BOOK REVIEW: The Joy of X by Steven H. Strogatz

The Joy of X: A Guided Tour of Mathematics, from One to InfinityThe Joy of X: A Guided Tour of Mathematics, from One to Infinity by Steven H. Strogatz
My rating: 5 of 5 stars Page

This is a mile-wide and inch-deep overview of mathematics. That is to say, it shines a light on a wide variety of subdisciplines, running from counting through subjects like topology, using rudimentary examples to give the reader insight into the kind of problems that can be solved. The book employs graphics, intuitive examples, and step-by-step explanation to clarify mathematics for individuals who didn’t get on so well with the subject the first time around.

The book’s thirty short chapters are divided into six sections: numbers (arithmetic,) relationships (roots, powers, etc.,) shapes (geometry,) change (calculus,) data (statistics,) and frontiers (group theory, topology, analysis, etc.) Like most popular mathematics books, formulas and equations are avoided to the extent possible. Even the notes that elaborate for curious readers use mathematical notation sparingly.

If you’re looking to give math a second try, this wouldn’t be a bad overview to get started. I don’t think it would be of much benefit to anyone who’s stayed in touch with mathematics, but it makes a fine light overview of the subject.

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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

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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.

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BOOK REVIEW: The Simpsons and Their Mathematical Secrets by Simon Singh

The Simpsons and Their Mathematical SecretsThe Simpsons and Their Mathematical Secrets by Simon Singh

My rating: 4 of 5 stars

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It will come as no surprise that television comedy writers are disproportionately Ivy League educated individuals. What may come as a surprise is that a number of comedies—particularly animated series—have a large number of technically and mathematically educated individuals on their writing staffs. Mathematicians, computer scientists, engineers, and physicists regularly work in hidden humor that only a math geek could love—or get—into episodes of The Simpsons and Futurama. Singh’s book explores the subtle mathematical references and humor that swoosh over the heads of most viewers.

While the title doesn’t mention Futurama, it should be noted that there are four chapters devoted to that series. (This in contrast to the 14 chapters dedicated to the much older show, The Simpsons.)

Let’s assume that nerds can be categorized into three sets: nerds, super-nerds, and mega-nerds. This book takes as its core demographic the largest of these groups, run-of-the-mill nerds. How does one define these three apparently arbitrary designations? A mega-nerd would see the humor in the equation scrawled on a blackboard in the background as he (or she) watched an episode of The Simpsons. (All Hail, King of the Nerds!) A super-nerd wouldn’t get many of these jokes as he (or she) watched, but he would freeze-frame the scene, and would have enough mathematical skill to decipher the cryptic jokes. A regular nerd misses the joke altogether, but is interested enough to take the time to read an explanation of these obscure references. (These categories are contrasted with the typical TV viewer, who doesn’t get the joke, but is blissful in his ignorance.)

While much of the book is devoted to these series’ mathematical gags—which range from the elementary to the arcane—Singh offers interesting insight into the writing process on shows with a team that mixes traditional writers (English and Literature majors) with mathematical types. One of the most interesting behind-the-scenes questions is why mathematical writers work so well for the The Simpsons? Futurama, being a science fiction series–and thus aimed at the geek/nerd nexus, isn’t so much a surprise, but Homer and his family don’t have any motive to be particularly mathematical—with the possible exception of the occasional reference by brainy Lisa. The chapters are arranged by various mathematical themes, such as prime numbers, pi, statistics, topology, etc.

There are some ancillary sections that deserve mention. First, there are a series of “quizzes” that consist of jokes with the set ups written as the question and the punchline serving as the answer. These jokes get progressively more complicated—starting with crude elementary school jokes (e.g. “Why did 5 eat 6?”) and ranging to the truly obscure (e.g. “What’s big, grey, and proves the uncountability of the decimal numbers?” The answer, if you’re wondering, is “Cantor’s Diagonal Elephant.”) Second, there are five appendices that are used to go into more mathematical depth on some of the topics under discussion. This is written as a book for the masses, and so attempts are made to minimize and simplify equations. There are equations and graphic representations, but they’re kept at a relatively elementary level of mathematics.

I enjoyed reading this book and would recommend it for anyone who—like me–kind of likes mathematics, but finds it more palatable with a spoonful of sugar. In this case, the sugar is the discussion of the humorous scenes of these two comedies.

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