Today, I’m thankful for the power in numbers.
Since the early days of the quarantine sparked by the COVID-19 pandemic, the world has witnessed some incredibly whacky behavior. As folks were mandated to stay and work within the confines of their homes – without the support and consolation of friends, travel, and even sports (God forbid!) – we all turned to interesting, if not eclectic, activities to occupy our time. Some humans metamorphosized into pack rats, scouring to collect every roll of toilet paper, every can of Lysol, and every bottle of hand sanitizer they could find. When my work was not occupying my time, I gravitated to music, exercise, and The New York Times daily crossword puzzle. Additionally, as you can probably surmise if you’re reading this blog, I found remarkable solace in writing. My lovely wife turned to Zoom calls with her girlfriends, daily sessions on the Peloton, and the pleasures of art projects. As for the latter, she became a Renaissance painter, courtesy of the ‘Paint-by-Numbers’ kits that arrived in the mail. Once one of these kits arrived, she would spend the next few days masterfully transforming a blank white canvas into an incredible depiction of some famous Renoir painting. The satisfaction she garnered from this activity was, to say the least, immense.
Now, you might think I’m going to proceed to tease my wonderful spouse for her choice of quarantine hobby. However, since I like being married, I would never go there. More so, how could I possibly stoop so low as to question a technique that has been passed down for nearly 500 years?
Indeed, it turns out that the first master of ‘paint by numbers’ was none other than the magnificent Florentine artist, Leonardo da Vinci. In his lifetime, Leonardo was not prolific when it came to painting pictures; in fact, he is credited with creating less than 20 pieces of painted art, and many of these remained unfinished – at least in the artist’s eyes. In fact, Leonardo continued to ‘tweak’ many of his paintings until his death. Nevertheless, among his finished works, several are credited as the most famous art pieces in the history of the world. So, as many young aspiring artists flocked to serve as apprentices to the famed artist, he would challenge his students with creative assignments. He would routinely provide canvases to them that contained numbered patterns. Each number corresponded to a specific color of oil paint, and his students would then diligently work to fill in those patterns as he went off to learn the intricacies of mathematic equations, perform his various science experiments, or draft his miniature sketches. Nearly 450 years later, in 1949, a commercial artist from Detroit named Dan Robbins, who had heard about da Vinci’s approach, decided to replicate the idea as a relaxing hobby for Americans. By 1955, 20 million ‘Paint-by-Numbers’ kits were being sold annually by the original Craft Master company where Robbins worked; that is, until the Company could no longer meet the demand. Eventually, like most of these paintings, the craze of ‘Paint-by-Numbers’ faded away.
But, one thing that has never fallen out of fashion has been the power of numbers.
Today, I wanted to spend a few minutes to heap praise on another Italian visionary who realized the beauty and awe associated with these numerical digits. Not much is known about Leonardo Pisano Fibonacci, an Italian mathematician and number theorist who lived around the turn of the 13th Century. In fact, unlike the other Leonardo, of whom we have numerous self-portraits as to what he looked like, we have no photographs or drawings of Leonardo Pisano Fibonacci. What we do know about this mastermind is that, despite being born in Pisa, he spent most of his childhood and young adult life in Northern Africa, near modern-day Algeria, where he gained an ardent interest in mathematics. While there, he became readily familiar with the Hindu-Arabic numbering system, characterized by the ten symbols (0-9) that today form the global basis of mathematics. Until that time, most of Europe was still operating with what the Romans had left behind after their Empire had crumbled. However, as Fibonacci would quickly recognize, the Roman numeral system was somewhat flawed, as it did not allow for partial numbering, failed to contain zero, and often required an abacus for complex equations. So, in an effort to simplify mathematics on the European continent, Fibonacci took to authoring his magnum opus, Liber Abaci - which is translated as the ‘Book of Calculations.’ Within the book, he introduced certain key concepts of mathematics that are now being taught to millions of ‘tortured’ youth around the world. Therein, he described the intricacies of the Hindu-Arabic numbering system, including its unique capacity to have place-value decimals. He was the first to describe fractions using a bar to separate the numerator from the denominator. Even more so, he introduced the world to the square root notation. His book was a veritable ‘math cookbook’ teaching any and all about how to perform numerical calculations. Interestingly, his book was primarily intended for tradesmen so that they could more easily track profits, losses, balances on loans, and other wonderful financial aspects. In due time, the book would find its way throughout the Italian republic states, including the commercial capitals in Florence and Venice, where it became the ‘numerical bible’ for teaching bankers the art of accounting.
So, I guess you can say that Fibonacci was the first true certified public accountant. Yet, what fascinated Fibonacci about the power of mathematics had little to do with its utilitarian value in ensuring proper financial transactions. Rather, he was enthralled by the ability of numbers to recapitulate ‘life’. In his famous ‘Book of Calculations,’ he was the first to pose mathematical word problems, which has been passed down into modern times, much to the dismay of every junior high school student. The answer to his most famous problem, which posed a puzzling question about the replication of rabbits, is celebrated on this fine day as the Fibonacci Sequence. His problem went something like this: Imagine a situation where 2 rabbits, one male and one female, are placed in a confined space. Assuming this pair can beget another pair of rabbits of the 2 genders in a month’s time, how many pairs of rabbits will there at the end of a year? Well, to answer the question, you need to add the sum of the two preceding numbers: 1, 1, 2, 3, 5, 8, 13, etc. Eventually, the ratio of the numbers in that sequence approaches a ‘golden ratio’ of 1.6180339, which allows for the outline of a logarithmic spiral where in the growth factor equals the golden ratio. Interestingly, the Fibonacci Sequence defines several natural equations in ‘life’, like the curvature of the spirals of snail shells, the pattern of petals on a flowering plant, the arrangement of leaves on a plant’s stem, and even the dimensions of the Great Pyramid of Giza.
So, on this day (Nov 23, or simply put, 11/23), we fittingly celebrate Fibonacci for all he gave the world. Unfortunately, not all things in life are described by the Fibonacci Sequence. If only the secret to life could be easily explained by a simple ratio of numbers, things would be a lot easier. But, the truth is that life can be explained in pictures, and numbers can help to paint an accurate portrayal of those pictures (as we just learned from the ‘Paint-by-Numbers’ kits invented by Dan Robbins and his predecessor, Leonardo da Vinci). How appropriate then that, on this exact day in 1936, the first edition of Time’s Life magazine, wherein the news was described entirely in photographs, hit bookstands throughout the United States. Photojournalism was born on that day, and eventually millions of Americans would begin to see the world through a simple picture.
They say a picture is worth a thousand words. Fibonacci might argue it’s probably 144, which incidentally is the answer to the question he posed about the number of rabbit pairs one might have at the end of 12 months’ time.
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