The Infinite Book

infinite book

John D. Barrow’s The Infinite Book: A Short Guide to the Boundless, Timeless, and Endless is just one of those things that people like me find inexplicably attractive.

Infinity. What is it? What is it not? Why should anyone care about something so intangible?

For many people. infinity is just a word that they’ve been taught means, “without bound; forever; bigger than anything; beyond comprehension.” It’s usually associated with mathematics, especially math of a “higher order,” like Calculus. And it seems intuitively familiar despite an utter lack of understanding for the most part.

Barrow takes the everyday view of infinities (because, as you’ll learn, there are different types of infinity – thank Georg Cantor for that (I’m serious)) and meticulously attempts to teach us where we’re wrong and where we’re right. He illustrates just how much we aren’t built to accurately register, mentally, the nuances of such concepts. As a passing example, what happens when you add any two numbers together? We all know that. That’s easy. You get a sum, a finite sum. One that you can, theoretically count up to. The same rule applies to the other major mathematical operations (division, subtraction, multiplication). However, what if I asked you to add a finite number to infinity? Or subtract a finite number from infinity? Whatever the operation, the outcome will be the same: we’ll still have infinity as an answer. You may ask if that infinity is the “same size” as the original infinite, and guess what, it is. If you double infinity you still have infinity, and both infinities are the “same size!”

Needless to say, common sense is not really our friend when it comes to such mind-boggling concepts. Case in point, there are different gradations of infinity, each level infinitely larger than the previous one. There are countable infinities, like the set of positive integers! And there are uncountable infinities, like the set of real numbers between any two points on the number line, no matter how small! Perhaps, most impressive of all is that there are an infinite number of levels of infinity!

Despite the general mathematical nature of infinity, Barrow shows how it finds its way into a multitude of human endeavors. How big is the universe? What does it mean to live forever, corporeally or spiritually? What would it take to time travel, and what might the consequences be given different structures of the universe and time (infinite, finite and boundless, or finite and bounded)? Are there other yous out there? What are the chances of finding intelligent life in the universe? And on and on. The infinite seems to be a surprisingly recurrent topic in human thought and for good reason.

There are times when the book requires a bit of concerted effort to understand, and on more than one occasion I found myself considering putting it down – not for lack of interest in the subject, but a distaste for the somewhat dense nature of some of the explanations. Points that I think should have been further explained, either through example or diagram, were not; others that I felt had been hashed out a hundred different ways found themselves once more under consideration. Barrow is clearly a scientist, and it seems odd that he would choose to skip over the more complicated details of things like topology and set theory, which are integral to making sense of the book’s main topic and its application to real-world interests.

Overall , though, I think it was well written and a definite read for anyone interested in the topic. If you’re afraid you won’t be able to understand the more intimate (mathematical) details of infinity – because you never took advanced math or you have, but never touched on set theory – you needn’t worry. Barrow covers the major details early on and with surprising clarity. There are a few topics (like the brief overview of general topology that prepares you for the chapter on spatial infinities) that even I found somewhat tough to follow; however, I don’t think it’s really necessary for the layman to know such things in order to appreciate the grander points being made. All in all, I think most people will benefit from reading The Infinite Book, and don’t feel bad if you find yourself asking what? after you’ve finished – it wouldn’t be worthwhile if it didn’t make you think.


This week’s book review is of Malcolm Gladwell’s Outliers: The Story of Success.

Embarrassingly, this book has been on my “To-read” list for at least a few years now. Like many of the books I own, it got pushed down the list as new ones more relevant to my particular academic interests appeared. (I generally read books that have something to do with human cognition, emotions, culture and society, and the sciences; sadly, works of fiction have been almost nonexistent in my reading repertoire the past several years.) Given my own ambitious nature, it’s not unusual for me to occasionally pick up a biography on a particularly successful person or, less often, something on the nature of success itself. That inclination and a rereading of some of the blog posts on Study Hacks about passion and success (found here, here, here, and here), ultimately led me to reconsider its place in the pile.

Outliers challenges the traditional notion of what individual success is, specifically by revealing what it means given all of the external influences on individuals. Many of us regard the success of people like Bill Gates or Steve Jobs as purely manifestations of individual will. These people had the drive to succeed, and they were brilliant beyond reason. That’s why they were able to achieve what they did. Such ideas are romanticized versions of the truth, however, ignoring the roles that society, opportunity, and chance play in the eventual hindrance or assistance of individual achievement. Gladwell takes us to task on these overly simplistic notions of success, showing through numerous examples that there is so much more to these stories.

In no way is he (or I) devaluing the hard work and intelligence that virtually epitomizes truly successful people. These are absolutely necessary traits, but we shouldn’t mistake them as the root causes of an individual’s success. Of course, determination and directed effort (practice) are indispensable on the road to success. You simply can’t reach the top if you aren’t willing to work hard for it. But we need to remember that working hard isn’t the only factor. Being a genius isn’t the only factor. Talented or not, the environment you grow up in has a huge impact on your ability to capitalize on your own skills. I won’t spoil the fun by giving you the examples that Gladwell uses to provide evidence for this radical revision of what success means; for that you’ll just have to read the book.

Outliers ties in nicely to the idea of interconnectedness that I’m fond of espousing. People aren’t islands, no matter how much they think they are. There is no such thing as “the individual” in the way we’re used to thinking about it, because, for the most part, everything we do was made possible by the combined efforts of numerous known and unknown forces. More than a few someones had to actually build the computer that Bill Gates eventually learned to program on. Multiple someones had to buy it, too. A whole slew of coincidences were necessary to get him to a point where he could even begin to conceive of the Microsoft we know today. There are so many factors at play in just that single success story, yet we tend to forget about them. (The whole backstory of Bill Gates’ success is discussed at length in the book.)

The book is compelling and a must-read for anyone who wants to better understand what really makes a person successful. Once you’ve finished Outliers, you should be thinking about the world very differently; hopefully, you’ll be convinced into thinking about the world less in terms of “me,” and more in terms of “we.”

CAD Monkeys, Dinosaur Babies, and T-Shaped People

For my first book review, I thought I’d start off with something I recently finished, and probably should have read sooner.

CAD Monkeys, Dinosaur Babies, and T-Shaped People: Inside the World of Design Thinking and How It Can Spark Creativity and Innovation, by Warren Berger, had been sitting on the floor at the foot of my bookshelves – I’ve run out of room on the shelves so new books get put into prioritized piles on the floor – for a good six months before I finally got around to reading it. Despite its sometimes obvious advice, I’m sad that I didn’t pick it up sooner. The book is full of anecdotes from famous designers utilizing various techniques from a simplified list of strategies, which Berger calls “Glimmer Principles,” aimed at introducing design thinking – creative problem-solving – as a means to overcoming some of society’s greatest challenges.

Berger starts off listing the major groupings of the principles: Universal, Business, Social, and Personal. Some of the principles are head-smackingly simple, yet manage to produce the all-too-familiar, “Wow. Why didn’t I think of that?” A perfect example of this is Ask stupid questions. Of course, he doesn’t mean ask questions that are stupid, but questions that might be perceived as stupid by someone who is very familiar with the field in question. So, for instance, asking why we make the things we make or what makes us happy, would qualify as “stupid” questions given that they challenge the very foundations of the problems that we’re trying to overcome. It’s all about asking why things are the way they are. Comically, the approach of the three-year-old asking why after every answer an adult provides reflects this nicely. Other principles, however, are patently obvious and don’t really provide much to the genre of enlightened thinking, such as the principle of Facing consequences. I understand the necessity of its inclusion in the strategy for creating innovative thinking, but I’m not sure it deserved an entire chapter in the book. A few pages and a nice anecdote could have covered it sufficiently.

Overall, I enjoyed the book, and I’d recommend it to anyone who is at all interested in getting a basic understanding of the important considerations made in coming up with creative solutions to a variety of problems. The book’s greatest strength, I think, is its clarification of what design really is. The word generally connotes ideas of fashion, interior decorating, and general beautification of products and people. However, Berger makes a strong case that design – especially good design thinking – is integral to finding real solutions to society’s most difficult problems, not to mention the personal problems we, as individuals, face every day.

A perspective-altering quote that sums things up rather nicely, courtesy of Warren Berger: “I design, therefore I am.”