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volume II: Synopsis

Part II: A brief history of dynamics

page 14: Isaac Newton

(1643-1727)

Newton began the work of bringing the heavens down to earth which reaches a culmination in the theology presented here. There is a lot of evidence to suggest that in his own mind Newton was, among many other things, a theologian, and historians of science are developing a deeper appreciation for the role of Newton;s theology in his physics, something clearly stated in the General Scholion in his Principia. The Newton Project, Isaac Newton

Newton, building on the work of the Galilean era, showed that the heavens and the earth are physically one. Using a mathematical model and astronomical observations, Newton demonstrated that the same forces govern both terrestrial and extraterrestrial bodies. Not only was this a major step toward a unified view of the Universe, but Newton's methods caused a revolution in mathematics. Mathematics is still expanding on the momentum it gained from his work. Newton

Newton postulated that all the physical motions of massive bodies obeyed three simple axioms or laws:

1. Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces acting upon it.
2. The change of motion is proportional to the motive force impressed; and it is made in the direction in which that force is impressed.
3. To every action there is always imposed an equal reaction; or the mutual actions of two bodies upon each other are always equal and opposite. Newton's Laws of Motion - Wikipedia

There are many sources of impressed force. In astronomical questions, we are mainly concerned with gravitation. Newton found that the attractive force between two massive bodies is proportional to the product of their masses divided by the distance between them squared.

These four laws could, in principle, explain all the motions of the solar system and its satellites. The first three laws became the foundation for engineering in the industrial age. Only toward the end of the nineteenth century did it become clear that Newton's laws have limited applicability. On the one hand, they failed to explain electromagnetic phenomena. This failure led to quantum mechanics. On the other, Newton's assumption of absolute space and time was to be replaced by Einstein's relativity. Quantum mechanics - Wikipedia, Special relativity - Wikipedia

Newton put the sciences of mechanics and astronomy on a sound footing, but his invention and application of calculus to modelling the motions of celestial bodies was to have even greater influence.

One might see that a central scientific issue over the last few thousand years has been the relationship between motion and stillness. How do we relate the eternal stillness of God to the chaotic dynamics of earth? In particular, how to relate the eternal truths of mathematics to this same dynamic world? The answer came with the invention of calculus, a mathematical version of the cinema. To study motion, break it into little steps. To see it more closely, make the steps smaller. To see it with mathematical precision, let the size of the steps approach zero as their number approaches infinity. Persistence of vision - Wikipedia, Calculus - Wikipedia

Newton's work added weight to Galileo's opinion that mathematics was the language of nature. Despite the mathematical advances made by Newton himself, however, there was still a long way to go before mathematicians were satisfied with the consistency and reliability of his methods. Calculus opened up once more questions of infinity and continuity that had troubled mathematicians since earliest times. Zeno's paradoxes - Wikipedia, Irrational number - Wikipedia

Since Newton's time, calculus has become the fundamental mathematical tool for studying the moving world of physics. Parmenides was the first recorded author to raise the problem of capturing the moving world in fixed text. The answers to this problem, in physics, are differential equations, fixed mathematical expressions that capture all that can be written down about a moving system. Parmenides - Wikipedia, Differential equation - Wikipedia

We may understand the roles of differential equations in physics and mathematical science in general by analogy with all forms of writing and communication. A novel, for instance, is a fixed text which represents the fixed points in the dynamic relationships between the set of characters and their environment. It is for the reader to imagine the mtions and emotions represented by the text. Novel - Wikipedia,

A novel is a message from author to reader which has been designed by the author to represent and communicate some chosen features of human life and experience. Like a novel, a differential equation generally has a large number of interpretations. When we come to quantum mechanics, we will see that the infinity of solutions of the 'wave equation' give rise to the notion of superposition. Superposition principle - Wikipedia

One of the most remarkable features of our world is the ability to encode enormously complex and significant states and events into very simple messages, like 'I love you'. The encoding and decoding of such a message in the human network is a product of our intelligence. It seems that ever since we became aware of ourselves, we have considered ourselves to be something very different from the rest of the Universe, specially created children of God. Jaynes

Newton brought the heavens down to earth, and Charles Darwin taught us that we are a product of evolution just like all the other creatures in our world. In particular the mathematical model presented on this site suggests that human intelligence is just one example of the overall intelligence of the Universe that created us. From this point of view, the human act of insight and the quantum 'collapse of the wavefunction' are both examples of encoding and decoding messages. Wave function collapse - Wikipedia, Lonergan

(revised 29 March 2013)

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Further reading

Books

Click on the "Amazon" link below each book entry to see details of a book (and possibly buy it!)

Buchwald, Jed Z, and I Bernard Cohen (Editors), Isaac Newton's Natural Philosophy, MIT Press 2000 Jacket: 'Newton studies have undergone radical changes in the last half-century as more of his work has been uncovered and more details of his life and intellectual context have come to light., This volume singles out two strands in recent Newton studies: the intellectual background to Newton's scientific thought and both specific and general aspects of his technical science. The essays make new claims concerning Newton's mathematical methods, experimental investigations and motivations, as well as the effect that this long presence had on science in England.' 
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Jaynes, Julian, The Origin of Consciousness in the Breakdown of the Bicameral Mind, Mariner Books 2000 Jacket: 'At the heart of this book is the revolutionary idea that human consciousness did not begin far back in animal evolution but is a learned process brought into being out of an earlier hallucinatory mentality by cataclysm and catastrophe only 3000 years ago and still developing.' 
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Lonergan, Bernard J F, Insight : A Study of Human Understanding (Collected Works of Bernard Lonergan : Volume 3), University of Toronto Press 1992 '... Bernard Lonergan's masterwork. Its aim is nothing less than insight into insight itself, an understanding of understanding' 
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Misner, Charles W, and Kip S Thorne, John Archibald Wheeler, Gravitation, Freeman 1973 Jacket: 'Einstein's description of gravitation as curvature of spacetime led directly to that greatest of all predictions of his theory, that the universe itself is dynamic. Physics still has far to go to come to terms with this amazing fact and what it means for man and his relation to the universe. John Archibald Wheeler. . . . this is a book on Einstein's theory of gravity. . . . ' 
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Moulton, Forest Ray, An Introduction to Celestial Mechanics, Dover 1970 Jacket: 'An unrivalled text in the field of celestial mechanics, Moulton's theoretical work on the prediction and interpretation of celestial phenomena has not been superseded.' 
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Newton, Isaac, and Albert Einstein (foreword), Edmund Whittaker (Introduction) Bernard Cohen (Preface), Opticks : Or a Treatise of the Reflections Inflections and Colours of Ligh, Dover 1952 Jacket: 'Here is one of the most readable of the great classics of physical science. First published in 1704, Newton's Opticks provides not only a survey of the 18th century knowledge about all aspects of light, but also a countless numnber of the author's unique scientific insights. It will impress the modern reader by its surprisingly contemporary viewpoint.' 
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Newton, Isaac, and Julia Budenz, I. Bernard Cohen, Anne Whitman (Translators), The Principia : Mathematical Principles of Natural Philosophy, University of California Press 1999 This completely new translation, the first in 270 years, is based on the third (1726) edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. ... The illuminating Guide to the Principia by I. Bernard Cohen, along with his and Anne Whitman's translation, will make this preeminent work truly accessible for today's scientists, scholars, and students. 
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Westfall, Richard S, Never at Rest: A Biography of Isaac Newton, Cambridge University Press 1983 Jacket: 'The richly detailed biography captures both the personal life and the scientific career of Isaac Newton, presenting a fully rounded picture of Newton the man, the scientist, the philosopher, the theologian and the public figure. Professor Westfall treats all aspects of Newton's career, but the account centers on a full description of Newton's achievements in science. Thus the core of the book describes the development of the calculus, the experimentation that altered the direction of the science of optics, and expecially the investigations in celestial dynamics that led to the law of universal gravitation.' 
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Links
Calculus - Wikipedia Calculus - Wikipedia, the free encyclopedia 'Calculus (Latin, calculus, a small stone used for counting) is a discipline in mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern university education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of equations.' back
Differential equation - Wikipedia Differential equation - Wikipedia,the free encyclopedia 'A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines. Differential equations arise in many areas of science and technology, specifically whenever a deterministic relation involving some continuously varying quantities (modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time value varies. Newton's laws allow one (given the position, velocity, acceleration and various forces acting on the body) to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly. back
Irrational number - Wikipedia Irrational number - Wikipedia, the free encyclopedia 'In mathematics, an irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and is therefore not a rational number. Informally, this means that an irrational number cannot be represented as a simple fraction. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable (and the rationals countable) it follows that almost all real numbers are irrational.' back
Isaac Newton The General Scholium to the Principia Mathematica 'Published for the first time as an appendix to the 2nd (1713) edition of the Principia, the General Scholium reappeared in the 3rd (1726) edition with some amendments and additions. As well as countering the natural philosophy of Leibniz and the Cartesians, the General Scholium contains an excursion into natural theology and theology proper. In this short text, Newton articulates the design argument (which he fervently believed was furthered by the contents of his Principia), but also includes an oblique argument for a unitarian conception of God and an implicit attack on the doctrine of the Trinity, which Newton saw as a post-biblical corruption. The English translation here is that of Andrew Motte (1729). Italics and orthography as in original.' back
Newtons Laws of Motion - Wikipedia Newton's Laws of Motion - Wikipedia, the free encyclopedia 'Newton's laws of motion are three physical laws that form the basis for classical mechanics, directly relating the forces acting on a body to the motion of the body. They were first compiled by Sir Isaac Newton in his work Philosophiae Naturalis Principia Mathematica, first published on July 5, 1687.' back
Novel - Wikipedia Novel - Wikipedia, the free encyclopedia 'A novel is a book of long narrative in literary prose. The genre has historical roots both in the fields of the medieval and early modern romance and in the tradition of the novella. The latter supplied the present generic term in the late 18th century. Further definition of the genre is historically difficult. The construction of the narrative, the plot, the way reality is created in the works of fiction, the fascination of the character study, and the use of language are usually discussed to show a novel's artistic merits.' back
Parmenides - Wikipedia Parmenides - Wikipedia, the free encyclopedia 'Parmenides of Elea (early 5th century BC) was an ancient Greek philosopher born in Elea, a Greek city on the southern coast of Italy. He was the founder of the Eleatic school of philosophy, his only known work is a poem which has survived only in fragmentary form. In it, Parmenides describes two views of reality. In the Way of Truth, he explained how reality is one; change is impossible; and existence is timeless, uniform, and unchanging. In the Way of Opinion, he explained the world of appearances, which is false and deceitful. These thoughts strongly influenced Plato, and through him, the whole of western philosophy.' back
Persistence of vision - Wikipedia Persistence of vision - Wikipedia, the free encyclopedia 'Persistence of vision is the phenomenon of the eye by which an afterimage is thought to persist for approximately one twenty-fifth of a second on the retina. The myth of persistence of vision is the mistaken belief that human perception of motion (brain centered) is the result of persistence of vision (eye centred). The myth was debunked in 1912 by Wertheimer but persists in many citations in many classic and modern film-theory texts. A more plausible theory to explain motion perception (at least on a descriptive level) are two distinct perceptual illusions: phi phenomenon and beta movement.' back
Quantum mechanics - Wikipedia Quantum mechanics - Wikipedia, the free encyclopedia 'Quantum mechanics, also known as quantum physics or quantum theory, is a theory of physics providing a mathematical description of the interaction of matter and energy.' back
Special relativity - Wikipedia Special relativity - Wikipedia, the free encyclopedia 'Special relativity . . . is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity—that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)—from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.' back
Superposition principle - Wikipedia Superposition principle - Wikipedia, the free encyclopedia 'In physics and systems theory, the superposition principle [1], also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually.' back
The Newton Project Newton's Religious Writings 'The Newton Project was conceived in 1998 and took on formalised existence with funding from the Arts and Humanities Research Board at the beginning of 2000. Our aim is to make it possible, for the first time in history, to grasp the organic unity of Newton's writing by garnering all his astonishingly diverse productions into a single, freely accessible electronic edition.' back
Wave function collapse - Wikipedia Wave function collapse - Wikipedia, the free encyclopedia 'In quantum mechanics, wave function collapse (also called collapse of the state vector or reduction of the wave packet) is the phenomenon in which a wave function—initially in a superposition of several different possible eigenstates—appears to reduce to a single one of those states after interaction with an observer. In simplified terms, it is the reduction of the physical possibilities into a single possibility as seen by an observer.' back
Zeno's paradoxes - Wikipedia Zeno's paradoxes - Wikipedia, the free encyclopedia 'Zeno's paradoxes are a set of problems generally thought to have been devised by Zeno of Elea to support Parmenides's doctrine that "all is one" and that, contrary to the evidence of our senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.' back

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