Information
Information is any entity or form that provides the answer to a question of some kind or resolves uncertainty. It is thus related to data and knowledge, as data represents values attributed to parameters, and knowledge signifies understanding of real things or abstract concepts. As it regards data, the information's existence is not necessarily coupled to an observer (it exists beyond an event horizon, for example), while in the case of knowledge, the information requires a cognitive observer.
Information Science
Information science is a field primarily concerned with the analysis, collection, classification, manipulation, storage, retrieval, movement, dissemination, and protection of information. Practitioners within and outside the field study application and usage of knowledge in organizations along with the interaction between people, organizations, and any existing information systems with the aim of creating, replacing, improving, or understanding information systems. Historically, information science is associated with computer science, library science, and telecommunications. However, information science also incorporates aspects of diverse fields such as archival science, cognitive science, commerce, law, museology, management, mathematics, philosophy, public policy, and social sciences.
Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.
Science
I was particularly interested in that, in working on Jurassic Park that aspect of what are the negative parts. Because in talking with the people who were doing this kind of research what I was hearing was that the most responsible of them were deciding not to proceed down certain lines of inquiry which is really a new phase in science. Traditionally in science what the scientists themselves have said is: "I might as well do it, because if I don't, someone else will. It is going to happen inevitably." I think there's recognition now, that it's no so inevitable and it's quite conceivable that if I don't do this research neither will anyone else. It's simply too dangerous.
Michael Crichton, interview Lost World section of Beyond Jurassic Park DVD.
Mathematics
Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, in conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.
E. W. Hobson, Presidential Address British Association for the Advancement of Science (1910) Nature Vol. 84 p. 290 as quoted by Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914) p. 184.
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