On Nonlinearity VI

"Up until now most economists have concerned themselves with linear systems, not because of any belief that the facts were so simple, but rather because of the mathematical difficulties involved in nonlinear systems [... Linear systems are] mathematically simple, and exact solutions are known. But a high price is paid for this simplicity in terms of special assumptions which must be made." (Paul A Samuelson, "Foundations of Economic Analysis", 1966)

"Linear relationships are easy to think about: the more the merrier. Linear equations are solvable, which makes them suitable for textbooks. Linear systems have an important modular virtue: you can take them apart and put them together again - the pieces add up. Nonlinear systems generally cannot be solved and cannot be added together. [...] Nonlinearity means that the act of playing the game has a way of changing the rules. [...] That twisted changeability makes nonlinearity hard to calculate, but it also creates rich kinds of behavior that never occur in linear systems." (James Gleick, "Chaos: Making a New Science", 1987)

"Never in the annals of science and engineering has there been a phenomenon so ubiquitous‚ a paradigm so universal‚ or a discipline so multidisciplinary as that of chaos. Yet chaos represents only the tip of an awesome iceberg‚ for beneath it lies a much finer structure of immense complexity‚ a geometric labyrinth of endless convolutions‚ and a surreal landscape of enchanting beauty. The bedrock which anchors these local and global bifurcation terrains is the omnipresent nonlinearity that was once wantonly linearized by the engineers and applied scientists of yore‚ thereby forfeiting their only chance to grapple with reality." (Leon O Chua, "Editorial", International Journal of Bifurcation and Chaos, Vol. l (1), 1991) 

"It remains an unhappy fact that there is no best method for finding the solution to general nonlinear optimization problems. About the best general procedure yet devised is one that relies upon imbedding the original problem within a family of problems, and then developing relations linking one member of the family to another. If this can be done adroitly so that one family member is easily solvable, then these relations can be used to step forward from the solution of the easy problem to that of the original problem. This is the key idea underlying dynamic programming, the most flexible and powerful of all optimization methods." (John L Casti, "Five Golden Rules", 1995)

"When it comes to modeling processes that are manifestly governed by nonlinear relationships among the system components, we can appeal to the same general idea. Calculus tells us that we should expect most systems to be 'locally' flat; that is, locally linear. So a conservative modeler would try to extend the word 'local' to hold for the region of interest and would take this extension seriously until it was shown to be no longer valid." (John L Casti, "Five Golden Rules", 1995)

"A system at a bifurcation point, when pushed slightly, may begin to oscillate. Or the system may flutter around for a time and then revert to its normal, stable behavior. Or, alternatively it may move into chaos. Knowing a system within one range of circumstances may offer no clue as to how it will react in others. Nonlinear systems always hold surprises." (F David Peat, "From Certainty to Uncertainty", 2002)

"In a linear system a tiny push produces a small effect, so that cause and effect are always proportional to each other. If one plotted on a graph the cause against the effect, the result would be a straight line. In nonlinear systems, however, a small push may produce a small effect, a slightly larger push produces a proportionately larger effect, but increase that push by a hair’s breadth and suddenly the system does something radically different." (F David Peat, "From Certainty to Uncertainty", 2002)

"Complex systems are full of interdependencies - hard to detect - and nonlinear responses." (Nassim N Taleb, "Antifragile: Things That Gain from Disorder", 2012)

"Why are nonlinear systems so much harder to analyze than linear ones? The essential difference is that linear systems can be broken down into parts. Then each part can be solved separately and finally recombined to get the answer. This idea allows a fantastic simplification of complex problems, and underlies such methods as normal modes, Laplace transforms, superposition arguments, and Fourier analysis. In this sense, a linear system is precisely equal to the sum of its parts. But many things in nature don’t act this way. Whenever parts of a system interfere, or cooperate, or compete, there are nonlinear interactions going on. Most of everyday life is nonlinear, and the principle of superposition fails spectacularly." (Steven H Strogatz, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering", 2015)

On Syllogism I

"The Syllogism consists of propositions, propositions consist of words, words are symbols of notions. Therefore if the notions themselves (which is the root of the matter) are confused and over-hastily abstracted from the facts, there can be no firmness in the superstructure. Our only hope therefore lies in a true induction." (Francis Bacon, The New Organon, 1620)

"[…] mathematics is not, never was, and never will be, anything more than a particular kind of language, a sort of shorthand of thought and reasoning. The purpose of it is to cut across the complicated meanderings of long trains of reasoning with a bold rapidity that is unknown to the mediaeval slowness of the syllogisms expressed in our words." (Charles Nordmann, "Einstein and the Universe", 1922)

"Knowledge is ours only if, at the moment of need, it offers itself to the mind without syllogisms or demonstrations for which there is no time." (André Maurois, "Un Art de Vivre" ["The Art of Living"], 1939)

"A serious threat to the very life of science is implied in the assertion that mathematics is nothing but a system of conclusions drawn from definitions and postulates that must be consistent but otherwise may be created by the free will of the mathematician. If this description were accurate, mathematics could not attract any intelligent person. It would be a game with definitions, rules and syllogisms, without motivation or goal." (Richard Courant & Herbert Robbins, "What Is Mathematics?", 1941)

"The construction of hypotheses is a creative act of inspiration, intuition, invention; its essence is the vision of something new in familiar material. The process must be discussed in psychological, not logical, categories; studied in autobiographies and biographies, not treatises on scientific method; and promoted by maxim and example, not syllogism or theorem." (Milton Friedman, "Essays in Positive Economics", 1953)

"[…] the distinction between rigorous thinking and more vague ‘imaginings’; even in mathematics itself, all is not a question of rigor, but rather, at the start, of reasoned intuition and imagination, and, also, repeated guessing. After all, most thinking is a synthesis or juxtaposition of advances along a line of syllogisms - perhaps in a continuous and persistent ‘forward'’ movement, with searching, so to speak ‘sideways’, in directions which are not necessarily present from the very beginning and which I describe as ‘sending out exploratory patrols’ and trying alternative routes." (Stanislaw M Ulam, "Adventures of a Mathematician", 1976)

"Since mental models can take many forms and serve many purposes, their contents are very varied. They can contain nothing but tokens that represent individuals and identities between them, as in the sorts of models that are required for syllogistic reasoning. They can represent spatial relations between entities, and the temporal or causal relations between events. A rich imaginary model of the world can be used to compute the projective relations required for an image. Models have a content and form that fits them to their purpose, whether it be to explain, to predict, or to control." (Philip Johnson-Laird, "Mental models: Toward a cognitive science of language, inference, and consciousness", 1983)

"Whenever I have talked about mental models, audiences have readily grasped that a layout of concrete objects can be represented by an internal spatial array, that a syllogism can be represented by a model of individuals and identities between them, and that a physical process can be represented by a three-dimensional dynamic model. Many people, however, have been puzzled by the representation of abstract discourse; they cannot understand how terms denoting abstract entities, properties or relations can be similarly encoded, and therefore they argue that these terms can have only 'verbal' or propositional representations." (Philip Johnson-Laird, "Mental Models: Towards a Cognitive Science of Language, Inference and Consciousness", 1983)

"Formal logic and the logical syllogism encapsulate connectedness in reasoning." (Marshall McLuhan & Eric McLuhan, "Laws of Media: The New Science", 1988)

"Metaphorizing is a manner of thinking, not a property of thinking. It is a capacity of thought, not its quality. It represents a mental operation by which a previously existing entity is described in the characteristics of another one on the basis of some similarity or by reasoning. When we say that something is (like) something else, we have already performed a mental operation. This operation includes elements such as comparison, paralleling and shaping of the new image by ignoring its less satisfactory traits in order that this image obtains an aesthetic value. By this process, for an instant we invent a device, which serves as the pole vault for the comparison’s jump. Once the jump is made the pole vault is removed. This device could be a lightning-speed logical syllogism, or a momentary created term, which successfully merges the traits of the compared objects." (Ivan Mladenov, "Conceptualizing Metaphors: On Charles Peirce’s marginalia", 2006)

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)

On Coherence (-1949)

"Principles taken upon trust, consequences lamely deduced from them, want of coherence in the parts, and of evidence in the whole, these are every where to be met with in the systems of the most eminent philosophers, and seem to have drawn disgrace upon philosophy itself." (David Hume, "A Treatise of Human Nature", 1739-40)

"The critical mathematician has abandoned the search for truth. He no longer flatters himself that his propositions are or can be known to him or to any other human being to be true; and he contents himself with aiming at the correct, or the consistent. The distinction is not annulled nor even blurred by the reflection that consistency contains immanently a kind of truth. He is not absolutely certain, but he believes profoundly that it is possible to find various sets of a few propositions each such that the propositions of each set are compatible, that the propositions of each such set imply other propositions, and that the latter can be deduced from the former with certainty. That is to say, he believes that there are systems of coherent or consistent propositions, and he regards it his business to discover such systems. Any such system is a branch of mathematics." (Cassius J Keyser, Science, New Series, Vol. 35 (904), 1912)

"A system is said to be coherent if every fact in the system is related every other fact in the system by relations that are not merely conjunctive. A deductive system affords a good example of a coherent system." (Lizzie S Stebbing, "A modern introduction to logic", 1930)

"Even these humble objects reveal that our reality is not a mere collocation of elemental facts, but consists of units in which no part exists by itself, where each part points beyond itself and implies a larger whole. Facts and significance cease to be two concepts belonging to different realms, since a fact is always a fact in an intrinsically coherent whole. We could solve no problem of organization by solving it for each point separately, one after the other; the solution had to come for the whole. Thus we see how the problem of significance is closely bound up with the problem of the relation between the whole and its parts. It has been said: The whole is more than the sum of its parts. It is more correct to say that the whole is something else than the sum of its parts, because summing is a meaningless procedure, whereas the whole-part relationship is meaningful." (Kurt Koffka, "Principles of Gestalt Psychology", 1935)

"Statistics is a scientific discipline concerned with collection, analysis, and interpretation of data obtained from observation or experiment. The subject has a coherent structure based on the theory of Probability and includes many different procedures which contribute to research and development throughout the whole of Science and Technology." (Egon Pearson, 1936)

"[…] reality is a system, completely ordered and fully intelligible, with which thought in its advance is more and more identifying itself. We may look at the growth of knowledge […] as an attempt by our mind to return to union with things as they are in their ordered wholeness. […] and if we take this view, our notion of truth is marked out for us. Truth is the approximation of thought to reality […] Its measure is the distance thought has travelled […] toward that intelligible system […] The degree of truth of a particular proposition is to be judged in the first instance by its coherence with experience as a whole, ultimately by its coherence with that further whole, all comprehensive and fully articulated, in which thought can come to rest." (Brand Blanshard, "The Nature of Thought" Vol. II, 1939)

"It is difficult, however, to learn all these things from situations such as occur in everyday life. What we need is a series of abstract and quite impersonal situations to argue about in which one side is surely right and the other surely wrong. The best source of such situations for our purposes is geometry. Consequently we shall study geometric situations in order to get practice in straight thinking and logical argument, and in order to see how it is possible to arrange all the ideas associated with a given subject in a coherent, logical system that is free from contradictions. That is, we shall regard the proof of each proposition of geometry as an example of correct method in argumentation, and shall come to regard geometry as our ideal of an abstract logical system. Later, when we have acquired some skill in abstract reasoning, we shall try to see how much of this skill we can apply to problems from real life." (George D Birkhoff & Ralph Beately, "Basic Geometry", 1940)

"[…] there is probably less difference between the positions of a mathematician and of a physicist than is generally supposed, [...] the mathematician is in much more direct contact with reality. This may seem a paradox, since it is the physicist who deals with the subject-matter usually described as 'real', but [...] [a physicist] is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics." (Godfrey H Hardy, "A Mathematician's Apology", 1940)

"Induction is the process of discovering general laws by the observation and combination of particular instances. […] Induction tries to find regularity and coherence behind the observations. Its most conspicuous instruments are generalization, specialization, analogy. Tentative generalization starts from an effort to understand the observed facts; it is based on analogy, and tested by further special cases." (George Pólya, "How to solve it", 1945)

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 Mind: Mental Models LV

"To imagine - to form an image - we must have the numerous relations of things present to the mind, and see the objects in their actual order. In this we are of course greatly aided by the mass of organised experience, which allows us rapidly to estimate the relations of gravity or affinity just as we remember that fire burns and that heated bodies expand. But be the aid great or small, and the result victorious or disastrous, the imaginative process is always the same." (George H Lewes, "The Principles of Success in Literature", 1865)

"The degree in which each mind habitually substitutes signs for images will be, CETERIS PARIBUS [with other conditions remaining the same], the degree in which it is liable to error. This is not contradicted by the fact that mathematical, astronomical, and physical reasonings may, when complex, be carried on more successfully by the employment of signs; because in these cases the signs themselves accurately represent the abstractness of the relations. Such sciences deal only with relations, and not with objects; hence greater simplification ensures greater accuracy. But no sooner do we quit this sphere of abstractions to enter that of concrete things, than the use of symbols becomes a source of weakness. Vigorous and effective minds habitually deal with concrete images." (George H Lewes, "The Principles of Success in Literature", 1865)

"The steps to scientific as well as other knowledge consist in a series of logical fictions which are as legitimate as they are indispensable in the operations of thought, but whose relations to the phenomena whereof they are the partial and not unfrequently merely symbolical representations must never be lost sight of." (John Stallo, "The Concepts and Theories of Modern Physics", 1884)

"Myths and science fulfil a similar function: they both provide human beings with a representation of the world and of the forces that are supposed to govern it. They both fix the limits of what is considered as possible." (François Jacob, "The Possible and the Actual", 1982)

"Many people would accept that we do not really have knowledge of the world; we have knowledge only of our representations of the world. Yet we seem condemned by our consitution to treat these representations as if they were the world, for our everyday experience feels as if it were of a given and immediate world." (Francisco Varela, "The Embodied Mind", 1991)

"The seemingly stable scene you normally see is really a mental model that you construct - the eyes are actually darting all around, producing a retinal image as jerky as an amateur video, and some of what you thought you saw was instead filled in from memory." (William H Calvin, "How Brains Think", 1996) 

"[…] the 'reality' that we perceive is based on mental models in which things don't usually change their shapes or disappear, despite their changing appearances. We mainly react to what we expect - and tend to represent the things that we see as though they remain the same as we move atomic." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006)

"We all construct mental models that describe our various mental states, bodies of knowledge about our abilities, depictions of our acquaintances, and collections of stories about our pasts. Then, whenever we use our models of ourselves, we tend to use terms like conscious - when those reflections lead to choices we make, and we use unconscious or unintentional to describe those activities that we regard as beyond our control." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006)

"We solve easy problems in routine ways, scarcely thinking about how we accomplish these - but when our usual methods don't work, we start to 'reflect' on what went wrong and find ourselves to be switching around in a network of 'models', each of which purports to represent some facet or aspect of ourselves, so that we end representing ourselves with a loosely connected collection of images, models, and anecdotes." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006) 

"Why must those models be simplifications? Each model must help us to focus on only those aspects that matter in some particular context; that's what makes a map more useful to us than seeing the entire landscape that it depicts. The same applies to what we store in our minds. Consider how messy our minds would become if we filled them up with descriptions of things whose details had too little significance. So instead, we spend large parts of our lives at trying to tidy up our minds - selecting the portions we want to keep, suppressing others we'd like to forget, and refining the ones we're dissatisfied with." (Marvin Minsky, "The Emotion Machine: Commonsense thinking, artificial intelligence, and the future of the human mind", 2006)

Systems Thinking IV

"One of the strongest benefits of the systems thinking perspective is that it can help you learn to ask the right questions. This is an important first step toward understanding a problem. […] Much of the value of systems thinking comes from the different framework that it gives us for looking at problems in new ways." (Virginia Anderson & Lauren Johnson, "Systems Thinking Basics: From Concepts to Causal Loops", 1997)

"[...] information feedback about the real world not only alters our decisions within the context of existing frames and decision rules but also feeds back to alter our mental models. As our mental models change we change the structure of our systems, creating different decision rules and new strategies. The same information, processed and interpreted by a different decision rule, now yields a different decision. Altering the structure of our systems then alters their patterns of behavior. The development of systems thinking is a double-loop learning process in which we replace a reductionist, narrow, short-run, static view of the world with a holistic, broad, long-term, dynamic view and then redesign our policies and institutions accordingly." (John D Sterman, "Business dynamics: Systems thinking and modeling for a complex world", 2000)

"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)

"Deep change in mental models, or double-loop learning, arises when evidence not only alters our decisions within the context of existing frames, but also feeds back to alter our mental models. As our mental models change, we change the structure of our systems, creating different decision rules and new strategies. The same information, interpreted by a different model, now yields a different decision. Systems thinking is an iterative learning process in which we replace a reductionist, narrow, short-run, static view of the world with a holistic, broad, long-term, dynamic view, reinventing our policies and institutions accordingly." (John D Sterman, "Learning in and about complex systems", Systems Thinking Vol. 3 2003)

"There exists an alternative to reductionism for studying systems. This alternative is known as holism. Holism considers systems to be more than the sum of their parts. It is of course interested in the parts and particularly the networks of relationships between the parts, but primarily in terms of how they give rise to and sustain in existence the new entity that is the whole whether it be a river system, an automobile, a philosophical system or a quality system." (Michael C. Jackson, "Systems Thinking: Creative Holism for Manager", 2003) 

"Systems thinking is only an epistemology, a particular way of describing the world. It does not tell us what the world is. Hence, strictly speaking, we should never say of something in the world: ‘It is a system’, only: ‘It may be described as a system.’" (John Mingers, Realising" Systems Thinking: Knowledge and Action in Management Science", 2006)

"At a time when the world is more messy, more crowded, more interconnected, more interdependent, and more rapidly changing than ever before, the more ways of seeing, the better. The systems-thinking lens allows us to reclaim our intuition about whole systems and hone our abilities to understand parts, see interconnections, ask 'what-if' questions about possible future behaviors, and be creative and courageous about system redesign. (Donella H Meadows, "Thinking in Systems: A Primer", 2008)

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

"Systems thinking is a mental discipline and framework for seeing patterns and interrelationships. It is important to see organizational systems as a whole because of their complexity. Complexity can overwhelm managers, undermining confidence. When leaders can see the structures that underlie complex situations, they can facilitate improvement. But doing that requires a focus on the big picture." (Richard L Daft, "The Leadership Experience", 2008)  

"Holism [is] the art - in contrast with reductionism - of seeing a complex system as a whole. Holism knows the limits to its understanding; it acknowledges that the system has its wildness, its privacy, its own reasons, its defenses against invasive explanation." (David Fleming, "Lean Logic", 2016)

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Systems Thinking III

"Systems thinking is a discipline for seeing the 'structures' that underlie complex situations, and for discerning high from low leverage change. That is, by seeing wholes we learn how to foster health. To do so, systems thinking offers a language that begins by restructuring how we think." (Peter Senge, "The Fifth Discipline", 1990)

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

"Systems thinking is a framework for seeing interrelationships rather than things, for seeing patterns rather than static snapshots. It is a set of general principles spanning fields as diverse as physical and social sciences, engineering and management." (Peter Senge, "The Fifth Discipline", 1990) 

"Systems philosophy brings forth a reorganization of ways of thinking. It creates a new worldview, a new paradigm of perception and explanation, which is manifested in integration, holistic thinking, purpose-seeking, mutual causality, and process-focused inquiry.” (Béla H. Bánáthy, "Systems Design of Education”, 1991)

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

"In the new systems thinking, the metaphor of knowledge as a building is being replaced by that of the network. As we perceive reality as a network of relationships, our descriptions, too, form an interconnected network of concepts and models in which there are no foundations. For most scientists such a view of knowledge as a network with no firm foundations is extremely unsettling, and today it is by no means generally accepted. But as the network approach expands throughout the scientific community, the idea of knowledge as a network will undoubtedly find increasing acceptance." (Fritjof Capra," The Web of Life: a new scientific understanding of living systems", 1996)

"It [system dynamics] focuses on building system dynamics models with teams in order to enhance team learning, to foster consensus and to create commitment with a resulting decision […] System dynamics can be helpful to elicit and integrate mental models into a more holistic view of the problem and to explore the dynamics of this holistic view […] It must be understood that the ultimate goal of the intervention is not to build a system dynamics model. The system dynamics model is a means to achieve other ends […] putting people in a position to learn about a messy problem [...] create a shared social reality […] a shared understanding of the problem and potential solutions [...] to foster consensus within the team [..]" (Jac A M Vennix, "Group Model Building: Facilitating Team Learning Using System Dynamics", 1996)

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

"Systems thinking practices the exact opposite of this analytic approach. Systems thinking studies the organization as a whole in its interaction with its environment. Then, it works backwards to understand how each part of that whole works in relation to, and support of, the entire system’s objectives. Only then can the core strategies be formulated." (Stephen G Haines, "The Systems Thinking Approach to Strategic Planning and Management", 2000)

"Systems, and organizations as systems, can only be understood holistically. Try to understand the system and its environment first. Organizations are open systems and, as such, are viable only in interaction with and adaptation to the changing environment." (Stephen G Haines, "The Systems Thinking Approach to Strategic Planning and Management", 2000)

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🪷On Mind: Mental Models XL

"When the Soul wants to experience something she throws out an image in front of her and then steps into it." (Eckhart von Hochheim [aka Meister Eckhart] cca. 14th century)

"Materialism is the recognition of 'objects in themselves' , or outside the mind; ideas and sensations are copies of images of those objects." (Vladimir Lenin, "Materialism and Empirio-Criticism", 1908) 

"Images apparently occupy a curious position somewhere between the statements of language, which are intended to convey a meaning, and the things of nature, to which we only can give a meaning." (Ernst Gombrich, "Symbolic Images", 1972) 

 "When one analyzes the pre-conscious step to concepts, one always finds ideas which consist of 'symbolic images'. The first step to thinking is a painted vision of these inner pictures whose origin cannot be reduced only and firstly to the sensual perception but which are produced by an 'instinct to imagining' and which are re-produced by different individuals independently, i. e. collectively [...] But the archaic image is also the necessary predisposition and the source of a scientific attitude. To a total recognition belong also those images out of which have grown the rational concepts." (Wolfgang Pauli, [Letter to Markus Fierz] 1948) 

" The symbol is the tool which gives man his power, and it is the same tool whether the symbols are images or words, mathematical signs or mesons." (Jacob Bronowski, "The Reach of Imagination", 1967) 

"To imagine means to make images and to move them about inside one's head in new arrangements." (Jacob Bronowski, "The Reach of Imagination", 1967)

"These organizational processes result in our perceptions being structured into units corresponding to objects and properties of objects. It is these larger units that may be stored and later assembled into images that are experienced as quasi-pictorial, spatial entities resembling those evoked during perception itself [...] It is erroneous to equate image representations with mental photographs, since this would overlook the fact that images are composed from highly processed perceptual encodings." (Stephen Kosslyn, "Image and Mind", 1980) 

"Vision is a process that produces from images of the external world a description that is useful to the viewer and not cluttered with irrelevant information." (David Marr, "Vision", 1982)

"We are a people captivated by the power and romance of metaphor, forever seeking the invisible through the image of the visible." (Lewis H Lapham, "Waiting For The Barbarians", 1997) 

"But because of the way in which depictions represent, there is a correspondence between parts and spatial relations of the representation and those of the object; this structural mapping, which confers a type of resemblance, underlies the way images convey specific content. In this respect images are like pictures. Unlike words and symbols, depictions are not arbitrarily paired with what they represent." (Stephen Kosslyn et al," The Case for Mental Imagery", 2006)

From Parts to Wholes (1800-1849)

"In every moment of her duration Nature is one connected whole; in every moment each individual part must be what it is, because all the others are what they are; and you could not remove a single grain of sand from its place, without thereby, although perhaps imperceptibly to you, altering something throughout all parts of the immeasurable whole." (Johann G Fichte, "The Vocation of Man”, 1800)

"It is the destiny of our race to become united into one great body, thoroughly connected in all its parts, and possessed of similar culture. Nature, and even the passions and vices of Man, have from the beginning tended towards this end. A great part of the way towards it is already passed, and we may surely calculate that it will in time be reached." (Johann G Fichte, "The Vocation of Man", 1800)

"It is probable that what we call thought is not an actual being, but no more than the relation between certain parts of that infinitely varied mass, of which the rest of the universe is composed, and which ceases to exist as soon as those parts change their position with regard to each other." (Percy B Shelley, "On a Future State", 1815)

"Each of the parts of philosophy is a philosophical whole, a circle rounded and complete in itself. In each of these parts, however, the philosophical Idea is found in a particular specificality or medium. The single circle, because it is a real totality, bursts through the limits imposed by its special medium, and gives rise to a wider circle. The whole of philosophy in this way resembles a circle of circles. The Idea appears in each single circle, but, at the same time, the whole Idea is constituted by the system of these peculiar phases, and each is a necessary member of the organisation." (Georg W F Hegel, "Encyclopedia of the Philosophical Sciences", 1816)

"When the whole and the parts are seen at once, as mutually producing and explaining each other, as unity in multeity, there results shapeliness." (Samuel T Coleridge, "Letters", 1836)

"Science is nothing but the finding of analogy, identity, in the most remote parts." (Ralph W Emerson, 1837)

"So far we have studies how, for each commodity by itself, the law of demand in connection with the conditions of production of that commodity, determines the price of it and regulates the incomes of its producers. We considered as given and invariable the prices of other commodities and the incomes of other producers; but, in reality the economic system is a whole of which the parts are connected and react on each other. An increase in the incomes of the producers of commodity A will affect the demand for commodities Band C, etc., and the incomes of their producers, and, by its reaction will involve a change in the demand for A. It seems, therefore, as if, for a complete and rigorous solution of the problems relative to some parts of the economic system, it were indispensable to take the entire system into consideration. But this would surpass the powers of mathematical analysis and of our practical methods of calculation, even if the values of all the constants could be assigned to them numerically." (Antoine A Cournot, "Researches into the Mathematical Principles of the Theory of Wealth", 1838)

"The component parts of a vegetable or animal substance do not lose their mechanical and chemical properties as separate agents, when, by a peculiar mode of juxtaposition, they, as an aggregate whole, acquire physiological or vital properties in addition. Those bodies continue, as before, to obey mechanical and chemical laws, in so far as the operation of those laws is not counteracted by the new laws which govern them as organized beings. […] Though there are laws which, like those of chemistry and physiology, owe their existence to a breach of the principle of Composition of Causes, it does not follow that these peculiar, or, as they might be termed, heteropathic laws, are not capable of composition with one another." (John S Mill, "A System of Logic: Ratioconative and Inductive", 1843) [the heteropathic laws is synonymous with emergence]

From Parts to Wholes (1900-1909)

"And as the ideal in the whole of Nature moves in an infinite process toward an Absolute Perfection, we may say that art is in strict truth the apotheosis of Nature. Art is thus at once the exaltation of the natural toward its destined supernatural perfection, and the investiture of the Absolute Beauty with the reality of natural existence. Its work is consequently not a means to some higher end, but is itself a final aim; or, as we may otherwise say, art is its own end. It is not a mere recreation for man, a piece of by-play in human life, but is an essential mode of spiritual activity, the lack of which would be a falling short of the destination of man. It is itself part and parcel of man's eternal vocation." (George H Howison, "The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Idealism", 1901) 

"Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments." (David Hilbert, "Mathematical Problems", Bulletin American Mathematical Society Vol. 8, 1901-1902)

"For if society lacks the unity that derives from the fact that the relationships between its parts are exactly regulated, that unity resulting from the harmonious articulation of its various functions assured by effective discipline and if, in addition, society lacks the unity based upon the commitment of men's wills to a common objective, then it is no more than a pile of sand that the least jolt or the slightest puff will suffice to scatter.“ (Émile Durkheim, 1903)

"From that time, the universe has steadily become more complex and less reducible to a central control. With as much obstinacy as though it were human, it has insisted on expanding its parts; with as much elusiveness as though it were feminine, it has evaded the attempt to impose on it a single will. Modern science, like modern art, tends, in practice, to drop the dogma of organic unity. Some of the mediaeval habit of mind survives, but even that is said to be yielding before the daily evidence of increasing and extending complexity. The fault, then, was not in man, if he no longer looked at science or art as an organic whole or as the expression of unity. Unity turned itself into complexity, multiplicity, variety, and even contradiction." (Henry Adams, "Mont Saint Michel and Chartres", 1904)

"Reduced to their most pregnant difference, empiricism means the habit of explaining wholes by parts, and rationalism means the habit of explaining parts by wholes. Rationalism thus preserves affinities with monism, since wholeness goes with union, while empiricism inclines to pluralistic views. No philosophy can ever be anything but a summary sketch, a picture of the world in abridgment, a foreshortened bird's-eye view of the perspective of events. And the first thing to notice is this, that the only material we have at our disposal for making a picture of the whole world is supplied by the various portions of that world of which we have already had experience. We can invent no new forms of conception, applicable to the whole exclusively, and not suggested originally by the parts." (William James, "A Pluralistic Universe", 1908)

"A system is a whole which is composed of various parts. But it is not the same thing as an aggregate or heap. In an aggregate or heap, no essential relation exists between the units of which it is composed. In a heap of grain, or pile of stones, one may take away part without the other part being at all affected thereby. But in a system, each part has a fixed and necessary relation to the whole and to all the other parts. For this reason we may say that a building, or a peace of mechanisme, is a system. Each stone in the building, each wheel in the watch, plays a part, and is essential to the whole." (James E Creighton, "An Introductory Logic"‎, 1909)

From Parts to Wholes (1930-1939)

"Everything abstract is ultimately part of the concrete. Everything inanimate finally serves the living. That is why every activity dealing in abstraction stands in ultimate service to a living whole." (Edith Stein, "The Ethos of Woman's Professions", 1930)

"To apply the category of cause and effect means to find out which parts of nature stand in this relation. Similarly, to apply the gestalt category means to find out which parts of nature belong as parts to functional wholes, to discover their position in these wholes, their degree of relative independence, and the articulation of larger wholes into sub-wholes." (Kurt Koffka, 1931)

"Even these humble objects reveal that our reality is not a mere collocation of elemental facts, but consists of units in which no part exists by itself, where each part points beyond itself and implies a larger whole. Facts and significance cease to be two concepts belonging to different realms, since a fact is always a fact in an intrinsically coherent whole. We could solve no problem of organization by solving it for each point separately, one after the other; the solution had to come for the whole. Thus we see how the problem of significance is closely bound up with the problem of the relation between the whole and its parts. It has been said: The whole is more than the sum of its parts. It is more correct to say that the whole is something else than the sum of its parts, because summing is a meaningless procedure, whereas the whole-part relationship is meaningful." (Kurt Koffka, "Principles of Gestalt Psychology", 1935)

"Maximal knowledge of a total system does not necessarily include total knowledge of all its parts, not even when these are fully separated from each other and at the moment are not influencing each other at all. Thus it may be that some part of what one knows may pertain to relations […] between the two subsystems (we shall limit ourselves to two), as follows: if a particular measurement on the first system yields this result, then for a particular measurement on the second the valid expectation statistics are such and such; but if the measurement in question on the first system should have that result, then some other expectation holds for that one the second. […] In this way, any measurement process at all or, what amounts to the same, any variable at all of the second system can be tied to the not-yet-known value of any variable at all of the first, and of course vice versa also." (Erwin Schrödinger, "The Present Situation in Quantum Mechanics", 1935)

"The existence of finality within the organism is undeniable. Each part seems to know the present and future needs of the whole, and acts accordingly. The significance of time and space is not the same for our tissues as for our mind. The body perceives the remote as well as the near, the future as well as the present." (Alexis Carrel, 1935)

"[Gestalt:] a system whose parts are dynamically connected in such a way that a change of one part results in a change of all other parts." (Kurt Lewin, "Principles of topological psychology", 1936)

"The realist method starts with the whole in order to distinguish the parts." (Étienne Gilson, "Methodical Realism", 1936)

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

"I see the tasks of social sciences to discover what kinds of order actually do exist in the whole range of the behavior of human beings; what kind of functional relationships between different parts of culture exist in space and over time, and what functionally more useful kinds of order can be created." (Robert S Lynd, "Knowledge of What?", 1939)

"The failure of the social sciences to think through and to integrate their several responsibilities for the common problem of relating the analysis of parts to the analysis of the whole constitutes one of the major lags crippling their utility as human tools of knowledge." (Robert S Lynd, "Knowledge of What?", 1939)

"The whole, though larger than any of its parts, does not necessarily obscure their separate identities." (William O Douglas, "Judicial Opinions", 1939)

From Parts to Wholes (1950-1959)

"For scientific endeavor is a natural whole the parts of which mutually support one another in a way which, to be sure, no one can anticipate." (Albert Einstein, "Out of My Later Years", 1950)

"What the worker needs is to see the plant as if he were a manager. Only thus can he see his part, from his part he can reach the whole. This ‘seeing’ is not a matter of information, training courses, conducted plant tours, or similar devices. What is needed is the actual experience of the whole in and through the individual's work." (Peter F Drucker, "The New Society", 1950)

"Every organism represents a system, by which term we mean a complex of elements in mutual interaction. From this obvious statement the limitations of the analytical and summative conceptions must follow. First, it is impossible to resolve the phenomena of life completely into elementary units; for each individual part and each individual event depends not only on conditions within itself, but also to a greater or lesser extent on the conditions within the whole, or within superordinate units of which it is a part. Hence the behavior of an isolated part is, in general, different from its behavior within the context of the whole. [...] Secondly, the actual whole shows properties that are absent from its isolated parts." (Ludwig von Bertalanffy, "Problems of Life", 1952)

"Individualism is the self-affirmation of the individual self as individual self without regard to its participation in its world. As such it is the opposite of collectivism, the self affirmation of the self as part of a larger whole without regard to its character as an individual self." (Paul Tillich, "The Courage to Be The Courage to Be", 1952)

"Every part of the system is so related to every other part that any change in one aspect results in dynamic changes in all other parts of the total system." (Arthur D Hall & Robert E Fagen, "Definition of System", General Systems Vol. 1, 1956)

"In our definition of system we noted that all systems have interrelationships between objects and between their attributes. If every part of the system is so related to every other part that any change in one aspect results in dynamic changes in all other parts of the total system, the system is said to behave as a whole or coherently. At the other extreme is a set of parts that are completely unrelated: that is, a change in each part depends only on that part alone. The variation in the set is the physical sum of the variations of the parts. Such behavior is called independent or physical summativity." (Arthur D Hall & Robert E Fagen, "Definition of System", General Systems Vol. 1, 1956)

"In our definition of system we noted that all systems have interrelationships between objects and between their attributes. If every part of the system is so related to every other part that any change in one aspect results in dynamic changes in all other parts of the total system, the system is said to behave as a whole or coherently. At the other extreme is a set of parts that are completely unrelated: that is, a change in each part depends only on that part alone. The variation in the set is the physical sum of the variations of the parts. Such behavior is called independent or physical summativity." (Arthur D Hall & Robert E Fagen, "Definition of System", General Systems Vol. 1, 1956)

"[...] the concept of 'feedback', so simple and natural in certain elementary cases, becomes artificial and of little use when the interconnexions between the parts become more complex. When there are only two parts joined so that each affects the other, the properties of the feedback give important and useful information about the properties of the whole. But when the parts rise to even as few as four, if every one affects the other three, then twenty circuits can be traced through them; and knowing the properties of all the twenty circuits does not give complete information about the system. Such complex systems cannot be treated as an interlaced set of more or less independent feedback circuits, but only as a whole. For understanding the general principles of dynamic systems, therefore, the concept of feedback is inadequate in itself. What is important is that complex systems, richly cross-connected internally, have complex behaviours, and that these behaviours can be goal-seeking in complex patterns." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"It is clear to all that the animal organism is a highly complex system consisting of an almost infinite series of parts connected both with one another and, as a total complex, with the surrounding world, with which it is in a state of equilibrium." (Ivan P Pavlov, "Experimental psychology, and other essays", 1957)

"[…] the comprehension of a structure requires intuitive knowledge of the ethology of its resistance and of its constituent materials." (Eduardo Torroja, "Philosophy of Structures/;, 1958)

From Parts to Wholes (1970-1979)

"In self-organizing systems, on the other hand, ‘control’ of the organization is typically distributed over the whole of the system. All parts contribute evenly to the resulting arrangement." (Francis Heylighen, "The Science Of Self-Organization And Adaptivity", 1970)

"The systems approach to problems focuses on systems taken as a whole, not on their parts taken separately. Such an approach is concerned with total - system performance even when a change in only one or a few of its parts is contemplated because there are some properties of systems that can only be treated adequately from a holistic point of view. These properties derive from the relationship between parts of systems: how the parts interact and fit together." (Russell L Ackoff, "Towards a System of Systems Concepts", 1971)

"A system in one perspective is a subsystem in another. But the systems view always treats systems as integrated wholes of their subsidiary components and never as the mechanistic aggregate of parts in isolable causal relations." (Ervin László, "Introduction to Systems Philosophy", 1972)

"In no system which shows mental characteristics can any part have unilateral control over the whole. In other words, the mental characteristics of the system are imminent, not in some part, but in the system as a whole." (Gregory Bateson, "Steps to an Ecology of Mind", 1972)

"Holists are distinguished from serialists in terms of the number of inferential statements they produce.[...] It is possible to distinguish the serialist from the holist by a tendency, on the part of a serialist, to preserve the order of the programme presentation format which is absent in the holist. Presented with a holist programme the serialist is unable to preserve the complete order but he does manage to preserve sequentially arranged fragments." (Gordon Pask, "Learning Strategies and Individual Competence", 1972)

"Yet while they exist, regardless of how long, each system has a specific structure made up of certain maintained relationships among its parts, and manifests irreducible characteristics of its own." (Ervin László, "Introduction to Systems Philosophy", 1972)

"In the Systems Age we tend to look at things as part of larger wholes rather than as wholes to be taken apart. This is the doctrine of expansionism. Expansionism brings with it the synthetic mode of thought much as reductionism brought with it." (Russell L Ackoff, "Redesigning the future", 1974)

"Science gets most of its information by the process of reductionism, exploring the details, then the details of the details, until all the smallest bits of the structure, or the smallest parts of the mechanism, are laid out for counting and scrutiny. Only when this is done can the investigation be extended to encompass the whole organism or the entire system. So we say. Sometimes it seems that we take a loss, working this way." (Lewis Thomas, "The Medusa and the Snail: More Notes of a Biology Watcher", 1974)

"When you are confronted by any complex social system […] with things about it that you’re dissatisfied with and anxious to fix, you cannot just step in and set about fixing with much hope of helping. This realization is one of the sore discouragements of our century […] You cannot meddle with one part of a complex system from the outside without the almost certain risk of setting off disastrous events that you hadn’t counted on in other, remote parts. If you want to fix something you are first obliged to understand […] the whole system. […] Intervening is a way of causing trouble." (Lewis Thomas, "The Medusa and the Snail: More Notes of a Biology Watcher", 1974)

"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)

"We have reversed the usual classical notion that the independent 'elementary parts' of the world are the fundamental reality, and that the various systems are merely particular contingent forms and arrangements of these parts. Rather, we say that inseparable quantum interconnectedness of the whole universe is the fundamental reality, and that relatively independent behaving parts are merely particular and contingent forms within this whole." (David Bohm, "On the Intuitive Understanding of Nonlocality as Implied by Quantum Theory", Foundations of Physics Vol 5 (1), 1975)

"If all of the elements in a large system are loosely coupled to one another, then any one element can adjust to and modify a local a local unique contingency without affecting the whole system. These local adaptations can be swift, relatively economical, and substantial." (Karl E Weick, "Educational organizations as loosely coupled systems", 1976)

"In a loosely coupled system there is more room available for self-determination by the actors. If it is argued that a sense of efficacy is crucial for human beings. when a sense of efficacy might be greater in a loosely coupled system with autonomous units than it would be in a tightly coupled system where discretion is limited." (Karl E Weick, "Educational organizations as loosely coupled systems", 1976)

"There is a strong current in contemporary culture advocating ‘holistic’ views as some sort of cure-all […] Reductionism implies attention to a lower level while holistic implies attention to higher level. These are intertwined in any satisfactory description: and each entails some loss relative to our cognitive preferences, as well as some gain [...] there is no whole system without an interconnection of its parts and there is no whole system without an environment." (Francisco Varela, "On being autonomous: The lessons of natural history for systems theory", 1977)

"A threat to any part of the environment is a threat to the whole environment, but we must have a basis of assessment of these threats, not so that we can establish a priority of fears, but so that we can make a positive contribution to improvement and ultimate survival." (Prince Philip, "The Environmental Revolution: Speeches on Conservation, 1962–77", 1978)

"When a mess, which is a system of problems, is taken apart, it loses its essential properties and so does each of its parts. The behavior of a mess depends more on how the treatment of its parts interact than how they act independently of each other. A partial solution to a whole system of problems is better than whole solutions of each of its parts taken separately." (Russell L Ackoff, "The future of operational research is past", The Journal of the Operational Research Society Vol. 30 (2), 1979)

"Given the five parts of the organization - operating core, strategic apex, middle line, technostructure, and support staff - we may now ask how they all function together. In fact, we cannot describe the one way they function together, for research suggests that the linkages are varied and complex. The parts of the organization are joined together by different flows - of authority, of work material, of information, and of decision processes." (Henry Mintzberg, "The structuring of organizations", 1979)

From Parts to Wholes (1990-1999)

"Because the individual parts of a complex adaptive system are continually revising their ('conditioned') rules for interaction, each part is embedded in perpetually novel surroundings (the changing behavior of the other parts). As a result, the aggregate behavior of the system is usually far from optimal, if indeed optimality can even be defined for the system as a whole. For this reason, standard theories in physics, economics, and elsewhere, are of little help because they concentrate on optimal end-points, whereas complex adaptive systems 'never get there'. They continue to evolve, and they steadily exhibit new forms of emergent behavior." (John H Holland, "Complex Adaptive Systems", Daedalus Vol. 121 (1), 1992)

"Systems theory is antireductionist; it asserts that no system can be adequately understood or totally explained once it has been broken down into its component parts." (Charles Zastrow, "Introduction to Social Work and Social Welfare: Empowering People", 1993)

"At the other far extreme, we find many systems ordered as a patchwork of parallel operations, very much as in the neural network of a brain or in a colony of ants. Action in these systems proceeds in a messy cascade of interdependent events. Instead of the discrete ticks of cause and effect that run a clock, a thousand clock springs try to simultaneously run a parallel system. Since there is no chain of command, the particular action of any single spring diffuses into the whole, making it easier for the sum of the whole to overwhelm the parts of the whole. What emerges from the collective is not a series of critical individual actions but a multitude of simultaneous actions whose collective pattern is far more important. This is the swarm model." (Kevin Kelly, "Out of Control: The New Biology of Machines, Social Systems and the Economic World", 1995)

"The basic principle of an autocatalytic network is that even though nothing can make itself, everything in the pot has at least one reaction that makes it, involving only other things in the pot. It's a symbiotic system in which everything cooperates to make the metabolism work - the whole is greater than the sum of the parts.“ (J Doyne Farmer, "The Second Law of Organization" [in The Third Culture: Beyond the Scientific Revolution], 1995)

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

"According to the systems view, the essential properties of an organism, or living system, are properties of the whole, which none of the parts have. They arise from the interactions and relationships among the parts. These properties are destroyed when the system is dissected, either physically or theoretically, into isolated elements. Although we can discern individual parts in any system, these parts are not isolated, and the nature of the whole is always different from the mere sum of its parts." (Fritjof Capra, "The Web of Life", 1996)

"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)

"The role of science, like that of art, is to blend proximate imagery with more distant meaning, the parts we already understand with those given as new into larger patterns that are coherent enough to be acceptable as truth. Biologists know this relation by intuition during the course of fieldwork, as they struggle to make order out of the infinitely varying patterns of nature." (Edward O Wilson, "In Search of Nature", 1996)

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

"We move from part to whole and back again, and in that dance of comprehension, in that amazing circle of understanding, we come alive to meaning, to value, and to vision: the very circle of understanding guides our way, weaving together the pieces, healing the fractures, mending the torn and tortured fragments, lighting the way ahead - this extraordinary movement from part to whole and back again, with healing the hallmark of each and every step, and grace the tender reward." (Ken Wilber, "The Eye of Spirit: An Integral Vision for a World Gone Slightly Mad", 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)

"Each element in the system is ignorant of the behavior of the system as a whole, it responds only to information that is available to it locally. This point is vitally important. If each element ‘knew’ what was happening to the system as a whole, all of the complexity would have to be present in that element." (Paul Cilliers, "Complexity and Postmodernism: Understanding Complex Systems" , 1998)

"Analysis of a system reveals its structure and how it works. It provides the knowledge required to make it work efficiently and to repair it when it stops working. Its product is know-how, knowledge, not understanding. To enable a system to perform effectively we must understand it - we must be able to explain its behavior—and this requires being aware of its functions in the larger systems of which it is a part." (Russell L Ackoff, "Re-Creating the Corporation", 1999)

🪷On Mind: Mental Models XXXVIII

"[...] in ordering our thoughts and images, we must always attend to those things which arc good in each thing so that in this way we are always determined to acting from an affect of joy." (Baruch Spinoza, "Ethics", 1677)

"The idea of any mode in which the human body is affected by external bodies must involve the nature of the human body and at the same rime the nature of the external body." (Baruch Spinoza, "Ethics", 1677)

"The images of things are affections of the human body whose ideas represent external bodies as present to us. […] the affections of the human body whose ideas present external bodies as present to us, we shall call things, though they do not reproduce [external] figures of things. And when the mind regards bodies in this way, we shall say that it imagines." (Baruch Spinoza, "Ethics", 1677)

"It is a mistake to reduce mater to the perception which we have of it, a mistake also to make of it a thing able to produce in us perceptions, but in itself is of another nature than they. Matter, in our view, is an aggregate of ‘images’. And by ‘image‘ we mean a certain existence which is more than that which the idealist calls a representation, but less than that which the realist calls a thing - an existence placed halfway between the ‘thing‘ and the ‘representation’. This conception of matter is simply that of common sense. [...] For common sense, then, the object exists in itself, and, on the other hand, the object is, in itself, pictorial, as we perceive it image it is, but a self-existing image." (Henri Bergson,"Matter and Memory", 1896)

"My eyes are useless for they render back only the image of the known. My whole body must become a constant beam of light, moving with an ever greater rapidity, never arrested, never looking back, never dwindling." (Henry Miller, "Tropic of Capricorn", 1939)

"A thought that is born within thought, an act of thought engendered within its own genealogy, neither given through innateness, nor presupposed in reminiscence, is a thought without image." (Gilles Deleuze, "Difference and Repetition" , 1968)

"What is in the present is what the image ‘represents‘, but not the image itself which, in cinema as in painting, is never to be confused with what it represents. The image itself is the system of the relationships between its elements, that is, a set of relationships from which the variable present only flows. […] What is specific in the image, as soon as it is creative, is to make perceptible, to make visible, relationships of time which cannot be seen in the represented object and do not allow them - selves to be reduced to the present." (Gilles Deleuze, "Cinema 2: The Time-Image" , 1980)

"The thing and the perception of the thing are one amid the same thing, one and the same image, but related in one or other of two systems of reference. The thing is the image as it is in itself, as it is related to all the other images to whose action it completely submits and on which it reacts immediately. But the perception of the thing is the same image related to another special image which frames it, and which only retains a partial action from it, and only reacts to it mediately." (Gilles Deleuze, "Cinema 1: The Movement Image", 1983)

"Philosophy, art, and science are not the mental objects of an objectified brain but the three aspects under which the brain becomes subject." (Gilles Deleuze, What is Philosophy?", 1991)

On Abstraction (2010-2019)

"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)

"Presumably, one can become a mathematical genius only if one has an outstanding capacity for forming vivid mental represen­tations of abstract mathematical concepts - mental images that soon turn into an illusion, eclipsing the human origins of mathematical objects and endowing them with the semblance of an independent existence." (Stanislas Dehaene," The Number Sense: How the Mind Creates Mathematics", 2011) 

"There is no way to guarantee in advance what pure mathematics will later find application. We can only let the process of curiosity and abstraction take place, let mathematicians obsessively take results to their logical extremes, leaving relevance far behind, and wait to see which topics turn out to be extremely useful. If not, when the challenges of the future arrive, we won’t have the right piece of seemingly pointless mathematics to hand." (Peter Rowlett, "The Unplanned Impact of Mathematics", Nature Vol. 475 (7355), 2011) 

"There is no unique, global, and universal relation of identity for abstract objects. [...] Abstract objects are of different sorts and this should mean, almost by definition, that there is no global, universal identity for sorts. Each sort X is equipped with an internal relation of identity but there is no identity relation that would apply to all sorts." (Jean-Pierre Marquis," Categorical foundations of mathematics, or how to provide foundations for abstract mathematics", The Review of Symbolic Logic Vol. 6 (1), 2012) 

"Abstraction is an essential knowledge process, the process (or, to some, the alleged process) by which we form concepts. It consists in recognizing one or several common features or attributes (properties, predicates) in individ­uals, and on that basis stating a concept subsuming those common features or attributes. Concept is an idea, associated with a word expressing a prop­erty or a collection of properties inferred or derived from different samples. Subsumption is the logical technique to get generality from particulars." (Hourya B Sinaceur," Facets and Levels of Mathematical Abstraction", Standards of Rigor in Mathematical Practice 18-1, 2014)

"In general, when building statistical models, we must not forget that the aim is to understand something about the real world. Or predict, choose an action, make a decision, summarize evidence, and so on, but always about the real world, not an abstract mathematical world: our models are not the reality - a point well made by George Box in his oft-cited remark that "all models are wrong, but some are useful". (David Hand, "Wonderful examples, but let's not close our eyes", Statistical Science 29, 2014) 

"Mathematical abstraction is the process of considering and manipulating op­erations, rules, methods and concepts divested from their reference to real world phenomena and circumstances, and also deprived from the content con­nected to particular applications. […] abstraction is the process of passing from things to ideas, properties and relations, to properties of relations and relations of properties, to properties of relations between properties, etc. Being a fundamental thinking process, abstraction has two faces: a logical face and evidently a psychological aspect that is the target of cognitive sciences." (Hourya B Sinaceur,"Facets and Levels of Mathematical Abstraction", Standards of Rigor in Mathematical Practice 18-1, 2014)

"Models can be: formulations, abstractions, replicas, idealizations, metaphors - and combinations of these. [...] Some mathematical models have been blindly used - their presuppositions as little understood as any legal fine print one ‘agrees to’ but never reads - with faith in their trustworthiness. The very arcane nature of some of the formulations of these models might have contributed to their being given so much credence. If so, we mathematicians have an important mission to perform: to help people who wish to think through the fundamental assumptions underlying models that are couched in mathematical language, making these models intelligible, rather than (merely) formidable Delphic oracles." (Barry Mazur, "The Authority of the Incomprehensible" , 2014)

"Mathematics is both abstract and concrete, revealing much of the mental experiment, working with unobserved abstractions and objects, and the current scientific progress depended on the ability to operate precisely with abstractions and force of reasoning; […]" (Octavian Stanasila, Metabolism of Mathematics and Computer Science No. 8, 2015)

"As mathematics gets more abstract, diagrams become more and more prominent as the ways that things fit together abstractly become both more subtle and more important. Moreover, the diagram often sums up the situation more succinctly than the explanation in words, [..]" (Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)

"Mathematics is particularly good at making things out of itself, like how higher-dimensional spaces are built up from lower-dimensional spaces. This is because mathematics deals with abstract ideas like space and dimensions and infinity, and is itself an abstract idea. […] Mathematics is abstract enough that we can always make more mathematics out of mathematics." (Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)

"The crucial concept that brings all of this together is one that is perhaps as rich and suggestive as that of a paradigm: the concept of a model. Some models are concrete, others are abstract. Certain models are fairly rigid; others are left somewhat unspecified. Some models are fully integrated into larger theories; others, or so the story goes, have a life of their own. Models of experiment, models of data, models in simulations, archeological modeling, diagrammatic reasoning, abductive inferences; it is difficult to imagine an area of scientific investigation, or established strategies of research, in which models are not present in some form or another. However, models are ultimately understood, there is no doubt that they play key roles in multiple areas of the sciences, engineering, and mathematics, just as models are central to our understanding of the practices of these fields, their history and the plethora of philosophical, conceptual, logical, and cognitive issues they raise." (Otávio Bueno, [in" Springer Handbook of Model-Based Science", Ed. by Lorenzo Magnani & Tommaso Bertolotti, 2017])

"The theory of groups is considered the language par excellence to study symmetry in science; it provides the mathematical formalism needed to tackle symmetry in a precise way. The aim of this chapter, therefore, is to lay the foundations of abstract group theory." (Pieter Thyssen & Arnout Ceulemans, "Shattered Symmetry: Group Theory from the Eightfold Way to the Periodic Table", 2017)

"This is how category theory arose, as a new piece of maths to study maths. In a way category theory is an ultimate abstraction. To study the world abstractly you use science; to study science abstractly you use maths; to study maths abstractly you use category theory. Each step is a further level of abstraction. But to study category theory abstractly you use category theory." (Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)

"In mathematical modeling, as in all of science, we always have to make choices about what to stress and what to ignore. The art of abstraction lies in knowing what is essential and what is minutia, what is signal and what is noise, what is trend and what is wiggle. It’s an art because such choices always involve an element of danger; they come close to wishful thinking and intellectual dishonesty." (Steven H Strogatz, "Infinite Powers: The Story of Calculus - The Most Important Discovery in Mathematics", 2019)

⚛On Physics: On Spacetime (1925-1939)

"[…] evolution is only one aspect of the order of nature, of the relations of cause and effect, of continuity of space and time, which pervade the universe and enable us to comprehend its simplicity of plan, its complexity of detail." (William D Matthew, Natural History Vol. 25 (2), 1925)

"I have now come to believe that the order of words in time or space is an ineradicable part of much of their significance – in fact, that the reason they can express space-time occurrences is that they are space-time occurrences, so that a logic independent of the accidental nature of spacetime becomes an idle dream. These conclusions are unpleasant to my vanity, but pleasant to my love of philosophical activity: until vitality fails, there is no reason to be wedded to one's past theories." (Bertrand Russell, "Review of The Meaning of Meaning", 1926)

"[...] it has even been doubted whether what goes on in the atom could ever be described within the scheme of space and time. From the philosophical standpoint, I would consider a conclusive decision in this sense as equivalent to a complete surrender. For we cannot really alter our manner of thinking in space and time, and what we cannot comprehend within it we cannot understand at all. There are such things - but I do not believe that atomic structure is one of them." (Edwin Schrödinger, "Quantisation as a Problem of Proper Values", Annalen der Physik Vol. 81 (4), 1926)

"Mathematicians call this combination [space and time] a quadratic form of the differentials of four variables, but we may call it more briefly, with Minkowski, ‘the Universe’." (Émile Borel, "Space and Time", 1926)

"In classical science, it was strange to find that action [...] should yet present the artificial aspect of an energy in space multiplied by a duration. As soon, however, as we realise that the fundamental continuum of the universe is one of space-time and not one of separate space and time, the reason for the importance of the seemingly artificial combination of space with time in the expression for the action receives a very simple explanation. Henceforth, action is no longer energy in a volume of space multiplied by a duration; it is simply energy in a volume of the world, that is to say, in a volume of four-dimensional space-time." (Aram D'Abro, "The Evolution of Scientific Thought from Newton to Einstein", 1927)

"The notion of causality has been greatly modified by the substitution of space-time for space and time [...] Thus geometry and causation become inextricably intertwined." (Bertrand Russell, "The Analysis of Matter", 1927)

"Written words differ from spoken words in being material structures. A spoken word is a process in the physical world, having an essential time-order; a written word is a series of pieces of matter, having an essential space-order." (Bertrand Russell, "An Outline of Philosophy", 1927)


"We wish to obtain a representation of phenomena and form an image of them in our minds. Till now, we have always attempted to form these images by means of the ordinary notions of time and space. These notions are perhaps innate; in any case they have been developed by our daily observations. For me, these notions are clear, and I confess that I am unable to gain any idea of physics without them. […] I would like to retain this ideal of other days and describe everything that occurs in this world in terms of clear pictures." (Hendrik A Lorentz, [Fifth Solvay Conference] 1927)

"Let us draw an arrow arbitrarily. If as we follow the arrow we find more and more of the random element in the world, then the arrow is pointing towards the future; if the random element decreases the arrow points towards the past. [...] I shall use the phrase 'time's arrow' to express this one-way property of time which has no analogue in space. (Arthur Eddington, "The Nature of the Physical World", 1928)

"The immensity of space is paralleled by that of time." (James Jeans, "Annual Report of the Board of Regents of the Smithsonian Institution", 1928)

"The mind-stuff is not spread in space and time. But we must presume that in some other way or aspect it can be differentiated into parts. Only here and there does it arise to the level of consciousness, but from such islands proceeds all knowledge. The latter includes our knowledge of the physical world." (Arthur Eddington, "The Nature of the Physical World", 1928)

"Standing on our microscopic fragment of a grain of sand, we attempt to discover the nature and purpose of the universe which surrounds our home in space and time." (Sir James H Jeans, "The Mysterious Universe", 1930)

"The concepts which now prove to be fundamental to our understanding of nature- a space which is finite; a space which is empty, so that one point [of our 'material' world] differs from another solely in the properties of space itself; four-dimensional, seven- and more dimensional spaces; a space which for ever expands; a sequence of events which follows the laws of probability instead of the law of causation - or alternatively, a sequence of events which can only be fully and consistently described by going outside of space and time - all these concepts seem to my mind to be structures of pure thought, incapable of realisation in any sense which would properly be described as material." (James Jeans, "The Mysterious Universe", 1930)

"In Newton's system of mechanics […] there is an absolute space and an absolute time. In Einstein's theory time and space are interwoven, and the way in which they are interwoven depends on the observer. Instead of three plus one we have four dimensions." (Willem de Sitter, "Relativity and Modern Theories of the Universe", Kosmos, 1932) 

"The very nature of the quantum theory [...] forces us to regard the space-time coordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features of the description, symbolizing the idealization of observation and description, respectively." (Niels Bohr, "Atomic Theory and the Description of Nature: Four Essays", 1934)

"We must, therefore, be prepared to find that further advance into this region will require a still more extensive renunciation of features which we are accustomed to demand of the space time mode of description. (Niels H D Bohr, "Atomic Theory and the Description of Nature", 1934)