Such - Michael Schmiechen, Berlin: Homepage

Transcription

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" ..., allein um mich von dem drückenden Gefühle zu
befreien, daß ihre Elemente nicht frei seien von Dunkelheiten und Unverständlichkeiten für mich. Nicht das einzig mögliche Bild der mechanischen Vorgänge, noch
auch das beste Bild, sondern überhaupt ein begreifbares
Bild wollte ich suchen und an diesem Beispiel zeigen,
daß ein solches möglich sei und wie es etwa aussehen
müsse."
Heinrich Hertz: Die Prinzipen der Mechanik
(1984/104).
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Closing operations
PROBLEMS
The problem is to terminate the present reconstruction of classical mechanics in
an organised fashion. This will be done by adhering to the model of the problem
solving process. Even if the procedure may look very clumsy the author does not
know how else he could possibly solve this final, very difficult problem.
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MODELS
In accordance with the second model adopted among the bootstraps, the generic, most elementary 'strategy' of the problem solving process, the methodically
ordered sequence of macro-operations, the closing operations on the meta-level of
the treatise are: to evaluate the results obtained and to assess the 'values' in view
of satisfaction and arrive at conclusions and decisions on the basis the results of
the foregoing operations.
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GOALS/PLANS
According to this model the goal is to perform these macro-operations as concisely and pragmatically as possible.
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Evaluation
" … von den tausenderlei Gedanken, die sich in seiner
Seele kreuzten, mochte ungefähr folgendes der Inhalt
sein: … "
Johann Wolfgang Goethe: Wilhelm Meisters
Lehrjahre. 1. Teil, 3. Buch, 12. Kapitel (BA 10/206).
PROBLEMS
According to the model of the macro-operations on the meta-level the purpose of
evaluating the results is to assign 'values' to the results independent of the assessment of these values in view of any purposes the author and his readers may have.
Classical Dynamics reconstructed
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24 Closing operations
In view of the intricacy of the subject the values to be assigned cannot possibly
be numerical values according to some objective scale constructed in accordance
with some invariance principle or requirement (to be) agreed upon.
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MODELS
The requirement governing the reconstruction attempted has been to avoid inconsistencies, incoherence and higher and lower professional superstition in expositions of the foundations of classical mechanics felt by the author.
GOALS/PLANS
The goal and the plan are to evaluate the individual chapters of the treatise concerning their internal consistency and their methodical arrangement following the
step by step procedure adopted for the whole exercise.
24.1.1
"Jeder Mensch erfindet sich früher oder später eine
Geschichte, die er für die Mechanik* hält."
* In the reference: sein Leben.
Max Frisch: Mein Name sei Gantenbein (1964).
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24.1.1.1
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General aspects
BACKGROUND
" … operibus credite, et non verbis …
… so glaubt doch den Werken, wenn ihr mir nicht
glauben wollt, … "
Johannes 10, 38.
The present investigation is part of a very personal attempt, lasting over
sixty years now, mostly devoted to mechanics ab ovo, to understand the implications of some of our fundamental concepts and theories by way of reconstructing them from what experts do and what the author has done for
decades and not from what experts, philosophers and historians of mechanics have written and what is mostly based on what has been written before
by somebody else and so on ad infinitum.
The final treatise took twelve years, much more time than expected and is
by no means finished, by definition cannot be finished. Thus this attempt to
reconstruct the micro-universe of classical mechanics is published as an intermediate draft of research in progress.
The whole exposition shows that it is not a textbook in the usual sense
and it is not 'eine Einführung' (Bellman, 1968/51):
" … the ponderous German style so typical of the six-hundred-page 'Einführung' … "
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The treatise itself is the result of very intricate feed back processes. The
manuscript has undergone a number of dramatic changes in the organisation
of the material based on insights gained during detailed in-depth studies on
all levels. No attempt has been made to document the random walk and the
various loops of this development.
24.1.1.2 PROBLEMS
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Despite serious discomfort with presentations of the fundamentals of
Newton's Principia expressed over the centuries since their first publication,
most prominently by Hertz, the foundations of classical mechanics are still
not understood, 'shrouded in mystery' (Jammer).
The need for 'finishing' classical mechanics, envisaged already by Newton
himself and explicitly asked for by Mach, has been attempted over and over
again, but is felt to have never successfully been completed, mostly due to
inadequate avenues, lately due to the lack of incentives claimed.
Since the publication of Einstein's theory of general relativity classical
mechanics is widely 'considered' to be 'wrong in principle'. The proponents
of this incredible story usually know only the 'standard' expositions in textbooks on theoretical physics, repeating Newton's axioms exactly as Newton
stated them. And they mistake these rudimentary expositions for classical
mechanics.
They hardly know anything about the later developments of classical mechanics most prominently by Euler, Lagrange and d'Alembert among others
and as practised today. This classical mechanics is a very healthy tree with a
large number of strong branches, all being of great practical interest and importance on terrestrial scale, the world we live in, and thus all flourishing
theoretically and experimentally.
But scientists and engineers practising classical mechanics do not usually
care for the foundations of their theories and do not take notice of the truly
incredible stories perpetuated by physicists, cultivating the 'off-springs' of
classical mechanics, and by historians and philosophers of mechanics.
The story is the more incredible as classical mechanics will continue to
serve as proto-mechanics of its off-springs, as Einstein noted in 1919,
among them relativistic and quantum mechanics, string mechanics (Greene,
2004) and brane mechanics (Randall, 2006) and others to come.
But evidently classical mechanics can serve its purpose only if not considered as obsolete, but if its foundations and implications are understood
and made 'absolutely' clear. Despite this very concise and sufficient argument the need for reconstruction of the fundamentals of classical mechanics
has been demonstrated in great detail.
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24.1.1.3 MODELS
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The present exercise is based on the instinctive belief that the foundations
of classical mechanics cannot be found and reconstructed 'within' mechanics
itself, but only 'outside'. For lack of a standard reference an engineering philosophy is provided ad hoc, sufficient for the purpose at hand and consequently classical mechanics is 'understood' by embedding it into an adequate
epistemology and adequate meta- and proto-theories.
From the beginning mechanics is understood as a physical theory, not as
mathematics, not as geometry, not or as play with glass beads nor as l'art
pour l'art. Accordingly it is phrased in terms of the 'language of dynamics' as
required by Kant, Goethe and Maxwell. The fact that even the elementary
theory can be dressed in many guises is the reason for the hopeless confusion of the essentially simple issues.
24.1.1.4 GOALS
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The goal has been to unfold the basic idea, the aperçu, where already possible in the axiomatic fashion, into a coherent 'picture' (Hertz) or 'story'
(Paulos) of mechanics in every detail, trying to avoid lower and higher professional superstition. This is not possible without offending the instinctive
beliefs of experts, who believe to know what they are talking about. Fierce
emotional reactions on preliminary presentations of the ideas do not change
the situation, but confirm this statement.
For the solution of specific mechanical problems, often conveniently
phrased in terms of singular magnitudes, fancy mathematical artifacts are
necessary. Not these artifacts and not the possible foundations of single
branches, but the intellectually satisfactory foundation of mechanics in general, of the common root, elementary mechanics, and of the trunk, continuum mechanics, from which all its branches arise, is subject and purpose of
the present exercise.
Classical mechanics understood in Goethe's sense is shown to provide
among others not only insights into existing solutions but clues for the solution of fundamental problems so far unsolved, most prominently the problem of gravity and some problems in ship theory.
The exposition is considered to provide the basis of an ISO standard to be
developed in international cooperation. Such a standard should serve as a
basic reference hopefully putting an end to the wasteful production of inadequate textbooks and lecture notes. Why should not mechanicians try to
reach a goal mathematicians have already reached?
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Preliminaries
24.1.2.1 BOOTSTRAPS
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The exposition starts with 'Bootstraps' permitting to pull ourselves out of
the 'morass of ignorance' (Popper). The general world model underlying the
whole treatise distinguishes
• various levels of problems, each level requiring its own explicit
models,
• and a generic strategy for solving all the problems at hand and all the
sub-problems arising.
• Already at that stage the initial problem is discussed, which can only
be solved by brute force, postulating axiomatic models conforming
to our 'principles', our current instinctive beliefs concerning objectivity.
24.1.2.2 PROLOGUE
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In the 'Prologue' it is explained that comprehending is possible only in the
context of coherent beliefs, by embedding classical mechanics into a hierarchy of meta- and proto-theories. This requirement of the principle of coherence cannot be met by studying historical sources, but only by systematical
reconstruction as attempted.
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24.1.2.3 OPENING OPERATIONS
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But the present undertaking itself is nolens volens deeply rooted in the
cultural and historical background. So in the 'Opening operations' the problem to be solved is illustrated by extensively quoting from historical and
more recent expositions.
As an interlude and motivation for impatient readers a 'philosophical' treatise concerning the concept of force in the history of mechanics is critically
analysed in detail and in the context of the rational theory to be further developed step be step.
Only after this introductory, very detailed demonstration of the unsatisfactory state of affairs the models, the goals and the plans underlying the
treatise are being developed in detail.
24.1.2.4 RELATED BACKGROUND
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The final section of the preliminaries is devoted to the 'Related background', including historical, philosophical, theoretical, pragmatic and personal aspects. Again the reader will meet with an abundance of quotations.
It took the author nearly half the effort of twelve years of dedicated work
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• to grasp the achievements over the centuries and to integrate them
into one coherent overall 'picture', and
• to point out the many traps and pitfalls and hopefully to avoid them
himself.
The result is this treatise of more than thousand pages with sketches of
axiomatic systems, where already possible, often 'contrary to' the tribal lore
and 'falsely held' beliefs.
24.1.3
Meta- and proto-mechanics
24.1.3.1 THEORY OF THEORIES
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The ground is laid in the chapter on 'Theory of theories', covering epistemology on the most elementary level. The fundamental model adopted is
the dual model of theories, the same Newton already adhered to, explicitly
distinguishing between the abstract, 'absolute', 'true', 'mathematical' theories
and their physical instances, their 'relative', 'apparent', 'common' interpretations in terms of 'sensible', 'external' measures.
The elementary theory of axiomatic systems and the usage of axiomatic
systems are explained in detail. Axiomatic systems are considered as representation spaces permitting various interpretations and instantiations, called
models or analogues of each other. Axiomatic systems provide coherent
formal languages necessary for the rational resolution of conflicts.
Additional axioms constituting special classes of systems are called constitutive laws, not as a matter of principle but of convenience. Their phenomenological parameters, to be identified from physical or numerical experiments, are the coordinates of the systems under consideration in the representation spaces set up.
For ready reference various mathematical structures, not only linear algebra as usual, the theory of probability and its interpretations and the logical
calculi are introduced in some detail. In even more detail theories for solving linear equations and for estimating spectra under 'real world' conditions
are developed, thus providing tools necessary for the identification of systems in practice.
24.1.3.2 PROTO-MECHANICS
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In the chapter on 'Proto-mechanics: abstract' the abstract mathematical,
'absolute' (Newton) Cartesian metrics of time and space are constituted
normatively by the similarity transformations, being explicit expressions of
our postulates concerning the invariance of temporal and spatial relationships.
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In view of perspective relativity to be treated in detail complex time-space
frames and the relativistic perspectives of physical events produced by unitary transformations are developed in extenso.
The introduction of chrono- and stereo-meters, for short 'clocks' and
'frames', used for 'measuring' temporal and spatial relationships, for the interpretation of the abstract concepts in terms of physical, 'relative' clocks
and frames is delayed until 'Elementary mechanics: abstract' has been developed. Historically the rules of handling and shaping bodies are the basis
of the abstraction of the Euclidean axioms.
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24.1.3.3 META-MECHANICS: ABSTRACT
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In the chapter on 'Meta-mechanics: abstract', meta-mechanics in the wide
sense, the theory of state space models, the operational version of Plato's
parable of the prisoners in the cave, is introduced in detail.
In classical mechanics this theory is necessary to deal adequately with
kinematics of rigid bodies and with generalised dynamics, typically including memory effects, observed if aggregation is based on too few generalised
'velocities' and 'coordinates'.
In view of their importance linear models are treated at length as well as
systems identification in noisy feedback loops.
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24.1.4
Elementary mechanics
24.1.4.1 META-MECHANICS: AD HOC
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An instance of abstract meta-mechanics of particular interest is 'Metamechanics: ad hoc', the theory of quantities in the original sense of extensities, contained in bodies of matter and changed by convective and diffusive
flows into and by production inside the bodies.
In view of the central role of this model the exposition does not take the
formal route but an intuitive approach. Following the meta-axioms the metaprinciples are introduced and the meta-theorems are derived. As the first instance the balance of the quantity of meta-matter is being considered.
24.1.4.2 ELEMENTARY MECHANICS: ABSTRACT
The following fundamental chapter 'Elementary mechanics: abstract', the
theory of translational motions of rigid bodies of ponderable matter, is conveniently and efficiently introduced as an instance of the theory of extensities, meta-mechanics ad hoc.
Despite this rational approach the reconstruction and exposition of this
central chapter turned out to be the hardest part of the whole exercise, a
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painful departure from long cherished falsely held beliefs and truly 'incredible', ritually repeated textbook phrases.
The quantity under consideration is the quantity of motion, Newton's motus quantitas, the extensity or quantity of motion of a body of ponderable
matter contained in the control volume, the surface of which is conveniently
taken to be the body surface.
Accordingly forces are identified either as diffusive momentum flows
across that surface into the body of matter or as momentum productions in
the body of matter inside the boundary. This insight puts an end to the futile
discussions on the concepts of forces as far as elementary mechanics is concerned; in aggregate mechanics 'forces' will be introduced as partial powers.
Balances of momentum have to meet our instinctive beliefs concerning
objectivity, our 'principles', requiring observer independence. We require
that they can be set up in any observation space, not only in inertial spaces
as is being widely, but falsely believed.
In accordance with Newton's fourth 'definition', a fundamental observation, and d'Alembert's principle the momentum balance is separated into its
material and immaterial components. Accordingly the 'natural', the fundamental observation space is that moving with the body under investigation.
This essential consequence of abstract elementary dynamics is called the
anti-Copernican turn, the basis of Einstein's theory of 'non-relativistic', classical general relativity.
According to the material balance of momentum the material momentum
diffusion across the body surface into a rigid body, alias surface force, and
the material momentum production in the body, alias body force or weight,
balance each other. In his 'Definition' IV Newton expressis verbis states the
observation that the latter vanishes with the former.
The corresponding immaterial balance of momentum, alias 'equation of
motion' is the equation of force free motion. Additional momentum productions and corresponding 'inertial forces' in observation spaces in arbitrary
translatory motion relative to the body are immaterial, apparent.
Traditionally the material forces are called 'lost forces', 'lost' for changes
of momentum. The underlying conception is missing the essential point and
this nearly 'universal' terminology clearly indicates that the nature of the
forces has not been understood.
24.1.4.3 FREE MOTIONS
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In case of free motions no diffusive momentum flow and thus no material
momentum production takes place. The bodies move completely free of material forces, their motions are 'apparent', 'neutral' in accordance with our instinctive beliefs and with the teaching of Aristotle, Galilei, d'Alembert and
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Einstein. This is straightforward classical mechanics, re-discovered by Einstein, without referring to the classical works.
While unconstrained motions have been and are of interest in celestial
mechanics the motions of bodies on terrestrial scale are governed by momentum diffusion and by momentum production, by 'lost' forces. Despite
these facts the case of free motions is still very often falsely considered as
classical mechanics.
As a result of this misconception the 'goal' of many reconstructions of
classical mechanics has been and still is 'to expel the concept of force from
our intellectual inventory' (Jammer). But the fact is that in the rudimentary
mechanics considered, forces worth that name do not occur from the outset
and thus they do not need to be expelled.
24.1.4.4 COSMOLOGY
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Universes do not consist of single bodies but of systems of bodies of ponderable matter, of systems of masses, of mass distributions. These singularities together with their physical mass potential represent Einstein's 'Bezugsmolluske', conveniently considered to be distinct from geometrical
space.
As has been mentioned the preferred, physical observation space is that
fixed in the body under consideration. Accordingly in a 'universe' consisting
of many bodies of matter the preferred observation space is defined by vanishing total momentum, corresponding to minimum, physical, 'space invariant' kinetic energy.
This energy may be due to a 'basic bang', coming from 'outside' into the
'mechanical universe', maybe by a chemical or a nuclear 'explosion'. The
'basic bang' is not another myth; it has nothing to do with the 'big bang' of
past and current cosmologies, but linking up with non-mechanical aspects of
the universe.
Classical mechanics as a 'local' theory of the motions of bodies of ponderable matter in complex Euclidean time-space does not provide for cosmological models dealing with the genesis and the evolution of the 'whole universe'.
24.1.4.5 GENERAL RELATIVITY
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Free motions of an individual body, to be specific assumed to take place
in the universe and the preferred observation space described, are driven
solely by immaterial momentum production in the body. Instead of considering the rate of change of momentum and the production of momentum it is
convenient to talk in terms of mass specific magnitudes, the acceleration and
the intensity of momentum production.
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In classical mechanics there is only 'one' mass, the invariant of translational inertia, the singularity of the mass potential. How the 'distinction' between the obsolete concepts of 'inertial' and 'gravitational' mass came about
remains obscure.
The outcome of the very delicate experiments by Eötvös and his followers
prove that the experiments have been performed correctly in the framework
of classical mechanics. Forces and mass are implicitly defined only by the
momentum balance, Newton's lex secunda and not otherwise, e. g., not by
the law of gravitation as is falsely claimed.
The basic equation of free motions in a universe is invariant under
changes of the observation space. According to the former statement on free
motions the intensity of momentum production vanishes in the body fixed
observation space. To call the intensity of momentum production 'acceleration of gravity' is inadequate, grossly misleading terminology.
That the momentum production judged from a given freely moving body
appears to be apparent has lead to two fundamental misconceptions concerning gravitation, which have prevented to understand gravitation so far:
• firstly, the local intensity of momentum production is not apparent.
Quite to the contrary, it is real; it is due to gradients of the mass potential. Einstein himself did not believe in his axiom concerning the
non-existence of 'aether' (1928), 'merely the powerless transmitter of
effects' (Weyl);
• secondly, 'all' gravity is not apparent. Quite to the contrary, it is immaterial only in case of free motions. Material momentum production, not occurring in rudimentary cosmologies, takes place 'as soon'
as motions are constrained.
24.1.4.6 ELEMENTARY KINEMATICS
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The section on elementary kinematics is among others prerequisite for the
interpretation of abstract proto-mechanics. The most interesting theorem
concerns kinematical relativity.
Freely moving bodies, assumed to be small and not interacting, and further to be at rest relative to each other in one observation space, move in exactly the same ways in any other observation space in arbitrary translational
motion relative to the first observation space. This 'observation' is a theorem
of kinematical relativity.
It is not to be confused with the so-called 'principle of local equivalence'
of gravitational with kinematical fields and the fact that bodies of ponderable matter also fall in the same ways in gravitational fields. The principle
and the fact mentioned played prominent roles in Einstein's theory of gen-
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eral relativity and are discussed in the context of theory of material production of momentum.
In talking about classical mechanics is definitely no longer sufficient and
acceptable to refer to Newton's exposition of his definitions and axioms.
This applies in particular to expositions of the theory of general relativity
and to philosophical investigations into the foundations of mechanics, which
have to be complemented according to the state of the art.
Surprisingly neither Newton nor Einstein, and none of their followers,
fully exploited the consequences of their ideas. Both have been very close to
the solution of the problem of gravitation, though from different points of
view, the material and the immaterial component of the momentum balance
respectively.
24.1.4.7 PROTO-MECHANICS: TIME, SPACE
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The chapter on 'Proto-mechanics: time, space' deals with the operational
interpretations or semantics of the abstract, 'absolute' metrics of time and
space in terms of 'some sensible, 'relative' measures' (Newton), of measurements by clocks and frames, respectively, meeting the normative requirements as closely as possible.
The 'banal' fact that clocks, frames and messengers are subject to the laws
of mechanics, as Newton already knew and as Einstein exploited much later,
permits to explain among others the 'gravity red-shift' and thus the 'twin
paradox'.
24.1.4.8 PERSPECTIVE RELATIVITY
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As an interlude the chapter on 'Perspective relativity' deals with the 'perspective' distortions 'produced' by messengers of finite speed, for simplicity
considered to move at constant speed on straight paths, i. e. in inertial observation spaces.
The theory developed on the basis of Augustinus' discussion of births
given simultaneous provides a perfect analogue of Einstein's theory of 'special' relativity. And the spectral description of 'trains' of messengers provides a perfect analogue of trains of photons, of light rays, and shed some
light on the particle-wave 'dualism'.
In case of bodies moving faster than the messengers available, observations are made using the set-up of highway patrols. In this case instead of
Lorentz distortions pseudo-hyperbolic distortions are 'produced'.
The 'relativistic' distortions or 'perspectives' discussed are not to be confused with the appearance of objects moving close to the speed of the messengers (Ruder).
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24.1.5
Elementary physics
24.1.5.1 ELEMENTARY DYNAMICS
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The chapter on 'Elementary dynamics' deals in detail with the physics of
momentum diffusion and production, though in rather general terms. Further
the concepts of mass and inertia are discussed and interpreted in terms of
measurements, hylometry. The chapter closes with the discussion of etalons
and with dynamometry, at this stage still rather rudimentary.
24.1.5.2 ELEMENTARY PHYSICS
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The chapter on 'Elementary physics' covers the theory of inertia and
gravitation. As expected the coherent reconstruction of the fundamentals
suggests a theory of inertia and gravity. According to Newton's law of gravitation the driving causes of motions of masses of ponderable matter are gradients of the mass potential in physical space.
Newton's fourth 'definition', his fundamental observation, and d'Alembert's principle suggest an abstract model of matter: 'contained' in the bodies
are the masses, the singularities of the mass potential suspended in very stiff
spring systems.
In this model the 'constant' of gravitation is a property, a macroscopic
phenomenological parameter of 'classical', ponderable matter. In the terminology of chemical kinetics it is the rate of 'reaction' with which the mass
produces momentum in a unit gradient of the mass potential.
24.1.5.3 STANDARD MODEL
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As this model applies to any part of a body it is in accordance with the
current standard model of nucleons: 'contained' in the nucleons are quarks
suspended in gluons (Klanner). Accordingly the constant of gravitation can
'in principle' be determined from the low frequency asymptotic dynamics of
the nucleons. The latter cannot be observed in colliders aiming at and resulting in the destruction of the nucleons.
Thus physicists recruiting incredibly large armies of engineers and scientists and investing incredibly large amounts of money in their hectic hunt for
gravity 'may be barking up the wrong tree' (Greene), while the constant of
gravitation has not yet been identified with the precision desirable.
Not the mathematics of the mass potential, not the geometry of space is in
question, but the physics of the mass potential, its interaction with its singularities is 'still shrouded in mystery'. Any theory of gravity deserving that
name must be a theory of the constant of gravitation.
As has been 'known' since antiquity and mentioned by Lucretius 'atoms',
nucleons for that 'matter' are extremely stable, while their constituents, proSchmiechen 09.09.2009
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duced in colliders of ever increasing power, cannot exist separately. As has
been stressed the simple model proposed is mechanical, but it is not mechanistic!
However fancy the constitution of the nucleons and the interactions of the
mass potential and its singularities may be, on the macroscopic level they
(have to) 'behave' mechanically, to 'result' in the 'universal' constant of
gravitation, describing the momentum production in ponderable matter in
response to gradients of the potential.
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Continuum mechanics
24.1.6.1 META-MECHANICS: LOCAL
Local mechanics is embedded into the meta-theory of continua.
• As first instance of particular interest the meta-theory of motions of
ideal continua has been developed, providing among others a metatheory of Schrödinger's wave equation.
• As second instance, of more interest in the present treatise, the metatheory of material continua is developed.
• Further local mechanics is conveniently and efficiently introduced as
an instance of the meta-theory of material continua. The chapter on
local mechanics is divided into sections on 'Dynamics of continua'
and 'Kinematics of continua'.
24.1.6.2 DYNAMICS OF CONTINUA
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Introducing Cauchy's universal equation for the motions of material continua, the local momentum balance, as an instance of the meta-theory of material continua provides insights into all its logical and factual implications.
In view of the molecular structure of matter the local balances of mass
and momentum establish relationships between probabilistic magnitudes
only. Already on the level of the local meta-balance the approach is generalised to include turbulent motions providing a new insight into the nature of
the diffusive flux of momentum due to turbulence.
For materials exhibiting no mass production and no local spin, for classical materials, the equation of continuity, i. e. the local balance of mass, and
Cauchy's universal local balance of momentum provide the sufficient basis
of mechanics, its focal points, the trunk of the whole flourishing tree of mechanics, the motions of bodies of ponderable matter.
This approach is in accordance with the 'Berliner Schule', although the author, being 'ein Berliner' since fifty years, does not consider himself a member of that school, even if that could be defined.
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24.1.6.3
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LOCAL PHYSICS: MOMENTUM DIFFUSION
The section deals with the local convective and diffusive momentum
fluxes and with the local material and immaterial momentum productions.
The convective momentum flux is determined by the choice of the control
surface, and is thus a 'matter' of book keeping. Accordingly the convective
inflow of momentum vanishes, if the control surface moves with the elementary body of matter as is assumed in elementary mechanics.
The remaining net diffusive inflow of momentum, the divergence of the
diffusive flux of momentum, traditionally called 'stress', is a 'material', a
physical process due to the molecular structure of matter. The diffusive flux
of momentum is thus independent of the observation space; it is 'space invariant'.
Due to the large variety of molecules, molecular and crystalline structures
there is a large variety of diffusive flux laws, in the professional jargon
called 'constitutive laws' or, in the 'material' mode of speech (Carnap),
'Stoffgesetze'. Axiomatic theories of such flux laws provide the space invariant formats of possible, 'acceptable' laws.
The phenomenological parameters of the laws have to be identified from
physical experiments. Theoretical derivations from molecular data etc have
been possible only in the simplest cases, if at all.
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LOCAL PHYSICS: MOMENTUM PRODUCTION
'Similarly' the momentum production in bodies of matter is partly due to
the choice of the observation space and is thus a 'matter' of book keeping
again. In observation spaces moving at constant, maybe vanishing speed
relative to the body under consideration, this total immaterial momentum
production vanishes together with the momentum!
Only the momentum production balancing the net diffusive momentum
inflow in accordance with Newton's fundamental observation, his fourth
'definition', and with d'Alembert's principle remains, is a physical process,
'space invariant' as momentum diffusion. According to the model implied by
Newton's fundamental observation Newton's law of gravitation is due to the
nuclear structure of the nucleons, constituting ponderable matter, and is
driven by gradients of the potential, respectively.
24.1.6.5 FORCE FIELDS ONLY IN BODIES
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In the context of the model developed the material process of momentum
production proper takes place in 'ponderable matter' only. Conceptually it
cannot take place in the space surrounding the body although 'universally'
assumed to be 'derived' from the gravity potential 'out there'.
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Adopting Einstein's operationalist point of view it can rather be 'postulated', that there is no gravity potential and no force field in empty space. No
experiment can be invented to prove that it exists. Any 'probe' is another
body of matter, part of the reference mollusc, and experiencing internal material momentum production, if constrained.
In view of this model all efforts to get rid of the force field in empty
space, nobody has ever seriously believed in, to 'expel the concept of force
[field in 'empty' space] from our intellectual inventory' (Jammer) are fights
against wind-mills. Different from the current 'tribal lore' (Truesdell) the
present exposition suggests that it is sufficient and satisfactory to ascribe
physical reality to the masses and their 'potential' constituting physical
space.
24.1.7
'Global mechanics'
24.1.7.1 GLOBAL MECHANICS
15
The chapter on 'Global mechanics' in the narrow sense deals with the integrals of the local balances of momentum and moment of momentum, the
global balances of momentum and spin, respectively, known under various
historical names. Their practical importance derives from the fact that they
are sufficient to describe rigid body motions.
20
24.1.7.2 'GENERALISED' MECHANICS
25
30
35
The reconstruction of 'Generalised mechanics' starts from the integrals of
mass, energy and momentum providing the most obvious aggregate global
descriptions. This approach is generalised by introducing weighted integrals
in general. Weights of particular interest are partial velocities in terms of
generalised non-holonomic speeds resulting in partial energy balances, in
their explicit form called Euler-Lagrange equation, and their ramifications
and variants.
These equations are of great importance in 'theoretical' mechanics, but often only special cases of limited interest are being considered. In 'classical'
expositions typically holonomous generalised speeds and conservation of
energy are postulated, which in the 'real world' engineers have to live in and
to deal with are the exceptions rather than the rules. As a consequence not
even rigid body motions can be treated.
In the real world generalised speeds are often non-holonomic and momentum changes are driven by diffusive momentum flows, which only in
the simplest cases can be treated by adding 'some damping', 'some dissipation functions'. The present exposition provides a derivation adequate for
advanced engineering applications, while the famous variational principles
1302
are of little, if no use in treating motions of continuous bodies of matter in
technology and cosmology.
24.1.7.3 'PRINCIPLES' OF MECHANICS
5
10
So-called principles of mechanics proper are stability criteria, on the next
level the principles of objectivity and material invariance, and on still another level deeply rooted instinctive beliefs, among them most prominently
the principle of coherence.
As a by-product, the stability criterion of Kármán vortex streets is derived
using Hertz' principle of least curvature, confirming in a few lines the classical result taking endless pages of derivations hard to follow. Since fifty
years, since his first project on water jet propulsion at the Berlin Model Basin, the author has been firmly convinced that this fundamental phenomenon
must follow directly from a general principle.
24.1.8
15
20
Rigid body motions et cetera
The treatise concludes with applications, with chapters on 'Rigid body
motions', on 'Rigid bodies in ideal fluids', on 'Propulsion mechanics' and on
'Motions in ideal wave media'. All expositions open new perspectives and
avenues, sometimes offering simple pragmatic solutions for fundamental
problems unsolved so far, impossible to be solved in the traditional theoretical framework, if any.
24.1.8.1 RIGID BODY MOTION
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35
'Rigid body mechanics' is developed in extenso. The dynamical state
equation independent of the observation space, in body fixed coordinates is
obtained as an instance of the general Euler-Lagrange equation or by 'stacking' the momentum and the spin equations.
The kinematics of rigid bodies is discussed in terms of Euler angles and in
view of identifying the location of the reference point and the orientation of
the body by moving platform systems based on strap-down field meters,
alias accelerometers.
24.1.8.2 RIGID BODIES IN FLUIDS
As has been mentioned the bodies of ponderable matter considered do not
necessarily remain identically the same. An instance of special interest to
naval architects and ocean engineers are fluids around moving solid bodies.
As examples of systems of bodies rigid bodies in incompressible fluids
are treated and a special chapter is devoted to the identification of the aggregate body and fluid properties either based on free motions or forced mo-
24.1 Evaluation
5
1303
tions. The calibration of balances including deflections provides an example
for the introduction of elastic bodies.
While the tensors of the translational inertia of solid bodies are spherical
the corresponding tensors of the surrounding fluids are not. As a result velocities and momenta are no longer in the same direction as in Newtonian
elementary dynamics. The resulting phenomena are of great importance in
manoeuvring and handling of marine systems and similar aeronautical systems, e. g., airships.
24.1.8.3 THEORY OF PROPULSION
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25
The theory of propulsion has been developed ab ovo. On the meta-level
the problems to be solved are conceived as problems in rational conflict
resolution. Consequently they are consistently solved by applying the model
based axiomatic method permitting to provide rational solutions of fundamental problems of naval architecture so far unsolved.
Among these problems are the evaluation of traditional steady speed trial
and the complete analysis of hull-propeller interactions from quasi-steady
trials on model and full scale under service conditions. Based on coherent
models and data the evaluations are consistently treated as problems of parameter identification.
Further the design of ducted propellers in the behind condition has been
treated as a problem of pump design, treating all interactions implicitly, forgetting about the naïve conception of propulsors as thrusters overcoming the
resistance of the vehicles to be propelled. In advanced hull adapted propulsor design there is no chance to continue along the traditional approach followed by naval architects due to the lack of necessary a priori information.
24.1.8.4 MOTIONS IN WAVE MEDIA
30
35
Finally various motions in ideal wave media have been treated, among
them motions of slender bodies exhibiting the phenomenon of increasing inertia as the speed approaches the wave speed, the 'laws' resembling those
known from perspective relativity.
Accordingly the theory has for some time excited physicists studying the
theory of special relativity. For hydrodynamicists and naval architects shallow water waves and the related phenomena are subjects of permanent interest and concern.
The chapter concludes with few remarks on the motions of waves in moving wave media, with the 'acoustic metric' resembling the metric of curved
space of the theory of general relativity.
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10
EVALUATIONS/ASSESSMENTS
The attempt has been made to summarise the results of the treatise without going
into the details and without assessing them in view of any purposes the author or
his readers may have.
Only the results of central chapters on elementary mechanics are recollected in
some detail. An insight gained during the systematic reconstruction is that classical
mechanics provides at least perfect analogues of Einstein's theories of relativity.
Concerning some fundamental phenomena the reconstruction suggests painful
departures from the traditional expositions of classical mechanics. From the outset
the study of gravity and of Einstein's theories of relativistic mechanics has not been
the purpose of this exercise.
CONCLUSIONS
The next step will have to be the assessment of the results obtained.
24.2
Assessment
" … man braucht eine Traumwelt, um die Eigenschaften der wirklichen Welt zu erkennen, in der wir zu leben
glauben … "
Paul Feyerabend: Wider den Methodenzwang
(1983/36 f).
15
20
25
PROBLEMS
According to the model adopted assessing the results is possible only in view of
purposes. The present treatise is not concerned with many different purposes but
with only one, the reconstruction of the fundamentals of classical mechanics.
The values to be assessed being not numerical the criteria of assessment can
only be non-numerical as well.
MODELS
In accordance with current practice the criterion is satisfaction. Depending on
subjective purpose and subjective satisfaction this appears not to be an objective
criterion.
30
GOALS/PLANS
The goal is to show how objectivity of assessment can be reached in terms of coherence as before and thus provide input for the final closing operations, drawing
conclusions and deriving future tasks.
24.2.1
35
Criteria
Criteria of satisfaction applied in assessing the local models developed
have been their internal consistency and, more important, their derivation as
instances of meta-theories. These are in fact not subjective criteria, but forSchmiechen 09.09.2009
24.2 Assessment
5
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15
mal criteria to be applied as soon as the models and meta-models have
reached a certain stage of maturity.
Not only consistent local models but also a whole coherent fabric of such
models, all of them embedded into meta-models has been developed. The
logic in developing this fabric has not yet been formalised.
Thus the present exposition may in places be found to be inconsistent, not
immune and not invariant. In an attempt to avoid the dangers of the informal
procedure, of fundamental errors, of circular arguments et cetera, the author
has been proceeding step by step as Hertz did (1956/35).
Following Hertz' argument no attempt has been made to construct ortholanguages and proceed in a perfectly formal fashion, which eventually will
be required on each level of discussion. Formalisation has to be a matter of
subsequent doctoral theses and standardisations.
If steps are exchanged the purpose of the exercise may not be reached.
The step by step procedure is closely related to the principle of methodical
order applied by Janich in his reconstruction of protophysics (1997/19 and
/319). During work on the draft the order of chapters and sections has been
changed many times in order to meet the requirements of methodical order.
24.2.2
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35
1305
Satisfaction
The author feels that he has reached his goal, to reconstruct and understand classical mechanics in Goethe's and Einstein's spirits, and at the same
time to provide a clear and detailed model of classical mechanics, the theory
of motions of bodies of ponderable matter in Euclidean time and space.
More than that the author has provided a coherent fabric of instinctive beliefs 'as much isolated and as free from irrelevant additions as possible' in
accordance with RussellB 's demand. The motivation for his undertaking has
been concisely characterised by the Jammer in his statement on the current
situation (1999.f/VII):
"In our present age of rapid technological progress the frightening discrepancy between our technical 'know-how' and our philosophical incomprehension, in general, of basic scientific conceptions seriously endangers
the integrity of our intellectual outlook."
With many colleagues the author feels that in the 21st century we can no
longer afford to walk around in the world we have to live in like children
with a 'solid body' of incoherent instinctive beliefs. The present treatise
opens many new avenues for research and teaching. Based on the results obtained so far the main tasks identified and to be undertaken concern the formal and the factual aspects.
1306
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10
As the author has shown in a large number of projects and papers the approach followed in the treatise and the solutions arrived at or at least proposed are promising dramatic conceptual, theoretical, technological and
commercial advantages.
Readers will have to decide for themselves whether they find the whole
fabric of instinctive beliefs intelligible and acceptable and will eventually
evaluate and assess the results up to now according to their own principles,
purposes and needs.
'Do you have references?' and 'Who has done this before?' are typical
questions deeply rooted in attitudes not particularly creative and innovative.
The only sensible approach at this stage is: 'I want to be the first to understand the simple models and to take advantage!'
15
The author feels that the results of his exercise satisfy his own intellectual requirements concerning consistency and simplicity. And after forty years of successful experience he knows for sure that the approach described is very powerful and
fertile.
20
CONCLUSIONS
The critical reader will notice the very cautious vocabulary: the author feels, his
exercise, his own requirements. And at the same time they will have noticed that
the results are in accordance with the present state of discussion in philosophy and
physics.
24.3
25
30
Conclusions
" 'I can't tell you just now what the moral of that is, but
I shall remember it in a bit.'
'Perhaps it hasn't one,' Alice ventured to remark.
'Tut, tut, child!' said the Duchess. 'Everything's got a
moral, if only you can find it.' "
Lewis Carroll: Alice's Adventures in Wonderland
(1988/88).
PROBLEMS
The problem is to draw conclusions concerning the achievements so far and the
future tasks.
35
MODELS
According to the model of the closing operations the remaining task is to take
decisions and define future tasks based on the assessment.
24.3 Conclusions
1307
GOALS/PLANS
The goal is to summarise the results and the future tasks as short as possible so
that they can be easily seen and followed. The open ends identified are both, of
formal and factual nature.
5
24.3.1
"Es ist eine große Stärkung beim Studieren, wenigstens für mich, alles was man liest so deutlich zu fassen,
daß man eigne Anwendungen davon, oder gar Zusätze
dazu machen kann. Man wird am Ende dann geneigt zu
glauben man habe alles selbst erfinden können, und so
was macht Mut. So wie nichts mehr abschreckt als das
Gefühl der Superiorität im Buch."
Georg Christoph Lichtenberg: Sudelbücher, J
(1789-93) 1322 (1984/450).
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Decisions
Based on the assessment of the results so far and in view of his age the
author has decided:
• to publish the manuscript as draft of work in progress, for the convenience of students with line numbers and ample margins; this is
felt to be the only way to obtain the feedback and peer reviews
asked for, not only by publishers;
• to continue updating the manuscript following his own ideas and in
response to critical and constructive input hopefully received from
readers; and
• to start work on the future tasks outlined in the next section.
24.3.2
Future tasks
"Überall angezeigt was noch zu leisten ist."
Georg Christoph Lichtenberg: Sudelbücher, F
(1776-80) 1115 (1984/312).
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35
The future tasks are related to formal and factual aspects of classical mechanics as reconstructed in the present treatise.
Concerning the formal aspects the main tasks to be tackled in sequence
are:
• to draft a concise text book reduced to the essential results and
• to formalise this condensed exposition as far as possible with the
goal to confirm and, where necessary, to correct the methodical reconstruction;
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25
• to draft an ISO standard along the lines of that exposition with the
goal to provide a reliable reference, that can be quoted without offending anybody's instinctive beliefs;
• and, last but not least,
• to draft corresponding high school and university courses on the
subject much along the line of lectures already delivered in cooperation with pertinent institutes, and
• to draft a popular exposition of the results.
Concerning the factual aspects the main tasks are:
• to understand the physics of the mass 'potential' constituting physical
space, and
• to study its interaction with its singularities contained in the nucleons, to derive the constant of gravitation from the low frequency asymptotic properties of the nucleons as far as possible, at least qualitatively.
The conceptual expositions and the technical elaborations of the details provide
insights confirming RussellB s' observation that 'among our instinctive beliefs many
have, by habit and association, become entangled with other beliefs, not really instinctive, but falsely supposed to be part of what is believed instinctively'.
CONCLUSIONS
Most of the models presented can be used as standard models and it is strongly
suggested that they should be standardised as mathematicians have standardised
their models. This suggestion is supported by the fact that sound standards contribute more to innovation than new inventions.
CLOSURE OF CHAPTER
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35
The closing operations have been performed in the same spirit and format of the
whole treatise, trying to adhere to clear cut instinctive beliefs and simple intelligible rules.
CONCLUSIONS
The claim that the goal has been reached is a personal claim. Of course the author is wondering if his results up to now are convincing colleagues and students to
adopt the pragmatic view point proposed.
25
"Thus, Gentle Reader, I have given thee a faithful History of my Travels for Sixteen Years, and above Seven
Months, wherein I have not been so studious of Ornament as Truth. I could perhaps like others have astonished thee with strange improbable Tales; but I rather
chose to relate plain Matter of Fact in the simplest Manner and Style; because my principal Design was to inform, and not to amuse thee."
Jonathan Swift: Gulliver's Travels. Part IV. A
Voyage to the Country of the Houyhnhnms
(2003/266).
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15
Epilogue
PROBLEMS/MODELS
In accordance with the model set forth in the prologue the epilogue provides a
meta-level to talk about the treatise after it has been finished as far as possible.
GOALS/PLANS
Consequently the goal of this epilogue is to wind up the treatise or, in terms of
an operational jargon, to evaluate the result of the exercise and draw useful conclusions, if any, on the (second) meta-level.
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30
35
25.1
Sound knowledge
"Es ist nicht das Wissen allein, was uns glücklich
macht − es ist die Qualität des Wissens − die subjektive
Beschaffenheit des Wissens. Vollkommenes Wissen ist
Überzeugung und sie ist's, die uns glücklich macht."
Novalis: Fragmente und Studien, 1800
(1981/565).
"Glück ist im Gehirn vielleicht ein kohärenter Zustand.
Ich erlebe es in der Forschung, wenn ich* weiss: jetzt
passt's." * In the reference: man.
Wolf SingerW: 'Sie sind doch Ihr Gehirn – wer
sonst?' (Epping, 2009/79).
Whatever problem the author touched in his micro-universe of discourse
he found many of the present solutions and expositions unsatisfactory, offending his instinctive beliefs, to be simply incredible, just unbelievable.
He does not share Truesdell's belief that (1984/292):
1309
1310
25 Epilogue
"By definition, now, there is no learning, because truth is dismissed as an
old-fashioned superstition."
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25
30
Instead he has shown by way of an explicit development that most of the
problems, even those Truesdell believed to have solved, can be adequately
solved step by step by embedding them into appropriate contexts and metatheories, definitely not just mathematics. This procedure provided at the
same time for the necessary economy d'Alembert and Mach among others
have been calling for.
Thus it has been possible to describe within the limits of this treatise the
whole tree of classical mechanics, its roots, elementary mechanics, its trunk,
continuum mechanics, and some of its branches, aggregate mechanics in
particular, as Hertz required:
" ... that we not only admit, as every one does, the permissibility of the
content of mechanics. But the dignity and the importance of the subject
demand, not simply that we should readily take for granted its logical
clearness, but that we should endeavour to show it by a representation so
perfect that there should be no longer any possibility for doubting it." Italics: MS.
In trying to reach these goals and to escape from the monstrous presentations of classical mechanics, the author followed Daedalus' engineering advice. Although the vehicle he has used is at least as fragile as that of Icarus
he feels that he has reached safe grounds.
The purpose of the exercise was the same as that stated by Clausewitz in
'Vom Kriege' (1991/1033; quotation following Oetinger, 2005/198):
"Das Notwendige und Allgemeine wollten wir herausheben, dem Individuellen und Zufälligen seinen Spielraum lassen, aber das Willkürliche, Unbegründete, das Spielende oder Phantastische oder Sophistische wollten
wir entfernen. Haben wir diesen Zweck erreicht, so sehen wir unsere Aufgabe als gelöst an."
But Janich rightly asks (1995/34):
"How can we have evidence of a success without presupposing the success?"
35
40
This problem can be avoided, if the paradigm to think in terms of purposes, as in constituting time, space and mass measurements and other instances in this treatise, is generalised. The overall model produced serves
the purpose of the producer, knowing that it may contain flaws until it is finally fully formalised along the lines indicated.
The readers have to judge whether they themselves find the hierarchy of
beliefs drafted 'as much isolated and as free from irrelevant additions as
possible' and 'thus, if they are found to harmonise, the whole system, becomes worthy of acceptance'. The coherent model, tries to bridge the gaps
between the various tribes of mechanicians still separate for various reasons.
25.1 Sound knowledge
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35
40
1311
Embedded into sound meta-mechanics and proto-mechanics it embraces
not only elementary Newtonian mechanics but classical mechanics of any
brand, 'analytical' and 'variational', down to the explicit Euler-Lagrange
equation and to Hamilton's less useful principle, respectively, even Hertz'
speculations on gravity.
The exercise presented is clearly indebted to the giants of classical mechanics and philosophy, on the shoulders on which we stand. But it shows at
the same time how necessary it is to adhere to Goethe's dictum (Faust I;
BA 08/170):
"Was du ererbt von deinen Vätern hast,
Erwirb es, um es zu besitzen.
Was man nicht nützt, ist eine schwere Last;
Nur was der Augenblick erschafft, das kann er nützen."
Only the first half of this quotation is the motto of Lanczos exposition of his
'Variational Principles' (1986/V), which have been shown to be direct offsprings of Newton's and Euler's mechanics, if we talk in terms of velocities
instead of displacements or locations.
And the only way to reach that goal has been pointed out by von Mises:
'less loose talk, ... and more positivism'. In particular we must reject lower
and higher professional superstition and epistemic relativism and 'fashionable nonsense' and demand explicit, intelligible models on each level of discussion and elaboration, the more so the more intricate the situations become, in which we have to decide and to act.
In his Postscript Feyerabend states (1991/164):
"I agree that a dialogue reveals more than an essay. It can provide arguments. It can show the effect of arguments on outsiders or on experts from
a different school, it makes explicit the loose ends which an essay or a book
tries to conceal and, most importantly, it can demonstrate the chimeral nature of what we believe to be the most solid part of our lives. The disadvantage is that all this is done on paper, not in actions, performed by life people, before our eyes. We are again invited to engage in some antiseptic kind
of activity or, to use different words, we are again invited merely to think."
The danger Feyerabend refers to has been stated expressis verbis at the
beginning in terms of a quotation from Tsar's introduction (1909/III). And,
following RussellB (1981/7): 'after realizing all the vagueness and confusion
that underlie our ordinary ideas'.
And 'the loose ends which an essay or a book tries to conceal' and 'most
importantly, to demonstrate the chimeral nature of what we believe to be the
most solid part of our lives' our 'instinctive beliefs', have been the main topic
of this treatise devoted to the 'obscure beginnings' (Weyl, 1959/10).
By a 'life person' it has been shown that it is not only 'possible to examine
ideas or systems of ideas in a loose way', but to do that in a coherent fashion
1312
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25
30
35
without denying 'the chimeral nature of what we believe to be the most solid
part', that all is based only on our 'instinctive beliefs'. Particularly in view of
the deepest problems we must not 'merely' think, but 'think deeper and
deeper' as the Chinese say. Or as the Berlin sewage workers say: 'The higher
the purpose, the deeper we dig', trying to cover up the mess they make.
The work here has been undertaken in the spirit of Wittgenstein, ending
the Prologue of his Tractatus with the remarks (1995/9-10):
"Wenn diese Arbeit einen Wert hat dann besteht er in zweierlei. Erstens
darin, daß in ihr Gedanken ausgedrückt sind, und dieser Wert wird um so
größer sein, je besser die Gedanken ausgedrückt sind. Je mehr der Nagel
auf den Kopf getroffen ist. − Hier bin ich mir bewußt, weit hinter dem
Möglichen zurückgeblieben zu sein. Einfach darum weil meine Kraft zur
Bewältigung der Aufgabe zu gering ist. − Mögen andere kommen und es
besser machen.
Dagegen scheint mir die Wahrheit der hier mitgeteilten Gedanken unantastbar und definitiv. Ich bin also der Meinung, das Problem im Wesentlichen endgültig gelöst zu haben. Und wenn ich mich hierin nicht irre, so besteht nun der Wert dieser Arbeit zweitens darin, daß sie zeigt, wie wenig
damit getan ist, daß diese Probleme gelöst sind."
The work has been done in the spirit of Enlightenment, not 'Erleuchtung'
coming from 'above', but 'Aufklärung', in the spirit of rationalism, scepticism and empiricism, in the spirit, not the dogmata of the Vienna Circle and
of Karl Popper, trying to overcome traditional ignorance, prejudice and superstition.
Wittgenstein's last point refers to the limits of rationalism described by
Jaspers (1999/69):
"Wahre Aufklärung dagegen zeigt zwar dem Denken und dem Fragenkönnen nicht absichtlich, von außen und durch Zwang, eine Grenze, wird
sich aber der faktischen Grenze bewußt. Denn sie klärt nicht nur das bis
dahin Unbefragte, die Vorurteile und vermeintlichen Selbstverständlichkeiten, sondern auch sich selber auf. Sie verwechselt nicht die Wege des Verstandes mit den Gehalten des Menschseins. Diese zeigen sich der Aufklärung zwar erhellbar durch einen vernünftig geführten Verstand, sind aber
nicht auf den Verstand zu gründen."
That ideas are generated not only in the 'antiseptic' environments of treatises, but also, or maybe preferably, in loose dinner talk and in the exchange
of post-modern nonsense is a different story, on yet another level.
25.2
40
25 Epilogue
Live ideas
"Die Philosophen haben die Welt nur verschieden interpretiert; es kömmt aber darauf an, sie zu verändern."
Karl Marx: 11. These über Feuerbach (1956/42).
25.2 Live ideas
1313
"Bislang glaubten die Philosophen, die Welt nur zu interpretieren, aber sie haben die Welt verändert."
Karl Marx paraphrased by Gianni Vattino
(Adrian, 2000).
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10
15
20
"Statt des törichten Ignorabismus heiße im Gegenteil
unsere Lösung: Wir müssen wissen, wir werden wissen."
David Hilbert, 1930; inscription on his tombstone, 1943.
Goethe did not believe that he could convince anybody, when explaining
the displacement of granite blocks by glaciers. That 'Establishment Stifles
Genius' has led Truesdell to a 'Praise of Disorganisation of Science'
(1984/397-402).
And Feyerabend starts the Postscript of his 'Three Dialogues on Knowledge' (1991/163):
"Rumour has it that while it is possible to examine ideas or systems of
ideas in a loose way, in letters, telephone calls, dinner conversations, the
proper form for explaining their shape, their implications and the reasons
for their acceptance is an essay or a book. The essay (the book) has a beginning, a middle and an end. There is an exposition, a development and a
result. After that the idea (the system) is as clear and as well-defined as a
dead butterfly in a collector's box."
In view of these pessimistic statements it is appropriate to look back and
remember the starting point of this short story of a long development, the
quotation from RussellB 's introduction to 'The Problems of Philosophy':
25
"All knowledge, we find, must be built up upon our instinctive beliefs,
and if these are rejected, nothing is left. But among our instinctive beliefs
some are much stronger than others, while many have, by habit and association, become entangled with other beliefs, not really instinctive, but
falsely supposed to be part of what is believed instinctively."
30
The treatise has demonstrated by way of example that 'engineering' philosophy can 'show us the hierarchy of our instinctive beliefs, beginning with
those which we hold most strongly, and presenting each as much isolated
and as free from irrelevant additions as possible.'
The exposition is purposely simple. A theory will only be grasped and accepted if its purpose, its necessity, its implications and its advantages are
communicated so clare et distincte, that nobody can escape it. The reasoning must be so simple that it can be repeated by heart in any particular situation. The rules to be followed should preferably be phrased as precise and
simple as the ten commandments in a language, which does not offend anybody's instinctive beliefs.
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40
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25 Epilogue
This is not a matter of pseudo-scientific formalism and abstruse philosophy. For daily applications and decision making axiomatic theories and their
operational interpretations must be plausible, although logicians and
mathematicians do not get tired to stress that in their platonic worlds plausibility is not necessary. Care has been taken 'to show that, in the form in
which they are finally set forth, our instinctive beliefs do not clash, but form
a harmonious system'.
Goethe in his old age felt (18.01.1825: Eckermann, 1911/104):
" … daß der Mensch trotz aller Dummheiten und Verwirrungen, von einer höheren Hand geleitet, doch zum glücklichen Ziel gelange."
And Paul Feyerabend at the end of his Postscript provides last but not least
an optimistic outlook:
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25
30
35
"But ideas, like butterflies, do not merely exist; they develop, they enter
into relations with other ideas and they have effects. ... The end of an essay,
or a book, though formulated as if it were an end, is therefore not really an
end, but a transition point which has received undue weight."
The ideas presented have been developed over fifty years. They are the result of
hard work and hard thinking about that work. Over the years many have been presented in opposition to the professional mainstream. Thus they never made good
friends, nor good dinner talk.
For 'educated' people it is fashionable to talk about the curved space-time of the
universe and the particle-zoo confined in the nucleons. 'Nobody' cares to understand the old-fashioned classical world, in which we live. It is 'wrong' anyway, they
are told to believe by people who have neither understood Newton's fundamental
work nor Einstein's references to classical mechanics. This is the most incredible
instinctive belief three hundred years later than the Principia and hundred years
later than Einstein's theories!
CONCLUSIONS
This is the end of the treatise and of the epilogue, but not the end of the ideas
presented. They are, far from being 'dead as the butterflies in the collector's box',
at home on another level of instinctive beliefs, in Plato's heaven of ideas. They are
abstract structures describing observed behaviour of reality, developed by homo
sapiens, prisoner in Plato's cave.
26
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Post scriptum
" 'So I was not dreaming, after all,' she said to herself,
unless we're all part of the same dream. Only I do hope
it's my dream, and not the Red King's! I don't like belonging to another person's dream,' she went on in a
rather complaining tone: 'I've great mind to go and wake
him, and see what happens!' "
Lewis Carroll: Through the Looking-Glass, VIII:
'It's My Own Invention' (1988/214).
In winding up the history of 'Gulliver's Travels' Jonathan Swift noted in
'A Voyage to the Country of the Houyhnhnms' (2003/267-270):
" … it is highly probable, that such Travellers who shall hereafter visit
the Countries described in this Work of mine, may by detecting my Errors
(if there be any) and adding many new Discoveries of their own, justle me
out of Vogue, and stand in my Place, making the World forget that I was
ever an Author. This indeed would be too great a Mortification if I wrote
for Fame: But, as my sole Intention was the Public Good, I cannot be altogether disappointed.
…
So that I hope I may with Justice pronounce myself an Author perfectly
blameless, against whom the Tribes of Answerers, Considerers, Observers,
Reflectors, Detectors, Remarkers, will never be able to find Matter for exercising their Talents.
…
Having thus answered the only objection that can ever be raised against
me as a Traveller, I here take a final Leave of all my Courteous Readers,
and return to enjoy my own Speculations …, to apply those excellent Lessons of Virtue which I learned …, ... "
1315
1316
26 Post scriptum
27
Acknowledgements
"Ich habe mich bisher bei der Methode mit Mehreren
zu arbeiten zu wohl befunden, als daß ich nicht solche
fortsetzen sollte. Ich weiß genau, wem ich dieses und jenes auf meinem Wege schuldig geworden, und es soll mir
eine Freude sein, es künftig öffentlich bekanntzumachen."
Johann Wolfgang Goethe (1960/13; GA 16/847).
"A man alone ain't got no bloody … chance."
Ernest Hemingway: To Have and Have Not.
Quotation following Denham Sutcliffe's in his after word to Herman Melville's 'Moby Dick'
(1961/541).
The present work would not have been possible without the encouragement, support and input of many people. In the 'Dedication' and the 'Personal background' the author has acknowledged the various influences of
many persons. The abundant quotations and the following, corresponding
list of references are also to be taken as acknowledgements of very diverse
influences.
Further, the author gratefully acknowledges valuable, in-depth discussions and disputes with students and colleagues during and after his presentations of lectures and of papers on various aspects of classical dynamics.
Many of them have received long explanatory mails, mostly helping the
author to clarify his ideas developed in a continuous inner dialogue, more or
less unconsciously following rules, the 'pragmatics for one person', doubtlessly more intricate than those recently proposed by Marcus Kracht (2008).
Among the many correspondents the author is particularly indebted to:
• Dipl.-Phys. Christoph Appel, debis Systemhaus (classical mechanics, gravitation),
• Prof. Dr. Lorrain Daston, Max-Planck-Institute für Wissenschaftsgeschichte Berlin (Newton's Principia, translations),
• Prof. Dr. Friedrich Herrmann, Universität Karlsruhe (elementary
mechanics, didactics of mechanics, Karlsruher Physik-Kurs),
• Dr.-Ing. Karsten Hochkirch, Dr.-Ing. Stefan Harries and Dr.-Ing.
Justus Heimann, Friendship Systems, Babelsberg (state space models, parameter identification, estimation of spectra),
1317
1318
27 Acknowledgements
• Prof. Dr. Ricardo Lopes Coelho, Universidade de Lisboa, formerly
Technische Universität Berlin (Hertz' 'Prinzipien der Mechanik',
concepts of force),
• Prof. em. Dr.-Ing. Dr. h. c. Horst Nowacki, formerly Technische
Universität Berlin (epistemology, theory of ships),
• Tim Nowacki, formerly Technische Universität Berlin (Plato's parable of the prisoners in the cave),
• Dr. Markus Pössel, Max-Planck-Institut für Gravitationsforschung
Potsdam (classical mechanics, gravitation),
• Dr. Oliver Passon, Zentral-Institut für Angewandte Mathematik Jülich (Bohmian mechanics),
• Dr. Volkmar Schüller, Max-Planck-Institut für Wissenschaftsgeschichte Berlin (Newton's Principia, translations),
• Prof. em. Dr.-Ing Heinrich Söding, formerly University Hamburg
(model of matter, gravitation),
• Dr. Dr. Dieter Suisky, Humboldt-Universität zu Berlin (theory of
special relativity, theory of continua),
• Dipl.-Phys. Keno Will, Stuttgart (didactics of mechanics, Karlsruher
Physik-Kurs),
• Dr.-Ing. habil. Klaus WagnerK, formerly VE Kombinat Schiffbau,
VEB Dieselmotorenwerk Rostock (applied 'dialectic' philosophy,
ship propulsion),
• Dr.-Ing. Boris Wyssusek, formerly Technische Universität Berlin
(epistemology, science management).
Other colleagues have figured as 'virtual' correspondents:
• Dr. Hans Sohst, formerly Teldix, Germany,
• Prof. em. Dr. Erich Wolf, formerly Technische Universität Berlin.
And last but not least the author wants to thank his son
• Dr. Carl Philipp SchmiechenCP for taking on the tasks of lector and
corrector during the 'final' stages of the first edition of work in progress, and for continuing discussions, which have been instrumental
in clarifying fundamental issues and improving their expositions.
During and following the work of the lector and corrector the author has
undertaken major re-arrangements and revisions of the manuscript. Accordingly a new cycle of discussions and corrections will be required in an asymptotic process, which at least for this second edition has been bluntly disrupted at a stage felt sufficient for starting a public discussion.
27 Acknowledgements
1319
For the remaining misconceptions, errors, mistakes and misprints solely
the ignorant author himself is to be blamed. He did not consciously and not
purposely build in nonsense and/or misprints as is sometimes done for various reasons, among them plagiarism.
He will gratefully consider and acknowledge any comments of his readers
pointing out necessary clarifications, corrections and additions. But he
kindly asks them to refrain from wasting their and his precious time by trying to teach him what he just had explained to them.
1320
27 Acknowledgements
28
Conventions
28.1
"Es war ihm unmöglich die Wörter nicht in dem Besitz
ihrer Bedeutungen zu stören."
Georg Christoph Lichtenberg: Sudelbücher, C
(1772-1773) 156 (1984/109).
5
28.1.1
10
Terminology
Rational names
"Other critics have objected to certain innovations in
[naming and] spelling, … In reply, I can only plead my
firm conviction that the popular usage is wrong."
Lewis Carroll; Sylvie and Bruno Concluded,
Preface (1982/461). [Addition]: MS.
The reason for the need of changes in names and symbols has been given
by Goethe (1947/301):
15
"An initial terminology suits a restricted, isolated phenomenon; is also
applied to yet others. Ultimately something no longer at all suitable still
continues in use." Translation by Sepper (1988/147).
In the original the complete text reads (GA17/739):
20
25
"Wenn wir ein Phänomen vorzeigen, so sieht der andre wohl, was wir
sehen; wenn wir ein Phänomen aussprechen, beschreiben, besprechen, so
übersetzen wir es schon in unsere Menschensprache. Was hier schon für
Schwierigkeiten sind, was für Mängel uns bedrohen, ist offenbar.
Echte Terminologie paßt auf ein beschränktes isoliertes Phänomen; wird
auch angewendet auf ein weiteres. Zuletzt wird das nicht mehr Passende
doch noch fortgebraucht."
Lichtenberg has further elaborated on terminology (1984/460):
30
"Nomenclatur. Auch hier ist die eingeschränkte Monarchie der Aristokratie vorzuziehen. Wenn man nur vernünfftig gewählte Ausdrücke gelten
machen will, so giebts eine Aristokratie, und dann welche sind dann die
vernüfftigsten und wer soll darüber entscheiden? Es können ja viele gleich
gut und vernünfftig gewählt sein ...
Am Umschaffen eingeführter Nahmen hat immer mehr Eitelkeit als
Nützlichkeit Antheil, denn gewöhnlich werden sie alsdann erst nützlich
wenn man sie so nimmt wie die alten, nemlich nicht mehr denckt, was die
1321
1322
28 Conventions
Dinge ihrem Wesen nach sind, die sie bezeichnen, sondern blos an die Dinge." Italics: MS.
5
10
15
20
25
30
35
40
Following Lichtenberg's advice no attempt has been made to change the
traditional names of concepts, even if they are grossly misleading. Remember d'Alembert's 'excuse'! But it has been stated over and over again 'was die
Dinge ihrem Wesen nach sind', as derived from the coherent context developed.
For sound decisions in science and in practice it has to be known 'was die
Dinge ihrem Wesen nach sind'. A large part of the present story is concerned
with the historical fact that this has at best been forgotten, more often, never
been known, resulting in the misleading traditional jargon.
Using the same terms generically for (very) different entities is common
practice not only in human communication. Context sensitivity is also to be
found in object oriented programming languages. The logical subtleties of
this practice have been beautifully discussed in a little paper by Kracht under the catching title 'Wer dies (nicht) liest, ist doof.' An example in the present treatise is the term 'model'. The reason in this case is the 'fact' that any
entity may be considered as a model of something else (Mahr, 2008).
In the treatise models are primarily considered as abstract, axiomatic systems describing the behaviour of micro-universes of discourse. Such models
may be based on, i. e., abstracted from (simplified) theoretical models of the
universes under discussion. And (other) instances of the abstract model are
sometimes also called models of the abstract theory and of each other. The
author has attempted to avoid confusion by adequate qualifications where
(he) felt necessary.
The forming and naming concepts are basic operations of children and of
mankind and have thus been subject of philosophical investigations since
antiquity (Martens, 2007/97-110). The standard example in many treatises is
'the table'. The present exposition is closely related to Wittgenstein's
'Sprachspiele' (1995/225-485).
In that sense the term 'complex' has only been used for complex-valued
mathematical magnitudes, while the colloquial uses of 'complex' and 'complexity' have finally and uniformly been changed to 'intricate' and 'intricacy',
respectively.
The clumsy terms 'real-valued', 'imaginary-valued' and 'complex-valued'
have been avoided in favour of the shorter terms 'real', 'imaginary' and
'complex'. The resulting ambiguity in the usage of the term 'real', not occurring in German, − 'reell' and 'real' being clearly distinct − , remains unresolved. As in many other cases readers are expected to guess the intended
meaning from the context.
28.1 Terminology
28.1.2
1323
Traditional names
" 'Ein, ja zwei Mal', gab Sancho zurück, 'wenn ich
mich recht erinnere, habe ich Euch schon gebeten, nicht
an meinen Worten zu flicken, solang Ihr nur begreift, was
ich meine. … ' "
Miguel de Cervantes Saavedra: Don Quijote
(2008/II, 64).
5
28.1.2.1 GENERAL TERMS
10
In the following table traditional and rational names of the more general
concepts are being listed together with symbols, if any.
Names: traditional, rational
Name: traditional, jargon
Symbol, if any Name: rational, explanation
'absolute'
abstract
abstract model, theory
axiomatic system
'accelerometers'
force field meters
aspect
A
extensity
A
ext
=Q
I=A
int
capacity
C=A
cap
motion
A = mot
intensity
momentum
Q = mot
speed, velocity
inertia
ext
quantity in the original sense, Menge
quality
motus
= M extensity of motion, Bewegungsmenge,
alias Bewegungs-'grösse'
mot int = V i
intensity of motion
cap
capacity of motion
mot
= Iij
Cauchy's equation
local momentum balance
densities of magnitudes
volume specific magnitudes
q
intensities of magnitudes
mass specific magnitudes
dynamics
theory of forces
'dynamics'
momentum balance in bodies of matter
in motion
equation of continuity
local balance of mass
equation of motion
momentum balance
field
'ubiquitous weasel' for essentially different 'distributions' in bodies of matter
first theorem
Newton's lex prima generalised
flux
body force
area specific flow
M
P
i
=F
body
i
momentum production
1324
28 Conventions
lost body force
M N i = M P mat i
momentum production, material, nuclear
inertial force
M K i = M P app i
momentum production, apparent, kinematical
surface force
M M i = F surf i
force field
fi
momentum diffusion, molecular
local intensity of momentum
production in bodies of matter
global balances
integrals of local balances
'image'
model
Kane's equations
partial energy balances
kinematics
kinematical theory of motions
kinetics
theory of motions due to forces
local balances
mass specific balances
mass
I k k/3 = m
mass field
ρ
invariant of translational inertia
local mass density in bodies of matter
intensities
mass specific magnitudes
mechanics
kinetics
'principle of equivalence'
Newton's lex secunda mis-interpreted
'principle of inertia'
Newton's lex prima mis-interpreted
'principles' of mechanics
weighted integrals of local momentum
balance
'relative'
interpreted
second axiom
Newton's lex secunda generalised
statics
momentum balance in bodies of matter
at rest
stress field
surface force
σij
local area specific diffusive momentum
flow in bodies of matter
M M i = F surf i
net diffusive momentum flow through
surface of bodies of matter
third axiom
velocity field
Newton's third law limited to diffusive
momentum flows
vi
local mass specific momentum in bodies of matter
28.1.2.2 AMBIGUOUS TERMS
5
In order to avoid any misconception the term 'driving force', found in
various contexts, has been replaced uniformly by the term 'driving cause',
always without inverted commata.
The term 'potential' occurring in that connection is ambiguous, as a noun
as well as an adjective. As noun it refers on the one hand to the 'potentiality',
28.2 Symbology
5
10
15
20
the 'possibility', and on the other hand to physical entities described in
mathematical terms. As adjective it refers on the one hand to 'possible', 'latent, in German 'potentiell', and on the other hand to magnitudes derived,
typically in the mathematical sense, from mathematical potentials describing
physical entities.
The terms 'principle' and 'law' are ubiquitous weasels and it is not always
possible to avoid the traditional, often misleading terminology found in historical and recent standard textbooks. As a young man the author has indeed
been grossly mislead by the unqualified jargon, and certainly not only the
author. In the following section on 'Symbology' adequate notations are proposed.
The term 'non-relativistic' used to qualify Schrödinger's equation of quantum mechanics is not particularly adequate in talking about 'classical' general relativity. Accordingly it has been uniformly replaced by 'classical'. A
problem arises with the term 'relativistic' itself.
In case of the classical 'special relativity', being physically different from
Einstein's theory, the term 'perspective relativity' has been introduced as
most appropriate. The author is aware that more work has to be done on the
related terminology and to be agreed upon.
28.2
28.2.1
25
30
35
1325
Symbology
Operational notations
The rational terminology is complemented by a corresponding rational
notation. Not only in view of computer aided knowledge engineering this
notation has to be 'operational'.
In the present treatise operational notation has not only been used for
(elements of) matrices but mathematical operations, qualifiers and identifiers as well, as has been explained and utilised in the 'ITTC List of Symbols
and Terminology' (Schmiechen, 1993/7 ff). In case of first names of authors
this notation permitted to produce the name index 'automatically'.
Vectors and tensors, in terms of their components referred to Cartesian
coordinates, are denoted by operational indices i , j , k . The same notation is
used for generalised and aggregate concepts using the indices u, v, w. Operators and qualifiers are denoted by superscripts, operational 'exponents'.
Sequences of operations are denoted in reverse Polish notation.
In the following it is suggested to use and standardise this technique consistently on all levels of discourse. This is the only way to escape the waste-
1326
28 Conventions
ful confusion of concepts in theoretical investigations and in practical applications, both computer aided already now.
Wittgenstein provides extended notes on notation in the Tractatus under
3.32.
5
10
15
28.2.2
'Principles', 'laws'
In view of the very diverse usage of the concepts of 'principle' and 'law'
the alert by inverted commata has been felt to be insufficient. Thus, in an attempt to guide readers it is proposed to qualify the terms explicitly in accordance with the structure of the present treatise.
If other structures are adopted the following qualifications may be no
longer appropriate and due to the usual lack of adequate terminology and
symbology and the well-known confusion arises. Here again the advantage
of a standardised approach promoted becomes evident.
The notation proposed in the following table has evolved during the final
stages of corrections, but during extended experimentation has been felt to
impair the readability.
'Principles' qualified
Symbol
Explanation
Examples
principles
all 'important' proposition
not necessarily 'fundamental', but
including theorems
principleM
meta-principle
principle of coherence
principle
A
axiom, basic proposition,
'fundamental' proposition
principleO
principles of objectivity
principles 'proper', in the narrow
sense: of space, frame, material invariance: principle, principle
principleF
formal principle
principles of (observation) space
and (reference) frame invariance
principleP
physical principle
principles of material invariance as
distinguish from formal space invariance
principleT
theorem, derived proposid'Alembert's principle
tion, 'important' proposition weighted integrals of local balances: 'integral principals' and
'variational principles': often themselves referred to as 'the principles
of mechanics'
principleS
stability criteria
Hertz principle of least curvature
Similarly the term 'law', 'Satz' (proposition, Lehrsatz), is used in various
meanings and educated readers are usually expected to guess what an author
28.3 References
1327
may have meant. Again, the notation proposed in the following table has not
yet been used in the treatise.
'Laws' qualified
Symbol
Explanation
Examples
laws
all 'important' propositions,
formal and factual
not necessarily 'fundamental'
lawM
meta-law
meta-axioms
law
axiom, basic propositions,
'fundamental' propositions
Newton's axioms
lawT
theorem, derived proposiImpuls- and Momenten-Satz
tion, 'important' proposition
lawF
formal law
rules of transformation
physical laws
laws of momentum diffusion and
production: e. g., Newton's law of
gravitation
A
P
law
28.3
5
28.3.1
References
Formats
Full references to books are stating the author, the year of publication (in
brackets) of the edition used and referred to by the author, the first names,
the title, the place of publication, the publisher, the year of publication, as
well as further information as available and of interest, e. g.:
10
15
Abbott (1992), Edwin A., pseudonym A. Square: Flatland. A Romance of Many
Dimensions. London: Seeley, 1884. Unabridged, corrected text: New York: Dover, 1992. Thrift editions. Text at Project Gutenberg: http://promo.net/pg .
References to papers in encyclopaediae, transactions, yearbooks, conference proceedings et cetera are referring to the volume in which the paper
appeared, e. g.:
Daston (2004), Lorraine: Scientific Error and the Ethos of Belief. In: MPIWG
2004/51-67.
20
Full references of papers in journals are stating the volume, the year of
publication (in brackets), the number of the issue and the first and final page
numbers, e. g.,:
Beller (1998), Mara: The Sokal Hoax: At Whom Are We Laughing? Physics Today 51 (1998) 9, 29-35.
1328
28.3.2
5
10
15
20
25
30
35
28 Conventions
Quotations
" … This and several other words in the passage were
italicised … in order, apparently, to help the reader appreciate Swift's irony."
Jonathan Swift: Gulliver's Travels. Notes
(2003/279).
"Our author's italics warn us to look for special importance."
John Tyerman WilliamsJT: Pooh and the philosophers (1996/152).
Caveat: Whenever the author happens to refer to 'all textbooks' this is to
be understood as abbreviation for 'all textbooks the author has inspected and
analysed in more or less detail, in any case according to the state of his insight at the time he happened to come across a book'.
References are identified by author and by year of the edition used by the
author and quoted from, maybe both or only the latter in brackets, e. g.,
(Mach, 1883). Full titles of books and papers are quoted in 'inverted commata', with only two exceptions, Newton's Principia and Wittgenstein's
Tractatus.
Quotations, some quite extended, have been freely provided for the benefit, convenience and unbiased information of the readers. Full references are
considered sufficient, meeting the requirements of the 'fair use doctrine' of
the copyright law (quotation to follow further down) as in case of papers
published in journals and presented at symposia and published in the proceedings.
Quotations are identified by the year of publication of the source, from
which the quotation has been taken, followed by a slash and the page number, e. g., Mach (1883/11). If such identification is missing the quotations
are by heart or from 'obscure' or lost sources.
The popular quotations by name and year of publication of the reference
in the text are not only completely satisfactory in most cases, but also very
efficient, avoiding additional, annoying tables of annotations as frequently
found (ScheibeE, 2006).
But sometimes they are not particularly sensible (Seiffert, 1992/4). Thus
in case of Newton's Principia mathematica the acronym PM has been used
for the Dover edition of Motte's translation, revised by Cajori, e. g., Newton
(PM/2).
In case of Goethe's collected works the acronyms BA for the Berliner
Ausgabe, GA for the Gedächtnis Ausgabe and AA for Artemis Goethe
28.3 References
5
10
15
20
25
30
35
40
1329
Gedenk-Ausgabe have been used. This type of notation may in future be
used in other cases as well.
Quotations are identified uniformly by "quotation marks". Quotation
marks within quotations have been replaced uniformly by 'inverted commata'. Where meaningless "quotation marks," at the ends of paragraphs
(CohenIB, 1999.g) have been changed to proper "quotation marks", before
replacing them by inverted commata.
Italics in the reference have been kept unchanged without notice. Bold or
wide print in the references have been replaced uniformly by italics and are
identified by Italics: in the reference bold or wide print.
Italics by the author are identified by Italics: MS. Additions and explanations are put into [square brackets], e. g., [Halb-] Bildung. Foreign words
and phrases are quoted in italics except for German terms.
In the 'Current English Usage' inverted commata are dealt with in an extended entry (WoodFT, 1970/124-128). The usage in the present treatise is
felt to be perfectly in line with the usage recommended (1970/126):
"D. Double and Single lnverted Commas. Generally, use double inverted
commas, though single ones may be more appropriate for one word or for a
brief phrase where double ones would give a 'heavy' appearance.
Where one set of inverted commas occurs inside another set, as, for example, a quotation within a passage of direct speech, use the double type
for the outer set. and the single for the contained set: …
(N.B. - This is the general practice in writing, though, some publishing
houses favour the reverse order in print, … If it is necessary to use inverted
commas frequently, the single type are less obtrusive than the double and
for this reason they have generally been used throughout the present
book.)" Italics: MS.
Short parts, maybe slightly modified or paraphrased, or single words from
quotations are identified by inverted commata, e. g., 'absolute' time and 'absolute space'. 'Loose talk' is also put into inverted commata, e. g., 'definition'
or 'argument' if there are none (/126):
"(iv) Inverted commas may also denote that a word is used in irony or
sarcasm, in a sense which is not its generally accepted one; or that it is a
slang or dialect term. For this last purpose, however, they should be e employed only if it is felt necessary to apologise for the use of such words.
Where the slang or dialect word is natural in its setting, no inverted commas should be used."
The original rule to put loose talk, the epi-language or rather jargon of the
author also into inverted commata, has been abandoned. To avoid lengthy
and clumsy explanations and just caution readers made the text completely
unreadable as the lector noticed. Caution is necessary at any stage of the
treatise!
1330
5
28 Conventions
Introductory and concluding remarks of chapters and sections are set in
italics to indicate that these remarks do not belong to that particular elaboration proper, but to its meta-level.
The elaborations proper proceed on the axiomatic level and on the epilevel of the discussion, mostly addressed to experts and teachers. The original intention to distinguish these two levels in print has not been followed in
view of readability. But at a later stage this may be advisable and even necessary. The formal part may then be directly used as a draft standard.
28.3.3
Translations
"Glaube keinem Zitat, das Du nicht selbst aus dem Zusammenhang gerissen hast!"
Johannes Rau, vormals Präsident der Bundesrepublik Deutschland.
10
15
20
25
30
35
In order to be useful for readers extensive quotations have been provided.
The wider contexts will hopefully permit to judge where the author misinterpreted the references. For any such mis-interpretation, often not easily detected, solely the author is responsible, as for any other mistake and misconception.
From the exposition it is evident that the present treatise is not an 'Encarta
text', produced by 'cut and paste' from encyclopaedias. About half the quotations have been copied by hand; others have been scanned from books and
journals. Both procedures are subject to mistakes, most of them easily detected, if any escaped the attention of the author.
Often quotations are taken from the German originals or translations into
German, most readily accessible to the author. Readers will prefer to refer to
the English originals or translations, mentioned in the references, if the author became aware of any. Additions and translations by the author are identified in italics, e. g., Translation: MS.
Even if translations are available they may not be very satisfactory. This
applies in particular to concepts relating to our mental activities. Typical examples are 'begreifen, Begriff', 'vorstellen, Vorstellung', 'anschauen, Anschauung' and 'verstehen, Verständnis'. The reason for the difficulties is that
the 'common' languages are not expressions of coherent world models due
to different historical developments to say the least. In order to provide
some guidance the following tentative table has been set up.
Activities: German, English
Activity
German
English
befinden
befinden
find
28.3 References
bemerken
begreifen
anschauen
sehen
einsehen
übersehen
vorstellen
modellieren
auffassen
verstehen
1331
Befund
finding
bemerken
note
Bemerkung
note
'verstehen'!
'understand'!
Begriff
concept, idea, 'notion'
anschauen
contemplate
Anschauung
contemplation
sehen
view
Sicht
view
Sichtweisen
view points
Vorstellungsarten (Goethe),
Interpretationswelten (Abel)
standpoints
einsehen
'realise'
Einsicht
insight
Totalidee (SchillerF)
aperçu (Goethe)
übersehen
'grasp'
Übersicht
overall view
vorstellen
imagine
Vorstellung
image, not a picture!
Vorstellungskraft
imagination
modellieren
model
Modell
model
auffassen
conceive
Auffassung
conception
verstehen
understand
comprehend
Verständnis
understanding
comprehension
meinen
glauben
überzeugen
meinen
'think'!
Meinung, 'Ansicht'!
opinion
glauben
believe
Glauben
belief
überzeugen
convince
Überzeugung
conviction
1332
28.4
28.4.1
15
20
25
Copyright
"Vor einigen Wochen meldete sich bei mir ein Mann
…, der aus zwei Paar alten seidenen Strümpfen ein Paar
neue machen konnte. Wir verstehen die Kunst aus ein
paar alten Büchern ein neues zu machen."
Georg Christoph Lichtenberg: Sudelbücher, F.
(1776-80) 135 (1984/249).
5
10
28 Conventions
Acknowledgements
The author is greatly indebted to all authors whose works he has quoted,
trying to adhere to the doctrine of fair use and the rules of academic conduct, in any case with due statement of the source.
Different from the regulations of the Copyright, a quotation to follow, the
author feels that 'fair use' and 'academic conduct' include acknowledging not
only 'the particular way an author has expressed himself, but that they primarily extend to the ideas, systems, or factual information conveyed' in the
works quoted.
The author is also greatly indebted to all owners of copyrights, maybe different from the authors. If any of them feels that the present author has infringed upon their rights he will act according to their requests, in particular
before publishing subsequent editions, if any.
Only in one case the author has repeatedly requested written permission
to reproduce a short paper in toto, without any response. In view of the very
large number of selective quotations, very often from books published decades ago, the author has relied on the doctrine of fair use as discussed below.
28.4.2
Doctrine of fair use
The following quotation on quotations has been taken from an internet entry of the US Copyright Office:
30
35
"One of the rights accorded to the owner of copyright is the right to reproduce or to authorize others to reproduce the work in copies or phonorecords. This right is subject to certain limitations found in sections 107
through 118 of the Copyright Act (title 17, U. S. Code). One of the more
important limitations is the doctrine of 'fair use'. Although fair use was not
mentioned in the previous copyright law, the doctrine has developed
through a substantial number of court decisions over the years. This doctrine has been codified in section 107 of the copyright law.
28.4 Copyright
5
10
15
20
25
30
35
40
1333
Section 107 contains a list of the various purposes for which the reproduction of a particular work may be considered 'fair', such as criticism,
comment, news reporting, teaching, scholarship, and research. Section 107
also sets out four factors to be considered in determining whether or not a
particular use is fair:
the purpose and character of the use, including whether such use is of
commercial nature or is for non-profit educational purposes;
the nature of the copyrighted work;
amount and substantiality of the portion used in relation to the copyrighted work as a whole; and
the effect of the use upon the potential market for or value of the copyrighted work.
The distinction between 'fair use' and infringement may be unclear and
not easily defined. There is no specific number of words, lines, or notes that
may safely be taken without permission. Acknowledging the source of the
copyrighted material does not substitute for obtaining permission.
The 1961 Report of the Register of Copyrights on the General Revision
of the U.S. Copyright Law cites examples of activities that courts have regarded as fair use: 'quotation of excerpts in a review or criticism for purposes of illustration or comment; quotation of short passages in a scholarly
or technical work, for illustration or clarification of the author's observations; use in a parody of some of the content of the work parodied; summary of an address or article, with brief quotations, in a news report; reproduction by a library of a portion of a work to replace part of a damaged
copy; reproduction by a teacher or student of a small part of a work to illustrate a lesson; reproduction of a work in legislative or judicial proceedings
or reports; incidental and fortuitous reproduction, in a newsreel or broadcast, of a work located in the scene of an event being reported'.
Copyright protects the particular way an author has expressed himself;
it does not extend to any ideas, systems, or factual information conveyed in
the work.
The safest course is always to get permission from the copyright owner
before using copyrighted material. The Copyright Office cannot give this
permission.
When it is impracticable to obtain permission, use of copyrighted material should be avoided unless the doctrine of 'fair use' would clearly apply
to the situation. The Copyright Office can neither determine if a certain use
may be considered 'fair' nor advise on possible copyright violations. If there
is any doubt, it is advisable to consult an attorney.
FL-102, Revised July 2006." Italics: MS.
According to these elaborations the author has no doubt, that all his more
than 1200 quotations meet the requirements of the doctrine of 'fair use', and
thus he did not consult an attorney.
1334
28 Conventions
In particular, he feels that 'the effects of the use upon the potential markets for or values of the copyrighted works', if any, will be positive in advertising for the publications quoted, even in cases of criticism and/or parody,
expressis verbis permitted.
5
10
15
28.4.3
Rules of conduct
At a later stage the author has inspected the 'Handbook for Students' on
'Academic Integrity at the Massachusetts Institute of Technology' to make
sure that he did not offend any rules of conduct (Brennecke, 2005).
Clearly the use of quotations purposely differs from that recommended.
Further, the naïve idea to quote from and paraphrase only 'important authorities' has not been observed for two reasons:
• firstly, reliable authorities have hardly been found, and
• secondly, from the outset the goal of the project has been to get
away from the repetition of the tribal lore and the litany by 'important authorities'. Quotations are rather intended to provide the flavour of the discussions, sometimes felt to be parodies of themselves,
and to demonstrate their deficiencies.
29
References
29.1
Author's basic work
"Alle meine Gedichte sind Gelegenheitsgedichte, sie
sind durch die Wirklichkeit angeregt und haben darin ihren Grund und Boden. Von Gedichten aus der Luft gegriffen halte ich nichts."
Johann Wolfgang Goethe: 18.09.1823 (Eckermann, 1911/37).
The following papers of the author contain basic work and many details, which
maybe of less interest to the general reader. All recent papers since about 1990
may be accessed on the website of the author www. m-schmiechen.de in the annotated 'News …' and directories of 'Recent papers …' and in the 'Bibliographies …'
or directly in the directory /HomepageClassic01 using the file names provided with
some of the following references.
Earlier papers mentioned in the text and in the bibliographies will hopefully
soon be added to the website as well.
Schmiechen (1958), Michael: Ansätze zu einer rationellen Theorie der kontinuierlichen, heterogenen Verbrennung flüssiger Brennstoffe in sauerstoffhaltigen
Gasgemischen. Berlin: Technische Universität, 1958. Diplomarbeit am
Lehrstuhl für Brennstofftechnik.
Schmiechen (1959), Michael: On the factual and logical implications of a macroscopic theory of rate processes in continuous, isotropic systems. London: Imperial College of Science and Technology, 1959. Thesis in a Post-Graduate Course
on Heat Transfer and Combustion.
Schmiechen (1960), Michael: Investigations into the stability of vortex streets.
1960?. Unpublished notes.
Schmiechen (1962), Michael: Untersuchungen über die hydrodynamischen Massen
an Schiffen. VWS-Bericht Nr. 233/62. 25.10.1962. Forschungsvorhaben der
Deutschen Forschungsgemeinschaft Schu 24/28.
Schmiechen (1963), Michael: Ansätze zu einer allgemeinen Strahltheorie hydrodynamischer Reaktionsantriebe in idealen Flüssigkeiten. 1963?. Unpublished manuscript, 182 pages.
Schmiechen (1964), Michael: Eine allgemeine Gleichung für Bewegungen starrer
Körper in Flüssigkeiten und ihre Anwendung auf ebene Bewegungen von Doppelkörpern. Mitteilungen der Versuchsanstalt für Wasserbau und Schiffbau, Berlin, Heft 48, 1964. Doctoral Dissertation Technische Universität Berlin.
Schmiechen (1964), M.: Fragen der Kursstabilität und Steuerfähigkeit von Schiffen. STG 58 (1964) 319-336.
1335
1336
29 References
Schmiechen (1968), Michael: Performance Criteria for Pulse-Jet Propellers. Proceedings 7th ONR Symp. on Naval Hydrodynamics (Rome, 1968) 1085/1104.
Schmiechen (1969), Michael: Design and Evaluation of Experiments for the Identification of Physical Systems. Cambridge, MA: Massachusetts Institute of Technology, 1969. Department of Naval Architecture and Marine Engineering, Report No. 69-1, 1969.
Schmiechen (1970.m), Michael: Über mögliche Kopplungen der Bewegungen bei
Tauchfahrzeugen. Schiffstechnik 17 (1970) 86, 33-36.
Schmiechen (1970.p), Michael: Über die Bewertung hydromechanischer Propulsionssysteme. Schiffstechnik 17 (1970) 89, 91-94.
Schmiechen (1972), Michael: On-line identification of manoeuvrability parameters
and adaptation of control. 13th ITTC (1972) Materials of Interest, 234-239.
Schmiechen (1973.s), Michael: On State Space Models and their Application to
Hydromechanic Systems. Tokyo: University of Tokyo, 1973. Department of
Naval Architecture, NAUT Report 5002.
Schmiechen (1973.c), Michael: Zur Theorie der Zentrifugen. 1973. Unpublished
manuscript.
Schmiechen (1978), Michael: Rationale Modelle idealer Propeller endlicher Belastung. Schiffstechnik 25 (1978) 121, 113-120. Discussion by J. A. Sparenberg:
Schiffstechnik 26 (1979) 2, 117-121.
Schmiechen (1980.c), M. et al.: An Experimental Investigation of the Hydrodynamic Characteristics of a Partially Cavitating Hydrofoil. Proceedings Nineteenth American Towing Tank Conference (Ann Arbor MI, 1980).
Schmiechen (1980.p1), Michael: Eine axiomatische Theorie der Wechselwirkungen zwischen Schiffsrumpf und -propeller. Fritz Horn zum 100. Geburtstag gewidmet. Schiffstechnik 27 (1980) 2, 67-99.
Schmiechen (1980.p2), Michael: Nachstrom und Sog aus Propulsionsversuchen allein. Eine rationale Theorie der Wechselwirkungen zwischen Schiffsrumpf und propeller. STG 74 (1980) 333-351.
Schmiechen (1982), Michael and Burkhard Müller-Graf: On the Stability of SemiDisplacement Craft. Second International Conference on Stability of Ships and
Ocean Vehicles, (Tokyo, Oct. 1982) 67-77.
Schmiechen (1983), Michael: On Optimal Ducted Propellers for Bodies of Revolution − A Speculative Reconstruction. Proceedings Internat. Symp. on Ship Hydrodynamics and Energy Saving, (El Pardo, 1983) Nr. VI, 2, S1-7.
Schmiechen (1984.a), Michael: Wake and Thrust Deduction from Propulsion Tests
Alone. A Rational Theory of Ship Hull-Propeller Interaction. Proceedings 15th
ONR Symp. on Naval Hydrodynamics (1984) 481-500.
Schmiechen (1984.b), Michael: Propellers in Oblique Flows: Boomerang Theory
and Simulation. A pastime exercise in computational mechanics. 1984. Unpublished manuscript and BASIC programme.
Schmiechen (1986), Michael: Implementation and Verification of a State Space
Model for Manoeuvring Ships. Technische Universität Berlin, Institut für
Schiffs- und Meerestechnik, HMS Report 1/86, 1986.
Schmiechen (1987), M. and Zhou, Lian-di: An Advanced Method for the Design of
Optimal Ducted Propellers behind Bodies of Revolution. VWS-Report No.
29.1 Author's basic work
1337
1083-1987; Final report on a Partnership in Engineering Sciences Sponsored by
Stiftung Volkswagenwerk.
Schmiechen (1988.s), Michael: Entwicklung eines Modells zur optimalen Ausnutzung der Fahr-Wassertiefen durch die Schiffahrt unter Einbeziehung von Sicherheitsaspekten. VWS-Bericht Nr. 1127 A/88. Im Auftrage des Bundesministeriums für Verkehr, Bonn.
Schmiechen (1988.p), Michael and Zhou, Lian-di: An Advanced Method for Design of Optimal Ducted Propellers behind Bodies of Revolution. Proceedings
SNAME Spring Meeting (1988) 29/39. 13th STAR Symp. and 3rd. IMSD Conf.
(Pittsburgh, June 8-10, 1988).
Schmiechen (1988), M.: Gleichungen und Parameter für die Bewegungen von Unterwasserfahrzeugen. VWS-Bericht Nr. 1132/88.
Schmiechen (1990), M.: Mathematisches Modell einer Antenne. VWS-Bericht Nr.
1157/90.
Schmiechen (1991), Michael: Proceedings 2nd International Workshop on the Rational Theory of Ship Hull-Propeller Interaction and its Applications (2nd
INTERACTION Berlin '91). Berlin: Versuchsanstalt für Wasserbau und Schiffbau, 1991. Mitteilungen der VWS, Heft 56, 1991. Containing among others
METEOR report ... /int_rep.pdf, BASIC program ... /int_bas.pdf, Oral discussions ... /int_orl.pdf and Written discussions ... /int_wrt.pdf .
Schmiechen (1992.u), Michael: Advanced Lectures on Recurring Topics. Unpublished Papers: 1. FTP: Fourier Transform Proper. 2. Implementation and Verification of a State Space Model for Manoeuvring Ships. 3. Bewegungen von Robotern in Strömungen (Motion of Robots in Flows). 4. Ship Hull Resistance and
Thrust Deduction from Overload Tests Alone. Berlin March, 1992.
Schmiechen (1992.g), Michael: Models in Ship Science. Proceedings First International Conference on Occasion of the 300th Anniversary of the Creation of the
Russian Fleet by Peter the Great, St. Petersburg, June 07-14, 1992. Paper ...
/mod_pa_e.pdf and presentation ... /mod_pr_e.pdf .
Schmiechen (1992.p), Michael., Andreas Voss u. Hartmut Engler: Entwurf und
Bewertung von Düsenpropellern mit Leitapparaten. VWS-Bericht Nr.1209/92;
FDS-Bericht Nr.245/93.
Schmiechen (1993.p1), Michael und Volker Goetz: Grundsatzversuche zu den
Wechselwirkungen zwischen Schiffsrumpf und -propeller. VWS-Bericht
Nr.1221/93; FDS-Bericht Nr.245/93.
Schmiechen (1993.p2), Michael: Entwurf und Bewertung von Düsenpropellern als
Pumpen. STG-Sprechtag 'Hydromechanik schneller Schiffe und ummantelter
Propeller', VWS Berlin und SVA Potsdam, 03./04.09.1993; VWS-Bericht
Nr.1229/93.
Schmiechen (1993.p3), Michael: Entwurf und Bewertung von Düsenpropellern als
Pumpen (Vortrag). STG 87 (1993) 236.
Schmiechen (1993.g), Michael (Editor): International Towing Tank Conference
Symbols and Terminology List, Version 1993. Berlin: Versuchsanstalt für
Wasserbau und Schiffbau, 1993. VWS Mitteilungen Heft 57. Outdated original
version .../satl_93.pdf, to be used only as 'historical' reference.
1338
29 References
Schmiechen (1994.p), Michael: Design and Evaluation of Ducted Propellers as
Pumps. Centenary of the Krylov Ship Research Institute, St. Petersburg, 1994.
Paper ... /pde_pa_e.pdf and presentation ... /pde_pr_e.pdf .
Schmiechen (1994.m), Michael: Über Newtons Axiome. Vorträge seit 1994. Presentation ... /newt_d5.pdf .
Schmiechen (1995.n), Michael und Klaus JordanK: Fuzzy Manoeuvring. Talk at the
25. Meeting of the STG Working Group on Manoeuvring at HowaldtswerkeDeutsche Werft Kiel on 12.10.1995. Paper ... /fuz_pap.pdf and Presentation ...
/fuz_prs.pdf .
Schmiechen (1995.m), Michael: On Newton's Axioms. Lectures since 1995. Presentation ... /newt_e5.pdf .
Schmiechen (1997), Michael: Modelle und Probleme der Schiffstheorie. Beitrag
zum Fest-Colloquium zur Verabschiedung des Autors aus der Versuchsanstalt
für Wasserbau und Schiffbau am 18.04.1997. Paper ... /mod_pa_d.pdf and presentation ... /mod_pr_d.pdf .
Schmiechen (1998.s), Michael: Auswertungen von Naturmessungen des Squat und
Vergleich mit bekannten Squat-Formeln. Berlin: VWS, 1998. VWS Bericht Nr.
1274/97. Band 1: Text, Band 2: Berechnungen.. Im Auftrage der WasserstraßenDirektion Nord, Kiel.
Schmiechen (1998.g), Michael and Bruce Johnson: Some Fundamental Considerations Concerning the History and Recent Development of the ITTC SaT List, the
International Towing Tank Conference Symbols and Terminology List. Proceedings First International Conference on Maritime Terminology, (ISTI Brussels,
May 15-16, 1998) 126-144. Brussels: Editions du Hazards, 1999. Paper ...
/mart_pap.pdf and presentation ... /mart_prs.pdf .
Schmiechen (1999.s), Michael: Auswertungen von Naturmessungen des Squat und
Vergleich mit bekannten Squat-Formeln. Berlin: VWS, 1999. VWS Bericht Nr.
1264/96. Meßquerschnitte, Ergebnisse.
Schmiechen (1999.g1), Michael: Lecture on the Identification of Systems. Institut
für Schiffbau und Meerestechnik of the Universität Rostock on April 28, 1999.
Presentation ... /sid_pr_d.pdf .
Schmiechen (1999.g2), Michael: Discussion of Östergaard's paper on safety and reliability of ship's structures at 100 Years STG in Berlin 24.- 29.05.1999. STG 93
(1999). Discussion ... /saf_disc.pdf .
Schmiechen (1999.p), Michael: Towards a rational evaluation of ship speed trials.
Summary paper with hyperlinks to all material published on the website. Berlin,
June 18, 1999. Paper ... /trl_sum.htm .
Schmiechen (1999.g3), Michael: Estimation of Spectra of Transient Functions
from Finite Sets of Sampled Values. STG-Sprechtag 'Schiffe im Seegang', Hamburg, 17.09.1998, 1/13. Schiffstechnik Ship Technology Research 46 (1999) 2,
111-127. Paper ... /ftp_pap.pdf, presentation ... /ftp_prs.pdf and discussion ...
/ftp_disc.pdf .
Schmiechen (2000), Michael: Zur Auswertung von Naturmessungen des Squat.
Paper presented at the Workshop on Squat organised by the Institut für Maritime
Studien at the Fachhochschule Oldenburg on 08./09.11.2000. Paper ...
/sqt_pa_o.pdf and presentation .... /sqt_pr_o.pdf . Subsequent presentations at
29.1 Author's basic work
1339
ISM University Rostock 29.11.2001, ISM Technical University Berlin
07.12.2001, Gdansk Ship Model Basin 18.01.2002.
Schmiechen (2001), Michael: Evaluating of Ship Speed Trial: Identifying Powering Parameters. Paper presented at the International Symposium on Ship Propulsion. Lavrentiev Lectures, St. Petersburg, June 19-21, 2001. Paper ...
/lav_pap.pdf and presentation ... /lav_prs.pdf .
Schmiechen (2002), Michael (Author, Editor and Publisher): Rational Evaluations
of Traditional and Quasi-steady Ship Speed Trials. Published on the occasion of
the 23rd ITTC Venice 2002 and of the Centenary of VWS, the Berlin Model Basin, in 2003. Berlin: in memoriam Versuchsanstalt für Wasserbau und Schiffbau,
2002. VWS Mitteilungen Heft 58, post mortem. Introductory chapter: ...
/vws_m58.pdf, with live links not only to all documents in the volume but to all
background material quoted ... /vws_m58.htm .
Schmiechen, (2003.g), Michael (Editor): Jubiläum der Eröffnung der Versuchsanstalt für Wasserbau und Schiffbau in Berlin am 07.07.1903. Vortragsveranstaltung der STG Fachausschüsse 'Geschichte des Schiffbaus' und 'Schiffshydrodynamik' auf der Schleuseninsel in Berlin am 22.11.2003. STG-Nr. 3010/VWS
Mitteilungen Heft 60, post mortem, Berlin 2003. In memoriam Versuchsanstalt
für Wasserbau und Schiffbau, Berlin. Available at: Schiffbautechnische Gesellschaft, Hamburg, www.stg-online.de.
Schmiechen (2003.p), Michael: Beiträge der VWS zur Erforschung der Propulsion
und Bewegungen von Schiffe. In: Schmiechen; 2003.f/139-202. See the paper...
/vws100pa.pdf, its presentation ... /vws100pr.pdf and its presentation with intermediate texts ... /vws100pc.pdf .
Schmiechen (2004), Michael (Author, Editor and Publisher): MARIC Lectures On
the Rational Theory of Ship Hull-Propeller Interaction and its Applications. Lecture Notes published on occasion of a course on Marine Propulsion held at the
Marine Design and Research Institute of China, MARIC, Shanghai May 26-31,
2004, with participants from Shanghai Ship and Shipping Research Institute,
China Ship Scientific Research Centre and Shanghai Jiao Tong University. VWS
Mitteilungen Heft 61, post mortem, Berlin 2004. In memoriam Versuchsanstalt
für Wasserbau und Schiffbau, Berlin.
Schmiechen (2005.m), Michael: Rationale Mechanik, Relativität und Gravitation.
Lecture prepared for the Einstein Centenary. First held at the Institut für Schiffsund Meerestechnik, Technische Universität Berlin on April 22, 2005. Handouts:
…/rat_m_d.pdf .
Schmiechen (2005.p), Michael: 25 Jahre Rationale Theorie der Propulsion. Fritz
Horn zum 125. Geburtstag. Prepared for the STG Summer Meeting May 17-19,
2005, presented at the 100th Annual Meeting of STG. Jahrbuch STG 99 (2005).
Paper ... /hpi_m_pa.pdf, presentation ... /hpi_m_pr.pdf and discussion ...
/hpi_m_cl.pdf .
Schmiechen (2006), Michael: Propulsor Hydrodynamics. Theme lecture. Presented
at the International Conference on Marine Hydrodynamics, MAHY 2006, held
January 05 to 07 at the Naval Science and Technological Laboratory at Visakhapatnam, India. Proceedings Int'l Conference in Marine Hydrodynamics 2006,
Vol.2, 611-631. Paper … /prop_pap.pdf, handout … /prop_hdo.pdf and presentation … /prop_prs.pdf .
1340
29 References
Schmiechen (2007), Michael: Ducted Propulsors in Open Water. First steps towards their rational evaluation. To be published in HANSA. Extended discussion … /prp_linf.pdf, paper, theoretical analysis … /prp_linp.pdf and numerical
analysis … /prp_lina.pdf .
Schmiechen (2009), Michael: 50 Years Rational Theory of Propulsion. Recent Results and Perspectives. Proceedings First International Symposium on Marine
Propulsion (Trondheim, Norway, June 22-24, 2009) 117-128. …
/prop_50_pap.pdf and … /prop_50_pre.pdf .
29.2 Sources referred to
29.2
1341
Sources referred to
"Manchmal las er noch ein paar Seiten in irgendeinem
der Bücher. Geschadet hat das fast nie."
Kästner für Erwachsene: Fabian (1966/158).
The present work would not have been possible without the author's collection of
standard references and of diverse texts and without easy access to the excellent libraries at Berlin, the library of VWS, the Berlin Model Basin, and the various libraries of the Technische Universität, department libraries in particular, all of
them in walking distance of the author's home. Occasionally the Internet with its
incredible wealth of very diverse information has been visited and tapped.
A
Abbott (1992), Edwin A., pseudonym A. Square: Flatland. A Romance of Many
Dimensions. London: Seeley, 1884. Unabridged, corrected text: New York: Dover, 1992. Thrift editions. Text at Project Gutenberg: http://promo.net/pg .
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Essentialismus und Relativismus. 1. Auflage. Frankfurt/M.: Suhrkamp, 1995.
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29 References
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Baer (1993), Günther: Spur eines Jahrhundertirrtums. Neue Gedanken zum physikalischen Weltbild. Dresden: Spur, 1993.
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1343
Bardina (1997), J. E., P. G. Huang and T. J. Coakley: Turbulence Modelling Validation, Testing and Development. NASA Technical Memorandum 110446,
April 1997.
Barnhart (1983), Richard M.: Along the Borders of Heaven. Sung and Yüan Paintings from the C. C. Wang Family Collection. New York: Metropolitan Museum
of Art, 1983.
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die Menschen konsequent dem zuwider, was die [Spiel-]Theorie 'rational' nennt
– und erzielen gerade durch ihr irrationales Verhalten größere Gewinne. Ein solches paradoxes Ergebnis schreit förmlich nach einer neunen Theorie [der Rationalität]. Spektrum (2007) 8, 82-88.
Bauer (1998), Martin, Helmut MayerH und Uwe Wittstock (Hrsg): Intellektuelle
Moden. Neue Rundschau 109 (1998) 3.
Baumann (1969), Richard: ALGOL-Manual der ALCOR-Gruppe. Einführung in
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30
30.1
Indices
Name index
A
Abattouy, M. 1378
Abbott, E. 73, 448, 1327, 1341, 1430
Abdel-Maksud, M. 1268, 1341
Abel, G. 6, 10, 31, 38, 61, 261, 274,
277, 278, 304, 313, 424, 528,
652, 1331, 1341
Abendroth, W. 1374
Abid, R. 977, 1341
Abkowitz, M. A. 1245, 1341
Abraham, R. 849, 1282, 1341, 1375
Achenbach, J. 243, 864
Adam, R. 71, 1341
Adhikari, S. 1341
Adrian, M. 127, 423, 1313, 1341
Agazzi, E. 252, 254, 418, 1341,
1342, 1354
Albring, W. 624, 789, 1274
Alekseevsky, D. V. 451, 455, 468,
1342
Allen, W. 82, 232, 242, 294, 305,
370, 593, 1351, 1372, 1375,
1378
Altenbach, H. a. J. 575, 1342
Amelino-Camelia, G. 734
Amtsberg, H. 307
Appel, C. 1061, 1317
Archimedes 2, 57, 97, 143, 1100,
1163, 1166, 1167, 1168, 1373
Aristarchos of Samos 258, 269, 1369
Aristotle 34, 39, 101, 114, 129, 178,
215, 218, 219, 220, 275, 282,
366, 635, 767, 798, 802, 1294,
1342
Arkani-Hamed, N. 73, 878, 1342
Arnold, V. I. 28, 300, 1086, 1342,
1373, 1382, 1383
Ashtekar 863
Asmuth, C. 1368
Asphaug, E. 837, 1342
Atwood, G. 642, 782, 1072
Augustinus, A. 199, 462, 467, 654,
656, 685, 686, 688, 690, 700,
710, 712, 724, 1297, 1342, 1355,
1371
Austin, J. L. 1344
B
Bach, J. S. 425, 879, 1362
Bacon, F. 197, 231, 847
Baer, G. 835, 1342
Balinski, M. 39, 1342
Balzer, W. 141, 253, 1342, 1356,
1360, 1382, 1384
Bär, C. 186, 1342
Barbour, J. 1342, 1345
Bardina, J. E. 977, 1343
Barginski, V. 817
Barnhart, R. M. 707, 1343
Barrow, J. D. 579, 635, 1343
Barthes, R. 277
Bartley, W. W. 1378
Bass, S. D. 186, 1343
Bassford, C. 1375
Basu, K. 61, 285, 1343
Bauer, M. 209, 1343, 1344, 1358,
1389
Baumann, R. 309, 1343
Bavin, V. 1262
Bayes, T. 273, 369
Bechtolsheim, L. 1376
1391
1392
Beck, A. 1347, 1357, 1360, 1362,
1363, 1364, 1373, 1374, 1380,
1382, 1386
Beckenstein, J. 1343
Becker, E. 913, 1343
Becker, P. v. 704, 1343
Beckermann, A. 217, 1343
Beckett, S. 1196
Beeley, P. 247, 1343
Behnke, H. 355, 1343
Beller, M. 245, 246, 251, 319, 418,
423, 909, 910, 1327, 1343
Bellman, R. 8, 25, 68, 116, 204, 330,
348, 391, 1288, 1343
Beltrami, E. 443, 448, 449
Belyaev, A. K. 1370
Bergemann, N. 1348
Bergmann, P. G. 626, 811, 812, 884,
1343, 1357
Berkeley, G. 49, 66, 76, 92, 128,
129, 131, 209, 225, 226, 322,
350, 424, 624, 652, 737, 739,
743, 747, 749, 757, 788, 806,
808, 828, 831, 1343, 1344, 1346,
1373
Berlin, I. 54, 55, 1344
Bernhart, J. 1342
Bernoulli, D. 78, 119, 128, 209, 214,
283, 505, 949, 1114, 1344
Bernoulli, E. 1354
Bernoulli, J. 78, 119, 209, 214, 579,
580, 899, 949, 1233, 1344
Bernoulli, R. 1354
Bertram, A. 967, 1344
Bessel, F. W. 768
Beste, D. 940, 1344
Beth, E. 42, 1356
Bettelheim, B. 62, 1344
Bierbichler, S. 759
Bieri, P. 1351
Bigelow 131
Binder, E. 1367
30 Indices
Birkhoff, G. 326, 343, 569, 570,
745, 844, 982, 1092, 1169, 1171,
1172, 1174, 1196, 1198, 1344
Birnbaum, R. 208, 1344
Bischof, M. 579, 1344
Bishop, R. E. D. 1377
Bismarck, O. v. 11, 325
Blackman, R. B. 409, 412, 1344
Blank, U. 198, 1344
Blau, J. L. 1363
Blind, K. 297, 1344
Blum, L. 131, 1344
Bocheński, I. M. 27, 37, 276, 313,
317, 345, 381, 383, 384, 386,
442, 607, 1344
Bödeker, K. 49
Bohm, D. 741, 870, 899, 902, 903,
904, 905, 906, 907, 910, 1059,
1345
Böhme, G. 43, 1344, 1374
Böhnigk, V. 1355
Bohr, N. 75, 76, 244, 246, 319, 378,
423, 860, 909, 910, 911
Boisonnade, A. 1367
Boltzmann, L. 76, 102, 106, 109,
111, 192, 291, 308, 466, 504,
705, 854, 933, 940, 941, 945,
946, 950, 992, 1009, 1060, 1061,
1066, 1345
Bolyai de Bolya, J. 443, 448
Bondi 663, 822, 1126
Bopp, F. 1382
Borel, E. 375
Borgo, S. 1359
Borkenau, F. 1371
Born, M. 156, 251, 289, 319, 538,
701, 1345
Börner, G. 1345, 1352
Bortoft, H. 12, 28, 62, 63, 65, 191,
231, 261, 321, 335, 719, 1345
Borzeszkowski, H.-H. v. 84, 86, 92,
107, 118, 131, 152, 154, 155,
161, 215, 250, 425, 824, 1345,
1370, 1385, 1387
Bos, H. 148
30.1 Name index
Boscovich, R. J. 94, 95, 96, 106,
132, 433, 498, 506, 815, 1012,
1345
Bose, H. L. 946, 1284
Bosnjacovic, F. 307
Bothezat, G. de 489, 725, 726, 1345
Bottema, O. 470, 631, 1037, 1125,
1127, 1128, 1129, 1130, 1345
Bouché, C. 1380
Boudri, J. C. 92, 144, 145, 146, 147,
1031, 1032, 1050, 1345
Bourbaki 340, 341, 589
Boussinesq, J. 820, 974, 976
Boyle, R. 506, 822, 855
Brackenridge, J. B. 160, 1346
Brackwell 1172
Bradley, J. 626, 637, 652, 663, 822,
828, 835, 1126, 1346, 1370
Brahe, T. 219
Braitenberg, V. 271, 1346
Brandhorst, A. 1377
Brandon, R. 259, 1346
Brecht, B. 156, 289
Brennecke, P. 1334, 1346
Bricmont, J. 77, 208, 245, 425, 445,
468, 986, 1346, 1382
Briessen, C. v. 306, 1346
Briessen, F. v. 11, 1346
Broadhurst, T. 1380
Brockman, J. 243, 244, 884, 885,
1346, 1365
Brody, T. 126, 337, 507, 1346
Bronowski , J. 277, 1346
Brooke, R. 220
Brose, H. L. 1388
Brown, G. B. 506, 626
Brunk, G. 991, 1346
Büchmann, G. 34, 1346
Büchner, G. 1, 4, 463, 1346
Buckingham, E. 176, 326, 569, 798,
799, 854, 1196, 1197, 1346
Budenz, J. 1374
Bührke, T. 1347
Bullough, R. K. 499, 1347
1393
Bunge, M. A. 103, 372, 860, 872,
1347, 1370, 1374
Burau, H. 905, 1347
Bürger, G. A. 11, 1193, 1347
Bürger, W. 1343
Burkhardt, J. J. 1354
Burns, J. A. 988, 1347
Burtt, E. A. 147
Bush, V. 53, 54, 56, 1347
Butler, S. 245, 1386
Büttner, J. 1378
Buyer, E. 937, 1347
Byrne, P. 248, 1347
C
Cajori, F. 86, 87, 88, 89, 90, 92, 159,
225, 501, 822, 1328, 1347, 1373,
1374
Calvet, C. 741, 857, 859, 1347
Campbell, N. R. 2, 18, 125, 126,
327, 335, 1347
Carmody, T. 1344
Carnap, R. 17, 21, 72, 77, 183, 184,
216, 278, 314, 323, 327, 334,
356, 362, 363, 364, 368, 372,
378, 440, 443, 444, 445, 450,
469, 475, 476, 554, 574, 627,
652, 665, 693, 816, 864, 882,
1300, 1347, 1348, 1372
Carnot, S. 704
Carr, B. J. 878, 1348
Carroll, J. B. 1388
Cartan, E. J. 880
Casado-Pascual, J. 1359
Cassirer, E. 216, 1372
Castellani, E. 498, 1348
Castin, Y. 946, 1348
Cauchy, A. L. B. 112, 113, 145, 200,
889, 895, 896, 933, 934, 935,
937, 939, 941, 943, 944, 945,
946, 947, 948, 949, 950, 951,
953, 955, 961, 963, 973, 981,
985, 987, 990, 991, 992, 994,
1003, 1009, 1023, 1029, 1030,
1394
1048, 1050, 1059, 1060, 1081,
1096, 1272, 1299, 1323, 1428
Caudry, P. J. 1347
Cavell, S. 1348
Cavendish, H. 181, 802
Cayley 969, 971, 1074, 1076
Cendra, H. 354, 1348
Cerutti, H. 1146, 1348
Cervantes de Saavedra, M. 5, 154,
407, 433, 458, 527, 1323, 1348
Chaitin, G. J. 342, 1348
Chalmers, A. F. 253, 427, 428, 1348
Chandrasekhar, S. 194, 195, 1348
Charleton, W. 505, 1348
Chen, X.-N. 499, 1276, 1281, 1282,
1349
Child, J. M. 95, 1345
Childers, D. G. 409, 1349
Chintschin, A. J. 375, 926, 1090,
1091, 1092, 1093, 1096, 1099,
1349
Chisholm, R. M. 39, 1349
Chladni, E. F. F. 65
Christini, D. J. 415, 1349
Christoffel, E. B. 513, 665, 1054,
1079, 1080
Chubykalo, A. E. 820, 1349
Chucholowski, A. 16, 1349
Claudius, M. 655, 708, 1117
Clausewitz, C. v. 13, 15, 17, 61, 62,
65, 78, 134, 141, 1310, 1349,
1375
Clausius, R. 308
Clavell, J. 1384
Clifton, T. 509, 753, 1349
Coakley, T. J. 1343
Cohen, I. B. 30, 86, 87, 88, 89, 90,
93, 140, 159, 160, 162, 178, 214,
215, 225, 501, 502, 590, 591,
751, 1329, 1349, 1373, 1374
Cohen, J. 1377
Cohen, L. 1370
Cohen, R. S. 1352, 1361
Cole, E. H. 1383
30 Indices
Coleman, B. D. 922, 974, 980, 1349
Coleridge, S. T. IX, 55, 378, 806,
1349
Colerus, E. 1350, 1369
Collins, H. 528, 1350
Colodny, R. G. 1350, 1355
Condillac, È. B. de 77
Condorcet, A. de 145
Connes, A. 13, 230, 864, 865, 1360
Copernicus, N. 8, 50, 114, 142, 171,
258, 438, 528, 529, 618, 622,
988, 995, 1117, 1350, 1389
Cordier, O. 1267
Coriolis, G.-G. 829, 953, 992, 1120,
1139
Coulson, C. A. 1350
Courtine, J. F. 1368
Cowen, R. 8, 1350
Cramer, F. 459, 1350
Cramer, G. 392
Cubero, D. 1359
Cunha, M. O. T. 1387
Cusanus, N. 31, 652, 837, 1350
D
Daedalus 280, 1310
Dallender, J. A. 1383
Damerow, P. 1378
Damm, S. 197, 204, 1350
Daniel, P. 819
Darwin, C. 103, 1092
Daston, L. 9, 31, 43, 44, 46, 54, 55,
60, 125, 151, 191, 192, 252, 283,
284, 306, 319, 431, 588, 610,
1317, 1327, 1350
Datton, D. 618, 1350
Davidson, D. A. 38, 1351
de Broglie 34, 870, 906, 907
De Gandt, F. 139, 211, 275, 277,
284, 1351
De Sabbata, V. 1351, 1371, 1380
Defoe, D. 50, 1351
Degas, E. 2
Dellian, E. 87
30.1 Name index
Democritus 225, 504
Denker, M. 79, 388, 1351, 1362
Derksen, A. A. 103, 1351
Descartes, R. 19, 58, 63, 85, 206,
215, 218, 232, 431, 435, 629,
635, 673, 797, 802, 808, 822,
827, 880, 883
Dewey, J. 32, 251, 286, 287
DeWitt, B. S. 1080, 1351
Dicke, R. H. 816, 817
Dickmann, H. 1237, 1362
Diels, H. 1369
Dijksterhuis, E. J. 140, 147
Dimopoulos, S. 1342
DIN 138, 350, 364, 501, 560, 588,
589, 774, 776, 779, 789, 972,
979, 1351
Dingler, H. 18, 118, 127, 218, 346,
481, 662, 689, 1351
Dittus, H. 1367
Dodgson, C. L. 615, 1348
Doetsch, G. 409, 1351
Dolaptschiew, B. 1097, 1099, 1351
Doré, G. 1349
Dörner, D. 1351
Dosch, H.-G. 1368
Dotzauer, G. 46, 1351
Doyle, J. C. 1351
Drago, A. 49, 1352
Drever, R. W. P. 751
Drösser, C. 343, 1352
Droste, x. 624
Duerr, H. P. 36, 247, 1346, 1352,
1380
Dugas, R. 206, 207, 934, 1352
Duhamel, J.-M.-C. 540
Dühring, E. K. 13, 18, 19, 20, 96,
97, 98, 99, 100, 102, 112, 114,
140, 193, 206, 208, 214, 218,
232, 323, 354, 651, 1352, 1353,
1371
Dunkel, J. 1359
Durand, D. 378, 379, 1352
Dürr, D. 906, 908, 909, 1352
1395
Dürr, S. 186, 849, 1352
Dvali, G. 1342
Dyke, M. v. 985, 1352
E
Ebener, D. 1369
Ebneth, M. 1389
Eckermann, J. P. VII, 3, 7, 20, 40,
45, 50, 51, 82, 117, 120, 127,
136, 206, 218, 223, 239, 327,
354, 525, 602, 911, 966, 1064,
1089, 1097, 1194, 1201, 1217,
1314, 1335, 1344, 1352
Eckhardt, U. 124, 1352
Eco, U. 205, 1352
Eddington, A. S. 244, 665, 1352
Edwards, M. R. 238, 1352, 1355
Ehlers, J. 494, 624, 640, 701, 704,
847, 880, 881, 1152, 1345, 1352,
1353
Einstein, A. IX, III, V, VII, III, 4, 9,
25, 34, 54, 55, 60, 61, 62, 64, 66,
69, 74, 75, 76, 90, 92, 101, 102,
103, 124, 125, 131, 150, 152,
153, 162, 166, 169, 170, 172,
178, 179, 180, 181, 182, 183,
185, 187, 188, 200, 219, 220,
222, 227, 232, 235, 236, 237,
242, 243, 244, 246, 255, 256,
268, 286, 288, 291, 318, 319,
322, 335, 419, 421, 422, 423,
425, 427, 432, 433, 435, 436,
437, 438, 439, 443, 447, 452,
458, 459, 465, 470, 475, 483,
485, 491, 496, 504, 505, 506,
507, 510, 511, 512, 513, 518,
519, 520, 523, 524, 542, 565,
566, 570, 572, 581, 595, 596,
598, 599, 601, 608, 610, 613,
615, 618, 622, 623, 624, 625,
626, 629, 634, 635, 637, 638,
639, 640, 652, 653, 655, 656,
658, 660, 661, 663, 666, 668,
669, 670, 671, 673, 677, 679,
683, 684, 686, 688, 690, 691,
1396
692, 693, 694, 697, 701, 702,
703, 704, 708, 709, 710, 711,
712, 713, 715, 716, 717, 718,
720, 723, 724, 725, 726, 727,
728, 729, 730, 731, 733, 734,
735, 741, 753, 764, 786, 790,
791, 793, 795, 796, 800, 810,
812, 813, 814, 815, 816, 819,
821, 822, 823, 824, 825, 826,
827, 828, 829, 830, 832, 833,
836, 837, 839, 840, 843, 844,
845, 846, 849, 850, 851, 852,
861, 863, 866, 869, 871, 875,
876, 877, 878, 880, 881, 882,
883, 884, 909, 918, 946, 994,
1005, 1027, 1033, 1080, 1081,
1135, 1145, 1148, 1149, 1150,
1151, 1154, 1155, 1157, 1159,
1199, 1272, 1276, 1279, 1282,
1283, 1284, 1289, 1294, 1295,
1296, 1297, 1301, 1304, 1305,
1314, 1325, 1339, 1345, 1353,
1355, 1356, 1369, 1370, 1373,
1374, 1375, 1377, 1384, 1387,
1388, 1428
Eisenhart, L. P. 1353
Ellis 131
Enders, P. 1384
Eneström 1354
Engels, F. 99, 100, 232, 233, 323,
354, 515, 651, 1353, 1371
Engler, H. 1263, 1337
Enquist, B. 1348, 1353
Enzensberger, H. M. 22, 1353
Eötvös, R. v. 810, 812, 816, 817,
818, 1296
Epping, B. 1309, 1353
Ericksen, J. L. 1385
Eringen, A. C. 200, 289, 290, 934,
935, 942, 947, 953, 954, 958,
960, 962, 967, 969, 970, 973,
1073, 1075, 1353
Erlenmeyer, M.-L. 1370
Erlichson, H. 731, 1354
Esch, T. 1371
Escher, M. C. 425, 1362
30 Indices
Esfeld, M. 228, 259, 1354
Euclid 19, 115, 151, 158, 174, 331,
332, 426, 451, 472, 476, 477,
513, 583, 649
Euler, L. IX, V, VII, III, 25, 75, 78,
82, 83, 90, 92, 103, 110, 112,
119, 121, 122, 123, 128, 131,
132, 137, 144, 145, 146, 147,
162, 163, 173, 182, 186, 187,
199, 201, 202, 209, 214, 250,
286, 332, 378, 432, 433, 434,
438, 439, 442, 479, 482, 497,
498, 501, 505, 506, 512, 579,
581, 584, 585, 586, 587, 601,
617, 618, 630, 631, 681, 740,
745, 750, 755, 760, 787, 788,
790, 805, 823, 826, 843, 844,
855, 867, 878, 896, 899, 902,
903, 941, 949, 978, 983, 1002,
1009, 1013, 1022, 1026, 1029,
1031, 1036, 1039, 1047, 1051,
1055, 1056, 1059, 1060, 1061,
1064, 1067, 1079, 1082, 1084,
1094, 1100, 1101, 1103, 1105,
1106, 1112, 1113, 1116, 1117,
1121, 1127, 1128, 1129, 1162,
1166, 1167, 1168, 1169, 1170,
1177, 1178, 1181, 1265, 1272,
1273, 1289, 1301, 1302, 1311,
1354, 1384, 1386
Evans, D. V. 1371
Everett, H. 248, 1347
F
Faivre, A. 1354
Falk, G. 117, 118, 119, 497, 880,
1108, 1354
Falk, S. 307
Farebrother, R. W. 395
Faye, J. 323, 418, 1354
Fehrmann, D. 1379
Feldenkrais, M. 1058
Fellmann, E. A. 1368, 1384
Ferreira, P. G. 1349
Feuerbach, L. 515, 1312
30.1 Name index
Feyerabend, P. K. III, 14, 17, 21, 31,
36, 42, 61, 62, 64, 70, 71, 73, 77,
91, 101, 103, 116, 190, 211, 231,
253, 254, 278, 281, 314, 318,
320, 325, 327, 328, 336, 337,
428, 1194, 1203, 1270, 1304,
1311, 1313, 1314, 1355, 1358,
1364, 1380
Feynman, R. P. 19, 237, 289, 325,
380, 507, 686, 851, 902, 1355
Fichte, J. G. 5, 55, 274, 340, 1355
Fielding, H. 5, 1355
Fienbork, M. 1382
Fierz, M. 1374
Filonov, P. 325
Fischer, E. P. 55, 60, 241, 242, 255,
256, 257, 1355
Flandern, T. v. 700, 730, 876, 1355
Flannery, B. F. 1377
Flasch, K. 462, 1355
Fleck, L. 286, 420
Flierl, K. 1344
Flügge, S. 1343, 1356, 1381, 1384,
1385
Föppl, A. 117, 649, 790, 802, 803,
804, 815, 863, 866, 1037, 1042,
1046, 1356
Förster, G. 1349
Föttinger, H. 1180, 1226, 1356
Fourier, J. B. J. 354, 390, 391, 394,
398, 399, 400, 401, 404, 405,
408, 409, 410, 414, 531, 541,
546, 777, 929, 945, 1337
Fowler, F. G. 1356
Fowler, H. W. 1, 1356
Fowler, M. 1118
Fraassen, B. C. v. 42, 1356
Francis, B. A. 847, 1351, 1376
Frank, D. 1346, 1371, 1385
Frege, G. 197, 315
Fresenius, R. 1219, 1230, 1232,
1235, 1237, 1239, 1254, 1256,
1356
Fresnel, A. J. 947
Freud, S. 46, 243
1397
Friedlander, S. K. 930, 974, 978,
1090, 1356
Friedmann, A. 118, 199, 234, 256,
356, 357, 359, 363, 440, 452,
458, 462, 467, 474, 475, 493,
494, 511, 514, 515, 516, 517,
518, 521, 652, 653, 654, 662,
664, 665, 666, 672, 673, 816,
876, 882, 883, 887, 992, 1152,
1154, 1155, 1356
Friedrichs 880
Frisch, M. 1288
Froböse, R. 247, 1356
Froude, R. E. 1194
Froude, W. 1194
Frühwald, W. 301, 1356
Fues, E. 1352, 1382
G
Gadamer, H. G. 31, 423
Gal, O. 1378
Gale, R. M. 425, 1356
Galilei, G. 4, 20, 66, 85, 96, 97, 98,
101, 103, 139, 140, 145, 155,
163, 178, 193, 219, 256, 258,
277, 290, 435, 558, 585, 588,
591, 635, 659, 667, 672, 677,
684, 686, 696, 697, 748, 831,
989, 1273, 1277, 1294, 1347
Galison, P. 191, 459, 1350, 1356
Gälli, M. 1351
Gamov, G. 242, 694, 1357
Gardner, M. 486, 596, 636, 655,
669, 671, 805, 837, 1151, 1349,
1357, 1379
Gasch, R. 1084, 1106, 1357
Gassendi, P. 505, 797
Gatski, T. 1341
Gauss, C. F. 99, 393, 443, 578, 652,
653, 805, 839, 998, 1020, 1024,
1025, 1027, 1376
Gawedzki, K. 538, 977, 1357
Gear, C. W. 1038
Geier, M. 77, 1357
1398
Gelernter, D. 885
Gelfert, H.-D. 604
Genz, H. 228, 291, 419, 653, 694,
741, 1357
Gerthsen, C. 702, 930, 974, 1357
Ghyczy, T. v. 1375
Gibson, B. 1363
Giddings, S. B. 1348
Giesekus, H. 972, 1357
Gil, T. 286, 1357
Gläser, M. 797, 1366
Gleick, J. 9, 28, 54, 76, 211, 212,
218, 635, 722, 791, 799, 800,
802, 1139, 1357
Gliemann, G. 1358
Glockner, H. 307
Göbel, E. O. 1357
Gobrecht, H. 818, 819, 1151, 1357
Gödel, K. 22, 342, 343, 425, 1362,
1373
Goede, W. C. 878, 1357
Goethe, J. W. IX, III, V, VII, III,
VII, 3, 4, 7, 8, 9, 15, 20, 27, 28,
29, 30, 31, 36, 40, 42, 45, 48, 49,
50, 51, 61, 62, 63, 64, 65, 67, 68,
69, 82, 83, 117, 120, 125, 127,
136, 150, 151, 152, 158, 162,
190, 191, 197, 204, 206, 211,
212, 217, 218, 223, 231, 232,
233, 234, 239, 240, 245, 251,
254, 255, 260, 261, 267, 273,
274, 275, 276, 300, 306, 307,
309, 313, 314, 315, 317, 321,
322, 323, 327, 334, 338, 340,
354, 370, 381, 408, 427, 487,
510, 523, 525, 526, 527, 537,
566, 587, 596, 602, 613, 641,
645, 648, 649, 654, 655, 719,
725, 738, 743, 770, 778, 785,
806, 822, 831, 841, 845, 847,
863, 873, 911, 940, 966, 1029,
1054, 1062, 1064, 1079, 1084,
1089, 1097, 1172, 1194, 1201,
1202, 1217, 1222, 1240, 1253,
1287, 1290, 1305, 1311, 1313,
30 Indices
1314, 1317, 1321, 1328, 1331,
1335, 1344, 1345, 1352, 1357,
1358, 1363, 1381, 1387, 1428,
1430
Gogol. N. V. 287
Goldenbaum, U. 1368
Goldstein, H. 113, 1358
Goldstein, S. 1352
Gönner, H. 46, 91, 245, 874, 877,
1358
Good, I. J. 375, 623, 1118, 1315,
1358
Goodstein, D. 291, 1358
Gram, J. P. 394, 395
Grassi, E. 1375
Grasskamp, W. 34, 1358
Grassmann, H. 557, 1053
Grau, A. 52, 1358
Green, R. 839, 1171, 1174, 1358,
1376
Greenberg, M. J. 623, 1358
Greene, B. R. 13, 73, 83, 185, 243,
636, 844, 845, 864, 875, 876,
877, 879, 880, 885, 1289, 1298,
1358
Greiff, B. v. 229, 1358
Gross, D. 438
Gross, P. R. 245, 1358
Grosse, H. 537, 767, 1093, 1357,
1359
Grossmann, R. 236, 315, 316, 423,
1359
Grotjans, H. 976
Grünbaum, A. 698
Grünbein, D. 301
Gruppe, O. F. 110, 111, 294, 460,
1343
Guarino, N. 389, 944, 1359
Gudzent, C. 1349
Guevara, 'Che' 421
Guicciardini, N. 85, 211, 284, 1359
Guilini, D. 74, 608, 1359
Gummert, P. 112, 115, 116, 137,
192, 210, 438, 521, 631, 743,
30.1 Name index
803, 942, 946, 1005, 1009, 1010,
1015, 1060, 1064, 1089, 1125,
1140, 1164, 1359
Gunsteren, L. A. v. 1229, 1359
Guth, A. 884, 885
H
Habermas, J. 47, 1359, 1374
Hackenbroich, L. 1349
Hadamard, J. 945
Hahlweg, W. 1349
Hahn, W. 1023, 1359
Haller, R. 39, 1349
Hamel, G. 109, 110, 111, 113, 114,
115, 120, 121, 122, 134, 136,
138, 210, 233, 235, 461, 498,
593, 612, 650, 944, 1036, 1053,
1060, 1061, 1079, 1169, 1174,
1175, 1359
Hamilton, D. P. 1347
Hamilton, W. R. 444, 476, 487, 500,
969, 971, 1065, 1074, 1085,
1086, 1089
Hänggi, P. 704, 705, 706, 1359
Hankins, T. L. 207, 1360
Hänsch, T. W. 402
Hardenberg, F. L. v. 1374
Harig, L. 364
Harper, W. 213, 1357, 1360, 1367
Harries, S. 1317
Harrison, J. 659, 680
Hartmann, H. 1363
Hartmann, M. 427, 1360
Hartmann, N. 229, 247, 419, 1360
Hasinger, G. 91, 92, 1360
Haustein, H.-D. 1360
Havas, P. 624
Hawking, S. 55, 289, 422, 425, 462,
463, 1284, 1355, 1360, 1367,
1387, 1388
Hayward, J. 247
Heber, I. 119, 300, 301, 1360
Hecker, M. 1357
Hedrick, E. R. 1366
1399
Heer, F. 525, 1368
Hegel G. F. W. 5, 100, 140, 196,
232, 240, 294, 307, 340, 425,
1062, 1360, 1361, 1362
Heidegger, M. 42, 282, 462, 856
Heidelberger, M. 142, 253, 1342,
1360
Heimann, J. 416, 1317, 1360
Heinke, H.-J. 1265, 1360, 1364
Heisenberg, W. 75, 76, 223, 240,
244, 319, 410, 870, 871, 872,
910, 911
Heithoff, T. 277, 1360
Hellemans, A. 13, 230, 864, 1360
Heller, K. D. 69, 197, 234, 437, 502,
504, 1360, 1370
Hellweg, C. 247
Helmholtz, H. 62, 63, 100, 133, 143,
228, 233, 340, 363, 365, 448,
476, 479, 480, 510, 661, 662,
738, 768, 827, 954, 955, 1025,
1088, 1361
Hemingway, E. 1317
Hentrich, D. 1351, 1361
Herapath 505
Herbrand, X 334
Hermann, A. 10, 1317, 1371
Hermlin, S. 14, 213, 377, 1361,
1366, 1374
Herrgott, G. 1350
Herring, H. 1362
Herrmann, F. 119, 300, 307, 790,
820, 990, 991, 1317, 1356, 1361,
1367
Hertz, H. III, 26, 28, 42, 43, 54, 67,
82, 95, 102, 104, 105, 106, 107,
109, 111, 118, 133, 135, 136,
141, 142, 148, 187, 193, 201,
223, 225, 234, 236, 273, 278,
279, 317, 321, 330, 333, 339,
342, 354, 422, 465, 498, 500,
504, 523, 562, 601, 602, 617,
629, 645, 649, 728, 736, 737,
738, 832, 860, 863, 881, 1020,
1025, 1026, 1027, 1032, 1035,
1400
1039, 1040, 1066, 1067, 1088,
1097, 1098, 1099, 1180, 1287,
1289, 1290, 1302, 1305, 1310,
1311, 1318, 1326, 1361
Hesse, L. O. 224, 453
Hestenes, D. 92, 93, 139, 196, 368,
443, 499, 500, 652, 1361
Hieronymus, E. 192
Hilbert, D. 111, 115, 151, 174, 288,
307, 331, 332, 340, 341, 353,
404, 406, 444, 449, 451, 494,
514, 556, 745, 746, 852, 865,
901, 904, 944, 1040, 1220, 1284,
1313, 1361
Hille, H. 655, 1361
Hinst, P. 437, 1361
Hintikka, J. 288, 342, 1361
Hipparchos, of Nicaea. 1117, 1118
Hochhuth, R. 10, 1362
Hochkeppel, W. 1348
Hochkirch, K. 398, 1317, 1362
Höckendorf, H. 1355
Hodgson, P. E. 1346
Höfener, H. 294, 1362
Hoffmann, B. 624
Hoffmann, E. 1387
Hoffmann, N. 1367
Hoffmeister, J. 1360
Hofmannsthal, H. v. 271, 600, 1362,
1366
Holbach, G. 1341, 1362
Hölder, E. 1120, 1362
Holl, H. G. 1356
Hooft, G. t' 865
Hooke, R. 126, 721, 922, 972, 973
Hoppe, E. 1354
Horgan, J. 249, 1362
Horn, F. 294, 307, 407, 1219, 1236,
1237, 1254, 1255, 1262, 1270,
1336, 1339, 1362
Horne, M. 1352
Horváth, Ö. 109, 1362
Hövelmann, G. H. 1362
Huang, P. G. 1343
30 Indices
Huber, F. 378, 1362
Hübner, K. 41, 223, 1362
Hughes, V. W. 390, 751
Hugoniot 945
Huiskens, G. 882, 1362
Humboldt, A. v. 60, 191, 1318,
1350, 1373, 1387
Hume, D. 77, 252, 424, 1362
Hurley, J. J. 623, 875, 1363
Hürter, T. 734, 1362
Hurwitz, A. 412
Husserl, E. 19, 27, 62, 276, 462
Huston 1082
Hüther, G. 3, 33, 64, 271, 292, 303,
305, 1363
Hutter, K. 1119, 1363
Huxley, T. H. 63, 1363
Huyghens 155, 659
I
Ibata, R. 323, 1363
Icarus 280, 349, 1310
Ince, S. 207, 1379
Infeld, L. 624, 1353
Ingold, G.-L. 861, 1363
Inhetveen, R. 1363
ISO VII, 8, 10, 79, 250, 297, 389,
390, 549, 588, 903, 979, 1198,
1202, 1203, 1204, 1205, 1210,
1211, 1212, 1214, 1216, 1254,
1290, 1308
Israel, W. 1360
Itô, K. 1376
ITTC 309, 1198, 1203, 1204, 1254,
1260, 1281, 1325, 1336, 1338,
1339, 1362, 1363
J
Jacob, O. 60, 122, 1343, 1346, 1354,
1382
Jacobi, C. G. J. 300, 1022, 1032,
1088
Jacobson, T. A. 1283, 1363
30.1 Name index
Jacovici, B. 820, 1363
James, W. 32, 33, 38, 40, 60, 75,
193, 244, 259, 261, 274, 286,
426, 1363
Jammer, M. 27, 130, 131, 137, 138,
139, 208, 340, 503, 582, 628,
745, 751, 753, 785, 806, 811,
812, 814, 815, 817, 818, 820,
831, 832, 1289, 1295, 1301,
1305, 1363, 1364
Janich, P. 17, 19, 21, 22, 40, 53, 70,
78, 127, 152, 198, 215, 218, 250,
253, 259, 260, 280, 282, 290,
323, 326, 363, 364, 435, 437,
445, 458, 460, 462, 467, 502,
503, 655, 656, 659, 660, 661,
673, 762, 763, 764, 765, 767,
819, 820, 874, 878, 1305, 1310,
1362, 1364, 1372
Janositz, P. 1365
Jargodzki, C. P. 937, 1347, 1364
Jaspers, K. 58, 1312, 1364
Jaumann, G. 957, 959, 964
Jaynes, J. 273, 426, 1364
Jelden, E. 1364, 1385
Jeltsch, S. 1351
Jerusalem, W. 1363
Jesseph, D. M. 1344
Jessop, T. E. 1343
Jewitt, D. 323, 1364
Joffe, J. 301, 1364
Jöhnke, K. 1363
Johnson, G. 885, 886, 1338, 1349
Jones, D. E. 5, 1355, 1361
Joost, U. 200, 1364
Jordan, K. 1338
Jordan, P. 246
Josephson, B. D. 769
Jürgens, D. 1268, 1364
K
Kaiser, R. 1344
Kakalios, J. 296, 1365
Kaluza, T. 858
1401
Kamlah, A. 141, 1342
Kandel, E. 302, 303, 1365, 1371
Kane, G. 507, 1365
Kane, T. R. 115, 116, 298, 438, 500,
630, 631, 1035, 1037, 1038,
1039, 1040, 1041, 1046, 1056,
1082, 1088, 1095, 1108, 1125,
1170, 1246, 1272, 1365
Kant, I. III, 9, 14, 34, 42, 53, 79, 85,
99, 158, 196, 213, 221, 223, 232,
238, 242, 243, 252, 255, 256,
257, 258, 265, 268, 283, 335,
339, 340, 341, 418, 425, 433,
434, 435, 442, 458, 461, 480,
481, 564, 645, 649, 655, 656,
661, 662, 852, 873, 874, 1062,
1290, 1347, 1361, 1365, 1369
Kargon, R. H. 1349
Karhunen, K. 1058
Kármán, T. v. 379, 1024, 1026,
1096, 1097, 1098, 1099, 1180,
1181, 1302
Karnopp, D. 301, 1365
Kast, B. 273, 1365
Kastberger, K. 1362
Kästner, E. 1341, 1365
Kaube, J. 243, 296, 1365
Kauffman, S. 1365
Kay, A. C. 388
Kay, J. M. 928, 930, 931, 1260,
1365
Kayser, H.-G. 308
Kayser, R. 509, 753, 1365
Keim, R. G. 1349
Keller, W. 655
Kennedy, J. F. 117
Keynes, J. M. 78, 1365
Khaleghy, M. 704, 1366
Kibble, 769, 771
Kibel, J. A. 1366
Kipphard, H. 335, 1366
Kirchhoff, G. 100, 612, 737, 738
Kirchner, E. 1384
Kitcher, P. 103, 1366
1402
Klaczko-Ryndziun, S. 425, 1366
Klanner, R. 185, 848, 850, 862,
1298, 1366
Klein, F. 78, 198, 208, 307, 440,
443, 444, 446, 447, 449, 450,
451, 470, 471, 472, 474, 476,
477, 556, 858, 944, 1066, 1086,
1366, 1428
Kleinpeter, 234
Kleist, H. v. 271, 377, 600, 1366
Kleyna, J. 1364
Klitzing, K. v. 769
Kluge, G. 117, 520, 1383
Kniebe, G. 1345
Knobloch, E. 392, 1366
Knothe, K. 1357
Knowlson, J. 281
Kober, H. 1343
Kobus, H. 1344
Koch, B.-P. 1369
Koch, C. 910
Kochsiek, M. 763, 764, 797, 804,
812, 814, 1366
Kockelmans, J. J. 41, 42, 53, 341,
1366
Koeppen, D. 307
Kohut, A. 1352
Kolmogoroff, A. 126, 367, 1366
Kontovas, C. A. 371, 1366
Korn, A. 609, 1350
Korte, H. 1112, 1366
Kosinov, N. 853, 1366
Kosinova, S. N. 1366
Kotik, I. 406, 1366
Kotschin, N. J. 945, 981, 1097,
1098, 1366
Koyré, A. 1374
Kracht, M. 1317, 1322, 1366
Kraft, P. 305, 1367
Kraft, V. 77, 1367
Krallmann, H. 1389
Krauss, L. M. 296, 534, 623, 660,
1367
Krausser, P. 1388
30 Indices
Kreimer, D. 865
Kreuzer, E. 296, 1084, 1367
Krienes, K. 1366
Kripke, S. 424
Krokov, R. 817
Kronecker, L. 1044
Krüger, C. 1350
Kruppa, C. 1260
Krüss, J. 708, 1367
Kuczera, J. 234, 1361
Kues, N. v. 1383
Kuhn, D. 1358
Kuhn, T. S. 33, 71, 103, 216, 273,
286, 418, 1367, 1372
Kuiper, G. 1367
Kümmel, P. 1196
Kunik, A. 1117, 1367
Kupiainen, A. 1346, 1357
Kurzweil, R. 884
Kvasz, L. 34, 216, 287, 808, 809,
1367
L
Lachmann, A. 48, 1367
Ladishenskaja, N. 986
Lagrange, J. L. de 78, 96, 98, 104,
110, 122, 123, 136, 144, 145,
146, 147, 177, 201, 202, 209,
214, 280, 378, 610, 617, 618,
631, 823, 835, 905, 913, 983,
1016, 1021, 1022, 1031, 1032,
1034, 1036, 1039, 1046, 1047,
1051, 1052, 1055, 1056, 1059,
1060, 1061, 1064, 1065, 1067,
1079, 1082, 1083, 1084, 1094,
1095, 1105, 1106, 1166, 1167,
1170, 1177, 1178, 1181, 1289,
1301, 1302, 1311, 1345, 1367
Lakatos, I. 427, 428, 650
Lamb, H. 924, 928, 937, 942, 974,
1097, 1179, 1180, 1271, 1273,
1367
Lamé, G. 972
Lämmerzahl, C. 1159, 1367
30.1 Name index
Lanczos, C. 82, 111, 112, 113, 114,
237, 487, 617, 702, 807, 978,
1005, 1006, 1021, 1022, 1023,
1024, 1025, 1032, 1033, 1035,
1040, 1044, 1060, 1084, 1085,
1086, 1088, 1094, 1096, 1151,
1154, 1177, 1311, 1367
Landau, L. D. III, 74, 222, 229, 230,
300, 1367
Landé 869
Landgraf, C. 544, 1367
Lange, S. 1348
Langevin, M. 827
Lanier, J. 885
Laplace, P. S. de 177, 223, 370, 371,
390, 391, 395, 399, 407, 408,
410, 411, 412, 413, 768, 835,
876, 898, 1276, 1351
Laporte, H. 1375
Larmor, J. 590, 1371
Lassalle, F. 99
Latour, B. 301, 877, 1368
Laue, M. v. 634, 635, 835, 1368
Launder, B. E. 1368
Le Sage 238, 1352
Lee, H. E. 1357, 1365, 1368, 1382,
1388
Lefèvre, W. 1378
Legendre, A. M. 768, 1084, 1085,
1086
Lehmann, E. 1194, 1368
Leibniz, G. W. v. 4, 6, 9, 16, 27, 36,
43, 49, 59, 66, 71, 76, 78, 81, 83,
85, 91, 92, 94, 95, 128, 129, 131,
134, 144, 145, 198, 210, 211,
215, 232, 246, 247, 250, 278,
322, 330, 344, 392, 430, 431,
432, 433, 435, 464, 525, 526,
528, 559, 588, 603, 604, 609,
613, 614, 621, 664, 735, 746,
751, 808, 809, 826, 828, 844,
854, 859, 873, 876, 933, 1126,
1341, 1343, 1350, 1352, 1367,
1368, 1369, 1372, 1376, 1384,
1388, 1390
1403
Leighton, R. B. 1355
Leinfellner, W. 280, 317, 320, 1369
Leinkauf, T. 1368
Leitner, A. 1380
Lelgemann, D. 269, 1369
Lemaître, G. 876
Lemmers, M. 297, 1344, 1369
Lenard, P. 1361
Lenin, W. I. 234, 235
Leonhardt, R. W. 1365
Leopoldina 641, 1358
Leplin, J. 213, 250, 1360, 1369
Lerond, J. B. 1350
Lesser, M. 1038, 1369
Lessing, G. E. 35, 1383
Lessmölmann, A. 387, 1369
Leuchs, A and G. 1388
Leven, R. 379, 1023, 1092, 1369
Levi-Civita, x. 513, 624, 1054, 1055,
1080
Levison, D. A. 1365
Levitt, N. 1358
Li Po 707
Li, W.-C. 1368
Lichtenberg, G. C. 8, 35, 38, 41, 43,
77, 78, 137, 198, 200, 212, 258,
275, 311, 322, 327, 339, 347,
426, 456, 467, 551, 581, 582,
620, 772, 776, 807, 810, 812,
817, 834, 841, 860, 876, 877,
902, 987, 988, 1307, 1321, 1322,
1332, 1364, 1369, 1430
Liebknecht, K. 1361
Liebscher, D.-E. 464, 1369
Lifschitz, J. M. III, 74, 222, 229,
230, 300, 1367
Lindner, G. F. L. 294
Lipschitz, R. 476
Liu, G.-S. 1341
Ljapunov, A. M. 1023
Lloyd, S. 884, 885, 886
Lobachevsky, N. J. 443, 448, 449,
455
Locke, J. 43, 45, 77
1404
Lockwood, M. 297
Loève, M. 1058
Longfellow, H. W. 201
Lopes Coelho, R. 67, 108, 142, 149,
161, 175, 186, 611, 765, 1032,
1318, 1369
Lorentz, H. A. 455, 456, 457, 483,
487, 489, 490, 491, 494, 495,
496, 624, 637, 683, 690, 694,
695, 696, 697, 698, 699, 706,
707, 711, 712, 715, 716, 717,
723, 725, 726, 728, 729, 730,
731, 732, 734, 852, 1080, 1282,
1297, 1369, 1384
Lorenzen, P. 118, 127, 152, 198,
221, 278, 383, 435, 481, 662,
764, 1345, 1363, 1369
Lovett, R. 1139
Lowe, E. J. 498, 1348
Luce, A. A. 1343
Lucretius, T. C. 36, 282, 470, 504,
506, 507, 824, 840, 851, 854,
879, 991, 1298, 1369
Ludwig, R. 256, 258, 339, 419, 434,
435, 458, 564, 661, 1365, 1369
Lukasiewicz, J. 387
Lurie, A. I. 115, 542, 923, 936,
1016, 1036, 1037, 1039, 1041,
1052, 1054, 1060, 1077, 1079,
1080, 1084, 1087, 1089, 1120,
1124, 1127, 1369, 1370
Luther, M. 246, 1353, 1361
M
Mach, E. 36, 47, 54, 59, 60, 69, 70,
73, 75, 76, 77, 82, 83, 92, 101,
102, 103, 105, 106, 107, 119,
128, 131, 138, 141, 148, 154,
155, 159, 179, 186, 193, 197,
199, 206, 210, 211, 213, 214,
232, 234, 235, 245, 246, 250,
252, 268, 273, 284, 322, 347,
422, 427, 437, 445, 459, 460,
478, 502, 503, 504, 506, 525,
556, 587, 629, 637, 638, 652,
30 Indices
727, 739, 743, 744, 746, 748,
811, 822, 823, 824, 825, 827,
828, 829, 835, 849, 855, 869,
876, 910, 1066, 1270, 1273,
1274, 1275, 1281, 1289, 1310,
1328, 1342, 1345, 1346, 1353,
1360, 1364, 1370, 1373, 1375,
1387
Madelung, E. 907
Mahr, B. 316, 1322, 1370
Maitland, F. 1376
Maldacena, J. 863, 864, 1370
Mallarmé, S. 2, 375, 377, 1370
Mangulis V. 406, 1366
Mannheim, K. 32, 258, 1370
Margenau, H. 380, 1370
Markoff, A. A. 870
Markovitz, H. 1349
Marquardt, O. 339, 1370
Marsden, J. E. 354, 1341, 1348,
1370
Martens, E. 9, 12, 30, 227, 295, 312,
340, 498, 874, 1322, 1370, 1371
Martin-Löf, P. 315, 1371
Marx, K. 13, 99, 243, 322, 651,
1312, 1313, 1353, 1371
Masilge, C. 1265
Masolo, C. 1359
Mathcad 201, 363, 395, 1099, 1110,
1244, 1371
Matter, K. 1354
Mautner, F. H. 1369
Mawson, C. O . S. 1379
Maxwell, J. C. III, 28, 31, 119, 121,
158, 308, 341, 368, 505, 574,
583, 590, 627, 645, 673, 705,
728, 760, 789, 790, 792, 815,
827, 852, 930, 938, 972, 974,
1012, 1025, 1027, 1054, 1290,
1371
Mayer, H. 1343
Mayer, J. R. 140
Mayer, M. E. 1384
Mazur, E. 302, 1371
McElholm, D. 1376
30.1 Name index
McEwan, I. 1346
McGlinn, S. 1346
McIntosh, E. 1356
Mciver, P. 405, 1371
McKinsey 134, 135
Mearns, H. 390
Medawar, P. B. 253, 1371
Meggle, G. 1342
Meitner, L. 1347
Meixner, U. 218, 1371
Melville, H. 10, 1317, 1371
Melzer, H. 1371
Meng, F. 1389
Meng, J.-H. 1383
Menne, A. 1344
Menter, F. 975, 976, 1371
Mercier, A. 276, 656, 732, 824, 1371
Mercier, P. 322, 1371
Merve, A. v. d. 1385
Meschkowski, H. 351, 384, 1371
Meyenn, K. v. 1374
Meyer, W. H. 1348
Michelet 55
Michell, J. 877
Michels-Wenz, U. 1374
Mie, G. 240, 852
Milne, A. A. 385, 740, 1372
Milonni, P. 868
Minachin, V. 1342, 1386
Minkowski, H. 73, 74, 455, 456,
484, 493, 494, 608
Minsky, M. 884
Mises, R. v. 77, 202, 212, 358, 367,
368, 370, 371, 372, 379, 428,
460, 872, 913, 1012, 1013, 1035,
1104, 1311, 1372
Mittelstaedt, P. 136, 263, 264, 268,
382, 436, 480, 482, 498, 559,
660, 661, 662, 764, 1372
Mittelstraß, J. 66, 67, 69, 141, 149,
188, 528, 1372
Möbuß, S. 856, 1372
Mohrs, T. 1351
Monken, H. 1387
1405
More, H. 91
Morgenstern, C. 604
Morgenstern, D. 84, 120, 130, 206,
498, 550, 604, 942, 944, 947,
981, 1032, 1048, 1060, 1089,
1372
Morley, E. W. 720, 826, 827
Mormann, T. 1372
Morsch, O. 402
Mosch, R. 307
Moses 276, 338, 626, 878
Mössbauer, R. 837
Most, G. W. 1368
Motte, A. 86, 87, 88, 89, 90, 140,
194, 1328, 1373, 1374, 1384
Motz, H. D. 28, 1372
Moulines, X. 235
MPIWG 43, 49, 57, 125, 207, 217,
230, 319, 431, 704, 727, 1062,
1097, 1327, 1345, 1350, 1358,
1359, 1373, 1378
Mueller, G. O. 725, 728, 1373
Mukunda, N. 1384
Müller, H. v. 1347
Müller-Graf, B. 1336
Mulligan, K. 1373
Münchhausen 11, 40, 177, 373, 621,
1193, 1347
Muschg, A. 1358
Musil, R. 235, 1370, 1373
Musser, G. 878, 1373
N
Nadolny, S. 20, 1373
Nagel, E. 342, 343, 1312, 1373,
1384
Nauenberg, M. 1349, 1374
Navier, C. L. M. H. 905, 919, 938,
939, 974, 976, 977, 979, 980,
981, 982, 985, 986, 1265
Nedden, M. z. 1389
Neff, K. 1364
Neumann, J. v. 244, 371
Neunzig, H. A. 197, 241, 1373
1406
Neurath, O. 323
Newman, J. N. 942, 985, 1049,
1171, 1274, 1275, 1276, 1281,
1373
Newman, J. R. 1373
Newton, I. IX, III, V, VII, III, VI, 7,
9, 18, 19, 25, 28, 30, 31, 40, 42,
54, 60, 66, 67, 71, 75, 76, 78, 80,
82, 83, 84, 85, 86, 87, 88, 89, 90,
91, 92, 93, 94, 95, 97, 103, 104,
112, 115, 117, 119, 123, 126,
128, 129, 131, 134, 136, 138,
139, 140, 142, 143, 144, 145,
146, 147, 148, 151, 153, 154,
155, 156, 157, 158, 159, 160,
161, 162, 163, 166, 169, 171,
173, 174, 178, 180, 181, 182,
184, 185, 186, 187, 188, 194,
195, 198, 199, 201, 209, 210,
211, 212, 213, 214, 215, 218,
220, 225, 232, 237, 240, 242,
247, 250, 255, 256, 267, 269,
275, 278, 282, 283, 284, 286,
296, 331, 332, 341, 350, 356,
363, 391, 399, 425, 427, 429,
430, 431, 432, 433, 434, 437,
438, 439, 442, 458, 459, 460,
461, 462, 465, 467, 469, 471,
477, 478, 479, 482, 489, 491,
494, 496, 497, 501, 502, 504,
506, 509, 512, 513, 520, 521,
538, 553, 556, 557, 558, 559,
560, 571, 574, 581, 583, 584,
585, 586, 588, 590, 591, 592,
593, 594, 595, 596, 600, 601,
604, 608, 610, 611, 612, 613,
615, 618, 619, 621, 622, 626,
629, 634, 637, 638, 639, 640,
642, 644, 645, 647, 651, 652,
655, 656, 657, 672, 673, 681,
686, 720, 721, 723, 726, 737,
738, 739, 740, 742, 745, 750,
751, 752, 755, 758, 760, 761,
762, 763, 766, 767, 781, 784,
785, 786, 790, 791, 795, 796,
797, 799, 800, 802, 805, 806,
807, 808, 810, 811, 813, 814,
30 Indices
815, 816, 818, 821, 822, 823,
824, 826, 827, 828, 831, 832,
835, 838, 840, 841, 842, 843,
844, 845, 851, 854, 855, 857,
858, 861, 866, 873, 875, 877,
879, 880, 884, 903, 922, 966,
972, 980, 999, 1022, 1027, 1031,
1059, 1084, 1106, 1113, 1133,
1139, 1140, 1141, 1148, 1152,
1157, 1163, 1177, 1183, 1194,
1270, 1284, 1289, 1292, 1294,
1296, 1297, 1298, 1300, 1311,
1314, 1317, 1318, 1323, 1324,
1327, 1328, 1338, 1342, 1345,
1346, 1347, 1348, 1349, 1351,
1357, 1359, 1360, 1365, 1373,
1374, 1380, 1381, 1384, 1387,
1389, 1428
Nicolai, H. 863, 1374
Niemz, M. H. 247
Nietsch, T. 1381
Nietzsche, F. 191, 241, 273, 301,
874
Noble, C.-A. 44, 1366
Noether, E. 1032, 1033, 1283, 1385
Nogué, J. C. 880, 1374
Noll, W. 110, 122, 128, 341, 611,
913, 935, 967, 968, 1195, 1349,
1374
Nollert, H.-P. 1379
Nordhoven, E. 158, 1374
Noske, R. 1355
Novak, H. 1351
Novalis V, 28, 35, 54, 62, 189, 190,
272, 297, 348, 364, 393, 439,
664, 744, 923, 933, 942, 1050,
1140, 1232, 1309, 1374
Nowacki, H. 389, 1237, 1318, 1362,
1374
Nozick, R. 424, 1375
O
Ockham, W. of 554
Oetinger, B. v. 13, 61, 62, 65, 134,
554, 1310, 1375
30.1 Name index
Ohanian H. C. 811, 1375
Oldroyd, J. G. 959
Olschki, L. 56
Onorato, M. 905, 1375
Osborne , A. R. 1375
Osiander, A. 142, 528
Ostwald, W. 76, 1066
Overbye, D. 885
Ovidius, P. N. 280, 1375
P
Padelt, E. 358, 659, 666, 765, 766,
767, 768, 769, 771, 1375
Padgett, 753
Pádua, S. 1387
Pais, A. 169, 180, 181, 504, 507,
624, 625, 638, 658, 684, 703,
718, 724, 727, 728, 729, 730,
735, 741, 823, 825, 826, 827,
849, 852, 1282, 1375
Papini, G. 258, 259
Parentani, R. 1363
Pargetter 131
Päsler, M. 497, 955, 1022, 1088,
1375
Passerello 1082
Passon, O. 899, 900, 902, 906, 907,
908, 1318, 1375
Pauli, W. 76, 246, 247, 319
Paulos, J. A. 7, 42, 82, 293, 294,
295, 305, 349, 370, 371, 376,
377, 397, 593, 907, 1290, 1375
Pauri, M. 1341
Paynter 301
Pei, M. 1375
Peirce, C. S. 139
Peña, L. de la 1346
Penrose, R. 419, 422, 423, 827, 910,
1355, 1360, 1375
Petitjean, P. 1380
Petronievic, B. 1345
Pfister, H. 1342
Pieper, A. 227, 1375
Pierson, W. J. 1383
1407
Pinch, T. 1350
Piron, J. 1381
Pittner, L. 1359
Planck, M. 34, 57, 64, 102, 151, 207,
230, 285, 402, 422, 431, 437,
504, 720, 746, 829, 853, 857,
858, 859, 861, 863, 865, 868,
870, 875, 877, 902, 903, 1027,
1317, 1318, 1370, 1373, 1375,
1378
Platon 30, 35, 43, 45, 55, 107, 125,
199, 246, 282, 293, 308, 319,
346, 418, 420, 422, 423, 426,
523, 524, 525, 550, 643, 644,
841, 843, 847, 874, 1225, 1293,
1314, 1318, 1375
Plotin 462
Pohl, R. W. 135, 180, 181, 326, 460,
468, 694, 702, 704, 705, 717,
719, 755, 770, 782, 803, 811,
813, 821, 830, 1054, 1375, 1376,
1379
Poincaré, H. 18, 304, 307, 446, 447,
449, 462, 467, 470, 474, 475,
476, 662, 664, 729, 730, 813,
814, 824, 1282, 1376
PoincaréL , L 23, 827, 1376
Poisson, S. D. 179, 716, 718, 719,
723, 788, 789, 833, 835, 945,
974, 980, 981
Poli, R. 316, 1376
Polkinhorne, J. C. 92, 1376
Pollack, J. 885
Pollock, J. L. 418, 1376
Polya, G. 14, 15, 16, 70, 371, 1376
Pompe, B. 1369
Pooh, B. 297, 385, 424, 598, 740,
786, 1328, 1372, 1388
Popp, K. 36, 81, 198, 1366, 1369,
1376
Pöppe, C. 380, 396, 1376
Popper, K. R. 5, 6, 7, 12, 33, 40, 42,
60, 70, 75, 76, 77, 103, 126, 188,
190, 229, 242, 254, 261, 263,
268, 270, 282, 287, 306, 328,
1408
329, 333, 334, 339, 346, 371,
372, 373, 374, 380, 427, 445,
465, 466, 589, 591, 856, 860,
869, 870, 871, 872, 904, 1291,
1312, 1376
Pörksen, B. 1356
Poser, H. 15, 28, 36, 67, 72, 85, 92,
103, 229, 230, 247, 253, 276,
287, 323, 325, 336, 344, 435,
525, 1368, 1376
Poset, C. 1387
Posner, R. 1342
Pössel, M. 172, 596, 634, 669, 701,
805, 851, 863, 1318, 1345, 1377
Post, B. 1375
Potter, F. 1364
Poundstone, W. 1377
Povilaitis, D. 1379
Poynting, J. H. 972
Prager, W. 289, 578, 919, 953, 954,
955, 958, 959, 967, 973, 1055,
1057, 1072, 1377
Prandtl, L. 930, 931, 974, 986, 1099,
1377
Pratchett, T. 41, 46, 73, 227, 243,
282, 417, 430, 436, 553, 581,
883, 1377
Press, W.H. 281, 395, 399, 413,
1038, 1346, 1354, 1358, 1377,
1379
Preston, J. 1355
Preuss, O. 1367
Preusser, W. 1353
Price, W. G. 302, 925, 1377
Prigogine, I. 41
Proclus 339, 476
Protagoras 647
Prümper, J. 1348
Psaraftis, H. N. 1366
Ptolemaeus, C. 655, 1117
Pukelsheim, F. 1342
Pulte, H. 146
30 Indices
Q
Qassemi, F. 1366
Quine, W. V. O. 259
R
Raatzsch, R. 196, 275, 347, 1377
Raddatz, F. J. 17
Radnitzky, G. 72, 246, 1378, 1381
Ramachandran 273
Ramond, P. 230, 1378
Ramsey, F. P. 1388
Randall, L. 217, 246, 329, 380, 427,
438, 450, 486, 507, 508, 636,
702, 720, 807, 851, 853, 880,
1289, 1378
Randow, G. v. 370, 1378
Rankine, W. J. M. 945, 1218, 1224
Rapoport, A. 127, 1378
Ratiu, T. S. 354, 1348
Rauchhaupt, U. v. 425, 1378
Rauner, M. 766, 1378
Ravielli, A. 1357
Ray, T. P. 721, 880, 884, 1378
Rayleigh, J. W. S. 768, 928
Reckling, K.-A. 115, 1060, 1359
Redtenbacher, F. J. 506
Reece, G. J. 1368
Reech, 815
Reggia, J. A. 1382
Reichenbach, H. 66, 69, 252, 314,
319, 339, 436, 494, 698, 727,
768, 881, 1378
Reinhardt, F. 441, 446, 447, 469,
471, 632, 1040, 1359, 1378
Remmert, R. 1343
Renn, J. 2, 107, 122, 123, 124, 125,
207, 218, 219, 228, 284, 1378
Resch-Esser, U. 877, 1378
Reuter, H. 1355, 1368
Reynolds, O. 928, 936, 937, 938,
939, 974, 978, 980, 986, 1175
Reynolds, R. J. 988, 1378
Rheinberger, H.-J. 469
30.1 Name index
Rheticus, G. J. 1117, 1350
Richter, L. 1351
Riegels, F. 1380
Rieger, S. 1378
Riemann, G. F. B. 73, 443, 475, 511,
513, 653
Ripota, P. 130, 238, 827, 876, 883,
1378
Rivlin, R. S. 959
Robb, A. 698
Robert, R. 1181, 1378
Rodi, W. 939, 975, 977, 1368, 1379
Roe, S. 2, 1379
Rogowski, A. 1381
Roll, P. G. 817
Roller, D. 1373
Rorty, R. 423
Rosa, H. 648, 1379
Rose, N. W. 1038, 1366
Rosenberg, P. 1195
Rosenberg, R. C. 301, 504, 1365
Rosenberg, S. 13, 523, 1379
Rosenbrock, H. H. 1038
Rosenkranz, K. 294
Rosnick, M. 1346
Ross, P. E. 296, 309, 1379
Roßler 1368
Roth, B. 1345
Roth, E. 206, 302
Rouse, H. 207, 1344, 1379
Routh, E. J. 115, 412, 1032, 1086,
1087, 1088, 1108, 1120, 1379
Rovelli, C. 329, 863, 864, 865, 1379
Rucker, R. 484, 1379
Ruder, H. 694, 703, 1297, 1379
Rudio, F. 1354
Rudolph, E. 1368
Rumsey, C. 1341
Ruppel, W. 1108, 1354
Russ, J. 16, 1379
Russell, B. III, 35, 36, 37, 38, 41, 46,
47, 77, 83, 119, 258, 261, 342,
348, 386, 418, 427, 805, 1270,
1409
1305, 1308, 1311, 1313, 1379,
1388
Russell, J. S. 499, 1379
Ruttmann, I. 1347
Rydberg, J. R. 854
Ryle, G. 591
Rynasiewicz, R. 431, 1380
S
Saint-Venant, B. de 980, 981
Sakharov, A. 866, 867, 905
Salomo 429
Samulat, G. 186, 323, 854, 1343,
1380
Sanchez-Palencia, E. 960, 1380
Sands, M. 1355
Sass, F. 307, 453, 456, 469, 774,
915, 1049, 1380
Sauer, J. 1366
Scannapieco, E. 1380
Schäfer, H. 307, 1357
Schalley, C. 1389
Schank, P.-G. 329, 1380
Scharnowski, S. 1350
Scheck, F. 93, 118, 216, 230, 881,
1060, 1380
Scheel, K. 768, 1380
Scheibe, E. 18, 64, 126, 158, 225,
226, 239, 240, 327, 419, 436,
446, 526, 902, 910, 911, 1066,
1328, 1380
Schelling, F. W. J. 55, 340
Schewe, K.-D. 390
Schiller, F. 4, 32, 130, 197, 204,
218, 252, 258, 313, 327, 627,
629, 782, 845, 1158, 1331, 1350
Schiller, X. 32
Schilpp, P. A. 1353, 1376
Schirawski, N. 649, 1380
Schleiermacher, F. E. D. 31, 340,
1375
Schlichting, H. 307, 931, 938, 942,
974, 975, 985, 986, 1260, 1380
Schlitt, H. 925, 1380
1410
Schlossberger, E. 291, 1380
Schmid, W. 1353
Schmidt, D. 1349
Schmidt, Erhard 395
Schmidt, Ernst 159, 704, 850, 1036,
1090, 1380
Schmidt, H. G. 1226, 1256, 1380
Schmidt, K. 1388
Schmidt, P. 1354
Schmidt, T. 1362
Schmidt, W. 1363
Schmiechen, C. P. 1318
Schmiechen, M. IX, VII, II, IV, 10,
342, 384, 393, 395, 398, 399,
400, 404, 411, 413, 414, 541,
543, 544, 561, 570, 807, 950,
1062, 1070, 1076, 1077, 1078,
1084, 1097, 1165, 1166, 1180,
1187, 1188, 1189, 1203, 1205,
1211, 1222, 1225, 1226, 1228,
1229, 1230, 1232, 1237, 1256,
1260, 1262, 1263, 1268, 1270,
1281, 1325, 1335, 1336, 1337,
1338, 1339, 1340, 1428
Schmutzer, E. 904, 1380
Schnädelbach, E. 36, 1380
Schneider, G. 544, 1367
Schneider, M. 439, 440, 494, 556,
640, 665, 679, 913, 914, 1380,
1381
Schnieder, E. 337, 1381
Schnieder, L. 1381
Schopenhauer, A. 312, 340, 514,
856, 1372, 1381
Schreier, W. 85, 1381
Schröder, J. 1365
Schrödinger, E. 13, 200, 246, 334,
419, 466, 868, 872, 895, 897,
899, 900, 902, 903, 904, 905,
908, 932, 1059, 1283, 1299,
1325, 1381
Schüller, V. 60, 86, 87, 88, 90, 140,
162, 211, 215, 282, 588, 1148,
1318, 1374, 1378
Schulz, G. 1374
30 Indices
Schuster, S. 291, 294, 308, 1346,
1353
Schütt, E. 556, 1381
Schützhold, R. 1283
Schwab, J. 1382
Schwanecke, H. 405, 1381
Schwaninger, A. 127
Schwanitz, D. 241, 242, 1381
Schwartz, M. 1389
Schwemmer, O. 221, 1369
Sedlmaier, E. 875
Sedow, L. I. 1218, 1262, 1381
Seiberg, N. 438
Seibold, F. 37, 1381
Seidel, S. 1358
Seiffert, H. 72, 91, 1328, 1381
Selleri, F. 1355, 1381
Semprun, J. 131, 1381
Senger, H. v. 62, 1381
Sepper, D. 4, 29, 83, 111, 162, 190,
191, 233, 260, 274, 276, 313,
314, 315, 322, 596, 1321, 1381
Serio, M. 1375
Serrin, J. 916, 941, 943, 944, 971,
981, 982, 1381
Sexl, R. U. 1374
Shapiro, I. I. 1151, 1157, 1158, 1381
Shara, M. 1363
Sharma, S. D. 416, 1237, 1381
Shepard, E. H. 1372
Sheppard, D. S. 1364
Sherwood, B. A. 212, 1381
Shimony, A. 908, 1352
Showalter, M. R. 1347
Shvartsman, O. V. 1386
Silcock, A. 122, 128, 245, 390, 420,
457, 1382
Simhoy, M. 827
Simon, E. 1377
Simon, H. A. 67, 158, 296, 1382
Simon, K.-H. 1366
Simonyi, C. 13, 523, 1379
Singer, G. 234, 474, 514, 1356
Singer, W. 1309, 1353
30.1 Name index
Sipper, M. 22, 1382
Smalltalk 388, 389, 1351, 1382
Smeaton, A. 1348
Smith, G. E. 1349, 1360, 1374
Smolin, L. 883, 1365, 1382
Snay, R. 309
Sneed, J. D. 67, 235, 254, 1382
Snow, C. P. 224, 241, 244, 262,
1382
Sobel, D. 659, 1382
Sobotta, H. 1382
Söding, H. 416, 1318
Soeder, H. 1378
Sohst, H. 1318
Sokal, A. 77, 153, 208, 245, 298,
424, 425, 445, 1327, 1343, 1382
Soliman, M. S. 1100, 1382
Solms, M. 46, 1382
Solodovnikov, A. S. 451, 1342
Solodovnikov, V. V. 548, 1382
Sommerfeld, A. 117, 118, 437, 635,
636, 863, 905, 1035, 1036, 1039,
1066, 1067, 1086, 1087, 1097,
1099, 1117, 1382
Sontag, S. 17
Southwell, R. V. 905, 1382
Spalding, D. B. 308, 704, 928, 1036,
1383
Sparenberg, J. A. 1226, 1256, 1336,
1380
Speiser, A. 1354
Spillner, V. 186, 1383
Spinoza, B. 468
Spolsky, J. 13
Springer, M. 910, 1383
Square, A. 1327, 1341, 1379, 1430
St. Denis, M. 925, 1383
Stachel, J. 1352
Stadler, F. 1372
Staguhn, G. 652, 837, 1383
Stallman, R. 396
Stapp, H. 910
Steck, M. 689
Steden, M. 1268, 1383
1411
Steeb, W.-H. 1367
Stegmüller, W. 8, 66, 67, 69, 188,
424, 1383
Stein, E. 1376
Stein, G. 467
Stein, K. 1376
Stein, N. v. d. 1268
Stein, W. 805
Steiner, H.-G. 355, 1343
Steiner, J. 1111, 1112
Steinhardt, P. 884
Steinle, F. 217, 1097, 1383
Stemper, I. 41
Stephan, C. 1342
Stephani, G. 117, 488, 1383
Stephenson, F. R. 655, 1383
Stewart, I. 1377
Stokes, G. G. 905, 919, 938, 939,
945, 969, 974, 976, 977, 979,
980, 981, 982, 985, 986, 1175,
1265
Straggas, J. 1346
Strasser, G. 1198
Straub, D. 18, 59, 86, 223, 224, 225,
1383
Strauch, D. 601, 1383
Strauss, B. 35, 1383
Strawson, P. F. 424
Streißler, A. 1346
Streißler, F. 1346
Stückrath, T. 781, 1176, 1383
Sturm, J. C. 1167
Sudarshan, E. C. G. 122, 744, 1384
Suisky, D. 431, 697, 896, 902, 1318,
1384
Sunzi 62, 1384
Suppes 2, 135, 142, 143, 144, 156,
177, 318, 350, 698, 1384
Sussman, G. J. 299, 1384
Sutcliffe, D. 1317
Swift, J. 7, 20, 44, 45, 85, 108, 117,
209, 251, 260, 270, 281, 293,
320, 438, 611, 798, 826, 1309,
1315, 1328, 1384
1412
Synge, J. L. 74, 275, 354, 608, 1095,
1384
Szabó, I. 4, 56, 65, 66, 84, 92, 96,
102, 112, 113, 120, 130, 138,
140, 206, 207, 210, 232, 287,
497, 550, 579, 587, 610, 612,
613, 624, 625, 631, 662, 752,
808, 941, 942, 947, 949, 974,
980, 981, 982, 985, 1015, 1016,
1021, 1022, 1025, 1026, 1048,
1059, 1060, 1064, 1083, 1089,
1112, 1125, 1166, 1167, 1168,
1372, 1384
T
Tahan, M. 39, 1384
Talkner, P. 1359
Talley, W. 1385
Tannenbaum, A. R. 1351
Tarski, A. 261, 262
Tattersall, I. 234, 272, 1385
Taube, G. 33, 1385
Taylor, B. 536
Taylor, D. W. 1194, 1385
Taylor, G. I. 925, 1385
Tegmark, M. 83, 469, 887, 1385
Teller, E. 156, 289, 378, 872, 1385
Teller, W. 1385
Tenniel, J. 1348
Tesar, L. 102, 107, 189, 196, 435,
506, 736, 824, 855, 856, 1385
Tesla, N. 511
Tetens, H. 138, 287, 673, 765, 767,
1385
Teukolsky, S. A. 1377
Thirring, H. 1378, 1385
Thomas, J. B. 1382
Thomson, W. Sir, Kelvin 1088, 1282
Thorp, R. 88, 89
Thüring, B. 502
Tieck, L. 433
Tietz, H. 1343
Tipler, F. F. 245, 1385
Tobies, R. 1032, 1385
30 Indices
Toffoli, T. 884, 886
Tolson, J. 245, 287, 1385
Tolstoi, L. 61
Topper, L. 1356
Törne, L. v. 1365
Toupin, R. 1385
Trautman, A. 881, 1353
Trechow, P. 305, 1385
Treder, H.-J. 33, 816, 824, 1154,
1155, 1385
Treitz, N. 445, 621, 622, 1036, 1148,
1385
Trostel, R. 967, 1344, 1385
True 93, 131
Truesdell, C. A. 29, 33, 41, 65, 66,
85, 92, 110, 113, 115, 117, 118,
123, 128, 129, 134, 135, 137,
147, 148, 200, 205, 206, 207,
208, 209, 213, 214, 231, 235,
249, 250, 253, 254, 269, 280,
283, 290, 311, 332, 340, 341,
387, 389, 431, 434, 499, 503,
505, 585, 589, 703, 803, 931,
934, 935, 936, 941, 942, 943,
944, 945, 946, 947, 958, 959,
960, 967, 968, 969, 1167, 1168,
1169, 1270, 1301, 1309, 1310,
1313, 1344, 1352, 1354, 1356,
1358, 1360, 1363, 1379, 1384,
1385, 1386
Tschechow, A. 43
Tucholski, K. 106
Tuck, E. O. 1275, 1281, 1386
Tukey, J. W. 409, 412, 1344
Tzénoff, I. 1061
U
Ueding, G. 1386
Ulenbrook, J. 525, 1386
Ulmann, G. 304, 1386
Unruh, W. G. 858, 1283
Urban, M. 270, 273, 439, 1386
Urstadt, B. 112, 248, 1386
30.1 Name index
V
Vagliente, V. N. 1367
Vakar, G. 1387
Valentiner, S. 835, 1386
Varignon 525
Vasek, T. 54, 104, 1386
Vattino, G. 1313
Veltman, M. 865
Vetter, H. 1355, 1367
Vetterling, W. T. 1377
Viehöver, U. 83, 1386
Vinberg, E. B. 451, 1342, 1386
Vinci, L. da 97, 379, 1181
Visser, M. 462, 463, 1284, 1387
Vlaev, S. J. 1349
Vogtsmann, K. 1342
Völker, G. 1383
Vollmer, G. 288, 1387
Voltaire 85, 92, 215, 1345, 1387
Volterra, V. 1061
Voronets, P. V. 1061
Voss, A. 1255, 1263, 1337
Vygotsky, L.S. 277, 1387
W
Waals, J. D. v. d. 868, 1090
Wagner, K. 15, 1244, 1247, 1318,
1387
Wagner, R. 1232, 1387
Wahsner, R. 84, 86, 103, 107, 131,
152, 154, 155, 161, 252, 425,
1062, 1345, 1370, 1387
Walborn, S. P. 1387
Wald, R. M. 1387
Waldrop, M. M. 20, 1387
Walley, J. T. 1361
Walther, P. 7, 1387
Walton, G. 728, 1387
Wand, G. 26, 421, 524, 691
Wang, C. C. 1343
Waterston 505
Webaliza 16
Webb, J. K. 1343
1413
Weber, J. 1351
Weber, M. 1387
Weber-Schäfer, P. 1377
Weigmann, K. 271, 1387
Weinberg 123, 228
Weinblum, G. 1218, 1381
Weingartner, P. 382, 1372, 1388
Weinig, P. 1378
Weinstein, A. 1342
Weischedel, W. 1365
Weiß, U. 1351
Weizsäcker, C. F. v. 27, 35, 37, 38,
74, 79, 220, 221, 222, 372, 374,
384, 458, 698, 911, 1388
Welzer, 302
Wertheim, M 1388
Weyl, H. 55, 199, 225, 238, 239,
240, 249, 268, 339, 357, 363,
381, 437, 438, 441, 444, 446,
450, 456, 458, 460, 461, 462,
465, 468, 469, 473, 474, 475,
485, 510, 511, 512, 513, 514,
515, 518, 521, 586, 621, 648,
649, 653, 664, 666, 673, 698,
793, 817, 823, 824, 826, 837,
840, 852, 853, 882, 883, 884,
934, 1113, 1149, 1150, 1151,
1153, 1296, 1311, 1388
Wheeler, J. A. 247, 877
Whewell, W. 820
Whitehead, A. N. 59, 1388
Whiting, K. A. 1379
Whitman, A. 162, 214, 1374
Whittacker 720, 721, 1373
Whorf, B. L. 231, 273, 277, 281,
587, 1388
Wiehart, A. 746, 1388
Wilkinson, J. 753, 1348
Will, C. M. 518, 637, 655, 657, 658,
733, 817, 1148, 1155, 1157,
1158, 1388
Wille, R. 1099, 1388
Williams, B. 347
1414
Williams, J. T. 204, 282, 297, 424,
476, 598, 643, 740, 786, 1328,
1388
Wilpert, P. 1363
Wilson, C. 1351
Wilson, G. V. 396
Wintermeyer, R. 1354
Wirth, L. 32, 258, 1370
Witten, E. 438
Wittenburg, J. 1038, 1106, 1388
Wittgenstein, L. 29, 42, 77, 201,
202, 215, 245, 262, 276, 277,
286, 287, 288, 296, 330, 331,
333, 334, 368, 418, 420, 424,
451, 462, 516, 525, 557, 567,
572, 616, 650, 736, 938, 1030,
1312, 1322, 1326, 1328, 1348,
1385, 1388
Wittkop, G. 1388
Wittmann, M. C. 1283, 1389
Wittstock, U. 1343
Woelk, U. 1389
Wohlwill, E. 4
Wolf, E. 1309, 1318, 1353
Wolfe, T. IX
Wolff, C. 86, 257, 1345
Wolschin, G. 509, 753, 802, 804,
861, 878, 989, 1389
Wood, F. T. 1329, 1389
Woollcott, A. 1348
Wormann 215, 216
Woronetz, P. W. 1061
Wright, R. M. v. 1373
Wu, Z.-J. 980, 984, 1389
Wundt, W. 232, 233, 1389
Würfel, P. 375, 1361
30 Indices
Wußing, H. 1389
Wyder, M. 1358
Wymore, A. W. 308, 526, 1084,
1389
Wyssusek, B. 38, 72, 272, 297, 298,
1318, 1389
Y
Yourgrau, W. 1385
Z
Zadeh, L. A. 387, 1382
Zalta, E. N. 1380
Zanghi, N. 1352
Zaoui, A. 1380
Zapparella, F. G. P. 96
Zaritzky, L. 753
Zeh, H. D. 1347, 1389
Zeigler, B. P. 346, 549, 1389
Zelter, C. F. 7, 120
Zemplén, G. 945
Zhou, Y. 1389
Ziegler, G. 37, 1389
Ziegler, P. 1358
Zimmermann, D. 1382
Zimmermann, P. 66, 287, 1384
Zimmermann, R. E. 66, 246, 650,
1389, 1390
Zita, K. 307
Zöllner, J. 1383
Zurmühl, R. 354, 360, 372, 393,
394, 397, 398, 401, 412, 453,
454, 969, 1076, 1110, 1390
30.2 Subject index
30.2
1415
Subject index
Subject indices are notoriously 0difficult 'subjects', particularly in the present
treatise departing purposely from the professional jargon and freely using journalistic jargon where felt enlightening and/or amusing.
Various concordance tables resulted in hopelessly clumsy subject indices. Finally a section index was found to meet the goals of the present treatise most adequately, even though some of the headings are purposely in journalistic style.
If readers come up with better ideas these can be easily tested and, maybe, implemented. In the electronic book edition envisaged any type of customised
searches can be performed.
A
' … kurzer Sinn'_10.6 641
A 'proof'_12.3.3 702
Absent, cyclic speeds_19.4.4 1088
'Absolute' time, space_11.5.1 672
Abstract chronometry_7.3 457
Abstract dynamometers_13.5.1 773
Abstract mass_13.3.3 762
Abstract stereometry_7.4 467
Abstract stereometry_7.4.2 469
Abstract theory_23.2.1 1277
Abstract theory of metacontinua_15.1 889
Abstract time_7.3.2 460
Abstract versus physical
space_7.7.4 517
Acknowledgements_27 1317
Acknowledgements_28.4.1 1332
'Acoustic metric'_23.4.1 1283
Acoustic quanta_12.5.5 722
'Active', 'passive'
masses_14.3.1 810
'Against method'_3.3.6 60
Aggregate descriptions_6.4.7 378
Aggregate dynamics_19.2 1045
Aggregate 'forces'_19.3 1067
Aggregate models_8.2.3 537
Aggregate momentum diffusion_19.3.1 1068
Aggregate momentum productions_19.3.2 1071
Alternative approaches_22.6.4 1247
Analytical distribution function_15.2.3 899
'Anomalies'?_20.3.8 1158
Anschauen, Anschauung_6.2.4 339
Anschauung_5.4.4 275
Apparent effects_12.6.1 723
Arguments 'in free fall'_10.5.3 634
Assessment_24.2 1304
Author's basic work_29.1 1335
'Axiomatic' approaches_4.2.3 114
'Axiomatic' continuum mechanics_16.1.4 942
Axiomatic meta-system_9.1.7 562
Axiomatic meta-theory_9.1 554
Axiomatic systems_6.2 330
Axiomatic systems: general_6.2.1 330
Axiomatic systems: usage_6.2.2 335
B
Balance of deviatoric
stress_17.1.3 964
Balance of kinetic energy_18.4.1 1014
Balance of mass_13.3.2 761
Balance of mass_18.1.6 1000
Balance of matter_9.4.1 572
Balance of pressure_17.1.2 963
Balance of rotation_16.2.3 954
Balance of spin_18.3.1 1007
1416
'Basic bang': 'absolute'
spaces_10.4.2 620
Basic concepts_20.2.1 1122
Basic design_22.8.6 1265
Basic idea_3.4.1 68
Basic linear models_8.3.5 544
Basic procedure_22.7.5 1260
Basic relativity_11.5.2 674
Basic structures_6.3.2 350
Basic theory_20.1.1 1104
'Bildung'_5.2.5 241
Black box models_8.1.1 524
Bodies at rest_21.1.2 1165
Bodies in fluids: momentum convection_21.2 1179
Bodies in motion_21.1.3 1168
Body fixed space_23.1.2 1273
Body forces_13.1.3 738
Boltzmann's equation_16.1.3 940
Boltzmann's 'Principe'_4.1.7 106
Bootstraps_2 11
Boscovich's Law_4.1.3 94
Boundary fixed in space_18.1.4 999
Boundary fixed in
space_18.2.3 1003
C
Calculi of classes_6.5.4 385
Calculi of predicates_6.5.3 385
Calculi of propositions_6.5.2 383
Calibration_21.4.1 1188
Carnap's 'Der Raum'_7.1.4 443
Cauchy's 'universal' equation_16.1.1 934
Causes and effects_14.1.1 786
Celestial bodies_20.3.1 1140
Central motions_20.3.2 1141
'Central' motions_20.3 1139
Changes of frames_20.1.2 1108
Chronometers_11.2.3 658
Chronometry_11.2 654
Circles: complex_7.2.7 456
Classical approaches_23.4.3 1284
30 Indices
Classical expositions_4.1 81
Classical logics_6.5.1 382
'Classical' quantum mechanics_15.2.5 902
Classical relativity_11.5 671
Clocks in moving
spaces_11.5.6 679
Clocks in one space_11.5.5 678
Closing operations_24 1287
Coherent beliefs_3.2 34
'Common practice'_14.3.3 814
Complex 4D-space_10.5.5 636
Complex frames_7.5.1 483
Complex spheres_7.2.3 452
Complex time-space
frames_7.5 483
Components of momentum production_10.3.2 604
Comprehending_3.1 26
Concept of aether_14.4 821
Concept of body_7.6.1 497
Concept of continuum_7.6.2 498
Concept of curved space_7.2.1 448
Concept of 'force' field_14.1.5 791
Concept of gravity field_14.1.6 793
Concept of 'lost' forces_10.3.5 610
Concept of space_7.4.1 468
Concepts of force_4.3 127
Concepts of force_13.1 735
Concepts of force: history_4.3.7 139
Concepts of matter_7.6 497
Concepts of time_7.3.1 458
Concepts of truth_5.3.4 258
Conclusions_24.3 1306
Configuration efficiencies_22.5.4 1235
Confusion of issues_12.6.5 730
Consequences_23.2.3 1279
Constant of gravitation_14.2.5 802
Constitutive equations_21.3.1 1182
Constrained motions_4.4.5 172
Continuity of meta-mass_15.1.3 892
Continuum mechanics_24.1.6 1299
30.2 Subject index
Convective rate of
change_16.2.2 953
Conventions_28 1321
Convolution_8.3.1 540
Copyright_28.4 1332
'Cosmic laziness'?_14.2.6 805
Cosmologies_14.8 873
Creativity_5.5.5 304
Criteria_24.2.1 1304
Current cosmologies_14.8.1 874
Curved spaces_7.2 447
Curved time_7.3.4 463
D
d'Alembert's principle: derived_10.3.4 609
d'Alembert's principle: 'interpreted'_10.3.6 612
d'Alembert's principle: reviewed_10.3.7 613
'Dark' ages_7.6.6 509
Decisions_24.3.1 1307
Deflection of light_20.3.4 1148
'Degenerate' case: holonomic
speed_19.4 1081
Densities_15.3.1 912
Densities, intensities_9.5.1 576
Density fields_15.1.1 890
Derived probabilities_6.4.2 368
Derived structures_6.3.3 354
'Differing' views_18.2.5 1005
Diffusive flows_21.1.1 1164
Diffusive momentum
flow_14.1.3 788
Diffusive momentum flux_17.2 965
Discrete, continuous time_8.1.7 532
Discussion_19.4.7 1094
Displacement wakes_22.5.2 1233
Distances_7.4.3 470
'Disturbing' effects_12.1.3 688
Doctrine of fair use_28.4.2 1332
Doppler effect, 'red
shift'_12.5.1 716
1417
Ducted propeller design_22.8 1261
Ducted propellers_22.7.2 1257
Dühring's assignment_4.1.4 96
Dynamics of continua_16.1 933
Dynamometers_21.4 1187
Dynamometry_13.5 772
E
Earlier models of matter_14.6.6 852
Einstein's experiment_12.2.1 690
Einstein's 'general relativity'_14.2.4 800
Einstein's theory validated_20.3.7 1157
Elasto-mechanics: continued_19.4.5 1088
Elementary and local dynamics_4.5.5 200
Elementary axiomatic system_10.1.7 596
Elementary axioms_10.1 582
Elementary clocks_11.2.2 656
Elementary dynamics_13 735
Elementary global balances_18 997
Elementary 'integrals'_18.1.1 997
Elementary kinematics_10.5 629
Elementary kinematics: abstract_10.5.1 630
Elementary mechanics_4.4.3 162
Elementary mechanics_24.1.4 1293
Elementary mechanics: abstract_10 581
Elementary momentum balance_10.1.3 589
Elementary physics_14 785
Elementary physics_24.1.5 1298
Elementary primitives_10.1.1 583
Elementary 'principles'_19.1.1 1030
Embedding_3.4 67
'Energetik'_19.2.7 1066
Energy and mixed
wakes_22.5.7 1238
Energy balance_22.6.2 1242
Energy dissipation_20.3.6 1155
1418
Energy equation_9.5.3 579
Energy principle_10.3.9 616
'Engineering' philosophy_4.5.3 195
Epilogue_25 1309
Epistemic logics_3.2.3 39
Equation of continuity_15.3.3 916
Equation of metamotion_15.2.1 897
Equation of motion_21.1.7 1175
Equivalence misinterpreted_10.4.6 626
'Equivalence principle'_14.3.2 812
Equivalent models_8.3.4 543
Equivalent propulsors_22.5.1 1233
Equivalent propulsors_22.8.2 1262
Estimation_6.4.5 375
Etalons: basic units_13.4.2 767
Etalons: realisations_13.4.3 768
'Euclidean' spaces_7.1.3 441
Euclid's 'Elements'_7.4.5 476
Euler-Lagrangean equation: explicit_19.3.5 1079
Euler's 'Naturlehre'_4.3.3 131
Evaluation_24.1 1287
Example: hyper-elastic material_19.3.4 1078
Example: ideal gas_17.4.3 991
Example: Kármán vortex
street_19.5.2 1097
Example: Stokesian fluids_19.3.3 1074
Exegesis of holy texts_3.1.3 29
Existence_6.7.2 420
Expected specific quantities_15.4.3 927
Experimental 'verification'_14.3.4 817
Extensity of motion_10.1.2 585
F
'Facta'_6.1.5 321
'Fashionable nonsense'_5.2.7 244
Feasibility study_22.8.3 1263
Feed back of noise_8.4.4 548
30 Indices
First meta-axiom_9.1.3 557
Fixed boundaries_18.4.2 1016
Fizeau's experiment_12.6.4 729
Flow and production laws_14.1 786
Flow meta-axioms_9.1.6 561
'Force' fields_13.1.4 740
'Force' potentials_9.5.2 578
Forces 'expelled'_10.4.7 627
Forcibly driven systems_19.1.4 1041
Formats_28.3.1 1327
Fourier transforms_6.6.2 398
'Freedom of choice'_7.4.4 474
Freely moving bodies_4.4.4 169
Further ramifications?_19.4.3 1087
Future tasks_24.3.2 1307
Fuzzy logics, linguistics_6.5.5 387
Fuzzy sets_6.3.4 356
G
Galilei transformation_11.5.4 677
General aspects_24.1.1 1288
General criteria?_19.5.3 1099
General discussion_6.1.7 327
General potentials_14.5.4 838
General relativity_17.4.5 993
'General' relativity_14.8.5 883
General relativity 1889_10.3.8 614
General relativity, objectivity_10.2.1 599
Generalised kinematics_19.1 1030
Generalised kinematics_19.1.2 1034
Generalised kinematics: applications_19.1.5 1042
Generalised position_19.1.3 1038
Generic hyperbolic 'rotation'_7.5.8 494
Generic Lorentz 'rotation'_7.5.5 489
Glasperlenspiel: a story_5.1.8 223
'Gleich-ortige' events_12.1.4 689
'Gleich-zeitig', 'gleichortig'_7.5.6 491
'Gleich-zeitige' events_12.1.2 685
30.2 Subject index
'Gleich-zeitige', general
events_12.2.3 695
'Gleich-zeitige', 'gleich-ortige'
events_12.1 684
Global balance of momentum_18.2 1001
Global balances of energy_18.4 1013
Global balances of spin_18.3 1006
Global balances: metatheory_18.1 997
Global dynamics, 'principles'_4.5.6 201
'Global mechanics'_24.1.7 1301
Global motions_20.2.4 1131
Global production
model_14.6.1 841
Global stability criteria_18.5 1020
Goal of the treatise_4.5.2 192
Goethe's method_3.3.7 62
'Gravitational' mass_14.3 809
'Gravity'_21.3.2 1184
'Gravity' potential_14.4.5 829
'Guide to the Principia'_5.1.4 214
Guiding principle_3.3.8 65
H
Hamel 'replaced'_4.2.5 120
Hamel's axioms_4.2.1 109
Hamilton's 'canonical' equations_19.4.2 1084
Hertz' motivation_4.1.6 104
'Higher standpoint'_3.4.5 75
Historical aspects_5.1 205
Historical cosmologies_14.8.3 879
Historical developments_3.3.4 56
Historical notes_13.1.5 742
Historical 'notes'_5.1.1 206
Historical remarks_16.2.5 958
Historical theories_14.6.7 854
'History'_22.6.8 1253
History of mechanics_5.1.6 218
'Hollow' universe_14.5.5 839
Home-made philosophy_5.3.1 249
1419
Homogeneous spaces_7.2.2 451
Hopeless confusion_4.3.5 136
Hopeless efforts_4.3.2 130
Horizons transcended_12.4.4 712
Hull-integrated propulsors_22.7 1256
Human nature_5.4.1 270
Hylometry_13.3 759
Hyperbolic planimetry_7.1.5 446
I
Ideal Atwood machine_13.5.7 782
Ideal dynamometers: kinetics_13.5.3 776
Ideal dynamometers: statics_13.5.2 774
'Ideal' objects_6.6 390
Ideal propulsor_22.4.2 1226
Ideal propulsors_22.3.1 1218
Ideal propulsors: behind_22.5 1232
Ideal propulsors: open_22.4 1224
Identification_21.3 1182
Identification_21.4.3 1189
'Identity' versus 'equivalence'_14.6.3 845
'In principio … '_6.2.3 338
Incompressible fluids_17.3.5 985
Incompressible fluids_21.1 1164
'Incredible' beliefs_4.3.1 128
Indices_30 1391
Induction, falsification_6.7.4 426
Inertia interpreted_13.2.3 749
'Inertial' spaces_10.5.6 637
'Initial' problem_2.3 17
Inspectional analysis_22.1.4 1198
Instance, 'analogy'_23.3 1280
Instances of balances: in general_9.4.2 574
Instinctive beliefs_3.2.1 35
Intellectual problems_3.3.1 48
Intensities of motion, of production_10.1.6 594
Interaction of masses_14.2.1 796
1420
Internal losses_22.7.3 1258
Interpretation of state_8.2.2 535
Interpretation of state_8.3.2 541
Interpretation theories_6.2.6 346
Interpretations_3.3.2 51
Interpretations_13.2.1 745
Interpreted kinematics_11.3.2 663
Interpreted mass_13.3.4 763
Interpreted state models_8.2 534
Interpreted stereometry_11.3.1 660
Interpreted time_11.2.1 654
Introduction_22.1 1194
Invariance of momentum diffusion_10.3.1 603
Inverse square potentials_11.4.3 670
ISO/DIS 15016 example_22.2.8 1214
'Isolated', 'free' systems_9.3.2 571
Isotropic turbulence_15.4.5 930
'It was to be otherwise
…'_14.4.2 823
J
Jet power, efficiency_22.4.3 1227
K
Kant's Copernican turn_5.3.3 255
Kinematical uncertainty_12.4.3 710
Kinematics of continua_16.2 951
Kinematics of messengers_12.1.1 684
Kinetic energy_17.3.3 983
Knowledge and belief_3.2.6 43
L
Lagrangean equation_19.4.1 1082
Lanczos' remarks_17.2.7 978
Lanczos' variations_4.2.2 111
Language of dynamics_3.1.2 28
Laplace transforms_6.6.3 407
Law of conservation_14.2.8 807
Law of gravitation_14.2 795
30 Indices
Law of gravitation: invariant_14.2.2 797
'Laws of nature'_6.1.6 325
Layers of the world_6.1.1 312
Levels of problems_2.1 11
Lex tertia: gravitation_14.2.7 806
Limited horizons_7.5.3 487
Limits of theory_4.1.2 90
'Line of action'_18.3.3 1011
Linear equations_6.6.1 391
Linear state models_8.3 540
Live ideas_25.2 1312
Local balance of energy_16.1.6 947
Local balances_9.5 576
Local balances of pressure
etc_17.1 961
Local balances revisited_15.4.2 926
Local mechanics: fields_16 933
Local momentum balance_14.1.2 787
Local momentum production_17.4 987
Local physics: internal
states_17 961
'Local' production models_14.6.4 847
Local wake axioms_22.6.3 1245
'Logic' of science_9.1.1 554
Logics_6.5 381
Longitudinal inertia 'in general'_23.1.4 1275
M
Mach's concerns_4.1.5 101
Mach's principle_14.4.1 822
Mass etalon 're-newed'_13.4.4 770
'Mass points' et cetera_4.2.4 117
Mass potential_14.4.6 833
Mass potential_14.5.1 834
Mass potentials_14.5 834
Mass prototypes_13.4.1 766
Mass specific quantities_15.3.4 917
Material invariance, equivalence_9.2.2 567
30.2 Subject index
Material momentum production_14.1.4 789
Material, immaterial production_9.2.3 568
Measurable magnitudes_6.3.5 356
Mechanical impedances_13.5.6 780
'Mechanistic' thinking_5.2.1 227
Merits of propulsors_22.4.6 1230
Meta- and protomechanics_24.1.3 1292
Meta-concepts_9.1.2 555
Meta-mechanics: abstract_8 523
Meta-mechanics: ad hoc_9 553
Meta-mechanics: local_15 889
Metaphysical views_5.2.2 231
Meta-principles_9.2 564
Meta-probability_6.4.1 366
Meta-proto-mechanics_7.1.2 439
Meta-proto-theory_7.1 429
Meta-'spaces'_6.2.5 343
Meta-theorems_9.3 570
Meta-theories_3.4.3 70
Meta-theories_6.1.4 320
Meta-theory_23.2 1277
Meta-theory of material continua_15.3 911
Meta-theory of propulsion_22.3 1217
Meta-theory of stress
laws_15.3.6 921
Meta-theory of turbulence_15.4 923
Meta-velocity field_15.1.2 891
'Methods' of research_3.3.5 58
'Midwife buried'_10.3.3 608
Minimum kinetic energy_18.4.4 1019
Minkowski frames_7.5.7 493
Mis-'interpretations'_12.6.2 725
Mittelstaedt's grand survey_5.3.6 263
Model of matter_14.6 840
Model of theories_6.1.3 317
Model of treatise_4.5.1 189
Model, Goal, Plan_4.5 189
1421
Models of processes_8.1.6 531
Models of propulsion_22.1.2 1195
Models of systems_8.1.3 527
Modes of aggregation_19.2.1 1046
Modest goal_3.4.2 68
Momentum balance_18.2.1 1002
Momentum balance_22.6.5 1249
Momentum convection_21.2.2 1181
Momentum diffusion_10.1.5 593
Momentum production_13.2.2 747
Momentum theory_22.4.1 1224
Momentum, inertia_21.1.5 1170
Monitoring of trials_22.2.4 1208
More recent expositions_4.2 108
Motions in steady potentials_10.4.3 622
Motions in unsteady potentials_10.4.4 623
Motions in wave media_23 1271
Motions of continua_15.1.5 895
Motions of ideal metacontinua_15.2 897
Motions under gravity_17.4.1 988
Motivation_6.3.1 348
Mountains of potential_10.5.4 636
Moving boundaries_18.1.5 1000
Moving force fields_21.2.1 1179
Moving platform systems_20.2.6 1134
Moving reference
frames_18.3.4 1012
Much nonsense_4.3.6 137
Multi-dimensional magnitudes_6.3.6 358
Münchhausen's Trilemma_3.2.4 40
'Mythical' foundations_3.2.5 41
N
Name index_30.1 1391
Nature of forces_10.1.4 591
'Nature of forces'_13.1.1 736
1422
Navier-Stokes equation_17.3.2 981
Need for protomechanics_7.1.1 430
Need for reconstruction_4.1.1 82
'New physics'_14.7.4 866
Newtonian fluids_17.3 979
Newtonian fluids: properties_17.3.1 979
Newton's Opticks_12.5.4 721
Newton's Principia_5.1.3 212
Newton's stereometry_7.4.6 478
Non-commutative geometry_14.7.3 864
'Non-existent' things_5.2.3 236
Non-inertial spaces_11.3.3 664
Non-trivial problem_4.3.4 134
Normalisation_7.2.6 455
O
Object orientation_6.5.6 387
Objective truth_5.3.5 261
Objectivity, causality,
events_7.3.3 462
Objects identified_12.4.1 707
Observation theories_6.2.7 347
Ontology_6.1.2 315
Opening operations_4 81
Operational interpretation_4.4.6 175
Operational notations_28.2.1 1325
Operations_8.2.1 535
Orthogonal frames_7.2.5 454
Other analogues_23.4.2 1283
Other approaches_3.4.6 78
Other derivations_12.2.5 697
Other instantiations_6.4.3 370
Outlook_22.8.8 1268
P
Paradigm of paradigms_3.1.5 33
Parameter identification_8.4.2 546
Partial energy balances_19 1029
Partial energy balances: appraised_19.2.4 1058
30 Indices
Partial energy balances: en detail_19.2.2 1048
Partial energy balances: en
gross_19.2.3 1050
Paths: space curves_10.5.2 632
Perihelion precession_20.3.5 1151
'Personal' aspects_5.5 292
Personal background_5.5.7 306
Perspective relativity_12 683
'Philosophical' approach_4.4.1 149
Philosophical aspects_5.2 227
Philosophical positions_5.1.5 215
Philosophical problems_7.4.7 479
Physical space_7.7 509
Plane potentials_11.4.1 667
Plausibility_6.4.6 377
Post scriptum_26 1315
Potential flows_21.1.4 1168
Potential meta-flows_15.2.2 898
Power spectra_12.5.2 718
Powering performance_22.6.7 1252
Pragmatic aspects_5.4 269
Pragmatism pure_22.1.3 1196
Preface_1 1
Preliminaries_24.1.2 1291
Pressure laws_17.1.1 962
Principal solution_8.4.3 547
Principle of coherence_3.2.2 37
Principle of equivalence_13.2.4 754
Principle of least constraints_18.5.2 1023
Principle of least curvature_18.5.3 1025
Principle of least curvature_19.5.1 1096
Principle of local equivalence_10.4.5 624
Principle of relativity_12.3 699
Principles of materiality_10.3 602
Principles of relativity, objectivity_10.2 598
'Principles', 'laws'_28.2.2 1326
Problems of propulsion_22.1.1 1194
Prologue_3 25
30.2 Subject index
Propellers behind_22.6.1 1241
Propulsion mechanics_22 1193
Propulsion: axiomatic system_22.3.2 1219
Propulsion: efficiencies_22.3.3 1220
Propulsion:
Goals/Plans_22.1.5 1199
Propulsor models_22.7.1 1256
Propulsor theory interpreted_22.7.4 1259
Propulsors are pumps_22.8.1 1261
Proto- and metamechanics_4.5.4 198
'Proto'-mechanics_15.2.6 906
Proto-mechanics interpreted_11.1 647
Proto-mechanics: abstract_7 429
Proto-mechanics: time,
space_11 647
'Prototypes', etalons_13.4 765
Pseudo-hyperbolic perspectives_12.4.5 713
Pseudo-twins_12.3.1 699
Psychological aspects_5.5.6 305
Pump theory_22.4.5 1229
Pupils and students_5.5.4 302
Purpose: simulation_8.4.1 545
Q
Quantities: extensities_6.3.8 364
Quantity of matter_7.6.3 500
Quantity of matter_9.4 572
Quantity of matter_13.3.1 760
'Quantum' description_12.5 716
Quantum gravity_14.7.2 861
'Quantum mechanics'_14.7.1 860
Quantum theory_14.7 859
Quasi-steady motions_21.3.5 1186
Quasi-steady trials_22.6 1240
'Quauterwelsch' and beyond_15.2.7 907
Quotations_28.3.2 1328
1423
R
Rate of dissipation_17.3.4 984
'Rational' approach_4.4.2 156
Rational mechanics_4.2.6 122
Rational model_8.3.3 542
Rational names_28.1.1 1321
Rational theory of continua_17.2.2 967
'Real' dynamometers_13.5.4 778
Real objects_6.7 416
Real propulsors in real
wakes_22.5.8 1239
'Reality'_6.7.1 417
Recent developments_17.2.6 975
Recent speculations_14.6.8 856
Reconstruction_3.3 47
References_28.3 1327
References_29 1335
Related background_5 205
Related efforts_4.2.7 125
Relative motion_20.1.4 1118
Relative motions_17.4.4 992
Relative motions_20.2.5 1133
Relativistic perspective_12.2.2 691
'Relativistic phenomena'_23.3.2 1281
Relativistic space_7.7.2 511
Relativistic temperature?_12.3.4 704
Relativity, objectivity_9.2.1 565
Religious beliefs_3.2.7 45
Re-normalisation_7.6.5 507
Resistance, damping_21.1.6 1173
Review_22.8.7 1267
Ridiculous caricature_10.5.7 639
Rigid bodies in fluids_21 1163
Rigid bodies, in fluids_4.5.7 202
Rigid body dynamics_20.1 1103
Rigid body kinematics_20.2 1122
Rigid body mechanics_20 1103
Rigid body motion_10.6.1 641
Rigid body motions et cetera_24.1.8 1302
1424
Rotating spaces_14.5.2 836
Rotation, precession_20.1.3 1114
Rotational motions_20.2.3 1127
Rules of conduct_28.4.3 1334
S
Sampled data_6.6.4 412
Satisfaction_24.2.2 1305
'Scales'_11.1.2 651
Scepticism_6.7.3 424
Scientific roots_3.3.3 53
Scientific 'systems'_3.1.4 32
Second meta-axiom_9.1.4 558
Serious doubts_5.3.7 267
Shallow water_23.3.1 1280
Similarity_9.2.4 569
Slender bodies_23.1.3 1274
Slender bodies_23.2.2 1278
Slow speed approximation_12.2.4 696
Social aspects_5.4.2 272
Solid body model_13.2.5 756
'Solutions' proposed_4.4 149
Solving problems_2.2 13
Sound knowledge_25.1 1309
Sources referred to_29.2 1341
Special case: force free motions_19.2.5 1063
Special case: potential
'forces'_19.2.6 1065
'Special' relativity_12.2 690
Specific magnitudes: intensities_15.1.4 894
Speed horizons_12.4 707
Speed 'limit'_12.4.2 708
Spherical bodies_14.5.3 837
Spin: classical materials_16.1.5 945
Spinning buckets_14.4.4 828
Stability criteria_19.5 1096
Stability of motion_21.1.8 1178
Staked global balances_18.3.2 1010
Standard material_12.6.3 728
30 Indices
Standard model of nucleons_14.6.5 849
State models: abstract_8.1 523
'State of the art'_7.7.5 518
State space model_9.1.8 563
State space models_8.1.2 525
'Statistical' mechanics_19.4.6 1089
Statistics_6.4.4 374
Steady conditions_18.1.3 999
Steady conditions_18.2.2 1003
Steady motions_21.3.3 1185
Steady motions reviewed_10.2.4 601
Steady motions: unconstrained_21.3.4 1186
Steady potentials: examples_11.4 667
Steady speed trials_22.2 1201
Steady states_9.3.1 571
Steady trials: contracted conditions_22.2.6 1212
Steady trials: further developments_22.2.9 1215
Steady trials: power required_22.2.5 1210
Steady trials: power supplied, current_22.2.3 1206
Steady trials: rational approach_22.2.2 1204
Steady trials: traditional approach_22.2.1 1202
Steady trials: verification, 'validation'_22.2.7 1213
Stereometry_11.3 660
Stiffness_21.4.2 1188
Stochastic processes_6.4.8 379
Stokesian fluids_17.2.3 969
'Stories'_5.5.1 292
Structure of matter_7.6.4 504
Structures_6.3 348
Structures, parameters_8.1.4 529
Subject index_30.2 1415
Subsonic motions of bodies_23.1 1271
30.2 Subject index
Substantial rates of
change_16.2.4 955
'Subtle matter'_14.2.3 799
Sufficient reasons_3.1.1 26
Surface forces_13.1.2 737
Symbology_28.2 1325
Systems identification_8.4 545
T
Teachers and experts_5.5.2 296
Teaching_5.5.3 300
Terminology_28.1 1321
Terminology, notation_6.3.7 362
The big bang_14.8.2 876
'The simplest theory'_10.6.2 643
Theorem on body fixed
spaces_10.2.3 600
Theorem on steady motions_10.2.2 599
Theorems on free motions_10.4 618
Theoretical aspects_5.3 249
Theories of relativity_14.8.4 880
Theories of science_5.3.2 252
'Theories' of time_7.3.5 464
Theory of gravitation_4.4.8 181
Theory of gravity_14.6.2 843
Theory of probability_6.4 366
Theory of theories_6 311
Third culture_5.2.6 243
Third meta-axiom_9.1.5 559
Thrust deduction_22.5.3 1234
Thrust deduction: limit_22.5.6 1237
Thrust deduction: transformed_22.5.5 1236
Thrust distribution_22.8.4 1263
Time, space sensations_11.1.1 648
Top-down approach_3.4.4 73
Total confusion_14.3.5 819
Traditional names_28.1.2 1323
Transcendentals_7.7.1 510
Transformations_7.2.4 453
1425
Translational motions_20.2.2 1124
Translations_28.3.3 1330
Turbulent diffusive flux_15.4.4 928
Turbulent fluctuations_15.4.1 924
Turbulent momentum diffusion_16.1.2 937
Turbulent momentum diffusion_17.2.5 974
Twin 'paradox'_11.4.2 668
Twins in perspective_12.3.2 701
Two and more bodies_20.3.3 1146
U
Uncertainty principles_14.7.6 870
Unconstrained translations_10.4.1 618
Uniform mass density_15.3.5 919
Uniform potential fields_17.4.2 988
Uniform potentials_11.5.3 674
Unitary transformations_7.5.2 485
Unity of physics_5.1.7 220
Universal models_8.2.4 538
'Universes floating
around'_14.8.6 884
Universes, reference molluscs_4.4.7 177
Unlimited horizons_7.5.4 488
Usage of dynamometers_13.5.5 779
V
Various flux laws_17.2.1 966
Various languages_5.4.5 277
Various motivations_5.4.7 286
Various names_5.4.6 282
Various notes_12.6 723
Various 'principles'_5.4.8 289
Various temperaments_5.4.3 274
Various traditions_5.1.2 209
Velocity field_15.3.2 914
Velocity field: basic concepts_16.2.1 951
1426
Virtual energy_18.5.1 1020
Visco-elastic materials_17.2.4 971
Void and aether_14.4.3 826
Vortex theory_22.4.4 1228
W
'Watt scale'_13.4.5 771
Wave equation_23.1.1 1272
'Wave' equation et cetera_15.2.4 901
Wave-body 'dualism'_14.7.5 868
30 Indices
'Wave'-corpuscle 'dualism'_12.5.3 719
Waves in moving wave media_23.4 1283
Weight and mass_13.2 744
Weighted integrals_18.1.2 998
Weyl's apotheosis_5.2.4 239
World geometry_7.7.3 514
World model_6.1 311
Z
'Zu Ende gekommen'_4.4.9 186
Continued from front page
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' rigid bodies in threedimensional 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 interlude classical special or perspective relativity, is treated in detail. A theory of
inertia and gravitation, developed on the basis of a model of matter suggested
by Newton's 'Definition IV' and d'Alembert's principle, is in accordance with
Einstein's 'anti-Copernican turn' and with the standard model of nucleons.
Further, classical macroscopic mechanics is treated as continuum mechanics. Accordingly, the local momentum balance, Cauchy's universal equation of
motion, is considered as the root of the healthy tree of classical mechanics. All
its global branches including 'generalised', alias 'analytical' mechanics are
shown to be 'nothing but' weighted integrals of the basic local momentum balance.
The final chapters deal the theories of dynamics and kinematics of rigid
bodies in vacuo and in fluids. The rational theory of motions and propulsion of
bodies in fluids, developed during the professional life of the author, demonstrates 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, respectively.
READERS
The treatise is addressed to 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 to everybody with a keen interest in understanding, in Goethe's sense, the world we live in. As Klein's famous 'Elementary Mathematics' of 1908, not only paraphrased by the demanding sub-title,
the work is specifically addressed to teachers-to-be.
AUTHOR
Until he retired in 1997 Michael Schmiechen 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). Since then he has continued to promote his
ideas at lectures and conferences around the world.
A 'romance' of many levels.
In the spirit of Edwin A. Abbott, alias
A. Square: Flatland.
M GG ii = M NN ii + M OO ii
"Eigentlich möchte diese Arbeit nicht spekulativ
genannt werden, denn es sind am Ende doch nur,
wie mich dünkt, die praktischen und sich selbst
rektifizierenden Operationen des gemeinen Menschenverstandes, der sich in einer höhern Sphäre
zu üben wagt."
Johann Wolfgang Goethe: Erfahrung
und Wissenschaft, Anlage zu einem Brief
an Schiller, 1798.
0 ii = M MM ii + M NN ii
" …, und wenn man gleich von einem höhern
Standpunkte mit diesem Werke [noch] nicht ganz
zufrieden sein kann, so bemerkt man doch mit
Vergnügen den guten Einfluß [nicht nur] auf Personen, die auf einer mittlern Stufe der Bildung
stehen." [Additions]: MS.
Johann Wolfgang Goethe: Italienische
Reise. Frascati 15.11.1786 (BA 14/299).
m d tt v ii = M OO ii + M KK ii
"Wer zwei Paar Hosen hat, mache eins zu Geld
und schaffe sich dieses Buch an."
Georg Christoph Lichtenberg: Sudelbücher, E (1775-1776) 78.
ISBN 978-3-8370-5307-4, -5308-1, -5309-8

Such - Michael Schmiechen, Berlin: Homepage

Transcription

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