E-raamat: Structural Stability And Morphogenesis: An Outline of a General Theory of Models [Taylor & Francis e-raamat]

Introduction		1	(11)
The Program		1	(1)
The succession of form		1	(1)
Science, and the indeterminism of phenomena		1	(1)
The theory of models		2	(2)
Formal models		2	(1)
Continous models		3	(1)
A historicophilosophical digression		4	(3)
Qualitative or quantitative		4	(1)
The Shadow of history		5	(1)
An extension of our basic intuition		6	(1)
The construction of a model		7	(5)
The catastrophe set		7	(1)
The independence of the substrate		8	(1)
Biological and inert forms		9	(1)
Conclusion		9	(1)
Appendix: The notion of an object		10	(2)
Form and Structural Stability		12	(9)
The Study of forms		12	(3)
The usual sense of form or shape		12	(1)
The space of forms		13	(1)
Structural Stability		14	(1)
Nonform forms		14	(1)
Geometrical forms		15	(1)
Structural stability and scientific observation		15	(4)
The conditions of scientific experiment		15	(1)
The quantum objection		16	(1)
Isomorphic processes		17	(1)
The nature of empirical functions		17	(1)
Regular points of a process		18	(1)
Structural stability and models		19	(2)
Structural Stability in Mathematics		21	(17)
The general problem		21	(8)
Continuous families and bifurcation		21	(1)
Algebraic geometry		21	(2)
Geometrical analysis		23	(1)
Differential topology		23	(2)
Differential equations		25	(3)
Functional analysis and partial differential equations		28	(1)
Algebra and morphogenesis		29	(9)
An example of bifurcation		29	(2)
The universal unfolding of a singularity of finite codimension		31	(1)
An example: the universal unfolding of y = x3		32	(1)
The general theory of the universal unfolding		33	(1)
The case of a function		34	(4)
Kinematic of Forms; Catastrophes		38	(17)
Spatial process		38	(2)
The morphology of a process		38	(1)
Attractors		38	(1)
The partition into basins		39	(1)
Mathematical models for regular processes		40	(2)
Static models		40	(1)
Metabolic models		40	(1)
Evolution of fields		41	(1)
Equivalence of models		41	(1)
Isomorphic processes		42	(1)
Catastrophes		42	(2)
Ordinary catastrophe points		42	(1)
Essential catastrophe points		43	(1)
Morphogenetic fields associated with local catastrophes		44	(3)
Static models		44	(1)
Stable singularities of wave fronts		45	(1)
Metabolic models		46	(1)
Preliminary classification of catastrophe		47	(1)
The domain of existence and basin of an attractor		47	(1)
Conflict and bifurcation catastrophes		47	(1)
Thermodynamical coupling		48	(5)
Microcanonical entropy		48	(1)
The interaction of two systems		49	(1)
The approach to the equilibrium state with thermodynamical interaction		50	(1)
Polarized dynamics		51	(1)
The pseudogroup of local equivalences of a field		52	(1)
The reduced field		53	(2)
The definition of the reduced field		53	(1)
The self-interaction of a field; the evolution of the reduced field		53	(2)
Elementary catastrophes on R4 Associated with Conflicts of Regimes		55	(46)
Fields of gradient dynamics and the associated static model		55	(2)
The competition between regimes		55	(1)
Maxwell's convention		56	(1)
The algebraic study of point singularities of a potential function		57	(3)
The catastrophe set		57	(1)
Bifurcation strata		57	(1)
A Study of isolated singular points; corank		58	(1)
The residual singularity		59	(1)
Catastrophes of corank one		60	(13)
Strata of codimension zero		61	(1)
Strata of codimension one		61	(1)
Strata of fold type		61	(1)
Conflict strata		62	(1)
Strata of codimension two		62	(1)
The transversal intersection of two fold strata		62	(1)
Strata of cusp points and the Riemann-Hugoniot catastrophe		62	(1)
Conflict strata		63	(1)
The transversal intersection of a fold stratum and a conflict stratum		64	(1)
Strata of codimension three		64	(1)
The swallow's tail		64	(3)
Transition strata		67	(1)
Conflict strata		68	(1)
Strata of codimension four: the butterfly		68	(5)
Elementary catastrophes of corank two		73	(20)
Umbilics		73	(1)
Classification of umbilics		74	(1)
The morphology of umbilics		75	(1)
The hyperbolic umbilic: the creast of the wave		75	(3)
The elliptic umbilic: the hair		78	(3)
A remark on the terminology		81	(1)
The parabolic umbilic: the mushroom		81	(9)
A general remark on bifurcation catastrophes		90	(3)
The morphology of breakers		93	(3)
Attractors of a metabolic field		96	(5)
General Morphology		101	(23)
The main types of forms and their evolution		101	(7)
Static and metabolic models		101	(1)
Competition of attractors of a Hamiltonian dynamic		102	(1)
Creation of a new phase; generalized catastrophes		103	(1)
Lump catastrophes		103	(1)
Bubble catastrophes		103	(1)
Laminar and filament catastrophes		103	(1)
Catastrophes with a spatial parameter		103	(2)
Superposition of catastrophes		105	(1)
Models for a generalized catastrophe; change of phase		105	(1)
The formalization of a generalized catastrophe		106	(2)
The geometry of a coupling		108	(5)
Mean field		109	(1)
Examples of mean fields associated with an elementary catastrophe		110	(1)
The fold		110	(1)
The cusp		110	(2)
Mean fields associated with a coupling		112	(1)
Mean field, scale, and catastrophes		113	(1)
Semantic models		113	(11)
Definition of a chreod		114	(1)
The subchreod of a chreod		115	(1)
The family tree of chreods		116	(1)
Conditional chreods and levels of organization		116	(1)
Examples of semantic models		117	(1)
The diffusion of a drop of ink in water		117	(1)
Feynman graphs in the theory of elementary particles		117	(1)
The analysis of a semantic model		118	(1)
The dynamical analysis of the chreods of a static model		118	(1)
Appendix: Spiral nebulae		119	(5)
The Dynamic of Forms		124	(27)
Models of mechanics		124	(2)
Limitations of classical and quantum models		124	(1)
Determinism		125	(1)
Information and topological complexity		126	(4)
The present use of the idea of information		126	(1)
The relative nature of complexity		127	(1)
Topological complexity of a form		127	(1)
The choice of a ground form		128	(1)
Complexity in a product space		129	(1)
Information, significance, and structural stability		130	(5)
Free interaction		130	(3)
The entropy of a form		133	(1)
Competition of resonances		134	(1)
Information and probability		134	(1)
Energy and spatical complexity		135	(3)
The spectrum		135	(1)
Sturm-Liouville theory in several dimensions		136	(2)
Aging of a dynamical system and the evolution of a field toward equilibrium		138	(1)
Formal dynamics		138	(6)
The origin of formal dynamics		139	(2)
Phenomena of memory and facilitation		141	(1)
Canalization of equilibrium		142	(1)
Threshold stabilization		143	(1)
Threshold stabilization and the theory of games		143	(1)
Other formal aspects of a coupling: coding		144	(1)
Form and information		144	(7)
Appendix 1: Conservation of energy and the first law of thermodynamics		146	(1)
Appendix 2: Topological complexity of a dynamic		147	(1)
Appendix 3: Infinite complexity of geometrical forms		148	(1)
The symmetry principle		148	(1)
The space and forms of a fountain space		149	(2)
Biology and Topology		151	(10)
The topological aspect of biological morphogenesis		151	(1)
Form in biology; the idea of a phenotype		152	(2)
The spatial form		152	(2)
The global form		154	(1)
Molecular biology and morphogenesis		154	(3)
The inadequacy of biochemistry		154	(2)
Morphology and biochemistry		156	(1)
Information in biology		157	(4)
Appendix: Vitalism and reductionism		158	(3)
Local Models in Embryology		161	(39)
The variety of local mechanisms of morphogenesis in biology		161	(1)
The presentation of the model		162	(5)
A discussion of historical theories		167	(2)
Development of mosaic type		167	(1)
Gradient theories		168	(1)
Models in primitive epigenesis of amphibia		169	(4)
Models for the primitive streak		173	(8)
Gastrulation in birds		173	(6)
The comparative topology of gastrulation in vertebrates		179	(2)
Models in mean epigenesis		181	(6)
Induction crossed by resonance: glandular scheme		181	(2)
Morphogenesis of a vertebrate limb		183	(1)
The morphogenetic field of a bone		183	(2)
The formation of muscles attached to a joint		185	(2)
Late epigenesis; some archetypal chreods associated with umbilics		187	(13)
Capture chreods		187	(4)
Genital chreods		191	(3)
Appendix: Neurulation and the formation of the spinal cord		194	(6)
Global Models for a Living being (Metazoa)		200	(56)
The static model		200	(7)
Preamble		200	(1)
The static global model		201	(2)
The geometry of regeneration in planarians		203	(1)
A digression: preformation and epigenesis		204	(3)
The metabolic model		207	(9)
Limitations of the static model		207	(1)
The epigenetic polyhedron		208	(1)
The regulation figure		209	(2)
A preliminary description of the global model		211	(1)
Self-reproducing singularities		212	(3)
The mixed model		215	(1)
The hydraulic model		216	(6)
Description of the model		216	(1)
Relationship between the hydraulic model and the metabolic model		217	(1)
The dynamic of gametogenesis		218	(1)
Reproduction in the hydraulic model		219	(2)
Interpretation of the animal-vegetal gradient		221	(1)
Interpretation of the internal variables		222	(1)
The formal analysis of organogenesis		222	(9)
Origins of organogenesis		222	(1)
Localization of functions		223	(4)
Formalism of reproduction, and the genetic material		227	(1)
Formal effects of localization: the reversibility of transistions and threshold stabilization		228	(2)
Organs of the embryo		230	(1)
A theoretical plan of a differentiation catastrophe		231	(6)
The origin of the germ structure		232	(1)
The frequent disapperance of organizing centers in embryology		233	(1)
Polarization		233	(3)
Embryological induction		236	(1)
Abnormal evolutions		237	(1)
Examples of organogenesis		237	(19)
Respiration and blood circulation		237	(1)
The origin of the blood circulation		237	(3)
The blood		240	(1)
The heart		241	(1)
Breathing		242	(1)
The nervous system		243	(1)
The origin of the nervous function		243	(1)
The structure and role of the nervous system		244	(1)
Epigenesis of the nervous system		245	(2)
Appendix 1: Plant morphology		247	(3)
Appendix 2: Physiological applications of the model: sickness and death		250	(1)
Appendix 3: The epigenesis of the nervous system: a theoretical scheme		251	(5)
Models in Ultrastructure		256	(24)
The division of a cell		256	(7)
The optimum size		256	(1)
Energy flux		257	(1)
Duplication of chromosomes		258	(3)
A model for crossing over at the molecular level		261	(2)
Mitosis		263	(3)
Mitosis in internal coordinates		263	(1)
Mitosis with spartial coordinates		264	(2)
Meiosis		266	(2)
Morphogenetic fields of cytoplasm		268	(3)
The theory of cytoplasmic structures		271	(5)
The idea of an enzyme		271	(1)
The structure of a shock wave, and transitional regimes		272	(1)
The rule of three states		273	(2)
The nucleus as a chemostat		275	(1)
Formal aspects of spatial duplication		276	(4)
The Basic Problems of Biology		280	(17)
Finality in biology		280	(3)
Finality and optimality		280	(1)
Chance and mutations		281	(2)
Irreversibility of differentiation		283	(3)
The main types of differentiation		283	(1)
The silent catastrophe		283	(1)
The catabolic catastrophe		283	(1)
Aging, or the sliding catabolic catastrophe		283	(1)
Sexuality		284	(1)
Irreversibility and death		285	(1)
The origin of life		286	(4)
Synthesis of life		286	(1)
The three-regime soup		286	(3)
Recapitulation		289	(1)
Evolution		290	(7)
Eigenforms of duplication		290	(2)
A hypothetical mechanism of the attraction of forms		292	(1)
Unusual stimuli		293	(1)
Bacteria and metazoa		293	(1)
Appendix 1: Finality and archetypal chreods		294	(1)
Appendix 2: The universal model		295	(2)
From Animal to Man: Thought and Language		297	(34)
A fundamental contradiction in biological regulation: the presistence of the subject and periodicity of actions		297	(6)
The predation loop		297	(3)
The reproduction loop		300	(2)
Sexuality		302	(1)
The animal mind		303	(2)
Genetic forms		303	(1)
Animal in quest of its ego		304	(1)
Dreaming		304	(1)
Play		304	(1)
Homo Faber		305	(4)
Organs and tools		306	(1)
An example: the construction of a club as a chreod		306	(3)
Homo Loquax		309	(4)
The double origin of language		309	(2)
Syntax and archetypal morphologies		311	(1)
The automatisms of language		312	(1)
The origin of geometry		313	(2)
Three important kinds of human activity		315	(3)
Art		315	(1)
Delirium		316	(1)
Human play		317	(1)
The Structure of Societies		318	(2)
Basic types of society		318	(1)
The military society		318	(1)
The fluid society		319	(1)
Other as pects of societies		319	(1)
Money		319	(1)
The mind of a society		319	(1)
Conclusion		320	(11)
Summary		320	(1)
Experimental control		321	(2)
Philosophical considerations		323	(1)
Epilogue		324	(1)
Appendix 1: A model for memory		325	(1)
The mechanism of acquiring a memory		326	(1)
Appendix 2: Grammar, languages, and writing		327	(4)
MATHEMATICAL SUMMARY: CONCEPTS AND NOTATIONS OF DIFFERENTIAL TOPOLOGY AND QUALITATIVE DYNAMICS		331	(10)
Real Euclidean q-dimensional space		331	(1)
Maps		332	(1)
Differentiable maps		333	(2)
Differential manifolds		335	(2)
Vector fields		337	(1)
Dynamical systems		337	(2)
Function spaces and infinite-dimensional manifolds		339	(2)
Index		341

René Thom, professor at I.H.E.S., Bures-sur-Yvette since 1963, he was born in Montbéliard, France on September 2, 1923. Professor Thom studied at the Ecole Normale Supérieure of Paris from 1943-46, and obtained his Ph.D. in Mathematical Sciences in 1951. After a year spent at a graduate college of Princeton University, he was professor at the faculty of sciences of Strasbourg University from 1954-1963. In 1954 Professor Thom invented and developed the theory of cobordism in algebraic topology. This classification of manifolds used homotopy theory in a fundamental way and became a prime example of a general cohomology theory. For this work, Professor Thom received the Field Medal in 1958. Later on at I.H.E.S., he originated, with E. C. Zeeman, the celebrated Catastrophe Theory. Professor Thom is a member of the American Academy of Arts and Sciences, Académie des Sciences de Paris, Deutsche Akademie der Naturforscher Leopoldina (DRG), and the Academy of Sciences of Brazil.