Knowledge Representation: Beyond Mental Models – Part III

Mental Models Series

Meaning is perceived, internalized, processed, externalized and communicated in, respectively by the mind through language. The morphological, syntactical and semantical structures as well the richness of the language(s) acquired have a considerable impact on our capability to describe and understand reality. Our mental space and structures evolve with the natural and diagrammatic languages used, the units of the language mapping to the units of our mental space.

At the base of any language are a set of signs and sounds we can easily recognize. Signs are written or printed marks that have standard meanings, while sounds are specific impressions we hear and which in given arrangements, when recognized, convey meanings. Signs together with shapes and objects form symbols that can be used to represent something else, their meaning being usually standardized, however one can assign them further meanings or create own symbols.

A word is a single unit of language that has meaning and can be spoken or written. Words are further grouped within expressions, sentences, propositions or phrases to convey a thought or idea, which are in turn further aggregated in simile, analogies, metaphors, parables and stories to convoy further meanings. A phrase is formed from multiple sentences that together convoy a certain meaning. An expression is a word or group of words used in a given situation or by particular people. A proposition is interpreted as either true or false.

A simile is the use of an expression that compares one thing with another using ‘as’ or ‘like’ in comparisons. An analogy is a comparison between things that have similar features or behavior, often used to help explain a principle or idea. A metaphor is an expression that describes one thing with the help of another thing considered to have similar characteristics. A parable is a short, simple story that teaches or explains an idea or truth, where a story is a description of a connected series of events and situations, either true or imagined.

Similes, analogies and metaphors are linguistic devices that add richness and further dimensions to our mental processes and meaning structures, from a literature as well a scientific aspect, if we consider that many of the scientific concepts are metaphors per se.    

Words or combinations of words can be used as labels for a concept. The totality of the words assimilated – for which a meaning is available – forms our vocabulary. Similes, analogies, metaphors, parables and stories can help clarify and enrich the meaning of a concept.

A phrase can attempt to describe a mental model, while a mental model can be built to understand or describe a phrase, however the two are not equivalent. In fact, to describe a model will be needed to describe its elements and the relations existing between them, together with the assumptions, beliefs and the constraints that hold. Often, despite the richness of a natural language’s vocabulary a description might need to use metaphors to convey an approximate meaning.

The given definitions are simplistic attempting to reflect the simplicity of the associations we hold between the various concepts, and together, concepts, associations and the meanings we hold form a mental model. Of course, the inner workings of the mind are much more complex, evidence for this complexity being the huge volume of books written over the centuries for the same purpose. There are also many intentional and unintentional gaps and probably misunderstandings, however the definitions are just an attempt to depict my understanding in the form of an externalized mental model. Luckily our mental models don’t need to be accurate in handling the reality and accomplishing the various tasks.

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Disclaimer: Most of the definitions were adapted from the Cambridge Dictionary, however there can be important deviations from the respective source.

Knowledge Representation: Beyond Mental Models – Part II

Mental Models Series

One can regard the mind as a mirror which mirrors what a person perceives, however the representations don’t necessarily reflect the reality faithfully, but are simplified to the degree we are able to incorporate the reality within our mental structures and their content. We can assume that the mind represents to some degree the physical as well the inner reality, such representations being hold within the mental space – the combined aggregation of such representations. Of interest are especially mental space’s basis units and their further aggregations.

The most important unit is the one of concept. A concept is an idea having a given meaning or set of meanings, considering that concepts can have different meanings when framed in different contexts, where the context is the situation or frame in which the specific meaning can be extrapolated. A concept can be associated with multiple language-specific and context-dependent labels, where a label can be a symbol, a name or a phrase used to identify the concept. The labels associated with a concept belong to the same class of meaning as they point to the same meaning.

Meaning is by itself a unit, denoting the (personal) interpretations we associate with perceptions, concepts, symbols, events, beliefs, opinions, thoughts, understandings or aggregates of them. Meaning is formed rather by the relations existing between these elements and the place they occupy in the network formed by their relations. Think of a complex network of such components in which the associations between the components together with the components allow us grouping them together in units (of meaning), which by aggregation can form further units over and over.

Typically, a unit of meaning is associated with a concept within a given context. Meaning is created within this complex network, each change in the network having the potential to result in a change of meaning that can further propagate into the network and lead thus to further changes, though usually the changes and their impact are small, almost neglectable.

Another type of unit of meaning is represented by the mental models we form to explain, describe or model reality’s phenomena. When one attempts externalizing a mental model into a form of representation then it becomes an external model, multiple external models may thus result depending on the level of abstraction or understanding used. A mental model has the role of delimiting the scaffold that attempts explaining the concept. The essence of understanding a concept is having a mental model that reflects the structure of that concept and the meanings associated with it.

In the attempt to understand the reality, we are forced to advance theories on how the phenomena work. A theory is a reasonable explanation for facts, conditions and events carrying with it the various assumptions (ideas accepted as true) and beliefs we hold, directly or indirectly. A theory can be associated with one or more models, and thus further with mental models.

Several (mental) models can be grouped within a broader structure called a view, structure that reflects our beliefs on how one or more related concepts depict the reality. When the concepts represent the backbone of a domain then the view becomes a worldview. When together with the (mental) models are considered the theories as well other tools used in the process one talks about a paradigm. Paradigm shifts involve fundamental changes in the basis concepts, theories or models of a domain, and thus can a greater impact within our networks of meaning.

The concepts considered by all these (meta-)structures have a representation also within our mental space, even if the space can’t be clearly delimited.

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Disclaimer: Most of the definitions were adapted from the Cambridge Dictionary, however there can be important deviations from the respective source.

Knowledge Representation: Beyond Mental Models – Part I

Mental Models Series

Many definitions can be quite abstract, especially those that attempt defining abstract things like a mental model, however, definitions are essential in obtaining a common ground to understand the concepts used. There are many attempts to define what a mental model is, however, to understand its place within the mental space is needed to describe at high-level how the mind works, in other words to create a mental model for it.

Probably the most important delimitation that needs to be made is the one between the physical and mental reality. The physical reality refers to the state of things as they are outside the mind, typically in the environment we live in, in opposition to the inner reality – the world of the mind, and on how the physical reality is perceived, imagined and reflected by the mind.

Reality concerns given environments and their main constituents – objects, situations, events, facts, and phenomena associated with it. The environment is the physical or mental space in which something exists or takes place. An object is an inanimate, animate or mental thing that can be perceived, a pattern that allowed us drawing a boundary around it. An event is something that happened, happens or will happen. A fact is something that is known to have happened or to exist. A situation is a set of things that are happening, respectively the conditions that exist in environment. A phenomenon is an observable fact, situation or event.

An object can refer to a single thing or a group of related or connected things part of the environment, or to the whole environment. A group of related things can form a class, while a group of connected things between which exists certain dependencies can be regarded as a system. Within the group, the arrangement and organization of the elements depict groups’ structure. By arrangement is denoted how the elements are ordered or positioned in respect to each other, while by organization the relations existing between the elements.

In addition, one can discuss about patterns, the way in which something is done, organized, or happens, as well about configuration, the arrangement or pattern identified at a given moment, respectively about form, the shape or appearance of something. A state is a given configuration from the total combination of configurations possible, while a condition is a state that imposes a limitation.

Perception is the quality of being aware of things through the physical senses, especially sight, involving the ability to notice and understand things. Experience is what we gain in the direct interaction with the reality, the physical objects by observing the phenomena. Knowing is the ability to process information and manipulate symbols to experience the world, generating in the process further information and symbols that describe our experience. Understanding is the ability to make experience meaningful and useful in form of structures of meanings (aka understandings) to the degree that the experience can be reused in similar situations.

Thinking is the process of using understandings to arrive to new understandings, thought being the act of thinking as well the unit of thinking expressed as an idea. Beliefs are understandings we consider as true, while opinions are thoughts or beliefs one has on specific matters. An idea is an understanding, thought, belief or opinion.

Reasoning is the process of using facts to arrive to new facts or understandings. Intuition is the understanding or knowing of something without needing to think or reason about it. Imagination is the ability to form new concepts, ideas or mental models in the mind, independently whether they exist, whether they are valid or true.

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Disclaimer: Most of the definitions were adapted from the Cambridge Dictionary, however there can be important deviations from the respective source.

Knowledge Representation: Defining Mental Models I

Mental Models

A mental model (aka mental representation/image/picture) is a mental structure that attempts to model (depict, imagine) how real or imaginary things look like, work or fit together. Thus, a mental model can correspond to an object, idea, a collection of information, objects or ideas, or anything else, concrete or abstract, that the mind is thinking about [1] consciously or unconsciously. The mental structure behaves likes an ‘analogical representative’ of the thing envisioned [2] being an abstraction as certain characteristics are eventually left out, either because are irrelevant, poorly understood, not perceived or simply forgotten.

A mental model is a blend of mental content – beliefs, assumptions, concepts, meanings, thoughts, intuitions, ideas, icons, symbols, analogs, metaphors, memories and even psychological or spatial-temporal contexts, together with the relationships existing between them.  I tend to believe that a mental model doesn’t necessarily have a definite structure within our mental space given the dynamics nature of its components. We are talking here about multiple substrata of meaning that can move beneath as the currents of a sea without the sailor being aware of it. The beneath currents are nothing but pulls, pushes and swings of the mental processing taking place inside the mind.

Even if they appear to have unity, mental models are rather amorphous or multifold. The unity is apparent, derived from their iconic aspect – when we look from above, they seem to have unity, however when we look under microscope at them the unity dissipates into the multitude of relations. To delimit a mental model’s structure one can make a cut when the relationships become weaker and weaker however also this weakness is apparent. Moreover, the mental space seems to be a combination, recombination, aggregation and overlapping of mental models that resemble the structure of a hypergraph.

A mental model is also a mechanism of explaining how the mind works, how it can perceive and represent reality, think, imagine, etc. Therefore, the mental models we hold are mainly unconscious unless we make them conscious when we start to evaluate their structure, delimitate their boundaries in one form or another, respectively identify the effect they have on us.

When one attempts to externalize a mental model into a form of representation then it becomes an external model, however it might need several adjustments spread over several iterations before it can become self-contained. During this process our internal model might change as well as new understanding is gained, as gaps in understanding are filled with facts, assumptions or other mental content.

In reverse, one attempts understanding a model, the internal projection being one or more mental models depending on our understanding and its various interpretations we depict. This might happen unconsciously as we acquire knowledge or the mind does its inner workings, or consciously when an active component is involved – playing with the model, analyzing its advantages, disadvantages, areas of applicability, presumptions, etc.

Some suppose that there’s a one-to-one mapping between an external and a mental model, thing which is not necessarily true. A many-to-many relation is more plausible considering that there can be multiple interpretations of an external model, and a mental model can result in multiple external models with different abstraction levels.

Several resources consider the mental models only as representations of external things though they can be also representations of fictitious things or even processes that take place within the mind. In the end, mental models are mental analogs of physical models as they attempt to abstract some of the important features of the reality or some aspects of it. Moreover, many of the characteristics of external models apply to mental models as well.

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Resources:
[1] Anders Ericsson & Robert Pool (2016) "Peak: Secrets from the New Science of Expertise"
[2] Jean-Paul Sartre (1940) "The Psychology of Imagination"

Knowledge Representation: Mental Models’ Fallacies (Part III: Professional Defects)

Mental Models

We perceive and interpret the world also through the knowledge and beliefs of our profession as many of the mental models we’ve acquired derive or relate to it. These mental models can help us make better sense of the quotidian life, however they can become a burden when they make us start ignoring or misinterpreting some (important) aspects of it.

This typically happens when the mental models derived from our profession lose their validity or accuracy when translated automatically from one environment to another, especially when we aren’t aware of the implications of this extension and the effect it has on us. When this happens, we can talk about a fallacy I arrived to know as a ‘professional defect’.

For example, a mathematician or somebody with strong mathematical background arrives to think of the world around him in terms of probability for an event to happen. On one side this can prove as a powerful tool to quantify and predict certain events, and evaluate complex situations, though might make the person ignore the area of impossible, expressed maybe in opportunities with small chances to happen, opportunities that when considered could have a huge impact on his live.

Not far from the previous example, a philosopher builds in his mind a world of ideas, and sooner or later arrives to evaluate the world around and his personal interactions with the world based on the philosophical currents he adheres to. No matter how complete and well-established a philosophy is, it’s a human based system of beliefs and models, with its loops and wholes. Sooner or later the philosopher will find himself trapped in the threads of his own philosophy as long he applies it too deep und unaware into his personal life. From this perspective it will be hard for a philosopher to be happy and content with his life.

A psychologist or somebody with a similar background may arrive to judge the people outside his praxis based on the traits they reveal. A doctor may start to see in people the predispositions to or existence of a given disease, arriving maybe to judge people based on certain health predispositions. A dentist might start evaluating people based on the denture they have. An artist may treat as inferior people those who don’t exhibit any artistic skills. Each profession comes with its own type of similar fallacies.

We spend an important part of our lives at work or thinking about work. For sure, models’ transition from professional to personal life may seem natural as the professional life extends itself sometimes beyond the borders of our profession – some coworkers become our friends, we spend more and more time in communities related to our profession. Moreover, we meet same type or similar situations in which the models we learned seem to apply naturally.

The problem comes usually when we ignore that we deal with a different type of environment with its own characteristics, with different groups of people having higher diversity reflected in their beliefs, skillset, hobbies, expectations and other characteristics than the ones we typically meet in professional life. An environmental change implies also changes of assumptions, setups, behavior, rules, aims, etc. When we are not aware of these nuances, then more likely we don’t adapt our models to the new situations derived from such changes.

It’s important to identify the professional defects we hold, especially those that have a considerable impact on our lives, become aware of them and address the feedback we receive accordingly. It’s up to us to do the work, to challenge and adapt our models as the environment changes.

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Note:
This was adapted after an older post on professional defects.

Systems Thinking: On Systems (Quotes)

"The whole is more than the sum of its parts." (Aristotle, "Metaphysics", cca. 335-323 BC)

"[…] when a problem arises either from within a republic or outside it, one brought about either by internal or external reasons, one that has become so great that it begins to make everyone afraid, the safest policy is to delay dealing with it rather than trying to do away with it, because those who try to do away with it almost always increase its strength and accelerate the harm which they feared might come from it." (Niccolò Machiavelli, "Discourses on Livy", 1531) 

"This interconnection or accommodation of all created things to each other, and each to all the others, brings it about that each simple substance has relations that express all the others, and consequently, that each simple substance is a perpetual, living mirror of the universe." (Gottfried W Leibniz,  "Monadology", 1714)

"Systems in many respects resemble machines. A machine is a little system, created to perform, as well as to connect together, in reality, those different movements and effects which the artist has occasion for.  A system is an imaginary machine invented to connect together in the fancy those different movements and effects which are already in reality performed. […] The machines that are first invented to perform any particular movement are always the most complex, and succeeding artists generally discover that, with fewer wheels, with fewer principles of motion, than had originally been employed, the fame effects may be more easily produced. The first systems, in the fame manner, are always the most complex, and a particular connecting chain, or principle, is generally thought necessary to unite every two seemingly disjointed appearances: but it often happens, that one great connecting principle is afterwards found to be sufficient to bind together all the discordant phænomena that occur in a whole species of things." (Adam Smith, "The Wealth of Nations", 1776)

"Systems in physical science […] are no more than appropriate instruments to aid the weakness of our organs: they are, properly speaking, approximate methods which put us on the path to the solution of the problem; these are the hypotheses which, successively modified, corrected, and changed in proportion as they are found false, should lead us infallibly one day, by a process of exclusion, to the knowledge of the true laws of nature." (Antoine L Lavoisier, "Mémoires de l’Académie Royale des Sciences", 1777)

"A good method of discovery is to imagine certain members of a system removed and then see how what is left would behave: for example, where would we be if iron were absent from the world: this is an old example." (Georg C Lichtenberg, Notebook J, 1789-1793)

"Delight at having understood a very abstract and obscure system leads most people to believe in the truth of what it demonstrates." (Georg C Lichtenberg, Notebook J, 1789-1793)

"We must think of each part as an organ, that produces the other parts (so that each reciprocally produces the other) […] Because of this, [the organism] will be both an organized and self-organizing being." (Immanuel Kant, "Critique of Judgment", 1790)

"§ 6. It is impossible for the human mind, itself a finite creation, to regard nature, whether her powers or her productions are considered, in the light of the whole manifestation of an infinite power, but only as parts or fragments of such manifestation. But to comprehend these as one whole, that is, as an eternal and immutable yet ever varying body, or, as innumerable forms of one highest whole, is the end. of all disquisition, the sum of which we call a System.

§ 7. A system contains within itself the seeds of some more complete evolution, but it does not admit of arbitrary alterations. Not that any absolute system can ever be contrived; for I am by no means of the opinion of those who expect that a system is to be as unchangeable as if it were petrified.

 § 8. If nature be closely pursued, a system is called Natural; if this Ariadnean thread be not followed, it is called Artificial or factitious.

§ 9. A system of nature proceeding from subjects of the most simple organization to such as are more perfect, or from the circumference to the centre, is called a Mathematical System.

§ 10. A system of nature which takes for the basis of its arrangement the order of development of individuals is called Physiological.

§ 11. Philosophical systems do not depend upon individual productions which are subject to continual variation, but upon eternal and unchangeable ideas. These always proceed from the centre to the circumference, or from the most perfect productions to those of a lower order.” (John Lindley, "Some Account of the Spherical and Numerical System of Nature o/M. Elias Fries", ‘Philosophical magazine: a journal of theoretical, experimental and applied physics’ Vol. 68, 1826)

"An established system is limited by its order of known or discovered elements." (Dmitry Mendeleyev, "A Natural System of the Elements and Its Use in Predicting the Properties of Undiscovered Elements", Journal of the Russian Chemical Society Vol. 3, 1871)

"There is a maxim which is often quoted, that ‘The same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more that once, so that the causes and effects cannot be the same in all respects. [...] There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts ‘That like causes produce like effects’. This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied; but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the ‘points’ causes a railway train to run into another instead of keeping its proper course." (James C Maxwell, "Matter and Motion", 1876)

"As long as the training of a naturalist enables him to trace the action only of a particular material system, without giving him the power of dealing with the general properties of all such systems, he must proceed by the method so often described in histories of science - he must imagine model after model of hypothetical apparatus, till he finds one which will do the required work. If this apparatus should afterwards be found capable of accounting for many of the known phenomena, and not demonstrably inconsistent with any of them, he is strongly tempted to conclude that his hypothesis is a fact, at least until an equally good rival hypothesis has been invented." (James C Maxwell, "Tait’s Thermodynamics", Nature Vol. XVII (431), 1878)

"In every symmetrical system every deformation that tends to destroy the symmetry is complemented by an equal and opposite deformation that tends to restore it. […] One condition, therefore, though not an absolutely sufficient one, that a maximum or minimum of work corresponds to the form of equilibrium, is thus applied by symmetry." (Ernst Mach, "The Science of Mechanics: A Critical and Historical Account of Its Development", 1893)

"Society is not a mere sum of individuals. Rather, the system formed by their association represents a specific reality which has its own characteristics. [...] The group thinks, feels, and acts quite differently from the way in which its members would were they isolated. If, then, we begin with the individual, we shall be able to understand nothing of what takes place in the group." (Émile Durkheim, "The Rules of Sociological Method", 1895)

"An act cannot be defined by the end sought by the actor, for an identical system of behaviour may be adjustable to too many different ends without altering its nature." (Émile Durkheim, "Suicide: A Study in Sociology", 1897)

"The ordinary logic has a great deal to say about genera and species, or in our nineteenth century dialect, about classes. Now a class is a set of objects compromising all that stand to one another in a special relation of similarity. But where ordinary logic talks of classes the logic of relatives talks of systems. A system is a set of objects compromising all that stands to one another in a group of connected relations. Induction according to ordinary logic rises from the contemplation of a sample of a class to that of a whole class; but according to the logic of relatives it rises from the contemplation of a fragment of a system to the envisagement of the complete system." (Charles S Peirce, "Cambridge Lectures on Reasoning and the Logic of Things: Detached Ideas on Vitally Important Topics", 1898)

"The state of a system at a given moment depends on two things - its initial state, and the law according to which that state varies. If we know both this law and this initial state, we have a simple mathematical problem to solve, and we fall back upon our first degree of ignorance. Then it often happens that we know the law and do not know the initial state. It may be asked, for instance, what is the present distribution of the minor planets? We know that from all time they have obeyed the laws of Kepler, but we do not know what was their initial distribution. In the kinetic theory of gases we assume that the gaseous molecules follow rectilinear paths and obey the laws of impact and elastic bodies; yet as we know nothing of their initial velocities, we know nothing of their present velocities. The calculus of probabilities alone enables us to predict the mean phenomena which will result from a combination of these velocities. This is the second degree of ignorance. Finally it is possible, that not only the initial conditions but the laws themselves are unknown. We then reach the third degree of ignorance, and in general we can no longer affirm anything at all as to the probability of a phenomenon. It often happens that instead of trying to discover an event by means of a more or less imperfect knowledge of the law, the events may be known, and we want to find the law; or that, instead of deducing effects from causes, we wish to deduce the causes." (Henri Poincaré, "Science and Hypothesis", 1902)

"There is not in Nature any system perfectly isolated, perfectly abstracted from all external action; but there are systems which are nearly isolated. If we observe such a system, we can study not only the relative motion of its different parts with respect to each other, but the motion of its centre of gravity with respect to the other parts of the universe." (Henri Poincaré, "Science and Hypothesis", 1902)

"A vital phenomenon can only be regarded as explained if it has been proven that it appears as the result of the material components of living organisms interacting according to the laws which those same components follow in their interactions outside of living systems." (Adolf E Fick, "Gesammelte Schriften" Vol. 3, 1904)

"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)

"The concept of an independent system is a pure creation of the imagination. For no material system is or can ever be perfectly isolated from the rest of the world. Nevertheless it completes the mathematician’s ‘blank form of a universe’ without which his investigations are impossible. It enables him to introduce into his geometrical space, not only masses and configurations, but also physical structure and chemical composition." (Lawrence J Henderson, "The Order of Nature: An Essay", 1917)

"The complexity of a system is no guarantee of its accuracy." (John P Jordan, "Cost accounting; principles and practice", 1920)

"Since the fundamental character of the living thing is its organization, the customary investigation of the single parts and processes cannot provide a complete explanation of the vital phenomena. This investigation gives us no information about the coordination of parts and processes. Thus, the chief task of biology must be to discover the laws of biological systems (at all levels of organization). We believe that the attempts to find a foundation for theoretical biology point at a fundamental change in the world picture. This view, considered as a method of investigation, we shall call ‘organismic biology’ and, as an attempt at an explanation, ‘the system theory of the organism’" (Ludwig von Bertalanffy, "Kritische Theorie der Formbildung", 1928)

"[…] to the scientific mind the living and the non-living form one continuous series of systems of differing degrees of complexity […], while to the philosophic mind the whole universe, itself perhaps an organism, is composed of a vast number of interlacing organisms of all sizes." (James G Needham, "Developments in Philosophy of Biology", Quarterly Review of Biology Vol. 3 (1), 1928) 

"Order is not sufficient. What is required, is something much more complex. It is order entering upon novelty; so that the massiveness of order does not degenerate into mere repetition; and so that the novelty is always reflected upon a background of system." (Alfred N Whitehead, "Process and Reality: An Essay in Cosmology", 1929)

"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)

"The chain of cause and effect could be quantitatively verified only if the whole universe were considered as a single system - but then physics has vanished, and only a mathematical scheme remains. The partition of the world into observing and observed system prevents a sharp formulation of the law of cause and effect." (Werner K Heisenberg, "The Physical Principles of the Quantum Theory", 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)

"Given a situation, a system with a Leerstelle [a gap], whether a given completion (Lueckenfuellung) does justice to the structure, is the 'right' one, is often determined by the structure of the system, the situation. There are requirements, structurally determined; there are possible in pure cases unambiguous decisions as to which completion does justice to the situation, which does not, which violates the requirements and the situation." (Max Wertheimer, "Some Problems in the Theory of Ethics", Social Research Vol. 2 (3), 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)

"When a transfer of matter to or from a system is also possible, the system may be called an open system." (Frank H MacDougall, "Thermodynamics and chemistry", ‎1939)

"This, however, is very speculative; the point of interest for our present enquiry is that physical reality is built up, apparently, from a few fundamental types of units whose properties determine many of the properties of the most complicated phenomena, and this seems to afford a sufficient explanation of the emergence of analogies between mechanisms and similarities of relation-structure among these combinations without the necessity of any theory of objective universals." (Kenneth Craik, "The Nature of Explanation", 1943)

"A system is defined as any combination of matter that we wish to study." (Earl B Millard, "Physical Chemistry for Colleges: A course of instruction", 1946)

"A system is difficult to define, but it is easy to recognize some of its characteristics. A system possesses boundaries which segregate it from the rest of its field: it is cohesive in the sense that it resists encroachment from without […]" (Marvin G Cline, "Fundamentals of a theory of the self: some exploratory speculations‎", 1950)

"Now a system is said to be at equilibrium when it has no further tendency to change its properties." (Walter J Moore, "Physical chemistry", 1950)

"[…] the characteristic tendency of entropy is to increase. As entropy increases, the universe, and all closed systems in the universe, tend naturally to deteriorate and lose their distinctiveness, to move from the least to the most probable state, from a state of organization and differentiation in which distinctions and forms exist, to a state of chaos and sameness." (Norbert Wiener, "The Human Use of Human Beings", 1950)

"Life is a potentially self-perpetuating open system of linked organic reactions, catalyzed stepwise and almost isothermally by complex and specific organic catalysts which are themselves produced by the system." (J Perrett, "Biochemistry and Bacteria", New Biology Vol. 12, 1952)

"A system is any portion of the universe set aside for certain specified purposes. For our concern, a system is set aside from the universe in a manner that will enable this system to be built without having to consider the total universe. Therefore, the system is set aside from the universe by its inputs and outputs - its boundaries. The system may be said to be in operation when its inputs are being transformed into the required outputs. (Incidently, we are not here concerned with completely closed systems.) The systems that do concern us all have a number of components within their boundaries which together effect the transformation of the inputs to the required outputs." (Kay Inaba et al, "A rational method for applying behavioral technology to man-machine system design", 1956) 

"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)

"Stability is commonly thought of as desirable, for its presence enables the system to combine of flexibility and activity in performance with something of permanence. Behaviour that is goal-seeking is an example of behaviour that is stable around a state of equilibrium. Nevertheless, stability is not always good, for a system may persist in returning to some state that, for other reasons, is considered undesirable." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"This 'statistical' method of specifying a system - by specification of distributions with sampling methods - should not be thought of as essentially different from other methods. It includes the case of the system that is exactly specified, for the exact specification is simply one in which each distribution has shrunk till its scatter is zero, and in which, therefore, 'sampling' leads to one inevitable result. What is new about the statistical system is that the specification allows a number of machines, not identical, to qualify for inclusion. The statistical 'machine' should therefore be thought of as a set of machines rather than as one machine." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"One of the most basic principles of biology is organization, which means that two things put together in a specific way form a new unit, a system, the properties of which are not additive and cannot be described in terms of the properties of the constituents. As points may be connected to letters, letters to words, words to sentences, etc., so atoms can join to molecules, molecules to organelles, organelles to cells, etc., every level of organization having a new meaning of its own and offering exciting vistas and possibilities." (Albert Szent-Györgyi, "Bioenergetics", 1957)

"A system is primarily a living system, and the process which defines it is the maintenance of an organization which we know as life." (Ralph W Gerard, "Units and Concepts of Biology", 1958)

"A deterministic system is one in which the parts interact in a perfectly predictable way. There is never any room for doubt: given a last state of the system and the programme of information by defining its dynamic network, it is always possible to predict, without any risk of error, its succeeding state. A probabilistic system, on the other hand, is one about which no precisely detailed prediction can be given. The system may be studied intently, and it may become more and more possible to say what it is likely to do in any given circumstances. But the system simply is not predetermined, and a prediction affecting it can never escape from the logical limitations of the probabilities in which terms alone its behaviour can be described." (Stafford Beer, "Cybernetics and Management", 1959)

"Control is an attribute of a system. This word is not used in the way in which either an office manager or a gambler might use it; it is used as a name for connectiveness. That is, anything that consists of parts connected together will be called a system." (Stafford Beer, "Cybernetics and Management", 1959)

"If a machine is a purposive system, then the machine's description will be given by an account of the successive states of the system as its purpose unfolds. This succession of states is given by a set of transitions of one item to another, and this set is known technically as a transformation. When the transforms obtained from a transformation include no fresh item, but are concerned with re-arranging the items that are there already, we speak of a closed system." (Stafford Beer, "Cybernetics and Management", 1959)

"In fact, it is empirically ascertainable that every event is actually produced by a number of factors, or is at least accompanied by numerous other events that are somehow connected with it, so that the singling out involved in the picture of the causal chain is an extreme abstraction. Just as ideal objects cannot be isolated from their proper context, material existents exhibit multiple interconnections; therefore the universe is not a heap of things but a system of interacting systems." (Mario Bunge, "Causality: The place of the casual principles in modern science", 1959)

"Any pattern of activity in a network, regarded as consistent by some observer, is a system, Certain groups of observers, who share a common body of knowledge, and subscribe to a particular discipline, like 'physics' or 'biology' (in terms of which they pose hypotheses about the network), will pick out substantially the same systems. On the other hand, observers belonging to different groups will not agree about the activity which is a system." (Gordon Pask, "The Natural History of Networks", 1960)

"Clearly, if the state of the system is coupled to parameters of an environment and the state of the environment is made to modify parameters of the system, a learning process will occur. Such an arrangement will be called a Finite Learning Machine, since it has a definite capacity. It is, of course, an active learning mechanism which trades with its surroundings. Indeed it is the limit case of a self-organizing system which will appear in the network if the currency supply is generalized." (Gordon Pask, "The Natural History of Networks", 1960)

"It is inherent in the logical character of the abstract self-organizing system that all available methods of organization are used, and that it cannot be realized in a single reference frame. Thus, any of the tricks which the physical model can perform, such as learning and remembering, may be performed by one or all of a variety of mechanisms, chemical or electrical or mechanical." (Gordon Pask, "The Natural History of Networks", 1960)

"Every isolated determinate dynamic system, obeying unchanging laws, will ultimately develop some sort of organisms that are adapted to their environments." (W Ross Ashby, "Principles of the self-organizing system", 1962)

"Roughly, by a complex system I mean one made up of a large number of parts that interact in a nonsimple way. In such systems, the whole is more than the sum of the parts, not in an ultimate, metaphysical sense, but in the important pragmatic sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to infer the properties of the whole." (Herbert Simon, "The Architecture of Complexity", Proceedings of the American Philosophical Society Vol. 106 (6), 1962)

"Thus, the central theme that runs through my remarks is that complexity frequently takes the form of hierarchy, and that hierarchic systems have some common properties that are independent of their specific content. Hierarchy, I shall argue, is one of the central structural schemes that the architect of complexity uses." (Herbert Simon, "The Architecture of Complexity", Proceedings of the American Philosophical Society Vol. 106 (6), 1962)

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

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

"The famous balance of nature is the most extraordinary of all cybernetic systems. Left to itself, it is always self-regulated." (Joseph W Krutch, Saturday Review, 1963)

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

"Beyond a critical point within a finite space, freedom diminishes as numbers increase. This is as true of humans as it is of gas molecules in a sealed flask. The human question is not how many can possibly survive within the system, but what kind of existence is possible for those who do survive." (Frank Herbert, "Dune", 1965) 

"System theory is basically concerned with problems of relationships, of structure, and of interdependence rather than with the constant attributes of objects. In general approach it resembles field theory except that its dynamics deal with temporal as well as spatial patterns. Older formulations of system constructs dealt with the closed systems of the physical sciences, in which relatively self-contained structures could be treated successfully as if they were independent of external forces. But living systems, whether biological organisms or social organizations, are acutely dependent on their external environment and so must be conceived of as open systems." (Daniel Katz, "The Social Psychology of Organizations", 1966)

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

"To find out what happens to a system when you interfere with it you have to interfere with it (not just passively observe it)." (George E P Box, "Use and Abuse of Regression", 1966)

"That a system is open means, not simply that it engages in interchanges with the environment, but that this interchange is an essential factor underlying the system's viability, its reproductive ability or continuity, and its ability to change. [...] Openness is an essential factor underlying a system's viability, continuity, and its ability to change."  (Walter F Buckley, "Sociology and modern systems theory", 1967)

"A structure is a system of transformations. Inasmuch as it is a system and not a mere collection of elements and their properties, these transformations involve laws: the structure is preserved or enriched by the interplay of its transformation laws, which never yield results external to the system nor employ elements that are external to it. In short, the notion of structure is composed of three key ideas: the idea of wholeness, the idea of transformation, and the idea of self-regulation." (Jean Piaget, "Structuralism", 1968)

"Evolution cannot be understood except in the frame of ecosystems." (Ramón Margalef, "Perspectives in Ecological Theory", 1968)

"Learning is any change in a system that produces a more or less permanent change in its capacity for adapting to its environment. Understanding systems, especially systems capable of understanding problems in new task domains, are learning systems." (Herbert A Simon, "The Sciences of the Artificial", 1968)

"Knowing reality means constructing systems of transformations that correspond, more or less adequately, to reality. They are more or less isomorphic to transformations of reality. The transformational structures of which knowledge consists are not copies of the transformations in reality; they are simply possible isomorphic models among which experience can enable us to choose. Knowledge, then, is a system of transformations that become progressively adequate." (Jean Piaget, "Genetic Epistemology", 1968)

"The more we are willing to abstract from the detail of a set of phenomena, the easier it becomes to simulate the phenomena. Moreover we do not have to know, or guess at, all the internal structure of the system but only that part of it that is crucial to the abstraction." (Herbert A Simon, "The Sciences of the Artificial", 1968)

"Thus, there exist models, principles, and laws that apply to generalized systems or their subclasses, irrespective of their particular kind, the nature of their component elements, and the relations or 'forces' between them. It seems legitimate to ask for a theory, not of systems of a more or less special kind, but of universal principles applying to systems in general. In this way we postulate a new discipline called General System Theory. Its subject matter is the formulation and derivation of those principles which are valid for ‘systems’ in general." (Ludwig von Bertalanffy, „General System Theory: Foundations, Development, Applications", 1968)

"You cannot sum up the behavior of the whole from the isolated parts, and you have to take into account the relations between the various subordinate systems which are super-ordinated to them in order to understand the behavior of the parts." (Ludwig von Bertalanffy, "General System Theory", 1968)

"[…] complex systems are counterintuitive. That is, they give indications that suggest corrective action which will often be ineffective or even adverse in its results." (Jay W Forrester, "Urban Dynamics", 1969)

"A cognitive system is a system whose organization defines a domain of interactions in which it can act with relevance to the maintenance of itself, and the process of cognition is the actual (inductive) acting or behaving in this domain. Living systems are cognitive systems, and living as a process is a process of cognition. This statement is valid for all organisms, with and without a nervous system." (Humberto R Maturana, "Biology of Cognition", 1970)

"A living system, due to its circular organization, is an inductive system and functions always in a predictive manner: what happened once will occur again. Its organization, (genetic and otherwise) is conservative and repeats only that which works. For this same reason living systems are historical systems; the relevance of a given conduct or mode of behavior is always determined in the past." (Humberto Maturana, "Biology of Cognition", 1970)

"Living systems are units of interactions; they exist in an ambience. From a purely biological point of view they cannot be understood independently of that part of the ambience with which they interact: the niche; nor can the niche be defined independently of the living system that specifies it." (Humberto Maturana, "Biology of Cognition", 1970)

"The systems approach goes on to discovering that every world-view is terribly restricted." (C West Churchman, 1970) 

"[…] as a model of a complex system becomes more complete, it becomes less understandable. Alternatively, as a model grows more realistic, it also becomes just as difficult to understand as the real world processes it represents." (Jay M Dutton & William H Starbuck," Computer simulation models of human behavior: A history of an intellectual technology", IEEE Transactions on Systems, 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 an isolated system, which cannot exchange energy and matter with the surroundings, this tendency is expressed in terms of a function of the macroscopic state of the system: the entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972) 

"The functional order maintained within living systems seems to defy the Second Law; nonequilibrium thermodynamics describes how such systems come to terms with entropy." (Ilya Prigogine, "Thermodynamics of Evolution", 1972) 

"Technology can relieve the symptoms of a problem without affecting the underlying causes. Faith in technology as the ultimate solution to all problems can thus divert our attention from the most fundamental problem - the problem of growth in a finite system." (Donella A Meadows, "The Limits to Growth", 1972)

"The notion of ‘system’ has gained central importance in contemporary science, society and life. In many fields of endeavor, the necessity of a ‘systems approach’ or ‘systems thinking’ is emphasized, new professions called ‘systems engineering’, ‘systems analysis’ and the like have come into being, and there can be little doubt that this this concept marks a genuine, necessary, and consequential development in science and world-view." (Ervin László, "Introduction to Systems Philosophy: Toward a New Paradigm of Contemporary Thought", 1972)

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

"There are two subcategories of holist called irredundant holists and redundant holists. Students of both types image an entire system of facts or principles. Though an irredundant holist's image is rightly interconnected, it contains only relevant and essential constitents. In contrast, redundant holists entertain images that contain logically irrelevant or overspecific material, commonly derived from data used to 'enrich' the curriculum, and these students embed the salient facts and principles in a network of redundant items. Though logically irrelevant, the items in question are of great psychological importance to a 'redundant holist', since he uses them to access, retain and manipulate whatever he was originally required to learn." (Gordon Pask, "Learning Strategies and Individual Competence", 1972) 

"There is nothing supernatural about the process of self-organization to states of higher entropy; it is a general property of systems, regardless of their materials and origin. It does not violate the Second Law of thermodynamics since the decrease in entropy within an open system is always offset by the increase of entropy in its surroundings." (Ervin László, "Introduction to Systems Philosophy", 1972)

"Whereas traditional reductionism sought to find the commonality underlying diversity in reference to a shared substance, such as material atoms, contemporary systems theory seeks to find common features in terms of shared aspects of organization." (Ervin László, "The Systems View of the World: A Holistic Vision for Our Time", 1972)

"The system of nature, of which man is a part, tends to be self-balancing, self-adjusting, self-cleansing. Not so with technology." (Ernst F Schumacher, "Small is Beautiful", 1973)

"Entropy theory is indeed a first attempt to deal with global form; but it has not been dealing with structure. All it says is that a large sum of elements may have properties not found in a smaller sample of them." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 1974)

"When a system is considered in two different states, the difference in volume or in any other property, between the two states, depends solely upon those states themselves and not upon the manner in which the system may pass from one state to the other." (Rudolf Arnheim, "Entropy and Art: An Essay on Disorder and Order", 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)

"A system may be specified in either of two ways. In the first, which we shall call a state description, sets of abstract inputs, outputs and states are given, together with the action of the inputs on the states and the assignments of outputs to states. In the second, which we shall call a coordinate description, certain input, output and state variables are given, together with a system of dynamical equations describing the relations among the variables as functions of time. Modern mathematical system theory is formulated in terms of state descriptions, whereas the classical formulation is typically a coordinate description, for example a system of differential equations." (E S Bainbridge, "The Fundamental Duality of System Theory", 1975)

"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)

"The following four propositions, which appear to the author to be incapable of formal proof, are presented as Fundamental Postulates upon which the entire superstructure of General Systemantics [...] is based [...] (1) Everything is a system. (2) Everything is part of a larger system. (3) The universe is infinitely systematizable, both upward (larger systems) and downward (smaller systems) (4) All systems are infinitely complex. (The illusion of simplicity comes from focusing attention on one or a few variables.)" (John Gall, "Systemantics", 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)

"For any system the environment is always more complex than the system itself. No system can maintain itself by means of a point-for-point correlation with its environment, i.e., can summon enough 'requisite variety' to match its environment. So each one has to reduce environmental complexity - primarily by restricting the environment itself and perceiving it in a categorically preformed way. On the other hand, the difference of system and environment is a prerequisite for the reduction of complexity because reduction can be performed only within the system, both for the system itself and its environment." (Thomas Luckmann & Niklas Luhmann, "The Differentiation of Society", 1977)

"All nature is a continuum. The endless complexity of life is organized into patterns which repeat themselves at each level of system." (James G Miller, "Living Systems", 1978)

"Information is carried by physical entities, such as books or sound waves or brains, but it is not itself material. Information in a living system is a feature of the order and arrangement of its parts, which arrangement provides the signs that constitute a ‘code’ or ‘language’." (John Z Young, "Programs of the Brain", 1978)

"An autopoietic system is organized (defined as a unity) as a network of processes of production (transformation and destruction) of components that produces the components that: (a) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produce them and, (b) constitute it (the machine) as a concrete unity in the space in which they exist by specifying the topological domain of its realization as such a network." (Francisco Varela, "Principles of Biological Autonomy", 1979)

"An autopoietic machine is a machine organized (defined as a unity) as a network of processes of production (transformation and destruction) of components which: (i) through their interactions and transformations continuously regenerate and realize the network of processes (relations) that produced them; and (ii) constitute it (the machine) as a concrete unity in space in which they (the components) exist by specifying the topological domain of its realization as such a network." (Humberto Maturana, "Autopoiesis and Cognition: The realization of the living", 1980)

"The relations that define a system as a unity, and determine the dynamics of interaction and transformations which it may undergo as such a unity constitute the organization of the machine." (Humberto Maturana, "Autopoiesis and cognition: The realization of the living", 1980)

"Heavy dependence on direct observation is essential to biology not only because of the complexity of biological phenomena, but because of the intervention of natural selection with its criterion of adequacy rather than perfection. In a system shaped by natural selection it is inevitable that logic will lose its way." (George A Bartholomew, "Scientific innovation and creativity: a zoologist’s point of view", American Zoologist Vol. 22, 1982)

"A system is an internally organised whole where elements are so intimately connected that they operate as one in relation to external conditions and other systems. An element may be defined as the minimal unit performing a definite function in the whole. Systems may be either simple or complex. A complex system is one whose elements may also be regarded as systems or subsystems." (Alexander Spirkin, "Dialectical Materialism", 1983)

"But structure is not enough to make a system. A system consists of something more than structure: it is a structure with certain properties. When a structure is understood from the standpoint of its properties, it is understood as a system." (Alexander Spirkin, "Dialectical Materialism", 1983)

"Structure is the type of connection between the elements of a whole. […] . Structure is a composite whole, or an internally organised content. […] Structure implies not only the position of its elements in space but also their movement in time, their sequence and rhythm, the law of mutation of a process. So structure is actually the law or set of laws that determine a system's composition and functioning, its properties and stability." (Alexander Spirkin, "Dialectical Materialism", 1983)

"Unfortunately, non-chaotic systems are very nearly as scarce as hen’s teeth, despite the fact that our physical understanding of nature is largely based upon their study." (Joseph Ford, "How Random Is a Coin Toss?" Physics Today Vol. 36 (4), 1983)

"Computation offers a new means of describing and investigating scientific and mathematical systems. Simulation by computer may be the only way to predict how certain complicated systems evolve." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"Dangers lurk in all systems. Systems incorporate the unexamined beliefs of their creators. Adopt a system, accept its beliefs, and you help strengthen the resistance to change." (Frank Herbert, "God Emperor of Dune", 1984)

"Scientific laws give algorithms, or procedures, for determining how systems behave. The computer program is a medium in which the algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms. When the computer program is executed, it causes the numbers and symbols to be modified in the way specified by the scientific laws. It thereby allows the consequences of the laws to be deduced." (Stephen Wolfram, "Computer Software in Science and Mathematics", 1984)

"Stability theory is the study of systems under various perturbing influences. Since there are many systems, many types of influences, and many equations describing systems, this is an open-ended problem. A system is designed so that it will be stable under external influences. However, one cannot predict all external influences, nor predict the magnitude of those that occur. Consequently, we need control theory. If one is interested in stability theory, a natural result is a theory of control." (Richard E Bellman, "Eye of the Hurricane: An Autobiography", 1984)

"The essential principal property of the adaptive system is its time-varying, self-adjusting performance. The need for such performance may readily be seen by realizing that if a designer develops a system of fixed design which he or she considers optimal, the implications are that the designer has foreseen all possible input conditions, at least statistically, and knows what he or she would like the system to do under each of these conditions." (Bernard Widrow & Samuel D Stearns "Adaptive Signal Processing", 1985)

"Any system that insulates itself from diversity in the environment tends to atrophy and lose its complexity and distinctive nature." (Gareth Morgan, "Images of Organization", 1986)

"Catastrophes are often stimulated by the failure to feel the emergence of a domain, and so what cannot be felt in the imagination is experienced as embodied sensation in the catastrophe. (William I Thompson, "Gaia, a Way of Knowing: Political Implications of the New Biology", 1987)

"Organization denotes those relations that must exist among the components of a system for it to be a member of a specific class. Structure denotes the components and relations that actually constitute a particular unity and make its organization real." (Humberto Maturana, "The Tree of Knowledge", 1987)

"The dynamics of any system can be explained by showing the relations between its parts and the regularities of their interactions so as to reveal its organization. For us to fully understand it, however, we need not only to see it as a unity operating in its internal dynamics, but also to see it in its circumstances, i.e., in the context to which its operation connects it. This understanding requires that we adopt a certain distance for observation, a perspective that in the case of historical systems implies a reference to their origin. This can be easy, for instance, in the case of man-made machines, for we have access to every detail of their manufacture. The situation is not that easy, however, as regards living beings: their genesis and their history are never directly visible and can be reconstructed only by fragments."  (Humberto Maturana, "The Tree of Knowledge", 1987)

"A system of variables is 'interrelated' if an action that affects or meant to affect one part of the system will also affect other parts of it. Interrelatedness guarantees that an action aimed at one variable will have side effects and long-term repercussions. A large number of variables will make it easy to overlook them." (Dietrich Dorner, "The Logic of Failure: Recognizing and Avoiding Error in Complex Situations", 1989)

"If we want to solve problems effectively […] we must keep in mind not only many features but also the influences among them. Complexity is the label we will give to the existence of many interdependent variables in a given system. The more variables and the greater their interdependence, the greater the system's complexity. Great complexity places high demands on a planner's capacity to gather information, integrate findings, and design effective actions. The links between the variables oblige us to attend to a great many features simultaneously, and that, concomitantly, makes it impossible for us to undertake only one action in a complex system." (Dietrich Dorner, "The Logic of Failure: Recognizing and Avoiding Error in Complex Situations", 1989)

"Autopoietic systems, then, are not only self-organizing systems, they not only produce and eventually change their own structures; their self-reference applies to the production of other components as well. This is the decisive conceptual innovation. […] Thus, everything that is used as a unit by the system is produced as a unit by the system itself. This applies to elements, processes, boundaries, and other structures and, last but not least, to the unity of the system itself." (Niklas Luhmann, "The Autopoiesis of Social Systems", 1990)

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

"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)

"Systems theory pursues the scientific exploration and understanding of systems that exist in the various realms of experience, in order to arrive at a general theory of systems: an organized expressing of sets of interrelated concepts and principles that apply to all systems." (Béla H Bánáthy, "Systems Design of Education", 1991)

"An internal model allows a system to look ahead to the future consequences of current actions, without actually committing itself to those actions. In particular, the system can avoid acts that would set it irretrievably down some road to future disaster ('stepping off a cliff'). Less dramatically, but equally important, the model enables the agent to make current 'stage-setting' moves that set up later moves that are obviously advantageous. The very essence of a competitive advantage, whether it be in chess or economics, is the discovery and execution of stage-setting moves." (John H Holland, 1992)

"Regarding stability, the state trajectories of a system tend to equilibrium. In the simplest case they converge to one point (or different points from different initial states), more commonly to one (or several, according to initial state) fixed point or limit cycle(s) or even torus(es) of characteristic equilibrial behaviour. All this is, in a rigorous sense, contingent upon describing a potential, as a special summation of the multitude of forces acting upon the state in question, and finding the fixed points, cycles, etc., to be minima of the potential function. It is often more convenient to use the equivalent jargon of 'attractors' so that the state of a system is 'attracted' to an equilibrial behaviour. In any case, once in equilibrial conditions, the system returns to its limit, equilibrial behaviour after small, arbitrary, and random perturbations." (Gordon Pask, "Different Kinds of Cybernetics", 1992)

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

 "What is a system? A system is a network of interdependent components that work together to try to accomplish the aim of the system. A system must have an aim. Without an aim, there is no system. The aim of the system must be clear to everyone in the system. The aim must include plans for the future. The aim is a value judgment.” (William E Deming, "The New Economics for Industry, Government, Education”, 1993)

"The impossibility of constructing a complete, accurate quantitative description of a complex system forces observers to pick which aspects of the system they most wish to understand." (Thomas Levenson, "Measure for Measure: A musical history of science", 1994)

"The prevailing style of management must undergo transformation. A system cannot understand itself. The transformation requires a view from outside. The aim [...] is to provide an outside view - a lens - that I call a system of profound knowledge. It provides a map of theory by which to understand the organizations that we work in." (Dr. W. Edwards Deming, "The New Economics for Industry, Government, Education", 1994)

"Complex adaptive systems have the property that if you run them - by just letting the mathematical variable of 'time' go forward - they'll naturally progress from chaotic, disorganized, undifferentiated, independent states to organized, highly differentiated, and highly interdependent states. Organized structures emerge spontaneously. [...]A weak system gives rise only to simpler forms of self-organization; a strong one gives rise to more complex forms, like life. (J Doyne Farmer, "The Third Culture: Beyond the Scientific Revolution", 1995)

"Self-organization refers to the spontaneous formation of patterns and pattern change in open, nonequilibrium systems. […] Self-organization provides a paradigm for behavior and cognition, as well as the structure and function of the nervous system. In contrast to a computer, which requires particular programs to produce particular results, the tendency for self-organization is intrinsic to natural systems under certain conditions." (J A Scott Kelso, "Dynamic Patterns : The Self-organization of Brain and Behavior", 1995)

"All systems evolve, although the rates of evolution may vary over time both between and within systems. The rate of evolution is a function of both the inherent stability of the system and changing environmental circumstances. But no system can be stabilized forever. For the universe as a whole, an isolated system, time’s arrow points toward greater and greater breakdown, leading to complete molecular chaos, maximum entropy, and heat death. For open systems, including the living systems that are of major interest to us and that interchange matter and energy with their external environments, time’s arrow points to evolution toward greater and greater complexity. Thus, the universe consists of islands of increasing order in a sea of decreasing order. Open systems evolve and maintain structure by exporting entropy to their external environments." (L Douglas Kiel, "Chaos Theory in the Social Sciences: Foundations and Applications", 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)

"Contrary to what happens at equilibrium, or near equilibrium, systems far from equilibrium do not conform to any minimum principle that is valid for functions of free energy or entropy production." (Ilya Prigogine, "The End of Certainty: Time, Chaos, and the New Laws of Nature", 1996) 

"Chaos appears in both dissipative and conservative systems, but there is a difference in its structure in the two types of systems. Conservative systems have no attractors. Initial conditions can give rise to periodic, quasiperiodic, or chaotic motion, but the chaotic motion, unlike that associated with dissipative systems, is not self-similar. In other words, if you magnify it, it does not give smaller copies of itself. A system that does exhibit self-similarity is called fractal. [...] The chaotic orbits in conservative systems are not fractal; they visit all regions of certain small sections of the phase space, and completely avoid other regions. If you magnify a region of the space, it is not self-similar." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"General relativity, one of the most famous theories, is formulated in terms of a nonlinear equation. This makes us wonder if some of the phenomena described by general relativity, namely black holes, objects orbiting black holes, and even the universe itself, can become chaotic under certain circumstances. [...] The problem is the equation itself, namely the equation of general relativity; it is so complex that the most general solution has never been obtained. It has, of course, been solved for many simple systems; if the system has considerable symmetry (e.g., it is spherical) the equation reduces to a number of ordinary equations that can be solved, but chaos does not occur in these cases. In more realistic cases—situations that actually occur in nature - chaos may occur, but the equations are either unsolvable or very difficult to solve. This presents a dilemma. If we try to model the system using many simplifications it won't exhibit chaos, but if we model it realistically we can't solve it." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

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

"The more we study the major problems of our time, the more we come to realise that they cannot be understood in isolation. They are systemic problems, which means that they are interconnected and interdependent." (Fritjof Capra, "The Web of Life: A New Scientific Understanding of Living Systems", 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)

"What is chaos? Everyone has an impression of what the word means, but scientifically chaos is more than random behavior, lack of control, or complete disorder. [...] Scientifically, chaos is defined as extreme sensitivity to initial conditions. If a system is chaotic, when you change the initial state of the system by a tiny amount you change its future significantly." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

"What is renormalization? First of all, if scaling is present we can go to smaller scales and get exactly the same result. In a sense we are looking at the system with a microscope of increasing power. If you take the limit of such a process you get a stability that is not otherwise present. In short, in the renormalized system, the self-similarity is exact, not approximate as it usually is. So renormalization gives stability and exactness." (Barry R Parker, "Chaos in the Cosmos: The stunning complexity of the universe", 1996)

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

"Even revolutionaries conserve; all cultures are conservative. This is so because it is a systemic phenomenon: all systems exist only as long as there is conservation of that which defines them." (Humberto M Romesin & Pille Bunnell, "Biosphere, Homosphere, and Robosphere: What has that to do with Business? Society for Organizational Learning", 1998)

"Is a random outcome completely determined, and random only by virtue of our ignorance of the most minute contributing factors? Or are the contributing factors unknowable, and therefore render as random an outcome that can never be determined? Are seemingly random events merely the result of fluctuations superimposed on a determinate system, masking its predictability, or is there some disorderliness built into the system itself?” (Deborah J Bennett, "Randomness", 1998)

"Self-organization is seen as the process by which systems of many components tend to reach a particular state, a set of cycling states, or a small volume of their state space (attractor basins), with no external interference." (Luis M Rocha, "Syntactic Autonomy", Proceedings of the Joint Conference on the Science and Technology of Intelligent Systems, 1998)

"The notion of system we are interested in may be described generally as a complex of elements or components directly or indirectly related in a network of interrelationships of various kinds, such that it constitutes a dynamic whole with emergent properties." (Walter F. Buckley, "Society: A Complex Adaptive System - Essays in Social Theory", 1998)

"The thing the ecologically illiterate don't realize about an ecosystem is that it's a system. A system! A system maintains a certain fluid stability that can be destroyed by a misstep in just one niche." (Frank Herbert, "Dune: House Atreides", 1999)

"I propose a new concept based on an interpretation of ecosystems: sympoietic systems. These are complex, self-organizing but collectively producing, boundaryless systems. A subsequent distinction between sympoietic and autopoietic systems is discussed. This distinction arises from defining a difference between three key system characteristics: 1) autopoietic systems have self-defined boundaries, sympoietic systems do not; 2) autopoietic systems are self-produced, sympoietic systems are collectively produced; and, 3) autopoietic systems are organizationally closed, sympoietic systems are organizationally ajar." (Beth Dempster, "Sympoietic and Autopoietic Systems: A New Distinction for Self-Organizing Systems". 2000)

"Formulation of a mathematical model is the first step in the process of analyzing the behaviour of any real system. However, to produce a useful model, one must first adopt a set of simplifying assumptions which have to be relevant in relation to the physical features of the system to be modelled and to the specific information one is interested in. Thus, the aim of modelling is to produce an idealized description of reality, which is both expressible in a tractable mathematical form and sufficiently close to reality as far as the physical mechanisms of interest are concerned." (Francois Axisa, "Discrete Systems" Vol. I, 2001)

"In principle, a self-organising system cannot be constructed, since its organisation and behaviour cannot be prescribed and created by an external source. It emerges autonomously in certain conditions (which cannot be prescribed either). The task of the researcher is to investigate in what kind of systems and under what kind of conditions self-organisation emerges." (Rein Vihalemm, "Chemistry as an Interesting Subject for the Philosophy of Science", 2001)

"Self-organization [is] the appearance of structure or pattern without an external agent imposing it." (Francis Heylighen, "The science of Self-organization and Adaptivity", 2001)

"Although the detailed moment-to-moment behavior of a chaotic system cannot be predicted, the overall pattern of its 'random' fluctuations may be similar from scale to scale. Likewise, while the fine details of a chaotic system cannot be predicted one can know a little bit about the range of its 'random' fluctuation." (F David Peat, "From Certainty to Uncertainty", 2002)

"Nature normally hates power laws. In ordinary systems all quantities follow bell curves, and correlations decay rapidly, obeying exponential laws. But all that changes if the system is forced to undergo a phase transition. Then power laws emerge-nature's unmistakable sign that chaos is departing in favor of order. The theory of phase transitions told us loud and clear that the road from disorder to order is maintained by the powerful forces of self-organization and is paved by power laws. It told us that power laws are not just another way of characterizing a system's behavior. They are the patent signatures of self-organization in complex systems." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"[…] networks are the prerequisite for describing any complex system, indicating that complexity theory must inevitably stand on the shoulders of network theory. It is tempting to step in the footsteps of some of my predecessors and predict whether and when we will tame complexity. If nothing else, such a prediction could serve as a benchmark to be disproven. Looking back at the speed with which we disentangled the networks around us after the discovery of scale-free networks, one thing is sure: Once we stumble across the right vision of complexity, it will take little to bring it to fruition. When that will happen is one of the mysteries that keeps many of us going." (Albert-László Barabási, "Linked: How Everything Is Connected to Everything Else and What It Means for Business, Science, and Everyday Life", 2002)

"One of the key insights of the systems approach has been the realization that the network is a pattern that is common to all life. Wherever we see life, we see networks." (Fritjof Capra, "The Hidden Connections: A Science for Sustainable Living", 2002)

"The phenomenon of emergence takes place at critical points of instability that arise from fluctuations in the environment, amplified by feedback loops." (Fritjof Capra, The Hidden Connections: A Science for Sustainable Living, 2002)

"Emergence is the phenomenon of properties, capabilities and behaviours evident in the whole system that are not exclusively ascribable to any of its parts." (Derek Hitchins, "Advanced Systems Thinking, Engineering and Management", 2003)

"The domain of systems science consists thus of all kinds of relational properties which are valid for particular classes of systems, or, in some rare instances, are valid for all systems. The chosen relational classification of systems determines the way in which the domain of systems is divided into subdomains, in a similar fashion as the domain of traditional science has been divided into subdomains of the various disciplines and specializations." (George J Klir & Doug Elias, "Architecture of Systems Problem Solving" 2nd Ed, 2003)

"The reconstruction problem can be stated as follows: Given a behavior system, viewed as an overall system, determine which sets of its subsystems, each viewed as a reconstruction hypothesis, are adequate for reconstructing the given system with an acceptable degree of approximation, solely from the information contained in the subsystems." (George J Klir & Doug Elias, "Architecture of Systems Problem Solving" 2nd Ed, 2003)

"All models are mental projections of our understanding of processes and feedbacks of systems in the real world. The general approach is that models are as good as the system upon which they are based. Models should be designed to answer specific questions and only incorporate the necessary details that are required to provide an answer." (Hördur V Haraldsson & Harald U Sverdrup, "Finding Simplicity in Complexity in Biogeochemical Modelling", 2004)

"Technology can relieve the symptoms of a problem without affecting the underlying causes. Faith in technology as the ultimate solution to all problems can thus divert our attention from the most fundamental problem - the problem of growth in a finite system - and prevent us from taking effective action to solve it." (Donella H Meadows & Dennis L Meadows, "The Limits to Growth: The 30 Year Update", 2004)

"What do people do today when they don’t understand 'the system'? They try to assign responsibility to someone to fix the problem, to oversee 'the system', to coordinate and control what is happening. It is time we recognized that 'the system' is how we work together. When we don’t work together effectively putting someone in charge by its very nature often makes things worse, rather than better, because no one person can understand 'the system' well enough to be responsible. We need to learn how to improve the way we work together, to improve 'the system' without putting someone in charge, in order to make things work." (Yaneer Bar-Yam, "Making Things Work: Solving Complex Problems in a Complex World", 2004)

"A conceptual model is a mental image of a system, its components, its interactions. It lays the foundation for more elaborate models, such as physical or numerical models. A conceptual model provides a framework in which to think about the workings of a system or about problem solving in general. An ensuing operational model can be no better than its underlying conceptualization." (Henry N Pollack, "Uncertain Science … Uncertain World", 2005)

"The progress of science requires the growth of understanding in both directions, downward from the whole to the parts and upward from the parts to the whole." (Freeman Dyson, "The Scientist As Rebel", 2006)

"Humans have difficulty perceiving variables accurately […]. However, in general, they tend to have inaccurate perceptions of system states, including past, current, and future states. This is due, in part, to limited ‘mental models’ of the phenomena of interest in terms of both how things work and how to influence things. Consequently, people have difficulty determining the full implications of what is known, as well as considering future contingencies for potential systems states and the long-term value of addressing these contingencies. " (William B. Rouse, "People and Organizations: Explorations of Human-Centered Design", 2007)

"Systemic problems trace back in the end to worldviews. But worldviews themselves are in flux and flow. Our most creative opportunity of all may be to reshape those worldviews themselves. New ideas can change everything." (Anthony Weston, "How to Re-Imagine the World", 2007)

"The second law of thermodynamics states that in an isolated system, entropy can only increase, not decrease. Such systems evolve to their state of maximum entropy, or thermodynamic equilibrium. Therefore, physical self-organizing systems cannot be isolated: they require a constant input of matter or energy with low entropy, getting rid of the internally generated entropy through the output of heat ('dissipation'). This allows them to produce ‘dissipative structures’ which maintain far from thermodynamic equilibrium. Life is a clear example of order far from thermodynamic equilibrium." (Carlos Gershenson, "Design and Control of Self-organizing Systems", 2007)

"A system, it is said, is a collection of parts together with their relationships that forms a whole that serves a purpose that is meaningful to the system alone, that is, not to its parts or their relationships." (John Boardman & Brian Sauser, "Systems Thinking: Coping with 21st Century Problems", 2008)

"Closed boundaries are simply not an option for any system. While being too open is risky, a system can only learn what this means by being willing to be open in the first place, and then adapting its behavior toward future openness based on its experience with its formative exchanges with the exterior. […] Openness becomes a powerful notion that systems of all types can exploit in order to do better, be better, and find better places to live. Openness becomes a portal for exercising other systems concepts such as boundary, wholes, exchanges (inputs and outputs), and process. It opens up new worlds, and closes down a few too." (John Boardman & Brian Sauser, "Systems Thinking: Coping with 21st Century Problems", 2008)

"[…] 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)

"The beauty of nature insists on taking its time. Everything is prepared. Nothing is rushed. The rhythm of emergence is a gradual, slow beat; always inching its way forward, change remains faithful to itself until the new unfolds in the full confidence of true arrival. Because nothing is abrupt, the beginning of spring nearly always catches us unawares. It is there before we see it; and then we can look nowhere without seeing it. (John O'Donohue, To Bless the Space Between Us: A Book of Blessings, 2008)

"Two systems concepts lie at the disposal of the architect to reflect the beauty of harmony: parsimony and variety. The law of parsimony states that given several explanations of a specific phenomenon, the simplest is probably the best. […] On the other hand, the law of requisite variety states that for a system to survive in its environment the variety of choice that the system is able to make must equal or exceed the variety of influences that the environment can impose on the system." (John Boardman & Brian Sauser, "Systems Thinking: Coping with 21st Century Problems", 2008)

"A model is a representation in that it (or its properties) is chosen to stand for some other entity (or its properties), known as the target system. A model is a tool in that it is used in the service of particular goals or purposes; typically these purposes involve answering some limited range of questions about the target system." (Wendy S Parker, "Confirmation and Adequacy-for-Purpose in Climate Modelling", Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 83, 2009)

"Nature is capable of building complex structures by processes of self-organization; simplicity begets complexity." (Victor J Stenger, God: "The Failed Hypothesis", 2010)

"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)

"System theorists know that it's easy to couple simple-to-understand systems into a ‘super system’ that's capable of displaying behavioral modes that cannot be seen in any of its constituent parts. This is the process called ‘emergence’." (John L Casti, [interview with Austin Allen], 2012)

"When some systems are stuck in a dangerous impasse, randomness and only randomness can unlock them and set them free." (Nassim N Taleb, "Antifragile: Things That Gain from Disorder", 2012) 

"A self–organizing system acts autonomously, as if the interconnecting components had a single mind. And as these components spontaneously march to the beat of their own drummer, they organize, adapt, and evolve toward a greater complexity than one would ever expect by just looking at the parts by themselves." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Complex systems defy intuitive solutions. Even a third-order, linear differential equation is unsolvable by inspection. Yet, important situations in management, economics, medicine, and social behavior usually lose reality if simplified to less than fifth-order nonlinear dynamic systems. Attempts to deal with nonlinear dynamic systems using ordinary processes of description and debate lead to internal inconsistencies. Underlying assumptions may have been left unclear and contradictory, and mental models are often logically incomplete. Resulting behavior is likely to be contrary to that implied by the assumptions being made about' underlying system structure and governing policies." (Jay W. Forrester, "Modeling for What Purpose?", The Systems Thinker Vol. 24 (2), 2013)

"Each systems archetype embodies a particular theory about dynamic behavior that can serve as a starting point for selecting and formulating raw data into a coherent set of interrelationships. Once those relationships are made explicit and precise, the "theory" of the archetype can then further guide us in our data-gathering process to test the causal relationships through direct observation, data analysis, or group deliberation." (Daniel H Kim, "Systems Archetypes as Dynamic Theories", The Systems Thinker Vol. 24 (1), 2013)

"Simplicity in a system tends to increase that system's efficiency. Because less can go wrong with fewer parts, less will. Complexity in a system tends to increase that system's inefficiency; the greater the number of variables, the greater the probability of those variables clashing, and in turn, the greater the potential for conflict and disarray. Because more can go wrong, more will. That is why centralized systems are inclined to break down quickly and become enmeshed in greater unintended consequences." (Lawrence K Samuels, "Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)

"Systems archetypes thus provide a good starting theory from which we can develop further insights into the nature of a particular system. The diagram that results from working with an archetype should not be viewed as the "truth," however, but rather a good working model of what we know at any point in time." (Daniel H Kim, "Systems Archetypes as Dynamic Theories", The Systems Thinker Vol. 24 (1), 2013)

"System meaning is informed by the circumstances and factors that surround the system. The contextual axiom's propositions are those which bound the system by providing guidance that enables an investigator to understand the set of external circumstances or factors that enable or constrain a particular system. The contextual axiom has three principles: (1) holism, (2) darkness, and (3) complementarity." (Patrick Hester & Kevin Adams," Systemic Thinking: Fundamentals for Understanding Problems and Messes", 2014)

"This spontaneous emergence of order at critical points of instability, which is often referred to simply as 'emergence', is one of the hallmarks of life. It has been recognized as the dynamic origin of development, learning, and evolution. In other words, creativity - the generation of new forms - is a key property of all living systems." (Fritjof Capra, "The Systems View of Life: A Unifying Vision", 2014)

"Although cascading failures may appear random and unpredictable, they follow reproducible laws that can be quantified and even predicted using the tools of network science. First, to avoid damaging cascades, we must understand the structure of the network on which the cascade propagates. Second, we must be able to model the dynamical processes taking place on these networks, like the flow of electricity. Finally, we need to uncover how the interplay between the network structure and dynamics affects the robustness of the whole system." (Albert-László Barabási, "Network Science", 2016)