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Constellations and Conjectures

Constellations and Conjectures
Author: N.R. Hanson
Publisher: Springer Science & Business Media
Total Pages: 277
Release: 2012-12-06
Genre: Science
ISBN: 9401024987

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An occurrence is explained by being related to prior events through known laws. Other intellectual activities may also constitute explanation - but this much certainly does. Ideally, an explained occurrence (0) could have been predicted in a connected way - by extrapolation from prior events (e) via the same laws (L). Schematically, 1 Explanation: 0 -Lt, 2, 3-(e e e )'-AI t 2 3 01 Prediction: (e e e )I-L , 2, 3_ +.11 t 2 3 t Thus Mars' backward loop in late summer, 1956, is explained by showing how this follows from (e ) its mean distance from sun and earth, (e ) its t 2 mean period of revolution, (e ) its past positions relative to earth, etc. 3 - by way of the laws of Celestial Mechanics (including (Lt) Kepler's Laws and Galileo's, (L2) Newton's, and (L3) those of Laplace and Lagrange. Moreover, this loop (0) could have been predicted from such events (e -e ) via the laws of Celestial Mechanics. t 3 This is an ideal situation. It crystallized late in the history of planetary theory. The Greeks found explanations for heavenly motions: the back ward loops were explained to their satisfaction. But they could not predict these motions, not in terms of Attic explanatory cosmologies.


Constellations and Conjectures

Constellations and Conjectures
Author: Norwood Russell Hanson
Publisher:
Total Pages: 282
Release: 1973
Genre:
ISBN:

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The Metaphysics of Dante's Comedy

The Metaphysics of Dante's Comedy
Author: Christian Moevs
Publisher: Oxford University Press
Total Pages: 321
Release: 2008-10-13
Genre: Literary Criticism
ISBN: 0195372581

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Moevs offers a treatment of the metaphysical picture that grounds and motivates 'The Divine Comedy', and the relation between those metaphysics and Dante's poetics. He arrives at the conclusion that Dante believed that all of what we perceive as reality is in fact a creation or projection of conscious being.


Philosophy of Language and the Challenge to Scientific Realism

Philosophy of Language and the Challenge to Scientific Realism
Author: Christopher Norris
Publisher: Psychology Press
Total Pages: 248
Release: 2004
Genre: Language Arts & Disciplines
ISBN: 9780415327855

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In this book Christopher Norris develops the case for scientific realism by tackling various adversary arguments from a range of anti-realist positions. Through a close critical reading he shows how they fail to make adequate sense on any rational, consistent, and scientifically-informed survey of the evidence. Along the way he incorporates a number of detailed case-studies from the history and philosophy of science. Norris devotes much of his discussion to some of the most prominent and widely influential source-texts of anti-realism. Also included are the sophisticated versions of verificationism developed - albeit in very different ways - by thinkers such as Michael Dummett and Bas van Fraassen. Central to Norris's argument is a prolonged engagement with the once highly influential but nowadays neglected work of Norwood Russell Hanson. This book will be welcomed especially by readers who possess some knowledge of the background debate and who wish to deepen and extend their understanding of these issues beyond an introductory level.


Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Author: Marc Fossorier
Publisher: Springer
Total Pages: 516
Release: 2003-07-31
Genre: Computers
ISBN: 3540467963

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This book constitutes the refereed proceedings of the 19th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-13, held in Honolulu, Hawaii, USA in November 1999. The 42 revised full papers presented together with six invited survey papers were carefully reviewed and selected from a total of 86 submissions. The papers are organized in sections on codes and iterative decoding, arithmetic, graphs and matrices, block codes, rings and fields, decoding methods, code construction, algebraic curves, cryptography, codes and decoding, convolutional codes, designs, decoding of block codes, modulation and codes, Gröbner bases and AG codes, and polynomials.


Number Theory and Geometry: An Introduction to Arithmetic Geometry

Number Theory and Geometry: An Introduction to Arithmetic Geometry
Author: Álvaro Lozano-Robledo
Publisher: American Mathematical Soc.
Total Pages: 488
Release: 2019-03-21
Genre: Arithmetical algebraic geometry
ISBN: 147045016X

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Geometry and the theory of numbers are as old as some of the oldest historical records of humanity. Ever since antiquity, mathematicians have discovered many beautiful interactions between the two subjects and recorded them in such classical texts as Euclid's Elements and Diophantus's Arithmetica. Nowadays, the field of mathematics that studies the interactions between number theory and algebraic geometry is known as arithmetic geometry. This book is an introduction to number theory and arithmetic geometry, and the goal of the text is to use geometry as the motivation to prove the main theorems in the book. For example, the fundamental theorem of arithmetic is a consequence of the tools we develop in order to find all the integral points on a line in the plane. Similarly, Gauss's law of quadratic reciprocity and the theory of continued fractions naturally arise when we attempt to determine the integral points on a curve in the plane given by a quadratic polynomial equation. After an introduction to the theory of diophantine equations, the rest of the book is structured in three acts that correspond to the study of the integral and rational solutions of linear, quadratic, and cubic curves, respectively. This book describes many applications including modern applications in cryptography; it also presents some recent results in arithmetic geometry. With many exercises, this book can be used as a text for a first course in number theory or for a subsequent course on arithmetic (or diophantine) geometry at the junior-senior level.


Teaching Science

Teaching Science
Author: Karl Maton
Publisher: Routledge
Total Pages: 308
Release: 2021-04-26
Genre: Education
ISBN: 1351129279

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Science has never been more important, yet science education faces serious challenges. At present, science education research only sees half the picture, focusing on how students learn and their changing conceptions. Both teaching practice and what is taught, science knowledge itself, are missing. This book offers new, interdisciplinary ways of thinking about science teaching that foreground the forms taken by science knowledge and the language, imagery and gesture through which they are expressed. This book brings together leading international scholars from Systemic Functional Linguistics, a long-established approach to language, and Legitimation Code Theory, a rapidly growing sociological approach to knowledge practices. It explores how to bring knowledge, language and pedagogy back into the picture of science education but also offers radical innovations that will shape future research. Part I sets out new ways of understanding the role of knowledge in integrating mathematics into science, teaching scientific explanations and using multimedia resources such as animations. Part II provides new concepts for showing the role of language in complex scientific explanations, in how scientific taxonomies are built, and in combining with mathematics and images to create science knowledge. Part III draws on the approaches to explore how more students can access scientific knowledge, how to teach professional reasoning, the role of body language in science teaching, and making mathematics understandable to all learners. Teaching Science offers major leaps forward in understanding knowledge, language and pedagogy that will shape the research agenda far beyond science education.