Overview
This page includes links to a few papers and talks that explain how modern research on natural complexity, through its detailed study of order and disorder, provides a suitable framework for visualizing the dynamics of mankind's actions, from which an invitation to peace and love may be drawn, as explained in the seminar class Chaos, Complexity & Christianity.
While the papers appeared in journals and conference proceedings: E:CO: Emergence: Complexity and Organization, Omega: Indian Journal for Science and Religion, Quaerentibus: Teología y Ciencias (in Spanish), and Events, the talks were given at various venues worldwide.
E:CO papers
Paper 1. Lessons from complexity: The hypotenuse the pathway of peace
This work explains how recent universal results pertaining to multiplicative cascades and fully developed turbulence entice all of us, in a logical way, to seek peace in a condition typified by the hypotenuse of a right-angled triangle.
Paper 2. More lessons from complexity: The origin the root of peace
This work explains how recent universal results pertaining to the transition from order to chaos via a cascade of bifurcations point us to a serene state, symbolized by the convergence to the origin in the root of a Feigenbaum's tree, in which we all may achieve peace.
Paper 3. Yet more lessons from complexity: Unity the key of peace
This work explains how recent universal results pertaining to power-laws, self-organized criticality and space-filling transformations provide additional and pertinent reminders that point us to unity as an essential element for us to achieve peace.
Omega papers
Paper 1. On the Nature of Equilibrium
Searching for equilibrium and its implied contentment is one of the most instinctive and fundamental tasks we human beings perform in our lives. This is particularly difficult in this day and age when the "turbulent forces" of modernity induce a fast pace of life that hinders our ability to be fully attentive to one another and to ourselves. During the past few decades a host of ideas have been established in order to study natural complexity, and in particular the one produced by turbulence. This work explains how such modern notions help us visualize the essential options we all face regarding equilibrium and shows how such ideas point us to one and only one serene state in which we all may achieve real peace. It is argued, citing a variety of Biblical passages, that such a desired condition may be approached via the dynamic practice of humility, repentance and love, in a manner that is epitomized by the teachings of Jesus Christ.
Paper 2. Faith Lessons from Chaotic Fig Trees
Searching for order and its implied harmony is one of the most pressing tasks we humans attempt during our lives. This quest is particularly difficult when the "evil" of "chaotic forces" propels us into restless and often helpless states whose intrinsic disorder hampers our ability to find our way to peace. During the past few decades a host of ideas have been established in order to study natural complexity, including the identification of pathways that progressively degrade "order" into the specific disorder of "chaos" and that define a host of chaotic trees, as epitomized by the iconic Feigenbaum tree, or "fig tree" in German. This work explains how such notions help us visualize the essential options we all face regarding order and disorder and shows how the ideas point us to the straight roots of such trees as the only common ground (i.e., "under the fig tree") where we all may achieve true order and peace. It is argued, citing a host of Biblical passages, that the modern concepts provide a rich symbolism consistent with ancient Scripture that, in particular, allows us to further appreciate, in a strikingly coincidental fashion, why Jesus may have, seemingly out of character, cursed and withered a fruitless fig tree as he rebuked the wind (evil in of itself in both instances) and why he may have asked us to learn a lesson from a fig tree and other trees (even from those chaotic ones budding in science twenty centuries later) as a mysterious and urgent precursor to his second coming. The implications of the notions regarding our need to be always watchful, including our prescribed conversion by coming down our own "fig trees," are emphasized.
Paper 3. On the Unitive Art of the Holy Trinity
The belief that God is made of three distinct persons: the Father, the Son and the Holy Spirit, is a fundamental doctrine in Christianity. This article introduces a mathematical construction having three united components that, in a special limiting case, helps us visualize key attributes of the Blessed Trinity: the Father in heaven via a loving and light-conducting bell curve concentrated at infinity, the Son in a uniform and serene histogram that satisfies the adagium "cut the mountains and fill the valleys," and the Holy Spirit in a space-filling transformation built by mid-point additions of unity that joins the Father and the Son and proceeds from both of them. This work explains how the scientific construct and contrary notions regarding power laws in natural and man-made complexity provides a general framework that allows us to appreciate the essential options we all face in our lives regarding order and disorder and shows how the ideas invite us to find order, peace and love, but only in the artful limit. The specific connections of the ideas with a variety of Biblical citations are emphasized.
Quaerentibus papers
Paper 1. Una Clase Inusual sobre Ciencia y Fe en una Universidad Secular: Caos, Complejidad y Cristiandad
Since 2001 I have been sharing at the University of California, Davis an original seminary entitled “Chaos, Complexity and Christianity”, which is available to all students. Going beyond the conventional theme included in the dialog between science and religion, this class intends to show how recent investigations about complexity, both natural and that induced my mankind, provide sound guidelines that invite to the love of Jesus Christ as the only solution to our problems and dreams, as He Himself affirms it. In this presentation, I summarize the specific materials, Scientific-Biblical, of the nine encounters that make up the class, cite some of the comments students have made throughout the years, and report on the consequences inherited by accepting the challenge of trying to illustrate the faith in a domain eminently secular. Starting in 1997, and recently once a year at Ateneo Pontificio Regina Apostolorum in Rome, I have had the opportunity of sharing lectures related to the class, which, in concordance with the festivities in 2016, were named “From Modern Science to God’s Mercy”. Here I also explain the content of such talks and relate my efforts of using them in diverse forums, ecclesiastical or not, in various countries.
Paper 2. De la Ciencia de la Complejidad al Amor de Jesús
The last decades have witnessed the development of a collection of ideas aimed at understanding and predicting the fragmentation induced by natural complexity. Among them there are the use of: (a) multiplicative cascades to model the turbulence caused by the power of the air; (b) chains of bifurcations to describe the orderly transitions and the eventual chaos produced by progressively heating a fluid; (c) processes having critical states to represent the ubiquitous power-laws present in natural violence; and (d) fractal transformations to reproduce the complex geometries seen in nature without invoking the concept of chance. This work reveals how such notions give rise to an impartial and coherent framework that allows us to visualize the dynamics and consequences of the divisive traits ever-present in humanity---including the essential options of order and disorder, love and indifference, and peace and anxiety that we all confront in our lives. Using such a referential framework and emphasizing the wickedness of the repetitively disintegrated and complex, the work explains how the ideas define a consistent bridge towards the redeeming love of Jesus Christ, and only towards his, in which “simplicity” specify the unique proper and saintly way for all, one that can only be achieved in “the root,” in what is “straight,” in “the origin,” and in “the positive,” satisfying, in the same spirit of the calls to conversion by John the Baptist, various geometric adages such as “fill the valleys and cut the mountains,” “come down the chaotic tree,” “may zero be your power,” and “let your transformation be fully positive,” which reflect the vital love to God and one another. Once the bridge between science and the Catholic faith is established, this work explains the relation that such ideas have with some symbols recently discovered in the Holy Shroud of Turin.
Papers at Conferences
Paper 1. From dissipation to conduction and from darkness to light. At FIAT LUX International Conference, Roma, June 2015
Mathematical transformations capable of transmuting spiky distributions, including those produced by natural turbulence, into smooth Gaussian densities, associated with calmness via Fourier law, are introduced. It is shown that such functions may be built in rather simple ways and that their graphs fill-up two-dimensional space in such a way that any small portion of such transformations yields, universally, Gaussian bells. It is explained how these limiting space-filling transformations represent unexpected remedies for the prescribed dissipation of turbulence into a desired condition of serenity based on heat conduction, and how one, based on ever-positive additions, defines a veritable antidote to disorder that ends up exchanging darkness into precious light, as its associated bell concentrates at infinity, inspiring us to exclaim “Where is o death your victory? Where is o death your sting?” (1 Cor 15:55). Surprisingly, it is also elucidated how the ever-positive case helps us visualize key attributes of the Most Holy Trinity and how such a scientific construct invites us to find order, peace and love, but only in the artful and spiritual limit, in which the curious story of St. Augustine and the child at the beach are harmonized
Paper 2. Lecciones a partir del caos: conversiones ecológicas y sobre todo espirituales. At X Congreso Latinoamericano de Ciencia y Religión, Córdoba, Argentina, September 2021
La degradación del medio ambiente, inducida por acciones humanas más allá de causas naturales, requiere de la definición de prácticas que lleven a la preservación de nuestra “casa común”. Sin duda, esto conlleva dejarles a las siguientes generaciones un planeta ordenado y no uno caracterizado por un caos generalizado. Empleando nociones desarrolladas precisamente por medio de la teoría del caos, este trabajo reitera la necesidad de una conversión ecológica y muestra cómo de esas mismas ideas surge a su vez un llamado a nuestra conversión espiritual. Utilizando un ícono fundamental de la teoría, el árbol de Feigenbaum (o la higuera en alemán), se explica el por qué “bajarnos del árbol” y residir en su raíz santa es nuestra mejor opción. Esto resulta ser así pues dicho estado es el único que evita maldiciones certeras tal y como le sucedió a una higuera real, que aparentemente sin culpa, fue secada por quien no desea nuestra perdición sino nuestra conversión. Enfatizando la universalidad de los resultados científicos, este artículo también esboza una posible relación entre las nociones caóticas (ecológicas o no) y el llamado siempre urgente y misericordioso que nos impele a estar preparados para una visitación majestuosa, una tanto anhelada como definitiva, así parezca improbable desde el ámbito de la ciencia.
Talks
Two posters presented at the 2008 National Faculty Leadership Conference may be downloaded here: one and two
Two talks related to the posters in the previous item are here: one and two
A series of talks delivered in Rome in 2013 under the title The key role of science in the new evangelization is here.
Another series of talks shared in Rome in 2016 to celebrate the Jubilee of Mercy, is here.
A lecture (in Spanish) aimed at dreaming true peace in Colombia and in the whole world is here.
A Tribute
A text and poem honoring David Breaux and Karim Abou Najm, who died tragically at Davis on April 2023, is here.
Contact Information
Carlos is available to share presentations about his work on peace. Contact him at cepuente@ucdavis.edu.
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