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volume II: Synopsis

Part II: A brief history of dynamics

page 9: Dynamics

Dynamics tries to explain why things behave as they do, seeking to understand the forces that move things. It is as old as the need for survival and is founded on revelation. The world reveals something about itself every time it moves. All living creatures, hunters, farmers and scientists study these revelations, looking for ways to predict and exploit future behaviour. Dynamics (mechanics) - Wikipedia, Thomas Aquinas

Theology studies the dynamics of the whole with a view to giving overall guidance to human activity. Traditional theology sees a Universe driven from outside by God. Here we understand that the Universe drives itself. Aquinas defined God as 'pure activity', and held that the Universe needed God to move it. Here, partly inspired by quantum mechanics, we see the Universe itself as pure activity, in no need of an God outside to move it. Theology - Wikipedia, Quantum mechanics - Wikipedia

The writer was a builder. My daily routine was a series of moves calculated to complete the structure I have contracted to erect. From an abstract point of view, building does not differ from dancing, the work of a computer or any other motion. Each is an ordered series of steps to and steps within steps leading to the larger goal.

Dynamics as a a science is possible because all motions have relatively fixed points, features that can be remembered, written down and communicated to others. Living creatures are continually in motion, yet they have fixed anatomy and habits which we can get to know and use to understand and control them. Planets have their orbits. Computers have their programs. Atoms have energy states, and so on. Fixed point (mathematics) - Wikipedia

Two important features of the world are that some things move more quickly than others, and that big moves can be broken down into small moves. These features give us windows into the world. We can explain slow things in terms of their faster parts, and vice versa. We can understand big moves through smaller movesd, and vice versa.

This structure in the world is reflected in our language. Some words point to relatively enduring entities like horses, trees and rocks. These words are called nouns. Other words point to activities, like sleeping, eating or painting, and are called verbs.

From a more physical point of view, the distinction between nouns and verbs is somewhat blurred. The world is rarely still. All words become verbs, differing only in the lifetime of the event to which they refer. So an empire, a sheep and a road accident are events to which we can ascribe a beginning, a middle and an end. The difference is that while an empire may take centuries a road accident can be over in a few seconds.

Big events are sets of smaller events. For me the biggest event is my life. I know that my life rests on a complex web of biological and physical events. Each of these may be analyzed down to quantum events. Quantum theories tell us that even though these fundamental events are almost infinitesimally small, their complexity may be infinite or even transfinite, and they are all unique. Looking in the opposite direction, I can see my life as an infinitesimal event in the Universe that creates and sustains me.

The formally distinguishable fixed parts of the Universe are many, yet in motion they are one. Everything contributes to one overall system, the unbounded life of God. My life is an event in the life of God, consequent upon some events, causing others, relatively irrelevant to others.

Theology studies the dynamics of the whole. By definition, there is nothing outside the whole. The only constraints on its behaviour lie within it. The fundamental internal constraint is consistency, or integrity. The consistency in a situation may be far from obvious. Part of the excitement of science is learning how apparently inconsistent parts work together.

Theology and physics are unified by the observation that the dynamics of the world is similar at all scales. Following this similarity, the history of dynamics opens up broader and broader perspectives until, standing on the shoulders of history, we can gain a glimpse of God

The foundations of modern physical dynamics are quantum field theory and general relativity. The mathematical structure of quantum field theory, even though it was first developed to deal with microscopic events, can be applied at any scale. This idea, modelled as the dynamics of communication networks, is the theoretical backbone of this site. Zee, Hobson, Efstathiou & Lasenby

(revised 28 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!)

Collins, Paul, Papal Power: A Proposal for Change in the Catholicism's Third Millennium, HarperCollinsReligious 1997 Jacket: 'The papacy of the Roman Catholic Church is the world's oldest continuous institution. Paul Collins, historian and inveterate Vatican watcher, has looked beyond the details of this astonishing parade of over 260 popes to uncover the dynamics of papal power. . . . He traces the developments in theory and reality that have led to a modern papacy that exercises virtually sole and total rule over the world's largest religious community. Collins' provocative . . . study proposes a new model in the Catholic Church as it enters its third millennium - one that would allow all Catholics to participate in the work and decision-making of the Church.' 
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Davis, Martin, Computability and Unsolvability, Dover 1982 Preface: 'This book is an introduction to the theory of computability and non-computability ususally referred to as the theory of recursive functions. The subject is concerned with the existence of purely mechanical procedures for solving problems. . . . The existence of absolutely unsolvable problems and the Goedel incompleteness theorem are among the results in the theory of computability that have philosophical significance.' 
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Galilei, Galileo, and Stillman Drake (translator), Discoveries and Opinions of Galileo: Including the Starry Messenger (1610 Letter to the Grand Duchess Christina), Doubleday Anchor 1957 Amazon: 'Although the introductory sections are a bit dated, this book contains some of the best translations available of Galileo's works in English. It includes a broad range of his theories (both those we recognize as "correct" and those in which he was "in error"). Both types indicate his creativity. The reproductions of his sketches of the moons of Jupiter (in "The Starry Messenger") are accurate enough to match to modern computer programs which show the positions of the moons for any date in history. The appendix with a chronological summary of Galileo's life is very useful in placing the readings in context.' A Reader. 
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Hobson, M P, and G. P. Efstathiou, A. N. Lasenby, General Relativity: An Introduction for Physicists, Cambridge University Press 2006 Amazon Editorial Reviews Book Description 'After reviewing the basic concept of general relativity, this introduction discusses its mathematical background, including the necessary tools of tensor calculus and differential geometry. These tools are used to develop the topic of special relativity and to discuss electromagnetism in Minkowski spacetime. Gravitation as spacetime curvature is introduced and the field equations of general relativity derived. After applying the theory to a wide range of physical situations, the book concludes with a brief discussion of classical field theory and the derivation of general relativity from a variational principle.'  
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Jammer, Max, Concepts of Force: A Study in the Foundations of Dynamics, Dover 1999 Reprint of the classic Harvard University Press edition of 1957 
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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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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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Yourgrau, Wolfgang, and Stanley Mandelstam, Variational Principles in Dynamics and Quantum Theory, Dover 1979 Variational principles serve as filters for parititioning the set of dynamic possibilities of a system into a high probability and a low probability set. The method derives from De Maupertuis (1698-1759) who formulated the principle of least action, which states that physical laws include a rule of economy, the principle of least action. This principle states that in a mathematically described dynamic system will move so as to minimise action. Yourgrau and andelstam explains the application of this principle to a variety of physical systems.  
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Zee, Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2003 Amazon book description: 'An esteemed researcher and acclaimed popular author takes up the challenge of providing a clear, relatively brief, and fully up-to-date introduction to one of the most vital but notoriously difficult subjects in theoretical physics. A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on. Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena. Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory--what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments,while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory. Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used.  
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Papers
Huberman, Bernardo A, Lada A Adamic, "Growth dynamics of the World-Wide Web", Nature, 401, 6749, 9 September 1999, page 131. 'The exponential growth of the World Wide Web has transformed it into n ecology of knowledge in which highly diverse information is linked in an extremely complex and arbitrary manner. But even so, as we show here, there is order hidden in the web. We find that web pages are distributed among sites according to a universal power law: may sites have only a few pages, whereas very few sites have hundreds of thousands of pages. Thjis universal distribution can be explained by using a simple stochastic dynamical gowth model.' . back
Links
Dynamics (mechanics) - Wikipedia Dynamics (mechanics) - Wikipedia, the free encyclopedia 'In the field of physics, the study of the causes of motion and changes in motion is dynamics. In other words the study of forces and why objects are in motion. Dynamics includes the study of the effect of torques on motion. These are in contrast to kinematics, the branch of classical mechanics that describes the motion of objects without consideration of the causes leading to the motion.' back
Fixed point (mathematics) - Wikipedia Fixed point (mathematics) - Wikipedia, the free encyclopedia 'In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is a point that is mapped to itself by the function. A set of fixed points is sometimes called a fixed set. That is to say, c is a fixed point of the function f(x) if and only if f(c) = c.' 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
Solar System Dynamics Group JPL Solar System Dynamics 'JPL's solar system dynamics WWW site provides information related to all known bodies in orbit around the sun. This site is maintained by the Solar System Dynamics Group of the Jet Propulsion Laboratory. ' back
Theology - Wikipedia Theology - Wikipedia, the free encyclopedia 'Augustine of Hippo defined the Latin equivalent, theologia, as "reasoning or discussion concerning the Deity"; Richard Hooker defined "theology" in English as "the science of things divine". The term can, however, be used for a variety of different disciplines or forms of discourse. Theologians use various forms of analysis and argument (philosophical, ethnographic, historical, spiritual and others) to help understand, explain, test, critique, defend or promote any of myriad religious topics.' back
Thomas Aquinas Summa Theologica I, 2, 3: Whether God exists? 'I answer that, The existence of God can be proved in five ways. The first and more manifest way is the argument from motion. . . . ' back
William Rowan Hamilton General Method in Dynamics 'Hamilton's first paper on dynamics is entitled `On a General Method in Dynamics; by which the Study of the Motions of all free Systems of attracting or repelling Points is reduced to the Search and Differentiation of one central Relation, or characteristic Function'. This was published in the Philosophical Transactions of the Royal Society (part II for 1834, pp. 247-308). This paper is available in the following formats: Plain TeX DVI PostScript PDF' back

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