Designing and Teaching a Novel Interdisciplinary Course on Complex

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Designing and Teaching a Novel Interdisciplinary Course on Complex Systems To Prepare New Generations To Address 21stCentury Challenges Pier Luigi Gentili* Department of Chemistry, Biology, and Biotechnology, University of Perugia, 06123 Perugia, Italy

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S Supporting Information *

ABSTRACT: The challenges that humanity is facing spur universities to reorganize chemistry education. A contribution to the project of reimagining chemistry education is a novel interdisciplinary course that presents the properties of complex systems through the theories of out-of-equilibrium thermodynamics, nonlinear dynamics, and natural computing. This course introduces upper-division undergraduate, graduate, or Ph.D. students to systems thinking and interdisciplinary knowledge about complex systems, which are two relevant assets for tackling the challenges of the 21st century.

KEYWORDS: Upper-Division Undergraduate, Graduate Education/Research, Interdisciplinary/Multidisciplinary, Problem Solving/Decision Making, Professional Development, Applications of Chemistry, Systems Thinking.

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INTRODUCTION The fate of Earth is in the hands of humanity, now more than ever. Scientific knowledge and technologies confer humans the power of perturbing the fragile stability of climate, ecosystems, and societies, and the delicate psychophysical well-being of every human. The job of today’s young people will be to get humanity through the coming period of peril and opportunity. Because today’s young people will collectively determine whether civilization survives or not, the goal of the current educators is to give them the foundations for making smart and wise choices. The challenges of the 21st century1−3 are global because they involve everyone on Earth; they require interdisciplinary approaches and systemic strategies to be tackled. Chemists along with scientists of other disciplines must contribute to guarantee sustainable economic growth worldwide. In other words, the continued development of human societies must be integrated with the maintenance of the earth system in a resilient and accommodating state.4 Chemists can significantly help by following the guidelines of green chemistry.5 Economies must transform from linear to circular, turning goods that are at the end of their service life into resources for others, minimizing waste.6 Natural resources must not be exhausted. The fragile stability of natural ecosystems, which is primarily based on their biodiversity, must be protected. Manufacturing processes and human activities must not affect the global climate and the geology of Earth. Political choices, made both locally and globally, should try to eradicate poverty from the world and ensure social justice. Incurable diseases, such as cancer, diabetes, HIV, © XXXX American Chemical Society and Division of Chemical Education, Inc.

and so forth, must be defeated. We must cope with antibiotic resistance. Moreover, scientists of any discipline must cooperate with legislators and possibly with philosophers and theologians to find shared solutions to bioethical issues. For instance, technology will enable humans to live longer, learn more, and gain the ability to connect to nanotechnological objects in or on our skulls and to supercomputers or to connect our brains to external devices. This so-called transhumanism will be within reach.1 Transhumanism is highly controversial and is raising major ethical arguments. These bioethical arguments need the contributions of all the disciplines, including chemistry, to be properly faced. In reality, every 21st-century challenge requires interdisciplinary efforts because they regard complex systems.7 Examples of complex systems include: • Unicellular and multicellular living beings • Human brains • Human immune systems • Ecosystems • Human societies • The macroeconomy • The climate and the geology of our planet Special Issue: Reimagining Chemistry Education: Systems Thinking, and Green and Sustainable Chemistry Received: January 11, 2019 Revised: July 1, 2019

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DOI: 10.1021/acs.jchemed.9b00027 J. Chem. Educ. XXXX, XXX, XXX−XXX

Journal of Chemical Education

Commentary

It is fair to declare that science is unable to describe complex systems exhaustively. One purpose of the course that is proposed here is to progressively explain why. First, it is instructive to show that scientific research is a marvelous, never-ending journey to discovering the secrets of nature.

It is fundamental that new generations are acquainted with the features of complex systems. Chemistry education must be reimagined if we want new generations of chemists to be ready to face the challenges of the 21st century effectively. The urgency of reorganizing chemical education is evidenced by some recent initiatives. In May 2017, the International Union of Pure and Applied Chemistry (IUPAC) started a new project for infusing systems thinking and sustainability considerations into the formal teaching of chemistry.8 In the last two years, some relevant publications spur chemists to transform their forma mentis to address challenges that require an interdisciplinary and systemic vision of our world.9−12 The Journal of Chemical Education has dedicated a special issue to the theme of reimagining chemistry education through spreading systems thinking approaches throughout educational programs.13 In my view, it is urgent that we give students in chemistry the opportunity to learn the theories and tools suitable to deal with complex systems. In this essay, I propose a novel interdisciplinary course on complex systems for upper-division undergraduate, graduate, Ph.D. students. In the rest of this work, I describe how to organize such a course, its possible contents, how it addresses chemistry learning objectives, and which additional skills and understandings the students in chemistry gain by attending it, with respect to traditional courses. My goal is to spark discussion and reflection among chemists about the importance of this novel interdisciplinary course on complex systems and how to implement it.

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SCIENTIFIC RESEARCH AS A NEVER-ENDING JOURNEY The journey to discovering the secrets of nature can be argued to have begun with the appearance of humans on Earth and is still in progress. So far, it has been punctuated by two “revolutionary” intellectual events:7 (i) the birth of philosophy in the ancient Greek colonies during the sixth century BC and (ii) the formulation and application of the experimental method for investigating natural phenomena. These two major intellectual events have induced profound and fundamental changes in the human methodology of gaining insights about nature. Philosophers formulate foundational questions about nature and the origin of everything, and they look for answers through a rigorous etiological rationalism based on data collected mainly by human senses. On the other hand, the experimental method is based on experiments that use instruments to gain objective, reproducible, and universally valid responses from nature. Experiments are dialogues between scientists and nature. The phenomenon that is under scrutiny is “distilled” from the rest, to make its analysis easier. Information collected in the experiments is quantitative, and the theories are expressed through mathematical formulas. Scientists constantly verify whether their theories and models are plausible or must be perfected. Students need to see that science is always evolving. The evolution of scientific knowledge is strongly correlated with technological development.7 The technological know-how of a certain age determines which kinds of tools and facilities are available to observe the natural phenomena. The sensitivity and resolution of the available instruments define the boundaries of the “observable universe”. In the 17th, 18th, and 19th centuries, scientists faced “simple problems”, involving two or a few more variables. Between the end of the 19th and the beginning of the 20th century, scientists also faced problems of so-called “disorganized complexity”, involving billions of variables.14 They tried to interpret the irreversibility of macroscopic phenomena by focusing their attention on the behavior of the huge number of particles underpinning every macroscopic object. They succeeded in their analysis of “disorganized complexity” by using probability theory and statistical mechanics. Since the second half of the 20th century, scientists have turned their attention to problems of “organized complexity”. The driving question has been: “If the second law of thermodynamics is true, how is it possible that certain systems spontaneously evolve toward more ordered states?” The answer must be found by studying complex systems. In my view, the core concepts that must be provided are

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GIVING RESPONSIBILITY TO YOUNGER GENERATIONS In order to face the compelling challenges of this century effectively, the involvement of everyone, especially young people, is needed. Table 1 reports a list of some principal 21stTable 1. Principal 21st-Century Challenges, the Complex Systems They Involve, and the Chemistry Disciplines Required to Face These Challenges Challenges

Complex Systems

Global warming Geological catastrophic eventsa Sustainable growth and circular economy Incurable diseases and antibiotic resistance

Climate Geology of Earth

Atmospheric chemistry Geochemistry

Ecosystems and macroeconomy

Green and sustainable chemistry

Living beings and the human bodyb Living beings and societies

Biochemistry, pharmaceutical chemistry, and medicinal chemistry Biochemistry and nanochemistryc

Bioethical issues

Chemistry Disciplines

a

Examples are earthquakes and volcanic eruptions. bParticularly the human immune and nervous systems. cSee the text about transhumanism.

• The multifaceted definition of entropy • The principles of nonequilibrium thermodynamics and nonlinear dynamics • The phenomena of temporal and spatial self-organization • Chaos • Fractals

century challenges, the complex systems they involve, and which kind of chemistry is required to tackle them. The chemical disciplines reported in Table 1 are, on their own, not enough to overcome the related 21st-century challenges. They need to be complemented by interdisciplinary knowledge of the general features of complex systems and a systemic perspective. These skills and attributes can be acquired by attending courses designed to introduce systems thinking. B

DOI: 10.1021/acs.jchemed.9b00027 J. Chem. Educ. XXXX, XXX, XXX−XXX

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First, students should be conscious that the predictive power of science has intrinsic limitations and unavoidable uncertainties. These uncertainties do not allow reasonable predictions of chaotic dynamics in the long term. Moreover, at the quantum level, Heisenberg’s principle notes the impossibility of determining accurately and simultaneously the position and momentum of a particle. Therefore, we cannot predict the dynamics of quantum entities. Second, complex systems exhibit variable patterns. Examples include the patterns that are analyzed in medical diagnosis or the aperiodic trends in the stock market. To try to recognize variable patterns, we collect, store, and process massive amounts of data, which nowadays are well-known as big data. Even though big data can be produced and characterized, universally valid and effective algorithms for recognizing variable patterns still need to be formulated. Third, natural complexity is strictly related to computational complexity.7 In fact, if we try to describe any complex system from its ultimate constituents, namely, atoms and molecules, we face an exponential problem having large dimensions. Exponential problems having large dimensions are solvable yet intractable because their exact solutions cannot be found in a reasonable time. A concrete example would be to describe a complex system by using the Schrödinger equation, shown here as eq 2:

These concepts should be presented by making examples not only from chemistry but also from other disciplines, such as biology, physics, economics, and geology. A synopsis of these ideas, their interdisciplinarity, and how they equip students with knowledge to deal with complex systems is provided in the Supporting Information.

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FEATURES OF COMPLEX SYSTEMS A complex system is composed of many constituents that usually are diverse, if not unique. These constituents are strongly interconnected. Therefore, a complex system can be described as a network. In fact, the etymology of the adjective “complex” derives from the Latin verb “cum-plectere” that means “to intertwine together”. Complex systems that are sharply different can be described as networks with distinct architectures. Natural networks are maintained far from the condition of thermodynamic equilibrium by external and internal gradients of intensive variables, such as temperature, pressure, concentrations of chemicals, and so on. Complex systems that involve only inanimate matter are driven by force fields (an example is the geology of Earth). On the other hand, the behavior of a complex system that includes living beings is information-based. In fact, a peculiarity of living beings is that of exploiting matter and energy to encode, process, store, and communicate information.7 Natural complexity (C) derives from a combination of three features: multiplicity (M), interconnection (Ic), and integration (Ig):15 C ∝ (M ) ⊂ (Ic) ⊂ (Ig)

ℏ

∂ |Ψ⟩ = /̂ |Ψ⟩ ∂t

(2)

The number of computational steps required to solve eq 2 grows exponentially with the number of atoms. With as few as 500 atoms, the number of computational steps is enormous: 2500 ≈ 3.3 × 10150. Even the fastest supercomputer in the world would require ≈7 × 10125 years. These three characteristics encountered in describing complex systems ultimately raise the following question: “How can we untangle complex systems?”

(1)

Many and often diverse nodes (multiplicity) that are strongly interconnected (interconnection) exhibit emergent properties because they integrate their features (integration). The symbol "⊂" expresses a peculiar combination of the three parameters: M, Ic, and Ig. Complexity and emergent properties can be encountered along a hierarchy of levels, for instance, at the molecular, supramolecular, and cellular levels, but also passing from cells to tissues, from tissues to organisms, and from organisms to societies and ecosystems. A property is emergent when it cannot be predicted even if we know all the characteristics of the elements of the system. The traditional reductionist approach is not appropriate when dealing with emergent properties. The whole is more than the sum of its parts. Systems thinking is required. One of the most striking examples of an emergent property is “life”. A living being’s isolated molecular constituents, DNAs, RNAs, proteins, phospholipids, water, salts, and so on, can never show life. Only if we consider all the constituents organized in the dynamic hierarchical structure of a cell can we observe the fantastic phenomenon of life. Complex systems can originate the phenomena of selforganization in space and time. Their dynamics can be • Stationary • Periodic • Aperiodic • Chaotic Unfortunately, any complex system cannot be described exhaustively. In other words, insurmountable difficulties arise in predicting the behavior of any complex system, especially in the long term. There are three fundamental reasons7 for this that students need to understand.

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HOW TO UNTANGLE COMPLEX SYSTEMS Students must now know the principal strategies to untangle complex systems and hence face 21st-century challenges. It is evident that smart methods are needed to cope with the level of big data being generated and its complexity. There are two main strategies to consider.7 One consists of improving current electronic computers, and the other is the interdisciplinary emergent field of natural computing. Current electronic computers are based on the von Neumann architecture, and so far, the pace of their improvement has been described by Moore’s law. Nowadays, computer companies are contriving new technologies that try to go beyond Moore’s law. The other strategy is the interdisciplinary research line of natural computing.7,16 Scientists working in this field draw inspiration from nature to propose new algorithms, new materials and architectures to compute, and new models and methodologies to interpret complex systems. The rationale is that information can be encoded by any distinguishable physicochemical state of matter. Within natural computing, there are two distinct programs (see Figure 1). In one, scientists draw inspiration from natural information systems, that is, from living beings (Figure 1A), such as a cell, a nervous system, an immune system, or a society. In the other distinct program, scientists exploit natural physicochemical laws to make computations, for example, using the laws of quantum C

DOI: 10.1021/acs.jchemed.9b00027 J. Chem. Educ. XXXX, XXX, XXX−XXX

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Commentary

algorithms can be highlighted by emphasizing the huge impact that artificial intelligence (AI) is having in the fight against 21st-century challenges.18 Finally, the way that chemists can boost the development of AI by exploiting out-of-equilibrium chemical systems, such as oscillating chemical reactions, can be noted. How such reactions mimic the dynamics of neurons19 can further elucidate the value of developing chemical understanding. Molecular, supramolecular, and systems chemistries can be used to implement fuzzy logic.20 Fuzzy logic plays a relevant role in AI because it is a good model of the human ability “to compute with words”. The implementation of sensors, neural networks, and effectors by molecular, supramolecular, and systems chemistries is promoting the development of chemical artificial intelligence21 and chemical robots,22 which complement the features of the hardware and software employed in conventional AI and robotics.

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COURSE IMPLEMENTATION An interdisciplinary course on complex systems for physical chemistry graduate students in the Chemistry, Biology, and Biotechnology Department of the University of Perugia (in Italy) has been taught since the 2009−2010 academic year. The key pedagogical motto for this course is the famous sentence pronounced by the Greek historian and essayist Plutarch (46−127 CE) in his Moralia: “Minds are not vessels to fill, but fires to kindle.” Student enthusiasm can be sparked by noting that to effectively face 21st-century challenges, we need to understand complex systems. Students should be aware that they study to build a better future for themselves and the whole of humanity because the challenges of this century are global. The course proposed here is designed like a journey to discovering the fantastic features of complex systems. As any valuable and unforgettable journey, it must be guided by curiosity and questions. Therefore, whenever new concepts and ideas are presented, they are introduced by formulating preliminary queries and, in some cases, advancing doubts on what science already knows. If the students have the necessary cultural background, it is provocative to invite them to imagine plausible answers. It is important to start from a systemic approach that is characteristic of thermodynamics: the features, spatial scale, and boundaries of the system under analysis are fixed. Then, basic physicochemical principles, expressed under

Figure 1. Research lines encompassed within natural computing, including (A) research lines inspired by natural information systems, such as cells (i.e., biomolecular information systems), the brain (i.e., neural information systems), the immune system (i.e., immune information systems), and societies (i.e., social information systems), and (B) alternative computational strategies formulated by exploiting fundamental physicochemical laws.

physics to develop quantum computation (see Figure 1B). Any physicochemical law describes causal events. Any causal event can be conceived as a computation wherein the causes are the inputs, the effects are the outputs, and the law governing the transformation is the algorithm of the computation. There are significant contributions that chemists have given to both strategies. For example, the seminal work in the field of DNA computing carried out by Adleman in 1994 can be presented.17 Adleman had the brilliant idea of exploiting the parallelism of the hybridization reaction between DNA strands to solve the “traveling salesman problem” quickly. The role of

Figure 2. Pictures of (A) Hele−Shaw cell and (B) dendritic fractal-like structure obtained by viscous fingering of a red aqueous solution injected in a viscous aqueous solution of 4% poly(vinyl alcohol) reticulated by sodium borate. See ref 7 for more details. D

DOI: 10.1021/acs.jchemed.9b00027 J. Chem. Educ. XXXX, XXX, XXX−XXX

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instead, science has to deal with clouds, that is, complex systems, having unique and hardly replicable behaviors. Third, the interdisciplinary field of natural computing offers a new vision of natural phenomena: any causal event is a particular kind of computation. Hence, the original epistemological pillar of mechanism, proposed after the formulation of the laws of classical physics in the 17th century, assumes a new semantics: the universe is a computing machine. This idea suggests a methodology to deal with complex systems and face 21st-century challenges.7 Such a methodology requires an analysis of a complex system at three levels, which are • The computational level, which consists of determining the inputs (the causes), outputs (the effects), and the computations that the system performs. • The algorithmic level, which consists of formulating algorithms that might carry out the computations defined in the previous level of analysis. • The implementation level, which consists of looking for mechanisms that can implement the algorithms. If such mechanisms exist, they will contribute to the development of technology. In conclusion, the interdisciplinary course on complex systems presented in this essay is a contribution to the project of reorganizing chemical education, promoted by IUPAC in 2017. It will help new generations face 21st-century challenges by molding polymath and interdisciplinary mindsets with strengthened aptitudes to observe, analyze, judge, and summarize. The proliferation of courses like the one proposed here will favor the growth of multidisciplinary research groups focused on complex systems. A widespread effort to study complex systems will likely spark a new “intellectual revolution”, originating a transdisciplinary theory on complex systems and merging chemistry and other scientific disciplines. The resulting theories about complex systems will be a valuable tool to tackle 21st-century challenges.

the shapes of equations, are exploited to unveil the behavior of the system. Often, numerical exercises are proposed to familiarize students with equations and formulas. When they are available, videos from sources such as Nature,23 the Science website,24 the LabRoots website,25 the video journal JoVE,26 TED Talks,27 and the Complexity Explorer website28 of the Santa Fe Institute can be included to further illustrate complexity and show students the interdisciplinary content of this subject. An essential stage in the learning process is the time that students spend in the laboratory. Experiments where students observe in practice the laws and principles learned in lecture are pursued. I usually propose four laboratory experiments. In one experiment, they observe the emergence of order in time by studying an oscillatory reaction.29,30 In another, they investigate the emergence of order in space through the analysis of chemical waves30 or the phenomenon of periodic precipitations.7,31 In a third one, students experience chaos by studying convection.32 In the fourth one, they generate and characterize fractal-like structures through the phenomenon of viscous-fingering in a Hele−Shaw cell (see Figure 2).7 Finally, students perform a computational experiment wherein they play with Turing patterns, through the software available on the webpage of Shigeru Kondo’s research group,33 and other models for complex systems (such as Cellular Automata and Swarm Intelligence)34 implemented in the freely available NetLogo software.

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CONCLUDING REMARKS On the basis of a survey of a web repository,28 courses on complex systems are more common in physics, computer science, mathematics, and complex systems departments than they are in chemistry. The new interdisciplinary course on complex systems proposed in this commentary is designed for either upper-division undergraduate, graduate, or Ph.D. students in chemistry. The mathematical background required to attend this course is knowledge of calculus. Moreover, students are supposed to have already completed the basic courses of general and inorganic chemistry, organic chemistry, and physical chemistry. A knowledge of classical and statistical equilibrium thermodynamics is mandatory. This course helps students become aware that to face 21stcentury challenges, it is necessary to investigate complex systems. Comprehension of complex systems requires knowledge of the principles of nonequilibrium thermodynamics and nonlinear dynamics. Polymath mindsets and interdisciplinary knowledge are required as well. Students discover that systems as diverse as ecosystems, the macroeconomy, cells, chemical reactions, climate, and societies have many points in common. Nevertheless, science faces strong limitations in predicting the behaviors of complex systems. Students understand the reasons for these limitations and become acquainted with strategies to tackle them. Investigation of complex systems generates three epistemological pillars in the minds of students, who will face 21st-century challenges. First, reductionism, which is the traditional methodology of scientific inquiry, is not satisfactory; it must be complemented by a systemic approach. Second, experiments on complex systems are not necessarily reproducible. Sometimes they are historical events. As it has been rightly alleged by the philosopher Karl Popper,35 science, in the past, had been occupied with clocks, that is, simple, deterministic systems having reproducible behaviors. Now,

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.9b00027. Synopsis of the foundational ideas for understanding the behavior of complex systems (PDF, DOCX)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Pier Luigi Gentili: 0000-0003-1092-9190 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS P.L.G. acknowledges the Department of Chemistry, Biology, and Biotechnology of the University of Perugia, Italy, for giving him the opportunity to deliver his interdisciplinary course titled Investigation into Complex Systems to graduate students in chemistry since the 2009−2010 academic year; the Erasmus + Program for funding his teaching activity at the University College of London and the University Paul Sabatier in Toulouse; his past students, because the lectures he gave them E

DOI: 10.1021/acs.jchemed.9b00027 J. Chem. Educ. XXXX, XXX, XXX−XXX

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(22) Hagiya, M.; Konagaya, A.; Kobayashi, S.; Saito, H.; Murata, S. Molecular Robots with Sensors and Intelligence. Acc. Chem. Res. 2014, 47, 1681−1690. (23) Nature Video Archive. Nature. http://www.nature.com/ nature/videoarchive/index.html/ (accessed June 30, 2019). (24) Videos. Science Magazine. http://www.sciencemag.org/videos/ (accessed June 30, 2019). (25) Videos. LabRoots website. https://www.labroots.com/videos/ (accessed June 30, 2019). (26) JoVE Video Journal. JoVE. https://www.jove.com/ (accessed June 30, 2019). (27) TED Talks. www.ted.com/ (accessed June 30, 2019). (28) Complexity Explorer. https://www.complexityexplorer.org/ (accessed June 30, 2019). (29) Briggs, T. S.; Rauscher, W. C. An Oscillating Iodine Clock Reaction. J. Chem. Educ. 1973, 50, 496. (30) Pojman, J. A.; Craven, R.; Leard, D. C. Chemical Oscillations and Waves in the Physical Chemistry Lab. J. Chem. Educ. 1994, 71, 84−90. (31) Sharbaugh, A. H.; Sharbaugh, A. H., Jr. An Experimental Study of the Liesegang Phenomenon and Crystal Growth in Silica Gels. J. Chem. Educ. 1989, 66, 589−594. (32) Gentili, P. L.; Dolnik, M.; Epstein, I. R. Photochemical Oscillator”: Colored Hydrodynamic Oscillations and Waves in a Photochromic System. J. Phys. Chem. C 2014, 118, 598−608. (33) Reaction diffusion simulator. 3D Morphologic. http://www.3dlogic.jp/en/simulation.html (accessed June 30, 2019). (34) Wilensky, U. NetLogo. Center for Connected Learning and Computer-Based Modeling, Northwestern University. https://ccl. northwestern.edu/netlogo/ (accessed June 30, 2019). (35) Popper, K. R. Of Clouds and Clocks. In Objective Knowledge: An Evolutionary Approach, revised ed.; Oxford University Press: Oxford, U.K., 1972; pp 206−255.

and the questions they asked him have been beneficial for organizing the course; CRC Press for inviting him to write a book about the innovative contents of his course (see ref 7); and Associate Editor Thomas A. Holme and the reviewers for their constructive and valuable suggestions in the preparation of the final version of this commentary.

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DOI: 10.1021/acs.jchemed.9b00027 J. Chem. Educ. XXXX, XXX, XXX−XXX