The Chirp team has a passion for reading. Whether it’s a beach read or Popular Science, we love to share and chat about the stack on our nightstand. So we asked the Chirpies to select a book that has somehow informed the way they think about their work and tell us all about it. First up is our Managing Director of Quantitative Research, Leslie Hagen, to tell us all about her pick: Math Without Numbers by Milo Beckman.
Untangling the Roots of Math
Do you ever just sometimes sit around and think about infinity, what that means, and how that maybe makes you a little uncomfortable? Neither do I. So when I read the premise and promise of this book, “The only numbers in this book are page numbers,” my curiosity was piqued.
Growing up, math was not my strength. I preferred the quiet imagination of books and writing to the esoteric numbers and symbols that math class offered. If you asked 12-year-old me to voluntarily read a book about abstract math, I would have laughed in your face and put my nose back into whatever Harry Potter volume I was reading at the time. And I shudder to think what that little version of me would do if you had told me that I would be a statistician for a living.
Math Without Numbers by Milo Beckman focuses on the fundamentals of math. In some ways it provides the missing answer to the question that plagued me in school: Why the heck are we doing this? We started with counting and adding, multiplying, and then we introduced letters and smaller numbers and undefined numbers and then actual Greek letters. But why? This book shed light on many, many aspects of math I had never considered and got me closer than ever before to answering the “why.”
Fun Facts. Math Without Numbers is highly visual and most pages are peppered with pictorial examples and representations of complex concepts. There are also little vignettes throughout with bulleted lists of “fun facts” on topics like circles, polytopes, and moon and sun math.
Theoretical Modeling. The book also provides some great real-life examples of ways to model high-dimensional spaces. According to Beckman, concepts such as “personality” exist as models that are based on systems that can be mathematically defined. They are multi-dimensional, plottable, and possibly infinite. For example, when baking, each ingredient in the recipe represents its own axis, as do the time mixed, temperature, and time baked.
In this topological model, the vast majority of points represent absolutely disgusting recipes, something like a gallon of baking powder plus one egg. The art of baking can be thought of as a process of testing out different points in this space and trying to find which ones are delicious. There’s a region of this baking space that’s called “cookies” and a region called “cake” and a smaller region inside there called “pound cake.”
The Continuum. We all know that infinity is a bottomless magic hat that always has one more rabbit in it. But Beckman uses a series of compelling visual proofs to show that no matter how you add or multiply infinities together, the sum/product is always equal to infinity. But, Beckman explains, there is something bigger than infinity: the continuum. Whereas infinity is still countable, the continuum is a “continuous infinity” equal to the number of points on a line.
“The continuum is bigger than infinity in the way that infinity is bigger than one. It’s unthinkably bigger. It’s a different type of bigger. It’s so big that regular infinity doesn’t even register in comparison…no matter how far you zoom in, it never thins out-a tiny slice of line still has a continuum of points.”
Bringing Approachability to Chirp’s Quantitative Research
Math Without Numbers deftly transforms abstract and complicated ideas by giving them context and color and making them digestible. Although they tend to be treated like some level of knowledge graspable only by a few, unapproachable words like “algorithm” and “simulation” actually mean something everyone can understand.
This is what I am tasked with in our quantitative practice at Chirp. The thing I was searching for in elementary school math is what I aim to bring to my work: making the opaque more clear and making the unapproachable more approachable.