Entire Theory Research Articles

Extended multiplet structure in Logarithmic Conformal Field Theories

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.

Conflicting Concepts of Self and The Michigan Womyn's Music Festival

Conflicting Concepts of Self and The Michigan Womyn's Music Festival

On the “Misogyny” Of Jean-Jacques Rousseau: The Letter to D'alembert in Historical Context

Evidence suggests that the feminist consensus on Jean-Jacques Rousseau’s ‘‘misogyny’’ is breaking down. 1 New studies are emerging that bring to light the many sympathetic portrayals of women in Rousseau’s works and the important role he ascribed to women within the family. Some modern feminists are even finding ways of reading Rousseau that speak to women’s concerns today. Overturning the notion that Rousseau was an arch-misogynist will be an uphill battle, however, given how very widespread it has become. Moreover, before we can arrive at a coherent and convincing appraisal of Rousseau’s views on women, a curious paradox needs to be addressed: even feminist admirers of Rousseau tend to accept the established feminist canon on him, and in fact build upon it. Therein lies a fundamental problem for Rousseau scholarship and for women’s studies in general. Early works of feminist criticism not only exposed Rousseau’s patriarchal and ‘‘functionalist’’ attitude toward women but denounced it as the fatal flaw in his entire political theory. According to Eva Figes, Rousseau’s attempt to ‘‘put woman firmly back in the home’’ was driven by a desire to repress the female sex and the related self-serving belief that a woman’s role should be confined to providing domestic ‘‘entertainment’’ for men. This view of women was ‘‘ironic’’ and even ‘‘illogical’’ given Rousseau’s otherwise egalitarian principles; indeed, if taken to their logical conclusion, Rousseau’s ideas on women made ‘‘utter nonHelena Rosenblatt is the author of Rousseau and Geneva: From the First Discourse to the Social Contract, 1749–1762 (Cambridge, 1994) and is currently writing a book on Benjamin Constant (1767–1830). This article was completed while the author was a fellow at the National Humanities Center. She would like to thank the participants in the Triangle French Cultural Seminars and the anonymous reviewers of French Historical Studies for their helpful criticism and comments. 1 According to both Webster’s and the Oxford English Dictionary, misogyny means ‘‘hatred of women.’’

Branching Exit Markov Systems and Superprocesses

Superprocesses (under the name continuous state branchingprocesses) appeared, first, in a pioneering work of S.Watanabe [J. Math. Kyoto Univ. 8 (1968)141 –167 ]. Deep results on paths of the super-Brownian motion were obtained by Dawson, Perkins, Le Gall and others. In earlier papers, a superprocess was interpreted as a Markov process $X_t$ in the space of measures. This is not sufficient for a probabilistic approach to boundary value problems. A reacher model based on the concept of exit measures was introduced by E.B.Dynkin [Probab. Theory Related Fields 89 (1991) 89 –115 ]. A model of a superprocess as a system of exit measures from time-space open sets was systematically developed in 1993 [E.B. Dynkin, Ann.Probab. 21 (1993)1185 –1262 ]. In particular, branchingand Markov properties of such a system were established and used to investigate partial differential equations. In the present paper, we show that the entire theory of superprocesses can be deduced from these properties.

Conformal Hamiltonian systems

Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two reduced conformal Poisson vector fields, again analogous to the dual pair construction for symplectic manifolds. Conformal Poisson systems form an interesting infinite-dimensional Lie algebra of foliate vector fields. Manifolds supporting such conformal vector fields include cotangent bundles, Lie–Poisson manifolds, and their natural quotients.

Genuine Fortuitousness. Where Did That Click Come From

The paper presents a revised view of quantum mechanics centered on the notion (“genuine fortuitousness”) that the click in a counter is a totally lawless event, which comes by itself. A crucial point is the distinction between events on the spacetime scene and the content of the symbolic algorism. A revised conception of matrix variables emerges, by which such a variable, as part of a whole, does not have a value, under any circumstance. This conception is at variance with that of indeterminate variables. A matrix variable not having a value does not enter spacetime and is not a measurable quantity, but manifests itself by a click in a counter with the remarkable property of having an onset, a beginning, from which the click develops. The individual click with its immense complexity is unique and lawless, even beyond probability. The notion of probability only applies to clicks in low resolution, and the completeness of a probabilistic theory is thereby seen in a new perspective. The genuinely fortuitous click is not produced by the impact of a particle, nor caused by an event in the source prior to the click in the counter. Indeed, there are no particles on the spacetime scene. The theory is thereby liberated from notions, which go with particles having indeterminate variables, and which have given to quantum mechanics the image of an unfathomable theory. With no particle as intermediary, the connection between source and detector is non-local, as is the entire theory, which deals exclusively with distributions of clicks. The locality permeating quantum mechanics is a symbolic one. The wave function enters in the sole role of encoding the probability distributions of clicks. The quest to understand the occurrence of the click in terms of the evolution of the wave function loses its meaning. However, click distributions in low resolution can be analyzed in terms of the connection between click distributions for different sets of counters, as given by the wave function. With increasing resolution, the probabilities, and the wave function, gradually lose significance, whereby the onset remains beyond reach. Thus, the downward path from events on the spacetime scene does not extend beyond the onset. The notion that quantum mechanics deals with particles (or fields) is rooted in the historical evolution but appears unable to accomodate genuine fortuitousness. The latter concept is given its due place by fully accepting the abstract nature of the matrix variables.

An Anisotropic Model for Annulus Tissue and Enhanced Finite Element Analyses of Intact Lumbar Disc Bodies

The current investigation addresses advanced FE analyses of intact lumbar intervertebral discs. Human disc body units basically consist of a fluid filled cavity (nucleus pulposus) approximately at the disc center and surrounding annulus tissue reinforced by collagen fibers (annulus fibrosus). For the latter component a constitutive model is presented which accounts for nonlinear anisotropic stress response. In contrast to state-of-the-art material descriptions mostly used in the literature (linear elasticity), the current approach provides numerical accuracy in the finite strain regime. Thus, local strain and stress distributions in the annulus fibrosus can properly be determined. Because of the highly nonlinear stress response of the constitutive equations, nonlinear material parameters are required. Although tensile properties of the human annulus fibrosus can already be found in the literature, these material data are not suitable for the current concept as will be shown. The entire constitutive theory is therefore based on a new experimental procedure for the determination of local, nonlinear and anisotropic stress response in annulus tissue. The constitutive model proves its applicability in representative numerical examples. In contrast to state-of-the-art FE analyses, the results do not exhibit parasitic strain (and stress) distributions in annulus tissue under physiological loading conditions. Hence, the current approach seems to be very attractive for refined spinal implant design.

A Critique of Ultimate Referentiality in the New Social Movement Theory of Alberto Melucci

Abstract: A critical examination of Alberto Melucci's social movement theory shows an operative assumption about the of society in his theory. Melucci assumes society as the unique, rational ground that renders society a reservoir of all meanings and conflicts. The actor's pregiven social position is assumed to predispose him or her with the ability to enter into certain conflicts. To show Melucci's operative assumption, three major theses in his theory are examined: (1) transition to the postindustrial society, (2) the middle class radicalism, (3) identity as latent and visible. It is argued that Melucci's notion of society has its roots in his parochial. institutional conception of politics that disregards the hegemonic formation of society and the political character of every social phenomenon and practice. This critique leads to an invitation to a sociology that treats social as loci of the political re-institution of society. Resume: Une examination critique de la theorie du nouveau mouvement social de Alberto Melucci suggere l'hypothese que la societe est referentielle d'apres cette theone. Melucci suppose que la societe est unique et rationnelle, et de plus, la source de toutes significations et conflits. La position sociale de l'acteur le donne la capacite d'entrer dans de certains conflits. Pour illustrer l'hypothese de Melucci, trois theses majeures de sa theorie sont examinees: 1) transition a une societe post-industrielle; 2) le nouveau radicalisme de la classe moyenne; 3) identites telle que [much less than] latente [much greater than] et [much less than] visible [much greater than]. L'auteur affirme que l'origine de la notion de Melucci de la societe se trouve dans sa conception paroissiale et institutionelle de la politique, conception qui ne prend pas en compte la formation hegemonique de la societe et le caractere politique de tout phenomene ou pratique social. Cette critique mene a une sociologie qui traite les nouvea ux mouvements sociaux comme les lieux de la reinstitution politique de la societe. The theoretical literature concerning social has clearly gone through major focal and analytical shifts in the past three decades. Such shifts are nowhere more evident than in the coinage and increasing application of the term social movements (especially during the 1980s). The social movement theory of Italian sociologist Alberto Melucci, one of the originators of the term (Melucci, 1989: 42, 204), deems identity as the cardinal characteristic that distinguishes the new from the older social movements. As such, Melucci belongs to a generation of prominent European theorists -- namely, Alain Touraine, Klaus Eder, Claus Offe -- who emphasize, each in a different way, the centrality of identity, as emphasis on individual or group particularity, in understanding social movements. (1) This paper will examine Melucci's conception of identity in order to show that his social movement theory hinges on an assumption that takes identity to be expressive of some deeper social fundament which surfaces in social movements' practices. I will discuss that this view of identity is symptomatic of an operative assumption about society as a foundation for theoretical moorage. I will also point out that the ultimate referentiality (as an assumed reference to a ground) in Melucci's theory takes place in spite of his acknowledgement that theory must critically reflect on certain older assumptions in order to be able to account for the emergence and increasing prevalence of the new social movements. A comprehensive investigation into Melucci's theory will be done by critically examining three theses around which, to varying degrees, Melucci's entire social movement theory is or has been organized. In each one of these three theses, Melucci tries to theoretically account for the appeals to i dentity in the in relation to a specific criterion: first, with respect to a shift from the industrial to the postindustrial societies in the West; second, in terms of the class origins of the movements' actors (a position which he criticizes later); and finally, in relation to individual or group autonomy or particularity. …

Prisoners of Hate: The Cognitive Basis of Anger, Hostility, and Violence

AARON T. BECK: Prisoners of Hate: The Cognitive Basis of Anger, Hostility, and Violence. HarperCollins Publishers, Inc., New York, 1999, 354 pp., $26.00, ISBN 0-06-019377-8. This volume offers an exceptionally broad-based look at manifestations of anger and hostility, integrating individual psychopathology, the psychology of small group interactions, and wider sociopolitical considerations. Written by one of the foremost innovators and scholars of psychotherapy in the last 50 years, it provides the reader with a comprehensive look at one of the most important problems of contemporary society, i.e., the diagnosis and management of inappropriate anger. In addition, for the reader unschooled in the concepts and techniques of cognitive therapy it serves as an introduction to an increasingly important treatment modality The latter of these purposes, i.e., a brief explication of the basic tenets of cognitive therapy, is realized immediately in the introduction. If one were looking for a brief (6 pages) summary of the entire theory of cognitive treatment, it would be found here. All of the major concepts-automatic thoughts, cognitive distortions, thought as a determinant of mood and affect, the value of correcting one's distortions, and so on-are laid out in a casual, conversational tone that completely belies the profound and radical nature of these constructs. Having reviewed his metapsychology in this way, Beck then goes on to discuss the pathogenesis of hatred within individuals. He describes a number of mental steps often covered by persons becoming angry, beginning with loss and fear and eventuating in blame and rage. His schematic diagrams are always clear without being oversimplistic, and each chapter flows into the next in a straightforward manner. Of interest to the student of comparative metapsychology is the degree to which Beck's concepts relate to those of psychoanalysis. Beck of course began in that tradition, so this in and of itself is not surprising, and he freely acknowledges his debt to Karen Horney (as well as to Albert Ellis). But it is still fascinating to read about projection and unconscious functioning in a cognitive-therapy textbook. Dynamic theorists will also appreciate Beck's speculations on the relationship between anger and low self-esteem. This kind of cross-theorizing is not the primary purpose of this book, so that these leads are scattered and not followed up in any systematic way, but they still tantalize the reader interested in psychotherapy integration. The second portion of the book shifts the focus from anger to violence. Here Beck lays out the application of his basic types of cognitive distortions, e. …

Perspective: Spiritual Issues at the End of Life: A Call for Discussion

When I am dying, I am quite sure that the central sues for me will not be whether I am put on ventilator, whether CPR is attempted when my heart stops, or whether I receive artificial feeding. Although each of these could be important, each will almost certainly be quite peripheral. Rather, my central concerns will be how to face my death, how to bring my life to a close, and how best to help my family go on without me. A ventilator will not help me do these things--not unless all I need is a little more time to get the job done. Unfortunately, however, bioethics has succumbed to the agendas of physicians. Physicians face ethical concerns about treatment decisions--when to offer, withhold, and withdraw various treatments--and treatment decisions have been the focus of bioethics as well. But the issues that most trouble patients and their families at the end of life are not these. To them, the end of life is a crisis. Spiritual? The word spiritual is ambiguous. As I use it, refers to concerns about the ultimate meaning and values in life. It has to do with our deepest sense of who we are and what life is all about. Spiritual does not imply any belief in a supreme being or in a life after this. Atheists have concerns just like everyone else. Spiritual, then, does not mean religious. Indeed, this sense of forces us to ask, How effectively do organized religions address the needs of their members? It may be that some organized religions--or some representatives of them--serve to silence concerns at the end of life or to distract people from them. Certainly many American churches do not talk much about death and dying. One minister confessed, talk a lot about what we believe comes after death. But we skip pretty quickly over dying itself, except to say to make your peace with the Lord. Often, there are strong social and religious pressures to suppress any doubts or questions; doubts and questions are taken as a sign of a weak faith. As a result, Christians can still find that their faith gives them no guidance about how to live the final chapter of life. We Suffer From People facing death suffer from an inability to find meaning in this last chapter of their lives; from a bleak, narrowly confined and abbreviated future; from inability to deal meaningfully with family and loved ones at this final opportunity; from total dependence on others; from loss of capabilities; from being turned from a contributor into a burden on others; from the indignity of being unable to take care of even basic bodily functions; from a sense that their bodies or their minds are betraying them; from being cast out of the world in which the healthy live; from guilt; from a sense of abandonment; from anger about all of this; and from isolation due to the reluctance of the healthy to broach the subject of dying. These are all issues, or at least quickly bring questions into view. Facing death brings to the surface questions about what life is all about. Long-buried assumptions and commitments are revealed. And many find that the beliefs and values they have lived by no longer seem valid or do not sustain them. These are the ingredients of a crisis, the stuff of suffering. Yet they are not the themes of bioethics. Some will object that they are not properly themes of ethics at all, but if they are the dominant concerns of dying patients, bioethics has failed to address patients' concerns at the end of life. This failure has ramifications throughout the discipline of bioethics. 1) Many patients show little interest in making treatment decisions. What difference does it make? one patient told her doctor. She was not asking: her tone and expression made it clear that any difference a treatment decision could make would not be important to her now. Advance directives and the entire theory of proxy decisions are also largely irrelevant to patient concerns at the end of life. …

Stability of solitary wave trains in Hamiltonian wave systems.

A class of Hamiltonian nonlinear wave equations possessing complex solitary waves with exponential decay is studied. It is shown that the interpulse interactions in a train of nearly identical solitary waves with large separations between the individual solitary waves are approximately described by a double Toda lattice system, with two variables at each lattice site. Under certain conditions, which are explicitly identified as Cauchy-Riemann equations, the two dynamical variables are real and imaginary parts of a single complex variable, leading to the complex Toda lattice equations, which is a discrete integrable dynamical system. This analysis generalizes to certain nonintegrable partial differential equations a recent result for the nonlinear Schrödinger equation, and is important for the study of nonlinear communications channels in optical fibers. An example, the cubic-quintic nonlinear Schrödinger equation, is worked out in detail to show that the theory can be carried through analytically. The theory is used to determine the stability of an infinite chain of nearly identical pulses separated by large time intervals. The entire theory is nonperturbative in the sense that the nonlinear wave equation need not be a weak perturbation of an integrable one.

Decomposing modules into direct sums of submodules with types

In this paper, using type submodules, we introduce TS-modules and TS-modules with ( T 3). These are weaker concepts than those of extending modules and quasi-continuous modules. We show that the entire decomposition theory of extending modules and quasi-continuous modules in Mohamed and Müller (Continuous and Discrete Modules, Cambridge Univ. Press, Cambridge, 1990) has an analogue for TS-modules and TS-modules with ( T 3). Besides, the study of TS-modules and TS-modules with ( T 3) also brings out a new concept of rings, namely, rings satisfying t-acc.

Time and memory: towards a pacemaker-free theory of interval timing.

A popular view of interval timing in animals is that it is driven by a discrete pacemaker-accumulator mechanism that yields a linear scale for encoded time. But these mechanisms are fundamentally at odds with the Weber law property of interval timing, and experiments that support linear encoded time can be interpreted in other ways. We argue that the dominant pacemaker-accumulator theory, scalar expectancy theory (SET), fails to explain some basic properties of operant behavior on interval-timing procedures and can only accommodate a number of discrepancies by modifications and elaborations that raise questions about the entire theory. We propose an alternative that is based on principles of memory dynamics derived from the multiple-time-scale (MTS) model of habituation. The MTS timing model can account for data from a wide variety of time-related experiments: proportional and Weber law temporal discrimination, transient as well as persistent effects of reinforcement omission and reinforcement magnitude, bisection, the discrimination of relative as well as absolute duration, and the choose-short effect and its analogue in number-discrimination experiments. Resemblances between timing and counting are an automatic consequence of the model. We also argue that the transient and persistent effects of drugs on time estimates can be interpreted as well within MTS theory as in SET. Recent real-time physiological data conform in surprising detail to the assumptions of the MTS habituation model. Comparisons between the two views suggest a number of novel experiments.

The Duhem—Hadamard hypothesis in thermofluiddynamics

The Duhem–Hadamard hypothesis (DHH) states that in a fluid flow the same equation relates the pressure, the mass density, and the temperature as in equilibrium. The entire theory of bodies concerning flow processes in engineering science and practice rests upon it. Our recent work on fundamentals of non-equilibrium phenomena suggests that the hypothesis are only approximate in some sense, but its mathematical formulation does not make clear what is being approximated. To get a preliminary clarification, the paper deals with two items: first, a theoretical basis is worked out to yield appropriate presuppositions for an efficient experimental program and, second, provisional experimental data are established by a new and precise set-up. Our theoretical examinations admit to derive definite distinguishing features of both non-equilibrium and equilibrium processes. The latter appear as a limiting case of the former and are identified with the hypothetical fluid state at rest. Only for this special state the thermal equation of state is representative of thermodynamic equilibrium. Yet, there is a second kind of equilibrium: the kinetic equilibrium defined for reversible flows. All theoretical considerations lead us to the conclusion that the DHH can only be justified for kinetic equilibria. The first phase of our research program allowed to learn that our high-precision measurement devices need to be improved in order to decide, whether this special kind of reversible flow exists as a real limiting case. Unlike this, our experiments prove that non-equilibrium states induced by the motions of the fluid cannot be described by the DHH.

Towards a theory of delegation for agent-based systems

In this paper a theory of delegation is presented. There are at least three reasons for developing such a theory. First, one of the most relevant notions of “agent” is based on the notion of “task” and of “on behalf of”. In order to found this notion a theory of delegation among agents is needed. Second, the notion of autonomy should be based on different kinds and levels of delegation. Third, the entire theory of cooperation and collaboration requires the definition of the two complementary attitudes of goal delegation and adoption linking collaborating agents. After motivating the necessity for a principled theory of delegation (and adoption) the paper presents a plan-based approach to this theory. We analyze several dimensions of the delegation/adoption (on the basis of the interaction between the agents, of the specification of the task, of the possibility to subdelegate, of the delegation of the control, of the help levels). The agent's autonomy and levels of agency are then deduced. We describe the modelling of the client from the contractor's point of view and vice versa, with their differences, and the notion of trust that directly derives from this modelling. Finally, a series of possible conflicts between client and contractor are considered: in particular collaborative conflicts, which stem from the contractor's intention to help the client beyond its request or delegation and to exploit its own knowledge and intelligence (reasoning, problem solving, planning, and decision skills) for the client itself.

Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories

It is an old speculation in physics that, once the gravitational field is successfully quantized, it should serve as the natural regulator of infrared and ultraviolet singularities that plague quantum field theories in a background metric. We demonstrate that at least part of this idea is implemented in a precise sense within the framework of four-dimensional canonical Lorentzian quantum gravity in the continuum. Specifically, we show that the Hamiltonian of the standard model supports a representation in which finite linear combinations of Wilson loop functionals around closed loops, as well as along open lines with fermionic and Higgs field insertions at the end points, are densely defined operators. This Hamiltonian, surprisingly, does not suffer from any singularities, it is completely finite without renormalization. This property is shared by string theory. In contrast to string theory, however, we are dealing with a particular phase of the standard model coupled to gravity which is entirely non-perturbatively defined and second quantized. Of course, to show that the entire theory is finite requires more: one would need to know what the physical observables are, apart from the Hamiltonian constraint, and whether they are also finite. However, with the results given in this paper this question can now be answered, at least in principle.

Memory as Construction in Viollet-le-Duc's Architectural Imagination

Memory as Construction in Viollet-le-Duc's Architectural Imagination Aron S. Vinegar The nineteenth-century architect and made a lasting impact on France's memory numerous Gothic Not surprisingly, theorist of its architectural past Eugene Viollet-le-Duc and its imagination of an architecture of the future — through his restorations of structures for France's state-run Monuments Historiques. he had a sophisticated conceptual, methodological, and practical understanding of the role of memory and is imagination in historical in scholarly investigation. This understanding is never explicitly discussed it commentary on Viollet-le-Duc, and practice of architectural In his Entretiens sur yet fundamental for his entire theory restoration. l' Architecture, a series of lectures published in two volumes beginning cal inquiry.' in 1863, Viollet-le-Duc offers a meta-methodologi- cal explanation of the roles memory and imagination first play in epistemologi- Viollet-le-Duc was directly inspired by D'Alembert's Pre- liminary Discourse to the volume of the Encyclopedic and Voltaire's discussion of Passive and Active Imagination in his Philosophical Dictio- nary.^ Included in cal tree of D'Alembert's Preliminary Discourse was a genealogi- knowledge the famous Systdme figure des connaissances humaines. The Syst^me figure was divided into three faculties which gave rise to three major divisions of knowledge: Memory, which produced his- tory; Reason, which resulted in philosophy and science; and Imagination, which created poetry and the fine arts. These faculties differed from each other according to how they processed sensations: memory received them, In the Pre- reason reflected upon them, and imagination combined them. liminary Discourse, D'Alembert provides a detailed commentary on each of the three faculties, their interaction, and order of operation within the mind, a formula which Viollet-le-Duc followed closely.' Viollet-le-Duc insists throughout the Entretiens that in architecture there is no invention ex-nihilo, we must necessarily have recourse to the past in order to originate in the present (Lecture VI, 173). ulty to Memory, the first fac- be exercised, involved recalling sensations or ideas passively received by the mind. Viollet-le-Duc like Voltaire and D'Alembert — uses the term memory and it passive imagination for this process rather than the word believed that although passive imagination alone could not create, the fundamental basis of creative imagination. was the Active imagination it is next faculty to come into play. According to Viollet-le-Duc was nothing

The seven deadly curs’d sins …Lust

The seven deadly curs’d sins …Lust

Neoplatonic Exegeses of Plato's Cosmogony ( Timaeus 27C-28C)

Neoplatonic Exegeses of Plato's Cosmogony(Timaeus27C-28C) JOHN F. PHILLIPS AMONGTHE MANYCONTROVERSIESto which the long history of interpretation of Plato's Timaeus has given rise, that concerning the eternity of the cosmos is one of the most enduring and complex, and the source of almost continuous debate from the time of Xenocrates to the present. The importance to all Platonists of a doctrinally consistent answer to the question of whether or not the universe had a beginning in time is made amply clear in the statement attributed to Iamblichus by Proclus (In Tim. I 219, 90) that proper understanding of the creation of the world is crucial for the entire theory of Nature. Iamblichus here refers obliquely to the orthodox Platonist position that the universe is not a temporal being subject to decay and destruction. The principal problem for all of them, of course, was that, taken literally, Plato's account of the creation in the Timaeus, particularly the passage 27C-a8C, appears to be an unequivocal affirmation of a temporal beginning to the cosmos. Especially troublesome was Plato's use of the verb y~yovev in Timaeus 28b 7, which seems to be an explicit claim for an &QX1]in time. That this passage did indeed refer to a temporal beginning was a point that was made repeatedly and forcefully by the chief opponents of the Platonists on this issue, the Peripatetics , who, following Aristotle, read the Timaeus creation account literally.' To counter such opposition, and to enhance their respective positions in their own internecine struggles centered on this question, various Platonists took ever more subtle interpretive approaches, some of the most contentious involving explanations of how Plato's use of y~yovev in 28B 7 could be seen to be compatible with the orthodox position that the creation of the universe was nontemporal. Most notable in this regard is the list, compiled by the Middle Platonist Calvenus Taurus in the second century A.D., of all the possible ' For the argument of Alexander Aphrodisias, see SimpliciusIn De Caelo I ao, pp. ~96ff. Reimer. [173] 174 JOURNAL OF THE HISTORY OF PHILOSOPHY 35:2 APRIL 1997 nontemporalist senses of the word 'created' (yewl~6v) which the best efforts of the Platonic exegetical tradition had produced. According to the Christian Neoplatonist John Philoponus, Taurus identified four such meanings2: M1) That which is not actually created, but is of the same genus as things that are created (zb ~d] yev61xevov Ix~v, ~v 6~ ~ cdJx~, 6v y~vet xo~gyev'q~o~g). M~) That which is conceptually composite, even if it has never in fact been combined (~6 ~mvo~q o~v0e~ov, xa~ et M1 ovwe0,fi). M3) That which is perpetually in the process of becoming (6e~ ~v t 0 y~veo0ctt). M4) That which has the cause of its existence in a higher source external to it (~b etvctt ct~ &D.ox60ev ~o'r~v • ~aQh ~o~ 0eo~). This list of meanings was for centuries the standard resource for Platonist exegeses of Timaeus 27C-28C, with the different schools arguing for one or more of them as the sense or senses in which Plato's use of the term was to be understood. Of these many and varied interpretations,s all of which were attempts to read a nontemporalist account into what is certainly on a prima facie reading a temporalist description of the creation of the universe, I wish to consider several which incorporate one or more of the meanings on Taurus' list, specifically M2, which holds that the universe is created in the sense of being a composite of matter and form; M 3, what Matthias Baltes4 terms the "physicalist" interpretation, according to which there was no moment when the cosmos came to be; it is rather perpetually becoming, or, to give it the common expression of antiquity, it has its being in its becoming; and M 4, the 2De Aet. Mundi VI 8, pp. 145, 13--147, 6 Rabe. Taurus' list was later expanded by Porphyry (ibid. VI 8, p. 148, 7ft.). These attempts to establish nontemporalist definitionsof yevrlx6vwere in part inspired by Aristotle'sown list of meanings in De Caelo 28ob15ff. Cf. Proclus In Tim...

The diffusion model for migration and selection in a plant population

The diffusion approximation is derived for migration and selection at a multiallelic locus in a partially selfing plant population subdivided into a lattice of colonies. Generations are discrete and nonoverlapping; both pollen and seeds disperse. In the diffusion limit, the genotypic frequencies at each point are those determined at equilibrium by the local rate of selfing and allelic frequencies. If the drift and diffusion coefficients are taken as the appropriate linear combination of the corresponding coefficients for pollen and seeds, then the migration terms in the partial differential equation for the allelic frequencies have the standard form for a monoecious animal population. The selection term describes selection on the local genotypic frequencies. The boundary conditions and the unidimensional transition conditions for a geographical barrier and for coincident discontinuities in the carrying capacity and migration rate have the standard form. In the diallelic case, reparametrization renders the entire theory of clines and of the wave of advance of favorable alleles directly applicable to plant populations.