🅳Robert B Dilts - Collected Quotes

"Another implication of the Law of Requisite Variety is that the member of a system that has the most flexibility also tends to be the catalytic member of that system. This is a significant principle for leadership in particular. The ability to be flexible and sensitive to variation is important in terms of managing the system itself." (Robert B Dilts, "Modeling with NLP", 1998)

"Behavior modeling involves observing and mapping the successful processes which underlie an exceptional performance of some type. It is the process of taking a complex event or series of events and breaking it into small enough chunks so that it can be recapitulated in some way. The purpose of behavior modeling is to create a pragmatic map or 'model' of that behavior which can be used to reproduce or simulate some aspect of that performance by anyone who is motivated to do so. The goal of the behavior modeling process is to identify the essential elements of thought and action required to produce the desired response or outcome. As opposed to providing purely correlative or statistical data, a 'model' of a particular behavior must provide a description of what is necessary to actually achieve a similar result." (Robert B Dilts, "Modeling with NLP", 1998)

"Competence involves consistency. But as soon as you are consistent in one area, you need to have flexibility in another area to be able to accommodate to the part of the system that is not changing." (Robert B Dilts, "Modeling with NLP", 1998)

"Features are the specific qualities or characteristics that we decide to filter for as we are modeling." (Robert B Dilts, "Modeling with NLP", 1998)

"From the NLP perspective, there are inductive transformations, through which we perceive patterns in, and build maps of, the world around us; and there are deductive transformations, through which we describe and act on our perceptions and models of the world. Inductive transformations involve the process of 'chunking up' to find the deeper structure patterns ('concepts', 'ideas', 'universals', etc.) in the collections of experiences we receive through our senses. Deductive transformations operate to 'chunk down' our experiential deep structures into surface structures; rendering general ideas and concepts into specific words, actions and other forms of behavioral output." (Robert B Dilts, "Modeling with NLP", 1998)

"In the NLP view, then, 'reality' is the relationship and interaction between deep structures and surface structures. Thus, there are many possible 'realities'. It is not as if there is 'a map' and 'a territory', there are many possible territories and maps, and the territory is continually changing, partially as a function of the way in which people's maps lead them to interact with that territory." (Robert B Dilts, "Modeling with NLP", 1998)

"[...] modeling involves achieving two simultaneous outcomes - getting a particular result, and, at the same time, learning explicitly how to do it. It is this feature that makes modeling one of the most powerful forms of 'learning to learn' that is available. [...] Modeling is the process of taking a complex event or phenomenon and breaking it into small enough chunks so that it can be recapitulated or applied in some way." (Robert B Dilts, "Modeling with NLP", 1998)

"Modeling is essentially a process of 'sharing ideas'. The ability to model effectively opens the door to many possibilities that have previously been unavailable to humankind. In addition to providing a methodology which can be used to make ideas more explicit and easier to communicate, modeling can transform the way we view and perceive one another." (Robert B Dilts, "Modeling with NLP", 1998)

"Models are not intended to either reflect or construct a single objective reality. Rather, their purpose is to simulate some aspect of a possible reality. In NLP, for instance, it is not important whether or not a model is 'true', but rather that it is 'useful'. In fact, all models can be perceived as symbolic or metaphoric, as opposed to reflective of reality. Whether the description being used is metaphorical or literal, the usefulness of a model depends on the degree to which it allows us to move effectively to the next step in the sequence of transformations connecting deeper structures and surface structures. Instead of 'constructing' reality, models establish a set of functions that serve as a tool or a bridge between deep structures and surface structures. It is this bridge that forms our 'understanding' of reality and allows us to generate new experiences and expressions of reality." (Robert B Dilts, "Modeling with NLP", 1998)

"Neural networks are computer structures, based on the way in which the brain functions. They are used to recognize complex patterns. They typically involve a number of interconnected elements that are used to create a type of "model" of some pattern or phenomenon. The model is formed as a function of the 'weights,' or strengths, of the connections between the elements in the network. This inner 'model' determines the output of the network." (Robert B Dilts, "Modeling with NLP", 1998)

"NLP contains a set of principles and distinctions which are uniquely suited to analyze and identify crucial patterns of values, behavior and interrelationships so that they may be put into pragmatic and testable implementations." (Robert B Dilts, "Modeling with NLP", 1998)

"NLP is the process by which the relevant pieces of these people's behavior was discovered and then organized into a working model." (Robert B Dilts, "Modeling with NLP", 1998)

"NLP operates from the assumption that the map is not the territory. As human beings, we can never know reality, in the sense that we have to experience reality through our senses and our senses are limited. [...] We can only make maps of the reality around us through the information that we receive through our senses and the connection of that information to our own personal memories and other experiences. Therefore, we don't tend to respond to reality itself, but rather to our own maps of reality." (Robert B Dilts, "Modeling with NLP", 1998)

"On one level, it's not possible to completely isolate anyone part of a system from another. People are influenced by many aspects of the system around them. It is important to take into account not only the processes that are happening within the individual, but also the influences on that person from the system around him or her." (Robert B Dilts, "Modeling with NLP", 1998)

"One of the goals of NLP is to identify problematic generalizations, deletions or distortions through the analysis of the 'syntax' or form of the surface structure and provide a system of tools so that a more enriched representation of the deep structure may be attained. Another goal of NLP, represented by the modeling process, is to be able to create better links and pathways between surface structures and deep structures." (Robert B Dilts, "Modeling with NLP", 1998)

"One of the real secrets of managing creativity effectively is determining where to put the point of flexibility. It is ultimately a matter of ecology." (Robert B Dilts, "Modeling with NLP", 1998)

"Perceiving a situation or experience from multiple perspectives allows a person to gain broader insight and understanding with respect to the event." (Robert B Dilts, "Modeling with NLP", 1998)

"Reality is a set of structural transforms of primary data taken from the world. The conversion of primary data into structures involves the selective deletion, distortion or generalization of primary data. The mind can neither mirror nor construct reality. 'Stronger' structures are formed from 'weaker' structures through selective destruction of information. Primary data becomes meaningful only after a series of such operations has transformed it to be congruent with a preexisting structure." (Robert B Dilts, "Modeling with NLP", 1998)

"The focus of most NLP modeling processes is at the level of capabilities, the how to level. Capabilities connect beliefs and values to specific behaviors. Without the how, knowing what one is supposed to do, and even why to do it, is largely ineffective. Capabilities and skills provide the links and leverage to manifest our vision, identity, values and beliefs as actions in a particular environment." (Robert B Dilts, "Modeling with NLP", 1998)

"The key to any effective model of behavior, however, is to find those distinctions which are the most fundamental, simple and impactful for producing practical results in the context in which one is operating." (Robert B Dilts, "Modeling with NLP", 1998)

"[...] the Law of Requisite Variety states that 'in order to successfully adapt and survive, a member of a system needs a certain minimum amount of flexibility, and that flexibility has to be proportional to the potential variation or the uncertainty in the rest of the system'. In other words, if someone is committed to accomplishing a certain goal, he or she needs to have a number of possible ways to reach it. The number of options required to be certain the goal can be reached depends on the amount of change that is possible within the system in which one is attempting to achieve the goal." (Robert B Dilts, "Modeling with NLP", 1998)

"The NLP modeling process consists of applying various strategies for examining the mental and physical processes which underlie a particular performance or the achievement of a particular result, and then creating some type of explicit map or description of those processes which can be applied for some practical purpose. Various modeling strategies delineate different sequences of steps and types of distinctions through which relevant patterns may discovered and formed into descriptions."  (Robert B Dilts, "Modeling with NLP", 1998)

"The objective of the NLP modeling process is not to end up with the one 'right' or 'true' description of a particular person's thinking process, but rather to make an instrumental map that allows us to apply the strategies that we have modeled in some useful way. An 'instrumental map' is one that allows us to act more effectively - the 'accuracy' or 'reality' of the map is less important than its 'usefulness'." (Robert B Dilts, "Modeling with NLP", 1998)

"[...] the philosophy of NLP is that effective learning and change involves initially setting goals, evidence and evidence procedures to reach a particular desired state. A wide coverage of strategies and activities are then provided in order to be able to vary the operations applied to reach goals." (Robert B Dilts, "Modeling with NLP", 1998)

"The primary function of NLP tools and techniques is to help to widen, enrich or add to our maps of the world. The basic presupposition of NLP is that the richer your map of the world is, the more possibilities that you have of dealing with whatever challenges occur in reality." (Robert B Dilts, "Modeling with NLP", 1998)

"[...] there is no one 'right' or 'correct' map of the world. We all have our own world view and that world view is based upon the sort of neurolinguistic maps that we have formed. It's these neurolinguistic maps that will determine how we interpret and how we react to the world around us and give meaning to our behaviors and our experiences, more so than reality itself. Thus, it is generally not external reality that limits us, constrains us, or empowers us, but rather it is our map of that reality. The basic idea of NLP is that if you can enrich or widen your map, you will perceive more choices available to you given the same reality." (Robert B Dilts, "Modeling with NLP", 1998)

"When modeling, it is important to always keep in mind that no single pattern finding method is foolproof." (Robert B Dilts, "Modeling with NLP", 1998)

💠On Problem Solving 13: On Technologies

"I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail." (Abraham H Maslow, "Toward a Psychology of Being", 1962)

"It is a commonplace of modern technology that there is a high measure of certainty that problems have solutions before there is knowledge of how they are to be solved." (John K Galbraith, "The New Industrial State", 1967)

"It is sheer nonsense to expect that any human being has yet been able to attain such insight into the problems of society that he can really identify the central problems and determine how they should be solved. The systems in which we live are far too complicated as yet for our intellectual powers and technology to understand." (C West Churchman, "The Systems Approach", 1968)

"Sometimes, where a complex problem can be illuminated by many tools, one can be forgiven for applying the one he knows best." (Robert E Machol, "Principles of Operations Research", 1975)

"The true line is not between hard natural science and soft social sciences, but between precise science limited to highly abstract and simple phenomena in the laboratory and inexact science and technology dealing with complex problems in the real world." (Herbert A Simon, "Models of My Life", 1991)

"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." (Donnella H Meadows et al," The Limits to Growth: The 30 Year Update, 2004)

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On Insight (1960-1969)

 "The attempt to characterize exactly models of an empirical theory almost inevitably yields a more precise and clearer understanding of the exact character of a theory. The emptiness and shallowness of many classical theories in the social sciences is well brought out by the attempt to formulate in any exact fashion what constitutes a model of the theory. The kind of theory which mainly consists of insightful remarks and heuristic slogans will not be amenable to this treatment. The effort to make it exact will at the same time reveal the weakness of the theory." (Patrick Suppes," A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences", Synthese  Vol. 12 (2/3), 1960)

"Model-making, the imaginative and logical steps which precede the experiment, may be judged the most valuable part of scientific method because skill and insight in these matters are rare. Without them we do not know what experiment to do. But it is the experiment which provides the raw material for scientific theory. Scientific theory cannot be built directly from the conclusions of conceptual models." (Herbert G Andrewartha, "Introduction to the Study of Animal Population", 1961)

"Since we are assured that the all-wise Creator has observed the most exact proportions of number, weight and measure in the make of all things, the most likely way therefore to get any insight into the nature of those parts of the Creation which come within our observation must in all reason be to number, weigh and measure." (Stephen Hales, "Vegetable Staticks", 1961)

"A point of view can be a dangerous luxury when substituted for insight and understanding." (Marshall McLuhan, "The Gutenberg Galaxy", 1962)

"The purpose of computing is insight, not numbers […] sometimes […] the purpose of computing numbers is not yet in sight." (Richard Hamming, [Motto for the book] "Numerical Methods for Scientists and Engineers", 1962)

"[…] it is more important to have beauty in one's equations that to have them fit experiment. […] It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress." (Paul A M Dirac, "The Evolution of the Physicist’s Picture of Nature ", Scientific American, 1963)

"The original insight is most likely to come when elements stored in different compartments of the mind drift into the open, jostle one another, and now and then form new combinations." (Eric Hoffer, "The Ordeal of Change", 1963)

"Mathematicians create by acts of insight and intuition. Logic then sanctions the conquests of intuition. It is the hygiene that mathematics practices to keep its ideas healthy and strong. Moreover, the whole structure rests fundamentally on uncertain ground, the intuition of humans. Here and there an intuition is scooped out and replaced by a firmly built pillar of thought; however, this pillar is based on some deeper, perhaps less clearly defined, intuition. Though the process of replacing intuitions with precise thoughts does not change the nature of the ground on which mathematics ultimately rests, it does add strength and height to the structure." (Morris Kline, "Mathematics in Western Culture", 1964)

"The moment of truth, the sudden emergence of new insight, is an act of intuition. Such intuitions give the appearance of miraculous flashes, or short circuits of reasoning. In fact they may be likened to an immersed chain, of which only the beginning and the end are visible above the surface of consciousness. The diver vanishes at one end of the chain and comes up at the other end, guided by invisible links." (Arthur Koestler, "The Act of Creation", 1964)

"All great insights and discoveries are not only usually thought by several people at the same time, they must also be re-thought in that unique effort to truly say the same thing about the same thing." (Martin Heidegger, "What Is A Thing", 1967)

"[…] the human reason discovers new relations between things not by deduction, but by that unpredictable blend of speculation and insight […] induction, which - like other forms of imagination - cannot be formalized." (Jacob Bronowski, "The Reach of Imagination", 1967)

"More than a burial ground for unacceptable ideas and wishes, the unconscious is the spawning ground of intuition and insight, the source of humor, of poetic imagery, and of scientific analogy." (Judith Groch, "The Right to Create", 1969)

On Insight (1990-1999)

 "Mathematics is amazingly compressible: you may struggle a long time, step by step, to work through some process or idea from several approaches. But once you really understand it and have the mental perspective to see it as a whole, there is a tremendous mental compression. You can file it away, recall it quickly and completely when you need it, and use it as just one step in some other mental process. The insight that goes with this compression is one of the real joys of mathematics." (William P Thurston, "Mathematical education", Notices AMS 37, 1990)

"[…] new insights fail to get put into practice because they conflict with deeply held internal images of how the world works [...] images that limit us to familiar ways of thinking and acting. That is why the discipline of managing mental models - surfacing, testing, and improving our internal pictures of how the world works - promises to be a major breakthrough for learning organizations." (Peter Senge, "The Fifth Discipline: The Art and Practice of the Learning Organization", 1990)

"Science is (or should be) a precise art. Precise, because data may be taken or theories formulated with a certain amount of accuracy; an art, because putting the information into the most useful form for investigation or for presentation requires a certain amount of creativity and insight." (Patricia H Reiff, "The Use and Misuse of Statistics in Space Physics", Journal of Geomagnetism and Geoelectricity 42, 1990)

"Insight is 'mental vision,' one of the ways in which the mind escapes the limits of the obvious or the familiar." (Jennifer James, "Thinking In The Future Tense", 1991) 

"It is not surprising to find many mathematical ideas interconnected or linked. The expansion of mathematics depends on previously developed ideas. The formation of any mathematical system begins with some undefined terms and axioms (assumptions) and proceeds from there to definitions, theorems, more axioms and so on. But history points out this is not necessarily the route that creativity" (Theoni Pappas, "More Joy of Mathematics: Exploring mathematical insights & concepts", 1991)

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

"The scope of Theories of Everything is infinite but bounded; they are necessary parts of a full understanding of things but they are far from sufficient to reveal everything about a Universe like ours. In the pages of this book, we have seen something of what a Theory of Everything might hope to teach us about the unity of the Universe and the way in which it may contain elements that transcend our present compartmentalized view of Nature's ingredients. But we have also learnt that there is more to Everything than meets the eye. Unlike many others that we can imagine, our world contains prospective elements. Theories of Everything can make no impression upon predicting these prospective attributes of reality; yet, strangely, many of these qualities will themselves be employed in the human selection and approval of an aesthetically acceptable Theory of Everything. There is no formula that can deliver all truth, all harmony, all simplicity. No Theory of Everything can ever provide total insight. For, to see through everything, would leave us seeing nothing at all." (John D Barrow, "New Theories of Everything", 1991)

"Fitting is essential to visualizing hypervariate data. The structure of data in many dimensions can be exceedingly complex. The visualization of a fit to hypervariate data, by reducing the amount of noise, can often lead to more insight. The fit is a hypervariate surface, a function of three or more variables. As with bivariate and trivariate data, our fitting tools are loess and parametric fitting by least-squares. And each tool can employ bisquare iterations to produce robust estimates when outliers or other forms of leptokurtosis are present." (William S Cleveland, "Visualizing Data", 1993)

"Puzzle composers share another feature with mathematicians. They know that, generally speaking, the simpler a puzzle is to express, the more attractive it is likely to be found: similarly, simplicity is for both a desirable feature of the solution. Especially satisfying solutions are often described as 'elegant', a word that - no surprise here - is also used by scientists, engineers and designers, indeed by anyone with a problem to solve. However, simplicity is by no means the only reward of success. Far from it! Mathematicians (and scientists and others) can reasonably expect two further returns: they are (in no particular order) firstly the power to do things, and secondly the perception of connections which were never before suspected, leading in turn to the insight and illumination that mathematicians expect from their best arguments." (David Wells, "You Are a Mathematician: A wise and witty introduction to the joy of numbers", 1995)

"[...] two related deficiencies have prevented real progress in understanding insight and its role in problem solving. First, we do not yet have a system of classifying problems into those in which insight occurs versus those in which it does not. However, only if we can isolate problems in which insight occurs will we be able to set on a firm base our theories of the mechanisms underlying insight. Second, formulation of such a taxonomic system requires that we agree on a definition of insight." (Robert W Weisberg, "Prolegomena to theories of insight in problem solving: a taxonomy of problems", 1995)

"Ideas about organization are always based on implicit images or metaphors that persuade us to see, understand, and manage situations in a particular way. Metaphors create insight. But they also distort. They have strengths. But they also have limitations. In creating ways of seeing, they create ways of not seeing. There can be no single theory or metaphor that gives an all-purpose point of view, and there can be no simple 'correct theory' for structuring everything we do." (Gareth Morgan, "Imaginization", 1997)

"Our searches for numerical order lead as often to terminal nuttiness as to profound insight." (Stephen J Gould, "Questioning the Millennium: A Rationalist's Guide to a Precisely Arbitrary Countdown", 1997)

"Cleaning up old proofs is an important part of the mathematical enterprise that often yields new insights that can be used to solve new problems and build more beautiful and encompassing theories." (Bruce Schecter, "My Brain is Open", 1998)

"We use mathematics and statistics to describe the diverse realms of randomness. From these descriptions, we attempt to glean insights into the workings of chance and to search for hidden causes. With such tools in hand, we seek patterns and relationships and propose predictions that help us make sense of the world."  (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"When scientists need to explain difficult points of theory, illustration by hypothetical example - rather than by total abstraction - works well (perhaps indispensably) as a rhetorical device. Such cases do not function as speculations in the pejorative sense - as silly stories that provide insight into complex mechanisms - but rather as idealized illustrations to exemplify a difficult point of theory." (Stephen Jay Gould, "Leonardo's Mountain of Clams and the Diet of Worms", 1998)

"We use mathematics and statistics to describe the diverse realms of randomness. From these descriptions, we attempt to glean insights into the workings of chance and to search for hidden causes. With such tools in hand, we seek patterns and relationships and propose predictions that help us make sense of the world."  (Ivars Peterson, "The Jungles of Randomness: A Mathematical Safari", 1998)

"Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation." (Kenneth E Iverson, "Math for the Layman", 1999)

On Insight (1980-1989)

"The thinking person goes over the same ground many times. He looks at it from varying points of view - his own, his arch-enemy’s, others’. He diagrams it, verbalizes it, formulates equations, constructs visual images of the whole problem, or of troublesome parts, or of what is clearly known. But he does not keep a detailed record of all this mental work, indeed could not. […] Deep understanding of a domain of knowledge requires knowing it in various ways. This multiplicity of perspectives grows slowly through hard work and sets the state for the re-cognition we experience as a new insight." (Howard E Gruber, "Darwin on Man", 1981)

"Instead of insight, maybe all a man gets is strength to wander for a while. Maybe the only gift is a chance to inquire, to know nothing for certain. An inheritance of wonder and nothing more." (William Least Heat-Moon, "Blue Highways", 1982)

"The heart of mathematics consists of concrete examples and concrete problems. Big general theories are usually afterthoughts based on small but profound insights; the insights themselves come from concrete special cases." (Paul Halmos, "Selecta: Expository writing", 1983)

"All the efforts of the researcher to find other models, conceptions, different mathematical forms, better linguistic modes of expression, to do justice to newly discovered layers of being mean self-transformation. The researcher in his place is the human being in self-transformation to more profound insight into what is given." (John H. Dessauer, Universitas: A Quarterly German Review of the Arts and Sciences Vol. 26 (4), 1984)

"When one combines the new insights gained from studying far-from-equilibrium states and nonlinear processes, along with these complicated feedback systems, a whole new approach is opened that makes it possible to relate the so-called hard sciences to the softer sciences of life - and perhaps even to social processes as well. […] It is these panoramic vistas that are opened to us by Order Out of Chaos." (Ilya Prigogine, "Order Out of Chaos: Man's New Dialogue with Nature", 1984)

"Mathematics is good if it enriches the subject, if it opens up new vistas, if it solves old problems, if it fills gaps, fitting snugly and satisfyingly into what is already known, or if it forges new links between previously unconnected parts of the subject It is bad if it is trivial, overelaborate, or lacks any definable mathematical purpose or direction It is pure if its methods are pure - that is, if it doesn't cheat and tackle one problem while pretending to tackle another, and if there are no gaping holes in its logic It is applied if it leads to useful insights outside mathematics. By these criteria, today's mathematics contains as high a proportion of good work as at any other period, and as any other area, and much of it manages to be both pure and applied at the same time." (Ian Stewart, "The Problems of Mathematics", 1987)

"One of the features that distinguishes applied mathematics is its interest in framing important questions about the observed world in a mathematical way. This process of translation into a mathematical form can give a better handle for certain problems than would be otherwise possible. We call this the modeling process. It combines formal reasoning with intuitive insights. Understanding the models devised by others is a first step in learning some of the skills involved, and that is how we proceed in this text, which is an informal introduction to the mathematics of dynamical systems." (Edward Beltrami, "Mathematics for Dynamic Modeling", 1987)

"Although discrete mathematics and statistics provide necessary foundations for computer engineering and social sciences, calculus remains the archetype of higher mathematics. It is a powerful and elegant example of the mathematical method, leading both to major applications and to major theories. The language of calculus has spread to all scientific fields; the insight it conveys about the nature of change is something that no educated person can afford to be without." (Mathematical Sciences Education Board, "Everybody Counts: A Report to the Nation on the Future of Mathematics Education", 1989)

🅱A Stafford Beer - Collected Quotes

"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)

"But in addition to what we decide to do by way of transformation, there are certain tendencies in the way systems behave of their own volition when left to their own devices. The convenient analogy for one of these processes is found in the second law of thermodynamics: an 'ordering' process goes on, for which the name is entropy. This can be explained without technicalities as the tendency of a system to settle down to a uniform distribution of its energy. The dissipation of local pockets of high energy is measured by an increase in entropy, until at maximum entropy all is uniform. According to this model, order is more 'natural' than chaos. This is the reason why it is convenient to discuss cybernetic systems, with their self-regulating tendency to attain stability or orderliness, in terms of entropy - a term which has been taken over to name a key tool of cybernetics." (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)

"A system in a dynamic state, that is to say, one which is operating, may pass quite rapidly from one state to another for an indefinite period, and accounting for this behaviour will obviously require a vast investigation." (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)

"It will be useful if we base the arbitrary classification of systems on two distinct criteria. One obviously valuable criterion is that of the system's complexity. Adopting this criterion, it will be possible to discuss systems according to a three-fold scheme. The least complex with which we shall be concerned may be called: simple but dynamic. A system which is not simple, but which has become highly elaborate and is richly interconnected, will be called: complex but describable. Thirdly, we may discuss systems which have be- come so complicated that, while they may still be designated as complex, they cannot be described in a precise and detailed fashion. Such systems will be called: exceedingly complex." (Stafford Beer, "Cybernetics and Management", 1959)

"There are many kinds of effective control inside deterministic systems, and feedback is only one of them. The most reliable control method is, after all, direct coupling - which can be used in the absence of natural variation in what is connected. In the probabilistic category, however, feedback offers the only really effective mechanism for controlling endemic variation." (Stafford Beer, "Cybernetics and Management", 1959)

"[...] there can be such a thing as a simple probabilistic system. For example, consider the tossing of a penny. Here is a perfectly simple system, but one which is notoriously unpredictable. It maybe described in terms of a binary decision process, with a built-in even probability between the two possible outcomes." (Stafford Beer, "Cybernetics and Management", 1959)

"[…] cybernetics studies the flow of information round a system, and the way in which this information is used by the system as a means of controlling itself: it does this for animate and inanimate systems indifferently. For cybernetics is an interdisciplinary science, owing as much to biology as to physics, as much to the study of the brain as to the study of computers, and owing also a great deal to the formal languages of science for providing tools with which the behaviour of all these systems can be objectively described." (A Stafford Beer, 1966)

"For cybernetics is an interdisciplinary science, owing as much to biology as to physics, as much to the study of the brain as to the study of computers, and owing also a great deal to the formal languages of science for providing tools with which the behaviour of all these systems can be objectively described." (A Stafford Beer, 1966)

"Probably the first clear insight into the deep nature of control […] was that it is not about pulling levers to produce intended and inexorable results. This notion of control applies only to trivial machines. It never applies to a total system that includes any kind of probabilistic element - from the weather, to people; from markets, to the political economy. No: the characteristic of a non-trivial system that is under control, is that despite dealing with variables too many to count, too uncertain to express, and too difficult even to understand, something can be done to generate a predictable goal. Wiener found just the word he wanted in the operation of the long ships of ancient Greece. At sea, the long ships battled with rain, wind and tides - matters in no way predictable. However, if the man operating the rudder kept his eye on a distant lighthouse, he could manipulate the tiller, adjusting continuously in real-time towards the light. This is the function of steersmanship. As far back as Homer, the Greek word for steersman was kubernetes, which transliterates into English as cybernetes." (Stafford Beer, "What is cybernetics?", Kybernetes, 2002) 

"The shocking thing is that there is truth in every one of these notions, and the reason is because cybernetics is an interdisciplinary subject. It must be complicated." (Stafford Beer, "What is cybernetics?", Kybernetes, 2002)

On Insight (-1899)

"[…] it is from long experience chiefly that we are to expect the most certain rules of practice, yet it is withal to be remembered, that observations, and to put us upon the most probable means of improving any art, is to get the best insight we can into the nature and properties of those things which we are desirous to cultivate and improve." (Stephen Hales, "Vegetable Staticks", 1727)

"Reason in a creature is a faculty of widening the rules and purposes of the use of all its powers far beyond natural instinct; it acknowledges no limits to its projects. Reason itself does not work instinctively, but requires trial, practice, and instruction in order gradually to progress from one level of insight to another." (Immanuel Kant, "Idea for a Universal History from a Cosmopolitan Point of View", 1784)

"Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers." (Carl F Gauss, cca. 1831)

"[...] it should be noted that the seeds of wisdom that are to bear fruit in the intellect are sown less by critical studies and learned monographs than by insights, broad impressions, and flashes of intuition." (Carl von Clausewitz, "On War", 1832)

"The insights gained and garnered by the mind in its wanderings among basic concepts are benefits that theory can provide. Theory cannot equip the mind with formulas for solving problems, nor can it mark the narrow path on which the sole solution is supposed to lie by planting a hedge of principles on either side. But it can give the mind insight into the great mass of phenomena and of their relationships, then leave it free to rise into the higher realms of action." (Carl von Clausewitz, "On War", 1832)

"The desire to explain what is simple by what is complex, what is easy by what is difficult, is a calamity affecting the whole body of science, known, it is true, to men of insight, but not generally admitted." (Johann Wolfgang von Goethe, "Maxims and Reflections", 1833)

"This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results." (William Whewell, "The Philosophy of the Inductive Sciences", 1858)

"The mysterious complexity of our life is not to be embraced by maxims... to lace ourselves up in formulas of that sort is to repress all the divine promptings and inspirations that spring from growing insight and sympathy." (George Eliot, "The Mill on the Floss", 1860)

"The sciences are said, and they are truly said, to have a mutual connection, that any one of them may be the better understood, for an insight into the rest." (Samuel Horsley, "Sermons", 1860)

"It often happens that the pursuit of the beautiful and appropriate, or, as it may be otherwise expressed, the endeavor after the perfect, is rewarded with a new insight into the true." (James J Sylvester, "Separation of the Roots of an Algebraical Equation", Philosophical Magazine, 1866)

"A law of nature, however, is not a mere logical conception that we have adopted as a kind of memoria technical to enable us to more readily remember facts. We of the present day have already sufficient insight to know that the laws of nature are not things which we can evolve by any speculative method. On the contrary, we have to discover them in the facts; we have to test them by repeated observation or experiment, in constantly new cases, under ever-varying circumstances; and in proportion only as they hold good under a constantly increasing change of conditions, in a constantly increasing number of cases with greater delicacy in the means of observation, does our confidence in their trustworthiness rise." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1873)

"Science corrects the old creeds, sweeps away, with every new perception, our infantile catechisms, and necessitates a faith commensurate with the grander orbits and universal laws which it discloses yet it does not surprise the moral sentiment that was older and awaited expectant these larger insights." (Ralph Waldo Emerson, "Letters and Social Aims", 1876)

"Our power of scientific insight is but feeble when compared with the profundity of nature, because deep truths require deep thought to enable us to understand and value them." (George Gore, 'The Art of Scientific Discovery", 1878)

"The aim of proof is, in fact, not merely to place the truth of a proposition beyond all doubt, but also to afford us insight into the dependence of one truth upon another. After we have convinced ourselves that a boulder is immovable, by trying unsuccessfully to move it, there remains the further question, what is it that supports it so securely." (Gottlob Frege, "The Foundations of Arithmetic", 1884)

"By thus thinking [by analogy] you will get a more real grasp of the subject and insight into the actual processes occurring in Nature - unknown though these may still strictly be - than if you employed the old ideas of action at a distance, or contented yourselves with no theory at all on which to link the facts. You will have made a step in the direction of the truth, but I must beg you to understand that it is only a step; that what modifications and additions will have to be made to it before it becomes a complete theory of electricity I am unable fully to tell you." (Oliver J Lodge, "Modern Views of Electricity", 1889)

"The history of science shows that great discoveries are made by means of imaginative insight, but it also teaches that mere imagination without dependence upon known facts is frequently a source of much mischief." (James E Creighton, "An Introductory Logic", 1898)

On Insight (2010-2019)

"The idea of natural computation has grown into a new scientific paradigm and has proved to be a rich source of new insights about nature. Many processes in nature exhibit key characteristics of computation, especially discrete units or steps and repetition according to a fixed set of rules. Although the processes may be highly complex, their regularity makes them highly amenable to simulation [...]." (David G Green & Tania Leishman, "Computing and Complexity: Networks, Nature and Virtual Worlds, Philosophy of Complex Systems, 2011)

"A genuine experience of the unexpected, in maths as much as in magic, demands of its performer at once originality of insight and a lightness of touch. Even a single step too many in a method renders ugly and clumsy the theorem or the trick." (Daniel Tammet, "Thinking in Numbers", 2012)

"Regression analysis, like all forms of statistical inference, is designed to offer us insights into the world around us. We seek patterns that will hold true for the larger population. However, our results are valid only for a population that is similar to the sample on which the analysis has been done." (Charles Wheelan, "Naked Statistics: Stripping the Dread from the Data", 2012)

"Understanding chaos requires much less advanced mathematics than other current areas of physics research such as general relativity or particle physics. Observing chaos and fractals requires no specialized equipment; chaos is seen in scores of everyday phenomena - a boiling pot of water, a dripping faucet, shifting weather patterns. And fractals are almost ubiquitous in the natural world. Thus, it is possible to teach the central ideas and insights of chaos in a rigorous, genuine, and relevant way to students with relatively little mathematics background." (David P Feldman, "Chaos and Fractals: An Elementary Introduction", 2012)

"An act of creativity is the result of an insight that arises discontinuously. Of course the insight must be preceded by something that is deeply problematic; it is so deeply problematic that a resolution may well seem impossible. This is why the resolution does not arise through systematic means but only occurs when all systematic approaches have been exhausted to no effect, that is, if you want to be creative you must sometimes be prepared to fly blind. This is not easy to do. Creativity involves living for protracted periods with the kind of tension that arises in situations of cognitive dissonance." (William Byers, "Deep Thinking: What Mathematics Can Teach Us About the Mind", 2015)

"Mathematical modeling is the modern version of both applied mathematics and theoretical physics. In earlier times, one proposed not a model but a theory. By talking today of a model rather than a theory, one acknowledges that the way one studies the phenomenon is not unique; it could also be studied other ways. One's model need not claim to be unique or final. It merits consideration if it provides an insight that isn't better provided by some other model." (Reuben Hersh, "Mathematics as an Empirical Phenomenon, Subject to Modeling", 2017)

"Sometimes mathematical advances happen by just looking at something in a slightly different way, which doesn’t mean building something new or going somewhere different, it just means changing your perspective and opening up huge new possibilities as a result. This particular insight leads to calculus and hence the understanding of anything curved, anything in motion, anything fluid or continuously changing." (Eugenia Cheng, "Beyond Infinity: An Expedition to the Outer Limits of Mathematics", 2017)

"Artificial intelligence is defined as the branch of science and technology that is concerned with the study of software and hardware to provide machines the ability to learn insights from data and the environment, and the ability to adapt in changing situations with high precision, accuracy and speed." (Amit Ray, "Compassionate Artificial Intelligence", 2018)

"The goal of data science is to improve decision making by basing decisions on insights extracted from large data sets. As a field of activity, data science encompasses a set of principles, problem definitions, algorithms, and processes for extracting nonobvious and useful patterns from large data sets. It is closely related to the fields of data mining and machine learning, but it is broader in scope." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

"The patterns that we extract using data science are useful only if they give us insight into the problem that enables us to do something to help solve the problem." (John D Kelleher & Brendan Tierney, "Data Science", 2018)

On Insight (2000-2009)

"Mathematics has given us dazzling insights into the power of exponential growth and how the same patterns recur in numbers, regardless of the phenomena being observed." (Richar Koch, "The Power Laws", 2000)

"Somehow mathematicians seem to long for more than just results from their proofs; they want insight." (John L Casti, "Mathematical Mountaintops: The Five Most Famous Problems of All Time", 2001)

"When we have difficulties solving a problem, insight into its solution can come about by restructuring the problem." (S Ian Robertson, "Problem Solving", 2001)

"Natural frequencies facilitate inferences made on the basis of numerical information. The representation does part of the reasoning, taking care of the multiplication the mind would have to perform if given probabilities. In this sense, insight can come from outside the mind." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"Why does representing information in terms of natural frequencies rather than probabilities or percentages foster insight? For two reasons. First, computational simplicity: The representation does part of the computation. And second, evolutionary and developmental primacy: Our minds are adapted to natural frequencies." (Gerd Gigerenzer, "Calculated Risks: How to know when numbers deceive you", 2002)

"Becoming a real researcher has been the ultimate humbling experience for me. Nature is the examiner from hell; if you find new things at all, you always find them the hard way, with sweat and tears. Only then do you notice that there was a really easy way to find them. But this insight rarely arrives before you have been utterly humiliated and reduced to despair." (João Magueijo, "Faster Than The Speed Of Light: The Story of a Scientific Speculation", 2003)

"Proofs should be as short, transparent, elegant, and insightful as possible." (Burkard Polster,"Q.E.D.: Beauty in Mathematical Proof", 2004)

"Central tendency is the formal expression for the notion of where data is centered, best understood by most readers as 'average'. There is no one way of measuring where data are centered, and different measures provide different insights." (Charles Livingston & Paul Voakes, "Working with Numbers and Statistics: A handbook for journalists", 2005)

"Insight is not a lightbulb that goes off inside our heads. It is a flickering candle that can easily be snuffed out." (Malcolm Gladwell, "Blink: The Power of Thinking Without Thinking", 2005)

"It is from this continuousness of thought and perception that the scientist, like the writer, receives the crucial flash of insight out of which a piece of work is conceived and executed. And the scientist (again like the writer) is grateful when the insight comes, because insight is the necessary catalyst through which the abstract is made concrete, intuition be given language, language provides specificity, and real work can go forward." (Vivian Gornick, "Women in Science: Then and Now", 2009)

On Insight (1970-1979)

"Insight doesn't happen often in the click of the moment, like a lucky snapshot, but it comes in its own time and more slowly and from nowhere but within." (Eudora Welty, "One Time, One Place", 1971)

"Early scientific thinking was holistic, but speculative - the modern scientific temper reacted by being empirical, but atomistic. Neither is free from error, the former because it replaces factual inquiry with faith and insight, and the latter because it sacrifices coherence at the altar of facticity. We witness today another shift in ways of thinking: the shift toward rigorous but holistic theories. This means thinking in terms of facts and events in the context of wholes, forming integrated sets with their own properties and relationships." (Ervin László, "Introduction to Systems Philosophy", 1972)

"Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework." (Melvin Schwartz, "Principles of Electrodynamics", 1972)

"Science cannot develop unless it is pursued for the sake of pure knowledge and insight. It will not survive unless it is used intensely and wisely for the betterment of humanity and not as an instrument of domination by one group over another." (Victor F Weisskopf, "Physics in the Twentieth Century: Selected Essays", 1972)

"Though we can say that mathematics is not art, some mathematicians think of themselves as artists of pure form. It seems clear, however, that their elegant and near aesthetic forms fail as art, because they are secondary visual ideas, the product of an intellectual set of restraints, rather than the cause of a felt insight realized in and through visual form." (Robert E Mueller, "Idols of Computer Art", 1972)

"[...] it is rather more difficult to recapture directness and simplicity than to advance in the direction of ever more sophistication and complexity. Any third-rate engineer or researcher can increase complexity; but it takes a certain flair of real insight to make things simple again." (Ernst F Schumacher, "Small Is Beautiful", 1973)

"The advantage of this way of proceeding is evident: insights and skills obtained on the model-side can be - certain transference criteria satisfied - transferred to the original, [in this way] the model-builder obtains a new knowledge about the modeled original […]" (Herbert Stachowiak, "Allgemeine Modelltheorie", 1973)

"All of us must cross the line between ignorance and insight many times before we truly understand." (David Hawkins, "The Informed Vision: Essays on Learning and Human Nature", 1974)

"The history of science is full of revolutionary advances that required small insights that anyone might have had, but that, in fact, only one person did." (Isaac Asimov, "The Three Numbers", Ellery Queen's Mystery Magazine, 1974)

"A metaphor is a word used in an unfamiliar context to give us a new insight; a good metaphor moves us to see our ordinary world in an extraordinary way." (Sallie McFague, "Speaking in Parables", 1975)

"To gauge the understanding and insight that metaphysics provides is to ask whether, in the final analysis, it helps us to cope with our world and harmonize our existence with nature, humanity, and ourselves, and leads to greater freedom and self-realization. Metaphysics is only the beginning. The end is human progress." (Rudolph Rummel, "Understanding Conflict and War: The dynamic psychological field", 1975)

"Mathematical induction […] is an entirely different procedure. Although it, too, leaps from the knowledge of particular cases to knowledge about an infinite sequence of cases, the leap is purely deductive. It is as certain as any proof in mathematics, and an indispensable tool in almost every branch of mathematics." (Martin Gardner, "Aha! Insight", 1978)

"The word ‘induction’ has two essentially different meanings. Scientific induction is a process by which scientists make observations of particular cases, such as noticing that some crows are black, then leap to the universal conclusion that all crows are black. The conclusion is never certain. There is always the possibility that at least one unobserved crow is not black." (Martin Gardner, "Aha! Insight", 1978)

"Every discovery, every enlargement of the understanding, begins as an imaginative preconception of what the truth might be. The imaginative preconception - a ‘hypothesis’ - arises by a process as easy or as difficult to understand as any other creative act of mind; it is a brainwave, an inspired guess, a product of a blaze of insight. It comes anyway from within and cannot be achieved by the exercise of any known calculus of discovery. " (Sir Peter B Medawar, "Advice to a Young Scientist", 1979)

"The truth is not in nature waiting to declare itself, and we cannot know a priori which observations are relevant and which are not; every discovery, every enlargement of the understanding begins as an imaginative preconception of what the truth might be. This imaginative preconception - a 'hypothesis' - arises by a process as easy or as difficult to understand as any other creative act of mind; it is a brainwave, an inspired guess, the product of a blaze of insight. It comes, anyway, from within and cannot be arrived at by the exercise of any known calculus of discovery." (Sir Peter B Medawar, "Advice to a Young Scientist", 1979)