William L. Harper
- Published in print:
- 2011
- Published Online:
- May 2012
- ISBN:
- 9780199570409
- eISBN:
- 9780191728679
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199570409.003.0003
- Subject:
- Philosophy, History of Philosophy, Philosophy of Science
This chapter reviews Newton’s definitions with emphasis on his theoretical concept of a centripetal force. It reviews his treatment of time, space, motion, Laws of Motion and their corollaries, ...
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This chapter reviews Newton’s definitions with emphasis on his theoretical concept of a centripetal force. It reviews his treatment of time, space, motion, Laws of Motion and their corollaries, before emphasizing the empirical support Newton cites for his Laws of Motion. The Laws of Motion, together with theorems derived from them, afford systematic dependencies that make orbital phenomena measure features of centripetal forces maintaining bodies in those orbits. This chapter gives an account of Newton’s inferences to the centripetal direction of and inverse-square variation of the forces maintaining satellites and planets in their respective orbits of Jupiter, Saturn and the sun. It also discusses a number of philosophical lessons these inferences can teach us about scientific method. Appendix 1 gives details of Newton’s appeal to pendulum experiments. Appendix 2 exhibits Newton’s proofs of propositions 1-4 of book 1. Appendix 3 extends Newton’s precession theorem to orbits of large eccentricity.Less
This chapter reviews Newton’s definitions with emphasis on his theoretical concept of a centripetal force. It reviews his treatment of time, space, motion, Laws of Motion and their corollaries, before emphasizing the empirical support Newton cites for his Laws of Motion. The Laws of Motion, together with theorems derived from them, afford systematic dependencies that make orbital phenomena measure features of centripetal forces maintaining bodies in those orbits. This chapter gives an account of Newton’s inferences to the centripetal direction of and inverse-square variation of the forces maintaining satellites and planets in their respective orbits of Jupiter, Saturn and the sun. It also discusses a number of philosophical lessons these inferences can teach us about scientific method. Appendix 1 gives details of Newton’s appeal to pendulum experiments. Appendix 2 exhibits Newton’s proofs of propositions 1-4 of book 1. Appendix 3 extends Newton’s precession theorem to orbits of large eccentricity.
Eric Watkins
- Published in print:
- 2001
- Published Online:
- February 2006
- ISBN:
- 9780195133059
- eISBN:
- 9780199786169
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195133056.003.0008
- Subject:
- Philosophy, Philosophy of Science
This paper notes a number of differences between Newton’s formulations of the laws of motion and Kant’s formulations of the laws of mechanics, and then argues that these differences are not ...
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This paper notes a number of differences between Newton’s formulations of the laws of motion and Kant’s formulations of the laws of mechanics, and then argues that these differences are not superficial. Their significance can be seen by taking Kant’s rationalist background into account. The essay also contains discussions of Kant’s claims concerning the infinite divisibility of matter, the equality of action and reaction, and action at a distance.Less
This paper notes a number of differences between Newton’s formulations of the laws of motion and Kant’s formulations of the laws of mechanics, and then argues that these differences are not superficial. Their significance can be seen by taking Kant’s rationalist background into account. The essay also contains discussions of Kant’s claims concerning the infinite divisibility of matter, the equality of action and reaction, and action at a distance.
Louis A. Girifalco
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228966
- eISBN:
- 9780191711183
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228966.003.0008
- Subject:
- Physics, History of Physics
Modern science could not advance until the ideas of force and mass were understood. Newton provided this understanding by stressing the role of momentum and by creating his three laws of motion. But ...
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Modern science could not advance until the ideas of force and mass were understood. Newton provided this understanding by stressing the role of momentum and by creating his three laws of motion. But notions were not rigorously based and left much undefined until Mach gave a detailed operational method for defining mass and force. Newton's genius and insight was illustrated by the fact that he got everything right in spite of this. When force and mass were examined with rigorous logic, they were found to be in accord with Newton's intuition.Less
Modern science could not advance until the ideas of force and mass were understood. Newton provided this understanding by stressing the role of momentum and by creating his three laws of motion. But notions were not rigorously based and left much undefined until Mach gave a detailed operational method for defining mass and force. Newton's genius and insight was illustrated by the fact that he got everything right in spite of this. When force and mass were examined with rigorous logic, they were found to be in accord with Newton's intuition.
JESPER LÜTZEN
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567370
- eISBN:
- 9780191717925
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567370.003.0016
- Subject:
- Physics, History of Physics
In the usual Newtonian-Laplacian image, Isaac Newton's three laws of motion are often taken as the basic ones. Heinrich Hertz, on the other hand, formulated one and only one law of motion: that every ...
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In the usual Newtonian-Laplacian image, Isaac Newton's three laws of motion are often taken as the basic ones. Heinrich Hertz, on the other hand, formulated one and only one law of motion: that every free system persists in its state of rest or of uniform motion in a straightest path. Hertz's fundamental law can be formulated as follows: a free system moves with constant speed along a path that is as straight as it can be without breaking the connections of the system. Hertz's formulation of the fundamental law was surprisingly stable throughout his work on mechanics. It was the geometry of systems of points that allowed Hertz to limit the laws of motion to his one simple, elegant and intuitively appealing fundamental law. Hertz mentioned one other law that could have replaced his fundamental law on free systems, namely, the law of least acceleration.Less
In the usual Newtonian-Laplacian image, Isaac Newton's three laws of motion are often taken as the basic ones. Heinrich Hertz, on the other hand, formulated one and only one law of motion: that every free system persists in its state of rest or of uniform motion in a straightest path. Hertz's fundamental law can be formulated as follows: a free system moves with constant speed along a path that is as straight as it can be without breaking the connections of the system. Hertz's formulation of the fundamental law was surprisingly stable throughout his work on mechanics. It was the geometry of systems of points that allowed Hertz to limit the laws of motion to his one simple, elegant and intuitively appealing fundamental law. Hertz mentioned one other law that could have replaced his fundamental law on free systems, namely, the law of least acceleration.
Louis A. Girifalco
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228966
- eISBN:
- 9780191711183
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228966.003.0006
- Subject:
- Physics, History of Physics
The law of gravitation could not be proved and could not be applied unless the basic laws of motion were understood. Newton realized this and in an amazing intellectual tour de force, he formulated ...
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The law of gravitation could not be proved and could not be applied unless the basic laws of motion were understood. Newton realized this and in an amazing intellectual tour de force, he formulated his famous three laws of motion that govern all of mechanics. All mechanics, from falling bodies, rotating machinery and automobiles, to aircraft and planetary motion; in short everything that moves and is subject to forces, are governed by Newton's laws of motion. This was the most important and far-reaching achievement in the history of physical science. It superseded all previous attempts to understand motion, and has never been surpassed. These laws properly stressed the importance of inertia, momentum, and reaction forces for the first time.Less
The law of gravitation could not be proved and could not be applied unless the basic laws of motion were understood. Newton realized this and in an amazing intellectual tour de force, he formulated his famous three laws of motion that govern all of mechanics. All mechanics, from falling bodies, rotating machinery and automobiles, to aircraft and planetary motion; in short everything that moves and is subject to forces, are governed by Newton's laws of motion. This was the most important and far-reaching achievement in the history of physical science. It superseded all previous attempts to understand motion, and has never been surpassed. These laws properly stressed the importance of inertia, momentum, and reaction forces for the first time.
JESPER LÜTZEN
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567370
- eISBN:
- 9780191717925
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567370.003.0002
- Subject:
- Physics, History of Physics
The period until 1860 saw a steady flow of interesting new theoretical discoveries in mechanics, even in the area of mechanics of systems of finitely many mass points. Moreover, there was a continued ...
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The period until 1860 saw a steady flow of interesting new theoretical discoveries in mechanics, even in the area of mechanics of systems of finitely many mass points. Moreover, there was a continued discussion about the meaning, nature, and foundations of the principles of mechanics and the concepts entering into them. These discussions went on till well into the 20th century, and provide the background and the mechanical context for Heinrich Hertz's book (Principles of Mechanics). This chapter presents the most important elements of this mechanical context for Hertz's work. First, the development of mechanics from Isaac Newton to Hertz is summarised, focusing on the different laws and principles of mechanics discussed by Hertz. Newton's laws of motion are examined, along with the principle of virtual work, d'Alembert's principle, Lagrange multipliers, principle of live force, principle of conservation of energy, Gauss's principle of least constraint, Jacobi's version of the principle of least action, Hamilton's equations of motion, and basic notions of mechanics. A terminology of concepts such as mass, space, time, distance, and force is also presented.Less
The period until 1860 saw a steady flow of interesting new theoretical discoveries in mechanics, even in the area of mechanics of systems of finitely many mass points. Moreover, there was a continued discussion about the meaning, nature, and foundations of the principles of mechanics and the concepts entering into them. These discussions went on till well into the 20th century, and provide the background and the mechanical context for Heinrich Hertz's book (Principles of Mechanics). This chapter presents the most important elements of this mechanical context for Hertz's work. First, the development of mechanics from Isaac Newton to Hertz is summarised, focusing on the different laws and principles of mechanics discussed by Hertz. Newton's laws of motion are examined, along with the principle of virtual work, d'Alembert's principle, Lagrange multipliers, principle of live force, principle of conservation of energy, Gauss's principle of least constraint, Jacobi's version of the principle of least action, Hamilton's equations of motion, and basic notions of mechanics. A terminology of concepts such as mass, space, time, distance, and force is also presented.
Emily R. Grosholz
- Published in print:
- 1991
- Published Online:
- October 2011
- ISBN:
- 9780198242505
- eISBN:
- 9780191680502
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198242505.003.0005
- Subject:
- Philosophy, History of Philosophy, Logic/Philosophy of Mathematics
This chapter reviews Descartes's laws of motion. It examines the consequences of the evanescent, unstable unity of Descartes's physical simples in the ...
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This chapter reviews Descartes's laws of motion. It examines the consequences of the evanescent, unstable unity of Descartes's physical simples in the context of his laws of motion, which introduces a second distinct system of relations — colliding bodies that conserve something like momentum. The instability of the simples worked against Descartes's attempt to establish vortices as high-level complex unities, and to differentiate matter into three elements. Moreover, the discussion argues that a tacit change of the relational structure forces a change in the items of physics, making them less plausibly identical with the items of geometry.Less
This chapter reviews Descartes's laws of motion. It examines the consequences of the evanescent, unstable unity of Descartes's physical simples in the context of his laws of motion, which introduces a second distinct system of relations — colliding bodies that conserve something like momentum. The instability of the simples worked against Descartes's attempt to establish vortices as high-level complex unities, and to differentiate matter into three elements. Moreover, the discussion argues that a tacit change of the relational structure forces a change in the items of physics, making them less plausibly identical with the items of geometry.
Daniel Brown
- Published in print:
- 1997
- Published Online:
- October 2011
- ISBN:
- 9780198183532
- eISBN:
- 9780191674051
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198183532.003.0008
- Subject:
- Literature, Poetry, 19th-century and Victorian Literature
This chapter examines the scientific basis of English poet Gerald Manley Hopkins' analogy in his works. Hopkins believed that the fundamental laws of motion provide the forms which serve to represent ...
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This chapter examines the scientific basis of English poet Gerald Manley Hopkins' analogy in his works. Hopkins believed that the fundamental laws of motion provide the forms which serve to represent more complex phenomena, and this logic was applied to most of his works. The principle of stress in mechanics also provided Hopkins with the formal terms to connect complex phenomena through analogy. This is evident from his formal metaphysics and in the observations of nature recorded in his poetry, journals, and diaries.Less
This chapter examines the scientific basis of English poet Gerald Manley Hopkins' analogy in his works. Hopkins believed that the fundamental laws of motion provide the forms which serve to represent more complex phenomena, and this logic was applied to most of his works. The principle of stress in mechanics also provided Hopkins with the formal terms to connect complex phenomena through analogy. This is evident from his formal metaphysics and in the observations of nature recorded in his poetry, journals, and diaries.
Oliver Johns
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics
Modern mechanics begins with the publication in 1687 of Isaac Newton’s Principia, in which he explains mathematically the motions of planets, moons, comets, and tides in what is now known as the ...
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Modern mechanics begins with the publication in 1687 of Isaac Newton’s Principia, in which he explains mathematically the motions of planets, moons, comets, and tides in what is now known as the three laws of motion. This chapter assumes that Newton’s three laws of motion refer fundamentally to point particles. After deriving the laws of momentum, angular momentum, and work-energy for point particles, it is shown that, given certain plausible and universally accepted additional axioms, essentially the same laws can be proved to apply to macroscopic bodies, considered as collections of the elementary point particles. This chapter also discusses Newton’s space and time, single point particle, collective variables, the law of momentum for collections, the law of angular momentum for collections, the work-energy theorem for collections, potential and total energy for collections, the center of mass, center of mass and momentum, center of mass and angular momentum, center of mass and torque, change of angular momentum, center of mass and the work-energy theorems, center of mass as a point particle, and special results for rigid bodies.Less
Modern mechanics begins with the publication in 1687 of Isaac Newton’s Principia, in which he explains mathematically the motions of planets, moons, comets, and tides in what is now known as the three laws of motion. This chapter assumes that Newton’s three laws of motion refer fundamentally to point particles. After deriving the laws of momentum, angular momentum, and work-energy for point particles, it is shown that, given certain plausible and universally accepted additional axioms, essentially the same laws can be proved to apply to macroscopic bodies, considered as collections of the elementary point particles. This chapter also discusses Newton’s space and time, single point particle, collective variables, the law of momentum for collections, the law of angular momentum for collections, the work-energy theorem for collections, potential and total energy for collections, the center of mass, center of mass and momentum, center of mass and angular momentum, center of mass and torque, change of angular momentum, center of mass and the work-energy theorems, center of mass as a point particle, and special results for rigid bodies.
David S. Sytsma
- Published in print:
- 2017
- Published Online:
- July 2017
- ISBN:
- 9780190274870
- eISBN:
- 9780190274894
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780190274870.003.0005
- Subject:
- Religion, Philosophy of Religion
This chapter addresses Baxter’s response to Copernicanism, substantial forms, Descartes’s laws of motion, and Henry More’s variant of mechanical philosophy. Baxter was far more concerned about ...
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This chapter addresses Baxter’s response to Copernicanism, substantial forms, Descartes’s laws of motion, and Henry More’s variant of mechanical philosophy. Baxter was far more concerned about changing notions of substance and causality than he was about Copernicanism. His objections to mechanical philosophy stemmed from a desire to affirm secondary causes as intrinsic sources of motion, which he regarded as important to a correct understanding of God and creation. He defended a concept of substantial form and objected to the theological foundation of Descartes’s first law of motion. Baxter also argued for the plausibility of various kinds of nonliving principles of motion against Henry More’s restriction of motion to spiritual beings.Less
This chapter addresses Baxter’s response to Copernicanism, substantial forms, Descartes’s laws of motion, and Henry More’s variant of mechanical philosophy. Baxter was far more concerned about changing notions of substance and causality than he was about Copernicanism. His objections to mechanical philosophy stemmed from a desire to affirm secondary causes as intrinsic sources of motion, which he regarded as important to a correct understanding of God and creation. He defended a concept of substantial form and objected to the theological foundation of Descartes’s first law of motion. Baxter also argued for the plausibility of various kinds of nonliving principles of motion against Henry More’s restriction of motion to spiritual beings.
Don S. Lemons
- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780262035903
- eISBN:
- 9780262338745
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262035903.003.0003
- Subject:
- Physics, History of Physics
The early modern period (1543-1785) contributed many physical concepts that are simple enough to be conveyed with a diagram. Copernicus’s heliocentric universe (1543), Galileo’s discovery of the ...
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The early modern period (1543-1785) contributed many physical concepts that are simple enough to be conveyed with a diagram. Copernicus’s heliocentric universe (1543), Galileo’s discovery of the mountains on the moon (1610), Kepler’s laws of planetary motion (1620), Boyle’s law (1662), Newton’s theory of color (1666), and Bernoulli’s principle (1733) are but six of the eighteen topics covered in this period. Experiments and observations that generated measurements became the norm.Less
The early modern period (1543-1785) contributed many physical concepts that are simple enough to be conveyed with a diagram. Copernicus’s heliocentric universe (1543), Galileo’s discovery of the mountains on the moon (1610), Kepler’s laws of planetary motion (1620), Boyle’s law (1662), Newton’s theory of color (1666), and Bernoulli’s principle (1733) are but six of the eighteen topics covered in this period. Experiments and observations that generated measurements became the norm.
Andrew Stewart Skinner
- Published in print:
- 1996
- Published Online:
- October 2011
- ISBN:
- 9780198233343
- eISBN:
- 9780191678974
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198233343.003.0009
- Subject:
- Economics and Finance, Economic History
Adam Smith's contribution to the field of political economy was designed to explain the working of a set of institutional arrangements that he regarded as the last of four stages of economic ...
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Adam Smith's contribution to the field of political economy was designed to explain the working of a set of institutional arrangements that he regarded as the last of four stages of economic development, and to elucidate the ‘laws of motion’ that governed its operations. The laws of motion, once stated, were designed to show that the control of resources could be left to the market and to explain the source of their increase. This perspective led directly to the demand that the state ought not to interfere with the economy. The same sentiments appear in the Wealth of Nations, albeit expressed with even greater force. According to Lord Robbins, Smith bequeathed to his successors in the Classical School an opposition to conscious paternalism, a belief that ‘central authority was incompetent to decide on a proper distribution of resources’. This chapter also considers Smith's views on economic liberalism, constraints on the functions of the state, the organization of educational provision, justice, public works and public services, and policy reform.Less
Adam Smith's contribution to the field of political economy was designed to explain the working of a set of institutional arrangements that he regarded as the last of four stages of economic development, and to elucidate the ‘laws of motion’ that governed its operations. The laws of motion, once stated, were designed to show that the control of resources could be left to the market and to explain the source of their increase. This perspective led directly to the demand that the state ought not to interfere with the economy. The same sentiments appear in the Wealth of Nations, albeit expressed with even greater force. According to Lord Robbins, Smith bequeathed to his successors in the Classical School an opposition to conscious paternalism, a belief that ‘central authority was incompetent to decide on a proper distribution of resources’. This chapter also considers Smith's views on economic liberalism, constraints on the functions of the state, the organization of educational provision, justice, public works and public services, and policy reform.
Lars Peter Hansen and Thomas J. Sargent
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691042770
- eISBN:
- 9781400848188
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691042770.003.0005
- Subject:
- Economics and Finance, History of Economic Thought
This chapter describes a planning problem that generates competitive equilibrium allocations and compares two methods for solving it. The first method uses state- and date-contingent Lagrange ...
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This chapter describes a planning problem that generates competitive equilibrium allocations and compares two methods for solving it. The first method uses state- and date-contingent Lagrange multipliers; the second uses dynamic programming. The first method reveals a direct connection between the Lagrange multipliers and the equilibrium prices in a competitive equilibrium to be analyzed in Chapter 7. The second method provides good algorithms for calculating both the law of motion for the optimal quantities and the Lagrange multipliers. The chapter also describes a set of MATLAB programs that solve the planning problem and represent its solution in various ways. These programs are used to solve the planning problem for six sample economies formed by choosing particular examples of the ingredients from Chapter 4.Less
This chapter describes a planning problem that generates competitive equilibrium allocations and compares two methods for solving it. The first method uses state- and date-contingent Lagrange multipliers; the second uses dynamic programming. The first method reveals a direct connection between the Lagrange multipliers and the equilibrium prices in a competitive equilibrium to be analyzed in Chapter 7. The second method provides good algorithms for calculating both the law of motion for the optimal quantities and the Lagrange multipliers. The chapter also describes a set of MATLAB programs that solve the planning problem and represent its solution in various ways. These programs are used to solve the planning problem for six sample economies formed by choosing particular examples of the ingredients from Chapter 4.
James E. Cutting
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780195393705
- eISBN:
- 9780199979271
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195393705.003.0002
- Subject:
- Psychology, Cognitive Psychology
In 1973, Gunnar Johansson launched the systematic study of the perception of the human body in motion. Merging his applied interests in traffic safety and his theoretical interests in vector analysis ...
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In 1973, Gunnar Johansson launched the systematic study of the perception of the human body in motion. Merging his applied interests in traffic safety and his theoretical interests in vector analysis and decomposition, Johansson produced captivating displays of people dancing and doing other ordinary activities, but with the people represented only by lights on their joints. This chapter discusses Johansson’s research and some of my own follow-up on his ideas, serving as background for ideas in this volume.Less
In 1973, Gunnar Johansson launched the systematic study of the perception of the human body in motion. Merging his applied interests in traffic safety and his theoretical interests in vector analysis and decomposition, Johansson produced captivating displays of people dancing and doing other ordinary activities, but with the people represented only by lights on their joints. This chapter discusses Johansson’s research and some of my own follow-up on his ideas, serving as background for ideas in this volume.
I.S. GLASS
- Published in print:
- 2008
- Published Online:
- January 2010
- ISBN:
- 9780199550258
- eISBN:
- 9780191718700
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199550258.003.0003
- Subject:
- Physics, History of Physics
This chapter begins by discussing Isaac Newton's biography and private life. It notes some of Newton's traits, which allowed him to face all the hurdles that came his way. It investigates how he ...
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This chapter begins by discussing Isaac Newton's biography and private life. It notes some of Newton's traits, which allowed him to face all the hurdles that came his way. It investigates how he developed his interest in the logical consistency in nature like the daily variations of the tides and the extent of the Moon's influence. It states that it was during the Bubonic plague years that he developed most of his basic mathematical ideas but remained secretive and failed to publicise them. It investigates how derived ideas such as the laws of motion and gravity. It also talks about his construction of the first reflecting telescope. This chapter also discusses how Newton gained recognition from his fellow researchers and how he tried to make more achievements, the Principia and the Opticks. It tells of some of the social acquaintances that Newton has made throughout his life as a scientist.Less
This chapter begins by discussing Isaac Newton's biography and private life. It notes some of Newton's traits, which allowed him to face all the hurdles that came his way. It investigates how he developed his interest in the logical consistency in nature like the daily variations of the tides and the extent of the Moon's influence. It states that it was during the Bubonic plague years that he developed most of his basic mathematical ideas but remained secretive and failed to publicise them. It investigates how derived ideas such as the laws of motion and gravity. It also talks about his construction of the first reflecting telescope. This chapter also discusses how Newton gained recognition from his fellow researchers and how he tried to make more achievements, the Principia and the Opticks. It tells of some of the social acquaintances that Newton has made throughout his life as a scientist.
Lars Peter Hansen and Thomas J. Sargent
- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691042770
- eISBN:
- 9781400848188
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691042770.003.0004
- Subject:
- Economics and Finance, History of Economic Thought
This chapter describes an economic environment with five components: a sequence of information sets, laws of motion for taste and technology shocks, a technology for producing consumption goods, a ...
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This chapter describes an economic environment with five components: a sequence of information sets, laws of motion for taste and technology shocks, a technology for producing consumption goods, a technology for producing services from consumer durables and consumption purchases, and a preference ordering over consumption services. A particular economy is described by a set of matrices that characterize the motion of information sets and of taste and technology shocks; matrices that determine the technology for producing consumption goods; matrices that determine the technology for producing consumption services from consumer goods; and a scalar discount factor that helps determine the preference ordering over consumption services. The chapter describes and gives examples of each component of the economic environment.Less
This chapter describes an economic environment with five components: a sequence of information sets, laws of motion for taste and technology shocks, a technology for producing consumption goods, a technology for producing services from consumer durables and consumption purchases, and a preference ordering over consumption services. A particular economy is described by a set of matrices that characterize the motion of information sets and of taste and technology shocks; matrices that determine the technology for producing consumption goods; matrices that determine the technology for producing consumption services from consumer goods; and a scalar discount factor that helps determine the preference ordering over consumption services. The chapter describes and gives examples of each component of the economic environment.
Oliver Johns
- Published in print:
- 2005
- Published Online:
- January 2010
- ISBN:
- 9780198567264
- eISBN:
- 9780191717987
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198567264.003.0016
- Subject:
- Physics, Atomic, Laser, and Optical Physics
It was apparent from its beginning that special relativity developed as the invariance theory of electrodynamics would require a modification of Newton’s three laws of motion. This chapter discusses ...
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It was apparent from its beginning that special relativity developed as the invariance theory of electrodynamics would require a modification of Newton’s three laws of motion. This chapter discusses that modified theory. The relativistically modified mechanics is presented and then recast into a fourvector form that demonstrates its consistency with special relativity. Traditional Lagrangian and Hamiltonian mechanics can incorporate these modifications. This chapter also discusses the momentum fourvector, fourvector form of Newton’s second law, conservation of fourvector momentum, particles of zero mass, traditional Lagrangian and traditional Hamiltonian, invariant Lagrangian, manifestly covariant Lagrange equations, momentum fourvectors and canonical momenta, extended and invariant Hamiltonian, manifestly covariant Hamilton equations, the Klein-Gordon equation, the Dirac equation, the manifestly covariant N-body problem, covariant Serret-Frenet theory, Fermi-Walker transport, and example of Fermi-Walker transport.Less
It was apparent from its beginning that special relativity developed as the invariance theory of electrodynamics would require a modification of Newton’s three laws of motion. This chapter discusses that modified theory. The relativistically modified mechanics is presented and then recast into a fourvector form that demonstrates its consistency with special relativity. Traditional Lagrangian and Hamiltonian mechanics can incorporate these modifications. This chapter also discusses the momentum fourvector, fourvector form of Newton’s second law, conservation of fourvector momentum, particles of zero mass, traditional Lagrangian and traditional Hamiltonian, invariant Lagrangian, manifestly covariant Lagrange equations, momentum fourvectors and canonical momenta, extended and invariant Hamiltonian, manifestly covariant Hamilton equations, the Klein-Gordon equation, the Dirac equation, the manifestly covariant N-body problem, covariant Serret-Frenet theory, Fermi-Walker transport, and example of Fermi-Walker transport.
Mary Domski
- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198746775
- eISBN:
- 9780191809057
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198746775.003.0003
- Subject:
- Philosophy, Philosophy of Science, History of Philosophy
This chapter examines the different ways in which Descartes and Newton balance their claim that laws of nature are true of the natural world with their commitment to our human inability to fully ...
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This chapter examines the different ways in which Descartes and Newton balance their claim that laws of nature are true of the natural world with their commitment to our human inability to fully comprehend God’s creation of nature. For both Descartes and Newton, there is a qualified notion of truth at play. Descartes’s laws of nature are true insofar as they capture God’s maintenance of nature only so far as we can understand. Nonetheless, they are afforded the highest degree of certainty and necessity that we can attain. Newton’s laws of motion are true insofar as they accurately describe the motions we witness in the sensible world. However, this truth is not based on mere inductive certainty; this chapter argues it is a truth that is characterized by rational certainty and thus closer to Descartes’s notion than we might expect from Newton’s ‘empirical’ method.Less
This chapter examines the different ways in which Descartes and Newton balance their claim that laws of nature are true of the natural world with their commitment to our human inability to fully comprehend God’s creation of nature. For both Descartes and Newton, there is a qualified notion of truth at play. Descartes’s laws of nature are true insofar as they capture God’s maintenance of nature only so far as we can understand. Nonetheless, they are afforded the highest degree of certainty and necessity that we can attain. Newton’s laws of motion are true insofar as they accurately describe the motions we witness in the sensible world. However, this truth is not based on mere inductive certainty; this chapter argues it is a truth that is characterized by rational certainty and thus closer to Descartes’s notion than we might expect from Newton’s ‘empirical’ method.
Rochel Gelman, Frank Durgin, and Lisa Kaufman
- Published in print:
- 1996
- Published Online:
- March 2012
- ISBN:
- 9780198524021
- eISBN:
- 9780191689093
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198524021.003.0006
- Subject:
- Psychology, Cognitive Psychology
This chapter presents an account of the origins and development of one's ability to classify moveable entities as either animate or inanimate. The account builds on the known abilities of young ...
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This chapter presents an account of the origins and development of one's ability to classify moveable entities as either animate or inanimate. The account builds on the known abilities of young infants to find three dimensional objects and to reason about some of their fundamental physical characteristics, for example, that they occupy space, move as a whole, or cannot pass through each other. This chapter also shows that motion paths are ambiguous for adults, not just infants. A moving object is perceived as inanimate when its motion path is consistent with Newtonian laws of motion. If the motion path violates Newtonian principles, then animacy is perceived.Less
This chapter presents an account of the origins and development of one's ability to classify moveable entities as either animate or inanimate. The account builds on the known abilities of young infants to find three dimensional objects and to reason about some of their fundamental physical characteristics, for example, that they occupy space, move as a whole, or cannot pass through each other. This chapter also shows that motion paths are ambiguous for adults, not just infants. A moving object is perceived as inanimate when its motion path is consistent with Newtonian laws of motion. If the motion path violates Newtonian principles, then animacy is perceived.
Danielle Macbeth
- Published in print:
- 2014
- Published Online:
- May 2014
- ISBN:
- 9780198704751
- eISBN:
- 9780191774232
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198704751.003.0004
- Subject:
- Philosophy, History of Philosophy
In the seventeenth century, Descartes transformed the practice of mathematics by introducing his symbolic language within which to formulate mathematical ideas, such as that of a circle or that of a ...
More
In the seventeenth century, Descartes transformed the practice of mathematics by introducing his symbolic language within which to formulate mathematical ideas, such as that of a circle or that of a product of sums, and to solve problems through the rule-governed manipulation of such signs in (elementary) algebra. The chapter explains how Descartes was able to achieve the cast of mind enabling him to learn to use symbols as he does, namely, through a profound and thoroughgoing metamorphosis in his conception of space and spatial drawings. It is also shown that Descartes’ metaphysics, both his new conception of nature in terms of laws of motion and his conception of the mind as a self-standing realm of freedom, are made possible by, and only fully intelligible in the light of, Descartes’ new sort of mathematical practice.Less
In the seventeenth century, Descartes transformed the practice of mathematics by introducing his symbolic language within which to formulate mathematical ideas, such as that of a circle or that of a product of sums, and to solve problems through the rule-governed manipulation of such signs in (elementary) algebra. The chapter explains how Descartes was able to achieve the cast of mind enabling him to learn to use symbols as he does, namely, through a profound and thoroughgoing metamorphosis in his conception of space and spatial drawings. It is also shown that Descartes’ metaphysics, both his new conception of nature in terms of laws of motion and his conception of the mind as a self-standing realm of freedom, are made possible by, and only fully intelligible in the light of, Descartes’ new sort of mathematical practice.
