Through the Eyes of Galileo's Heirs: Deciphering the Laws of Nature Through the Language of Mathematics

Abstract

When I was a graduate student at Yale, back in what seems like the Paleozoic era, one of the courses that I took was called “Statistics for Morphometrics.” It was designed for those graduate students, like me, who were planning to eventually use some assortment of measures and statistics in our budding morphology-based dissertation work. The course was taught by a very bright fellow named Ray Heimbuch, an advanced graduate student in physical anthropology who already had a reputation for his exceptional skills in these areas. His presentations were extraordinary, and took his pupils deep into the continually evolving science of how one extracts meaningful data from the geometry of form. As he became more and more granular, we grasped that he saw the world in mathematical and geometric images beyond what most of the overwhelmed and struggling students, particularly me, could envision, now or, probably ever. With each presentation, it became clearer to me that I would have to accrue his incredible abilities and mathematical “eyes” if I was to undertake the research I wished to pursue. Or, I could become his really good friend. A few years later (with my successful Dissertation completed, and many papers hatched; e.g., see Laitman et al. 1978, 1979; Laitman and Heimbuch, 1982), I was the best man at Ray’s wedding. Some weeks back as I penned this essay, I had the privilege of listening to Mike Hausman, our Professor and Chair of Orthopedics at Mount Sinai, and an internationally renown surgeon, as he taught my first-year anatomy students about the hand. I met Mike when I was his Teaching Assistant at Yale, also back in the Paleozoic, and noticed even then his extraordinary mind and special ability to see structure through mathematics and geometry. I again sat in awe in my lecture hall as this physician-surgeon-mathematician taught my class, not solely about the muscles or bones of the hand, but about the extraordinary patterns and geometric codes buried within the structure of nature’s form. My young physicians-to-be sat enraptured as he guided them to the intersection of geometric shape and regularity of form, of Fibonacci numbers and patterns appearing from feathers to the shells of a nautilis to the fingers of the hand. And he took them back to the words of insight from one of the greatest minds of all time, Galileo Galilei, and his guiding principle that the laws of nature can only be understood through the language of mathematics itself (Galilei, 1623). One of the observations that life has shown me is that some people’s minds are wired very differently from others. No great or unique insight here, but it’s what I’ve seen. In my inch of the scientific world—working on head and neck structures such as the larynx or ear—I’ve been amazed by how many of the surgeons, for example, who approach vocal folds are also extraordinary singers, or those who meticulously seek to reconstruct one’s hearing are also talented musicians. No group, however, has impressed—awed might be a better term—me more than those who see the world through mathematical equations or through the ever-morphing lenses of geometry.