THE FIG TREE & THE BELL
THE FIG TREE & THE BELL Chaos, Complexity & Christianity Carlos E. Puente c 2011 Carlos E. Puente
DEDICATION To Alvaro and Elizabeth Aldama, who, at the appointed time, pointed me to the source of good dreams; to Father Rafael García Herreros, whose simple and unexpected touch instilled in me the goodness of becoming a dreamer; to Aurita de Gutiérrez, my able spiritual godmother, who confirmed that God would give me the needed fortitude to dream on; to my family and friends who have helped me throughout my attempts, especially Puentecito, Connie, Patricia, Juanqui, Illya, Mario, Xiomara, Andrés Camilo, Silvia María, Enrique, Gloria, Jorge, Fernando, Willie, Patricia, Danilo, Walter, Lucy, Rebecation, Esperanza, Alicia, Humberto, Homero, Carlos Eduardo, Carlangas, Roro, María Clara, Felipe, Germán, Duartecito, Gabriel, Marisa, Alex, Lílian, Walter, Irma, Stephen, Andra, Akin, Benito, Karen, Chucho, Kristina, Cecilio, Nelson, Marc, Bellie, Andrea, Jorge, Miguel, Huai-Hsien, Jacobo, Alberto, Alejandro, Jairo, Alberto, Aquiles, Darío, Rafael, Ignacio, Pete, Daniele, Juan, Don Pedrito, Manu, Vijay, Indira, Miguel, Fabian, Montero, Los Caballeros, Los Coequiperos, Los Primos, and the Folsom Gang, who have all nurtured my dreams, and Marta, Cristina, and Mariana, who fulfill my loveliest dream; to Saint Nathanael, seen under the fig tree, who has inspired yet another beautiful dream, this time of a baby boy, to confirm wisdom; to Saint Jude Thaddeus, my Patron Saint, who intercedes so that I may one day achieve it; and, above all, to Jesus Christ, who, by His ineffable and merciful sacrifice, repairs all dreams.
CONTENTS Preface ix I Lessons from Turbulence 1 II Lessons from Chaos 47 III Lessons from Fractal Wires 107 IV Other Lessons to Peace 155 Notes 191 Acknowledgments 215 Biblical References 221 Index 225
PREFACE This book presents a collection of reflections, gathered and refined over the past twenty years, that reveal consistent connections between Biblical writings and topics of modern science that encompass key aspects of fractal geometry, chaos theory, and complexity research. These links, springing first via symbols and metaphors from my own scientific work at the University of California, Davis, gradually clarified to assemble into an unexpected invitation to the love and peace of Jesus Christ. Before summarizing the contents of the book, I would like to mention a few facts about myself. I was born in Cartagena de Indias, in lovely Colombia, South America, and have been in the United States since 1980. After finishing undergraduate degrees in Mathematics and Civil Engineering at Universidad de los Andes in the capital city of Bogotá, I came north to pursue my graduate work at the Massachusetts Institute of Technology, the famed MIT. There, I got a couple of master s degrees, in Civil Engineering and Operations Research, and my doctorate in Hydrology, the science of water. My original plan was to return to my home country, but destiny conspired against it and I have been blessed living at beautiful Davis since 1986. So that you may better appreciate the materials before you, I ought to say that when I began my academic career, I was not much of a believer and certainly not a religious person. I was baptized by my parents as a Catholic, but my family did not practice their religion much, except for attending weddings, baptisms and funerals. Although I believed in the existence of a creator God, I
x Preface thought of Him as an unapproachable and remote being and, as such, I just went ahead with my life, like everybody else. As I came to Davis, the scientific fields of fractal geometry and chaos theory were in full bloom and those beautiful and overarching ideas had a deep impact on my approach to hydrologic research. I immersed myself into the physics and mathematics literature and, little by little, I gained understanding about the emerging field of complexity and its fascinating universality, a key trait that allowed using the same notions in seemingly disparate disciplines. By 1989, when I was a starting Assistant Professor, some beautiful ideas came to me. Rather surprisingly, with my students we discovered an unforeseen mathematical bridge between disorder and order that, although inspired by my field of science, went beyond my hydrologic expectations. As shall be explained in detail later on, we found, and in truth not searching for it, that there was a fractal mapping shaped as a convoluted but structured wire capable of transforming the ever-present spikes reflecting the violence of any turbulence into the smooth and harmonious bell curve, a signature of much calmer molecular diffusion and a universal icon of freedom and independence. These findings, providing a surprising universal antidote to disorder and a rather curious transmutation of energy dissipation into energy conduction, inspired searching for such a transformation. Despite our efforts, however, we were not able to identify it in the natural world, for violence precedes calmness and vice versa, and these two extremes hardly happen at once. Notwithstanding my inherent resistance, the ideas hinted to a topic that we scientists prefer not to talk about, and that is Love. At first, I felt shy about what I saw and I covered my face with the shame of an aspiring scientist, but, invariably, I kept repeating the key questions over and over. What can universally exchange any type of disorder into order? What can repair dissipation and death into conduction and life? The answer was love indeed and thus opened my heart to find more of it. Few weeks after the joy of the discoveries and following the sound advice of a good friend and his wife, a dear couple gratefully acknowledged in my dedication, I experienced for the first time the
Preface xi conducting flame of God. This happened in a mystical night of algorithmic conversion, forgiving and asking for forgiveness until reaching my very bottom, and then experiencing an unforgettable peace, definitely beyond my understanding, accompanied by the soothing warmth of heat conduction in my heart, that confirmed to my very core the essence of the scientific findings. 1 Soon after my unexpected epiphany and the rejoicing and support of dear friends, I started to read the Bible, which I have never considered before. As I read on, I wondered how I could have neglected such beauty, for the Word of God made lovely sense as it spoke directly to me. As time passed, and no doubt aided by the clarity brought by life s trials and tribulations that followed, I started to notice a consistent language linking the words of Holy Scripture with the symbols of modern science, especially in regards to my newfound field of complexity. As I spent my first sabbatical year in 1996 at the world-renowned Santa Fe Institute, specialized in complexity research, I decided to study Scripture in earnest trying to write down the connections I saw before me. This is how a first version of this manuscript came to be a couple of years later. As time passed since my leave, I started to share talks about the materials herein, especially in Spanish, as a way to bring attention and promote peace in the midst of the violent problems facing my beloved Colombia at the time. But, as the horrendous events of 9/11 happened, I began giving talks in English, hoping to contribute, now, to world peace. Since 2001, I have shared a class at UC Davis entitled as the attractive sub-title of this book: Chaos, Complexity, and Christianity. I have also given numerous related presentations at national and international conferences, and I have published several papers about the ideas. It is based on such accumulated experience on two languages and the supporting responses I have received throughout the years that I feel confident that the notions herein may contribute to foster inner and world peace. In keeping with the universal nature of the book, I have tried to write this work in a style that I hope shall bring enlightenment to a general audience. For this purpose, the chapter s explanations rely
xii Preface on an extensive set of graphs and contain as little mathematics as possible, leaving technical details and references in a set of notes at the end of the book. The thesis of this work is that all of us, humans with a soul, may learn from recent advances about how complexity happens in nature, so that we choose not to follow such universal mechanisms leading to violence and distress but instead seek peace and love. The book is divided into four chapters that include diverse lessons from complexity, as follows: I II III IV Lessons from Turbulence Lessons from Chaos Lessons from Fractal Wires Other Lessons to Peace The first lesson pertains to the dynamics of natural turbulence. Here, it is shown how the concept of multiplicative cascades may not only be used to represent the turbulent dissipative energies present in nature, but also our own propensity to violence and the presence of wealth inequalities in the world. Employing a rich collection of images that include as counterparts the equilibrium of uniformity and the aptly-named devil s staircases associated with fragmentation, this chapter argues that we may learn from the simple and repetitive ways of nature in order to avoid the deadly consequences of disunion. This lesson also shows, via an assortment of Scriptural citations, how the Biblical proverbs cut the mountains and fill the valleys and love one another in truth qualify the unique reconciled solution that defines peace, justice, and friendship for all, a condition that turns out to be characterized also by the geometric proverb the hypotenuse: the pathway of peace, which symbolizes the ever-straight and saintly actions of Jesus Christ. The second chapter deals with chaos theory and its implications. Here, it is summarized how the iteration of simple non-linear mappings gives rise to chains of bifurcations that define a variety of chaotic trees, as exemplified by the iconic Feigenbaum diagram, or the fig tree, in German. Relying on the universality of the
Preface xiii notions, it is explained how, in matters of peace, such ideas guide us to the Biblical proverb come down the tree, for only in the straight roots lies a common state in which we all may achieve true happiness, unity, and love. This lesson explains how these modern concepts also provide a rich symbolism consonant with Scripture that, in particular, allows us to appreciate why Jesus cursed and dried up a fruitless fig tree, and why it may be pertinent to pay attention to an ancient lesson from a fig tree, and other trees, even trees springing from modern science centuries later, for, as Jesus hints, they may represent mysterious and yet urgent precursors of upcoming cosmic events. This chapter further explains that while there is indeed a veritable escape to the root via a delightful hopscotch of purification consistent with the concept of purgatory, it is best to be prepared to avoid the also very real hellish state of utter confusion in which the chaotic dynamics wander forever in high heat. For it is shown, consonant with the first lesson, that true reconciliation may only be fulfilled by surrendering to the halo of zero, which is also the saintly Origin that represents God the Father. The third lesson explains the previously mentioned discoveries of a transformation capable of reversing disorder into order, one that takes turbulence into the bell. Here the underlying construction is explained in detail to show how a simple fractal wire, illuminated by the outcomes of cascades as found in turbulence, yields, as shadows, objects that resemble, for suitable dimensions, the typical observations found while studying a variety of complex systems, including those associated with hydrologic applications, such as rainfall sets defined over one and higher dimensions. With these Platonic notions fully defined, for they remind us, by the shadows, of Plato s famous allegory of the caveman, it is then shown how the Gaussian bell appears as a limiting universal shadow, for a host of great many illuminations, when wires fill all their available space and reach their maximum possible dimensions. This lesson then argues that the limiting bell represents our ultimate invitation to peace and harmony, especially through an ever-positive transforming wire that yields a singular bell concentrated at infinity, one that, by inverting the entropy of any illu-
xiv Preface mination, ends up inviting us to plenitude in a heavenly state of life, surely of a highest spiritual dimension in which love rules, as dissipation and death no longer operate. Connections of these redeeming ideas with God s invitation to faith and the cross are emphasized via the geometric proverb let your transformation be positive and unitive, together with other theological vistas that include even a representation of the Most Holy Trinity in the ever-positive limiting case and the appearance of the ever-beautiful ice crystals and the rosette of life s DNA as mathematical designs inside a higher-dimensional bell. The final chapter weaves yet additional symbols from other topics of complexity such as power laws and self-organized criticality, as found in nature in earthquakes, avalanches, forest fires, etc. and as generated by us humans in wealth inequalities and wars. As before, it is argued that by avoiding the complex and the violent we would achieve a superior state that leads us to God s true power via the fulfillment of the proverb make zero your own power, as reflected in our own holiness and love. This lesson also summarizes the message of the book using additional Biblical citations and further associations that include some recent connections between the notions herein and the image on the Holy Shroud of Turin. To conclude, I would like to add that I write these notions knowing very well that many times I don t fulfill what I explain here. Nevertheless, I share these ideas in the spirit of friendship, sincerely hoping that this work, which also includes some poetic musings gathered during the years, may contribute to mend our broken world. I would also like to say that I offer this work as an attempt to heed the call from former Pope John Paul II for a new evangelization. Davis, July 25, 2011 On the Feast of the Apostle Saint James