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
By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and in effect increases... mental power... Probably nothing in the modern world would have more astonished a Greek mathematician than to learn that, under the influence of compulsory education, the whole population of Western Europe, from the highest to the lowest, could perform the operation of division for the largest numbers. This fact would have seemed to him a sheer impossibility.
Alfred North Whitehead, An Introduction to Mathematics (1911) Ch. 5, p. 59.
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