194 research outputs found
Pictorial Narratives and Temporal Refinement
Refinements are proposed to the default reading of two successive pictures p,p' as p and then p'. The refinements are based on the Aristotelian dictum, no time without change, and the principle of inertia, no change without force, guided by the adage, a picture's worth a thousand words. Words describing pictures are formalized as predicates, some stative and some non-stative (expressing forces), and interpreted (in either case) over strings qua models, subject to finite-state projections supporting variable granularity. A form of string iconicity is explored, with an eye to more transparent representations
Scientific methods: an online book
BookThis book was originally intended as ˜How to do science™, or ˜How to be a scientist™, providing guidance for the new scientist, as well as some reminders and tips for experienced researchers. Such a book does not need to be written by the most expert or most famous scientist, but by one who likes to see the rules of play laid out concisely. It does need to be written by a working scientist, not by a philosopher of science. The first half of the book, called ˜Scientist's Toolbox", retains this original focus on what Jerome Brumer called the structure of science -- its methodologies and logic. This objective is still present in the second half of the book, ˜Living Science". In researching that section, however, I was fascinated by the perspectives of fellow scientists on ˜What it is like to be a scientist." Encountering their insights into the humanity of science, I found resonance with my already intense enjoyment of the process of science. Gaither and Cavazon-Gaither [2000] provide many additional scientific quotations on the experience of science
Mathematical metaphors and philosophical structures
The purpose of this study was to examine relationships between mathematics and philosophy. The first part of the study examined the history and basic doctrines of idealism, realism, pragmatism, and existentialism. This was a basic overview which would familiarize the reader with the teachings of each philosophical system. Mathematical topics and structure were then used to model and evaluate each of the philosophies. By using mathematical metaphors to evaluate each philosophical structure, the reader could decide which beliefs would have worth to his or her life. The second part of the study addressed the problem of choice. The belief that humans have few choices and that only one of those choices would bring success was evaluated using the binomial distribution to mathematically model the Greek dialectic. The belief that humans have an infinite number of choices was evaluated using Georg Cantor's mathematical argument that there are infinitely many decimal fractions on the finite line segment between zero and one
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