Untangling Complex Systems, page 3
13.3.1.3
DNA and RNA Computing ......................................464
13.3.1.4
Evolutionary Computing .......................................... 467
13.3.1.5
Artificial Immune Systems ......................................468
13.3.1.6
Cellular Automata ....................................................469
13.3.1.7
Artificial Intelligence, Fuzzy Logic, and Robots ..... 471
13.3.1.8
Protein Computing ................................................... 476
13.3.1.9
Amorphous Computing ............................................ 477
13.3.1.10 Building Models of Complex Systems: ODEs,
Boolean Networks, and Fuzzy Cognitive Maps ....... 477
13.3.1.11 Agent-Based Modeling ............................................. 479
13.3.2 Computing by Exploiting the Physicochemical Laws .................. 482
13.3.2.1 Thermodynamics ...................................................... 482
13.3.2.2
Classical Physics.......................................................484
13.3.2.3
Computing with Subatomic Particles, Atoms,
and Molecules...........................................................486
13.3.2.4
The “Ultimate Laptop” ............................................. 491
13.4
Last Conclusive Thoughts and Perspectives ............................................. 491
13.5
Last Motivating Sentences Pronounced by “Important People” ............... 493
13.6
Key Questions ........................................................................................... 494
13.7
Key Words ................................................................................................. 494
13.8
Hints for Further Reading ......................................................................... 495
13.9 Exercises .................................................................................................... 495
13.10
Solutions of the Exercises ......................................................................... 497
Appendix A: Numerical Solutions of Differential Equations ..................................................503
Appendix B: The Maximum Entropy Method ..........................................................................507
Appendix C: Fourier Transform of Waveforms ....................................................................... 513
Appendix D: Errors and Uncertainties in Laboratory Experiments ..................................... 517
Appendix E: Errors in Numerical Computation ...................................................................... 531
References ..................................................................................................................................... 535
Index .............................................................................................................................................. 559
Preface
SCOPE AND GENESIS
Complex Systems are natural systems that science is unable to describe exhaustively. Examples
of Complex Systems are both unicellular and multicellular living beings; human brains; human
immune systems; ecosystems; human societies; the global economy; the climate and geology of our
planet. Science cannot predict the behavior of such systems, especially in the long term. Why is it
so important to study Complex Systems? Because humanity must tackle compelling challenges that
affect Complex Systems. For example, we need to predict catastrophic events, such as earthquakes
and volcanic eruptions, to avoid many deaths. We struggle to protect our ecosystems and the envi-
ronment from climate change and the risk of shrinking biodiversity. We need to find innovative
solutions to guarantee a worldwide sustainable economic growth, primarily by focusing on the
energy issue. We also need to find creative solutions to ensure stability and justice in our societies.
Finally, there are still incurable diseases that must be defeated. I have made a list of what I like to
call “Natural Complexity Challenges.” To try to win the “Natural Complexity Challenges,” we need
to understand Complex Systems deeply. But this is not an easy task because Complex Systems are
intertwined networks, working in out-of-equilibrium conditions, which exhibit emergent properties,
such as self-organization phenomena and chaotic behaviors in time and space. I decided to con-
tribute to the untangling of Complex Systems by writing this book. This book is an account of an
amazing scientific and intellectual journey I made to understand Natural Complexity. I have under-
taken my trip, equipped with the fundamental principles of physical chemistry, and in particular,
the Second Law of Thermodynamics that describes the spontaneous evolution of our universe. Two
central questions have guided me:
1. If the Second Law of Thermodynamics is true, how is it possible to observe the spontane-
ous emergence of order in time and space? Is it possible to violate the Second Law?
2. What are the common features of Complex Systems? When and how do the emergent
properties emerge?
To find answers to my questions, I have gone on a marvelous interdisciplinary journey. I dealt with
many disciplines; particularly, chemistry, biology, physics, economy, and philosophy. Chapter 1
presents an excursus on the evolution of the scientific knowledge and its mutual fruitful relationship
with technology. Chapter 2 is a thorough analysis of the Second Law of Thermodynamics and to
understand if its violation is feasible. Chapters 3 and 4 present the principles of Non-Equilibrium Thermodynamics. Then, the theory of Non-Linear Dynamics is introduced by the description of
the emergence of the temporal order in ecosystems (Chapter 5), economy (Chapter 6), within a living being (Chapter 7), and in a chemical laboratory (Chapter 8). Chapter 9 describes the emergence of spatial order in chemistry, along with examples regarding biology, physics, and geology. Then,
Chapter 10 introduces the concept of Chaos in time, whereas Chapter 11 covers Chaos in space by presenting fractals. Chapter 12 offers the typical features of Complex Systems and outlines the link between Natural Complexity and Computational Complexity. Finally, Chapter 13 proposes strategies to try to untangle Complex Systems and win the Complexity Challenges.
PURPOSES
This book has four principal objectives and one hope. First, it traces a new interdisciplinary didactic path
in Chemistry. This book is useful for graduate students in Chemistry, who want to learn the principles
and theories regarding Non-Equilibrium Thermodynamics, Non-Linear Dynamics, and Complexity.
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Preface
Second, the contents I present should boost the spread of interdisciplinary courses in Complex
Systems to universities around the world. Teachers of Complexity can choose this textbook when
they want to highlight the relevant contribution of chemistry.
Third, this book contributes to the training of a new generation of PhD students and researchers
who want to comprehend Complex Systems and win the Complexity Challenges.
Fourth, I want to stimulate public and private funding agencies to sustain interdisciplinary
projects on Complex Systems.
This book terminates with a question: “Can we formulate a new scientific theory for under-
standing and predicting the behavior of Complex Systems?” I hope that someone, also inspired
by this text, will contribute to the formulation of that scientific theory that we have been waiting
for many years.
ADVICE AND NOTES FOR STUDENTS AND INSTRUCTORS
In every chapter, after the presentation of the theory, I offer a list of key questions and key words
that want to help students in fixing the most important concepts that have been presented. Teachers
can exploit these lists to check the level of preparation of their students. Then, I suggest books and
papers for deepening the knowledge of the proposed content. All the chapters, except the first, offer
exercises with solutions. These exercises are useful tools to test the degree of understanding of the
theory and the subjects presented in each chapter. My suggestion is that students solve all the exer-
cises by themselves. Some of the exercises require the numerical solution of differential equations.
The solutions that I propose have been obtained by using MATLAB software. Students can use any
other software they are familiar with.
LIMITATIONS AND APOLOGIES
Regarding the references, I apologize if the reader is upset by any omissions as I did not want the
chapters to be exhaustive reviews of all the work done on that particular subject. But rather, some
representative and didactic examples are proposed. No implication is intended towards the impor-
tance of works cited relative to works not cited. I apologize in advance for those cases where my
selection is faulty. The subject of Complexity is amazingly rich and polyhedral, and apologies are
offered to those readers whose favorite topics are omitted. Of course, this book is the report of a
wonderful personal journey, and it could be enriched by additional content.
Regarding the Figures, I decided to print them in black and white to maintain a low manufacturing
price of the book and make it more affordable.
Whoever wants to suggest me either improvements or constructive corrections or share their
experience in using this textbook, please send me an e-mail to the following address: pierluigigen-
tili@gmail.com.
MATLAB® is a registered trademark of The MathWorks, Inc. For product information, please
contact:
The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760-2098 USA
Tel: 508 647 7000
Fax: 508-647-7001
E-mail: info@mathworks.com
Web: www.mathworks.com
Acknowledgments
First, I want to acknowledge Dr. Lance Wobus, who in Summer 2011, after reading one of my
papers related to the field of Natural Computing, sent an e-mail proposing that I write a book on
that topic. Despite being aware of the commitment, I accepted his invitation after extending the
subject of the book to the content of my teaching activity that regards Complex Systems and the role
that Natural Computing can play in the comprehension of Complexity. I am also thankful to Senior
Editor Barbara (Glunn) Knott and Editorial Assistant Danielle Zarfati, who trusted in my project
and helped me to finalize the publication of this book.
I am grateful all my school teachers and professors at the Chemistry Department of Perugia
University, who, along with my family members and friends, contributed to my knowledge and my
forma mentis. In particular, I like to mention Prof. Giuseppe Cardaci, who taught me the principles
of Non-Equilibrium Thermodynamics and made me passionate about that field. I am also grateful
to my tutors of degree and PhD thesis in Chemistry, Prof. Giovanna Favaro, Prof. Gian Gaetano
Aloisi, Prof. Aldo Romani and Prof. Massimo Olivucci, who helped me to grow as a researcher. The
mind of the researcher, including his knowledge, his skills, and his questions, is like a mosaic whose
pieces are made from the books and papers he reads, the lectures he attends, and the colleagues he
meets and works with. In particular, I acknowledge all my direct collaborators, who are too numer-
ous to be listed here. Among them, I want to mention those who helped me to understand Complex
Systems and hosted me in their groups. They are Prof. Irving R. Epstein, Prof. Milos Dolnik,
Prof. Vladimir Vanag (now working at Immanuel Kant Baltic Federal University) of the Brandeis
University (MA, USA), Prof. Jean-Claude Micheau of the Université Paul Sabatier-Toulouse III
(France), Prof. Peter Bentley of the University College of London (UK), and Prof. Peter Tompa
of the Vrije University in Brussels (Belgium). Moreover, I want to mention those who noticeably
helped me to develop my research on Natural Computing, who are Prof. Mark B. Heron, Prof.
Raimondo Germani, and Prof. Hiroshi Gotoda. I am also grateful to the Santa Fe Institute for pro-
viding exciting courses and other educational materials related to the Complex Systems science on
the “Complexity Explorer” website. I also want to acknowledge Dr. Veronica Dodero, Dr. Federico
Rossi, Dr. Marcello Budroni, Dr. Christophe Coudret and Dr. Otto Hadač for fruitful discussions
on some of the themes of this book and for suggesting me significant references. I thank Mr. Danilo
Pannacci and Prof. Cristiano Zuccaccia for their sharp questions about some of the subjects of
this book, and for the lively discussions that we had during our shared lunchtimes. I also want to
acknowledge my past students because the lectures that I gave them and the questions they asked
me have been very beneficial for writing this manuscript. I thank Mr. Andrea Nicoziani who helped
me to build a Hele-Shaw cell used for an experiment proposed in Chapter 11. I thank Mr. Antonio
Maria Cinti for bringing me a sample of malachite and one of agate with traces of periodic precipi-
tations, whose pictures are shown in Chapter 9. I thank Mr. Nicomede Pelliccia for helping me in
preparing some pictures. Then, I want to thank all my family, specifically, my parents, who have
never stopped encouraging me in my studies and research. My father helped me also to understand
the principles of the economy. Finally, I am grateful to God for the gift of life and for infusing me
the passion of scrutinizing His Creation. The more I study nature, the more I find it is breathtaking
and amazing. I thank God for guiding me in my research and for all the keen scientists who allowed
me to meet, so far.
xvii
About the Author
Pier Luigi Gentili is a PhD in Chemistry. His research and teaching activities are focused on
Complex Systems. He is trusting in Natural Computing as an effective strategy to understand
Complex Systems and face the Computational Complexity Challenges. In particular, he is developing
the innovative Chemical Artificial Intelligence. He has several collaborations and work experience
in many laboratories such as, the “Photochemistry and Photophysics Group” of the University of
Perugia (Italy); the “Nonlinear Dynamics Group” of the Brandeis University (USA); the “European
Laboratory of Nonlinear Spectroscopy” in Florence (Italy); the “Center for Photochemical Sciences”
of the Bowling Green State University (USA); the “Laboratory of Computational Chemistry and
Photochemistry” of the University of Siena (Italy).
ORCID: 0000-0003-1092-9190
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Introduction
1
A life without research is not worthy of being lived.
Socrates (470–399 BC)
The most beautiful thing we can experience is the Mysterious. It is the source of all true art
and science.
Albert Einstein (1879–1955 AD)
1.1 THE NEVER-ENDING JOURNEY TO DISCOVERING
THE SECRETS OF NATURE
One of the most precious gifts of our life is the possibility of appreciating the beauty of nature. For
example, the bright colors and the peaceful silence of a breathtaking sunset admired on top of a
mountain; the variety of perfumes, colors, and shapes of flowers; the magnificence of grand trees
(see Figure 1.1); the astonishing vastness of a starry sky. These are just a few examples of a countless number of marvels we can enjoy.
We can scrutinize the beauty of nature simply by using our senses of sight, hearing, smell,
taste, and touch. In fact, our senses are “endo-somatic tools” we use to collect information about
the outside world. The information collected by the sensory cells is transduced in electrochemical
signals that are sent to the brain. Within our brain, such information satisfies our unquenchable
“perceptual curiosity” of always experiencing something completely new, and “diversive curios-
ity” that refers to the relentless desire we must explore and seek new stimulation to avoid boredom
(Livio 2017). However, we also have “epistemic curiosity” to satisfy. It represents our “appetite for
knowledge.” Epistemic curiosity spurs us to get acquainted with natural wonders and understand
how they originated.
I think that everybody will agree with me if I say that the beauty of nature resides in its harmony,
organization, functionality, efficiency, variety, complexity.... In other words, the beauty of nature derives from the presence of an inherent logos ( λóγος), i.e., a rational logic based on laws and
principles that are universal in space and time. The natural marvels have drawn the attention and
ignited the curiosities of many men and women in the course of history. This attraction is still active,
and it will never cease until the end of life on earth. People who dedicated their lives, entirely or
partly, to the study of nature, can be called “Philo-physicists,” from the Greek “φίλος- φύσις,” which
