Boston in Fractals

Beyond Numeracy: Ruminations of a Numbers Man is a book about math that was written in alphabetical sequence. The chapter on “Fractals” appears after “Mathematical Folklore” and just before “Functions.”

It’s not a recent book. John Allen Paulos, then and now a professor of mathematics at Temple University, published Beyond Numeracy in 1991. Still, the clarity and wit of Dr. Paulos’ writing is a timeless as the Pythagorean Theorem. (Yes, there’s a chapter about that too). 

His writing is so precise and clear that even a mathematical dimwit like me can understand fractals to at least a modest degree after reading the two chapters in which he discusses them. (The second chapter on fractals - “Human Consciousness, Its Fractal Nature” - appears later in the book, sandwiched between “Groups and Abstract Algebra” and “Humor and Mathematics”). You will find much to chew on and much to smile at in Dr. Paulos’ books.

Dr. Paulos describes fractals as “curves, surfaces or higher-dimensioned figures which have the property of maintaining their characteristic structure under magnification, more of the same sort of complexity being revealed the closer one looks at them.”

To over-simplify (you find a lot of over-simplification in my writing), you can zoom in on many things – a fern leaf, the shoreline of North America, a song, even a lengthy conversation or a relationship – and that detailed view will closely approximate what you see from a higher level. The closer you look, the more of the same you will see … only in finer detail.  As you pull back, you will see those patterns blend into a recognizable replication of that detail.

For example, a branch of a tree is likely to contain many twigs. Most trees sprout many branches. Focus on a branch or a twig and you will see the unmistakable likeness of a tree. Pull back and focus on the tree and you will see the sum of its branches and twigs.

Business travel has taken me to the Boston area roughly a dozen times a year for more than two-dozen years. Like most people who spend time in Boston, I’ve grown to understand, admire and enjoy the community’s uninhibited spirit and frankness.

The savage and heartless bombing near the finish line of the Boston Marathon five years go exposed countless stories of courage and unbearable sadness; stories of love, loyalty and inspiration; stories that – together - portray the collage of personalities and neighborhoods that comprise the Boston that we think we know.

Eight-year-old Martin Richard was the first of the three victims of the Boston Marathon bombing to be publicly identified, and, with his bright and innocent smile, was one of the first faces of the tragedy that helped fuel our outrage and our sorrow. We learned that Martin was a hockey fan when a widely-circulated picture showed him at a Boston Bruins game, beaming as the players skated in their pregame warmup in the background. The Bruins played a game two nights after the bombing. Just 13 words into the national anthem … after “so proudly” … singer Rene Rancourt lowered his microphone, and a chorus of 17,565 Bostonians joined together in a soul-stirring a cappella version of the anthem that was the first hymn of renewal for the city. (You can watch it here).

Few will ever forget Jeff Bauman … especially those of us who viewed the most horrific pictures of the bomb’s immediate aftermath. Helpless, with his legs partially blown away, he was rescued by Carlos Arredondo – “the guy in the cowboy hat” – who improvised a tourniquet, raced him in a wheelchair past the medical tent, and lifted him into an ambulance that would speed him to the care that saved the life that Arredondo helped extend. Then we learned that Arredondo carried his own wounds. In 2004, when a contingent of Marines informed him of his son’s death from sniper fire in Iraq, Arredondo erupted in volcanic grief, torching his son's van, and accidentally setting himself on fire. And then, back to Jeff Bauman. Out of surgery, still too groggy to speak, he wrote for his brother: “Bag, saw the guy, looked right at me.” And the search for the two murderers had its first promising lead.

Pierre Rouzier is a doctor for the sports teams at the University of Massachusetts. In his volunteer role at the finish line, Dr. Rouzier spent several hours treating cramps, sprains and dehydration. Like so many of his fellow heroes, he ran straight to the mayhem after the bombs blew, improvising splints and tourniquets, bringing comfort and care through the chaos. Dr. Rouzier also provided an eloquent analogy for the carnage. The 2013 NCAA Final Four basketball tournament had taken place about two weeks before the marathon. Sports fans across the country watched in horror when Louisville forward Kevin Ware landed awkwardly and suffered a gruesome open fracture of his right tibia. In the aftermath of the bombing Dr. Rouzier noted: “In a strip of sidewalk that was maybe 20 feet by 40 feet, there were probably 20 Kevin Wares.”

Pierre Rouzier also told the journalist: “I was treating limbs; I wish I was treating hearts and souls.” Oh, he was. Oh, he did. Just like Carlos Arredondo and Rene Rancourt and David Big Papi “This is our f------ city… Stay strong” Ortiz. Just like the people of Boston who rallied together, and who stand together, stronger than ever.

I thought I knew Boston. I knew I loved Boston. At street level, and from 30,000 feet, those stories from five years ago gave me a truer and deeper appreciation for unique heart of Boston and the people who make the town so strong.

Originally posted to LinkedIn on April 16, 2018