(Disponível também em português)

Do you know the Fibonacci sequence? It is a numerical series developed by Leonardo Fibonacci – also known as Leonardo of Pisa, Leonardo Pisano or Leonardo Bigollo (1170 – 1250). This sequence starts with two numbers “1”, and the next number is always the addition of the two previous ones. Thus, we have: 1, 1, 2 (= 1 + 1), 3 (= 2 + 1), 5 (= 3 + 2), 8, 13, 21, 34, 55, and so on. Interestingly, the farer these numbers deviate from the origin of the series (the two initial “1”), the more the division of a number by the preceding one approaches a constant rate of 1.618, called “Golden Number”, “Golden Ratio”, or simply “Phi” (Φ) in Science and the Arts. This figure seems to represent the proportion of everything natural that we consider “beautiful”. If you’re a fan of recurring decimals or those other absurd infinite numbers, such as “pi” (π) and “e” (natural logarithm or Euler’s number), run after the n^{th} decimal of this constant. But if you just want to figure out this question under a practical perspective – which can be revealed in a glance – roughly divide the size of the legs of that spectacular lady you know by the size of the middle section of her body, and then the size of this middle section by the length of her neck plus her head: if you always find something around 1.618, you will clearly understand what I’m talking about!

One can say: “and what does it means? Nothing!”. Really?? Let’s see: the ratio between rays of each spiral segment of a snail’s shell; the ratio between the dimensions of multiple leaves, bigger and smaller, aligned at the branch of a plant; the ratio of the growth rings diameter inside tree trunks; the division of the size of the hand carpal bones by the finger phalanges, and even each mathematical division you can sense as “beauty” in the aesthetics of that pretty lady we talked before (admittedly, it is applicable to handsome guys too …), all these attributes follow exactly the blessed Golden Ratio! Even worse: do you remember that piece of art you love? That one you saw in a museum, and did not know exactly the reason why it has thrilled you that much? Just check it out and you’ll see that this ratio also applies. And the artist knew it!! If he was really good, he did that on purpose. Amazing, isn’t it?

Interesting, in a symbolic concept, is that these numbers also represent important milestones in our lives. Don’t you believe me, right? You probably think that, after getting old, I am converting myself into a mystical delusionary. Then look, because this is the point I was intending to talk about…

Let’s start with this: from 0 to 1 year old, our biggest learning is about to survive. Don’t you agree? Biologically, this is the first challenge of babies. When we reach 1-year-old age, we have the rudiments of speech and mobility. By the Nature Law, not having this should be lethal. The 2-year-old moment marks the upright locomotion (even running!). Amazing what this had represented (and, incredibly, still represents), beside the opposable thumb, for the human supremacy among species… 3 years old, and we have just installed in our head the toolbox that will allow us to jump into the symbolic thought. Neurons completed their myelination (i.e., you won’t stick ice-cream on your forehead anymore!). We have started to make projections of our three-dimensional world into the two dimensions of a paper. 5-years-old phase paves the way for cognition. At that stage, we ask “why” for everything, and we start to use the acquired knowledge to argue against our “teachers” so far… This is time to let Dad and Mom down, with those embarrassing questions and comments! Do you disagree?… Between 5 and 8 years old, we develop capabilities that will allow us to dominate writing and numbers, which opens the newest (and most important) window to the symbolic thought. 8 to 13 years old – plenty childhood – this is the fundamental period to forge our character. To smoke or not; to steal or not; and, of course, to lye or not… The upper age limit of this range -13 years old – defines (almost formally) our entry in the conflicts and delusions of adolescence. Bar mitzvah (and I am not Jewish…). Next stop: 21 years old! At this point we reach our legal majority. Since 13, we were just teenager kids, full of contradictions, melodramas and new experiences. From 21 to 34, we start and consolidate our professional lives. Ready-set-go: at 34 (after the famous crisis of 29), we already know what we’ll be when we grow up… From 34 to 55, we intensely live our mature phase – building things, destroying things (and, unfortunately, destroying people too…), giving birth and raising children, enriching or impoverishing… In the ending years of this tenth Fibonacci spiral (really, this is the cycle nr. 10; you can count the squares in the chart!), we clearly and consciously can see the glimpse of the next (and probably the last) cycle. Remember: the upper age limit for the next step, considering the Fibonacci sequence of life, would sum long 89 years… My father and his father died both at 78. Get out there is still for few people – probably and genetically, not for me…

I completed this April my tenth Fibonacci cycle. I’m aging 55. A tip: over the last 10 years, I realized that I am not “middle-aged” anymore: except for three old ladies – one in the inner Japan, one in Ukraine and the last one in Greece –, beside that pipe-smoking little lady from Minas Gerais State, NOBODY lives for 110 years! It is true that I am still trying to unravel the secret of that pork-eater Minas’ Grandma, annoyingly low cholesterol levels, almost 120 years-old (if I ‘m lucky, I’ll find out…).

The fact is that probabilities point out that this would be my last Fibonacci cycle. Like the previous ones, this will also be intensely lived. Today, I am not working on what I have always done well. I became a consultant (i.e., I put my experience – euphemistic word for old advanced age – for sale, with good acceptance so far…). I got back to the Academy seats in a Master Degree course (no matter the age, just keep learning!). If life smiles at me during this new cycle, I will be gifted with grandchildren (preferably granddaughters: I would love a little girl calling me “Grandpa”…). As a good friend of mine used to say: “if sometime I say I’m ready, please cut the ribbons, inaugurate myself, and put down the coffin!”. I have no idea what tomorrow reserves to me. Fact is that this is my last Fibonacci sequence. And I’ll enjoy it the most, for sure!

Therefore, HAPPY NEW FIBONACCI CYCLE! For me, of course… And for you too. Even if you are not in a Fibonacci “age limit”. Happy cycle to you and to those who believe that life only ends at the last gasp. I just need to draw your attention to one last important point: after the 11^{th} cycle, which begins at 55 and ends at age 89, the next is supposed to end at 144. Even with a lot of optimism, I think we will not make it! Enjoy your life, as I’ll surely enjoy mine. Laugh a lot. Be as you like. Do what gives you pleasure and joy. And do not dismiss any chance of being happy! This is truly sustainable. This is the only thing that really worth.