Here's Looking at Euclid: A Surprising Excursion through the Astonishing World of Math

Hello all! So, I said this blog was going to be about work and pleasure, which—luckily for me—are basically the same thing. This post will therefore be closer to the work side, in which I will describe a book I just finished. A review of sorts, if you wish, though my intention isn't to pass judgment on quality, but rather explain what I have learned from this book with respect to what I study.

I read the majority of this lovely little book by Alex Bellos on planes, in the U-Bahn (the Berlin subway), at the pool yesterday, and overall in transit. Thankfully, for a book about mathematics, the title was aptly chosen—it was an "excursion" and not a textbook. The book reads like narrative, and therefore not like mathematics (which should ideally be read with a pencil and paper). The author takes you by the hand and provides a survey course on what makes math interesting, why knowing it is important, and what mathematics tells us about ourselves. All in all, I would highly recommend it for anyone—whether they be a lover or hater of the subject.

Why did I read this book? Well, there were a few reasons. First off, I'm always curious to hear how popular authors make math accessible to a general reading public. While my dissertation isn't exactly intended for a general public, those who read my work are often mathematically ignorant given that there is a huge divide between the sciences and humanities in academia today. One of the biggest challenges I will face in writing my dissertation will be to make the mathematics in the OuLiPo accessible as well as entertaining, so reading books such as this one helps me get a sense of how to accomplish this rhetorically speaking.

Second, Alex Bellos is my advisor's son, and he has mentioned this book (and its sequel, The Grapes of Math) several times. One of the strangest aspects of reading Here's Looking at Euclid was the sense of déjà vu. I've heard many of the stories related in this book before, from my advisor, who has a similar way of explaining difficult concepts, telling stories, and dealing with serious material in a nonthreatening manner.

Additionally, the sheer volume of knowledge this book deals with so effortlessly reminded me of the importance of breadth. While there is always a tendency to write about something so specific that no one knows anything about it, or rather to facilitate the research and assure yourself that you haven't missed anything, there is a real charm to works that cover large periods, jump from one century to another, and string together seemingly separate cultures and studies into one larger narrative. The OuLiPo, I believe, is the sort of topic for which one should do just that.

In any case, I don't want to spoil the book, but let me tell you a few of the topics so that you all know how exciting it would be to read!

1) I found the story about the tribe that only has the words to denote the first five numbers fascinating—specifically for how it digresses into a discussion of a logarithmic way of understanding mathematics.

2) The discussion of gambling was so fascinating that yesterday at the food, I started discussing it with Eileen's high school friend Mac (who is a professional skateboarder). I was telling him specifically about the gambler's paradox (how a gambler might think that playing at one machine rather than another will pay out more, because that machine is hot or something) and an activity the author described in which one person flips a coin a certain number of times and writes out the order of heads and tails while another person writes out what they think that number of random coin flips might be. If one carries this out, it is always easy to tell which one was written by a human and which was the actual coin flip. Mac was so interested, he insisted that we try it ourselves, and even though I had already explained the phenomenon to him, our results still supported Bellos' book. As Bellos writes: "Because our brains are bad at understanding randomness, probability is the branch of math most riddled with paradoxes and surprises. We instinctively attribute patterns to situations, even when we know there are none." (224)

3) The pages about the normal bell curve which ended with a musing on how difficult counting and measuring actually is was mind boggling!

4) The history of numbers, explaining how abstraction originally occurred and how that sort of thought has infiltrated our language of numbers.

5) The chapter on recreational mathematics and mathematical games was delightful! And I learned a lot about the history of Sudoku.

6) The history of Pi—a must read for anyone who has ever been curious!

7) General musings on language and mathematics, which I think will be useful for me as I continue. Mathematics invents a language with which you can manipulate abstractions. With the proper language, it doesn't matter if you even understand the abstraction fully, you can still work out problems and make the language accomplish things. Then, results seem as though they were intrinsic in the language, whereas the language is really a construct and the abstraction itself is what behaves that way.

In any case, I would recommend it. Fascinating read for anyone, and written in such a way that it is enjoyable, quick, and easy. You don't even realize how much you are learning.