Society values both creativity and heritage. This may also be true in the digital dimensions. A convergent look at mathematics, computers and biology reveals clues to what may emerge. The capacity of the imagination remains unbounded so far.
How many mathematicians does it take to prove whether a lightbulb is screwed in? These essays are from a workshop in Essen in 2006. The ways that the practice of mathematics has developed in the last three decades due to computerized visualization and experimentation may hint at its future. This book has three parts for seventeen chapters by eighteen contributors on proofs including their nature, aspects of teaching, cognitive development, experiments and diagrams. Proofs of the correctness by writing texts of algorithms were what ancient mathematicians used. Solutions are often based on common intuitions which can be further explored. Proofs are often discovered by mathematical experimentation, rather than deduction, which involves intuitive, inductive, or analogical reasoning through conjecture, verification, global or heuristic refutation, and understanding. Tools may be a proof of a mathematical form, or a way to explore a domain, via the notion of the semiotic potential of an artifact. Three different worlds of mathematics can be distinguished, the conceptual-embodied such as gears, perceptual-symbolic such as conics, and axiomatic-formal such as deductions. Individuals have warrants for truth that compensate for uncertainties in their mathematical proofs and that become more sophisticated over time. Situations that reinforce theoretical proofs over pragmatic are required for this type of research to result. Methods of proof can be used in other mathematical contexts. Though the history of mathematics encourages perseverance, each step of a proof stands without historical context since changes in language use may become a source of fallibility. The philosophy of mathematics shows the evolution of proofs and how they support empirical science and other symbolic endeavors. Much mathematical theorizing also occurs prior to the formulation of the axioms used as contextual definitions. The types of thesis as to why the Greeks invented proof include the socio-political, the internalist and the philosophical influence. Descartes’ arithmetization of geometry and the calculation of magnitudes was refined by Arnauld and Lamy. Can compare Frege and Russell, Peirce and Dewey, or Wittgenstein on how proof as picture shows what was proved and should get the same result, while proof as experiment shows procedure which can remain static and get different results. Lakoff and Núñez considered mathematics to be a cognitive system of conceptual metaphors based upon the sensory motor system.
Ba, Japanese for place or environment, is also the notion of computerized creativity support. Heidegger described technology as a quest for truth through creativity. Social science needs to better understand knowledge creation in science and tech. A constructive evolutionary objectivism episteme has ten postulates based on several principles. The evolutionary falsification principle measures fitness by number of tests passed. The emergence principle states that qualitatively different properties emerge from complexity, e.g. as software is different from hardware. The multimedia principle holds that historical records of knowledge will stimulate creativity by including complex visual and preverbal elements in addition to words. New concepts in science will be based on horizontal changes in mathematics. Technology and basic science form a feedback loop. The intellectual environment is a heritage of humanity worth preserving. Creative holism has a systemic approach to organization. Academic knowledge creation involves social, technical and mathematical approaches. Interdisciplinary approaches to mathematical modeling attempt to provide qualitative improvements. The book develops a testable creative environment (CE) to support scientific research. Roadmapping is a kind of knowledge creation process which can use various types of IT principles and tools for academic research. Software and tools for brainstorming and group debate are biased towards commercially goal-oriented organizations and need significant changes for academic use. Knowledge discovery requires interactions between AI and human reviewers, e.g. inclusion of user preferences in data mining. Seven creative spirals are proposed as tools for prescriptive synthesis in the process of learning. Survey results are presented for questions related to knowledge creation support. The book has twenty-one authors. There are four parts for eighteen chapters on models of creative processes, tools, diverse tools, and philosophical issues. It has many figures and tables including the spiral representations of processes, the triple helix model and JAIST Nanatsudaki model. The major text points are emphasized in box outlines. The content also has the hierarchical summaries of introduction and conclusion for each chapter and as a whole. Other topics include machine learning, statistics, virtual labs, gaming, criteria, and distance and e-learning, This is a followup to the editors’ previous publication on Creative Space, 2005. This book may also be of interest to inventors and innovators outside of entirely academic domains since learning advantages are key to most other pursuits. .
The scenario planner’s philosophy involves stories, patterns in uncertainties, common solutions, and simulation. This age was formed between 800 and 200BC by ideas which arose simultaneously in the East and West. The rate of change is quickening. According to the author’s Law of unintended consequences, human nature will likely be changed. The book tries to look ahead by defining scenarios which conform to facts and identify the predetermineds, critical uncertainties, wild cards, embedded assumptions and early warnings. These are based on progress in the areas of genetics, robotics, info, and nano (GRIN). Each of them may have its own philosophy, e.g. connecting living and nonliving things, open-source, unlimited creativity or skepticism. There are eight chapters, suggested readings, and notes. Seven major scenarios, some of which have celebrities, include the LUC above, Curve of exponential increase, Singularity/Vinge, Heaven/Kurzweil, Hell/Joy, Prevail/Lanier, and Transcend/Bostrom. This topic was inspired by work at Darpa, e.g. meals which last for days of exertion, or treatments for muscular dystrophy. This title was recommended for its discussion of risks by scifi & philosophy editor Schneider 2009.
The reader may wonder what set of rules are actually developed for each case. Also, there may be situations where science exceeds tech, in which case the artifacts are less evident and, though intelligence may expand wisdom, paradox seems to increase due to censorship.
According to Ray Bradbury, it takes a million words to become proficient at writing. If average is 200-250 words per page in a novel, that becomes 4000 to 5000 pages. The average novel is 100k words or 300-400 pages. Therefore, it would take 10 novels to become good. One of the Kindle authors, in contrast, sold over 29k ebooks at about 2 dollars each in a year and expects Amazon to double royalties soon. This is a tutorial for fiction novelists written by published and award-winning writers. It has three parts on art, craft, and business for thirty-three chapters by eighteen contributors. It might be classified as self-help since it assumes that the reader has finished, or is working on, a novel that needs to be published. The book contains a series of blog-like entries and links on why and how the authors write. In most cases, the rules were personally discovered through trial and error. So, while one debunks the agent career planning myth and says to be an artist, another shows what customers want and includes a pitch letter and instructions for how to get an agent. The Writers Market also has such lists. The anecdotes are absorbing and evoked various emotions, e.g. suspense or laughter. The reader is reminded that fame ups the odds for a bestseller, and recommendations improve sales e.g. through social networking. Other tips include: know what the book is about in a premise sentence or story line; include protagonist, antagonist, setting, conflict, stakes, atmosphere and genre; and write from research once immersed or overwhelmed. It shows the advantages and disadvantages of each POV and how to choose. The anatomy of the three-act story structure is described along with the use of imagery and dialogue. This book is not about the internet, except to say that editors may notice a web page and readers appreciate newsletters. It has a glossary of terms for writing professionals. This title wasn’t included in google books yet. Had originally found it on the Kindle directory, and it can also be downloaded free from its companion website.
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