"An important symptom of an emerging understanding is the capacity to represent a problem in a number of different ways and to approach its solution from varied vantage points; a single, rigid representation is unlikely to suffice." (Howard Gardner, "The Unschooled Mind", 1991)
"On this view, we recognize science to be the search for algorithmic compressions. We list sequences of observed data. We try to formulate algorithms that compactly represent the information content of those sequences. Then we test the correctness of our hypothetical abbreviations by using them to predict the next terms in the string. These predictions can then be compared with the future direction of the data sequence. Without the development of algorithmic compressions of data all science would be replaced by mindless stamp collecting - the indiscriminate accumulation of every available fact. Science is predicated upon the belief that the Universe is algorithmically compressible and the modern search for a Theory of Everything is the ultimate expression of that belief, a belief that there is an abbreviated representation of the logic behind the Universe's properties that can be written down in finite form by human beings." (John D Barrow, New Theories of Everything", 1991)
"Somehow the breathless world that we witness seems far removed from the timeless laws of Nature which govern the elementary particles and forces of Nature. The reason is clear. We do not observe the laws of Nature: we observe their outcomes. Since these laws find their most efficient representation as mathematical equations, we might say that we see only the solutions of those equations not the equations themselves. This is the secret which reconciles the complexity observed in Nature with the advertised simplicity of her laws." (John D Barrow, "New Theories of Everything", 1991)
"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)
"A mental model is not normally based on formal definitions but rather on concrete properties that have been drawn from life experience. Mental models are typically analogs, and they comprise specific contents, but this does not necessarily restrict their power to deal with abstract concepts, as we will see. The important thing about mental models, especially in the context of mathematics, is the relations they represent. […] The essence of understanding a concept is to have a mental representation or mental model that faithfully reflects the structure of that concept. (Lyn D. English & Graeme S. Halford, "Mathematics Education: Models and Processes", 1995)
"The representational nature of maps, however, is often ignored - what we see when looking at a map is not the word, but an abstract representation that we find convenient to use in place of the world. When we build these abstract representations we are not revealing knowledge as much as are creating it." (Alan M MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)
"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)
"A certain theory of representation implies a certain theory of meaning - and meaning is what we live by." (Paul Cilliers, "Complexity and Postmodernism", 1998)
"A model is an external and explicit representation of part of reality as seen by the people who wish to use that model to understand, to change, to manage, and to control that part of reality in some way or other." (Michael Pidd, "Just Modeling through: A Rough Guide to Modeling", Interfaces, Vol. 29, No. 2, 1999)
"In broad terms, a mental model is to be understood as a dynamic symbolic representation of external objects or events on the par. t of some natural or artificial cognitive system. Mental models are thought to have certain properties which make them stand out against other forms of symbolic representations." (Gert Rickheit & Lorenz Sichelschmidt, "Mental Models: Some Answers, Some Questions, Some Suggestions", 1999)
"What it means for a mental model to be a structural analog is that it embodies a representation of the spatial and temporal relations among, and the causal structures connecting the events and entities depicted and whatever other information that is relevant to the problem-solving talks. […] The essential points are that a mental model can be nonlinguistic in form and the mental mechanisms are such that they can satisfy the model-building and simulative constraints necessary for the activity of mental modeling." (Nancy J Nersessian, "Model-based reasoning in conceptual change", 1999)
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