🪸On Systems Thinking: On Large Scale

"Almost everyone now acknowledges that theory and experiment, model making, theory construction and linguistics all go together, and that the successful development of a science of behavior depends upon a ‘total approach’ in which, given that the computer ‘is the only large-scale universal model’ that we possess, ‘we may expect to follow the prescription of Simon and construct our models - or most of them - in the form of computer programs’." (Frank H George,"Cognition", 1962) [attributed to Alan M Turing] 

“As our mental eye penetrates into smaller and smaller distances and shorter and shorter times, we find nature behaving so entirely differently from what we observe in visible and palpable bodies of our surroundings that no model shaped after our large-scale experiences can ever be ‘true’. A complete satisfactory model of this type is not only practically inaccessible, but not even thinkable. Or, to be precise, we can, of course, think of it, but however we think it, it is wrong; not perhaps quite as meaningless as a ‘triangular circle’, but more so than a ‘winged lion’.” (Erwin Schrödinger, “Science and Humanism”, 1952)

"The word model is used as a noun, adjective, and verb, and in each instance it has a slightly different connotation. As a noun 'model' is a representation in the sense in which an architect constructs a small-scale model of a building or a physicist a large-scale model of an atom. As an adjective 'model' implies a degree or perfection or idealization, as in reference to a model home, a model student, or a model husband. As a verb 'to model' means to demonstrate, to reveal, to show what a thing is like." (Russell L Ackoff, "Scientific method: optimizing applied research decisions", 1962)

"Simple rules can have complex consequences. This simple rule has such a wealth of implications that it is worth examining in detail. It is the far from self-evident guiding principle of reductionism and of most modern investigations into cosmic complexity. Reductionism will not be truly successful until physicists and cosmologists demonstrate that the large-scale phenomena of the world arise from fundamental physics alone. This lofty goal is still out of reach. There is uncertainty not only in how physics generates the structures of our world but also in what the truly fundamental rules of physics are." (William Poundstone, "The Recursive Universe", 1985)

"The large-scale computer models of systems ecology do not fit under the heading of holism at all. Rather they are forms of large-scale reductionism: the objects of study are the naively given 'parts' -abundances or biomasses of populations. No new objects of study arise at the community level. The research is usually conducted on a single system - a lake, forest, or prairie - and the results are measurements of and projections for that lake, forest, or prairie, with no attempts to find the properties of lakes, forests, or prairies in general. Such modeling requires vast amounts of data for its simulations, and much of the scientific effort goes into problems of estimation." (Richard Levins & Richard C Lewontin, "The Dialectical Biologist", 1985)

"The evident power of simple heuristics […] teaches us the important lesson that global behavior patterns, and social organization, can emerge out of local interactions. Organisms do not necessarily need to have an over-riding plan nor do they require awareness of the large-scale. Grand patterns and processes can emerge as the nett effect of small-scale, local behavior."(David G Green, 2000) 

"The really crucial question in multi-object systems is whether local interactions do grow into large-scale patterns." (David G Green, 2000)

"Statistical mechanics is the science of predicting the observable properties of a many-body system by studying the statistics of the behaviour of its individual constituents, be they atoms, molecules, photons etc. It provides the link between macroscopic and microscopic states. […] classical thermodynamics. This is a subject dealing with the very large. It describes the world that we all see in our daily lives, knows nothing about atoms and molecules and other very small particles, but instead treats the universe as if it were made up of large-scale continua. […] quantum mechanics. This is the other end of the spectrum from thermodynamics; it deals with the very small. It recognises that the universe is made up of particles: atoms, electrons, protons and so on. One of the key features of quantum mechanics, however, is that particle behaviour is not precisely determined (if it were, it would be possible to compute, at least in principle, all past and future behaviour of particles, such as might be expected in a classical view). Instead, the behaviour is described through the language of probabilities." (A Mike Glazer & Justin S Wark, "Statistical Mechanics: A survival guide", 2001)

"Physics deals with both the large and the small. Its domain of study includes the interior of the nucleus of an atom as well as the exterior of a galaxy. It is, therefore, natural for the scope of physical theories to switch between global, or large-scale, and local, or small-scale regimes. Such an interplay between the local and the global has existed ever since Newton and others discovered the mathematical translation of this interplay: Derivatives are defined as local objects while integrals encompass global properties." (Sadri Hassani, "Mathematical Methods: For Students of Physics and Related Fields", 2009)

"Black Swans (capitalized) are large-scale unpredictable and irregular events of massive consequence - unpredicted by a certain observer, and such un - predictor is generally called the 'turkey' when he is both surprised and harmed by these events. [...] Black Swans hijack our brains, making us feel we 'sort of' or 'almost' predicted them, because they are retrospectively explainable. We don’t realize the role of these Swans in life because of this illusion of predictability. […] An annoying aspect of the Black Swan problem - in fact the central, and largely missed, point - is that the odds of rare events are simply not computable." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)

"The sensitivity of chaotic systems to initial conditions is particularly well known under the moniker of the 'butterfly effect', which is a metaphorical illustration of the chaotic nature of the weather system in which 'a flap of a butterfly’s wings in Brazil could set off a tornado in Texas'. The meaning of this expression is that, in a chaotic system, a small perturbation could eventually cause very large-scale difference in the long run." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

📓On Literature: On Authority (From Fiction to Science-Fiction)

"It is no bad thing to be a king - to see one's house enriched and one's authority enhanced." (Homer, "The Odyssey", cca. 750-700 BC)

"Even the best of men in authority are liable to be corrupted by passion. We may conclude then that the law is reason without passion, and it is therefore preferable to any individual." (Aristotle, "Politics", cca. 335-323 BC)

"Old age, especially an honored old age, has so great authority, that this is of more value than all the pleasures of youth." (Marcus Tullius Cicero, "Cato Maior de Senectute" ["On Old Age"], 44 BC) 

"Almost all the opinions we have are taken on authority and on credit." (Michel de Montaigne, "De la phisionomie" ["Of Physiognomy"], 1588)

"For rightly is truth called the daughter of time, not of authority." (Francis Bacon, "Novum Organum", 1620)

"Authority without wisdom is like a heavy axe without an edge, fitter to bruise than polish." (Anne Bradstreet, "Meditations Divine and Moral", 1666)

"Lawful and settled authority is very seldom resisted when it is well employed." (Samuel Johnson, The Rambler no. 50, 1750)

"Always acknowledge a fault frankly. This will throw those in authority off their guard and give you opportunity to commit more." (Mark Twain, "More Maxims of Mark", 1927)

"Man cannot do without beauty, and this is what our era pretends to want to disregard. It steels itself to attain the absolute and authority; it wants to transfigure the world before having exhausted it, to set it to rights before having understood it. Whatever it may say, our era is deserting this world." (Albert Camus,"Helen's Exile", 1948)

"I accept nothing on authority. A hypothesis must be backed by reason, or else it is worthless." (Isaac Asimov, "I, Robot", 1950)

"Objective evidence is the ultimate authority. Recorders may lie, but Nature is incapable of it." (Walter M Miller Jr, "A Canticle for Leibowitz", 1959

"Freedom of conscience entails more dangers than authority and despotism." (Michel Foucault, "Madness and Civilization", 1961)

"The robots are not technologically minded. They were not built to be. They were built to bolster human vanity and pride, to meet a strange longing that seems to be built into the human ego - the need to have other humans (or a reasonable facsimile of other humans) to minister to our wants and needs, human slaves to be dominated, human beings over which a man or woman (or a child) can assert authority, thus building up a false feeling of superiority." (Clifford D Simak, "A Choice of Gods", 1972)

"It is unusual for us to discover an imperial power-system in space. As a rule, such archaic forms of authority wither long before the relevant species drags itself off the home planet." (Iain M Banks, "The Player of Games", 1988)

📓On Literature: On Edges (From Fiction to Science Fiction)

"Moreover, the universe as a whole is infinite, for whatever is limited has an outermost edge to limit it, and such an edge is defined by something beyond. Since the universe has no edge, it has no limit; and since it lacks a limit, it is infinite and unbounded. Moreover, the universe is infinite both in the number of its atoms and in the extent of its void." (Epicurus," Letters", [Letter to Herodotus] cca. 305 BC)

"It is the sharpness of our mind that gives the edge to our pains and pleasures." (Michel de Montaigne, "Essais", 1580)

"Authority without wisdom is like a heavy axe without an edge, fitter to bruise than polish." (Anne Bradstreet, "Meditations Divine and Moral", 1666)

"A great Empire, like a great Cake, is most easily diminished at the Edges." (Benjamin Franklin, "Rules By Which A Great Empire May Be Reduced To A Small One", The Public Advertiser, 1773)

"Life as we call it, is nothing but the edge of the boundless ocean of existence when it comes upon soundings." (Oliver W Holmes Jr, "The Professor at the Breakfast Table", 1860)

"[...] only on the edge of the grave can man conclude anything." (Henry Adams, "The Education of Henry Adams", 1907)

"We have come to the edge of a world of which we have no experience, and where all our preconceptions must be recast." (D'Arcy W Thompson, "On Growth and Form" Vol. 1, 1917)

"Life is a travelling to the edge of knowledge, then a leap taken." (David H Lawrence, "Reflections on the Death of a Porcupine and Other Essays", 1988) 

"All our words from loose using have lost their edge." (Ernest Hemingway, "Death in the Afternoon", 19325

"We do not truly see light, we only see slower things lit by it, so that for us light is on the edge-the last thing we know before things become too swift for us." (Clive S Lewis, "Out of the Silent Planet", 1938)

"War creates no absolutely new situation: it simply aggravates the permanent human situation so that we can no longer ignore it. Human life has always been lived on the edge of a precipice." (Clive S Lewis, "Learning in War-Time", 1939)

"Sooner or later we will come to the edge of the Solar System and will be looking out across the ultimate abyss. Then we must choose whether we reach the stars — or whether we wait until the stars reach us." (Arthur C Clarke, "The Challenge of the Spaceship". 1959)

"When they [radio astronomers] grew weary at their electronic listening posts, when their eyes grew dim with looking at unrevealing dials and studying uneventful graphs, they could step outside their concrete cells and renew their dull spirits in communion with the giant mechanism they commanded, the silent, sensing instrument in which the smallest packets of energy, the smallest waves of matter, were detected in their headlong, eternal flight across the universe. It was the stethoscope with which they took the pulse of the all and noted the birth and death of stars, the probe with which, here on an insignificant planet of an undistinguished star on the edge of its galaxy, they explored the infinite." (James Gunn, "The Listeners", 1968)

"Whole worlds formed in a pregnant void: not spherical worlds merely, but dodeka-spherical, and those much more intricate than that. Not merely seven colors to play with, but seven to the seventh and to the seventh again. Stars vivid in the bright light. You who have seen stars only in darkness. be silent! Asteroids that they ate like peanuts, for now they were all metamorphic giants. Galaxies like herds of rampaging elephants. Bridges so long that both ends of them receded over the light-speed edges. Waterfalls, of a finer water, that bounced off galaxy clusters as if they were boulders." (Raphael A Lafferty, "Sky", 1971)

"Every judgment teeters on the brink of error. To claim absolute knowledge is to become monstrous. Knowledge is an unending adventure at the edge of uncertainty." (Frank Herbert, "Children of Dune", 1976)

"The distinction between sanity and insanity is narrower than the razor's edge, sharper than a hound's tooth, more agile than a mule deer. It is more elusive than the merest phantom. Perhaps it does not even exist; perhaps it is a phantom." (Philip K Dick,"VALIS", 1981)

"Living systems are never in equilibrium. They are inherently unstable. They may seem stable, but they're not. Everything is moving and changing. In a sense, everything is on the edge of collapse. Michael Crichton, "Jurassic Park", 1990)

"Every judgment teeters on the brink of error. To claim absolute knowledge is to become monstrous. Knowledge is an unending adventure at the edge of uncertainty." (Frank Herbert, "Children of Dune", 1976)

"Mechs built, that was inevitable. They sought to make of the world a place of straight lines and sharp edges, geometry made real. Eternal, rigid certainties. Men were of a different order. They sought the curved, the flexible, the liveand unenduring. They lived and died." (Gregory Benford, "At the Double Solstice", 1988)

"At the edge of chaos, unexpected outcomes occur. The risk to survival is severe." (Michael Crichton, "Jurassic World", 1997) 

🪸On Systems Thinking: On Ecology (2000-2009)

"Ecological rationality uses reason – rational reconstruction – to examine the behavior of individuals based on their experience and folk knowledge, who are ‘naïve’ in their ability to apply constructivist tools to the decisions they make; to understand the emergent order in human cultures; to discover the possible intelligence embodied in the rules, norms and institutions of our cultural and biological heritage that are created from human interactions but not by deliberate human design. People follow rules without being able to articulate them, but they can be discovered." (Vernon L Smith, "Constructivist and ecological rationality in economics",  2002)

"Organizations need to undergo fundamental changes, both in order to adapt to the new business environment and to become ecologically sustainable." (Fritjof Capra, "The Hidden Connections", 2002)

"Ecology, on the other hand, is messy. We cannot find anything deserving of the term law, not because ecology is less developed than physics, but simply because the underlying phenomena are more chaotic and hence less amenable to description via generalization." (Lev Ginzburg & Mark Colyvan," Ecological Orbits: How Planets Move and Populations Grow", 2004)

"Limiting factors in population dynamics play the role in ecology that friction does in physics. They stop exponential growth, not unlike the way in which friction stops uniform motion. Whether or not ecology is more like physics in a viscous liquid, when the growth-rate-based traditional view is sufficient, is an open question. We argue that this limit is an oversimplification, that populations do exhibit inertial properties that are noticeable. Note that the inclusion of inertia is a generalization - it does not exclude the regular rate-based, first-order theories. They may still be widely applicable under a strong immediate density dependence, acting like friction in physics." (Lev Ginzburg & Mark Colyvan, "Ecological Orbits: How Planets Move and Populations Grow", 2004)

"It is science that brings us an understanding of the true complexity of natural systems. The insights from the science of ecology are teaching us how to work with the checks and balances of nature, and encouraging a new, rational, limited-input, environmentally sound means of vineyard management that offers a third way between the ideologically driven approach of Biodynamics and conventional chemical-based agricultural systems." (Jamie Goode," The Science of Wine: From Vine to Glass", 2005)

"An ecology provides the special formations needed by organizations. Ecologies are: loose, free, dynamic, adaptable, messy, and chaotic. Innovation does not arise through hierarchies. As a function of creativity, innovation requires trust, openness, and a spirit of experimentation - where random ideas and thoughts can collide for re-creation." (George Siemens, "Knowing Knowledge", 2006)

"Knowledge flow can be likened to a river that meanders through the ecology of an organization. In certain areas, the river pools and in other areas it ebbs. The health of the learning ecology of the organization depends on effective nurturing of flow." (George Siemens, "Knowing Knowledge", 2006)

"[ecology:] the scientific study of the distribution and abundance of organisms and the interactions that determine distribution and abundance." (Michael Begon et al, "Ecology: From individuals to ecosystems", 2006)

"Nodes and connectors comprise the structure of a network. In contrast, an ecology is a living organism. It influences the formation of the network itself." (George Siemens, "Knowing Knowledge", 2006)

"The living world can be viewed as a biological hierarchy that starts with subcellular particles, and continues up through cells, tissues and organs. Ecology deals with the next three levels: the individual organism, the population (consisting of individuals of the same species) and the community (consisting of a greater or lesser number of species populations). At the level of the organism, ecology deals with how individuals are affected by (and how they affect) their environment. At the level of the population, ecology is concerned with the presence or absence of particular species, their abundance or rarity, and with the trends and fluctuations in their numbers. Community ecology then deals with the composition and organization of ecological communities." (Michael Begon et al, "Ecology: From individuals to ecosystems", 2006)

"We need to renegotiate our contract with nature. Ecology is a unifying force that can diminish intolerance and expand our empathy towards others - both human and animal." (Gregory Colbert, "Peace and Harmony: The Message of Our Discovery", [Photo No. 427] 2006)

"When we focus on designing ecologies in which people can forage for knowledge, we are less concerned about communicating the minutiae of changing knowledge. Instead, we are creating the conduit through which knowledge will flow." (George Siemens, "Knowing Knowledge", 2006

"Any new dominant communications medium leads to a new information ecology in society that inevitably changes the way ideas, feelings, wealth, power and influence are distributed and the way collective decisions are made." (Al Gore,"The Assault on Reason", 2007)

"Social ecology is based on the conviction that nearly all of our present ecological problems originate in deep-seated social problems. It follows, from this view, that these ecological problems cannot be understood, let alone solved, without a careful understanding of our existing society and the irrationalities that dominate it. To make this point more concrete: economic, ethnic, cultural, and gender conflicts, among many others, lie at the core of the most serious ecological dislocations we face today - apart, to be sure, from those that are produced by natural catastrophes." (Murray Bookchin, "Social Ecology and Communalism", 2007)

"This new model of development would be based clearly on the goal of sustainable human well-being. It would use measures of progress that clearly acknowledge this goal. It would acknowledge the importance of ecological sustainability, social fairness, and real economic efficiency. Ecological sustainability implies recognizing that natural and social capital are not infinitely substitutable for built and human capital, and that real biophysical limits exist to the expansion of the market economy." (Robert Costanza, "Toward a New Sustainable Economy", 2008)

"In ecology, we are often interested in exploring the behavior of whole systems of species or ecosystem composed of individual components which interact through biological processes. We are interested not simply in the dynamics of each species or component in isolation, but the dynamics of each species or component in the context of all the others and how those coupled dynamics account for properties of the system as a whole, such as its persistence. This is what people seem to mean when they say that ecology is ‘holistic’, an otherwise rather vague term." (John Pastor, "Mathematical Ecology of Populations and Ecosystems", 2008)

"Much of what we deal with in ecology are rates of change of biological objects: growth of an organism, decay of a dead leaf, fluctuations in populations, accumulation or erosion of soil, increases or decreases in lake levels, etc. But rates of change are some of the hardest things to measure. What we measure are static properties such as the sizes of objects at different times and then infer that change has taken place between those two measurements." (John Pastor, "Mathematical Ecology of Populations and Ecosystems", 2008)

"Therefore, mathematical ecology does not deal directly with natural objects. Instead, it deals with the mathematical objects and operations we offer as analogs of nature and natural processes. These mathematical models do not contain all information about nature that we may know, but only what we think are the most pertinent for the problem at hand. In mathematical modeling, we have abstracted nature into simpler form so that we have some chance of understanding it. Mathematical ecology helps us understand the logic of our thinking about nature to help us avoid making plausible arguments that may not be true or only true under certain restrictions. It helps us avoid wishful thinking about how we would like nature to be in favor of rigorous thinking about how nature might actually work." (John Pastor, "Mathematical Ecology of Populations and Ecosystems", 2008)

"What literally defines social ecology as ‘social’ is its recognition of the often overlooked fact that nearly all our present ecological problems arise from deep-seated social problems. Conversely, present ecological problems cannot be clearly understood, much less resolved, without resolutely dealing with problems within society." (Murray Bookchin, "What is Social Ecology", 2009)

🪸On Systems Thinking: On Ecology (1990-1999)

"Systems thinking is a discipline for seeing wholes. It is a framework for seeing interrelationships rather than things, for seeing patterns of change rather than static 'snapshots'. It is a set of general principles- distilled over the course of the twentieth century, spanning fields as diverse as the physical and social sciences, engineering, and management. [...] During the last thirty years, these tools have been applied to understand a wide range of corporate, urban, regional, economic, political, ecological, and even psychological systems. And systems thinking is a sensibility for the subtle interconnectedness that gives living systems their unique character." (Peter Senge, "The Fifth Discipline", 1990)

"To halt the decline of an ecosystem, it is necessary to think like an ecosystem." (Douglas P Wheeler, EPA Journal, 1990)

"The cybernetics phase of cognitive science produced an amazing array of concrete results, in addition to its long-term (often underground) influence: the use of mathematical logic to understand the operation of the nervous system; the invention of information processing machines (as digital computers), thus laying the basis for artificial intelligence; the establishment of the metadiscipline of system theory, which has had an imprint in many branches of science, such as engineering (systems analysis, control theory), biology (regulatory physiology, ecology), social sciences (family therapy, structural anthropology, management, urban studies), and economics (game theory); information theory as a statistical theory of signal and communication channels; the first examples of self-organizing systems. This list is impressive: we tend to consider many of these notions and tools an integrative part of our life […]" (Francisco Varela, "The Embodied Mind", 1991)

"Ecological Economics studies the ecology of humans and the economy of nature, the web of interconnections uniting the economic subsystem to the global ecosystem of which it is a part." (Robert Costanza, "Ecological Economics: the science and management of sustainability", 1992)

"When the study of the household (ecology) and the management of the household (economics) can be merged, and when ethics can be extended to include environmental as well as human values, then we can be optimistic about the future of humankind. Accordingly, bringing together these three 'E's' is the ultimate holism and the great challenge for our future." (Eugene Odum," Ecology and our endangered life-support systems", 1993)

"Progressively higher levels of organization are attained as catalytic cycles on one level interlock and form hypercycles: these are systems on a higher level of organization. Thus molecules emerge from a combination of chemically active atoms; protocells emerge from sequences of complex molecules; eukaryotic cells emerge among the prokaryotes; metazoa make their appearance among the protozoa and converge in still higher-level ecological and social systems." (Ervin László, "Vision 2020: Reordering Chaos for Global Survival" , 1994)

"If machines knew as much about each other as we know about each other (even in our privacy), the ecology of machines would be indomitable." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"In the past several years, social work has increasingly focused on an ecological model. This model integrates both treatment and reform by conceptualizing and emphasizing the dysfunctional transactions between people and their physical and social environments. Human beings are viewed as developing and adapting through transactions with all elements of their environments. An ecological model gives attention to both internal and external factors. It does not view people as passive reactors to their environments but, rather, as being involved in dynamic and reciprocal interactions with them." (Charles Zastrow, "The practice of social work", 1995)

"The new paradigm may be called a holistic world view, seeing the world as an integrated whole rather than a dissociated collection of parts. It may also be called an ecological view, if the term 'ecological' is used in a much broader and deeper sense than usual. Deep ecological awareness recognizes the fundamental interdependence of all phenomena and the fact that, as individuals and societies we are all embedded in (and ultimately dependent on) the cyclical process of nature." (Fritjof Capra & Gunter A. Pauli," Steering business toward sustainability", 1995

"A major clash between economics and ecology derives from the fact that nature is cyclical, whereas our industrial systems are linear. Our businesses take resources, transform them into products plus waste, and sell the products to consumers, who discard more waste […]" (Fritjof Capra, "The Web of Life", 1996)

"Economics emphasizes competition, expansion, and domination; ecology emphasizes cooperation, conservation, and partnership." (Fritjof Capra, "The Web of Life", 1996)

"Statistical hypothesis testing is commonly used inappropriately to analyze data, determine causality, and make decisions about significance in ecological risk assessment,[...] It discourages good toxicity testing and field studies, it provides less protection to ecosystems or their components that are difficult to sample or replicate, and it provides less protection when more treatments or responses are used. It provides a poor basis for decision-making because it does not generate a conclusion of no effect, it does not indicate the nature or magnitude of effects, it does address effects at untested exposure levels, and it confounds effects and uncertainty[...]. Risk assessors should focus on analyzing the relationship between exposure and effects[...]."  (Glenn W Suter, "Abuse of hypothesis testing statistics in ecological risk assessment", Human and Ecological Risk Assessment 2, 1996)

"These, then, are some of the basic principles of ecology - interdependence, recycling, partnership, flexibility, diversity, and, as a consequence of all those, sustainability... the survival of humanity will depend on our ecological literacy, on our ability to understand these principles of ecology and live accordingly." (Fritjof Capra, "The Web of Life", 1996)

"Understanding ecological interdependence means understanding relationships. It requires the shifts of perception that are characteristic of systems thinking - from the parts to the whole, from objects to relationships, from contents to patterns. [...] Nourishing the community means nourishing those relationships." (Fritjof Capra, "The Web of Life", 1996)

"Economics emphasizes competition, expansion, and domination; ecology emphasizes cooperation, conservation, and partnership." (Fritjof Capra, "The Web of Life", 1996) 

"Ecology, as it is currently practiced, sometimes deals with human impacts on ecosystems, but the more common tendency is to stick to 'natural' systems."(Robert Costanza & Janis King, "The first decade of ecological economics", Ecological Economics 28 (1), 1999)

🪸On Systems Thinking: On Social Networks

"Structure always affects function. The structure of social networks affects the spread of information and disease; the structure of the power grid affects the stability of power transmission. The same must be true for species in an ecosystem, companies in the global marketplace, cascades of enzyme reactions in living cells. The layout of the web must profoundly shape its dynamics." (Steven Strogatz, "Sync: The Emerging Science of Spontaneous Order", 2003)

"Connectivity harbors other risks too. As we create more links among the nodes of our technological and social networks, these networks sometimes developed unexpected patterns of connections that make breakdown more likely. They can, for instance, develop harmful feedback loops - what people commonly call vicious circles - that reinforce instabilities and even lead to collapse." (Thomas Homer-Dixon, "The Upside of Down: Catastrophe, Creativity, and the Renewal of Civilization", 2006)

"Social network analysis has been important for the further development of graph theory, for example with respect to introducing metrics for identifying importance of people or groups. For example, a person having many connections to other people may be considered relatively important. Likewise, a person at the center of a network would seem to be more influential than someone at the edge. What graph theory provides us are the tools to formally describe what we mean by relatively important, or having more influence. Moreover, using graph theory we can easily come up with alternatives for describing importance and such. Having such tools has also facilitated being more precise in statements regarding the position or role that person has within a community." (Maarten van Steen, "Graph Theory and Complex Networks: An Introduction", 2010)

"[...] the contexts in which a social network is embedded will generally have significant effects on its structure. Each individual in a social network has a distinctive set of personal characteristics, and similarities and compatibilities between two people’s characteristics can strongly influence whether a link forms between them. Each individual also engages in a set of behaviors and activities that can shape the formation of links within the network. These considerations suggest what we mean by a network’s surrounding contexts: factors that exist outside the nodes and edges of a networks, but which nonetheless affect how the network’s structure evolves." (David Easley & Jon Kleinberg, "Networks, Crowds, and Markets: Reasoning about a Highly Connected World", 2010)

"Social network analysis conceptualises individuals or groups as ‘points’ and their relations to each other as ‘lines’. It is concerned with the patterns formed by the points and lines and involves exploring these patterns, mathematically or visually, in order to assess their effects on the individuals and organisations that are the members of the ‘networks’ formed by the intersecting lines that connect them. It therefore takes the metaphorical idea of interaction as forming a network of connections and gives this idea a more formal representation in order to model structures of social relations. Treating a social structure as a network is the cornerstone of social network analysis." (John Scott," What is Social Network Analysis?", 2012)

"A system which is usually composed of large number of possibly heterogeneous interacting agents, which are seen to exhibit emergent behavior. Emergence implies that system level behavior (macro level) cannot be inferred from observation of individual level behavior of its constituents (micro level). This absence of explicit links between the micro and macro levels makes complex systems especially difficult to analyze using traditional statistical and analytical techniques to study the dynamics of behavior. One typically requires the use of bottom up simulation based methods to study such systems. Complex systems are ubiquitous - markets, societies, social networks, the Internet, weather, ecosystems, are just a few examples." (Stephen E Glavin & Abhijit Sengupta, "Modelling of Consumer Goods Markets: An Agent-Based Computational Approach", Handbook of Research on Managing and Influencing Consumer Behavior, 2015)

"With the birth of Internet-based social networks, information on personal interaction on a large-scale became available and the interest in developing mathematical models that are able to capture and explain certain stylized features of large and complex real-world networks has grown significantly. Among the most central phenomena observed in large-scale real-world networks is the so-called small-world phenomenon, which refers to the fact that despite the large network size most of the nodes have a surprisingly small graph (hop count) distance in between them, and the so-called scale-free nature of networks, meaning that the degree sequence has polynomial decay." (Francesca Biagini et al (Eds), "Network Science: An Aerial View", 2019)

"A small-world network is characterized by a high clustering coefficient and a short average path length, meaning that most nodes can be reached from any other node through a small number of intermediate connections. This structure often mirrors real-world social networks, where individuals are typically connected through a few mutual acquaintances, allowing for rapid information dissemination." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025)

"The concept of temporal graphs is useful in all the real-world problems that can be represented as a graph, where the nodes and edges of the graph may change over time. For example, temporal graphs are extensively applied in modeling social networks. By capturing the evolving relationships between individuals, temporal graphs enable a more accurate representation of social dynamics. This is particularly useful for predicting changes in friendships, community structures, and the information diffusion over time." (Aldo Marzullo et al, "Graph Machine Learning" 2nd Ed., 2025) 

🪸On Systems Thinking: On Function (1960-1969)

 

"The last, and most important, characteristic of systems is that they are automatic. Although the degree of automaticity may vary over a wide spectrum, there are no systems in which human beings perform all control functions; conversely, there will probably never be systems in which no human beings are involved." (Charles D Flagle et al, "Operations Research and Systems Engineering", 1960)

"To say a system is 'self-organizing' leaves open two quite different meanings. There is a first meaning that is simple and unobjectionable. This refers to the system that starts with its parts separate" (so that the behavior of each is independent of the others' states) and whose parts then act so that they change towards forming connections of some type. Such a system is 'self-organizing' in the sense that it changes from 'parts separated' to 'parts joined'. […] In general such systems can be more simply characterized as 'self-connecting', for the change from independence between the parts to conditionality can always be seen as some form of 'connection', even if it is as purely functional […] 'Organizing' […] may also mean 'changing from a bad organization to a good one' […] The system would be 'self-organizing' if a change were automatically made to the feedback, changing it from positive to negative; then the whole would have changed from a bad organization to a good." (W Ross Ashby, "Principles of the self-organizing system", 1962)

"A system has order, flowing from point to point. If something dams that flow, order collapses. The untrained might miss that collapse until it was too late. That's why the highest function of ecology is the understanding of consequences." (Frank Herbert, "Dune", 1965)

"From a pessimistic viewpoint, it can be stated that there is no good general way of structuring a system. However, from an optimistic point of view one can say that a number of good ways of structuring systems exist and that some are better than others for any particular system. In this and the following sections, there will be a presentation of a number of structuring approaches that have merit and have been employed successfully, including functional structuring, equipment structuring, and use of various coordinate systems." (Harold Chestnut, "Systems Engineering Tools", 1965)

"The process of formulating and structuring a system are important and creative, since they provide and organize the information, which each system. establishes the number of objectives and the balance between them which will be optimized". Furthermore, they help identify and define the system parts. Furthermore, they help identify and define the system parts which make up its 'diverse, specialized structures and subfunctions'." (Harold Chestnut, "Systems Engineering Tools", 1965)

"The Systems engineering method recognizes each system is an integrated whole even though composed of diverse, specialized structures and sub-functions. It further recognizes that any system has a number of objectives and that the balance between them may differ widely from system to system. The methods seek to optimize the overall system functions according to the weighted objectives and to achieve maximum compatibility of its parts." (Harold Chestnut, "Systems Engineering Tools", 1965)

"The homeostatic principle does not apply literally to the functioning of all complex living systems, in that in counteracting entropy they move toward growth and expansion." (Daniel Katz, "The Social Psychology of Organizations", 1966)

"Traditional organizational theories have tended to view the human organization as a closed system. This tendency has led to a disregard of differing organizational environments and the nature of organizational dependency on environment. It has led also to an over-concentration on principles of internal organizational functioning, with consequent failure to develop and understand the processes of feedback which are essential to survival." (Daniel Katz, "The Social Psychology of Organizations", 1966)

"Despite two centuries of study, the integrals of general dynamical systems remain covered with darkness. To save the classical thermostatics, the practical success of which is shown by the wide use to which it has been put, we must find a way out. That is, we must find some mathematical connection between time averages of the functions of physical interest and the corresponding simple canonical averages." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Traditional organizational theories have tended to view the human organization as a closed system. This tendency has led to a disregard of differing organizational environments and the nature of organizational dependency on environment. It has led also to an over-concentration on principles of internal organizational functioning, with consequent failure to develop and understand the processes of feedback which are essential to survival." (Daniel Katz, "The Social Psychology of Organizations", 1966)

"The mathematical models for many physical systems have manifolds as the basic objects of study, upon which further structure may be defined to obtain whatever system is in question. The concept generalizes and includes the special cases of the cartesian line, plane, space, and the surfaces which are studied in advanced calculus. The theory of these spaces which generalizes to manifolds includes the ideas of differentiable functions, smooth curves, tangent vectors, and vector fields. However, the notions of distance between points and straight lines (or shortest paths) are not part of the idea of a manifold but arise as consequences of additional structure, which may or may not be assumed and in any case is not unique." (Richard L Bishop & Samuel I Goldberg, "Tensor Analysis on Manifolds", 1968)

"Perhaps the most important single characteristic of modern organizational cybernetics is this: That in addition to concern with the deleterious impacts of rigidly-imposed notions of what constitutes the application of good 'principles of organization and management' the organization is viewed as a subsystem of a larger system(s), and as comprised itself of functionally interdependent subsystems." (Richard F Ericson, "Organizational cybernetics and human values", 1969)

🪸On Systems Thinking: On Function (-1959)

"A state of equilibrium in a system does not mean, further, that the system is without tension. Systems can, on the contrary, also come to equilibrium in a state of tension" (e.g., a spring under tension or a container with gas under pressure).The occurrence of this sort of system, however, presupposes a certain firmness of boundaries and actual segregation of the system from its environment" (both of these in a functional, not a spatial, sense). If the different parts of the system are insufficiently cohesive to withstand the forces working toward displacement" (i.e., if the system shows insufficient internal firmness, if it is fluid), or if the system is not segregated from its environment by sufficiently firm walls but is open to its neighboring systems, stationary tensions cannot occur. Instead, there occurs a process in the direction of the forces, which encroaches upon the neighboring regions with diffusion of energy and which goes in the direction of an equilibrium at a lower level of tension in the total region. The presupposition for the existence of a stationary state of tension is thus a certain firmness of the system in question, whether this be its own inner firmness or the firmness of its walls." (Kurt Lewin, "A Dynamic Theory of Personality", 1935)

"An organization is a subordinate system of a specific larger system, the cooperative system, whose components are physical, biological, and personal systems. The relations with other organizations… are outside this specific cooperative system. Other organizations are a part of the social environment of the organization. It is for this reason I have used the phrase 'complex of organizations' rather than 'system'. Usually the most significant relationships of a unit organization are those with the specific cooperative system of which it is a part. It is this system which primarily and on the whole in most instances determines the chief conditions of the organization's existence." (Chester Barnard, "The Functions of the Executive The Functions of the Executive", 1938)

"The first implication of the principle of immanent change may be formulated as follows: As long as it exists and functions, any sociocultural system incessantly generates consequences which are not the results of the external factors to the system, but the consequences of the existence of the system and of its activities." (Pitirim A Sorokin, "Social and Cultural Dynamics" Vol. 4, 1937-1941)

"The first attempts to consider the behavior of so-called 'random neural nets' in a systematic way have led to a series of problems concerned with relations between the 'structure' and the 'function' of such nets. The 'structure' of a random net is not a clearly defined topological manifold such as could be used to describe a circuit with explicitly given connections. In a random neural net, one does not speak of 'this' neuron synapsing on 'that' one, but rather in terms of tendencies and probabilities associated with points or regions in the net." (Anatol Rapoport, "Cycle distributions in random nets", The Bulletin of Mathematical Biophysics 10(3), 1948)

"Systems engineering embraces every scientific and technical concept known, including economics, management, operations, maintenance, etc. It is the job of integrating an entire problem or problem to arrive at one overall answer, and the breaking down of this answer into defined units which are selected to function compatibly to achieve the specified objectives. [...] Instrument and control engineering is but one aspect of systems engineering - a vitally important and highly publicized aspect, because the ability to create automatic controls within overall systems has made it possible to achieve objectives never before attainable, While automatic controls are vital to systems which are to be controlled, every aspect of a system is essential. Systems engineering is unbiased, it demands only what is logically required. Control engineers have been the leaders in pulling together a systems approach in the various technologies." (Instrumentation Technology, 1957)

"The Systems Engineering method recognizes each system is an integrated whole even though composed of devices, specialized structures and sub-functions. It is further recognized that any system has a number of objectives and that the balance between them may differ widely from system to system. The methods seek to optimize the overall system function according to the weighted objectives and to achieve maximum capability of its parts." (Jack A Morton, "Integrating of Systems Engineering with Component Development", Electrical Manufacturing, 1959)

🦋On Chaos Theory: On Edge of Chaos

"Living systems exist in the solid regime near the edge of chaos, and natural selection achieves and sustains such a poised state." (Stuart Kauffman, "The Origins of Order: Self-organization and selection in evolution", 1993) 

"Complexity theory began with an interest on how order spring from chaos. According to complexity theory, adaption is most effective in systems that are only partially connected. The argument is that too much structure creates gridlock, while too little structure creates chaos. […] Consequently, the key to effective change is to stay poised on this edge of chaos. Complexity theory focuses managerial thinking on the interrelationships among different parts of an organization and on the trade-off of less control for greater adaptation." (Shona Brown, "Competing on the Edge, 1998)  

"The self-similarity of fractal structures implies that there is some redundancy because of the repetition of details at all scales. Even though some of these structures may appear to teeter on the edge of randomness, they actually represent complex systems at the interface of order and disorder. " (Edward Beltrami, "What is Random?: Chaos and Order in Mathematics and Life", 1999)

"The central proposition in [realistic thinking] is that human actions and interactions are processes, not systems, and the coherent patterning of those processes becomes what it becomes because of their intrinsic capacity, the intrinsic capacity of interaction and relationship, to form coherence. That emergent form is radically unpredictable, but it emerges in a controlled or patterned way because of the characteristic of relationship itself, creation and destruction in conditions at the edge of chaos." (Ralph D Stacey et al, "Complexity and Management: Fad or Radical Challenge to Systems Thinking?", 2000) 

"Networks are not en route from a random to an ordered state. Neither are they at the edge of randomness and chaos. Rather, the scale-free topology is evidence of organizing principles acting at each stage of the network formation process." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002) 

"Systems are thus seen by complexity as being ‘on the edge of chaos'. Order and chaos are in a kind of balance where the components are neither fully locked into place but yet do not fully dissolve into anarchy. chaos is not complete anarchic randomness but there is a kind of 'orderly disorder' present within all such dynamic systems." (John Urry, "Global Complexity", 2003) 

"Chaos cuts with two edges. We have seen how it is impossible to retrieve past history from current observations. We will now show that it is impossible to predict future states from the current observations." (Ivar Ekeland, "The Best of All Possible Worlds", 2006)

"Although the potential for chaos resides in every system, chaos, when it emerges, frequently stays within the bounds of its attractor(s): No point or pattern of points is ever repeated, but some form of patterning emerges, rather than randomness. Life scientists in different areas have noticed that life seems able to balance order and chaos at a place of balance known as the edge of chaos. Observations from both nature and artificial life suggest that the edge of chaos favors evolutionary adaptation." (Terry Cooke-Davies et al, "Exploring the Complexity of Projects", 2009) 

"Things evolve to evolve. Evolutionary processes are the linchpin of change. These processes of discovery represent a complexity of simple systems that flux in perpetual tension as they teeter at the edge of chaos. This whirlwind of emergence is responsible for the spontaneous order and higher, organized complexity so noticeable in biological evolution - one–celled critters beefing up to become multicellular organisms." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013) 

"Only at the edge of chaos can complex systems flourish. This threshold line, that edge between anarchy and frozen rigidity, is not a like a fence line, it is a fractal line; it possesses nonlinearity." (Stephen H Buhner, "Plant Intelligence and the Imaginal Realm: Beyond the Doors of Perception into the Dreaming of Earth", 2014) 

"Even more important is the way complex systems seem to strike a balance between the need for order and the imperative for change. Complex systems tend to locate themselves at a place we call 'the edge of chaos'. We imagine the edge of chaos as a place where there is enough innovation to keep a living system vibrant, and enough stability to keep it from collapsing into anarchy. It is a zone of conflict and upheaval, where the old and new are constantly at war. Finding the balance point must be a delicate matter - if a living system drifts too close, it risks falling over into incoherence and dissolution; but if the system moves too far away from the edge, it becomes rigid, frozen, totalitarian. Both conditions lead to extinction. […] Only at the edge of chaos can complex systems flourish. This threshold line, that edge between anarchy and frozen rigidity, is not a like a fence line, it is a fractal line; it possesses nonlinearity."(Stephen H Buhner, "Plant Intelligence and the Imaginal Realm: Beyond the Doors of Perception into the Dreaming of Earth", 2014) 

"To remedy chaotic situations requires a chaotic approach, one that is non-linear, constantly morphing, and continually sharpening its competitive edge with recurring feedback loops that build upon past experiences and lessons learned. Improvement cannot be sustained without reflection. Chaos arises from myriad sources that stem from two origins: internal chaos rising within you, and external chaos being imposed upon you by the environment. The result of this push/pull effect is the disequilibrium [...]." (Jeff Boss, "Navigating Chaos: How to Find Certainty in Uncertain Situations", 2015) 

𒇫On Topology: On Neighborhoods (1990-1999)

"Formally, a Cantor set is defined as a set that is totally disconnected, closed, and perfect. A totally disconnected set is a set that contains no intervals and therefore has no interior points. A closed set is one that contains all its boundary elements. (A boundary element is an element that contains elements both inside and outside the set in arbitrarily small neighborhoods.) A perfect set is a nonempty set that is equal to the set of its accumulation points. All three conditions are met by our middle-third - erasing construction, the original Cantor set." (Manfred Schroeder, "Fractals, Chaos, Power Laws Minutes from an Infinite Paradise", 1990)

"Differentiability of a function can be established by examining the behavior of the function in the immediate neighborhood of a single point a in its domain. Thus, all we need is coordinates in the vicinity of the point a. From this point of view, one might say that local coordinates have more essential qualities. However, if are not looking at individual surfaces, we cannot find a more general and universal notion than smoothness." (Kenji Ueno & Toshikazu Sunada, "A Mathematical Gift, III: The Interplay Between Topology, Functions, Geometry, and Algebra", Mathematical World Vol. 23, 1996)

"Continuous functions can move freely. Graphs of continuous functions can freely branch off at any place, whereas analytic functions coinciding in some neighborhood of a point P cannot branch outside of this neighborhood. Because of this property, continuous functions can mathematically represent wildly changing wind inside a typhoon or a gentle breeze." (Kenji Ueno & Toshikazu Sunada, "A Mathematical Gift, III: The Interplay Between Topology, Functions, Geometry, and Algebra", Mathematical World Vol. 23, 1996)

"Differentiability of a function can be established by examining the behavior of the function in the immediate neighborhood of a single point a in its domain. Thus, all we need is coordinates in the vicinity of the point a. From this point of view, one might say that local coordinates have more essential qualities. However, if are not looking at individual surfaces, we cannot find a more general and universal notion than smoothness." (Kenji Ueno & Toshikazu Sunada, "A Mathematical Gift, III: The Interplay Between Topology, Functions, Geometry, and Algebra", Mathematical World Vol. 23, 1996)

"Similarly to the graphs of continuous functions, graphs of differentiable (smooth) functions which coincide in a neighborhood of a point P can branch off outside of the neighborhood. Because of this property, differentiable functions can represent smoothly changing natural phenomena." (Kenji Ueno & Toshikazu Sunada, "A Mathematical Gift, III: The Interplay Between Topology, Functions, Geometry, and Algebra", Mathematical World Vol. 23, 1996)