On Maps (1990-1999)

"Physicists' models are like maps: never final, never complete until they grow as large and complex as the reality they represent." (James Gleick, "Genius: The Life and Science of Richard Feynman, Epilogue", 1992)

"Geometry and topology most often deal with geometrical figures, objects realized as a set of points in a Euclidean space (maybe of many dimensions). It is useful to view these objects not as rigid (solid) bodies, but as figures that admit continuous deformation preserving some qualitative properties of the object. Recall that the mapping of one object onto another is called continuous if it can be determined by means of continuous functions in a Cartesian coordinate system in space. The mapping of one figure onto another is called homeomorphism if it is continuous and one-to-one, i.e. establishes a one-to-one correspondence between points of both figures." (Anatolij Fomenko, "Visual Geometry and Topology", 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, "The Fifth Discipline Fieldbook: Strategies and Tools for Building a Learning Organization", 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)

"Maps, due to their melding of scientific and artistic approaches, always involve complex interaction between the denotative and the connotative meanings of signs they contain." (Alan MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"The fact that map is a fuzzy and radial, rather than a precisely defined, category is important because what a viewer interprets a display to be will influence her expectations about the display and how she interacts with it." (Alan MacEachren, "How Maps Work: Representation, Visualization, and Design", 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 MacEachren, "How Maps Work: Representation, Visualization, and Design", 1995)

"A coordinate is a number or value used to locate a point with respect to a reference point, line, or plane. Generally the reference is zero. […] The major function of coordinates is to provide a method for encoding information on charts, graphs, and maps in such a way that viewers can accurately decode the information after the graph or map has been generated. " (Robert L Harris, "Information Graphics: A Comprehensive Illustrated Reference", 1996)

"A good map tells a multitude of little white lies; it suppresses truth to help the user see what needs to be seen. Reality is three-dimensional, rich in detail, and far too factual to allow a complete yet uncluttered two-dimensional graphic scale model. Indeed, a map that did not generalize would be useless. But the value of a map depends on how well its generalized geometry and generalized content reflect a chosen aspect of reality." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"If we know when a sequence approaches a point or, as we say, converges to a point, we can define a continuous mapping from one metric space to another by using the property that a converging sequence is mapped to the corresponding converging sequence." (Kenji Ueno & Toshikazu Sunada, "A Mathematical Gift, III: The Interplay Between Topology, Functions, Geometry, and Algebra", Mathematical World Vol. 23, 1996)

"Not only is it easy to lie with maps, it's essential. To portray meaningful relationships for a complex, three-dimensional world on a flat sheet of paper or a video screen, a map must distort reality. As a scale model, the map must use symbols that almost always are proportionally much bigger or thicker than the features they represent. To avoid hiding critical information in a fog of detail, the map must offer a selective, incomplete view of reality. There's no escape from the cartographic paradox: to present a useful and truthful picture, an accurate map must tell white lies." (Mark S Monmonier, "How to Lie with Maps" 2nd Ed., 1996)

"People respond to their experience, not to reality itself. We do not know what reality is. Our senses, beliefs, and past experience give us a map of the world from which to operate." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)

"The nature of maps and of their use in science and society is in the midst of remarkable change - change that is stimulated by a combination of new scientific and societal needs for geo-referenced information and rapidly evolving technologies that can provide that information in innovative ways. A key issue at the heart of this change is the concept of ‘visualization’." (Alan MacEachren, "Exploratory cartographic visualization: advancing the agenda", 1997)

"Delay time, the time between causes and their impacts, can highly influence systems. Yet the concept of delayed effect is often missed in our impatient society, and when it is recognized, it’s almost always underestimated. Such oversight and devaluation can lead to poor decision making as well as poor problem solving, for decisions often have consequences that don’t show up until years later. Fortunately, mind mapping, fishbone diagrams, and creativity/brainstorming tools can be quite useful here." (Stephen G Haines, "The Manager's Pocket Guide to Strategic and Business Planning", 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)

"Having a choice is better than not having a choice. Always try to have a map for yourself that gives you the widest and richest number of choices. Act always to increase choice. The more choices you have, the freer you are and the more influence you have." (Joseph O’Connor, "Leading With NLP: Essential Leadership Skills for Influencing and Managing People", 1998)

"In NLP terms, then, a master is not someone who already knows the answers and has the solutions but someone who is able to ask worthwhile questions and direct the process of learning, problem solving and creativity to form new maps of the world that lead to useful new answers and possibilities." (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)

"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)

"Our brain is mapping the world. Often that map is distorted, but it's a map with constant immediate sensory input." (Edward O Wilson, [interview] 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 pursuit of science is more than the pursuit of understanding. It is driven by the creative urge, the urge to construct a vision, a map, a picture of the world that gives the world a little more beauty and coherence than it had before." (John A Wheeler, "Geons, Black Holes, and Quantum Foam: A Life in Physics", 1998)

"A collective mental map functions first of all as a shared memory. Various discoveries by members of the collective are registered and stored in this memory, so that the information will remain available for as long as necessary. The storage capacity of this memory is in general much larger than the capacities of the memories of the individual participants. This is because the shared memory can potentially be inscribed over the whole of the physical surroundings, instead of being limited to a single, spatially localized nervous system. Thus, a collective mental map differs from cultural knowledge, such as the knowledge of a language or a religion, which is shared among different individuals in a cultural group but is limited by the amount of knowledge a single individual can bear in mind." (Francis Heylighen, "Collective Intelligence and its Implementation on the Web", 1999)