Newton's Principia revisited: Volume 3: Global and propulsion mechanics
()
About this ebook
IMPORTANCE. Classical mechanics will remain the basic reference and tool for mechanics on terrestrial and planetary scale as well as the proto-theory of relativistic and quantum mechanics. But it can only serve its purpose if it is not considered as obsolete, but if its foundations and implications are understood and made 'absolutely' clear.
METHOD. Based on the 'instinctive belief' that the foundations of classical mechanics cannot be found and reconstructed within mechanics itself but only 'outside', classical mechanics is 'understood' by embedding it into an adequate theory of knowledge and adequate proto- and meta-theories in terms of the 'language of dynamics'. Evidence is produced that available philosophical expositions are not adequate for the purpose at hand.
Mechanics is treated as part of physics, not of mathematics. Not sophisticated mathematical artifacts, necessary for solving specific problems, but the intellectually satisfactory foundation of mechanics in general is subject and purpose of the exercise. The goal is reached using axiomatic systems as models.
SCOPE. Following an account of the unsatisfactory state of affairs the treatise covers the epistemological foundations, abstract proto-mechanics, i. e. the theories of time and space, meta-mechanics, i. e. the theories of state space models and of quantities proper, and, as an instance of the latter, abstract elementary mechanics, the theory of translational motions of 'small' solid bodies in three-dimensional Euclidean space, including classical general relativity. Subsequently the theory of classical kinematics is developed as basis for interpreted proto-mechanics and interpreted elementary mechanics. As an amusing interlude classical special relativity is treated in detail.
On the basis of a model of matter suggested by Newton's 'Definition IV' and d'Alembert's principle a theory of inertia and gravitation has been developed, which is in accordance with the standard model of nucleons and may be of interest to physicists. Gradients of the mass potential of physical space are considered as causes of momentum productions in bodies of ponderable matter. This point of view permits to avoid many problems so far unsolved.
Further, classical macroscopic mechanics is treated as continuum mechanics. Accordingly Cauchy's universal equation of motion is considered as the root of the healthy tree of classical mechanics. All its global branches including 'generalised' mechanics are shown to be 'nothing but' weighted integrals of the basic local momentum balance.
The final chapters deal with the theories of dynamics and kinematics of rigid bodies in vacuo and in fluids. The rational theories of motions and propulsion of bodies in fluids, developed by the author, demonstrate the power of the axiomatic approach. The treatise proper ends with a section on motions in wave media. The closing operations of evaluation, assessment and conclusions provide an executive summary, the assessment of the results so far and the decisions based on these results.
READERS. All teachers and students of physics and mechanics, theoretical and applied, as well as of didactics, philosophy and history of physics and mechanics, in fact everybody interested in understanding, in Goethe's sense, the world we live in.
Michael Schmiechen
Until he retired in 1997 the author has been Deputy Director, Head of Research and Development at the Versuchsanstalt für Wasserbau und Schiffbau (VWS), the Berlin Model Basin, and apl. Professor for Hydromechanical Systems at the Institut für Schiffs- und Meerestechnik (ISM), Technische Universität Berlin (TUB). Ever since he continued to promote his ideas at lectures and conferences around the world. Details of his curriculum vitae and his personal background are to be found on his website www.m-schmiechen.de .
Read more from Michael Schmiechen
Newton's Principia revisited: Volume 1: Meta- and protomechanics Rating: 0 out of 5 stars0 ratingsNewton's Principia revisited: Volume 2: Elementary and local mechanics Rating: 0 out of 5 stars0 ratings
Related to Newton's Principia revisited
Related ebooks
Photons: The History and Mental Models of Light Quanta Rating: 4 out of 5 stars4/5Transcendental Curves in the Leibnizian Calculus Rating: 5 out of 5 stars5/5Einstein's Theory of Relativity Rating: 4 out of 5 stars4/5Continuous Linear Representations Rating: 0 out of 5 stars0 ratingsThe Absolute Differential Calculus (Calculus of Tensors) Rating: 0 out of 5 stars0 ratingsThe Conceptual Foundations of the Statistical Approach in Mechanics Rating: 3 out of 5 stars3/5An Interpretive Introduction to Quantum Field Theory Rating: 3 out of 5 stars3/5Relativity: The Special and The General Theory A Popular Exposition Rating: 0 out of 5 stars0 ratingsPhilosophical Introduction to Set Theory Rating: 0 out of 5 stars0 ratingsUnderstanding Relativity: A Simplified Approach to Einstein's Theories Rating: 5 out of 5 stars5/5The Principle of Relativity with Applications to Physical Science Rating: 0 out of 5 stars0 ratingsSimilarity and Dimensional Methods in Mechanics Rating: 0 out of 5 stars0 ratingsAxiomatics of Classical Statistical Mechanics Rating: 5 out of 5 stars5/5Lie Groups for Pedestrians Rating: 4 out of 5 stars4/5Relativity (Barnes & Noble Library of Essential Reading): The Special and the General Theory Rating: 0 out of 5 stars0 ratingsTopoi: The Categorial Analysis of Logic Rating: 5 out of 5 stars5/5Minimal Flows and Their Extensions Rating: 0 out of 5 stars0 ratingsInterpolation Functors and Interpolation Spaces Rating: 0 out of 5 stars0 ratingsThe Principles of Physical Optics: An Historical and Philosophical Treatment Rating: 5 out of 5 stars5/5Rotations, Quaternions, and Double Groups Rating: 3 out of 5 stars3/5Particle Accelerators: From Big Bang Physics to Hadron Therapy Rating: 0 out of 5 stars0 ratingsComputability, Complexity, Logic Rating: 0 out of 5 stars0 ratingsScientific Autobiography: And Other Papers Rating: 3 out of 5 stars3/5Group Theory and Its Applications Rating: 0 out of 5 stars0 ratingsPopular scientific lectures Rating: 0 out of 5 stars0 ratingsPhilosophic Foundations of Quantum Mechanics Rating: 4 out of 5 stars4/5Uniform Fréchet Algebras Rating: 0 out of 5 stars0 ratingsThe Concept of Nature Rating: 5 out of 5 stars5/5Relativity - The Special and General Theory Rating: 4 out of 5 stars4/5Nuclear Physics Rating: 4 out of 5 stars4/5
Reviews for Newton's Principia revisited
0 ratings0 reviews
Book preview
Newton's Principia revisited - Michael Schmiechen
Bibliografische Information der Deutschen Bibliothek:
Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen National Bibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.ddb.de abrufbar.
Volume 1: ISBN 978-3-8370-5307-4
Volume 2: ISBN 978-3-8370-5308-1
Volume 3: ISBN 978-3-8391-6001-5
Dieses Werk ist urheberrechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die der Übersetzung, des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tabellen, der Funksendung, der Mikroverfilmung oder der Vervielfältigung auf anderen Wegen und der Speicherung in Datenverarbeitungsanlagen, bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. Eine Vervielfältigung dieses Werkes oder von Teilen dieses Werkes ist auch im Einzelfall nur in den Grenzen der gesetzlichen Bestimmungen des Urheberrechtsgesetzes der Bundesrepublik Deutschland vom 9. September 1965 in der jeweils geltenden Fassung zulässig. Sie ist grundsätzlich vergütungspflichtig. Zuwiderhandlungen unterliegen den Strafbestimmungen des Urheberrechtsgesetzes.
The moral rights of Michael Schmiechen to be identified as the sole author of this work are asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
© Michael Schmiechen Berlin 2009
Herstellung und Verlag
Books on Demand GmbH
Norderstedt near Hamburg
Germany
Printed on lasting paper.
"… absence of synonymy, clash of meanings, absurdity are desirable. Presence of synonymy, intuitive appeal, agreement with customary modes of speech, far from being the philosophical virtue, indicates that not much progress has been made and that the business of investigating what is commonly accepted has not even started."
Paul Feyerabend: How to be a good empiricist (1999/101 f).
PROBLEM
The present treatise is devoted to the task of philosophy on the most modest level, to reconstruct our ‘instinctive beliefs’ in classical mechanics and to present them ‘as much isolated and as free from irrelevant additions as possible’ as RussellB demanded in 1912. The same motivation drove many authors since the appearance of Newton’s Principia, among them most prominently Hertz in constructing his ‘Prinzipien der Mechanik’, posthumously published in 1894.
IMPORTANCE
Classical mechanics will remain our basic reference and tool for mechanics on terrestrial and planetary scale as well as the proto-theory of ‘relativistic’ and quantum mechanics, as noted by Einstein 1919. It can only serve its purpose if it is not considered as obsolete, but if its foundations and implications are understood and made ‘absolutely’ clear.
The relation of the theory of general relativity to classical mechanics is similar to the relation of quantum theory to classical mechanics as claimed by Landau and Lifschitz in 1965, though that claim has never been substantiated (Laughlin 2007/58):
Sie enthält die klassische Mechanik als Grenzfall und bedarf gleichzeitig dieses Grenzfalls zu ihrer eigenen Begründung.
METHOD
Based on the instinctive belief that the foundations of classical mechanics cannot be found and reconstructed within mechanics itself but only ‘outside’, classical mechanics is ‘understood’ by embedding it into an adequate theory of knowledge and adequate proto- and meta-theories in terms of the ‘language of dynamics’ as demanded by Kant, Goethe and specifically by Maxwell in 1877. Evidence is produced that available philosophical expositions, provided they are sufficiently explicit, are not adequate for the purpose at hand.
Mechanics is part of physics, not of mathematics. Thus not the sophisticated mathematical artifacts, necessary for solving specific problems, but the intellectually satisfactory foundations of mechanics in general are subject and purpose of the present exercise. The goal is reached using axiomatic systems as models constituting representation spaces in accordance with Kant’s Copernican turn and Poincaré’s conventionalism.
Newton’s Principia and related ‘principles’ revisited
Classical Dynamics reconstructed in the spirits of Goethe, Euler and Einstein
Elementary Mechanics from an advanced standpoint and vice versa
This simple minded contribution
to mankind’s unended quest
is humbly dedicated to the Creator
of the immeasurable Universe.
And it is gratefully dedicated to all,
who made this work possible:
to my wife Susanne,
to our four children,
and to the generations of my ancestors,
of my teachers and of my colleagues,
and, last but not least, of my students;
and it is dedicated to all researchers,
teachers, historians and philosophers
of physics and mechanics.
In the spirit of Goethe and
following Newton, Euler and Einstein
a local model is being offered,
embedded into a hierarchy of few,
hopefully coherent and acceptable,
yet instinctive beliefs, our ‘principles’,
the mythical foundations of science,
subject to superstition and fashion,
and thus subject to change with
further evolution of rationality.
Prof. Dr.-Ing. Michael Schmiechen
until his retirement on 31.03.1997
Deputy Director, Head of Research and Development,
at the Versuchsanstalt für Wasserbau und Schiffbau (VWS),
the Berlin Model Basin, and
apl. Professor for Hydromechanical Systems
at the Institut für Schiff- sund Meerestechnik (ISM)
of Technische Universität Berlin (TUB)
Bartningallee 16, D-10557 Berlin (Tiergarten), Germany
Phone: +49-(0)30-392 71 64, E-mail: m.schm@t-online.de
Website: http://www.m-schmiechen.de
The website will be permanently archived by the Deutsche Nationalbibliothek at Leipzig in accordance with the DNB Law of July 22, 2006.
It contains links to all papers, presentations and worked examples of the author since about 1990, and hopefully in the near future to all prior work as well.
Covering
General subjects
Mechanics in general
Motions of vehicles
Propulsion in general
Ducted propulsors
Various materials
in sections
Recent additions
Papers annotated
Bibliographies
and further
Terms of usage
Letters (yet) unanswered
Fields of research
Biography of the author
Personal background (5.5.7)
Useful links
"Die Physik ist nichts, als die Lehre
von der Phantasie."
Novalis: Studienheft 1799 (1981/521).
Advertisement
From Newton’s advertisements to the first two editions of his Opticks, (1952/CXXI ff):
Advertisement to the First Edition, April 1, 1704:
"Part of my ensuing Discourse about Mechanics was … put together out of scatter’d Papers. To avoid being engaged in Disputes about these Matters, I have hitherto delayed the printing, and should still have delayed it, had not the Importunity of Friends prevailed upon me. If any other Papers writ on this Subject are got out of my Hands they are imperfect, and were perhaps written before I had tried all the Ideas here set down, and fully satisfied my self about the Laws of Motion. I have here publish’d what I think proper to come abroa’d, wishing that it may not be translated into another Language without my Consent.
… The gravitation, I have endeavoured to give an Account of: but for want of sufficient Observations leave that Matter to be farther examined. Many Subjects I have also left imperfect, not having tried all the Considerations which I intended when I was about these Matters, nor repeated some of those which I did try, until I had satisfied my self about all their Circumstances. To communicate what I have tried, and leave the rest to others for farther Enquiry, is all my Design in publishing these Papers. …."
Italics: paraphrases*: MS.
* Different from the standard usage in the sense of ‘rewording’ the term ‘paraphrase’ is used for the ‘result of an imitation’ in the sense of ‘parody, caricature, burlesque, travesty’ throughout the whole treatise (Roget’s Pocket Thesaurus. A Treasury of Synonyms and Antonyms. 1949).
Advertisement to the Second Edition, July 16, 1717:
… at the End … I have added some Questions. And to shew that I do not take Gravity for an essential Property of Bodies, I have added one Question concerning its Cause, chusing to propose it by way of a Question, because I am not yet satisfied about it for want of Experiments.
Note
Heutzutage will freilich niemand mehr etwas von Exposition wissen; die Wirkung, die man sonst im dritten Akt erwartete, will man jetzt schon in der ersten Szene haben, und man bedenkt nicht, daß es mit der Poesie wie mit dem Seefahren ist, wo man erst auf einer gewissen Höhe sein muß, bevor man mit vollen Segeln gehen kann.
Johann Wolfgang Goethe: 27.03.1831 (Eckermann, 1911/341).
Readers will find a number of ‘cross-sections’ worth noting before getting involved in the text. Right before the detailed table of ‘Contents’ the ‘Survey’ on the following page provides an overview of the material covered in three volumes. The ‘Preface’ is addressed to colleagues and friends, trying to catch their interest and asking them to join me in my continuing effort to clarify the foundations of classical mechanics and eventually jointly to arrive at an ISO standard meeting the current state of science and technology, hopefully offending nobodies instinctive beliefs.
At the end, in the ‘Closing operations’ the section ‘Evaluation’ provides an abstract, in parts a summary of the treatise. The appendices include the ‘Acknowledgements’, the ‘Conventions’ adopted, the ‘References’ and finally by the ‘Indices’. For the convenience of readers the Preliminaries, including the overall ‘Contents’, the ‘Preface’ and the ‘Bootstraps’, as well as the ‘Conventions’, the overall ‘References’ and ‘Indices’, are repeated in all three volumes.
In plunging into the text readers are invited to follow their own curiosity as the author has done in his research. If the philosophy, the theory of theories, the protoand meta-mechanics are not to their tastes they may dive directly into the more technical sections of interest to them. These provide solutions for a number of fundamental problems, which have not been solved before due to the proud ignorance of the problems and of ‘theory’ and ‘philosophy’ still to be met among ‘practicians’ and ‘theoreticians’ as well.
Maybe these solutions motivate readers to go back and grasp, for their own advantage, the merits and power of the axiomatic method explained in detail and applied consistently. In view of the very many levels of discussion and the incredible confusion of issues and jargons a shorter text would not have served the purpose at this stage. Despite its scope and size the treatise is still unfinished, work in progress and Goethe has provided a good excuse for its publication (BA 11/300):
Eine solche Arbeit braucht nicht im höchsten Grade ausgeführt und vollendet zu sein; wenn sie gut gesehen, gedacht und fertig ist, so ist sie für den Liebhaber oft reizender als ein größeres, ausgeführtes Werk.
Survey
For the convenience of readers and, last but not least, in view of book production the material conceived as a single coherent treatise is published in three separate paperbacks. The publication as an e-book is envisaged.
Preliminaries
Contents, Preface, Bootstraps
Part 1: Meta- and proto-mechanics
Prologue
Opening operations: Problems, Models, Goals
Related background: cultural, personal
Theory of theories: ‘meta-physics’ explicit
Proto-mechanics: abstract: time and space
Meta-mechanics: abstract: state space models
Part 2: Elementary and local mechanics
Meta-mechanics: ad hoc: balances of quantities
Elementary mechanics: abstract: dynamical relativity
Proto-mechanics: interpreted: physical measurements
Perspective, kinematical relativity: speed horizons
Elementary dynamics: concepts of ‘force’
Elementary physics: inertia and gravitation
Meta-mechanics: local: balances of quantities
Local mechanics: continuum mechanics
Local mechanics: stress laws
Part 3: Global and propulsion mechanics
Global balances: elementary: weighted integrals
Global mechanics: abstract: partial energy balances
Rigid body mechanics: kinematics, dynamics
Rigid bodies in fluids: axiomatic approach
Propulsion mechanics: rational approach
Motions in wave media: various models
Closing operations: Evaluation Assessment, Conclusions
Epilogue, Post scriptum, Acknowledgements
Conventions, References, Indices
Contents
… I do not think ‘The Rime of the Ancient Mariner’ was for Coleridge an escape from reality: I think it was reality, I think he was on the ship and made the voyage and felt and knew it all.
Thomas Wolfe, 1932 (Coleridge, 1967/VI).
1 Preface
2 Bootstraps
2.1 Levels of problems
2.2 Solving problems
2.3 ‘Initial’ problem
Part 1
Meta- and proto-mechanics
3 Prologue
3.1 Comprehending
3.1.1 Sufficient reasons
3.1.2 Language of dynamics
3.1.3 Exegesis of holy texts
3.1.4 Scientific ‘systems’
3.1.5 Paradigm of paradigms
3.2 Coherent beliefs
3.2.1 Instinctive beliefs
3.2.2 Principle of coherence
3.2.3 Epistemic logics
3.2.4 Münchhausen’s Trilemma
3.2.5 ‘Mythical’ foundations
3.2.6 Knowledge and belief
3.2.7 Religious beliefs
3.3 Reconstruction
3.3.1 Intellectual problems
3.3.2 Interpretations
3.3.3 Scientific roots
3.3.4 Historical developments
3.3.5 ‘Methods’ of research
3.3.6 ‘Against method’
3.3.7 Goethe’s method
3.3.8 Guiding principle
3.4 Embedding
3.4.1 Basic idea
3.4.2 Modest goal
3.4.3 Meta-theories
3.4.4 Top-down approach
3.4.5 ‘Higher standpoint’
3.4.6 Other approaches
4 Opening operations
4.1 Classical expositions
4.1.1 Need for reconstruction
4.1.2 Limits of theory
4.1.3 Boscovich’s Law
4.1.4 Dühring’s assignment
4.1.5 Mach’s concerns
4.1.6 Hertz’ motivation
4.1.7 Boltzmann’s ‘Principe’
4.2 More recent expositions
4.2.1 Hamel’s axioms
4.2.2 Lanczos’ variations
4.2.3 ‘Axiomatic’ approaches
4.2.4 ‘Mass points’ et cetera
4.2.5 Hamel ‘replaced’
4.2.6 Rational mechanics
4.2.7 Related efforts
4.3 Concepts of force
4.3.1 ‘Incredible’ beliefs
4.3.2 Hopeless efforts
4.3.3 Euler’s ‘Naturlehre’
4.3.4 Non-trivial problem
4.3.5 Hopeless confusion
4.3.6 Much nonsense
4.3.7 Concepts of force: history
4.4 ‘Solutions’ proposed
4.4.1 ‘Philosophical’ approach
4.4.2 ‘Rational’ approach
4.4.3 Elementary mechanics
4.4.4 Freely moving bodies
4.4.5 Constrained motions
4.4.6 Operational interpretation
4.4.7 Universes, reference molluscs
4.4.8 Theory of gravitation
4.4.9 ‘Zu Ende gekommen’
4.5 Model, Goal, Plan
4.5.1 Model of treatise
4.5.2 Goal of the treatise
4.5.3 ‘Engineering’ philosophy
4.5.4 Proto- and meta-mechanics
4.5.5 Elementary and local dynamics
4.5.6 Global dynamics, ‘principles’
4.5.7 Rigid bodies, in fluids 5 Related background
5.1 Historical aspects
5.1.1 Historical ‘notes’
5.1.2 Various traditions
5.1.3 Newton’s Principia
5.1.4 ‘Guide to the Principia’
5.1.5 Philosophical positions
5.1.6 History of mechanics
5.1.7 Unity of physics
5.1.8 Glasperlenspiel: a story
5.2 Philosophical aspects
5.2.1 ‘Mechanistic’ thinking
5.2.2 Metaphysical views
5.2.3 ‘Non-existent’ things
5.2.4 Weyl’s apotheosis
5.2.5 ‘Bildung’
5.2.6 Third culture
5.2.7 ‘Fashionable nonsense’
5.3 Theoretical aspects
5.3.1 Home-made philosophy
5.3.2 Theories of science
5.3.3 Kant’s Copernican turn
5.3.4 Concepts of truth
5.3.5 Objective truth
5.3.6 Mittelstaedt’s grand survey
5.3.7 Serious doubts
5.4 Pragmatic aspects
5.4.1 Human nature
5.4.2 Social aspects
5.4.3 Various temperaments
5.4.4 Anschauung
5.4.5 Various languages
5.4.6 Various names
5.4.7 Various motivations
5.4.8 Various ‘principles’
5.5 ‘Personal’ aspects
5.5.1 ‘Stories’
5.5.2 Teachers and experts
5.5.3 Teaching
5.5.4 Pupils and students
5.5.5 Creativity
5.5.6 Psychological aspects
5.5.7 Personal background
5.5.8
6 Theory of theories
6.1 World model
6.1.1 Layers of the world
6.1.2 Ontology
6.1.3 Model of theories
6.1.4 Meta-theories
6.1.5 ‘Facta’
6.1.6 ‘Laws of nature’
6.1.7 General discussion
6.2 Axiomatic systems
6.2.1 Axiomatic systems: general
6.2.2 Axiomatic systems: usage
6.2.3 ‘In principio … ‘
6.2.4 Anschauen, Anschauung
6.2.5 Meta-’spaces’
6.2.6 Interpretation theories
6.2.7 Observation theories
6.3 Structures
6.3.1 Motivation
6.3.2 Basic structures
6.3.3 Derived structures
6.3.4 Fuzzy sets
6.3.5 Measurable magnitudes
6.3.6 Multi-dimensional magnitudes
6.3.7 Terminology, notation
6.3.8 Quantities: extensities
6.4 Theory of probability
6.4.1 Meta-probability
6.4.2 Derived probabilities
6.4.3 Other instantiations
6.4.4 Statistics
6.4.5 Estimation
6.4.6 Plausibility
6.4.7 Aggregate descriptions
6.4.8 Stochastic processes
6.5 Logics
6.5.1 Classical logics
6.5.2 Calculi of propositions
6.5.3 Calculi of predicates
6.5.4 Calculi of classes
6.5.5 Fuzzy logics, linguistics
6.5.6 Object orientation
6.6 ‘Ideal’ objects
6.6.1 Linear equations
6.6.2 Fourier transforms
6.6.3 Laplace transforms
6.6.4 Sampled data
6.7 Real objects
6.7.1 ‘Reality’
6.7.2 Existence
6.7.3 Scepticism
6.7.4 Induction, falsification
7 Proto-mechanics: abstract
7.1 Meta-proto-theory
7.1.1 Need for proto-mechanics
7.1.2 Meta-proto-mechanics
7.1.3 ‘Euclidean’ spaces
7.1.4 Carnap’s ‘Der Raum’
7.1.5 Hyperbolic planimetry
7.2 Curved spaces
7.2.1 Concept of curved space
7.2.2 Homogeneous spaces
7.2.3 Complex spheres
7.2.4 Transformations
7.2.5 Orthogonal frames
7.2.6 Normalisation
7.2.7 Circles: complex
7.3 Abstract chronometry
7.3.1 Concepts of time
7.3.2 Abstract time
7.3.3 Objectivity, causality, events
7.3.4 Curved time
7.3.5 ‘Theories’ of time
7.4 Abstract stereometry
7.4.1 Concept of space
7.4.2 Abstract stereometry
7.4.3 Distances
7.4.4 ‘Freedom of choice’
7.4.5 Euclid’s ‘Elements’
7.4.6 Newton’s stereometry
7.4.7 Philosophical problems
7.5 Complex time-space frames
7.5.1 Complex frames
7.5.2 Unitary transformations
7.5.3 Limited horizons
7.5.4 Unlimited horizons
7.5.5 Generic Lorentz ‘rotation’
7.5.6 ‘Gleich-zeitig’, ‘gleich-ortig’
7.5.7 Minkowski frames
7.5.8 Generic hyperbolic ‘rotation’
7.5.9
7.6 Concepts of matter
7.6.1 Concept of body
7.6.2 Concept of continuum
7.6.3 Quantity of matter
7.6.4 Structure of matter
7.6.5 Re-normalisation
7.6.6 ‘Dark’ ages
7.7 Physical space
7.7.1 Transcendentals
7.7.2 Relativistic space
7.7.3 World geometry
7.7.4 Abstract versus physical space
7.7.5 ‘State of the art’
8 Meta-mechanics: abstract
8.1 State models: abstract
8.1.1 Black box models
8.1.2 State space models
8.1.3 Models of systems
8.1.4 Structures, parameters
8.1.5 Transformations
8.1.6 Models of processes
8.1.7 Discrete, continuous time
8.2 Interpreted state models
8.2.1 Operations
8.2.2 Interpretation of state
8.2.3 Aggregate models
8.2.4 Universal models
8.3 Linear state models
8.3.1 Convolution
8.3.2 Interpretation of state
8.3.3 Rational model
8.3.4 Equivalent models
8.3.5 Basic linear models
8.4 Systems identification
8.4.1 Purpose: simulation
8.4.2 Parameter identification
8.4.3 Principal solution
8.4.4 Feed back of noise
Part 2
Elementary and local mechanics
9 Meta-mechanics: ad hoc 9.1 Axiomatic meta-theory
9.1.1 ‘Logic’ of science
9.1.2 Meta-concepts
9.1.3
9.1.4 First meta-axiom
9.1.5 Second meta-axiom
9.1.6 Third meta-axiom
9.1.7 Flow meta-axioms
9.1.8 Axiomatic meta-system
9.1.9 State space model
9.2 Meta-principles
9.2.1 Relativity, objectivity
9.2.2 Material invariance, equivalence
9.2.3 Material, immaterial production
9.2.4 Similarity
9.3 Meta-theorems
9.3.1 Steady states
9.3.2 ‘Isolated’, ‘free’ systems
9.4 Quantity of matter
9.4.1 Balance of matter
9.4.2 Instances of balances: in general
9.5 Local balances
9.5.1 Densities, intensities
9.5.2 ‘Force’ potentials
9.5.3 Energy equation
10 Elementary mechanics: abstract
10.1 Elementary axioms
10.1.1 Elementary primitives
10.1.2 Extensity of motion
10.1.3 Elementary momentum balance
10.1.4 Nature of forces
10.1.5 Momentum diffusion
10.1.6 Intensities of motion, of production
10.1.7 Elementary axiomatic system
10.2 Principles of relativity, objectivity
10.2.1 General relativity, objectivity
10.2.2 Theorem on steady motions
10.2.3 Theorem on body fixed spaces
10.2.4 Steady motions reviewed
10.3 Principles of materiality
10.3.1 Invariance of momentum diffusion
10.3.2 Components of momentum production
10.3.3 ‘Midwife buried’
10.3.4 d’Alembert’s principle: derived
10.3.5 Concept of ‘lost’ forces
10.3.6 d’Alembert’s principle: ‘interpreted’
10.3.7 d’Alembert’s principle: reviewed
10.3.8 General relativity 1889
10.3.9 Energy principle
10.3.10
10.4 Theorems on free motions
10.4.1 Unconstrained translations
10.4.2 ‘Basic bang’: ‘absolute’ spaces
10.4.3 Motions in steady potentials
10.4.4 Motions in unsteady potentials
10.4.5 Principle of local equivalence
10.4.6 Equivalence misinterpreted
10.4.7 Forces ‘expelled’
10.5 Elementary kinematics
10.5.1 Elementary kinematics: abstract
10.5.2 Paths: space curves
10.5.3 Arguments ‘in free fall’
10.5.4 Mountains of potential
10.5.5 Complex 4D-space
10.5.6 ‘Inertial’ spaces
10.5.7 Ridiculous caricature
10.6 ‘… kurzer Sinn’
10.6.1 Rigid body motion
10.6.2 ‘The simplest theory’
11 Proto-mechanics: time, space
11.1 Proto-mechanics interpreted
11.1.1 Time, space sensations
11.1.2 ‘Scales’
11.2 Chronometry
11.2.1 Interpreted time
11.2.2 Elementary clocks
11.2.3 Chronometers
11.3 Stereometry
11.3.1 Interpreted stereometry
11.3.2 Interpreted kinematics
11.3.3 Non-inertial spaces
11.4 Steady potentials: examples
11.4.1 Plane potentials
11.4.2 Twin ‘paradox’
11.4.3 Inverse square potentials
11.5 Classical relativity
11.5.1 ‘Absolute’ time, space
11.5.2 Basic relativity
11.5.3 Uniform potentials
11.5.4 Galilei transformation
11.5.5 Clocks in one space
11.5.6 Clocks in moving spaces
12 Perspective relativity
12.1 ‘Gleich-zeitige’, ‘gleich-ortige’ events
12.1.1 Kinematics of messengers
12.1.2 ‘Gleich-zeitige’ events
12.1.3 ‘Disturbing’ effects
12.1.4 ‘Gleich-ortige’ events
12.2 ‘Special’ relativity
12.2.1 Einstein’s experiment
12.2.2 Relativistic perspective
12.2.3 ‘Gleich-zeitige’, general events
12.2.4 Slow speed approximation
12.2.5 Other derivations
12.3 Principle of relativity
12.3.1 Pseudo-twins
12.3.2 Twins in perspective
12.3.3 A ‘proof’
12.3.4 Relativistic temperature?
12.4 Speed horizons
12.4.1 Objects identified
12.4.2 Speed ‘limit’
12.4.3 Kinematical uncertainty
12.4.4 Horizons transcended
12.4.5 Pseudo-hyperbolic perspectives
12.5 ‘Quantum’ description
12.5.1 Doppler effect, ‘red shift’
12.5.2 Power spectra
12.5.3 ‘Wave’-corpuscle ‘dualism’
12.5.4 Newton’s Opticks
12.5.5 Acoustic quanta
12.6 Various notes
12.6.1 Apparent effects
12.6.2 Mis-’interpretations’
12.6.3 Standard material
12.6.4 Fizeau’s experiment
12.6.5 Confusion of issues
13 Elementary dynamics
13.1 Concepts of force
13.1.1 ‘Nature of forces’
13.1.2 Surface forces
13.1.3 Body forces
13.1.4 ‘Force’ fields
13.1.5 Historical notes
13.2 Weight and mass
13.2.1 Interpretations
13.2.2 Momentum production
13.2.3 Inertia interpreted
13.2.4 Principle of equivalence
13.2.5 Solid body model
13.3 Hylometry
13.3.1 Quantity of matter
13.3.2 Balance of mass
13.3.3 Abstract mass
13.3.4 Interpreted mass
13.4 ‘Prototypes’, etalons
13.4.1 Mass prototypes
13.4.2 Etalons: basic units
13.4.3 Etalons: realisations
13.4.4 Mass etalon ‘re-newed’
13.4.5 ‘Watt scale’
13.5 Dynamometry
13.5.1 Abstract dynamometers
13.5.2 Ideal dynamometers: statics
13.5.3 Ideal dynamometers: kinetics
13.5.4 ‘Real’ dynamometers
13.5.5 Usage of dynamometers
13.5.6 Mechanical impedances
13.5.7 Ideal Atwood machine
14 Elementary physics
14.1 Flow and production laws
14.1.1 Causes and effects
14.1.2 Local momentum balance
14.1.3 Diffusive momentum flow
14.1.4 Material momentum production
14.1.5 Concept of ‘force’ field
14.1.6 Concept of gravity field
14.2 Law of gravitation
14.2.1 Interaction of masses
14.2.2 Law of gravitation: invariant
14.2.3 ‘Subtle matter’
14.2.4 Einstein’s ‘general relativity’
14.2.5 Constant of gravitation
14.2.6 ‘Cosmic laziness’?
14.2.7 Lex tertia: gravitation
14.2.8 Law of conservation
14.3 ‘Gravitational’ mass
14.3.1 ‘Active’, ‘passive’ masses
14.3.2 ‘Equivalence principle’
14.3.3 ‘Common practice’
14.3.4 Experimental ‘verification’
14.3.5 Total confusion
14.4 Concept of aether
14.4.1 Mach’s principle
14.4.2 ‘It was to be otherwise …’
14.4.3 Void and aether
14.4.4 Spinning buckets
14.4.5 ‘Gravity’ potential
14.4.6 Mass potential
14.5 Mass potentials
14.5.1 Mass potential
14.5.2 Rotating spaces
14.5.3 Spherical bodies
14.5.4 General potentials
14.5.5 ‘Hollow’ universe
14.6 Model of matter
14.6.1 Global production model
14.6.2 Theory of gravity
14.6.3 ‘Identity’ versus ‘equivalence’
14.6.4 ‘Local’ production models
14.6.5 Standard model of nucleons
14.6.6 Earlier models of matter
14.6.7 Historical theories
14.6.8 Recent speculations
14.7 Quantum theory
14.7.1 ‘Quantum mechanics’
14.7.2 Quantum gravity
14.7.3 Non-commutative geometry
14.7.4 ‘New physics’
14.7.5 Wave-body ‘dualism’
14.7.6 Uncertainty principles
14.8 Cosmologies
14.8.1 Current cosmologies
14.8.2 The big bang
14.8.3 Historical cosmologies
14.8.4 Theories of relativity
14.8.5 ‘General’ relativity
14.8.6 ‘Universes floating around’
15 Meta-mechanics: local
15.1 Abstract theory of meta-continua
15.1.1 Density fields
15.1.2 Meta-velocity field
15.1.3 Continuity of meta-mass
15.1.4 Specific magnitudes: intensities
15.1.5 Motions of continua
15.2 Motions of ideal meta-continua
15.2.1 Equation of meta-motion
15.2.2 Potential meta-flows
15.2.3 Analytical distribution function
15.2.4 ‘Wave’ equation et cetera
15.2.5 ‘Classical’ quantum mechanics
15.2.6 ‘Proto’-mechanics
15.2.7 ‘Quauterwelsch’ and beyond
15.3 Meta-theory of material continua
15.3.1 Densities
15.3.2 Velocity field
15.3.3 Equation of continuity
15.3.4 Mass specific quantities
15.3.5 Uniform mass density
15.3.6 Meta-theory of stress laws
15.4 Meta-theory of turbulence
15.4.1 Turbulent fluctuations
15.4.2 Local balances revisited
15.4.3 Expected specific quantities
15.4.4 Turbulent diffusive flux
15.4.5 Isotropic turbulence
16 Local mechanics: fields
16.1 Dynamics of continua
16.1.1 Cauchy’s ‘universal’ equation
16.1.2 Turbulent momentum diffusion
16.1.3 Boltzmann’s equation
16.1.4 ‘Axiomatic’ continuum mechanics
16.1.5 Spin: classical materials
16.1.6 Local balance of energy
16.2 Kinematics of continua
16.2.1 Velocity field: basic concepts
16.2.2 Convective rate of change
16.2.3 Balance of rotation
16.2.4 Substantial rates of change
16.2.5 Historical remarks
17 Local physics: internal states
17.1 Local balances of pressure etc
17.1.1 Pressure laws
17.1.2 Balance of pressure
17.1.3 Balance of deviatoric stress
17.2 Diffusive momentum flux
17.2.1 Various flux laws
17.2.2 Rational theory of continua
17.2.3 Stokesian fluids
17.2.4 Visco-elastic materials
17.2.5 Turbulent momentum diffusion
17.2.6 Recent developments
17.2.7 Lanczos’ remarks
17.3 Newtonian fluids
17.3.1 Newtonian fluids: properties
17.3.2 Navier-Stokes equation
17.3.3 Kinetic energy
17.3.4 Rate of dissipation
17.3.5 Incompressible fluids
17.4 Local momentum production
17.4.1 Motions under gravity
17.4.2 Uniform potential fields
17.4.3 Example: ideal gas
17.4.4 Relative motions
17.4.5 General relativity
Part 3
Global and propulsion mechanics
18 Elementary global balances
18.1 Global balances: meta-theory
18.1.1 Elementary ‘integrals’
18.1.2 Weighted integrals
18.1.3 Steady conditions
18.1.4 Boundary fixed in space
18.1.5 Moving boundaries
18.1.6 Balance of mass
18.2 Global balance of momentum
18.2.1 Momentum balance
18.2.2 Steady conditions
18.2.3 Boundary fixed in space
18.2.4 Moving boundaries
18.2.5 ‘Differing’ views
18.3 Global balances of spin
18.3.1 Balance of spin
18.3.2 Staked global balances
18.3.3 ‘Line of action’
18.3.4 Moving reference frames
18.4 Global balances of energy
18.4.1 Balance of kinetic energy
18.4.2 Fixed boundaries
18.4.3 Moving boundaries
18.4.4 Minimum kinetic energy
18.5 Global stability criteria
18.5.1 Virtual energy
18.5.2 Principle of least constraints
18.5.3 Principle of least curvature
19 Partial energy balances
19.1 Generalised kinematics
19.1.1 Elementary ‘principles’
19.1.2 Generalised kinematics
19.1.3 Generalised position
19.1.4 Forcibly driven systems
19.1.5 Generalised kinematics: applications
19.1.6 Transformations
19.2 Aggregate dynamics
19.2.1 Modes of aggregation
19.2.2 Partial energy balances: en detail
19.2.3 Partial energy balances: en gross
19.2.4 Partial energy balances: appraised
19.2.5 Special case: force free motions
19.2.6 Special case: potential ‘forces’
19.2.7 ‘Energetik’
19.3 Aggregate ‘forces’
19.3.1 Aggregate momentum diffusion
19.3.2 Aggregate momentum productions
19.3.3 Example: Stokesian fluids
19.3.4 Example: hyper-elastic material
19.3.5 Euler-Lagrangean equation: explicit
19.4 ‘Degenerate’ case: holonomic speed
19.4.1 Lagrangean equation
19.4.2 Hamilton’s ‘canonical’ equations
19.4.3 Further ramifications?
19.4.4 Absent, cyclic speeds
19.4.5 Elasto-mechanics: continued
19.4.6 ‘Statistical’ mechanics
19.4.7 Discussion
19.5 Stability criteria
19.5.1 Principle of least curvature
19.5.2 Example: Kármán vortex street
19.5.3 General criteria?
20 Rigid body mechanics
20.1 Rigid body dynamics
20.1.1 Basic theory
20.1.2 Changes of frames
20.1.3 Rotation, precession
20.1.4 Relative motion
20.2 Rigid body kinematics
20.2.1 Basic concepts
20.2.2 Translational motions
20.2.3 Rotational motions
20.2.4 Global motions
20.2.5 Relative motions
20.2.6 Moving platform systems
20.3 ‘Central’ motions
20.3.1 Celestial bodies
20.3.2 Central motions
20.3.3 Two and more bodies
20.3.4 Deflection of light
20.3.5 Perihelion precession
20.3.6 Energy dissipation
20.3.7 Einstein’s theory validated
20.3.8 ‘Anomalies’?
21 Rigid bodies in fluids
21.1 Incompressible fluids
21.1.1 Diffusive flows
21.1.2 Bodies at rest
21.1.3 Bodies in motion
21.1.4 Potential flows
21.1.5 Momentum, inertia
21.1.6 Resistance, damping
21.1.7 Equation of motion
21.1.8 Stability of motion
21.2 Bodies in fluids: momentum convection
21.2.1 Moving force fields
21.2.2 Momentum convection
21.3 Identification
21.3.1 Constitutive equations
21.3.2 ‘Gravity’
21.3.3 Steady motions
21.3.4 Steady motions: unconstrained
21.3.5 Quasi-steady motions
21.4 Dynamometers
21.4.1 Calibration
21.4.2 Stiffness
21.4.3 Identification
22 Propulsion mechanics
22.1 Introduction
22.1.1 Problems of propulsion
22.1.2 Models of propulsion
22.1.3 Pragmatism pure
22.1.4 Inspectional analysis
22.1.5 Propulsion: Goals/Plans
22.2 Steady speed trials
22.2.1 Steady trials: traditional approach
22.2.2 Steady trials: rational approach
22.2.3 Steady trials: power supplied, current
22.2.4 Monitoring of trials
22.2.5 Steady trials: power required
22.2.6 Steady trials: contracted conditions
22.2.7 Steady trials: verification, ‘validation’
22.2.8 ISO/DIS 15016 example
22.2.9 Steady trials: further developments
22.3 Meta-theory of propulsion
22.3.1 Ideal propulsors
22.3.2 Propulsion: axiomatic system
22.3.3 Propulsion: efficiencies
22.4 Ideal propulsors: open
22.4.1 Momentum theory
22.4.2 Ideal propulsor
22.4.3 Jet power, efficiency
22.4.4 Vortex theory
22.4.5 Pump theory
22.4.6 Merits of propulsors
22.5 Ideal propulsors: behind
22.5.1 Equivalent propulsors
22.5.2 Displacement wakes
22.5.3 Thrust deduction
22.5.4 Configuration efficiencies
22.5.5 Thrust deduction: transformed
22.5.6 Thrust deduction: limit
22.5.7 Energy and mixed wakes
22.5.8 Real propulsors in real wakes
22.6 Quasi-steady trials
22.6.1 Propellers behind
22.6.2 Energy balance
22.6.3 Local wake axioms
22.6.4 Alternative approaches
22.6.5 Momentum balance
22.6.6 Thrust deduction
22.6.7 Powering performance
22.6.8 ‘History’
22.7 Hull-integrated propulsors
22.7.1 Propulsor models
22.7.2 Ducted propellers
22.7.3 Internal losses
22.7.4 Propulsor theory interpreted
22.7.5 Basic procedure
22.8 Ducted propeller design
22.8.1 Propulsors are pumps
22.8.2 Equivalent propulsors
22.8.3 Feasibility study
22.8.4 Thrust distribution
22.8.5 Thrust deduction
22.8.6 Basic design
22.8.7 Review
22.8.8 Outlook
23 Motions in wave media
23.1 Subsonic motions of bodies
23.1.1 Wave equation
23.1.2 Body fixed space
23.1.3 Slender bodies
23.1.4 Longitudinal inertia ‘in general’
23.2 Meta-theory
23.2.1 Abstract theory
23.2.2 Slender bodies
23.2.3 Consequences
23.3 Instance, ‘analogy’
23.3.1 Shallow water
23.3.2 ‘Relativistic phenomena’
23.4 Waves in moving wave media
23.4.1 ‘Acoustic metric’
23.4.2 Other analogues
23.4.3 Classical approaches
24 Closing operations
24.1 Evaluation
24.1.1 General aspects
24.1.2 Preliminaries
24.1.3 Meta- and proto-mechanics
24.1.4 Elementary mechanics
24.1.5 Elementary physics
24.1.6 Continuum mechanics
24.1.7 ‘Global mechanics’
24.1.8 Rigid body motions et cetera
24.2 Assessment
24.2.1 Criteria
24.2.2 Satisfaction
24.3 Conclusions
24.3.1 Decisions
24.3.2 Future tasks
25 Epilogue
25.1 Sound knowledge
25.2 Live ideas
26 Post scriptum
27 Acknowledgements
End of Part 3
28 Conventions
28.1 Terminology
28.1.1 Rational names
28.1.2 Traditional names
28.2 Symbology
28.2.1 Operational notations
28.2.2 ‘Principles’, ‘laws’
28.3 References
28.3.1 Formats
28.3.2 Quotations
28.3.3 Translations
28.4 Copyright
28.4.1 Acknowledgements
28.4.2 Doctrine of fair use
28.4.3 Rules of conduct
29 References
29.1 Author’s basic work
29.2 Sources referred to
30 Indices
30.1 Name index
30.2 Subject index
Tables, figures
"‘When I use a word’ Humpty Dumpty said, in rather a scornful tone, ‘it means just what I choose it to mean – neither more nor less.’
‘The question is’, said Alice, ‘whether you can make words mean so many different things.’
‘The question is,’ said Humpty Dumpty, ‘which is to be the master - that’s all.’ "
Lewis Carroll: Through the Looking-Glass (1988/196).
Most of the tables are rudimentary constitutive calculi, ‘matrices’ defining the meaning of terms and expressions as used in the present treatise by their positions in the ‘matrices’.
Newton’s axiomatic system
‘Rational’ elementary dynamics
Momentum production: terminology
Mechanics: ‘dual model’
World model: levels
World model: aspects
Theories: dual model
Theories: purposes
Axiomatic theories: structure
Mechanics: levels of theory
Axiomatic theories: purposes
Methods of thinking
Sets: concept
Relations: concept
Functions: concept
Structures: concept
Structures: fundamental
Extensities: concept
Meta-probability: axiomatics
OOP: Variables
‘Spaces’
Systems: concept
Systems: black box model
Systems: state space model
Systems: notation
Processes: notation
Systems: structure
Systems: macro-operations
Quantities: axiomatic system
Invariance: types
Abstract theory: instantiated
Quantitas motus: axiomatic system
Momentum production: concepts
Momentum production: terminology
‘Gleich-zeitige’ events
Einstein’s experiment
Einstein’s experiment analysed
‘Gleich-zeitige’ events
Pseudo-twins in absolute frame Pseudo-twins in relativistic frame
Translation: axiomatic system Names: traditional, rational
‘Principles’ qualified ‘Laws’ qualified
Activities: German, English
1 Preface
Unglücklicher, Sie scheinen auch an Idealen zu laborieren*.
Georg Büchner: Leonce und Lena. Ein Lustspiel (1952/35).
* "labour v.i.& t. Use labour, exert oneself; work hard; strive for …or to …; advance with difficulty …; be troubled … or impeded; suffer under …[the pains of childbirth]; (of ship) roll or pitch heavily; (arch. or poet.) till (ground); elaborate work out in detail, treat at length …; … "
The Concise Oxford Dictionary of Current English (FowlerHW, 1958).
Dear Colleagues, dear Friends!
This second edition of my lasting effort to ‘reconstruct’ the fundamentals of classical dynamics is a snapshot of work in progress. Even after twelve years of dedicated thinking and writing, extreme ‘produktionsethischer Bravheit’ (Thomas Mann), trying to render the structure and the underlying arguments as intuitive as possible and their expositions as clear as possible, it cannot possibly be more than a ‘final’ draft.
PROBLEM
In the preface to ‘Sylvie and Bruno’ Lewis Carroll has described the problems encountered (1982/256):
And thus it came to pass that I found myself at last in possession of a huge unwieldy mass of literature, - … - which only needed stringing together, up on the thread of a consecutive story; to constitute the book I hoped to write. Only! The task, at first, seemed absolutely hopeless, and gave me a far clearer idea, than I ever had before, of the meaning of the word ‘chaos’: and I think it must have been. ten years, or. more; before I had. succeeded in classifying these odds-and-ends sufficiently to see what sort of a story they indicated: for the story had to grow out of the incidents, not the incidents out of the story.
In trying to answer the questions concerning the foundations of science, classical mechanics in particular, bothering not only me but certainly many of you, I have been re-thinking, re-arranging and re-writing whole chapters, sections, sub-sections, every single sentence, based on the insights gained up to that particular stage and aware of Mallarmé’s remark (Roe, 2007/402):
[Edgar Degas] könne sich nicht erklären, sagte er zu Stéphane Mallarmé, warum ihm Gedichte so schlecht von der Hand gingen, wo es ihm doch an Ideen nicht mangele. ‘Aber lieber Degas, …, man schreibt Gedich-te ja auch nicht mit Ideen, sondern mit Worten.’
The last complete re-arrangements of abstract elementary and of abstract global mechanics became possible and necessary while the manuscript was being revised following the suggestions of my lector, spell and grammar checked, finalised for printing. And I am still on my way to the ideal I see before me since early students’ days, ‘ideal’ not to be misunderstood in the sense of ‘The Platonic Self-Image of Scientists’ as will be seen (Renn, 2004/25 f).
Following the suggestion of Lewis Carroll blank pages should have been inserted here and there, at least some spaces for meta-texts have been left for later completion (1988/529):
"‘… the shyest and most intermittent talker must seem fluent in letter-[and book-]writing. He may have taken half-an-hour to compose his second sentence; but there it is, close after the first!’
‘Then letters [and books] don’t express all that they might express?’
‘That’s merely because our system of letter-[and book-] writing is incomplete. A shy writer ought to be able to show that he is so. Why shouldn’t he make pauses in writing, just as he would do in speaking? He might leave blank spaces - say half a page at a time. … "[Italics]: MS.
BACKGROUND
In view of the vast literature the undertaking to reconstruct the foundations of classical mechanics looks extremely, maybe too ambitious and a warning is in place at this stage: This is not a textbook in the ordinary sense, but rather the draft of a research report and a reader, ‘ein Lesebuch’. Closely related are the ‘Foundations of Science’ by Campbell, a work never completed, the ‘Preface’ starting with the paragraph (1957/V):
The object and nature of this book is sufficiently explained in the introduction; here I will only warn the reader who gets no further that, in spite of its title, it is not an elementary treatise on physics. On the other hand, although there is a just prejudice against an author who seeks to disarm criticism, I would explain here how the book came to be written – not in order to explain its faults away, but in order, by giving notice of them, to render them less harmful.
Another warning in connection with another work of Campbell is due to Suppes (1983.f/35):
"Wenn Archimedes oder Ptolemäus Campbell’s ‘Physics: The Elements’ gekannt hätten, [dann] hätten sie sicher den Rückgang im Anspruch auf
Analyse und begriffliche Klarheit, der über eine Zeit von zweitausend Jahren stattgefunden hat, fast unglaublich gefunden."
Goethe in a conversation with Eckermann mentioned another problem (06.12.1829, 1911/274):
‘Da die Konzeption so alt ist,’ sagte Goethe, ‘und ich seit funfzig Jahren darüber nachdenke, so hat sich das innere Material so sehr gehäuft, daß jetzt das Ausscheiden und Ablehnen die schwere Operation ist.’
Most of the basic themes of the present work have already been stated explicitly in notes jotted down in a card index during the years 1969 to 1973. Dominating topics have been metaphysics, the interrelations of formal and factual constituents of our knowledge and our ‘principles’ down to standards to be developed. At that stage even the project of a book has already been defined, from the language to be adopted down to its format, its production and its distribution.
Notes dated August 1982 stressed the importance of systematic axiomatisation. At the same time the whole pragmatic approach, supposed hopefully to avoid pitfalls and superstition, was allocated to the Preface. Further the importance of rules of procedure and their intelligibility has already been stressed, as it is now.
EXPERIENCE
But it took further thirty years of experience in mechanics, mostly in hydromechanical systems research and development at the Versuchsanstalt für Wasserbau und Schiffbau, VWS, the Berlin Model Basin, and continuous reflection of that experience to explore the early ideas and demonstrate their fertility.
Concerning experience the ‘Operating instructions for a human brain’ state (Hüther, 2005/11 f):
"Es hat lange gedauert, bis mir das endlich klar wurde und bis ich verstanden hatte, daß das, was uns bei all unseren Entscheidungen leitet, nicht unser Geist oder unser Bewußtsein ist, auch nicht all unser auswendig ge-lerntes oder von fragwürdigen Quellen übernommenes Wissen, sondern die Erfahrungen, die wir während unserer bisherigen Entwicklung gesammelt haben. Die Erfahrungen, die ein Mensch im Lauf seines Lebens gemacht hat, sind fest in seinem Gehirn verankert, sie bestimmen seine Erwartungen, sie lenken seine Aufmerksamkeit in eine ganz bestimmte Richtung, sie legen fest, wie er das, was er erlebt, bewertet, und wie er auf das reagiert, was ihn umgibt und auf ihn einstürmt. In gewisser Weise sind diese individuell gemachten Erfahrungen also der wichtigste und wertvollste Schatz, den ein Mensch besitzt. Er kann ihn nicht nur für sich selbst nutzen, sondern – wenn er einmal die Erfahrung gemacht hat, daß Verschenken sehr viel Freude macht – auch versuchen, ihn an andere weiterzugeben. Das Besondere an diesem Erfahrungsschatz ist, daß er dadurch, daß man ihn benutzt und verteilt, nicht immer kleiner, sondern immer größer wird." Italics: MS.
‘My’ present situation has been roughly described by Sepper (1988/96): "
… in the course of human life what turns possibility into actuality is the aperçu, the moment of insight in which we glimpse what the future may bring and which spurs us to invest the necessary labour. Through the aperçu we recognise a totality, the context in which the particular takes its place, and thus the aperçu is by its nature the anticipation of the whole, if not the whole. But the aperçu is problematic. ‘A decisive aperçu is to be regarded as an inoculated disease: One does not get rid of it till one has fought the disease through’ (Goethe; GA 16/713.)."
Thus Goethe’s translation of Büchner’s ‘laborieren’ is ‘kranken’ and not just ‘arbeiten’.
At this stage I need to offer not only ‘eine dunkle Totalidee’ (Friedrich SchillerF), but already detailed elaborations permitting rigorous discussions and criticism. Despite their sheer ‘volume’ they are not a mere collection of material as Wohlwill’s two volumes on ‘Galilei und sein Kampf für die copernicanische Lehre’ (Szabó, 1987/551):
Sicher hat Wohlwill mit bewundernswertem Fleiß, ja mit Verbissenheit, eine riesige, geradezu erdrückende Masse an Material über Galilei zusammengetragen, die durch viele Belanglosigkeiten amorph geworden war: Wohlwill wollte alles bringen, aber hinterließ einen wenig befriedigenden Torso.
And rigorous discussions and criticism, ‘peer reviews’ is what I am asking for as Leibniz did in his ‘Specimen Dynamicum’ (2000/241):
Seitdem wir eine neue, noch zu begründende Wissenschaft der Dynamik erwähnt haben, haben viele ausgezeichnete Männer an verschiedenen Orten eine ausführlichere Erläuterung dieser Lehre verlangt. Da nun die Zeit, um ein Buch zu schreiben, noch nicht zur Verfügung steht, werden wir an diesem Ort darbieten, was einiges Licht anzünden könnte, welches vielleicht sogar zu uns mit Gewinn zurückkehren wird, wenn wir die Meinungen derjenigen hervorlocken, die Kraft des Denkens mit Menschlichkeit im Ausdruck verbunden haben; wir erklären, daß auch deren Urteile uns willkommen sein werden, und wir hoffen, daß sie dem Fortschritt des Werkes hilfreich sein werden.
Although theories of classical general and special relativity will be developed in detail the present exercise is not an attempt to understand Einstein’s theories but a reconstruction of classical mechanics in Einstein’s spirit.
DISCUSSIONS
The original intention to discuss, with friends and specialists, various ‘separate’ subjects and aspects prior to publication of the whole draft turned out to be impractical, even impossible. There are no ‘separate’ subjects and aspects. Sub-subjects became visible only during the evolution of the whole manuscript and make sense and can be scrutinised only in the whole coherent fabric of the underlying instinctive beliefs and their axiomatic formulations, where this stage of maturity has been reached.
In that sense I kindly ask as Fichte did in a Prologue (1961/9):
Die künftigen Beurteiler dieser Schrift bitte ich auf das Ganze einzugehen und jeden einzelnen Gedanken aus dem Gesichtspunkte des Ganzen anzusehen.
Similar requests are to be found not only in other philosophical works, of Hegel and others, but even at the end of Fielding’s very strong ‘Bones for the critics’ in his ‘Tom Jones’ (1964/IV, 56-61; 2007).
Cervantes in his ‘Don Quijote’ addresses the problem as follows (2008/II, 41):
"‘Jedenfalls ist es ein großes Wagnis, ein Buch in Druck zu geben, denn unter allen unmöglichen Dingen ist nichts unmöglicher, als eines zu verfassen, das alle, die es lesen, überzeugt und zufriedenstellt.’
‘Besagtes über mich’ sagte Don Quijote, ‘wird wohl wenige zufriedengestellt haben.’
‘Aber nein, im Gegenteil, stultorum infinitus est numerus, die Zahl derer, denen die Geschichte gefallen hat, ist unendlich groß.’ "
And Popper in his ‘Unended Quest’ adds (1978/30).
… always remember that it is impossible to speak in such a way that you cannot be misunderstood: … If greater precision is needed, it is needed because the problem to be solved demands it.
As will be discussed in detail a completely formalised exposition is far beyond the horizon of my capability and beyond the goal of my treatise: to develop and to communicate a ‘total idea’ indebted to, but intended to transcend the traditions of many schools of mechanics. In view of the ‘incredible’ literature of any of these schools there was of course no chance to think about all problems and ponder all the ideas proposed, put them into context or dismantle pseudo-problems and sheer speculations based on incoherent models and professional superstition.
RULE DRIVEN
Though not fully formalised, such undertaking cannot be but rule driven and the rules are made explicit as far as possible. The procedure is similar to composition in literature and music. In the context given most things are ‘self-evident’. A famous example is Beethoven’s manuscript of the piano concerto in c-minor opus 37, in which the composer fill in the central piano part; he used to improvise this as being ‘selfevident’ – to him.
This does not imply that I was always successful in my ongoing endeavour to adhere to my own rules and meet the standards set forth, essentially rules of self-organisation, ‘natural unfolding’, as close as possible to an ars inveniendi (Leibniz) and to some ‘Kalkül des Verstehens’ (Abel, 1995/405 f), both being unavailable.
Smart readers will immediately detect, not only when it comes to open ends and missing meta-texts, where I am still many hours, even weeks of hard work away from my goal and where I failed to reach my goal or am even utterly mistaken. Or where I stepped myself into the good old traps and pitfalls I carefully pointed out before, a very painful experience I often made.
They may correct and continue in the spirit and based on the results of my exercise so far, knowing that I could not possibly answer all the questions arising during the work, forget about all the questions that occur to readers in the context developed. But there is no way back!
The situation is very similar to any industrial research and development project, experienced over and over again. When the client receives the report on the work he ordered and hopefully paid for, he is wondering why the new questions arising from that work have not been studied. The simple answer is that the scope is creeping up with hindsight and that the client has not (yet) contracted, forget about paid for any further studies.
WORK IN PROGRESS
Readers will note that even at this advanced stage I am still experimenting, trying to find the most adequate orders, expositions and corresponding notations on every level of discussion. And they will note that I have not