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Développement humain et loi log-périodique
Abstract
Abstract – Human development and log-periodic laws. We suggest applying the log-periodic law formerly used to describe various crisis phenomena, in biology (evolutionary leaps), inorganic systems (earthquakes), societies and economy (economic crisis, market crashes) to the various steps of human ontogeny. We find a statistically significant agreement between this model and the data. To cite this article: R. Cash et al., C.R. Biologies 325 (2002) 585-590. ©2002 Académie des Sciences / Editions scientifiques et médicales Elsevier SAS Human ontogeny / log-periodic law / human evolution Résumé – Nous proposons d’appliquer la loi log-périodique utilisée pour décrire divers phénomènes de crises, biologiques
... 30 The idea that physics should be based on neuropsychology is also supported by Fidelman's work. 31 27 "Let us therefore rather imagine the image of an infinitely small elastic band, contracted, if it were possible, into a mathematical point. We slowly start stretching it, so that the point turns into a line which grows continuously. ...
... Pöppel 1989, p. 380 (my translation) 30 Lakoff & Núñez' 2000. 31 Fidelman 2002, 2004 a,b,c and personal communication. ...
This paper reviews various approaches to modelling reality by differentiating notions of time which underly those models. Basic notions of time presupposed in physical theories are briefly described and analyzed in terms of the levels of description taken into account, the interfacial cut assumed between the observer and the rest of the world, the resulting observer perspectives and the extent to which these notions are based on temporal natural constraints. Notions of time in physical theories are secondary constructs, derived from our primary experiences of time. Therefore, we must regard our theories as anthropocentric – derived from abstractions and metaphors resulting from our embodied cognition. Theories based on the notion of fractal time and fractal space-time are generalizations or alternative descriptions which allow for a more differentiated modelling of reality. The resulting temporal observer perspectives allow for further differentiation. The notion of fractal time logically precedes those of fractal space-time, as it is based on the primary experiences of time: succession, simultaneity, duration and an extended Now. Against this background, the internal differentiation of the observer and his degree of both conscious and unconscious contextualization turn out to be vital ingredients in our reality generation game. I am fully aware of the fact that the selection of concepts presented here is neither complete nor unbiased and is coloured by my own temporal observer perspective.
We propose a physical representation of the log-periodicity law which has been evidenced in the field of seismic physics, species evolution, astronomical systems, economy, history, and human organizations. Calling “fractal state” a truncated fractal obtained for a finite number of iterations, i.e., defined for a finite scale range, we define a fractal length, a fractal time of interaction, and finally a fractal mass for the fractal states of a fractal. The introduction of the mass of a fractal allows showing the existence of a quantum structure due to the fractal structure which leads to a Planck–Einstein-like law. Inspired by the work of Louis de Broglie on the “hidden thermodynamics of the particle,” we introduce a “kinetic chain temperature” which gives access to a thermodynamical description of log-periodicity. We found that log-periodic systems are characterized by a constant entropy production between two consecutive fractal states. The parameter g of log-periodicity finds here a clear and simple physical interpretation. It quantifies the increase of fractal length or fractal time with the number of iterations of the fractal state.
The discoveries of Quaternary faunal series in the fossil record led to a first chronology of prehistory with alternating warm and cold-climate fauna. It was completed by characteristic environmental associations. Later, with the development of evolutionary character quantifications and of geometrical morphology methods, the evolution of species allowed the establishment of an ever higher-resolution biochronology which also has climatic and environmental significance. Biological dates are fairly precise but always relative to each other. New advances in palaeontology show that the evolution of species is not always linear, but is generally discontinuous, following complex non-linear schemata. Faunal evolution seems to follow scale-laws similar to those existing in physical critical phenomena, which are related to fractal structures occurring on small or large scales. This new approach will give a better understanding of faunal evolution and its practical use will improve the degree of resolution in biochronology.
In natural sciences, the “tree of life” is reconstructed using retrodiction. It should be followed from the present to the past. But we need to tell a story, which course is from the past to the present. So a number of misunderstandings occur, the fi rst of them being cosmic fi nalism. It is important to understand that evolutionary facts are proved using two kinds of scientifi c reasoning, the one of nomologicaldeductive sciences and the one of paletiological-abductive sciences, and both are equally valid. Confusing them is also a great source of misunderstandings and political manipulations in non-biologists. We also detect a number of pitfalls and biases inherent to the use and abuse of narrative for telling the history of life. These pitfalls are not only misleading public’s minds, but also researchers’ minds, especially those who think they can map a mathematical law onto a succession of dates of arbitrarily chosen events. Then we provide a series of dates of arbitrarily chosen events related to the history of life and earth.
Previously we have analyzed some evolutions in human activities by a log-periodic power law. In this article the historical chronology of chemical elements discoveries and the one of new particle accelerators are presented. Our goal is to check if all these studies are consistent with the results of L. Nottale, J. Chaline and P. Grou in paleontology, financial crisis pattern… Conclusively, we found a significant agreement with the Scale Relativity Theory proposed by L. Nottale.
Many critical phenomena were described by a log periodic law (evolutionary tree, earthquake, financial index, economic crisis⋯). To confirm this universality we present here the appliance of a log periodic function to the succession of ski lift kinds. The agreement is good. The deceleration of this chronology from a critical epoch suggests that no new technology of lift could be expected before many years.
Introduction Abandonment of the hypothesis of space-time differentiability Towards a fractal space-time Relativity and scale covariance Scale differential equations Quantum-like induced dynamics Conclusion Bibliography
This commentary addresses the question of the meaning of critique in relation to objectivism or dogmatism. Inspired by Kant’s
critical philosophy and Husserl’s phenomenology, it defines the first in terms of conditionality, the second in terms of oppositionality.
It works out an application on the basis of Salthe’s (Found Sci 15 4(6):357–367, 2010a) paper on development and evolution, where competition is criticized in oppositional, more than in conditional terms.
Continuity versus discontinuity, linear versus nonlinear in species evolution. Species evolution is a topic where concepts of continuity and discontinuity have been opposed for two centuries. What is the situation today in biological evolution ? The statistical distribution of appearances and disappearances among rodent species follows power laws, suggesting nonlinearity and fractal structures. Thus, the domain of living beings seems to be extended, through critical physical phenomena, to the analysis of linear versus nonlinear biological phenomena. These observations are consistent with the new scale relativity theory of Nottale, which predicts many domains of resolution in nature separated by scale dependence or scale independence. Despite some scale-dependence particular to various levels of biological organization, the fact that they are also characterized by scale-independence suggests that they could be described by new fundamental laws revealing their potentially fractal and irreversible character. In the proximity of the critical time, specific to each system, the system becomes unstable and fractal, and shows precursor events at an accelerated rate leading up to the critical time. After the critical time, the system shows replicate events, in a decelerating manner. The discontinuous appearance of a number of clades follows a log-periodic law with a middle scale report of 1.73. This law, first applied to earthquakes, stock market crashes, demography, and physical turbulences, and now also being applied with success to macroevolutionary patterns, seems to have a certain universality. To cite this article : J. Chaline, C. R. Palevol 2 (2003).
In this review paper, we recall the successive steps that we have followed in the construction of the theory of scale relativity. The aim of this theory is to derive the physical behavior of a nondifferentiable and fractal space-time and of its geodesics (to which wave-particles are identified), under the constraint of the principle of relativity of all scales in nature. The first step of this construction consists in deriving the fundamental laws of scale dependence (that describe the internal structures of the fractal geodesics) in terms of solutions of differential equations acting in the scale space. Various levels of these scale laws are considered, from the simplest scale invariant laws to the log-Lorentzian laws of special scale relativity. The second step consists in studying the effects of these internal fractal structures on the laws of motion. We find that their main consequence is the transformation of classical mechanics in a quantum-type mechanics. The basic quantum tools (complex, spinor and bi-spinor wave functions) naturally emerge in this approach as consequences of the nondifferentiability. Then the equations satisfied by these wave functions (which may themselves be fractal and nondifferentiable), namely, the Schrödinger, Klein-Gordon, Pauli and Dirac equations, are successively derived as integrals of the geodesics equations of a fractal space-time. Moreover, the Born and von Neumann postulates can be established in this framework. The third step consists in addressing the general scale relativity problem, namely, the emergence of fields as manifestations of the fractal geometry (which generalizes Einstein's identification of the gravitational field with the manifestations of the curved geometry). We recall that gauge transformations can be identified with transformations of the internal scale variables in a fractal space-time, allowing a geometric definition of the charges as conservative quantities issued from the symmetries of the underlying scale space, and a geometric construction of Abelian and non-Abelian gauge fields. All these steps are briefly illustrated by examples of application of the theory to various sciences, including the validation of some of its predictions, in particular in the domains of high energy physics, sciences of life and astrophysics.
We give a “direction for use” of the scale relativity theory and apply it to an example of spontaneous multiscale integration
including four embedded levels of organization (intracellular, cell, tissue and organism-like levels). We conclude by an update
of our analysis of the arctic sea ice melting.
KeywordsRelativity–Scale–Macroscopic quantum mechanics
The cosmological theory of the author, discussed in (Greben in Found Sci 15(2):153–176, 2010), has a number of implications for the interpretation of initial conditions and the fine-tuning problem as discussed by Vidal
(Found Sci 15(4):375–393, 2010a).
KeywordsEarly universe–Constants of nature–Fine tuning
According to the scenario of cosmological artificial selection (CAS) and artificial cosmogenesis, our universe was created
and possibly even fine-tuned by cosmic engineers in another universe. This approach shall be compared to other explanations,
and some far-reaching problems of it shall be discussed.
KeywordsAnthropic principle–Big bang–Cosmic artificial selection–Cosmic natural selection–Cosmology–Fine-tunings–Simulation
So far, the sciences of complexity have received less attention from philosophers than from scientists. Responding to Salthe’s
(Found Sci 15, 4(6):357–367, 2010a) model of evolution, I focus on its metaphysical implications, asking whether the implications of his canonical developmental
trajectory (CDT) must be materialistic as his reading proposes.
KeywordsCausation–Complex systems–Emergence–Evolution–Materialism–Reduction
As was mentioned by Nicolas Lori in his (Found Sci, 2010) commentary, the definition of Information in Physics is something about which not all authors agreed. According to physicists
like me Information decreases when Entropy increases (so entropy would be a negative measure of information), while many physicists,
seemingly the majority of them, are convinced of the contrary (even in the camp of Quantum Information Theoreticians). In
this reply I reproduce, and make more precise, some of my arguments, that appeared here and there in my (2010) paper, in order to clarify the presentation of my personal point of view on the subject.
KeywordsInformation–Entropy–Quantum
We have demonstrated, using the Cantor dust method, that the statistical distribution of appearance and disappearance of rodents
species (Arvicolid rodent radiation in Europe) follows power laws strengthening the evidence for a fractal structure set.
Self-similar laws have been used as model for the description of a huge number of biological systems. With Nottale we have
shown that log-periodic behaviors of acceleration or deceleration can be applied to branching macroevolution, to the time
sequences of major evolutionary leaps (global life tree, sauropod and theropod dinosaurs postural structures, North American
fossil equids, rodents, primates and echinoderms clades and human ontogeny). The Scale-Relativity Theory has others biological
applications from linear with fractal behavior to non-linear and from classical mechanics to quantum mechanics.
KeywordsSpeciation-Extinction-Macroevolution-Scale relativity-Log-periodic laws
Jan Greben criticized fine-tuning by taking seriously the idea that “nature is quantum mechanical”. I argue that this quantum
view is limited, and that fine-tuning is real, in the sense that our current physical models require fine-tuning. Second,
I examine and clarify many difficult and fundamental issues raised by Rüdiger Vaas’ comments on Cosmological Artificial Selection.
KeywordsFine tuning–Far future–Entropy of the universe–Universe simulation–Cosmological artificial selection–Artificial cosmogenesis
The canonical developmental trajectory (CDT), as represented in this paper is both conservative and emergentist. Emerging
modes of existence, as new informational constraints, require the material continuation of prior modes upon which they are
launched. Informational constraints are material configurations. The paper is not meant to be a direct critique of existing
views within science, but an oblique one presented as an alternative, developmental model.
KeywordsCritique–Emergence–Information–Materialism
If we assume that the constants of nature fluctuate near the singularity when a black hole forms (assuming, also, that physical
black holes really do form singularities) then a process of evolution of universes becomes possible. We explore the implications
of such a process for the origin of life, interstellar travel, and the human future.
KeywordsQuantum gravity-Evolution-Anthropic principle-Black holes
In the years since I first thought of the possibility of producing artificial black holes, my focus on it has shifted from
the role of life in the universe to a practical suggestion for the middle-term future, which I think of as on the order of
a few centuries.
KeywordsGeneral relativity–Black holes
I discuss some of the speculations proposed by Stewart (2010a). These include the following propositions: the cooperation at larger and larger scales, the existence of larger scale processes,
the enhancement of the tuning as the universe cycle repeats, the transmission between universes and the motivations to produce
a new universe.
KeywordsFar future–Evolution of the universe–Fine-tuning
This document is the Special Issue of the First International Conference on the Evolution and Development of the Universe (EDU 2008). Please refer to the preface and introduction for more details on the contributions. Keywords: acceleration, artificial cosmogenesis, artificial life, Big Bang, Big History, biological evolution, biological universe, biology, causality, classical vacuum energy, complex systems, complexity, computational universe, conscious evolution, cosmological artificial selection, cosmological natural selection, cosmology, critique, cultural evolution, dark energy, dark matter, development of the universe, development, emergence, evolution of the universe evolution, exobiology, extinction, fine-tuning, fractal space-time, fractal, information, initial conditions, intentional evolution, linear expansion of the universe, log-periodic laws, macroevolution, materialism, meduso-anthropic principle, multiple worlds, natural sciences, Nature, ontology, order, origin of the universe, particle hierarchy, philosophy, physical constants, quantum darwinism, reduction, role of intelligent life, scale relativity, scientific evolution, self-organization, speciation, specification hierarchy, thermodynamics, time, universe, vagueness. Comment: 355 pages, Special Issue of the First International Conference on the Evolution and Development of the Universe (EDU 2008) (online at: http://evodevouniverse.com/wiki/Conference_2008) To be published in Foundations of Science. Includes peer-reviewed papers, commentaries and responses (metadata update)
Dans le champ scientifique, les agents peuvent choisir de collaborer à la science ‘normal’, se placer à l’avant-garde la plus légitime (les ‘supercodes’, la ‘matière noire’, etc.), ou encore développer leurs recherches dans un nouveau cadre théorique, avec tous les risques que cela comporte. La marginalité d’une théorie soulève la question de la stratégie de ceux qui y collaborent même au détriment de leur ‘intérêt’ à court terme, qui orient plutôt vers la compétition immédiate pour occuper les positions centrales dans les domaines déjà constitués. La théorie de la relativité d’échelle (TRE) présente l’intérêt d’une telle situation car elle ouvre une possibilité qu’il faut créer de toutes pièces. S’y investir engage davantage que le choix d’un projet ‘risque’ (par sa difficulté même) dans le cadre d’un paradigme existant car, d’une part, la TRE innove par rapport aux bases conceptuelles déjà acceptées par tous et, d’autre part, se trouve aussi marginalisée par rapport à l’avant-garde la plus légitime (comme celle des ‘supercodes’). Ainsi, le cas de la TRE permet d’étudier une région du champ scientifique peu explorée par une sociologie des sciences qui fixe surtout son regard sur les cas extrêmes : histoire de théories devenues reconnues ou controverses spectaculaires. La TRE occupe encore, en 2006, une position marginale dans le champ de la physique. Sont statut diffère toutefois radicalement des ‘théories’ produites à l’extérieur du champ, sans correspondre pour autant à celui de la science stabilisée et sanctionnée : comme nous allons le montrer par une analyse bibliométrique détaillée, sa diffusion au sein du champ scientifique est relativement modeste mais réelle, et ses résultats, quand ils reçoivent la sanction d’une publication scientifique, sont rarement pris en compte par les chercheurs qui n’y collaborent pas déjà. Cette situation d’isolement au sein du champ révèle une tension conflictuelle entre la transformation que vise à opérer l’innovation théorique et les normes de l’évaluation normale entre pairs. En conclusion, nous comparerons la stratégie du fondateur de la TRE avec celle d’autres chercheurs ayant opéré, à un certain moment de leur carrière, une réorientation de leur trajectoire scientifique, afin de mettre en évidence les conditions sociales de bifurcation qui mettent en péril le capital scientifique cumulé jusque-là.
In the first part of this contribution, we review the development of the
theory of scale relativity and its geometric framework constructed in terms of
a fractal and nondifferentiable continuous space-time. This theory leads (i) to
a generalization of possible physically relevant fractal laws, written as
partial differential equation acting in the space of scales, and (ii) to a new
geometric foundation of quantum mechanics and gauge field theories and their
possible generalisations. In the second part, we discuss some examples of
application of the theory to various sciences, in particular in cases when the
theoretical predictions have been validated by new or updated observational and
experimental data. This includes predictions in physics and cosmology (value of
the QCD coupling and of the cosmological constant), to astrophysics and
gravitational structure formation (distances of extrasolar planets to their
stars, of Kuiper belt objects, value of solar and solar-like star cycles), to
sciences of life (log-periodic law for species punctuated evolution, human
development and society evolution), to Earth sciences (log-periodic
deceleration of the rate of California earthquakes and of Sichuan earthquake
replicas, critical law for the arctic sea ice extent) and tentative
applications to system biology.
In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, which aims at describing the effects of a non-differentiable and fractal (i.e., explicitly scale dependent) geometry of space-time. The first paper of this series was devoted, in this new framework, to the construction from first principles of scale laws of increasing complexity, and to the discussion of some tentative applications of these laws to biological systems. In this second review and perspective paper, we describe the effects induced by the internal fractal structures of trajectories on motion in standard space. Their main consequence is the transformation of classical dynamics into a generalized, quantum-like self-organized dynamics. A Schrödinger-type equation is derived as an integral of the geodesic equation in a fractal space. We then indicate how gauge fields can be constructed from a geometric re-interpretation of gauge transformations as scale transformations in fractal space-time. Finally, we introduce a new tentative development of the theory, in which quantum laws would hold also in scale space, introducing complexergy as a measure of organizational complexity. Initial possible applications of this extended framework to the processes of morphogenesis and the emergence of prokaryotic and eukaryotic cellular structures are discussed. Having founded elements of the evolutionary, developmental, biochemical and cellular theories on the first principles of scale relativity theory, we introduce proposals for the construction of an integrative theory of life and for the design and implementation of novel macroscopic quantum-type experiments and devices, and discuss their potential applications for the analysis, engineering and management of physical and biological systems and properties, and the consequences for the organization of transdisciplinary research and the scientific curriculum in the context of the SYSTEMOSCOPE Consortium research and development agenda.
In these two companion papers, we provide an overview and a brief history of the multiple roots, current developments and recent advances of integrative systems biology and identify multiscale integration as its grand challenge. Then we introduce the fundamental principles and the successive steps that have been followed in the construction of the scale relativity theory, and discuss how scale laws of increasing complexity can be used to model and understand the behaviour of complex biological systems. In scale relativity theory, the geometry of space is considered to be continuous but non-differentiable, therefore fractal (i.e., explicitly scale-dependent). One writes the equations of motion in such a space as geodesics equations, under the constraint of the principle of relativity of all scales in nature. To this purpose, covariant derivatives are constructed that implement the various effects of the non-differentiable and fractal geometry. In this first review paper, the scale laws that describe the new dependence on resolutions of physical quantities are obtained as solutions of differential equations acting in the scale space. This leads to several possible levels of description for these laws, from the simplest scale invariant laws to generalized laws with variable fractal dimensions. Initial applications of these laws to the study of species evolution, embryogenesis and cell confinement are discussed.
Basing our discussion on the relative character of all scales in nature
and on the explicit dependence of physical laws on scale in quantum
physics, we apply the principle of relativity to scale transformations.
This principle, in combination with its breaking above the Einstein-de
Broglie wavelength and time, leads to the demonstration of the existence
of a universal, absolute and impassable scale in nature, which is
invariant under dilatation. This lower limit to all lengths is
identified with the Planck scale, which now plays for scale the same
role as is played by light velocity for motion. We get new scale
transformations of a Lorentzian form and generalize the de Broglie and
Heisenberg relations. As a consequence the high energy length and mass
scales now decouple, energy and momentum tending to infinity when
resolution tends to the Planck scale, which thus plays the role of the
previous zero point. This theory solves the problem of divergence of
charge and mass (self-energy) in electrodynamics, implies that the four
fundamental couplings (including gravitation) converge at the Planck
energy, improves the agreement of GUT predictions with experimental
results, and allows one to get precise estimates of the values of the
fundamental coupling constants.
Rapid events, instabilities and cultural changes are numerous during the Quaternary (climates, species evolution, socio-economic systems). Non-linear laws of fractal type are well adapted to their analyze. A log-periodic behavior described by complex fractal dimensions can be applied to inorganic phenomena (earthquakes, stock market crashes), but also to organic phenomena such as biological evolution (chronology of major evolutionary leaps of rodents, dinosaurs, equids, primates, echinoderms). We apply this type of model to the acceleration observed in the economic crisis / no-crisis pattern in Western and pre-Columbian civilizations. The first tests reinforce the universality of the log-periodic model in the description of critical temporal evolutionary phenomena and suggest the existence of vaster underlying laws.
We analyse in terms of a fractal tree the time sequences of major evolutionary leaps at various scales : from the scale of the "global" tree of life (appearance of life to homeothermy), to the distinct scales of organization of clades, such as sauropod and theropod dinosaurs, North American equids, rodents, primates including hominids, and echinoderms. We also apply this type of model to the acceleration observed in the economic crisis / no-crisis pattern in Western and pre-Columbian civilizations. In each case we find that these data are consistent with a log-periodic law of acceleration or deceleration, to a high level of statistical significance. Such a law is characterized by a critical epoch of convergence T c specific to the lineage under consideration. These results support a description of evolutionary trees in terms of critical phenomena.
The theory of scale relativity attempts to generalize the laws of mechanics to continuous but non-differentiable motion. This implies at least three consequences: a) the space-time and its geodesics become fractal; b) there are an infinity of geodesics between any two points, which leads to a non-deterministic description; c) the concept of velocity becomes two-valued, which we account for in terms of a complex formalism. Then the fundamental equation of dynamics can be integrated under the form of a Schrödinger equation. Its solutions define probability densities which we interpret in terms of naturally hierarchized morphologies. This theoretical approach also leads to suggest some generalizations of scale invariant laws, which could be applied in domains other than physics.
Several authors have proposed discrete renormalization group models of earthquakes, viewing them as a kind of dynamical critical phenomena. Here, we propose that the assumed discrete scale invariance stems from the irreversible and intermittent nature of rupture which ensures a breakdown of translational invariance. As a consequence, we show that the renormalization group entails complex critical exponents, describing log-periodic corrections to the leading scaling behavior. We use the mathematical form of this solution to fit the time to failure dependence of the Benioff strain on the approach of large earthquakes. This might provide a new technique for earthquake prediction for which we present preliminary tests on the 1989 Loma Prieta earthquake in northern California and on a recent build-up of seismic activity on a segment of the Aleutian-Island seismic zone. The earthquake phenomenology of precursory phenomena such as the causal sequence of quiescence and foreshocks is captured by the general structure of the mathematical solution of the renormalization group.
We present an analysis of the time behavior of the S&P 500 (Standard and Poors) New York stock exchange index before and after the October 1987 market crash and identify precursory patterns as well as aftershock signatures and characteristic oscillations of relaxation. Combined, they all suggest a picture of a kind of dynamical critical point, with characteristic log-periodic signatures, similar to what has been found recently for earthquakes. These observations are confirmed on other smaller crashes, and strengthen the view of the stockmarket as an example of a self-organizing cooperative system.
Knowledge of precursors and predictors of human parturition would be important both for our understanding of the controlling mechanisms and for practical use in the detection and diagnosis of various abnormalities of the birth process. They involve a multitude of genetic, metabolic, nutritional, hormonal and environmental factors. Present research is however hindered by the lack of a clear recognized correlation between the time evolution of these various variables and the initiation of parturition. Here, we propose a coherent logical framework which allows us to rationalize the various laboratory and clinical observations on maturation, the triggering mechanisms of parturition, the existence of various abnormal patterns as well as the effect of external stimuli of various kinds. Within the proposed mathematical model, parturition is seen as a “critical” instability or phase transition from a state of quietness, characterized by a weak incoherent activity of the uterus in its various parts as a function of time (state of activity of many small incoherent intermittent oscillators), to a state of globally coherent contractions where the uterus functions as a single macroscopic oscillator. Our approach gives a number of new predictions and suggests a strategy for future research and clinical studies, which present interesting potentials for improvements in predicting methods and in describing various abnormal prenatal situations.
We analyse the time sequences of major evolutionary leaps at various scales, from the scale of the global tree of life, to the scales of orders and families such as sauropod dinosaurs, North American fossil Equidae, rodents, and primates including the Hominidae. In each case we find that these data are consistent with a log- periodic law to high level of statistical significance. Such a law is characterized by a critical epoch of convergence Tc specific to the lineage under consideration and that can be interpreted as the end of that lineage's capacity to evolve.RésuméLes séquences temporelles des grands sauts évolutifs sont analysées à diverses échelles, depuis celle de l'arbre global de la vie jusqu'à celles d'ordres ou de familles telles que les dinosaures sauropodes, les équidés fossiles d'Amérique du Nord, les rongeurs et les primates, incluant les hominidés. Dans tous les cas, nous trouvons que ces données peuvent êitre ajustées, avec, une haute signification statistique, par une loi log-périodique caractérisée par une époque critique de convergence Tc, qui dépend de la lignée considérée et qui peut s'interpréter comme la fin de la capacité d'évolution de cette lignée.
Anew geometrical structure (geometry of intermittency) is applied to the evolutionary tree. Through the introduction of a principle of entropy flux conservation, one can recover and explain the log-periodical law, recently evidenced in the sequence of the main palaeontological events.
The Kadanoff theory of scaling near the critical point for an Ising ferromagnet is cast in differential form. The resulting differential equations are an example of the differential equations of the renormalization group. It is shown that the Widom-Kadanoff scaling laws arise naturally from these differential equations if the coefficients in the equations are analytic at the critical point. A generalization of the Kadanoff scaling picture involving an "irrelevant" variable is considered; in this case the scaling laws result from the renormalization-group equations only if the solution of the equations goes asymptotically to a fixed point.
We propose that catastrophic events are "outliers" with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades. We describe a unifying approach for modeling and predicting these catastrophic events or "ruptures," that is, sudden transitions from a quiescent state to a crisis. Such ruptures involve interactions between structures at many different scales. Applications and the potential for prediction are discussed in relation to the rupture of composite materials, great earthquakes, turbulence, and abrupt changes of weather regimes, financial crashes, and human parturition (birth). Future improvements will involve combining ideas and tools from statistical physics and artificial/computational intelligence, to identify and classify possible universal structures that occur at different scales, and to develop application-specific methodologies to use these structures for prediction of the "crises" known to arise in each application of interest. We live on a planet and in a society with intermittent dynamics rather than a state of equilibrium, and so there is a growing and urgent need to sensitize students and citizens to the importance and impacts of ruptures in their multiple forms.
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