour picture of the Cosmic Microwave Background radiation that is shown on the cover. As you can see from the image above, if this is correct, then the universe is a whole lot more interesting that I thought it was. It's a shame the text wasn't updated to reflect the new edition. Also, the BICEP2 results form quite a big piece of evidence in favour of his view of inflation - unfortunately the book seems to have been published just before these were effectively dismissed, which would put Tegmark's reflections on BICEP in a very different light.

I won't spend too much on what I wasn't convinced by in the content, but a few key points are that he makes several deductions from infinity which I don't think can be justified (you have to be very careful, deducing things from infinity), for all his enthusiasm I wasn't sold on the many worlds interpretation of quantum mechanics, and I think in the final part of the book he makes the common error of conflating models and reality.

However, as I mentioned up front, I didn't care - because even when I didn't agree with him, I found the book really made me think. Which surely is a mark of class.
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on 30 January 2014
Do you enjoy great detective puzzles? Do you like noticing small anomalies, and turning them into clues to an unexpected explanation? Do you like watching world-class scientists at work, piecing together insights to create new theories, and coping with disappointments when their theories appear to be disproved?

In the book “Our mathematical universe”, the mysteries being addressed are some of the very biggest imaginable:
*) What is everything made out of?
*) Where does the universe come from? For example, what made the Big Bang go “bang”?
*) What gives science its authority to speak with so much confidence about matters such as the age and size of the universe?
*) Is it true that the constants of nature appear remarkably “fine-tuned” so as to allow the emergence of life – in a way suggesting a miracle?
*) What does modern physics (including quantum mechanics) have to teach us about mind and consciousness?
*) What are the chances of other intelligent life existing in our galaxy (or even elsewhere in our universe)?
*) What lies in the future of the human race?

The author, Max Tegmark, is a Swedish-born professor of physics at MIT. He’s made a host of significant contributions to the development of cosmology – some of which you can read about in the book. But in his book, he also shows himself in my view to be a first class philosopher and a first class communicator.

Indeed, this may be the best book on the philosophy of physics that I have ever read. It also has important implications for the future of humanity.

There are some very big ideas in the book. It gives reasons for believing that our universe exists alongside no fewer than four different types of parallel universes. The “level 4 multiverse” is probably one of the grandest conceptions in all of philosophy. (What’s more, I’m inclined to think it’s the correct description of reality. At its heart, despite its grandness, it’s actually a very simple theory, which is a big plus in its favour.)

Much of the time, the writing in the book is accessible to people with pre-university level knowledge of science. On occasion, the going gets harder, but readers should be able to skip over these sections. I recommend reading the book all the way through, since the last chapter contains many profound ideas.

I think you’ll like this book if:
*) You have a fondness for pure mathematics
*) You recognise that the scientific explanation of phenomenon can be every bit as uplifting as pre-scientific supernatural explanations
*) You are ready to marvel at the ingenuity of scientific investigators going all the way back to the ancient Greeks (including those who first measured the distance from the Earth to the Sun)
*) You are critical of “quantum woo woo” hand-waving that says that quantum mechanics proves that consciousness is somehow a non-local agent (and that minds will survive bodily death)
*) You want to find more about Hugh Everett, the physicist who first proposed that “the quantum wave function never collapses”
*) You have a hunch that there’s a good answer to the question “why is there something rather than nothing?”
*) You want to see scientists in action, when they are confronted by evidence that their favoured theories are disproved by experiment
*) You’re ready to laugh at the misadventures that a modern cosmologist experiences (including eminent professors falling asleep in the audience of his lectures)
*) You’re interested in the considered viewpoint of a leading scientist about matters of human existential risk, including nuclear wars and the technological singularity.

Even more than all these good reasons, I highlight this book as an example of what the world badly needs: clear, engaging advocacy of the methods of science and reason, as opposed to mysticism and obscurantism.
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on 19 July 2014
The first part of this book tells the story of long ago and of the very small in the manner of a detective story. Tegmark tells us what needs explaining - what we can all observe or what scientists cab on serve - and how successively strong theories have pushed our knowledge forward. Clearly the field has made great progress since I last reed about these things and I find it hard to praise this part of the book too strongly - it was a gripping read for someone who knows as little as I did and left me feeling I understood the Big Bang, inflation, quantum physics and so on - which I found quite remarkable.

In the second part of the book Tegmark turns more philosophical. He sets out the view first that all properties of the world are mathematical properties. And the view that every mathematical possibility is a reality in some possible universe. I was left thinking this might be true or then again it might not. What I also felt was that there are very serious philosophical implications of the interpretation of quantum physics that Tegmark argues for - persuasively. If all the things that might happen to me do happen to me - in some world - and the question is simply 'what world am I in?' This might seem to raise some quite serious philosophical issues about the nature of the self. Not issues that grip Tegmark though...indexicals - I, here and now and so on - seem particularly worth thinking about further. I also wonder whether theories like natural selection through evolution hood is some of Tegmark's possible worlds but not others....

So I felt the first part of the book was great but the second part is less interesting...
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on 4 September 2014
The first part is an excellent summary of cosmology and quantum physics that's the most readable and informative I've read to date.Or maybe that's an effect of having read too many books in the same genre. Either way the author makes light work of issues other authors struggle with, and each chapter concludes with a helpful brief outline to ease the process.
The second part of the book deals with more esoteric subject matters,which is more challenging for the lay reader and requires more abstract imaginative processing to comprehend.
Overall I found the book is readable and I rarely counted the pages or became over taxed intellectually,which to me, is the sign of an excellent author.
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on 16 January 2015
It does not work on Kindle because there are too many diagrams. But Max is great fun and I love him BUT (sort Max) I only rate him three because on with this book you should get a free Kindle version with the hard copy because of the diagrams that can't be easily related to the explanatory text on Kindle.
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on 27 October 2014
An absolutely fantastic piece of writing. The first 2/3 or so focus on established theories and slightly more controversial theories, including multiverse levels I-IV. The last 1/3 focusses on his new idea for a mathematical universe.

It is not difficult to read and he explains concepts thoroughly. In most places (whilst I don't want to spoil) Tegmark's arguments follow logically and his idea is certainly very, very interesting indeed.

I've enjoyed reading this book more than any other this year and was compelled to share my 5* review - as I so rarely am..!

Enjoy a new angle of looking at cosmology!
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on 29 September 2015
This is a very interesting and thought-provoking book.
I have always thought the Everitt parallel-universe theory mad, and still do. Peter Schor's factorization algorithm
is often regarded as using the results of calculations done in parallel universes; but I remember no such idea in
Schor's paper. Different kinds of mathematics can make the same predictions about quantum theory. Do they
all correspond to reality?
And why should I believe our Max Tegmark when his counterparts in parallel universes are saying the opposite?
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on 21 February 2016
I fascinating tour of Tegmark's physics and mathematics view of the ultimate nature of reality, which touches on some mind blowing concepts, such as: an infinite physical universe, where everything may occur, including infinite versions of yourself separated by unsurmountable distance; and quantum suicide where you may in fact experience immortality (but everyone else sees you die). This book is definitely worth reading through for all these existential challenges. On the downside, these are all thought experiments that are probably impossible to prove as right or wrong (how can you verify if two possibilities both happen, since you can only experience one?) and perhaps the mathematical basis for reality is actually rooted in a socially constructed mathematical basis for understanding reality. Also Tegmark doesn't point us towards any practical outcomes of the theories described, apart from a final chapter on how unique and fragile we may be in the multiverse, and how we need to protect our future from existential threats (with the techie favourite AI enslaving us all as the favourite threat). I'd really like to have read some more predictions about where current experiments around gravity waves and Higgs bosons might lead.

But nonetheless this is the most enjoyable popular science book I have read in some years, and kept me hooked till the last page. Highly recommended.
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on 23 March 2014
If Max Tegmark is correct (and I have to say I think he *is*), we inhabit a universe that is just one of several hierarchies of multiverse that exist by virtue of the fact that they are mathematical structures. Not simply "describable" by mathematics, but that they fundamentally *are* maths. It's a conclusion that a lot of people have reacted against, and some of the implications are mind-boggling, but Max outlines his reasoning with wit and clarity in this very enjoyable romp between the physics of the Very Big to the Very Small and back to us humans. What is the meaning of Life? What *gives* meaning to the Universe? The ultimate answer is *us*, self-aware substructures within a larger mathematical entity, apparently evolving as the Schroedinger wavefunction through infinite-dimensioned Hilbert space, seeding clones at every quantum decoherence point, generating vast (infinite) numbers of parallel universes that are themselves part of this grander mathematical multiverse.

Max writes in an accessible and engaging style - it is clear that he is enjoying himself in coming up with his ideas (they seem to usually strike him when he's riding a bike (unlike a huge truck in Stockholm when he was a kid, fortunately for the Max in this universe) or walking in a park with one of his colleagues - in some ways these little biographical details add to the charm, and allow parallels to be drawn to the incredible writing of Richard Feynman.

That said, you can tell that Max knows this is an uphill struggle - many of his ideas strike deeply at some of the core notions we have as humans. Could there really be an infinite number of "yous" within *this* contiguous spacetime, not to mention within an infinite number of parallel spinoffs of this universe, each with the same subjective feeling that they are unique? These are not concepts that Max tosses out to deal with tricky problems - they are a fundamental prediction of certain formulations of physics. I have to say that I have not read a better description of cosmic inflation than Max presents here - I thought I had run the gamut of popular science descriptions, but this book makes several aspects much clearer, and provokes the reader to think on a wider level about the implications, and how we might test them.

The final chapter is a gem - what are the major existential threats facing humanity, and what should we be doing about them? As far as we can tell, we are alone in the Universe. He's a bit pessimistic here, in thinking that other civilisations are unlikely, and I very much hope that he is wrong (or do I?), but even so, there are multiple hazards that we will need to avoid if we are going to fulfil the role that we seem compelled to adopt - WE are what gives the universe meaning, so WE need to protect ourselves, our planet, our science. Whether it's dodging asteroids, or avoiding hostile artificial intelligence take-over, we would do well to plan ahead. Increasing scientific literacy is critical - this will drive both research and the intelligent use of new information as it arises. In the end, this is the only way we can hope to avoid a possible Great Cosmic Filter - if it lies ahead of our current technological state, it could well be the reason why we have not found other alien civilisations yet.

Is this an easy introduction to a complex subject? Is it a sales pitch for a radical reformulation of what we think of as "reality"? Is it Max's musings through the worlds of physics and ethics? It's all of the above and more. In at least *some* universes it is destined to become a classic, and those are the universes that are most likely to retain intelligent life. Probably.
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on 19 April 2015
Tegmark takes a mathematical approach without being too mathematical. He posits the notion that earth supports conscious life, which is a mathematics aware that it is information emergent from mathematics. Its as if consciousness is an equation with both sides mathematically defined in such a way that exchanges between sides cannot go unnoticed. Whenever information passes from one side of the equation to another, the result is instantaneous self awareness in order for the mathematical structures to reconcile and be in balance. Consciousness is the eternal imbalance of two sides of a set of equations containing 32 fixed parameters, but simply capable of nonlinear adjustment. The sets of equations, Tegmark describes by their various degrees of universality of information. Being permanently in disequilibrium, we have the driving force of consciousness at many levels and subject to many different systems ...
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