visualization

"Let's not pretend that mental phenomena can be mapped on to the characteristics of billiard balls."

"If we then make the obvious assumption that the content of a map is appropriate to its purpose, there yet remains the equally significant evaluation of the visual methods employed to convey that content."

"Where, after all, do universal human rights begin? In small places, close to home—so close and so small that they cannot be seen on any map of the world."

"There are no maps to lead us where we are going, to this new world of our own making. As the world looks back to nine decades of war, of strife, of suspicion, let us also look forward—to a new century, and a new millennium, of peace, freedom and prosperity."

"There's no road map on how to raise a family: it's always an enormous negotiation."

"No map contains all the information about the territory it represents. The road map we get at the gasoline station may show all the roads in the state, but it will not as a rule show latitude and longitude. A physical map goes into details about the topography of a country but is indifferent to political boundaries. Furthermore, the scale of the map makes a big difference. The smaller the scale the less features will be shown."

"A fundamental value in the scientific outlook is concern with the best available map of reality. The scientist will always seek a description of events which enables him to predict most by assuming least. He thus already prefers a particular form of behavior. If moralities are systems of preferences, here is at least one point at which science cannot be said to be completely without preferences. Science prefers good maps."

"Wars of nations are fought to change maps. But wars of poverty are fought to map change."

"Pierre Bourdieu, a French sociologist, observed that elites in a society typically maintain their power not simply by controlling the means of production (ie money), but by dominating the cultural discourse too (ie a society’s intellectual map). And what is most important in relation to that cognitive map is not what is overtly stated and discussed – but what is left unstated, or ignored."

"In fact, it is Shakespeare who gives us the map of the mind. It is Shakespeare who invents Freudian Psychology. Freud finds ways of translating it into supposedly analytical vocabulary."

"Many technologies for mapping and viewing are closely connected to the growth of surveillance in contemporary society and the power of defining who sees and who is seen (Parenti 2003, pp. 3, 9; Dodge & Perkins 2009). The use of surveillance technologies to examine the past does not exclude the present: When satellite imagery is used to search for archaeological sites and their spatial relationships to landforms, images of contemporary settlements and land use are also part of the picture. This intrusion into people’s lives takes place without consent, informed or otherwise."

"The map is not the territory, and the name is not the thing named."

"There are few results of man‟s activities that so closely parallel man's interests and intellectual capabilities as the map."

"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."

"Understanding how maps work and why maps work (or do not work) as representations in their own right and as prompts to further representations, and what it means for a map to work, are critical issues as we embark on a visual information age."

"Man always kills the thing he loves, and so we the pioneers have killed our wilderness. Some say we had to. Be that as it may, I am glad I shall never be young without wild country to be young in. Of what avail are forty freedoms without a blank spot on the map?"

"Heinz performs the magic trick of convincing us that the familiar objects of our existence can be seen to be nothing more than tokens for the behaviors of the organism that apparently create stable forms. These stabilities persist, for that organism, as an observing system. This is not to deny an underlying reality that is the source of objects, but rather to emphasize the role of process, and the role of the organism in the production of a living map, a map that is so sensitive that map and territory are conjoined."

"The map is not the territory … The only usefulness of a map depends on similarity of structure between the empirical world and the map."

"Two important characteristics of maps should be noticed. A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness."

"Now, to use the famous metaphor by Alfred Korzybski in his Science and Sanity (1933), this verbal world ought to stand in relation to the extensional world as a map does to the territory it is supposed to represent. If a child grows to adulthood with a verbal world in his head which corresponds fairly closely to the extensional world that he finds around him in his widening experience, he is in relatively small danger of being shocked or hurt by what he finds, because his verbal world has told him what, more or less, to expect. He is prepared for life. If, however, he grows up with a false map in his head [...] he will constantly be running into trouble, wasting his efforts, and acting like a fool. He will not be adjusted to the world as it is: he may, if the lack of adjustment is serious, end up in a mental hospital. (editor's link)"

"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."

"We invented a nonexistent Plan, and They not only believed it was real but convinced themselves that They had been part of it for ages, or rather They identified the fragments of their muddled mythology as moments of our Plan, moments joined in a logical, irrefutable web of analogy, semblance, suspicion. But if you invent a plan and others carry it out, it's as if the Plan exists. At that point it does exist. Hereafter, hordes of Diabolicals will swarm through the world in search of the map. We offered a map to people who were trying to overcome a deep private frustration. What frustration? Belbo's first file suggested it to me: There can be no failure if there really is a Plan. Defeated you may be, but never through any fault of your own. To bow to a cosmic will is no shame. You are not a coward; you are a martyr."

"A map is not the territory. - Alfred Korzybski"

"In generalizing lies the difficulty of scientific map-making, for it no longer allows the cartographer to rely merely on objective facts but requires him to interpret them subjectively. To be sure the selection of the subject matter is controlled by considerations regarding its suitability and value, but the manner in which this material is to be rendered graphically depends on personal and subjective feeling. But the latter must not predominate: the dictates of science will prevent any erratic flight of the imagination and impart to the map a fundamentally objective character in spite of all subjective impulses. It is in this respect that maps are distinguished from fine products of art. Generalized maps and, in fact, all abstract maps should, therefore, be products of art clarified by science."

"This seems highly likely, especially as it has been shown that in several systems mutations affecting the same amino acid are extremely near together on the genetic map."

"You fall in love with somebody who fits within what I call your 'love map,' an unconscious list of traits that you build in childhood as you grow up. And I also think that you gravitate to certain people, actually, with somewhat complementary brain systems."

"We may think of maps and mapping as an objective process, but that would be an illusion. What gets mapped, and more importantly, what does not, is a product of various social, economic, and political phenomena. Quite apart from border disputes and contentious sovereignty, mapping also reflects political priorities. Creating the survey data that can be used in maps is expensive, and large-scale mapping endeavors are typically the preserve of states, whose ability to deliver that data often depends on resources that compete with other governmental priorities. This is true especially in resource-constrained settings."

"“It does not appear to be too difficult,” Alain agreed. “But I remember being cautioned that maps carry their own illusions, often making appear simple a journey which is actually far more difficult in practice.”"

"History is not everything, but it is a starting point. History is a clock that people use to tell their political and cultural time of day. It is a compass they use to find themselves on the map of human geography. It tells them where they are but, more importantly, what they must be."

"Believable fairy-stories must be intensely practical. You must have a map, no matter how rough. Otherwise you wander all over the place. In The Lord of the Rings I never made anyone go farther than he could on a given day"

"The three basic mechanisms of averaging, feedback and division of labor give us a first idea of a how a CMM [Collective Mental Map] can be developed in the most efficient way, that is, how a given number of individuals can achieve a maximum of collective problem-solving competence. A collective mental map is developed basically by superposing a number of individual mental maps. There must be sufficient diversity among these individual maps to cover an as large as possible domain, yet sufficient redundancy so that the overlap between maps is large enough to make the resulting graph fully connected, and so that each preference in the map is the superposition of a number of individual preferences that is large enough to cancel out individual fluctuations. The best way to quickly expand and improve the map and fill in gaps is to use a positive feedback that encourages individuals to use high preference paths discovered by others, yet is not so strong that it discourages the exploration of new paths."

"A face is a road map of someone's life. Without any need to amplify that or draw attention to it, there's a great deal that's communicated about who this person is and what their life experiences have been."

"Ideas, unlike solid structures, do not perish. They remain immortal, immaterial and everywhere, like all Divine things. Ideas are a golden, savage landscape that we wander unaware, without a map. Be careful: in the last analysis, reality may be exactly what we think it is."

"I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit."

"A conceptual model is simply a framework or schematic to understand the interaction of workforce education and development systems with other variables in a society."

"If the Greeks had had a mind to reduce mathematics to one field... their only choice would have been to reduce arithmetic to geometry... it is hardly surprising that for nearly two millennia geometry took pride of place in mathematics. And it would have been obvious to any mathematician that a geometrical problem could not be stated or solved in the language of numbers, since the geometrical universe had more structure than the numerical universe. If one desired to translate geometrical problems into the language of numbers, one would have to invent (or discover) more numbers."

"The conceptual model is a non-software specific description of the simulation model that is to be developed, describing the objectives, inputs, outputs, content, assumptions and simplifications of the model."

"Although there is no study which presents so simple a beginning as that of geometry, there is none in which difficulties grow more rapidly as we proceed, and what may appear at first rather paradoxical, the more acute the student the more serious will the impediments in the way of his progress appear. This necessarily follows in a science which consists of reasoning from the very commencement, for it is evident that every student will feel a claim to have his objections answered, not by authority, but by argument, and that the intelligent student will perceive more readily than another the force of an objection and the obscurity arising from an unexplained difficulty, as the greater is the ordinary light the more will occasional darkness be felt. To remove some of these difficulties is the principal object of this Treatise."

"Let us calculate the motion of bodies, but also consult the plans of the Intelligence that makes them move. It seems that the ancient philosophers made the first attempts at this sort of science, in looking for metaphysical relationships between numbers and material bodies. When they said that God occupies himself with geometry, they surely meant that He unites in that science the works of His power with the perspectives of His wisdom. From the all too few ancient geometers who undertook such studies, we have little that is intelligible or well-founded. The perfection which geometry has acquired since their time puts us in a better position to succeed, and may more than compensate for the advantages that those great minds had over us."

"To-day, thanks to Einstein, we have definite reasons for believing that ultra-precise observation of nature has revealed our natural geometry arrived at with solids and light rays to be slightly non-Euclidean and to vary from place to place. So although the non-Euclidean geometers never suspected it (with the exception of Gauss, Riemann and Clifford), our real world happens to be one of the dream-worlds whose possible existence their mathematical genius forsaw."

"A more thorough study of Euclid's axioms and postulates proved them to be inadequate for the deduction of Euclid's geometry. ...Hilbert and others succeeded in filling the gap by stating explicitly a complete system of postulates for Euclidean and non-Euclidean geometries alike. Among the postulates missing in Euclid's list was the celebrated postulate of Archimedes, according to which, by placing an indefinite number of equal lengths end to end along a line, we should eventually pass any point arbitrarily selected on the line. Hilbert, by denying this postulate, just as Lobatchewski and Riemann had denied Euclid's parallel postulate, succeeded in constructing a new geometry known as non-Archimedean. It was perfectly consistent but much stranger than the classical non-Euclidean varieties. Likewise, it was proved possible to posit a system of postulates which would yield Euclidean or non-Euclidean geometries of any number of dimensions; hence, so far as rational requirements of the mind were concerned, there was no reason to limit geometry to three dimensions."

"O king, through the country there are royal roads and roads for common citizens, but in geometry there is one road for all."

"A conceptual level view of an object design describes the key abstractions. While someone might think of key abstractions as being nothing more or nothing less than high-level descriptions of "candidate classes", I prefer to consider a conceptual design from a slightly different angle--I'm thinking about design at a slightly different level. An object-oriented application is a set of interacting objects. Each object is an implementation of one or more roles. A role supports a set of related (cohesive) responsibilities. A responsibility is an obligation to perform a task or know certain information. And objects don't work in isolation, they collaborate with others in a community to perform the overall responsibilities of the application. So a conceptual view, at least to start, is a distillation of the key object roles and their responsibilities (stated at a fairly high level). More than likely (unless you form classification hierarchies and use inheritance and composition techniques) many candidates you initially model will map directly to a single class in some inheritance hierarchy. But I like to open up possibilities by think first of roles and responsibilities, and then as a second step towards a specification-level view, mapping these candidates to classes and interfaces."

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

"[T]he ratios between straight and curved lines are not known, and I believe cannot be discovered by human minds, and therefore no conclusion based upon such ratios can be accepted as rigorous and exact."

"When Ptolemy once asked Euclid if geometry could not be mastered by an easier process than by studying the Elements, Euclid returned the answer, "There is no royal road to geometry.""

"Sometimes, however, a conceptual model is only a first step, and the second step is a mathematical representation of the conceptual model"

"It is a remarkable fact in the history of geometry, that the Elements of Euclid, written two thousand years ago, are still regarded by many as the best introduction to the mathematical sciences."

"What surprised me, which Google was part of, is that superficial search techniques over large bodies of stuff could get you what you wanted. I grew up in the AI tradition, where you have a complete conceptual model, and the information retrieval tradition, where you have complex vectors of key terms and Boolean queries. The idea that you can index billions of pages and look for a word and get what you want is quite a trick. To put it in more abstract terms, it's the power of using simple techniques over very large numbers versus doing carefully constructed systematic analysis."

"Aristotle (384-322 B.C.), the systematiser of deductive logic, though not a professed mathematician, promoted the science of geometry by improving some of the most difficult definitions. His Physics contains passages with suggestive hints of the principle of virtual velocities. About this time there appeared a work called Mechanica, of which he is regarded by some as the author. Mechanics was totally neglected by the Platonic school."