Our Mathematical Universe: My Quest for the Ultimate Nature of Reality Kindle Edition

The author holds an unredeemed Platonic conception of mathematics and I will state at the outset of this review that I have a Kantian conception of mathematics. For Max Tegmark, the physical world is not only described mathematically, “…but that it is mathematics.” This is to claim too much. I will concede that mathematics occupies a privileged intermediate space between physical science and metaphysical speculation but I cannot conceded that existence is mathematical. To do so actually reaches back to the Pythagorean perspective of reality upon which Plato built. The mathematical structure that Tegmark sees as the instantiation of the physical world is one that has been found to be riddled with paradoxes and proven to be incomplete. I do not think that mathematics can be regarded as an a explanation in itself of anything. Physical theories are not what they are because of mathematics. Mathematics are the language in which we state our theories about the physical universe. That is, nothing is the way it is because of a mathematical principle. However, even if reality can be described mathematically, it does not follow that the final or ultimate ontology of realty is mathematical. If the ultimate nature of reality is mathematical it follows that mathematics is the cause of ultimate reality. This is, I am sorry, prima facie absurd. For example, we can describe everything we take to be reality with words, but it does not follow that the final or ultimate ontology of realty is linguistic. What is most interesting is that, from either or any philosophical perspective, paradoxes and incompleteness notwithstanding, the practical application mathematics proceeds and works as the author more than adequately demonstrates in this book. Mathematics still provides the most precise manner in which to express our theories, but it is also possible that we have a cognitive bias to seek theories to explain the universe that can be expressed mathematically. My concern here is more philosophical than practical.Thinkers working in the philosophy of mathematics since the time of Plato are traditionally separated between those who say that mathematical statements are true about the physical world (empiricists view), those who feel that this does not do justice to the inexorability of mathematics and claim an eternal truth status for mathematics (Platonic view) and a third view offered by Kant which is that mathematical statements are true for the 'form of our intuition'; that we bring them to the world to organize our experience of exigence to better navigate the world (intuitionist view). For Wittgenstein (twentieth-century), the whole idea that mathematics is concerned with the discovery of truth is a mistake. This mistake arose from the treatment of pure mathematics as an area of study apart from application to the physical sciences. When mathematics is treated as a tool, or a series of techniques for calculating, measuring, analyzing etc, philosophical questions about the nature mathematics simply do not arise. The philosophical nature of mathematics is so mush resolved as it dissolved by Wittgenstein.From a purely utilitarian point of view, what matters most is that mathematics works and produces results. But since all mathematical models of the physical world break down at some point, combined with many inconstancies, paradoxes and unproven assumptions found at the heart of mathematics, I come down on the side of it being a human invention like chess, but a great invention it is!!!! Mathematics is not the language in which the universe is written, it is a selective tool which we use to explore the universe. Both chess and mathematics are highly useful systems, but constitutive of their rules, rules that are subjectively imposed by humans. In this frame of mind, we can take the “shackles” off our thinking – we need not wait around for a new discovery. Instead, we can be creative and free to invent more, better and new mathematics as needed. What the author does not see is that mathematics is a human creation, a tool that we use to explain physical reality to ourselves, not a feature of nature to be discovered.In author’s defense, this book is not intended purely as a history of mathematics, but I think Russell’s paradox (shockingly not mentioned in this book) demonstrates that mathematics is a human invention. Russell’s paradox shows that mathematics is not rooted in logic as both Russell and Frege had originally set out to demonstrate. It is not objective. Mathematics is not the product of logic and objectivity separate or apart from the sensible subjective world. Mathematics, and logic, is more as Kant described it after all, its origins lie not in objective knowledge but in our own a priori subjective intuitions about space and time. Mathematics is not fundamentally an objective science - the product our discoveries about reality. Instead, at its foundations, it is a synthetic enterprise and its findings are based on our ability to use our imagination and harness our intuition. Mathematics is not a body of immutable absolute truth as Pythagoras, and later Plato, tells us and with which the author agrees. Rather, it is a collection of useful problem-solving techniques constructed upon, and built up from, the most banal tautologies.The fact that we constantly fall into paradoxes combined with our ability to construct logical contradictions and traps demonstrates that the basis of logic itself is flawed or contains fundamental contradictions, e.g., again Russell’s paradox which is the result of a logical contradiction in the use of classifications to explain numbers and organize reality, number is a mathematical notion and class is a logical notion. The relationship between the internal reality of the human mind and external physical reality is a cacophony of concatenated asymmetrical subjective approximations that we invent and impose. Mathematics is the human way of imposing organization and determination onto an underlying reality of randomness and indeterminacy. To know mathematics, to know something about math & logic shows more about how human beings think, perceive and reason; not an objective truth about reality. Tegmark recognizes the subjectivism in a field such as economics, but not in mathematics, the only difference is the degree of subjectivity. Mathematics is not a body of metaphysical truths out there to be found. This is to succumb to a seductive ontological temptation. There is nothing there to be found that we did not put there ourselves. The author tells us that mathematical equations offer us a window into the working of nature. Maybe he is correct for reasons he does not realize, nature as we describe it with our mathematics is our subjective imposition so of course nature is full paradox and contraction because we put them there. Nature does not create paradoxes and contractions, humans do this. We then make the mistake of looking back on our subjective impositions upon the physical world and please ourselves by calling them objective.Mathematics is an abstraction of the human mind, it does not have a separate existence to be discovered. There is no unified origin of everything, call it truth, math, science or God. The meaning is not in the mathematics, we do the mathematics and create the meaning. Mathematics is a discursive exercise. Instead, the author treats us to a curious mathematical fantasy whereby the path to ultimate knowledge is opened.All knowledge cannot ultimately be squeezed into a form of pure mathematics. Knowledge cannot be narrowly reduced to necessary truths.

In this book, physicist Max Tegmark makes an argument for the possibility of a reality in which the universe is a mathematical structure a theory that predicts a Level IV multiverse (i.e. one in which various universes all have different physical laws and aren’t spread out across one infinite space [i.e. not “side-by-side.”]) Nobel Laureate Eugene Wigner wrote a famous paper entitled, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” The article describes one of the great mysteries of science, namely, how come mathematics describes our universe so well and with such high precision. Tegmark’s answer is because the universe is fundamentally mathematical—or at least he suspects it could be.The first chapter serves as an introduction, setting the stage by considering the core question with which the book is concerned, “What is reality?” The book then proceeds in three parts. The first, Chapters 2 through 6, discuss the universe at the scale of the cosmos. Chapters two and three consider space and time and answer such questions as how big is the universe and where did everything come from. Chapter 4 explores many examples of mathematics’ “unreasonable effectiveness” in explaining our universe with respect to expansion and background radiation and the like (a more extensive discussion is in Ch. 10.) The fifth chapter investigates the big bang and our universe’s inflation. The last chapter in part one introduces the idea of multiverses and how the idea of multiple universes acts as an alternative explanation to prevailing notions in quantum physics (e.g. collapsing wave functions)—and, specifically, Tegmark describes the details of the first two of four models of the multiverse (i.e. the ones in which parallel universes are out there spread out across and infinite space), leaving the other two for the latter parts of the book.Part two takes readers from the cosmological scale to the quantum scale, reflecting upon the nature of reality at the smallest scales—i.e. where the world gets weird. Chapter 7 is entitled “Cosmic Legos” and, as such, it describes the building blocks of our world as well as the oddities, anomalies, and counter-intuitive characteristics of the quantum realm. Chapter 8 brings in the Level III approach to multiverses and explains how it negates the need for waveform collapse that mainstream physics requires we accept (i.e. instead of a random outcome upon observation, both [or multiple] outcomes transpire as universes split.)The final part is where Tegmark dives into his own theory. The first two parts having outlined what we know about the universe, and some of the major remaining mysteries left unexplained or unsubstantiated by current theories, Tegmark now makes his argument for why the Mathematical Universe Hypothesis (MUH) is at least as effective at explaining reality as any out there, and how it might eliminate some daunting mysteries.Chapter 9 goes back to the topic of the first chapter, namely the nature of reality and the differences between our subjective internal reality, objective external reality, and a middling consensus reality. Chapter 10 also elaborates on the nature of reality, but this time by exploring mathematical and physical reality. Here he elaborates on how the universe behaves mathematically and explains the nature of mathematical structures—which is important as he is arguing the universe and everything in it may be one. Chapter 11 is entitled, “Is Time and Illusion?” and it proposes there is a block of space-time and our experience of time is an artifact of how we ride our world lines through it—in this view we are braids in space-time of the most complex kind observed. A lot of this chapter is about what we are and are not. Chapter 12 explains the Level IV multiverse (different laws for each universe) and what it does for us that the others do not. Chapter 13 is a bit different. It describes how we might destroy ourselves or die out, but that, it seems, is mostly a set up for a pep talk. You see, Tegmark has hypothesized a universe in which one might feel random and inconsequential, and so he wants to ensure the reader that that isn’t the case so that we don’t decide to plop down and watch the world burn.While this book is about 4/5ths pop science physics book, the other 1/5th is a memoir of Tegmark’s trials and tribulations in coloring outside the lines with his science. All and all, I think this serves the book. The author avoids coming off as whiny in the way that scientists often do when writing about their challenges in obtaining funding and / or navigating a path to tenure that is sufficiently novel but not so heterodox as to be scandalous. There’s just enough to give you the feeling that he’s suffered for his science without making him seem ungrateful or like he has a martyr complex.Graphics are presented throughout (photos, computer renderings, graphs, diagrams, etc.), and are essential because the book deals in complex concepts that aren’t easily translated from mathematics through text description and into a layman’s visualization. The book has endnotes to expand and clarify on points, some of which are mathematical—though not all. It also has recommended reading section to help the reader expand their understanding of the subject.I enjoyed this book and found it to be loaded with food-for-thought. If Tegmark’s vision of the universe does prove to be meritorious, it will change our approach to the world. And, if not, it will make good fodder for sci-fi.

Having recently read an introduction to the philosophy of Mathmatics, I wanted to follow up by hearing about someone who tackles head on, one of the ancient questions, why a field of abstraction such as numbers, works so incredibly well at explaining the real world. Why have mathmatical patters developed by a single person with his pen, later have independent applications in the real world?This is perhaps best expressed in the title of one of Eugene Wigner's papers, 'the unreasonable effectiveness of Mathmatics in the natural sciences'. Why do a few simple formulas explain the fundemental structures of the universe?Since as far back as Pythagoras, one proposal is that Mathmatics in the fundemental substance of the universe. This is a bold and controversial thesis. There are many that try to defend Mathmatical platonism, that in some sense the realm of Mathmatics really exists. However few go as far as Max Tegmark and postulate that the Universe simple is one elaborate mathmatical structure. Whilst hard to accept, I find this an interesting and exciting idea, which is worth exploring. It would certainly explain why our physical theories are so full of equations that are simple and work so well.This subject alone could be elaborated across many books, however this hardly scratches the surface of all the topics that the author takes on. He throws out opinions on space, time, multiple universes, consciousness, the end of time, the meaning of life, the possibility of reality being a computer generation. This is a whistle stop tour of all the mind bending physical and metaphysical subjects you can think of.Of course much of this is wild speculation, however I love to hear about the crazy big ideas and he might just be right about one of two things. Why should physicists stick to number crunching, they're as informed as anyone and entitled to take on the big philosophical questions. However it's up to the philosophers to check for inconsistentcies and perhaps breath a little more restraint into the picture. These questions will live on as long as humans are alive and it's always exciting to hear another radical voice. This is well worth reading.

I join the consensus reality that this is a well written account of a couple of decades of exploring the big questions facing Physics and Philosophy and of a personal journey developing a coherent explanation for what we observe.I particularly like the anecdotes, illustrations, tables, summaries (in bullet points) and general handholding. He’s what I call a generous author.Consequently while I started as a sceptic, I finished accepting and feeling I understood the logic of his ‘crazy’ hypothesis.Like other reviewers, I wasn’t so impressed by the more skimmable last chapter, which seemed far less well constructed and less grounded, with a lot of ‘I think’ opinions about our fragile position in the universe. He probably feels he’s earned the right to bend our ears a bit, and indeed I think he has.However I felt his strongest conclusion came in the previous chapter where he declares, “We’ve found ourselves inhabiting a reality far grander than our ancestors ever dreamed of, and this means that our future potential for life is much grander than we thought.”

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.

Well thought out and very readable and believable, as a scientist. Lots of great ideas to think about, many that I cannot disagree with. However, and it's only a personal feeling, when we got to the 4 parallel universes, i was not persuaded enough to want to read the detail to the end, so speed-read so I didn't miss anything. However, of all the books on the theory of everything that I have read, this was the most compelling.

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.