Normally, I like to include enough in a review that it helps me to recall the main content or the thrust of the book. But Tegmark's book kind of defies this process. First, because it's reasonably long (400 pages), second, because it carries a series of very dense arguments and third because, in the latter sections, he seems to be carried away with fantasies (that may or may not be actual....but are certainly hard to follow and concur with). So I've given up on the idea that I'm going to write a resume of the book here. Just impossible. Tegmark himself, actually does a great job, at the end of every chapter, in including a "potted version" of the thrust of his arguments in that chapter. Here's an example from Chapter 11:
THE BOTTOM LINE
• Mathematical structures are eternal and unchanging: they don't exist in space and time-rather, space and time exist in (some of) them. If cosmic history were a movie, then the mathematical structure would be the entire DVD.
• The Mathematical Universe Hypothesis (MUH) implies that the flow of time is an illusion, as is change.
• The MUH implies that creation and destruction are illusions, since
structure, but also all the stuff therein, including the particles that we're made of. Mathematically, this stuff seems to correspond to
"fields": numbers at each point in spacetime that encode what's there.
• The MUH implies that you're a self-aware substructure that is part of the mathematical structure. In Einstein's theory of gravity, you're a remarkably complex braidlike structure in spacetime, whose intricate pattern corresponds to information processing and self-awareness. In quantum mechanics, your braid pattern branches like a tree.
• The movielike subjective reality that you're perceiving right now exists only in your head, as part of your brain's reality model, and it includes not merely edited highlights of here and now, but also a selection of prerecorded distant and past events, giving the illusion that time flows.
• You're self-aware rather than just aware because your brain's reality model includes a model of yourself and your relation to the outside world: your perceptions of a subjective vantage point you call "I" are qualia, just as your subjective perceptions of "red" and "sweet" are.
• The theory that our external physical reality is perfectly described by a mathematical structure while still not being one is 100% unscientific in the sense of making no observable predictions whatsoever.
• You should expect your current observer moment to be a typical one among all observer moments that feel like you. Such reasoning leads to controversial conclusions regarding the end of humanity, the stability of our Universe, the validity of cosmological inflation, and whether you're a disembodied brain or simulation.
• It also leads to the so-called measure problem, a serious scientific crisis that calls into question the ability of physics to predict anything at all.

He writes really well. Rarely, did I need to re-read a paragraph several times to grasp what he was saying. And he has lots of clever metaphors to help the reader grasp certain complex concepts.
And when I keep coming back to my reasons for being skeptical of string theory and multiple universes I am reminded of the anecdote Tegmark relates (p191) of Bryce deWitt saying to Hugh Everett that he liked his math but was really bothered by his gut feeling that he just didn't FEEL like he was constantly splitting into parallel versions of himself. Everett, responded with the question..."Do you feel like you're orbiting the sun at thirty kilometres per second?" "Touché! " Bryce had exclaimed and conceded defeat on the spot.
Actually, though Tegmark seems to be an avid advocate for the multiple world's hypothesis and, in fact four levels of multiverses ....this is probably not the main thrust of his narrative, He came up with the idea that reality is just a mathematical concept. I find it both hard to grasp this and even harder to try and explain what he means. I think he's coming at it from the perspective of a particle physicist: so if you can define a particle in terms of mathematical equations and constants then that's all that is really needed the mathematical concept IS the reality. [I guess we all actually want to think of the particle as being something that you could "hold in your hand"....or in a magnetic field etc. but Tegmark is arguing that that is not reality any more than the mathematical concept of the particle]. I kind of get the impression that Tegmark is secretly hoping that at least one of his really wild ideas (like this) will take off and become the new paradigm and he'll be accorded accolades like Einstein and be awarded the Nobel prize and biographers will line up to describe how he came up with the idea....hence his detailed descriptions of the time and circumstances of how he came up with various ideas.....and who else might have been involved. Though, I wonder, if and when the fame comes, whether all will recollect exactly as Tegmark has set out?).
He does raise some really interesting questions which I've puzzled about. Such as the issue of introducing infinity into equations and explanations. It seems to me that this has created all sorts of amazing scenarios (like an infinite number of worlds inside an infinite number of worlds. Part of the problem is that it seems to me that infinity in these situations is being treated as a number when it is not a number.....it is a concept. What happens if we replace infinity (in all these scenarios) with just a very large number.....like 10 to power of 38. How does this affect the outcome? I recall reading Roger Penrose's book: " Fashion, Faith, and Fantasy in the New Physics of the Universe" where he seemed to have all sorts of mathematical objections to string theory and multiple universes etc. (apart from his own gut feeling which seemed to take a leading role in his thinking).
Anyway, I followed Tegmark in the early chapters and found myself more or less in agreement but as his flights of fantasy (non scientific, as he admits himself in most cases) grew more and more extreme with his Level IV Multiverse......I found myself with drawing. It was like reading the stories from Sinbad the Sailor. Entertaining...yes...sort of. But graspable and reasonable? NO. I'm still hoping and expecting that somebody will come up with some concepts that are simpler and still connect the quantum world with gravity. Personally, I think the concept of time may be at the root of most of these issues. There's certainly something contradictory with our ideas about time.
Look, this is a significant book and profoundly interesting as well as being well written. Hard to give it anything less than 5 stars. Maybe iIll come back to it and re-read bits of it. ( )

-1 to the author's giant ego, -1 to some parts being non-science while presented as science ( )

I really wish I were smart enough to understand all the concepts in this book. On the plus side, in another universe I breezed through the whole thing. Nodding wisely and making notes on small errors. I gave it four stars because the author is so enthusiastic about sharing his knowledge and ideas and I really think he dumbed it down as much as was possible. It's worth the time and effort to read it--really. Prepare for your mind to be blown. As far as his argument for the the nature of reality being math, well we already know the answer is 42. So we've got that going for us. ( )

Interesting but entirely unconvincing ( )

Max Tegmark says that there are three stages of any significant physical or mathematical theory - first its insignificance (Einstein's famous papers on special relativity languished for years in relative obscurity before he was propelled to fame), then its controversy (Everett and parallel universes, or even Schrödinger and his equation), and finally acceptance - as much as quantum physics doesn't make 'sense', it is at more or less a consensus to which an alternative has yet to be found.

This piece is a study of the author's own theory, which I would say is stuck between the first and the second stages (above). To many, it is simply a way of life that math more or less explains the universe and/or multiverse - why, though? Tegmark's simple but highly controversial answer, to which he devoted the book, is that we, as in the entirety of everything there was, is and ever will be, are self-aware parts of a mathematical structure.

To put it even more dramatically, Tegmark says that time is an illusion, and we might as well be living in a Mandelbrot set fractal for all we know. Segregating reality into four parts with humans being in one corner of the lowest level is a sobering thought, to say the least. However, he repeatedly hammers the point that we might be the luckiest creatures in existence, as the existence of a particular reality is not a guarantee for the existence of sentient intelligence as well.

Sprinkled with personal anecdotes which only humanise the staggering conclusions, this is a book meant to be absorbed, not devoured. Reading it in a day might not do it justice, as this has no Math whatsoever, but is still technical enough to get the point across - so you are free to ruminate on the possible conclusions.

I am excited to see where Tegmark's Mathematical Universe Hypothesis (MUH) is going to go, notwithstanding it being proven or disproven (although I would bet on the former). There are very few books that I have read that rekindle my interest in the world around me (such as Asimov, Feynman and Penrose), and this is one of those. A must-read. ( )