"Images are defined to be information structures, with different kind of images representing different kind of information about what the actor is doing, why and how, and what kind of progress is being made." (Terence R. Mitchell & Lee R Beach, "Organizational behavior and human decision processes", 1990)
"'Mental models' are deeply ingrained assumptions, generalizations, or even pictures or images that influence how we understand the world and how we take action. Very often, we are not consciously aware of our mental models or the effects they have on our behavior. […] Mental models focus on the openness needed to unearth shortcomings in our present ways of seeing the world. [...] Mental models are deeply held internal images of how the world works, images that limit us to familiar ways of thinking and acting. Very often, we are not consciously aware of our mental models or the effects they have on our behavior." (Peter Senge, "The Fifth Discipline", 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 M Senge, "The Fifth Discipline: The Art and Practice of the Learning Organization", 1990)
"Perceptual interpretive processes are applied to mental images in much the same way that they are applied to actual physical objects. In this sense, imagined objects can be 'interpreted' much like physical objects." (Ronald A. Finke, "Creative Imagery", 1990)
"A distinctive feature of mathematics, that feature in virtue of which it stands as a paradigmatically rational discipline, is that assertions are not accepted without proof. […] By proof is meant a deductively valid, rationally compelling argument which shows why this must be so, given what it is to be a triangle. But arguments always have premises so that if there are to be any proofs there must also be starting points, premises which are agreed to be necessarily true, self-evident, neither capable of, nor standing in need of, further justification. The conception of mathematics as a discipline in which proofs are required must therefore also be a conception of a discipline in which a systematic and hierarchical order is imposed on its various branches. Some propositions appear as first principles, accepted without proof, and others are ordered on the basis of how directly they can be proved from these first principle. Basic theorems, once proved, are then used to prove further results, and so on. Thus there is a sense in which, so long as mathematicians demand and provide proofs, they must necessarily organize their discipline along lines approximating to the pattern to be found in Euclid's Elements." (Mary Tiles,"Mathematics and the Image of Reason" , 1991)
"Hard though the scientists of mental imagery try, they cannot get around the fact that the representations they deal with are like pictures. […] The methods have to assume, and the experiments continually corroborate, that having imagery is somehow like perceptual seeing, and that it is somehow like seeing pictures. […] The minimal reason for this assumption is that people do naturally talk of seeing pictures before their mind’s eye." (Eva T H Brann,"The World of Imagination", 1991)
"The most persuasive positive argument for mental images as objects is [that] whenever one thinks one is seeing something there must be something one is seeing. It might be an object directly, or it might be a mental picture. [This] point is so plausible that it is deniable only at the peril of becoming arbitrary. One should concede that the question whether mental images are entities of some sort is not resolvable by logical or linguistic analysis, and believe what makes sense of experience." (Eva T H Brann,"The World of Imagination" , 1991)
"The vision and the core values inspire the creation of the image, but the core ideas are the stuff" of which the image is made. The core ideas that designers generated in the course of using the framework will have to be arranged in sets that enhance the creation of the image and the design of the system." " (Béla H Bánáthy, "Systems Design of Education", 1991)
"For a musician, visualization is the process of picturing in our minds eye what we hear in our mind's ear. Visualization is something we all do. In fact, putting a visual form before the mind's eye or forming a mental image is something that precedes most things that we do." (Jerry Bergonzi, "Melodic Structures", 1992)
"Mathematical modeling is about rules - the rules of reality. What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of ‘model’, is that the mathematical model is an image or picture of reality painted with logical symbols instead of with words, sounds or watercolors." (John L Casti, "Reality Rules: The Fundamentals", 1992)
"The popular image of mathematics as a collection of precise facts, linked together by well-defined logical paths, is revealed to be false. There is randomness and hence uncertainty in mathematics, just as there is in physics." (Paul Davis, "The Mind of God", 1992)
"It is astonishingly beautiful and interesting, how thought is absent when you have an insight. Thought cannot have an insight. It is only when the mind is not operating mechanically in the structure of thought that you have an insight. Having had an insight, thought draws a conclusion from that insight. And then thought acts and thought is mechanical. So I have to find out whether having an insight into myself, which means into the world, and not drawing a conclusion from it is possible. If I draw a conclusion, I act on an idea, on an image, on a symbol, which is the structure of thought, and so I am constantly preventing myself from having insight, from understanding things as they are." (Jiddu Krishnamurti," On Mind and Thought", 1993)
"A world view is a coherent collection of concepts and theorems that must allow us to construct a global image of the world, and in this way to understand as many elements of our experience as possible." (Diederick Aerts et al, "World views: From Fragmentation to Integration", 1994)
"A world view is a system of co-ordinates or a frame of reference in which everything presented to us by our diverse experiences can be placed. It is a symbolic system of representation that allows us to integrate everything we know about the world and ourselves into a global picture, one that illuminates reality as it is presented to us within a certain culture. […] A world view is a coherent collection of concepts and theorems that must allow us to construct a global image of the world, and in this way to understand as many elements of our experience as possible." (Diederick Aerts et al, World views: From Fragmentation to Integration", 1994)
"Every mathematician knows and can give many examples from his scientific work when it appears much more difficult to feel or 'see' a correct hypothesis than later to prove it. Visual images are particularlyo ften used in geometry and topology where one has to work with multidimensional objects which, in principle, do not always admit picturing in a three-dimensional space." (Anatolij Fomenko, "Visual Geometry and Topology", 1994)
"Geometrical intuition plays an essential role in contemporary algebro-topological and geometric studies. Many profound scientific mathematical papers devoted to multi-dimensional geometry use intensively the 'visual slang' such as, say, 'cut the surface', 'glue together the strips', 'glue the cylinder', 'evert the sphere' , etc., typical of the studies of two and three-dimensional images. Such a terminology is not a caprice of mathematicians, but rather a 'practical necessity' since its employment and the mathematical thinking in these terms appear to be quite necessary for the proof of technically very sophisticated results.(Anatolij Fomenko, "Visual Geometry and Topology", 1994)
"I believe that philosophy is part of literature, and not the reverse. Writing is not possible without images. Yet, images don't have to be descriptive; they can be concepts […]. Concepts are mental images." (Paul Virilio, [interview with Louise Wilson] 1994)
"[...] images are probably the main content of our thoughts, regardless of the sensory modality in which they are generated and regardless of whether they are about a thing or a process involving things; or about words or other symbols, in a given language, which correspond to a thing or process. Hidden behind those images, never or rarely knowable by us, there are indeed numerous processes that guide the generation and deployment of those images in space and time. Those processes utilize rules and strategies embodied in dispositional representations. They are essential for our thinking but are not a content of our thoughts." (Antonio R Damasio, "Descartes' Error. Emotion, Reason, and the Human Brain", 1994)
"Just as music comes alive in the performance of it, the same is true of mathematics. The symbols on the page have no more to do with mathematics than the notes on a page of music. They simply represent the experience." (Keith Devlin, "Mathematics: The Science of Patterns", 1994)
"Mental models are the images, assumptions, and stories which we carry in our minds of ourselves, other people, institutions, and every aspect of the world. Like a pane of glass framing and subtly distorting our vision, mental models determine what we see. Human beings cannot navigate through the complex environments of our world without cognitive ‘mental maps’; and all of these mental maps, by definition, are flawed in some way." (Peter M Senge et al, "The Fifth Discipline Fieldbook: Strategies and Tools for Building a Learning Organization", 1994)
"Modem geometry and topology take a special place in mathematics because many of the objects they deal with are treated using visual methods. […] Each mathematician has his own system of concepts of the intrinsic geometry of his" (specific) mathematical world and visual images which he associated with some or other abstract concepts of mathematics" (including algebra, number theory, analysis, etc.). It is noteworthy that sometimes one and the same abstraction brings about the same visual picture in different mathematicians, but these pictures born by imagination are in most cases very difficult to represent graphically, so to say, to draw." (Anatolij Fomenko, "Visual Geometry and Topology", 1994)
"A number is a process that has long ago been thingified so thoroughly that everybody thinks of it as a thing. It is just as feasible-though less familiar to most of us-to think of an operation or a function as a thing. For example, we might talk of square root" as if it were a thing- and I mean here not the square root of any particular number, but the function itself. In this image, the square-root function is a kind of sausage machine: you stuff a number in at one end and its square root pops out at the other." (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)
"The image of mathematics raised by this description of its basic objects is something like a tree, rooted in numbers and branching into ever more esoteric data structures as you proceed from trunk to bough, bough to limb, limb to twig…" (Ian Stewart, "Nature's Numbers: The unreal reality of mathematics", 1995)
"When we visually perceive the world, we do not just process information; we have a subjective experience of color, shape, and depth. We have experiences associated with other senses" (think of auditory experiences of music, or the ineffable nature of smell experiences), with bodily sensations" (e.g., pains, tickles, and orgasms), with mental imagery" (e.g., the colored shapes that appear when one tubs one's eyes), with emotion" (the sparkle of happiness, the intensity of anger, the weight of despair), and with the stream of conscious thought." (David Chalmers, "The Puzzle of Conscious Experience", Scientific American, 1995)
"Artificial intelligence comprises methods, tools, and systems for solving problems that normally require the intelligence of humans. The term intelligence is always defined as the ability to learn effectively, to react adaptively, to make proper decisions, to communicate in language or images in a sophisticated way, and to understand." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)
"Generalization is the process of matching new, unknown input data with the problem knowledge in order to obtain the best possible solution, or one close to it. Generalization means reacting properly to new situations, for example, recognizing new images, or classifying new objects and situations. Generalization can also be described as a transition from a particular object description to a general concept description. This is a major characteristic of all intelligent systems." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)
"If we are to have meaningful, connected experiences; ones that we can comprehend and reason about; we must be able to discern patterns to our actions, perceptions, and conceptions. Underlying our vast network of interrelated literal meanings" (all of those words about objects and actions) are those imaginative structures of understanding such as schema and metaphor, such as the mental imagery that allows us to extrapolate a path, or zoom in on one part of the whole, or zoom out until the trees merge into a forest." (William H Calvin, "The Cerebral Code", 1996)
"Our mental model of the way the world works must shift from images of a clockwork, machinelike universe that is fixed and determined, to the model of a universe that is open, dynamic, interconnected, and full of living qualities." (Joseph Jaworski, "Synchronicity: The Inner Path of Leadership", 1996)
"The logic of the emotional mind is associative; it takes elements that symbolize a reality, or trigger a memory of it, to be the same as that reality. That is why similes, metaphors and images speak directly to the emotional mind." (Daniel Goleman, "Emotional Intelligence", 1996)
"The power of images consists largely in the fact that they integrate different types of knowledge and experience." (David Gooding, "Creative Rationality", 1996)
"The role of science, like that of art, is to blend proximate imagery with more distant meaning, the parts we already understand with those given as new into larger patterns that are coherent enough to be acceptable as truth. Biologists know this relation by intuition during the course of fieldwork, as they struggle to make order out of the infinitely varying patterns of nature." (Edward O Wilson, "In Search of Nature", 1996)
"The seemingly stable scene you normally see is really a mental model that you construct - the eyes are actually darting all around, producing a retinal image as jerky as an amateur video, and some of what you thought you saw was instead filled in from memory." (William H Calvin, "How Brains Think", 1996)
"Discourses are ways of referring to or constructing knowledge about a particular topic of practice: a cluster" (or formation) of ideas, images and practices, which provide ways of talking about, forms of knowledge and conduct associated with, a particular topic, social activity or institutional site in society. These discursive formations, as they are known, define what is and is not appropriate in our formulation of, and our practices in relation to, a particular subject or site of social activity." (Stuart Hall, "Representation: Cultural Representations and Signifying Practices", 1997)
"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. The challenge facing modern managers is to become accomplished in the art of using metaphor to find new ways of seeing, understanding, and shaping their actions." (Gareth Morgan, "Imaginization", 1997)
"Suppose the reasoning centers of the brain can get their hands on the mechanisms that plop shapes into the array and that read their locations out of it. Those reasoning demons can exploit the geometry of the array as a surrogate for keeping certain logical constraints in mind. Wealth, like location on a line, is transitive: if A is richer than B, and B is richer than C, then A is richer than C. By using location in an image to symbolize wealth, the thinker takes advantage of the transitivity of location built into the array, and does not have to enter it into a chain of deductive steps. The problem becomes a matter of plop down and look up. It is a fine example of how the form of a mental representation determines what is easy or hard to think." (Steven Pinker, "How the Mind Works", 1997)
"Visual thinking is often driven more strongly by the conceptual knowledge we use to organize our images than by the contents of the images themselves. Chess masters are known for their remarkable memory for the pieces on a chessboard. But it's not because people with photographic memories become chess masters. The masters are no better than beginners when remembering a board of randomly arranged pieces. Their memory captures meaningful relations among the pieces, such as threats and defenses, not just their distribution in space.(Steven Pinker, "How the Mind Works", 1997)
"We are a people captivated by the power and romance of metaphor, forever seeking the invisible through the image of the visible." (Lewis H Lapham, "Waiting For The Barbarians", 1997)
"Intuition isn't direct perception of something external. It's the effect in the mind/brain of manipulating concrete objects - at a later stage, of making marks on paper, and still later, manipulating mental images. This experience leaves a trace, an effect, in your mind/brain." (Reuben Hersh, "What Is Mathematics, Really?", 1998)
"Specialization, once a maneuver methodically to collect information, now is a manifestation of information overloads. The role of information has changed. Once justified as a means of comprehending the world, it now generates a conflicting and contradictory, fleeting and fragmentation field of disconnected and undigested data." (Stelarc, From Psycho-Body to Cyber-Systems: Images as Post-human Entities, 1998)
"According to the representational format claim, images constitute a class of mental models that is particularly suited to represent visually perceptible information. More specifically, an image can be conceived of as a viewer centered projection of an underlying mental model which, in turn, represents spatiotemporal aspects of external objects or events. Unlike propositional or network representations, images depict, rather than describe, a particular state of affairs." (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)"
"Cultural archetypes are the unconscious models that help us make sense of the world: they are the myths, narratives, images, symbols, and files into which we organize the data of our life experience" (Clotaire Rapaille,"Cultural Imprints", Executive Excellence Vol. 16 (10), 1999)
"Imagining the unseeable is hard, because imagining means having an image in your mind. And how can you have a mental image of something you have never seen? Like perception itself, the models of science are embedded inextricably in the current worldview we call culture." (K C Cole, "First You Build a Cloud and Other Reflections on Physics as a Way of Life", 1999)
"In order to be able to embrace a multitude of external situations, mental models must cope with a variety of representational formats - from quasi-verbal propositions to quasi-pictorial images. " (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)
"Metaphors can have profound signi?cance because, as images or ?gures, they allow the mind to grasp or discover unsuspected ideal and material relationships between objects." (Giuseppe Del Re, "Cosmic Dance", 1999)
"The spirit of mathematics and the essence of its beauty is remarkably fragile, because mathematics is about ideas and about thought. Mathematics takes place in the mind, and no two minds are the same. After many years of study and work, a mathematician may stumble on a vast and beautiful vista that unifies and simplifies many things that once appeared disparate and complicated. Mathematicians can share a beautiful mathematical vista with one another, but there is no camera that can easily capture an image of such a vista to convey it in full to people who have not trudged along many of the same trails." (Silvio Levy,"The Eightfold Way: The Beauty of Klein’s Quartic Curve", 1999)
"Within image theory, it is suggested that important components of decision-making processes are the different 'images' that a person may use to evaluate choice options. Images may represent a person's principles, goals, or plans. Decision options may then match or not match these images and be adopted, rejected, considered further, depending on circumstances." (Deborah J Terry & Michael A Hogg, "Attitudes, Behavior, and Social Context: The Role of Norms and Group Membership", 1999)
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