BOOK REVIEW: Our Mathematical Universe by Max Tegmark

Our Mathematical Universe: My Quest for the Ultimate Nature of RealityOur Mathematical Universe: My Quest for the Ultimate Nature of Reality by Max Tegmark
My rating: 4 of 5 stars

Amazon page

 

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.

View all my reviews

BOOK REVIEW: The Grand Design by Stephen Hawking w/ Leonard Mlodinow

The Grand DesignThe Grand Design by Stephen Hawking
My rating: 4 of 5 stars

Amazon page

 

Why is there a universe, and why is it as it is? This is the question addressed by “The Grand Design.” These questions have been taken up in many ways by many disciplines in addition to science (e.g. mythology, religion, and philosophy), and science, itself, is continuously attempting to hone in on an explanation that is consistent with observed reality. Hawking and Mlodinow suggest that, for now, the leading contender is M-theory.

The authors advocate for M-theory, but also for the [relevant] notion of model-dependent realism. M-theory predicts that quantum fluctuations are causing a continuous spawning of new universes—each with its own laws of nature (or lack thereof.) Most of the bubble universes in this frothy multiverse don’t have staying power, but a few—like ours—are governed by laws that not only allow them to blossom, but also to spawn life. Besides the existence of a multiverse of universes governed by differing sets of laws, there are some other predictions of the M-theory model that remain to be proven. These include the existence of eleven dimensions, most of which are curled up and must be curled up in a certain way according to a set of laws and conditions. The theory also predicts that there will exist “objects” of various dimensionality up to nine. [Whether we will ever be able to test any of these predictions remains unclear.]

What’s this model-dependent realism bit? This is the idea that what we know of reality exists through models that connect observations to a set of rules. Within the limited space for which we have observations, there is no requirement that there be a solitary model or mapping between rules and observations. Because of this, there may be multiple theories. Physics has been long looking for a grand unified theory (GUT) or a Theory of Everything (TOE) that explains all the laws of the universe in one fell swoop. Hawking suggests that such a solitary theory may not be found given our limitations, and that we may have to exploit different theories for different situations. This belief is important because M-theory isn’t a unified theory but a grouping of theories that each work well in certain domains. Needless to say, this isn’t a particularly satisfying notion for the many physicists who are hoping for a more satisfying level of elegance.

The book consists of eight chapters. The first, entitled “The Mystery of Being,” is a brief description of the central question and an outline of why M-theory is proposed as the answer. Chapter two gives an overview of our evolving understanding of the laws that govern the universe, and sets up the important idea that the configuration of the universe is contingent upon the form of the laws governing it. The third chapter is where the authors argue for model-dependent realism, while discussing the arguments of realists and anti-realists as well. Chapter four describes alternate histories and the idea that the probability of an observation is dependent upon all possible histories that could have led to said observations. This bit of quantum strangeness is crucial to reconciling the central question. The next chapter describes the forces seen in our universe and considers attempts to unify the four forces (i.e. gravity, electromagnetism, the weak nuclear force, and the strong nuclear force) in a single theory that explains it all—a ToE. Chapter six discusses our universe with particular respect to its steady expansion that has allowed galaxies and solar systems to form. Chapter seven goes further, exploring the nature of a universe that could support the development and evolution of life. There are a wide variety of precise conditions needed to produce intelligent life. We live in a narrow band with respect to our distance from our star in which our type of life could be created. If the orbit of the sun was more elliptical or our axis wasn’t stabilized by a moon, we couldn’t be—and those features require laws that support them. The authors also examine how the chemistry of our universe is conducive to the development of complex life. The final chapter uses a discussion of a primitive computer game called “the game of life” to show how a model shapes reality as we know it. This grid-based game has only a few rules, and yet if there are more than a few pixels at the beginning, it becomes impossible for us to predict an outcome. With the complexity we see in our universe, this situation is vastly greater.

The book contains many graphics, mostly color, to clarify ideas that are difficult to comprehend via verbal description, or sometimes just to add levity. The only ancillary matter is a brief glossary of terms that come up in the book. There are no notes and no bibliography.

I found this book to be thought-provoking. However, I don’t know why it had the feel of a sales pitch. It repeats the theme of “M-theory is the best game in town” ad nauseam. This repetition draws attention to itself because the book fails to directly challenge those who critique M-theory in any depth or detail. It also fails to take on the question of how it is that M-theory might be taken from a purely theoretical construct to one that can be tested. (It makes falsifiable claims, but does that matter if we may never have a capacity to test those claims?) Those aspects wouldn’t be necessary if the book wasn’t making a pitch. [It felt like the book may have wanted to convince its pop-sci readers that–while they would only have a foggy idea of the why M-theory might have merit at the end of the book–they should remember that it’s the best–so that no funding gets cut from M-theory research and delivered to other lines of inquiry. In other words, the take-away sometimes feels like: “Stephen Hawking is super-smart, and he says ‘vote M-theory.’”]

I would recommend this book for those interested in the big picture of our universe’s existence, but as a neophyte it has made me want to read Woit’s “Not Even Wrong” or Smolin’s “The Trouble with Physics” just so that I’ll know what the critics are saying.

View all my reviews