Note: I enrolled in a College Algebra class this semester as part of my revisionist education project. One of the assignments is to read a book on mathematics and write about it. Being quite busy with learning all I’m supposed to be learning right now, I haven’t time to write much on this blog, so I thought I’d post my book review here as a short-term solution. I hope to post here at greater length about my mathematical journey in a few weeks.
FLATLAND, A ROMANCE OF MANY DIMENSIONS by Edwin Abbott Abbott
Flatland, by Edwin Abbott Abbott (1838-1926), was the perfect book to start my mathematical journey, for several reasons. Abbott lived pretty much right in the middle of the Victorian age, which is the period of literature I know best. This means that while his book is mathematical in nature and seems strange and alien in its subject (at least to me), its wordiness and heavy, formal style are somehow comforting at the same time. Aside from the oddness of the subject itself (life in a two-dimensional world), some of the themes in the novella were essentially Victorian. Take, as one example, the upward mobility of shapes, going from triangles, to squares, to pentagons and hexagons as generations “improve” themselves, which reflects the Victorians’ belief in the perfectability of human nature over time, as well as the ability to move from one socioeconomic status to the next higher one. While we think of social mobility as a purely American invention, it was surely present in nineteenth-century England. One need only point to Patrick Bronte, father of the Bronte sisters, who was born in squalor in Ireland but managed to secure a scholarship to Cambridge University and become a clergyman, or to Charles Dickens, whose grandparents were servants in a rich household, to demonstrate that a Victorian might be born a square, or even a triangle, but could hope one day to have hexagonal grandsons.
In other words, while the things Abbott wrote about were unfamiliar to me as far as the two-dimensional world he created goes, many of the accompanying characterizations were not. Moreover, there were some really enjoyable surprises within the book as well. I was particularly amused by the portrayal of women as vicious lines who, through their raging fury or even simple inattention to their relative positions, could maim or destroy their more mild-mannered mates, offspring, as well as innocuous bystanders. (How any offspring was ever produced in this world, however, was never covered in Flatland. Some things, I suppose, are better left unimagined.) In addition, the power struggle between the chromatists and the opposition, the traditionalist, anti-color party, was reminiscent of all political struggles, and so quite familiar as well. In short, Flatland, while a bit difficult to read, was intriguing and creative, and I am glad I read the book to its conclusion.
To be clear, I ended up liking the book, and I give it four out of four stars, not for its plot, or for its characterization, and certainly not for its verbose and weighty style, but because it became a symbol for my own journey into the study of mathematics. As I began the course, I had to quickly relearn concepts and skills that had been buried for well nigh fifty years, beneath Shakespeare plays and Elizabethan sonnets, Victorian novels, and Romantic poetry. As soon as I had dusted off my meager mathematical skills, however, I was deluged with other, new concepts that demanded all the brainpower I had to digest them. Then, while I was busy learning these new concepts, I found I had forgotten the older ones that I should have known all along and had just re-learned. It was all very frustrating and, frankly, an embarrassing exercise in intellectual humility. To be honest, early in the semester, I had to make up my mind to stick with the course even if that meant failing it—something I’d never done in my life up to this point.
Enter Edwin Abbott Abbott with his two last names and his strange little book. Once I began reading it, I quickly came to realize that my journey as a reader and my journey as a student were similar. Look at it this way: In signing up for Math 130 (College Algebra), I had entered an unusual world, one that had rules and laws that I knew very little about. I had to immerse myself in them, barely understanding them, simply trusting that they would become clearer and more understandable as I proceeded through the course. The same was true of reading Flatland. The only way to get through this book, I’ll maintain, is to buckle up and settle back for a very strange ride. I’d say the same is true for studying College Algebra.
When, after a week or so of starting the book and concentrating on my math homework, I began to have dreams about equations, square roots, and graphing polynomials, I realized something very interesting was happening in my brain: I was changing my perception of the world. In fact, one night I dreamt that my husband, to whom I often go for help as he studied Electrical Engineering (albeit some 40 years ago), gave me an edible and a magic mushroom, both of which I ate without question and was immediately rewarded by understanding everything I needed to about math. Yet I’ll argue the dreams were not just amusing; I believe they were my brain at work, struggling to adapt to new information and new perceptions. Indeed, I take them as a sign that I was beginning, with oh-so-tiny baby steps, to see the world from a more mathematical perspective. It’s a lot like those three-dimensional pictures that you have to concentrate on not concentrating on to be able to see. It takes a bit of work to see an interesting scene rather than zig-zagging blocks and shapes, but the effort is well worth it in the end, when you are rewarded with a three-dimensional view somehow transcribed onto a flat piece of paper. I hope that the same will be true of Math 130.
Learning math, for those of us to whom math is not second nature, demands that we forge new perceptions and that we learn to see and think in totally new ways. This is easy to posit, but very hard to accomplish. I suspect it’s easier the younger one is, but no matter one’s age, it is difficult to craft new perceptive tools with which to look at a changed world. In other words, studying math is a trippy experience—we might as well admit that—and Flatland is a trippy little book, and for this reason, it turned out to be the perfect start to Math 130 for me.