Mental Models LXIII (Limitations VIII)

"Beliefs are generalizations about the past projected onto the present and future to shape it in the image of the past. [...] When we generalize from incomplete or unrepresentative experience, we form mental models that make the wrong predictions, but because beliefs act as self-fulfilling prophecies it is hard to find out, because we are less open to counter examples." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)

"People’s mental models are apt to be deficient in a number of ways, perhaps including contradictory, erroneous, and unnecessary concepts. As designers, it is our duty to develop systems and instructional materials that aid users to develop more coherent, useable mental models. As teachers, it is our duty to develop conceptual models that will aid the learner to develop adequate and appropriate mental models. And as scientists who are interested in studying people’s mental models, we must develop appropriate experimental methods and discard our hopes of finding neat, elegant mental models, but instead learn to understand the messy, sloppy, incomplete, and indistinct structures that people actually have." (Donald A Norman, "Some Observations on Mental Models" [in "Mental Models", Ed(s). Dedre Gentner & Albert L Stevens], 1983)

"To begin with, we must understand that any mindset consists of mental models, or concepts, that influence our interpretation of situations and predispose us to certain responses. These models, which are replete with beliefs and assumptions, thus strongly determine the way we understand the world and act in it. The irony is, they become so ingrained in us, as tendencies and predispositions, that we seldom pay attention to them." (Stephen G Haines, "The Manager's Pocket Guide to Strategic and Business Planning", 1998)

"Short-term memory can hold 7 ± 2 chunks of information at once. This puts a rather sharp limit on the effective size and complexity of a causal map. Presenting a complex causal map all at once makes it hard to see the loops, understand which are important, or understand how they generate the dynamics. Resist the temptation to put all the loops you and your clients have identified into a single comprehensive diagram." (John D Sterman, "Business Dynamics Systems Thinking and Modeling for a Complex World", 2000)

"Our mental maps are often not terribly accurate, based as they are on our own selective experience, our knowledge and ignorance, and the information and misinformation we gain from others; nevertheless, these are the maps we depend on every day." (Peter Turchi, "Maps of the Imagination: The writer as cartographer", 2004)

"The most serious problem in applied ethics, or at least in business ethics, is not that we frame experiences; it is not that these mental models are incomplete, sometimes biased, and surely parochial. The larger problem is that most of us either individually or as managers do not realize that we are framing, disregarding data, ignoring counterevidence, or not taking into account other points of view." (Patricia H Werhane "A Place for Philosophers in Applied Ethics and the Role of Moral Reasoning in Moral Imagination", Business Ethics Quarterly 16 (3), 2007)

"Although good ethical decision-making requires us carefully to take into account as much relevant information as is available to us, we have good reason to think that we commonly fall well short of this standard – either by overlooking relevant facts completely or by underestimating their significance. The mental models we employ can contribute to this problem. As we have explained, mental models frame our experiences in ways that both aid and hinder our perceptions. They enable us to focus selectively on ethically relevant matters. By their very nature, they provide incomplete perspectives, resulting in bounded awareness and bounded ethicality. Insofar as our mental modeling practices result in unwarranted partiality, or even ethical blindness, the desired reflective process is distorted. This distortion is aggravated by the fact that our mental models can have this distorting effect without our consciously realizing it. Thus, although we cannot do without mental models, they leave us all vulnerable to blindness and, insofar as we are unaware of this, self-deception." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)

"Mental models serve to conceptualize, focus and shape our experiences, but in so doing, they sometimes cause us to ignore data and occlude critical reflection that might be relevant or, indeed, necessary to practical decision-making. [...] distorting mental models are the foundation

or underpinning of many of the impediments to effective ethical decision-making." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience",  2013)

"We identify and analyze distorting mental models that constitute experience in a manner that occludes the moral dimension of situations from view, thereby thwarting the first step of ethical decision-making. Examples include an unexamined moral self-image, viewing oneself as merely a bystander, and an exaggerated conception of self-sufficiency. These mental models, we argue, generate blind spots to ethics, in the sense that they limit our ability to see facts that are right before our eyes – sometimes quite literally, as in the many examples of managers and employees who see unethical behavior take place in front of them, but do not recognize it as such." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience",  2013)

Robert L Flood - Collected Quotes

"In general, we seem to associate complexity with anything we find difficult to understand." (Robert L Flood, "Complexity: a definition by construction of a conceptual framework", Systems Research and Behavioral Science, 1987)

"A systems description of a situation is: an assembly of elements related in an organized whole. An element may be anything that is discernible by a noun or a noun phrase that all informed observers would agree exists. An element must normally be capable of behavior such that it has some significant property(ies) that may change. A relationship can be said to exist between A and B if the behavior of either is influenced by the other." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Any subject area with 'science' in its title strongly implies a distinct branch of systematic and well-formulated knowledge and the pursuit of principles for achieving this, suggesting that a science should have a clearly recorded and coherent historical development." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Cybernetics, although not ignoring formal networks, suggests that an informal communications structure will also be present such that complex conversations at a number of levels between two or more individuals exist." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"In cybernetics a system is normally described as a black box whereby the whole of a system's generative mechanisms are lumped into a single transfer function (TF). This acts on an input to produce an output. To ensure that the output is monitored, so that a system may remain homeostatic (the critical variables remain within acceptable limits) or attain a new steady state (according to input decisions, say), the output of the TF is brought back into its input where the difference between the desired and actual levels is identified. This is known as feedback." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Man's attempts to control, service, and/ or design very complex situations have, however, often been fraught with disaster. A major contributory factor has been the unwitting adoption of piecemeal thinking, which sees only parts of a situation and its generative mechanisms. Additionally, it has been suggested that nonrational thinking sees only the extremes (the simple 'solutions' ) of any range of problem solutions. The net result of these factors is that situations exhibit counterintuitive behavior; outcomes of situations are rarely as we expect, but this is not an intrinsic property of situations; rather, it is largely caused by neglect of, or lack of respect being paid to, the nature and complexity of  a situation under investigation." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Negative feedback is associated with seeking defined objectives via control parameters; and positive feedback is either contained replication and growth or uncontained and unstable growth, which may lead to structural changes or death." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Nonlinear systems (the graph of at least one relationship displays some curved feature) are notoriously more difficult to comprehend than linear systems, that is, they are more complex. Consequently they are also more difficult to control. This is exemplified by the volumes of elegant mathematics that have been developed in the search for optimal control of linear systems." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Organized simplicity occurs where a small number of significant factors and a large number of insignificant factors appear initially to be complex, but on investigation display hidden simplicity." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Synergy is a term that is also used to describe the emergence of unexpected and interesting properties." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Systems thinking is a framework of thought that helps us to deal with complex things in a holistic way. The formalization of (giving an explicit, definite, and conventional form to) this thinking is what we have termed systems theory." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"The activities of a system are thought of as processes occurring in a structure. Structure defines the way in which the elements are related to each other, providing the supporting framework in which the processes occur." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"The concept of entropy relates to the tendency of things to move toward greater disorder, or disorganization. […] The second law of thermodynamics expresses precisely the same concept. This states that heat dissipates from a central source and the energy becomes degraded, although total energy remains constant (the first law of thermodynamics). Entropy suggests that organisms, organizations, societies, machines, and so on, will rapidly deteriorate into disorder and "death." The reason they do not is because animate things can self-organize and inanimate things may be serviced by man. These are negentropic activities which require energy. Energy, however, can be made available only by further degradation. Ultimately, therefore, entropy wins the day and the attempts to create order can seem rather a daunting task in the entropic scheme of things. Holding back entropy, however, is another of the challenging tasks for the systems scientist." (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"The state of development of mathematical theory in relation to some attributes of complexity is a clear measure of our ability/inability to deal with that attribute […]" (Robert L Flood & Ewart R Carson, "Dealing with Complexity: An introduction to the theory and application of systems", 1988)

"Different methodologies express different rationalities stemming from alternative theoretical positions which they reflect. These alternative positions must be respected, and methodologies and their appropriate theoretical underpinnings developed in partnership. (Robert L Flood, "Creative Problem Solving", 1991) 

"In the modern systems approach, the concept "system" is used not to refer to things in the world but to a particular way of organising our thoughts about the world." (Robert L Flood, "Creative Problem Solving", 1991)

On Randomness VI (Systems II)

"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necessarily so) to their motion and dynamics. They are liable, for all that, to instabilities chaos, as commonly interpreted of chaotic form, where nowadays, is remote from the random. Chaos is a peculiar situation in which the trajectories of a system, taken in the traditional sense, fail to converge as they approach their limit cycles or 'attractors' or 'equilibria'. Instead, they diverge, due to an increase, of indefinite magnitude, in amplification or gain." (Gordon Pask, "Different Kinds of Cybernetics", 1992)

"Entropy [...] is the amount of disorder or randomness present in any system. All non-living systems tend toward disorder; left alone they will eventually lose all motion and degenerate into an inert mass. When this permanent stage is reached and no events occur, maximum entropy is attained. A living system can, for a finite time, avert this unalterable process by importing energy from its environment. It is then said to create negentropy, something which is characteristic of all kinds of life." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"For the study of the topology of the interactions of a complex system it is of central importance to have proper random null models of networks, i.e., models of how a graph arises from a random process. Such models are needed for comparison with real world data. When analyzing the structure of real world networks, the null hypothesis shall always be that the link structure is due to chance alone. This null hypothesis may only be rejected if the link structure found differs significantly from an expectation value obtained from a random model. Any deviation from the random null model must be explained by non-random processes." (Jörg Reichardt, "Structure in Complex Networks", 2009)

"[...] a high degree of unpredictability is associated with erratic trajectories. This not only because they look random but mostly because infinitesimally small uncertainties on the initial state of the system grow very quickly - actually exponentially fast. In real world, this error amplification translates into our inability to predict the system behavior from the unavoidable imperfect knowledge of its initial state." (Massimo Cencini et al, "Chaos: From Simple Models to Complex Systems", 2010)

"Chaos is a phenomenon encountered in science and mathematics wherein a deterministic (rule-based) system behaves unpredictably. That is, a system which is governed by fixed, precise rules, nevertheless behaves in a way which is, for all practical purposes, unpredictable in the long run. The mathematical use of the word 'chaos' does not align well with its more common usage to indicate lawlessness or the complete absence of order. On the contrary, mathematically chaotic systems are, in a sense, perfectly ordered, despite their apparent randomness. This seems like nonsense, but it is not." (David P Feldman, "Chaos and Fractals: An Elementary Introduction", 2012)

"Systems subjected to randomness - and unpredictability - build a mechanism beyond the robust to opportunistically reinvent themselves each generation, with a continuous change of population and species." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)

"When some systems are stuck in a dangerous impasse, randomness and only randomness can unlock them and set them free. You can see here that absence of randomness equals guaranteed death. The idea of injecting random noise into a system to improve its functioning has been applied across fields. By a mechanism called stochastic resonance, adding random noise to the background makes you hear the sounds (say, music) with more accuracy." (Nassim N Taleb, "Antifragile: Things that gain from disorder", 2012)

"A system in which a few things interacting produce tremendously divergent behavior; deterministic chaos; it looks random but its not." (Christopher Langton)

On Randomness XIX (Chaos II)

"The chaos theory will require scientists in all fields to, develop sophisticated mathematical skills, so that they will be able to better recognize the meanings of results. Mathematics has expanded the field of fractals to help describe and explain the shapeless, asymmetrical find randomness of the natural environment." (Theoni Pappas, "More Joy of Mathematics: Exploring mathematical insights & concepts", 1991)

"Chaos demonstrates that deterministic causes can have random effects […] There's a similar surprise regarding symmetry: symmetric causes can have asymmetric effects. […] This paradox, that symmetry can get lost between cause and effect, is called symmetry-breaking. […] From the smallest scales to the largest, many of nature's patterns are a result of broken symmetry; […]" (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"Systems, acting dynamically, produce (and incidentally, reproduce) their own boundaries, as structures which are complementary (necessarily so) to their motion and dynamics. They are liable, for all that, to instabilities chaos, as commonly interpreted of chaotic form, where nowadays, is remote from the random. Chaos is a peculiar situation in which the trajectories of a system, taken in the traditional sense, fail to converge as they approach their limit cycles or 'attractors' or 'equilibria'. Instead, they diverge, due to an increase, of indefinite magnitude, in amplification or gain." (Gordon Pask, "Different Kinds of Cybernetics", 1992)

"Often, we use the word random loosely to describe something that is disordered, irregular, patternless, or unpredictable. We link it with chance, probability, luck, and coincidence. However, when we examine what we mean by random in various contexts, ambiguities and uncertainties inevitably arise. Tackling the subtleties of randomness allows us to go to the root of what we can understand of the universe we inhabit and helps us to define the limits of what we can know with certainty." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"Randomness, chaos, uncertainty, and chance are all a part of our lives. They reside at the ill-defined boundaries between what we know, what we can know, and what is beyond our knowing. They make life interesting." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"There are only patterns, patterns on top of patterns, patterns that affect other patterns. Patterns hidden by patterns. Patterns within patterns. If you watch close, history does nothing but repeat itself. What we call chaos is just patterns we haven't recognized. What we call random is just patterns we can't decipher. what we can't understand we call nonsense. What we can't read we call gibberish. There is no free will. There are no variables." (Chuck Palahniuk, "Survivor", 1999)

"Heat is the energy of random chaotic motion, and entropy is the amount of hidden microscopic information." (Leonard Susskind, "The Black Hole War", 2008)

"Chaos is impatient. It's random. And above all it's selfish. It tears down everything just for the sake of change, feeding on itself in constant hunger. But Chaos can also be appealing. It tempts you to believe that nothing matters except what you want." (Rick Riordan, "The Throne of Fire", 2011)

"A system in which a few things interacting produce tremendously divergent behavior; deterministic chaos; it looks random but its not." (Chris Langton)

On Automata II

"It bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what a tiny piece of space-time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed and the laws will turn out to be simple, like the checker board with all its apparent complexities." (Richard P Feynman, "The Character of Physical Law", 1965)

"Perhaps the most exciting implication [of CA representation of biological phenomena] is the possibility that life had its origin in the vicinity of a phase transition and that evolution reflects the process by which life has gained local control over a successively greater number of environmental parameters affecting its ability to maintain itself at a critical balance point between order and chaos." ( Chris G Langton, "Computation at the Edge of Chaos: Phase Transitions and Emergent Computation", Physica D (42), 1990)

"Cellular automata are now being used to model varied physical phenomena normally modelled by wave equations, fluid dynamics, Ising models, etc. We hypothesize that there will be found a single cellular automaton rule that models all of microscopic physics; and models it exactly." (Edward Fredkin, "Nonlinear Phenomena", Physica D (45), 1990)

"Over and over again we will see the same kind of thing: that even though the underlying rules for a system are simple, and even though the system is started from simple initial conditions, the behavior that the system shows can nevertheless be highly complex." (Stephen Wolfram, "A New Kind of Science", 2002)

"Cellular Automata (CA) are discrete, spatially explicit extended dynamic systems composed of adjacent cells characterized by an internal state whose value belongs to a finite set. The updating of these states is made simultaneously according to a common local transition rule involving only a neighborhood of each cell." (Ramon Alonso-Sanz, "Cellular Automata with Memory", 2009) 

"Cellular automata are dynamical systems that are discrete in space, time, and value. A state of a cellular automaton is a spatial array of discrete cells, each containing a value chosen from a finite alphabet. The state space for a cellular automaton is the set of all such configurations." (Burton Voorhees, "Additive Cellular Automata", 2009) 

"Cellular automata (CA) are idealizations of physical systems in which both space and time are assumed to be discrete and each of the interacting units can have only a finite number of discrete states." (Andreas Schadschneider et al, "Vehicular Traffic II: The Nagel–Schreckenberg Model" , 2011)

"Discrete dynamic systems that evolve in space and time. A cellular automaton is composed of a set of discrete elements – the cells – connected with other cells of the automaton, and in each time unit each cell receives information about the current state of the cells to which it is connected. The cellular automaton evolve according a transition rule that specifies the current possible states of each cell as a function of the preceding state of the cell and the states of the connected cells." (Francesc S. Beltran et al, "A Language Shift Simulation Based on Cellular Automata", 2011)

"Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogenous, simple units, the atoms or cells. [...] Secondly, CA are abstract: they can be specified in purely mathematical terms and physical structures can implement them. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems." (Francesco Berto & Jacopo Tagliabue, "Cellular Automata", Stanford Encyclopedia of Philosophy, 2012) [source]

"One of the unique features of typical CA [ cellular automata] models is that time, space, and states of cells are all discrete. Because of such discreteness, the number of all possible state-transition functions is finite, i.e., there are only a finite number of “universes” possible in a given CA setting. Moreover, if the space is finite, all possible configurations of the entire system are also enumerable. This means that, for reasonably small CA settings, one can conduct an exhaustive search of the entire rule space or phase space to study the properties of all the 'parallel universes'." (Hiroki Sayama, "Introduction to the Modeling and Analysis of Complex Systems", 2015)

Joseph Weizenbaum - Collected Quotes

"A higher-level formal language is an abstract machine." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation", 1976)

"A theory is, of course, not merely any grammatically correct text that uses a set of terms somehow symbolically related to reality. It is a systematic aggregate of statements of laws. Its content, its very value as theory, lies at least as much in the structure of the interconnections that relate its laws to one another, as in the laws themselves." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"Computers make possible an entirely new relationship between theories and models. I have already said that theories are texts. Texts are written in a language. Computer languages are languages too, and theories may be written in them. Indeed, for the present purpose we need not restrict our attention to machine languages or even to the kinds of 'higher-level' languages we have discussed. We may include all languages, specifically also natural languages, that computers may be able to interpret. The point is precisely that computers do interpret texts given to them, in other words, that texts determine computers' behavior. Theories written in the form of computer programs are ordinary theories as seen from one point of view." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"Machines, when they operate properly, are not merely law abiding; they are embodiments of law. To say that a specific machine is 'operating properly' is to assert that it is an embodiment of a law we know and wish to apply. We expect an ordinary desk calculator, for example, to be an embodiment of the laws of arithmetic we all know." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"Man is not a machine, [...] although man most certainly processes information, he does not necessarily process it in the way computers do. Computers and men are not species of the same genus. [...] No other organism, and certainly no computer, can be made to confront genuine human problems in human terms. [...] However much intelligence computers may attain, now or in the future, theirs must always be an intelligence alien to genuine human problems and concerns." (Joesph Weizenbaum, Computer Power and Human Reason: From Judgment to Calculation, 1976)

"Programming systems can, of course, be built without plan and without knowledge, let alone understanding, of the deep structural issues involved, just as houses, cities, systems of dams, and national economic policies can be similarly hacked together. As a system so constructed begins to get large, however, it also becomes increasingly unstable. When one of its subfunctions fails in an unanticipated way, it may be patched until the manifest trouble disappears. But since there is no general theory of the whole system, the system itself can be only a more or less chaotic aggregate of subsystems whose influence on one another's behavior is discoverable only piecemeal and by experiment. The hacker spends part of his time at the console piling new subsystems onto the structure he has already built - he calls them 'new features' - and the rest of his time in attempts to account for the way in which substructures already in place misbehave. That is what he and the computer converse about." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"The aim of the model is of course not to reproduce reality in all its complexity. It is rather to capture in a vivid, often formal, way what is essential to understanding some aspect of its structure or behavior." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"The computer programmer is a creator of universes for which he alone is the lawgiver. No playwright, no stage director, no emperor, however powerful, has ever exercised such absolute authority to arrange a stage or field of battle and to command such unswervingly dutiful actors or troops." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"The connection between a model and a theory is that a model satisfies a theory; that is, a model obeys those laws of behavior that a corresponding theory explicitly states or which may be derived from it. [...] Computers make possible an entirely new relationship between theories and models. [...] A theory written in the form of a computer program is [...] both a theory and, when placed on a computer and run, a model to which the theory applies." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

"There is a distinction between physically embodied machines, whose ultimate function is to transduce energy or deliver power, and abstract machines. i.e., machines that exist only as ideas. The laws which the former embody must be a subset of the laws that govern the real world. The laws that govern the behavior of abstract machines are not necessarily so constrained. One may, for example, design an abstract machine whose internal signals are propagated among its components at speeds greater than the speed of light, in clear violation of physical law. The fact that such a machine cannot actually be built does not prohibit the exploration of its behavior." (Joseph Weizenbaum, "Computer power and human reason: From judgment to calculation" , 1976)

Machines XI (Life vs. Machine II)

"The moral universe is so closely linked to the physical universe that it is scarcely likely that they are not one and the same machine." (Denis Diderot, "Eléments de Physiologie", 1875)

"Thanks to the psycho-physical reversibility, we can materialize the act of creation. Undoubtedly, the inventive machine has not yet been created, but we can see its creation soon." (Stefan Odobleja, "Consonant Psychology", 1938)

"In any case there is an intense modern interest in machines that imitate life. The great difference between magic and the scientific imitation of life is that where the former is content to copy external appearance, the latter is concerned more with performance and behavior." (William G Walter," An imitation of life", 1950) 

"We are always looking for metaphors in which to express our ideas of life, for our language is inadequate for all its complexities. Life is a labyrinth.[...] Life is a machine.[...] Life is a laboratory.[...] It is but a metaphor. When we speak of ultimate things we can, maybe, speak only in metaphors. Life is a dance, a very elaborate and complex dance [...]." (Charles Singer, "A Short History of Scientific Ideas to 1900", 1959)

"The machine rules. Human life is rigorously controlled by it, dominated by the terribly precise will of mechanisms. These creatures of man are exacting. They are now reacting on their creators, making them like themselves. They want well-trained humans; they are gradually wiping out the differences between men, fitting them into their own orderly functioning, into the uniformity of their own regimes. They are thus shaping humanity for their own use, almost in their own image." (Paul A Valéry, "Fairy Tales for Computers", 1969)

"The environment makes up a huge, enormously complex living machine that forms a thin dynamic layer on the earth’s surface, and every human activity depends on the integrity and the proper functioning of this machine. Without the photosynthetic activity of green plants, there would be no oxygen for our engines, smelters, and furnaces, let alone support for human and animal life. Without the action of the plants, animals, and microorganisms that live in them, we could have no pure water in our lakes and rivers. Without the biological processes that have gone on in the soil for thousands of years, we could have neither food crops, oil, nor coal. This machine is our biological capital, the basic apparatus on which our total productivity depends. If we destroy it, our most advanced technology will become useless and any economic and political system that depends on it will founder. The environmental crisis is a signal of this approaching catastrophe." (Barry Commoner, "The Closing Circle: Nature, Man & Technology", 1971)

"In his emotional involvement with the machine, the engineer cannot help but feel at times that he has come face to face with a strange but potent form of life." (Samuel C Florman, "The Existential Pleasures of Engineering", 1976)

"Life, a watery, carbon-based macromolecular system, is reproducing autopoeisis. The autopoetic view of life is circular. Life is a metabolic machine which not only reproduces but fi ercely stores and uses information in order to resist breaking down." (Lynn Margulis & Dorion Sagan, "Microcosmos", 1986)

"On balance, the cartesian metaphor of organism as machine has proved to be a good idea. Ideas do not have to be correct in order to be good; its only necessary that, if they do fail, they do so in an interesting way." (Robert Rosen)

Systems Thinking V

"[Systems thinking is] A new way to view and mentally frame what we see in the world; a worldview and way of thinking whereby we see the entity or unit first as a whole, with its fit and relationship to its environment as primary concerns." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"The beauty of this [systems thinking] mindset is that its mental models are based on natural laws, principles of interrelationship, and interdependence found in all living systems. They give us a new view of ourselves and our many systems, from the tiniest cell to the entire earth; and as our organizations are included in that great range, they help us define organizational problems as systems problems, so we can respond in more productive ways. The systems thinking mindset is a new orientation to life. In many ways it also operates as a worldview - an overall perspective on, and understanding of, the world." (Stephen G Haines, "The Managers Pocket Guide to Systems Thinking & Learning", 1998)

"As a meta-discipline, systems science will transfer its content from discipline to discipline and address problems beyond conventional reductionist boundaries. Generalists, qualified to manage today’s problem better than the specialist, could be fostered. With these intentions, systems thinking and systems science should not replace but add, complement and integrate those aspects that seem not to be adequately treated by traditional science." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"Systems thinking expands the focus of the observer, whereas analytical thinking reduces it. In other words, analysis looks into things, synthesis looks out of them. This attitude of systems thinking is often called expansionism, an alternative to classic reductionism. Whereas analytical thinking concentrates on static and structural properties, systems thinking concentrates on the function and behaviour of whole systems. Analysis gives description and knowledge; systems thinking gives explanation and understanding." (Lars Skyttner, "General Systems Theory: Ideas and Applications", 2001)

"System Thinking is a common concept for understanding how causal relationships and feedbacks work in an everyday problem. Understanding a cause and an effect enables us to analyse, sort out and explain how changes come about both temporarily and spatially in common problems. This is referred to as mental modelling, i.e. to explicitly map the understanding of the problem and making it transparent and visible for others through Causal Loop Diagrams (CLD)." (Hördur V Haraldsson, "Introduction to System Thinking and Causal Loop Diagrams", 2004)

"[systems thinking is]  thinking holistically and conscientiously about the world by focusing on the interaction of the parts and their influence within and over the system." (Kambiz E Maani, "Systems Thinking and the Internet from Independence to Interdependence", Encyclopedia of Information Science and Technology, Second Edition, 2009)

"Systems thinking, in contrast, focuses on how the thing being studied interacts with the other constituents of the system - a set of elements that interact to produce behaviour - of which it is a part. This means that instead of isolating smaller and smaller parts of the system being studied, systems thinking works by expanding its view to take into account larger and larger numbers of interactions as an issue is being studied. This results in sometimes strikingly different conclusions than those generated by traditional forms of analysis, especially when what is being studied is dynamically complex or has a great deal of feedback from other sources, internal or external. Systems thinking allows people to make their understanding of social systems explicit and improve them in the same way that people can use engineering principles to make explicit and improve their understanding of mechanical systems." (Raed M Al-Qirem & Saad G Yaseen, "Modelling a Small Firm in Jordan Using System Dynamics" [in "Handbook of Research on Discrete Event Simulation Environments: Technologies and Applications"], 2010)

"Understanding interdependency requires a way of thinking different from analysis. It requires systems thinking. And analytical thinking and systems thinking are quite distinct. [...] Systems thinking is the art of simplifying complexity. It is about seeing through chaos, managing interdependency, and understanding choice. We see the world as increasingly more complex and chaotic because we use inadequate concepts to explain it. When we understand something, we no longer see it as chaotic or complex." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture", 2011)

"Systems thinking focuses on optimizing for the whole, looking at the overall flow of work, identifying what the largest bottleneck is today, and eliminating it." (Matthew Skelton & Manuel Pais, "Team Topologies: Organizing Business and Technology Teams for Fast Flow", 2019)

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Mental Models LXII

"A mental model is a collection of 'connected' autonomous objects. Running  a mental model corresponds to modifying the parameters of the model by propagating information using the internal rules and specified topology. Running a mental model can also occur when autonomous objects change state. For us the definition of state is distinct from the current parameter values of an object. A state change consists of the replacement of one set of behavior rules with another." (Michael D Williams et al, "Human Reasoning About a Simple Physical System", [in "Mental Models", Ed(s). Dedre Gentner & Albert L Stevens], 1983)

"Central to this conception of mental models is the notion of autonomous objects. An autonomous object is a mental object with an explicit representation of state, an explicit representation of its topological connections to other objects, and a set of internal parameters. Associated with each autonomous object is a set of rules which modify its parameters and thus specify its behavior." (Michael D Williams et al, "Human Reasoning About a Simple Physical System", [in "Mental Models", Ed(s). Dedre Gentner & Albert L Stevens], 1983)

"In the consideration of mental models we need really consider four different things: the target system, the conceputal model of that target system, the user’s mental model of the target system, and the scientist's conceptualization of that mental model. The system that the person is learning or using is, by definition, the target system. A conceptual model is invented to provide an appropriate representation of the target system, appropriate in the sense of being accurate, consistent, and complete." (Donald A Norman, "Some Observations on Mental Models" [in "Mental Models", Ed(s). Dedre Gentner & Albert L Stevens], 1983)

"The purpose of a mental model is to allow the person to understand and to anticipate the behavior of a physical system. This means that the model must have predictive power, either by applying rules of inference or by procedural derivation (in whatever manner these properties may be realized in a person); in other words, it should be possible for people to ' run' their models mentally. This means that the conceptual mental model must also include a model of the relevant human information processing and knowledge structures that make it possible for the person to use a mental model to predict and understand the physical system." (Donald A Norman, "Some Observations on Mental Models" [in "Mental Models"], Ed(s). Dedre Gentner & Albert L Stevens], 1983)

"From a functional point of view, mental models can be described as symbolic structures which permit people: to generate descriptions of the purpose of a system, to generate descriptions of the architecture of a system, to provide explanations of the state of a system, to provide explanations of the functioning of a system, to make predictions of future states of a system." (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)

"Under the label 'cognitive maps', mental models have been conceived of as the mental representation of spatial aspects of the environment. A mental model, in this sense, comprises the topology of an area, including relevant districts, landmarks, and paths. [...] Under the label 'naive physics', mental models have been conceived of as the mental representation of natural or technical systems. A mental model, in this sense, comprises the effective determinants, true or not, of the functioning of a physical system. [...] Under the label 'model based reasoning', the mental models notion is featured in yet another area of cognitive science - deductive reasoning. In contrast to the commonly held view that logical competence depends on formal rules of deduction, it has been argued that reasoning is a semantic process based on the manipulation of mental models. [...] Finally, under terms like 'discourse model', 'situation model', or 'scenario', mental models have been conceived of as the mental representation of a verbal description of some real or fictional state of affairs. The role of mental models in the comprehension of discourse is discussed in more detail below." (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)

"A mental model is an internal representation with analogical relations to its referential object, so that local and temporal aspects of the object are preserved. It comes somewhat close to the mental images people report having in their minds whilst processing information. The great advantage of the notion of mental models, however, is its ability to include the notion of a partner model and the notion of a situation model. Thus, mental models can build a bridge to the other two dimensions of communication, namely interaction and situation." (Gert Rickheit et al, "The concept of communicative competence" [in "Handbook of Communication Competence"], 2008)

"Because all mental models or mindsets are incomplete, we can engage in second-order studies, evaluations, judgments, and assessments about our own and other operative mental models. Of course this is highly complex since the act of reflection is itself a further of framing or reframing." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)

"Mental models bind our awareness within a particular scaffold and then selectively can filter the content we subsequently receive. Through recalibration using revised mental models, we argue, we cultivate strategies anew, creating new habits, and galvanizing more intentional and evolved mental models. This recalibration often entails developing a strong sense of self and self-worth, realizing that each of us has a range of moral choices that may deviate from those in authority, and moral imagination." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)

"These framing perspectives or mental models construe the data of our experiences, and it is the construed data that we call 'facts'. What we often call reality, or the world, is constructed or socially construed in certain ways such that one cannot get at the source of the data except through these construals." (Patricia H Werhane et al, "Obstacles to Ethical: Decision-Making Mental Models, Milgram and the Problem of Obedience", 2013)

On Fractals I

"Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently." (Benoît Mandelbrot, "The Fractal Geometry of Nature", 1982)

"I coined fractal from the Latin adjective fractus. The corresponding Latin verb frangere means 'to break': to create irregular fragments [...] how appropriate for our needs!" (Benoît Mandelbrot, "The Fractal Geometry of Nature", 1982)

"The chaos theory will require scientists in all fields to, develop sophisticated mathematical skills, so that they will be able to better recognize the meanings of results. Mathematics has expanded the field of fractals to help describe and explain the shapeless, asymmetrical find randomness of the natural environment." (Theoni Pappas, "More Joy of Mathematics: Exploring mathematical insights & concepts", 1991)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"I believe that scientific knowledge has fractal properties; that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think, is the secret of the Universe." (Isaac Asimov, "A Way of Thinking", The Magazine of Fantasy and Science Fiction, 1994)

"It is time to employ fractal geometry and its associated subjects of chaos and nonlinear dynamics to study systems engineering methodology (SEM). [...] Fractal geometry and chaos theory can convey a new level of understanding to systems engineering and make it more effective." (Arthur D Hall, "The fractal architecture of the systems engineering method", "Systems, Man and Cybernetics", Vol. 28 (4), 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)

"In plain English, fractal geometry is the geometry of the irregular, the geometry of nature, and, in general, fractals are characterized by infinite detail, infinite length, and the absence of smoothness or derivative." (Philip Tetlow, "The Web’s Awake: An Introduction to the Field of Web Science and the Concept of Web Life", 2007)

"The economy is a nonlinear fractal system, where the smallest scales are linked to the largest, and the decisions of the central bank are affected by the gut instincts of the people on the street." (David Orrell, "The Other Side Of The Coin", 2008)

"Geometric pattern repeated at progressively smaller scales, where each iteration is about a reproduction of the image to produce completely irregular shapes and surfaces that can not be represented by classical geometry. Fractals are generally self-similar (each section looks at all) and are not subordinated to a specific scale. They are used especially in the digital modeling of irregular patterns and structures in nature." (Mauro Chiarella, "Folds and Refolds: Space Generation, Shapes, and Complex Components", 2016)

On Synergy I

 "Synergy is the only word in our language that means behavior of whole systems unpredicted by the separately observed behaviors of any of the system's separate parts or any subassembly of the system's parts." (R Buckminster Fuller, "Operating Manual for Spaceship Earth", 1963)

"Synergy means behavior of whole systems unpredicted by the behavior of their parts taken separately." (R Buckminster Fuller, "Synergetics: Explorations in the Geometry of Thinking", 1975)

"There is a multilayering of global networks in the key strategic activities that structure and destructure the planet. When these multilayered networks overlap in some node, when there is a node that belongs to different networks, two major consequences follow. First, economies of synergy between these different networks take place in that node: between financial markets and media businesses; or between academic research and technology development and innovation; between politics and media." (Manuel Castells, "The Rise of the Network Society", 1996)

"With the growing interest in complex adaptive systems, artificial life, swarms and simulated societies, the concept of “collective intelligence” is coming more and more to the fore. The basic idea is that a group of individuals (e. g. people, insects, robots, or software agents) can be smart in a way that none of its members is. Complex, apparently intelligent behavior may emerge from the synergy created by simple interactions between individuals that follow simple rules." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)

"Systems thinking means the ability to see the synergy of the whole rather than just the separate elements of a system and to learn to reinforce or change whole system patterns. Many people have been trained to solve problems by breaking a complex system, such as an organization, into discrete parts and working to make each part perform as well as possible. However, the success of each piece does not add up to the success of the whole. to the success of the whole. In fact, sometimes changing one part to make it better actually makes the whole system function less effectively." (Richard L Daft, "The Leadership Experience", 2002)

"Self-organization can be seen as a spontaneous coordination of the interactions between the components of the system, so as to maximize their synergy. This requires the propagation and processing of information, as different components perceive different aspects of the situation, while their shared goal requires this information to be integrated. The resulting process is characterized by distributed cognition: different components participate in different ways to the overall gathering and processing of information, thus collectively solving the problems posed by any perceived deviation between the present situation and the desired situation." (Carlos Gershenson & Francis Heylighen, "How can we think the complex?", 2004)

"Synergy is the combined action that occurs when people work together to create new alternatives and solutions. In addition, the greatest opportunity for synergy occurs when people have different viewpoints, because the differences present new opportunities. The essence of synergy is to value and respect differences and take advantage of them to build on strengths and compensate for weaknesses." (Richard L Daft, "The Leadership Experience" 4th Ed., 2008)

"Synergy occurs when organizational parts interact to produce a joint effect that is greater than the sum of the parts acting alone. As a result the organization may attain a special advantage with respect to cost, market power, technology, or employee." (Richard L Daft, "The Leadership Experience" 4th Ed., 2008)

"In short, synergy is the consequence of the energy expended in creating order. It is locked up in the viable system created, be it an organism or a social system. It is at the level of the system. It is not discernible at the level of the system. It is not discernible at the level of the system's components. Whenever the system is dismembered to examine its components, this binding energy dissipates." (J-C Spender, "Organizational Knowledge, Collective Practice and Penrose Rents", 2009)

"Synergy is defined as the surplus gained by working together. A task which couldn’t be fulfilled by one individual, can be completed by the work of different individuals together. To maximize synergy, first, the initial task is divided into different sub-tasks. Different agents perform different tasks, which is called division of labor. An end product of one work is used for another work, which is called workflow. Finally, everything needs to be put together. We call this aggregation. This isn’t as linear as it looks. At every step in the process it can happen that a task is divided into sub tasks or aggregated with other tasks." (Evo Busseniers, "Self-organization versus hierarchical organization", [thesis] 2018)

Complex Systems VII

"A complex system is a system formed out of many components whose behavior is emergent, that is, the behavior of the system cannot be simply inferred from the behavior of its components. The amount of information necessary to describe the behavior of such a system is a measure of its complexity." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"Strategy in complex systems must resemble strategy in board games. You develop a small and useful tree of options that is continuously revised based on the arrangement of pieces and the actions of your opponent. It is critical to keep the number of options open. It is important to develop a theory of what kinds of options you want to have open." (John H Holland, [presentation] 2000)

"Abstract formulations of simply stated concrete ideas are often the result of efforts to create idealized models of complex systems. The models are 'idealized' in the sense that they retain only the most fundamental properties of the original systems. The vocabulary is chosen to be as inclusive as possible so that research into the model reveals facts about a wide variety of similar systems. Unfortunately, it is often the case that over time the connection between a model and the systems on which it was based is lost, and the interested reader is faced with something that looks as if it were created to be deliberately complicated - deliberately confusing - but the original intention was just the opposite. Often, the model was devised to be simpler and more transparent than any of the systems on which it was based." (John Tabak, "Beyond Geometry: A new mathematics of space and form", 2011)

[complex system:] "A system whose intricacy impedes the forecasting of its behaviour." (Valentina M Ghinea, "Modelling and Simulation of the Need for Harmonizing the European Higher Education Systems", Handbook of Research on Trends in European Higher Education Convergence, 2014)

"The problem of complexity is at the heart of mankind's inability to predict future events with any accuracy. Complexity science has demonstrated that the more factors found within a complex system, the more chances of unpredictable behavior. And without predictability, any meaningful control is nearly impossible. Obviously, this means that you cannot control what you cannot predict. The ability ever to predict long-term events is a pipedream. Mankind has little to do with changing climate; complexity does." (Lawrence K Samuels, "The Real Science Behind Changing Climate", 2014)

"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)

[complex system:] "The occurrence of new phenomena generated unpredictably by the interaction of simple rules and individual mechanisms that are in constant flux and interaction. Emergence suggests something novel is perpetually emerging at a systems/global level as the world and environment constantly shifts and changes at a mechanistic/local level." (Kathy Sanford & Tim Hopper, "Digital Media in the Classroom: Emergent Perspectives for 21st Century Learners", Handbook of Research on Digital Media and Creative Technologies, 2015)

"A system characterized by the number of the elements that constitute it, and by the nature of the interactions between these elements." (Manuela Piscitelli, "Application of Complexity Theory in Representation of the City", Handbook of Research on Chaos and Complexity Theory in the Social Sciences, 2016)

"A complex system means a system whose perceived complicated behaviors can be attributed to one or more of the following characteristics: large number of element, large number of relationships among elements, non-linear and discontinuous relationship, and uncertain characteristics of elements." (Chunfang Zhou, "Fostering Creative Problem Solvers in Higher Education: A Response to Complexity of Societies", Handbook of Research on Creative Problem-Solving Skill Development in Higher Education, 2017)

[complex system:] "System made up of many interconnected elements on various levels; interactions on lower levels give rise to events on higher levels." (Naomi Thompson & Joshua Danish, "Designing BioSim: Playfully Encouraging Systems Thinking in Young Children", Handbook of Research on Serious Games for Educational Applications, 2017)

Complex Systems V

"Complexity is the characteristic property of complicated systems we don’t understand immediately. It is the amount of difficulties we face while trying to understand it. In this sense, complexity resides largely in the eye of the beholder - someone who is familiar with s.th. often sees less complexity than someone who is less familiar with it. [...] A complex system is created by evolutionary processes. There are multiple pathways by which a system can evolve. Many complex systems are similar, but each instance of a system is unique." (Jochen Fromm, The Emergence of Complexity, 2004)

"In complexity thinking the darkness principle is covered by the concept of incompressibility [...] The concept of incompressibility suggests that the best representation of a complex system is the system itself and that any representation other than the system itself will necessarily misrepresent certain aspects of the original system." (Kurt Richardson, "Systems theory and complexity: Part 1", Emergence: Complexity & Organization Vol.6 (3), 2004)

"The basic concept of complexity theory is that systems show patterns of organization without organizer (autonomous or self-organization). Simple local interactions of many mutually interacting parts can lead to emergence of complex global structures. […] Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or 'punctuations' of all sizes. In the critical state, events which would otherwise be uncoupled became correlated." (Jochen Fromm, "The Emergence of Complexity", 2004)

"Complexity arises when emergent system-level phenomena are characterized by patterns in time or a given state space that have neither too much nor too little form. Neither in stasis nor changing randomly, these emergent phenomena are interesting, due to the coupling of individual and global behaviours as well as the difficulties they pose for prediction. Broad patterns of system behaviour may be predictable, but the system's specific path through a space of possible states is not." (Steve Maguire et al, "Complexity Science and Organization Studies", 2006)

"Thus, nonlinearity can be understood as the effect of a causal loop, where effects or outputs are fed back into the causes or inputs of the process. Complex systems are characterized by networks of such causal loops. In a complex, the interdependencies are such that a component A will affect a component B, but B will in general also affect A, directly or indirectly.  A single feedback loop can be positive or negative. A positive feedback will amplify any variation in A, making it grow exponentially. The result is that the tiniest, microscopic difference between initial states can grow into macroscopically observable distinctions." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"The butterfly effect demonstrates that complex dynamical systems are highly responsive and interconnected webs of feedback loops. It reminds us that we live in a highly interconnected world. Thus our actions within an organization can lead to a range of unpredicted responses and unexpected outcomes. This seriously calls into doubt the wisdom of believing that a major organizational change intervention will necessarily achieve its pre-planned and highly desired outcomes. Small changes in the social, technological, political, ecological or economic conditions can have major implications over time for organizations, communities, societies and even nations." (Elizabeth McMillan, "Complexity, Management and the Dynamics of Change: Challenges for practice", 2008)

"[a complex system is] a system in which large networks of components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation via learning or evolution." (Melanie Mitchell, "Complexity: A Guided Tour", 2009)

"A typical complex system consists of a vast number of identical copies of several generic processes, which are operating and interacting only locally or with a limited number of not necessary close neighbours. There is no global leader or controller associated to such systems and the resulting behaviour is usually very complex." (Jirí Kroc & Peter M A Sloot, "Complex Systems Modeling by Cellular Automata", Encyclopedia of Artificial Intelligence, 2009)

Complex Systems III

"Complexity must be grown from simple systems that already work." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"Even though these complex systems differ in detail, the question of coherence under change is the central enigma for each." (John H Holland," Hidden Order: How Adaptation Builds Complexity", 1995)

"By irreducibly complex I mean a single system composed of several well-matched, interacting parts that contribute to the basic function, wherein the removal of any one of the parts causes the system to effectively cease functioning. An irreducibly complex system cannot be produced directly (that is, by continuously improving the initial function, which continues to work by the same mechanism) by slight, successive modification of a precursor, system, because any precursors to an irreducibly complex system that is missing a part is by definition nonfunctional." (Michael Behe, "Darwin’s Black Box", 1996)

"A dictionary definition of the word ‘complex’ is: ‘consisting of interconnected or interwoven parts’ […] Loosely speaking, the complexity of a system is the amount of information needed in order to describe it. The complexity depends on the level of detail required in the description. A more formal definition can be understood in a simple way. If we have a system that could have many possible states, but we would like to specify which state it is actually in, then the number of binary digits (bits) we need to specify this particular state is related to the number of states that are possible." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"When the behavior of the system depends on the behavior of the parts, the complexity of the whole must involve a description of the parts, thus it is large. The smaller the parts that must be described to describe the behavior of the whole, the larger the complexity of the entire system. […] A complex system is a system formed out of many components whose behavior is emergent, that is, the behavior of the system cannot be simply inferred from the behavior of its components." (Yaneer Bar-Yamm, "Dynamics of Complexity", 1997)

"Complex systems operate under conditions far from equilibrium. Complex systems need a constant flow of energy to change, evolve and survive as complex entities. Equilibrium, symmetry and complete stability mean death. Just as the flow, of energy is necessary to fight entropy and maintain the complex structure of the system, society can only survive as a process. It is defined not by its origins or its goals, but by what it is doing." (Paul Cilliers,"Complexity and Postmodernism: Understanding Complex Systems", 1998)

"There is no over-arching theory of complexity that allows us to ignore the contingent aspects of complex systems. If something really is complex, it cannot by adequately described by means of a simple theory. Engaging with complexity entails engaging with specific complex systems. Despite this we can, at a very basic level, make general remarks concerning the conditions for complex behaviour and the dynamics of complex systems. Furthermore, I suggest that complex systems can be modelled." (Paul Cilliers," Complexity and Postmodernism", 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)

On Networks XI (Neural Networks II)

"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)

"The terms 'black box' and 'white box' are convenient and figurative expressions of not very well determined usage. I shall understand by a black box a piece of apparatus, such as four-terminal networks with two input and two output terminals, which performs a definite operation on the present and past of the input potential, but for which we do not necessarily have any information of the structure by which this operation is performed. On the other hand, a white box will be similar network in which we have built in the relation between input and output potentials in accordance with a definite structural plan for securing a previously determined input-output relation." (Norbert Wiener, "Cybernetics: Or Control and Communication in the Animal and the Machine", 1948)

"Neural nets have no central control in the classical sense. Processing is distributed over the network and the roles of the various components (or groups of components) change dynamically.  This does not preclude any part of the network from developing a regulating function, but that will be determined by the evolutionary needs of the system." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"Neural networks conserve the complexity of the systems they model because they have complex structures themselves. Neural networks encode information about their environment in a distributed form. […] Neural networks have the capacity to self-organise their internal structure." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"The internal structure of a connectionist network develops through a process of self-organisation, whereas rule-based systems have to search through pre-programmed options that define the structure largely in an a priori fashion. In this sense, learning is an implicit characteristic of neural networks. In rule-based systems, learning can only take place through explicitly formulated procedures." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems", 1998)

"An artificial neural network is a massive parallel distributed processor made up of simple processing units. It has the ability to learn from experiential knowledge expressed through interunit connections strengths, and can make such knowledge available for use." (Yorgos Goletsis et al, "Bankruptcy Prediction through Artificial Intelligence", 2009)

"ANN is a pattern matching technique that uses training data to build a model and uses the model to predict unknown samples. It consists of input, output, and hidden nodes and connections between nodes. The weights of the connections are iteratively adjusted in order to get an accurate model." (Indranil Bose, "Data Mining in Tourism", 2009)

"Just as they did thirty years ago, machine learning programs (including those with deep neural networks) operate almost entirely in an associational mode. They are driven by a stream of observations to which they attempt to fit a function, in much the same way that a statistician tries to fit a line to a collection of points. Deep neural networks have added many more layers to the complexity of the fitted function, but raw data still drives the fitting process. They continue to improve in accuracy as more data are fitted, but they do not benefit from the 'super-evolutionary speedup'."  (Judea Pearl & Dana Mackenzie, "The Book of Why: The new science of cause and effect", 2018)

"[a neural network is] a computing system made up of a number of simple, highly interconnected processing elements, which process information by their dynamic state response to external inputs." (Robert Hecht-Nielsen)

On Automata I

"Ninety-nine [students] out of a hundred are automata, careful to walk in prescribed paths, careful to follow the prescribed custom. This is not an accident but the result of substantial education, which, scientifically defined, is the subsumption of the individual." (William T Harris, "The Philosophy of Education", 1889)

"We are automata entirely controlled by the forces of the medium being tossed about like corks on the surface of the water, but mistaking the resultant of the impulses from the outside for free will. The movements and other actions we perform are always life preservative and tho seemingly quite independent from one another, we are connected by invisible links." (Nikola Tesla, "My Inventions", 1919)

"Besides electrical engineering theory of the transmission of messages, there is a larger field [cybernetics] which includes not only the study of language but the study of messages as a means of controlling machinery and society, the development of computing machines and other such automata, certain reflections upon psychology and the nervous system, and a tentative new theory of scientific method." (Norbert Wiener, "Cybernetics", 1948)

"Automata have begun to invade certain parts of mathematics too, particularly but not exclusively mathematical physics or applied mathematics. The natural systems (e.g., central nervous system) are of enormous complexity and it is clearly necessary first to subdivide what they represent into several parts that to a certain extent are independent, elementary units. The problem then consists of understanding how these elements are organized as a whole. It is the latter problem which is likely to attract those who have the background and tastes of the mathematician or a logician. With this attitude, he will be inclined to forget the origins and then, after the process of axiomatization is complete, concentrate on the mathematical aspects." (John Von Neumann, "The General and Logical Theory of Automata", 1951)

"A world of automata – of creatures that worked like machines – would hardly be worth creating." (Clive S Lewis, Mere Christianity, 1952)

"Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"Cellular automata are mathematical models for complex natural systems containing large numbers of simple identical components with local interactions. They consist of a lattice of sites, each with a finite set of possible values. The value of the sites evolve synchronously in discrete time steps according to identical rules. The value of a particular site is determined by the previous values of a neighbourhood of sites around it." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"Cellular automata may be considered as discrete dynamical systems. In almost all cases, cellular automaton evolution is irreversible. Trajectories in the configuration space for cellular automata therefore merge with time, and after many time steps, trajectories starting from almost all initial states become concentrated onto 'attractors'. These attractors typically contain only a very small fraction of possible states. Evolution to attractors from arbitrary initial states allows for 'self-organizing' behaviour, in which structure may evolve at large times from structureless initial states. The nature of the attractors determines the form and extent of such structures." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"Finite Nature is a hypothesis that ultimately every quantity of physics, including space and time, will turn out to be discrete and finite; that the amount of information in any small volume of space-time will be finite and equal to one of a small number of possibilities. [...] We take the position that Finite Nature implies that the basic substrate of physics operates in a manner similar to the workings of certain specialized computers called cellular automata." (Edward Fredkin, "A New Cosmogony", PhysComp ’92: Proceedings of the Workshop on Physics and Computation, 1993)

On Nonlinearity II

"Indeed, except for the very simplest physical systems, virtually everything and everybody in the world is caught up in a vast, nonlinear web of incentives and constraints and connections. The slightest change in one place causes tremors everywhere else. We can't help but disturb the universe, as T.S. Eliot almost said. The whole is almost always equal to a good deal more than the sum of its parts. And the mathematical expression of that property - to the extent that such systems can be described by mathematics at all - is a nonlinear equation: one whose graph is curvy." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"Today the network of relationships linking the human race to itself and to the rest of the biosphere is so complex that all aspects affect all others to an extraordinary degree. Someone should be studying the whole system, however crudely that has to be done, because no gluing together of partial studies of a complex nonlinear system can give a good idea of the behaviour of the whole." (Murray Gell-Mann, 1997)

"Much of the art of system dynamics modeling is discovering and representing the feedback processes, which, along with stock and flow structures, time delays, and nonlinearities, determine the dynamics of a system. […] the most complex behaviors usually arise from the interactions (feedbacks) among the components of the system, not from the complexity of the components themselves." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"The mental models people use to guide their decisions are dynamically deficient. […] people generally adopt an event-based, open-loop view of causality, ignore feedback processes, fail to appreciate time delays between action and response and in the reporting of information, do not understand stocks and flows and are insensitive to nonlinearities that may alter the strengths of different feedback loops as a system evolves." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Most physical processes in the real world are nonlinear. It is our abstraction of the real world that leads us to the use of linear systems in modeling these processes. These linear systems are simple, understandable, and, in many situations, provide acceptable simulations of the actual processes. Unfortunately, only the simplest of linear processes and only a very small fraction of the nonlinear having verifiable solutions can be modeled with linear systems theory. The bulk of the physical processes that we must address are, unfortunately, too complex to reduce to algorithmic form - linear or nonlinear. Most observable processes have only a small amount of information available with which to develop an algorithmic understanding. The vast majority of information that we have on most processes tends to be nonnumeric and nonalgorithmic. Most of the information is fuzzy and linguistic in form." (Timothy J Ross & W Jerry Parkinson, "Fuzzy Set Theory, Fuzzy Logic, and Fuzzy Systems", 2002)

"Swarm intelligence can be effective when applied to highly complicated problems with many nonlinear factors, although it is often less effective than the genetic algorithm approach [...]. Swarm intelligence is related to swarm optimization […]. As with swarm intelligence, there is some evidence that at least some of the time swarm optimization can produce solutions that are more robust than genetic algorithms. Robustness here is defined as a solution’s resistance to performance degradation when the underlying variables are changed. (Michael J North & Charles M Macal, Managing Business Complexity: Discovering Strategic Solutions with Agent-Based Modeling and Simulation, 2007)

"[…] our mental models fail to take into account the complications of the real world - at least those ways that one can see from a systems perspective. It is a warning list. Here is where hidden snags lie. You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long-term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays. You are likely to mistreat, misdesign, or misread systems if you don’t respect their properties of resilience, self-organization, and hierarchy." (Donella H Meadows, "Thinking in Systems: A Primer", 2008)

"You can’t navigate well in an interconnected, feedback-dominated world unless you take your eyes off short-term events and look for long term behavior and structure; unless you are aware of false boundaries and bounded rationality; unless you take into account limiting factors, nonlinearities and delays." (Donella H Meadow, "Thinking in Systems: A Primer", 2008)

"A network of many simple processors ('units' or 'neurons') that imitates a biological neural network. The units are connected by unidirectional communication channels, which carry numeric data. Neural networks can be trained to find nonlinear relationships in data, and are used in various applications such as robotics, speech recognition, signal processing, medical diagnosis, or power systems." (Adnan Khashman et al, "Voltage Instability Detection Using Neural Networks", 2009)

"Linearity is a reductionist’s dream, and nonlinearity can sometimes be a reductionist’s nightmare. Understanding the distinction between linearity and nonlinearity is very important and worthwhile." (Melanie Mitchell, "Complexity: A Guided Tour", 2009)

On Nonlinearity I

"In complex systems cause and effect are often not closely related in either time or space. The structure of a complex system is not a simple feedback loop where one system state dominates the behavior. The complex system has a multiplicity of interacting feedback loops. Its internal rates of flow are controlled by nonlinear relationships. The complex system is of high order, meaning that there are many system states (or levels). It usually contains positive-feedback loops describing growth processes as well as negative, goal-seeking loops. In the complex system the cause of a difficulty may lie far back in time from the symptoms, or in a completely different and remote part of the system. In fact, causes are usually found, not in prior events, but in the structure and policies of the system." (Jay Wright Forrester, "Urban dynamics", 1969)

"Self-organization can be defined as the spontaneous creation of a globally coherent pattern out of local interactions. Because of its distributed character, this organization tends to be robust, resisting perturbations. The dynamics of a self-organizing system is typically non-linear, because of circular or feedback relations between the components. Positive feedback leads to an explosive growth, which ends when all components have been absorbed into the new configuration, leaving the system in a stable, negative feedback state. Non-linear systems have in general several stable states, and this number tends to increase (bifurcate) as an increasing input of energy pushes the system farther from its thermodynamic equilibrium. " (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"[The] system may evolve through a whole succession of transitions leading to a hierarchy of more and more complex and organized states. Such transitions can arise in nonlinear systems that are maintained far from equilibrium: that is, beyond a certain critical threshold the steady-state regime become unstable and the system evolves into a new configuration." (Ilya Prigogine, Gregoire Micolis & Agnes Babloyantz, "Thermodynamics of Evolution", Physics Today 25 (11), 1972)

"An artificial neural network is an information-processing system that has certain performance characteristics in common with biological neural networks. Artificial neural networks have been developed as generalizations of mathematical models of human cognition or neural biology, based on the assumptions that: 1. Information processing occurs at many simple elements called neurons. 2. Signals are passed between neurons over connection links. 3. Each connection link has an associated weight, which, in a typical neural net, multiplies the signal transmitted. 4. Each neuron applies an activation function (usually nonlinear) to its net input (sum of weighted input signals) to determine its output signal." (Laurene Fausett, "Fundamentals of Neural Networks", 1994)

"Symmetry breaking in psychology is governed by the nonlinear causality of complex systems (the 'butterfly effect'), which roughly means that a small cause can have a big effect. Tiny details of initial individual perspectives, but also cognitive prejudices, may 'enslave' the other modes and lead to one dominant view." (Klaus Mainzer, "Thinking in Complexity", 1994)

"[…] nonlinear interactions almost always make the behavior of the aggregate more complicated than would be predicted by summing or averaging."  (John H Holland," Hidden Order: How Adaptation Builds Complexity", 1995)

“[…] self-organization is the spontaneous emergence of new structures and new forms of behavior in open systems far from equilibrium, characterized by internal feedback loops and described mathematically by nonlinear equations.” (Fritjof  Capra, “The web of life: a new scientific understanding of living  systems”, 1996)

"Bounded rationality simultaneously constrains the complexity of our cognitive maps and our ability to use them to anticipate the system dynamics. Mental models in which the world is seen as a sequence of events and in which feedback, nonlinearity, time delays, and multiple consequences are lacking lead to poor performance when these elements of dynamic complexity are present." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"Even if our cognitive maps of causal structure were perfect, learning, especially double-loop learning, would still be difficult. To use a mental model to design a new strategy or organization we must make inferences about the consequences of decision rules that have never been tried and for which we have no data. To do so requires intuitive solution of high-order nonlinear differential equations, a task far exceeding human cognitive capabilities in all but the simplest systems."  (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"All forms of complex causation, and especially nonlinear transformations, admittedly stack the deck against prediction. Linear describes an outcome produced by one or more variables where the effect is additive. Any other interaction is nonlinear. This would include outcomes that involve step functions or phase transitions. The hard sciences routinely describe nonlinear phenomena. Making predictions about them becomes increasingly problematic when multiple variables are involved that have complex interactions. Some simple nonlinear systems can quickly become unpredictable when small variations in their inputs are introduced." (Richard N Lebow, "Forbidden Fruit: Counterfactuals and International Relations", 2010)

On Randomness XII (Chaos I)

"Chaos is but unperceived order; it is a word indicating the limitations of the human mind and the paucity of observational facts. The words ‘chaos’, ‘accidental’, ‘chance’, ‘unpredictable’ are conveniences behind which we hide our ignorance." (Harlow Shapley, "Of Stars and Men: Human Response to an Expanding Universe", 1958)

"The term ‘chaos’ currently has a variety of accepted meanings, but here we shall use it to mean deterministically, or nearly deterministically, governed behavior that nevertheless looks rather random. Upon closer inspection, chaotic behavior will generally appear more systematic, but not so much so that it will repeat itself at regular intervals, as do, for example, the oceanic tides." (Edward N Lorenz, "Chaos, spontaneous climatic variations and detection of the greenhouse effect", 1991)

"The term chaos is used in a specific sense where it is an inherently random pattern of behaviour generated by fixed inputs into deterministic (that is fixed) rules (relationships). The rules take the form of non-linear feedback loops. Although the specific path followed by the behaviour so generated is random and hence unpredictable in the long-term, it always has an underlying pattern to it, a 'hidden' pattern, a global pattern or rhythm. That pattern is self-similarity, that is a constant degree of variation, consistent variability, regular irregularity, or more precisely, a constant fractal dimension. Chaos is therefore order (a pattern) within disorder (random behaviour)." (Ralph D Stacey, "The Chaos Frontier: Creative Strategic Control for Business", 1991)

"In nonlinear systems - and the economy is most certainly nonlinear - chaos theory tells you that the slightest uncertainty in your knowledge of the initial conditions will often grow inexorably. After a while, your predictions are nonsense." (M Mitchell Waldrop, "Complexity: The Emerging Science at the Edge of Order and Chaos", 1992)

"Intriguingly, the mathematics of randomness, chaos, and order also furnishes what may be a vital escape from absolute certainty - an opportunity to exercise free will in a deterministic universe. Indeed, in the interplay of order and disorder that makes life interesting, we appear perpetually poised in a state of enticingly precarious perplexity. The universe is neither so crazy that we can’t understand it at all nor so predictable that there’s nothing left for us to discover." (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1997)

"When we look at the world around us, we find that we are not thrown into chaos and randomness but are part of a great order, a grand symphony of life. Every molecule in our body was once a part of previous bodies-living or nonliving-and will be a part of future bodies. In this sense, our body will not die but will live on, again and again, because life lives on. We share not only life's molecules but also its basic principles of organization with the rest of the living world. Arid since our mind, too, is embodied, our concepts and metaphors are embedded in the web of life together with our bodies and brains. We belong to the universe, we are at home in it, and this experience of belonging can make our lives profoundly meaningful." (Fritjof Capra, "The Hidden Connections", 2002)

"[…] we would like to observe that the butterfly effect lies at the root of many events which we call random. The final result of throwing a dice depends on the position of the hand throwing it, on the air resistance, on the base that the die falls on, and on many other factors. The result appears random because we are not able to take into account all of these factors with sufficient accuracy. Even the tiniest bump on the table and the most imperceptible move of the wrist affect the position in which the die finally lands. It would be reasonable to assume that chaos lies at the root of all random phenomena." (Iwo Białynicki-Birula & Iwona Białynicka-Birula, "Modeling Reality: How Computers Mirror Life", 2004) 

"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)

"Most systems in nature are inherently nonlinear and can only be described by nonlinear equations, which are difficult to solve in a closed form. Non-linear systems give rise to interesting phenomena such as chaos, complexity, emergence and self-organization. One of the characteristics of non-linear systems is that a small change in the initial conditions can give rise to complex and significant changes throughout the system." (Robert K Logan, "The Poetry of Physics and The Physics of Poetry", 2010)

"A system in which a few things interacting produce tremendously divergent behavior; deterministic chaos; it looks random but its not." (Christopher Langton)