Tangled Origins Of The Leibnizian Calculus, The: A Case Study Of A Mathematical Revolution
Tangled Origins Of The Leibnizian Calculus, The: A Case Study Of A Mathematical Revolution

Author: Richard C Brown

Publisher: World Scientific

Published: 2012-03-23

Total Pages: 333

ISBN-13: 9814401617

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This book is a detailed study of Gottfried Wilhelm Leibniz's creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known “calculi” Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz.This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz's mathematical achievement or general issues in the field.

The Tangled Origins of the Leibnizian Calculus
The Tangled Origins of the Leibnizian Calculus

Author: Richard C. Brown

Publisher: World Scientific

Published: 2012

Total Pages: 333

ISBN-13: 9814390801

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This book is a detailed study of Gottfried Wilhelm Leibniz''s creation of calculus from 1673 to the 1680s. We examine and analyze the mathematics in several of his early manuscripts as well as various articles published in the Acta Eruditorum. It studies some of the other lesser known OC calculiOCO Leibniz created such as the Analysis Situs, delves into aspects of his logic, and gives an overview of his efforts to construct a Universal Characteristic, a goal that has its distant origin in the Ars Magna of the 13th century Catalan philosopher Raymond Llull, whose work enjoyed a renewed popularity in the century and a half prior to Leibniz. This book also touches upon a new look at the priority controversy with Newton and a Kuhnian interpretation of the nature of mathematical change. This book may be the only integrated treatment based on recent research and should be a thought-provoking contribution to the history of mathematics for scholars and students, interested in either Leibniz''s mathematical achievement or general issues in the field."

Leibniz’s Correspondence in Science, Technology and Medicine (1676 –1701)
Leibniz’s Correspondence in Science, Technology and Medicine (1676 –1701)

Author: James O'Hara

Publisher: BRILL

Published: 2024-08-01

Total Pages: 1091

ISBN-13: 900468736X

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Leibniz’s correspondence from his years spent in Paris (1672-1676) reflects his growth to mathematical maturity whereas that from the years 1676-1701 reveals his growth to maturity in science, technology and medicine in the course of which more than 2000 letters were exchanged with more than 200 correspondents. The remaining years until his death in 1716 witnessed above all the appearance of his major philosophical works. The focus of the present work is Leibniz's middle period and the core themes and core texts from his multilingual correspondence are presented in English from the following subject areas: mathematics, natural philosophy, physics (and cosmology), power technology (including mining and transport), engineering and engineering science, projects (scientific, technological and economic projects), alchemy and chemistry, geology, biology and medicine.

Transcendental Curves in the Leibnizian Calculus
Transcendental Curves in the Leibnizian Calculus

Author: Viktor Blasjo

Publisher: Academic Press

Published: 2017-04-22

Total Pages: 284

ISBN-13: 0128132981

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Transcendental Curves in the Leibnizian Calculus analyzes a mathematical and philosophical conflict between classical and early modern mathematics. In the late 17th century, mathematics was at the brink of an identity crisis. For millennia, mathematical meaning and ontology had been anchored in geometrical constructions, as epitomized by Euclid's ruler and compass. As late as 1637, Descartes had placed himself squarely in this tradition when he justified his new technique of identifying curves with equations by means of certain curve-tracing instruments, thereby bringing together the ancient constructive tradition and modern algebraic methods in a satisfying marriage. But rapid advances in the new fields of infinitesimal calculus and mathematical mechanics soon ruined his grand synthesis. Descartes's scheme left out transcendental curves, i.e. curves with no polynomial equation, but in the course of these subsequent developments such curves emerged as indispensable. It was becoming harder and harder to juggle cutting-edge mathematics and ancient conceptions of its foundations at the same time, yet leading mathematicians, such as Leibniz felt compelled to do precisely this. The new mathematics fit more naturally an analytical conception of curves than a construction-based one, yet no one wanted to betray the latter, as this was seen as virtually tantamount to stop doing mathematics altogether. The credibility and authority of mathematics depended on it. - Brings to light this underlying and often implicit complex of concerns that permeate early calculus - Evaluates the technical conception and mathematical construction of the geometrical method - Reveals a previously unrecognized Liebnizian programmatic cohesion in early calculus - Provides a beautifully written work of outstanding original scholarship

Monadological Intimacy
Monadological Intimacy

Author: Jeff Lambert

Publisher: Rowman & Littlefield

Published: 2024-08-15

Total Pages: 209

ISBN-13: 1666925926

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Monadological Intimacy: The Relational Operation of Folds in Leibniz and Deleuze analyzes and explains G.W. Leibniz’s theories of folds and relations to claim there is a common operation of inclusion inherent to both theories, an operation that produces a uniquely monadic form of intimacy. Utilizing key insights from Gilles Deleuze’s The Fold: Leibniz and the Baroque, Jeff Lambert considers the role of what is “virtual” and “ideal” for Leibniz in his theory of relations. However, Deleuze’s interpretation is not without flaws, and this book proposes an understanding of the operations of inclusion that is quite different from the view given by Deleuze in The Fold. Specifically, Lambert contends that relational inclusion has four primary “orders” that coincide with the four types of relations found across Leibniz’s oeuvre: complexion, comparison, congruence, and concurrence. Throughout each order of relations, different forms of interconnection play out through an intimate and immediate representation of the universe. Monadological Intimacy argues that the intimate and immediate representation of the universe within each monad utilizes the same operation of inclusion at work in how Leibniz describes the ideal continuum in each distinct fold of motion.

The Best Writing on Mathematics 2013
The Best Writing on Mathematics 2013

Author: Mircea Pitici

Publisher: Princeton University Press

Published: 2014-01-19

Total Pages: 272

ISBN-13: 0691160414

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The year's finest writing on mathematics from around the world, with a foreword by Nobel Prize–winning physicist Roger Penrose This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Newton And Modern Physics
Newton And Modern Physics

Author: Peter Rowlands

Publisher: World Scientific

Published: 2017-08-07

Total Pages: 311

ISBN-13: 1786343320

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This book looks at how Newton's theories can be linked to modern day problems and solutions in physics. Newton created an abstract system of theorizing which has been applied to all aspects of the physical world, however he had difficulties in persuading his contemporaries of its unique merits. A detailed study of Newton's writings, published and unpublished, suggests that he had an almost archetypally powerful mode of thinking guaranteed to produce 'correct' results even in areas of physics where systematic study only began long after his time. Newton and Modern Physics investigates this phenomenon, looking at examples of where Newton's principles have relevance to modern day thinking — the study of Newton's work in both seventeenth century and present-day contexts helps to enhance our understanding of both.

Are Science and Mathematics Socially Constructed?
Are Science and Mathematics Socially Constructed?

Author: Richard C. Brown

Publisher: World Scientific

Published: 2009

Total Pages: 336

ISBN-13: 9812835253

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This book is a history, analysis, and criticism of what the author calls OC postmodern interpretations of scienceOCO (PIS) and the closely related OC sociology of scientific knowledgeOCO (SSK). This movement traces its origin to Thomas Kuhn''s revolutionary work, The Structure of Scientific Revolutions (1962), but is more extreme. It believes that science is a OC social constructionOCO, having little to do with nature, and is determined by contextual forces such as the race, class, gender of the scientist, laboratory politics, or the needs of the military industrial complex.

Galileo Unbound
Galileo Unbound

Author: David D. Nolte

Publisher: Oxford University Press

Published: 2018-07-12

Total Pages: 384

ISBN-13: 0192528505

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Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Sophie's World
Sophie's World

Author: Jostein Gaarder

Publisher: Farrar, Straus and Giroux

Published: 2007-03-20

Total Pages: 735

ISBN-13: 1466804270

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A page-turning novel that is also an exploration of the great philosophical concepts of Western thought, Jostein Gaarder's Sophie's World has fired the imagination of readers all over the world, with more than twenty million copies in print. One day fourteen-year-old Sophie Amundsen comes home from school to find in her mailbox two notes, with one question on each: "Who are you?" and "Where does the world come from?" From that irresistible beginning, Sophie becomes obsessed with questions that take her far beyond what she knows of her Norwegian village. Through those letters, she enrolls in a kind of correspondence course, covering Socrates to Sartre, with a mysterious philosopher, while receiving letters addressed to another girl. Who is Hilde? And why does her mail keep turning up? To unravel this riddle, Sophie must use the philosophy she is learning—but the truth turns out to be far more complicated than she could have imagined.