The Reception of Newton's Principia
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Cultural Gap: an International Physicist’S Experience
Bridging the Socio- Cultural Gap: An International Physicist’s Experience J. Pedro Ochoa Berkeley Lab APS March Meeting: Experiences and Issues of Young Physicist’s on the International Arena Dallas, TX – March 2011 1 Wednesday, July 20, 2011 Let’s start with an example… Some quick facts about the academic career of Isaac Newton, arguably the best physicist of all times: Born in Lincolnshire Educated at King’s School, Grantham Attended Trinity College in Cambridge His advisors were Isaac Barrow and Benjamin Pulleyn He was appointed the Lucasian Professor of Mathematics at Cambridge Mentored notable students such as Roger Cotes and William Whiston. Died in Kensington at age 67 2 Wednesday, July 20, 2011 Let’s start with an example… Some quick facts about the academic career of Isaac Newton, arguably the best physicist of all times: England Born in Lincolnshire Educated at King’s School, Grantham Attended Trinity College in Cambridge His advisors were Isaac Barrow and Benjamin Pulleyn He was appointed the Lucasian Professor of Mathematics at Cambridge Mentored notable students such as Roger Cotes and William Whiston. Died in Kensington at age 67 2 Wednesday, July 20, 2011 Let’s start with an example… Some quick facts about the academic career of Isaac Newton, arguably the best physicist of all times: England Born in Lincolnshire England Educated at King’s School, Grantham Attended Trinity College in Cambridge His advisors were Isaac Barrow and Benjamin Pulleyn He was appointed the Lucasian Professor of Mathematics -
Leibniz' Dynamical Metaphysicsand the Origins
LEIBNIZ’ DYNAMICAL METAPHYSICSAND THE ORIGINS OF THE VIS VIVA CONTROVERSY* by George Gale Jr. * I am grateful to Marjorie Grene, Neal Gilbert, Ronald Arbini and Rom Harr6 for their comments on earlier drafts of this essay. Systematics Vol. 11 No. 3 Although recent work has begun to clarify the later history and development of the vis viva controversy, the origins of the conflict arc still obscure.1 This is understandable, since it was Leibniz who fired the initial barrage of the battle; and, as always, it is extremely difficult to disentangle the various elements of the great physicist-philosopher’s thought. His conception includes facets of physics, mathematics and, of course, metaphysics. However, one feature is essential to any possible understanding of the genesis of the debate over vis viva: we must note, as did Leibniz, that the vis viva notion was to emerge as the first element of a new science, which differed significantly from that of Descartes and Newton, and which Leibniz called the science of dynamics. In what follows, I attempt to clarify the various strands which were woven into the vis viva concept, noting especially the conceptual framework which emerged and later evolved into the science of dynamics as we know it today. I shall argue, in general, that Leibniz’ science of dynamics developed as a consistent physical interpretation of certain of his metaphysical and mathematical beliefs. Thus the following analysis indicates that at least once in the history of science, an important development in physical conceptualization was intimately dependent upon developments in metaphysical conceptualization. 1. -
THE EARTH's GRAVITY OUTLINE the Earth's Gravitational Field
GEOPHYSICS (08/430/0012) THE EARTH'S GRAVITY OUTLINE The Earth's gravitational field 2 Newton's law of gravitation: Fgrav = GMm=r ; Gravitational field = gravitational acceleration g; gravitational potential, equipotential surfaces. g for a non–rotating spherically symmetric Earth; Effects of rotation and ellipticity – variation with latitude, the reference ellipsoid and International Gravity Formula; Effects of elevation and topography, intervening rock, density inhomogeneities, tides. The geoid: equipotential mean–sea–level surface on which g = IGF value. Gravity surveys Measurement: gravity units, gravimeters, survey procedures; the geoid; satellite altimetry. Gravity corrections – latitude, elevation, Bouguer, terrain, drift; Interpretation of gravity anomalies: regional–residual separation; regional variations and deep (crust, mantle) structure; local variations and shallow density anomalies; Examples of Bouguer gravity anomalies. Isostasy Mechanism: level of compensation; Pratt and Airy models; mountain roots; Isostasy and free–air gravity, examples of isostatic balance and isostatic anomalies. Background reading: Fowler §5.1–5.6; Lowrie §2.2–2.6; Kearey & Vine §2.11. GEOPHYSICS (08/430/0012) THE EARTH'S GRAVITY FIELD Newton's law of gravitation is: ¯ GMm F = r2 11 2 2 1 3 2 where the Gravitational Constant G = 6:673 10− Nm kg− (kg− m s− ). ¢ The field strength of the Earth's gravitational field is defined as the gravitational force acting on unit mass. From Newton's third¯ law of mechanics, F = ma, it follows that gravitational force per unit mass = gravitational acceleration g. g is approximately 9:8m/s2 at the surface of the Earth. A related concept is gravitational potential: the gravitational potential V at a point P is the work done against gravity in ¯ P bringing unit mass from infinity to P. -
A Conjecture of Thermo-Gravitation Based on Geometry, Classical
A conjecture of thermo-gravitation based on geometry, classical physics and classical thermodynamics The authors: Weicong Xu a, b, Li Zhao a, b, * a Key Laboratory of Efficient Utilization of Low and Medium Grade Energy, Ministry of Education of China, Tianjin 300350, China b School of mechanical engineering, Tianjin University, Tianjin 300350, China * Corresponding author. Tel: +86-022-27890051; Fax: +86-022-27404188; E-mail: [email protected] Abstract One of the goals that physicists have been pursuing is to get the same explanation from different angles for the same phenomenon, so as to realize the unity of basic physical laws. Geometry, classical mechanics and classical thermodynamics are three relatively old disciplines. Their research methods and perspectives for the same phenomenon are quite different. However, there must be some undetermined connections and symmetries among them. In previous studies, there is a lack of horizontal analogical research on the basic theories of different disciplines, but revealing the deep connections between them will help to deepen the understanding of the existing system and promote the common development of multiple disciplines. Using the method of analogy analysis, five basic axioms of geometry, four laws of classical mechanics and four laws of thermodynamics are compared and analyzed. The similarity and relevance of basic laws between different disciplines is proposed. Then, by comparing the axiom of circle in geometry and Newton’s law of universal gravitation, the conjecture of the law of thermo-gravitation is put forward. Keywords thermo-gravitation, analogy method, thermodynamics, geometry 1. Introduction With the development of science, the theories and methods of describing the same macro system are becoming more and more abundant. -
Pioneers in Optics: Christiaan Huygens
Downloaded from Microscopy Pioneers https://www.cambridge.org/core Pioneers in Optics: Christiaan Huygens Eric Clark From the website Molecular Expressions created by the late Michael Davidson and now maintained by Eric Clark, National Magnetic Field Laboratory, Florida State University, Tallahassee, FL 32306 . IP address: [email protected] 170.106.33.22 Christiaan Huygens reliability and accuracy. The first watch using this principle (1629–1695) was finished in 1675, whereupon it was promptly presented , on Christiaan Huygens was a to his sponsor, King Louis XIV. 29 Sep 2021 at 16:11:10 brilliant Dutch mathematician, In 1681, Huygens returned to Holland where he began physicist, and astronomer who lived to construct optical lenses with extremely large focal lengths, during the seventeenth century, a which were eventually presented to the Royal Society of period sometimes referred to as the London, where they remain today. Continuing along this line Scientific Revolution. Huygens, a of work, Huygens perfected his skills in lens grinding and highly gifted theoretical and experi- subsequently invented the achromatic eyepiece that bears his , subject to the Cambridge Core terms of use, available at mental scientist, is best known name and is still in widespread use today. for his work on the theories of Huygens left Holland in 1689, and ventured to London centrifugal force, the wave theory of where he became acquainted with Sir Isaac Newton and began light, and the pendulum clock. to study Newton’s theories on classical physics. Although it At an early age, Huygens began seems Huygens was duly impressed with Newton’s work, he work in advanced mathematics was still very skeptical about any theory that did not explain by attempting to disprove several theories established by gravitation by mechanical means. -
Newton.Indd | Sander Pinkse Boekproductie | 16-11-12 / 14:45 | Pag
omslag Newton.indd | Sander Pinkse Boekproductie | 16-11-12 / 14:45 | Pag. 1 e Dutch Republic proved ‘A new light on several to be extremely receptive to major gures involved in the groundbreaking ideas of Newton Isaac Newton (–). the reception of Newton’s Dutch scholars such as Willem work.’ and the Netherlands Jacob ’s Gravesande and Petrus Prof. Bert Theunissen, Newton the Netherlands and van Musschenbroek played a Utrecht University crucial role in the adaption and How Isaac Newton was Fashioned dissemination of Newton’s work, ‘is book provides an in the Dutch Republic not only in the Netherlands important contribution to but also in the rest of Europe. EDITED BY ERIC JORINK In the course of the eighteenth the study of the European AND AD MAAS century, Newton’s ideas (in Enlightenment with new dierent guises and interpre- insights in the circulation tations) became a veritable hype in Dutch society. In Newton of knowledge.’ and the Netherlands Newton’s Prof. Frans van Lunteren, sudden success is analyzed in Leiden University great depth and put into a new perspective. Ad Maas is curator at the Museum Boerhaave, Leiden, the Netherlands. Eric Jorink is researcher at the Huygens Institute for Netherlands History (Royal Dutch Academy of Arts and Sciences). / www.lup.nl LUP Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. 1 Newton and the Netherlands Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. 2 Newton and the Netherlands.indd | Sander Pinkse Boekproductie | 16-11-12 / 16:47 | Pag. -
Basic Concepts of Set Theory, Functions and Relations 1. Basic
Ling 310, adapted from UMass Ling 409, Partee lecture notes March 1, 2006 p. 1 Basic Concepts of Set Theory, Functions and Relations 1. Basic Concepts of Set Theory........................................................................................................................1 1.1. Sets and elements ...................................................................................................................................1 1.2. Specification of sets ...............................................................................................................................2 1.3. Identity and cardinality ..........................................................................................................................3 1.4. Subsets ...................................................................................................................................................4 1.5. Power sets .............................................................................................................................................4 1.6. Operations on sets: union, intersection...................................................................................................4 1.7 More operations on sets: difference, complement...................................................................................5 1.8. Set-theoretic equalities ...........................................................................................................................5 Chapter 2. Relations and Functions ..................................................................................................................6 -
Are Large Cardinal Axioms Restrictive?
Are Large Cardinal Axioms Restrictive? Neil Barton∗ 24 June 2020y Abstract The independence phenomenon in set theory, while perva- sive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper, I argue that whether or not large cardinal axioms count as maximality prin- ciples depends on prior commitments concerning the richness of the subset forming operation. In particular I argue that there is a conception of maximality through absoluteness, on which large cardinal axioms are restrictive. I argue, however, that large cardi- nals are still important axioms of set theory and can play many of their usual foundational roles. Introduction Large cardinal axioms are widely viewed as some of the best candi- dates for new axioms of set theory. They are (apparently) linearly ordered by consistency strength, have substantial mathematical con- sequences for questions independent from ZFC (such as consistency statements and Projective Determinacy1), and appear natural to the ∗Fachbereich Philosophie, University of Konstanz. E-mail: neil.barton@uni- konstanz.de. yI would like to thank David Aspero,´ David Fernandez-Bret´ on,´ Monroe Eskew, Sy-David Friedman, Victoria Gitman, Luca Incurvati, Michael Potter, Chris Scam- bler, Giorgio Venturi, Matteo Viale, Kameryn Williams and audiences in Cambridge, New York, Konstanz, and Sao˜ Paulo for helpful discussion. Two anonymous ref- erees also provided helpful comments, and I am grateful for their input. I am also very grateful for the generous support of the FWF (Austrian Science Fund) through Project P 28420 (The Hyperuniverse Programme) and the VolkswagenStiftung through the project Forcing: Conceptual Change in the Foundations of Mathematics. -
The Newton-Leibniz Controversy Over the Invention of the Calculus
The Newton-Leibniz controversy over the invention of the calculus S.Subramanya Sastry 1 Introduction Perhaps one the most infamous controversies in the history of science is the one between Newton and Leibniz over the invention of the infinitesimal calculus. During the 17th century, debates between philosophers over priority issues were dime-a-dozen. Inspite of the fact that priority disputes between scientists were ¡ common, many contemporaries of Newton and Leibniz found the quarrel between these two shocking. Probably, what set this particular case apart from the rest was the stature of the men involved, the significance of the work that was in contention, the length of time through which the controversy extended, and the sheer intensity of the dispute. Newton and Leibniz were at war in the later parts of their lives over a number of issues. Though the dispute was sparked off by the issue of priority over the invention of the calculus, the matter was made worse by the fact that they did not see eye to eye on the matter of the natural philosophy of the world. Newton’s action-at-a-distance theory of gravitation was viewed as a reversion to the times of occultism by Leibniz and many other mechanical philosophers of this era. This intermingling of philosophical issues with the priority issues over the invention of the calculus worsened the nature of the dispute. One of the reasons why the dispute assumed such alarming proportions and why both Newton and Leibniz were anxious to be considered the inventors of the calculus was because of the prevailing 17th century conventions about priority and attitude towards plagiarism. -
THE 1910 PRINCIPIA's THEORY of FUNCTIONS and CLASSES and the THEORY of DESCRIPTIONS*
EUJAP VOL. 3 No. 2 2007 ORIGinal SCienTifiC papeR UDK: 165 THE 1910 PRINCIPIA’S THEORY OF FUNCTIONS AND CLASSES AND THE THEORY OF DESCRIPTIONS* WILLIAM DEMOPOULOS** The University of Western Ontario ABSTRACT 1. Introduction It is generally acknowledged that the 1910 Prin- The 19101 Principia’s theory of proposi- cipia does not deny the existence of classes, but tional functions and classes is officially claims only that the theory it advances can be developed so that any apparent commitment to a “no-classes theory of classes,” a theory them is eliminable by the method of contextual according to which classes are eliminable. analysis. The application of contextual analysis But it is clear from Principia’s solution to ontological questions is widely viewed as the to the class paradoxes that although the central philosophical innovation of Russell’s theory of descriptions. Principia’s “no-classes theory it advances holds that classes are theory of classes” is a striking example of such eliminable, it does not deny their exis- an application. The present paper develops a re- tence. Whitehead and Russell argue from construction of Principia’s theory of functions the supposition that classes involve or and classes that is based on Russell’s epistemo- logical applications of the method of contextual presuppose propositional functions to the analysis. Such a reconstruction is not eliminativ- conclusion that the paradoxical classes ist—indeed, it explicitly assumes the existence of are excluded by the nature of such func- classes—and possesses certain advantages over tions. This supposition rests on the repre- the no–classes theory advocated by Whitehead and Russell. -
KAREN THOMSON CATALOGUE 103 UNIQUE OR RARE with A
KAREN THOMSON CATALOGUE 103 UNIQUE OR RARE with a Newtonian section & a Jane Austen discovery KAREN THOMSON RARE BOOKS CATALOGUE 103 UNIQUE OR RARE With a Newtonian section (1-8), and a Jane Austen discovery (16) [email protected] NEWTONIANA William Jones’ copy [1] Thomas Rudd Practicall Geometry, in two parts: the first, shewing how to perform the foure species of Arithmeticke (viz: addition, substraction, multiplication, and division) together with reduction, and the rule of proportion in figures. The second, containing a hundred geometricall questions, with their solutions & demonstrations, some of them being performed arithmetically, and others geometrically, yet all without the help of algebra. Imprinted at London by J.G. for Robert Boydell, and are to be sold at his Shop in the Bulwarke neer the Tower, 1650 £1500 Small 4to. pp. [vii]+56+[iv]+139. Removed from a volume of tracts bound in the eighteenth century for the Macclesfield Library with characteristically cropped inscription, running titles, catchwords and page numbers, and shaving three words of the text on H4r. Ink smudge to second title page verso, manuscript algebraic solution on 2Q3 illustrated below, Macclesfield armorial blindstamp, clean and crisp. First edition, one of two issues published in the same year (the other spelling “Practical” in the title). William Jones (1675-1749) was employed by the second Earl of Macclesfield at Shirburn Castle as his mathematics instructor, and at his death left his pupil and patron the most valuable mathematical library in England, which included Newton manuscript material. Jones was an important promoter of Isaac Newton’s work, as well as being a friend: William Stukeley (see item 6), in the first biography of Newton, describes visiting him “sometime with Dr. -
Cotton Mather's Relationship to Science
Georgia State University ScholarWorks @ Georgia State University English Theses Department of English 4-16-2008 Cotton Mather's Relationship to Science James Daniel Hudson Follow this and additional works at: https://scholarworks.gsu.edu/english_theses Part of the English Language and Literature Commons Recommended Citation Hudson, James Daniel, "Cotton Mather's Relationship to Science." Thesis, Georgia State University, 2008. https://scholarworks.gsu.edu/english_theses/33 This Thesis is brought to you for free and open access by the Department of English at ScholarWorks @ Georgia State University. It has been accepted for inclusion in English Theses by an authorized administrator of ScholarWorks @ Georgia State University. For more information, please contact [email protected]. COTTON MATHER’S RELATIONSHIP TO SCIENCE by JAMES DANIEL HUDSON Under the Direction of Dr. Reiner Smolinski ABSTRACT The subject of this project is Cotton Mather’s relationship to science. As a minister, Mather’s desire to harmonize science with religion is an excellent medium for understanding the effects of the early Enlightenment upon traditional views of Scripture. Through “Biblia Americana” and The Christian Philosopher, I evaluate Mather’s effort to relate Newtonian science to the six creative days as recorded in Genesis 1. Chapter One evaluates Mather’s support for the scientific theories of Isaac Newton and his reception to natural philosophers who advocate Newton’s theories. Chapter Two highlights Mather’s treatment of the dominant cosmogonies preceding Isaac Newton. The Conclusion returns the reader to Mather’s principal occupation as a minister and the limits of science as informed by his theological mind. Through an exploration of Cotton Mather’s views on science, a more comprehensive understanding of this significant early American and the ideological assumptions shaping his place in American history is realized.