Functional Integration and the Mind
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Generative Models, Structural Similarity, and Mental Representation
The Mind as a Predictive Modelling Engine: Generative Models, Structural Similarity, and Mental Representation Daniel George Williams Trinity Hall College University of Cambridge This dissertation is submitted for the degree of Doctor of Philosophy August 2018 The Mind as a Predictive Modelling Engine: Generative Models, Structural Similarity, and Mental Representation Daniel Williams Abstract I outline and defend a theory of mental representation based on three ideas that I extract from the work of the mid-twentieth century philosopher, psychologist, and cybernetician Kenneth Craik: first, an account of mental representation in terms of idealised models that capitalize on structural similarity to their targets; second, an appreciation of prediction as the core function of such models; and third, a regulatory understanding of brain function. I clarify and elaborate on each of these ideas, relate them to contemporary advances in neuroscience and machine learning, and favourably contrast a predictive model-based theory of mental representation with other prominent accounts of the nature, importance, and functions of mental representations in cognitive science and philosophy. For Marcella Montagnese Preface Declaration This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration except as declared in the Preface and specified in the text. It is not substantially the same as any that I have submitted, or, is being concurrently submitted for a degree or diploma or other qualification at the University of Cambridge or any other University or similar institution except as declared in the Preface and specified in the text. I further state that no substantial part of my dissertation has already been submitted, or, is being concurrently submitted for any such degree, diploma or other qualification at the University of Cambridge or any other University or similar institution except as declared in the Preface and specified in the text. -
Funaional Integration for Solving the Schroedinger Equation
Comitato Nazionale Energia Nucleare Funaional Integration for Solving the Schroedinger Equation A. BOVE. G. FANO. A.G. TEOLIS RT/FIMÀ(7$ Comitato Nazionale Energia Nucleare Funaional Integration for Solving the Schroedinger Equation A. BOVE, G.FANO, A.G.TEOLIS 3 1. INTRODUCTION Vesto pervenuto il 2 agosto 197) It ia well-known (aee e.g. tei. [lj - |3| ) that the infinite-diaeneional r«nctional integration ia a powerful tool in all the evolution processes toth of the type of the heat -tanefer or Scbroediager equation. Since the 'ieid of applications of functional integration ia rapidly increasing, it *«*ae dcairahle to study the «stood from the nuaerical point of view, at leaat in siaple caaea. Such a orograa baa been already carried out by Cria* and Scorer (ace ref. |«| - |7| ), via Monte-Carlo techniques. We use extensively an iteration aethod which coneiecs in successively squa£ ing < denaicy matrix (aee Eq.(9)), since in principle ic allows a great accuracy. This aetbod was used only tarely before (aee ref. |4| ). Fur- chersjore we give an catiaate of che error (e«e Eqs. (U),(26)) boch in Che caaa of Wiener and unleabeck-Ometein integral. Contrary to the cur rent opinion (aae ref. |13| ), we find that the last integral ia too sen sitive to the choice of the parameter appearing in the haraonic oscilla tor can, in order to be useful except in particular caaea. In this paper we study the one-particle spherically sysssetric case; an application to the three nucleon probUa is in progress (sea ref. |U| ). St»wp«wirìf^m<'oUN)p^woMG>miutoN«i»OMtop«fl'Ht>p>i«Wi*faif»,Piijl(Mi^fcri \ptt,mt><r\A, i uwh P.ei#*mià, Uffcio Eanfeai SaMfiM», " ~ Hot*, Vi.1. -
НОВОСИБИРСК Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia
ИНСТИТУТ ЯДЕРНОЙ ФИЗИКИ им. Г.И. Будкера СО РАН Sudker Institute of Nuclear Physics P.G. Silvestrcv CONSTRAINED INSTANTON AND BARYON NUMBER NONCONSERVATION AT HIGH ENERGIES BIJ'DKERINP «292 НОВОСИБИРСК Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia P.G.SUvestrov CONSTRAINED INSTANTON AND BARYON NUMBER NON-CONSERVATION AT HIGH ENERGIES BUDKERINP 92-92 NOVOSIBIRSK 1992 Constrained Instanton and Baryon Number NonConservation at High Energies P.G.Silvestrov1 Budker Institute of Nuclear Physics, 630090 Novosibirsk, Russia Abstract The total cross section for baryon number violating processes at high energies is usually parametrized as <r«,toi oe exp(—.F(e)), where 5 = Л/З/EQ EQ = у/^ттпш/tx. In the present paper the third nontrivial term of the expansion is obtain^. The unknown corrections to F{e) are expected to be of 8 3 2 the order of c ' , but have neither (mhfmw) , nor log(e) enhance ment. The .total cross section is extremely sensitive to the value of single Instanton action. The correction to Instanton action A5 ~ (mp)* log(mp)/</2 is found (p is the Instanton radius). For sufficiently heavy Higgs boson the pdependent part of the Instanton action is changed drastically, in this case even the leading contribution to F(e), responsible for a growth of cross section due to the multiple produc tion of classical Wbosons, is changed: ©Budker Institute of Nuclear Physics 'етаЦ address! PStt.VESTBOV®INP.NSK.SU 1 Introduction A few years ago it was recognized, that the total crosssection for baryon 1БЭ number violating processes, which is small like ехр(4т/а) as 10~ [1] 2 (where a = р /(4тг)) at low energies, may become unsuppressed at TeV energies [2, 3, 4]. -
International Journal of Action Research Volume 5, Issue 1, 2009
International Journal of Action Research Volume 5, Issue 1, 2009 Editorial Werner Fricke, Øyvind Pålshaugen 5 Popular Education and Participatory Research: Facing Inequalities in Latin America Danilo R. Streck 13 Organizing – A Strategic Option for Trade Union Renewal? Klaus Dörre, Hajo Holst, Oliver Nachtwey 33 Phronesis as the Sense of the Event Ole Fogh Kirkeby 68 Opening to the World through the Lived Body: Relating Theory and Practice in Organisation Consulting Robert Farrands 114 Book review Olav Eikeland (2008): The Ways of Aristotle. Aristotelian phrónêsis, Aristotelian Philosophy of Dialogue, and Action Research reviewed by Ole Fogh Kirkeby 144 Phronesis as the Sense of the Event Ole Fogh Kirkeby In this article, the Greek concept of phronesis is analyzed on the basis of its philosophical roots, and the indispensability of its strong normative content is emphasized. This creates a distance to most of the recent under- standing of phronesis as prudence, and hence as practical wisdom with a pragmatic and strategic content. The strong dilemmas created by the nor- mative background of real phronesis present management and leadership as a choice in every situation. From this foundation, phronesis is inter- preted as primarily the sense of the event, and an alternative concept of the event is developed. The presentation of the event also demands a theory of the relation of mind and matter, and hence of the body in the event. This is achieved under inspiration from Stoic philosophy. With this in mind, the more serious approaches to practical wisdom: phronesis as determinant of meta-concepts of research; phronesis as a liberating organizational strategy of learning; phronesis as a strategy of knowledge management; phronesis as a narrative strategy; and phronesis as the capacity of the leader, are presented and analyzed. -
Scott Marratto CV
MARRATTO :: CURRICULUM VITAE (UPDATED 1 APRIL 20) SCOTT MARRATTO ASSOCIATE PROFESSOR OF PHILOSOPHY HUMANITIES DEPARTMENT MICHIGAN TECHNOLOGICAL UNIVERSITY CONTACT INFORMATION • Humanities Department Michigan Technological University 1400 Townsend Drive Houghton, MI 49931-1295 • Phone: (906) 487-2613 • Email: [email protected] • Web: mtu.edu/humanities/department/faculty-staff/faculty/marratto/ AREAS OF SPECIALIZATION AND COMPETENCE • AOS: 19th and 20th Century Continental Philosophy (especially Phenomenology), Social and Political Philosophy • AOC: Philosophy of Science and Technology, Ethics, Ancient Philosophy, Aesthetics, Philosophy of Mind ACADEMIC POSITIONS • Associate Professor of Philosophy, Humanities Department, Michigan Technological University, 2011-present • Director of Graduate Studies in Rhetoric, Theory and Culture, Humanities Department, Michigan Technological University, 2015-2018 • Senior Fellow, Foundation Year Programme, University of King’s College, Halifax, 2010- 2011 • Instructor, Contemporary Studies Programme, University of King’s College, Halifax, 2009-2011 • Teaching Fellow, Foundation Year Programme, University of King’s College, Halifax, 2007-2010 EDUCATION • University of Guelph, PhD, Philosophy (2010) • University of Guelph, MA, Philosophy (2005) • University of Toronto, Special/Non-degree, Philosophy (2001-2) • University of Western Ontario, BA, Sociology (2001) PUBLICATIONS Books 1 MARRATTO :: CURRICULUM VITAE (UPDATED 1 APRIL 20) • The Intercorporeal Self: Merleau-Ponty on Subjectivity. Albany, NY: State University of New York Press (2012). o Reviews: Symposium: Canadian Journal of Continental Philosophy, March (2013); Notre Dame Philosophical Reviews, February (2013); Review of Metaphysics 67 (2013); Avant V (2014); Word and Text: A Journal of Literary Studies and Linguistics 3 (2013). • The End of Ethics in a Technological Society. Montreal, QC: McGill-Queens University Press (2008). (With Lawrence E. Schmidt.) Book Chapters • “Intercorporeality.” In 50 Concepts for a Critical Phenomenology, eds. -
Supersymmetric Path Integrals
Communications in Commun. Math. Phys. 108, 605-629 (1987) Mathematical Physics © Springer-Verlag 1987 Supersymmetric Path Integrals John Lott* Department of Mathematics, Harvard University, Cambridge, MA 02138, USA Abstract. The supersymmetric path integral is constructed for quantum mechanical models on flat space as a supersymmetric extension of the Wiener integral. It is then pushed forward to a compact Riemannian manifold by means of a Malliavin-type construction. The relation to index theory is discussed. Introduction An interesting new branch of mathematical physics is supersymmetry. With the advent of the theory of superstrings [1], it has become important to analyze the quantum field theory of supersymmetric maps from R2 to a manifold. This should probably be done in a supersymmetric way, that is, based on the theory of supermanifolds, and in a space-time covariant way as opposed to the Hamiltonian approach. Accordingly, one wishes to make sense of supersymmetric path integrals. As a first step we study a simpler case, that of supersymmetric maps from R1 to a manifold, which gives supersymmetric quantum mechanics. As Witten has shown, supersymmetric quantum mechanics is related to the index theory of differential operators [2]. In this particular case of a supersymmetric field theory, the Witten index, which gives a criterion for dynamical supersymmetry breaking, is the ordinary index of a differential operator. If one adds the adjoint to the operator and takes the square, one obtains the Hamiltonian of the quantum mechanical theory. These indices can be formally computed by supersymmetric path integrals. For example, the Euler characteristic of a manifold M is supposed to be given by integrating e~L, with * Research supported by an NSF postdoctoral fellowship Current address: IHES, Bures-sur-Yvette, France 606 J. -
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties
The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties Chen Sagiv1, Nir A. Sochen1, and Yehoshua Y. Zeevi2 1 Department of Applied Mathematics University of Tel Aviv Ramat-Aviv, Tel-Aviv 69978, Israel [email protected],[email protected] 2 Department of Electrical engineering Technion - Israel Institute of Technology Technion City, Haifa 32000, Israel [email protected] Abstract. The uncertainty principle is a fundamental concept in the context of signal and image processing, just as much as it has been in the framework of physics and more recently in harmonic analysis. Un- certainty principles can be derived by using a group theoretic approach. This approach yields also a formalism for finding functions which are the minimizers of the uncertainty principles. A general theorem which associates an uncertainty principle with a pair of self-adjoint operators is used in finding the minimizers of the uncertainty related to various groups. This study is concerned with the uncertainty principle in the context of the Weyl-Heisenberg, the SIM(2), the Affine and the Affine-Weyl- Heisenberg groups. We explore the relationship between the two-dimensional affine group and the SIM(2) group in terms of the uncertainty minimizers. The uncertainty principle is also extended to the Affine-Weyl-Heisenberg group in one dimension. Possible minimizers related to these groups are also presented and the scale-space properties of some of the minimizers are explored. 1 Introduction Various applications in signal and image processing call for deployment of a filter bank. The latter can be used for representation, de-noising and edge en- hancement, among other applications. -
Justice, Respublica and Empire: Subsidiarity and Hierarchy In
chapter 7 Justice, Res Publica and Empire: Subsidiarity and Hierarchy in the Roman Empire Frédéric Hurlet The objective of this study is to synthesize and extend research conducted in connection with the series of three international conferences held at the Villa Vigoni (Menaggio, Como) from 2010 to 2012, on the exercise of justice in the Roman Empire during the High Empire and late Antiquity. As indi- cated by the title chosen for the publication (Recht haben und Recht bekom- men im Imperium Romanum: das Gerichtswesen der römischen Kaiserzeit und seine dokumentarische Evidenz), the purpose of these meetings was notably to underscore the wealth and diversity of documentation on the subject of judi- cial practice.1 With this in mind, it was less a matter of focusing on normative sources—late-antique compilations that have been amply explored since the nineteenth century—than of emphasizing what the large number of inscrip- tions and papyri discovered during the twentieth and twenty-first centuries have contributed to our knowledge of how justice operated on an everyday basis and how it was experienced by those subject to it. This work has certainly fulfilled its goal in this regard through the use of epigraphic and papyrological documents, some of which had never been published. 1 The Intrinsic Links between Justice and Power in Antiquity The relative documentary abundance on the exercise of justice in the Roman Empire is in truth not surprising. It is a consequence of the central role that justice, as well as the functioning of the judiciary institutions tasked with applying law, played in the everyday life of the Empire’s inhabitants, whether in a global (imperial) or local setting (on the level of the different types of communities that formed the Empire’s base units). -
On Physical Multiple Realization
ON PHYSICAL MULTIPLE REALIZATION BY RONALD P. ENDICOTT Perhaps no argument has done more to set the direction of contemporary philosophy of mind than the “multiple realizability argument.” First championed by Hilary Putnam and later reformulated by Jerry Fodor, the argument begins with the observation that a given psychological property can be realized by any number of diverse physical systems, and then ends with the conclusion that psychological properties are irreducible vis-à-vis the physical sciences.^ Its target, in other words, is type physicalism and the unity of science, as traditionally conceived. According to one popular criticism, however, the multiple realizability argument has been discredited by the fact that physical properties are also multiply realized} But this, I believe, is a mistake. While the criticism does serve to bring a number of important issues into better focus, it can be shown that the facts about physical multiple realization are perfectly consistent with the Putnam-Fodor style argument, and that, when such facts are rightly understood, they do not vitiate the original point about the irreducibility of psychological properties. /. Multiple Realization In spite of much talk about multiple realization, philosophers have generally been content to leave this central concept unanalyzed. I shall try to remedy this situation by indicating the two most salient features of the concept. First, there is the idea that a property is realized by a number of diverse states, which I take to mean that different state types can provide lawfully sufficient conditions for the instantiation of the multiply realized property. And second, there is the idea that among this range of diverse Pacific Philosophical Quarterly 70 (1989) 212-224 0279-0750/89/0300-0212 $01.30 Copyright © 1989 University of Southern California ON PHYSICAL MULTIPLE REALIZATION 213 states, there are no lawfully necessary and sufficient conditions for the instantiation of that property. -
Introduction to Supersymmetric Theory of Stochastics
entropy Review Introduction to Supersymmetric Theory of Stochastics Igor V. Ovchinnikov Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA 90095, USA; [email protected]; Tel.: +1-310-825-7626 Academic Editors: Martin Eckstein and Jay Lawrence Received: 31 October 2015; Accepted: 21 March 2016; Published: 28 March 2016 Abstract: Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order’s omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, 1/ f noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized criticality, etc. Although several successful approaches to various realizations of DLRO have been established, the universal theoretical understanding of this phenomenon remained elusive. The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS). There, DLRO is the spontaneous breakdown of the topological or de Rahm supersymmetry that all stochastic differential equations (SDEs) possess. This theory may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity. The STS is also an interdisciplinary construction. This theory is based on dynamical systems theory, cohomological field theories, the theory of pseudo-Hermitian operators, and the conventional theory of SDEs. Reviewing the literature on all these mathematical disciplines can be time consuming. -
Philosophy of Mind and the Problem of Free Will in the Light of Quantum Mechanics
Philosophy of Mind and the Problem of Free Will in the Light of Quantum Mechanics. Henry P. Stapp Lawrence Berkeley National Laboratory University of California Berkeley, California 94720 Abstract Arguments pertaining to the mind-brain connection and to the physical effectiveness of our conscious choices have been presented in two recent books, one by John Searle, the other by Jaegwon Kim. These arguments are examined, and it is explained how the encountered difficulties arise from a defective understanding and application of a pertinent part of contemporary science, namely quantum mechanics. The principled quantum uncertainties entering at the microscopic levels of brain processing cannot be confined to the micro level, but percolate up to the macroscopic regime. To cope with the conflict between the resulting macroscopic indefiniteness and the definiteness of our conscious experiences, orthodox quantum mechanics introduces the idea of agent-generated probing actions, each of which specifies a definite set of alternative possible empirically/experientially distinguishable outcomes. Quantum theory then introduces the mathematical concept of randomness to describe the probabilities of the various alternative possible outcomes of the chosen probing action. But the agent-generated choice of which probing action to perform is not governed by any known law or rule, statistical or otherwise. This causal gap provides a logical opening, and indeed a logical need, for the entry into the dynamical structure of nature of a process that goes beyond the currently understood quantum mechanical statistical generalization of the deterministic laws of classical physics. The well-known quantum Zeno effect can then be exploited to provide a natural process that establishes a causal psychophysical link within the complex structure consisting of a stream of conscious experiences and certain macroscopic classical features of a quantum mechanically described brain. -
Chapter 3 Feynman Path Integral
Chapter 3 Feynman Path Integral The aim of this chapter is to introduce the concept of the Feynman path integral. As well as developing the general construction scheme, particular emphasis is placed on establishing the interconnections between the quantum mechanical path integral, classical Hamiltonian mechanics and classical statistical mechanics. The practice of path integration is discussed in the context of several pedagogical applications: As well as the canonical examples of a quantum particle in a single and double potential well, we discuss the generalisation of the path integral scheme to tunneling of extended objects (quantum fields), dissipative and thermally assisted quantum tunneling, and the quantum mechanical spin. In this chapter we will temporarily leave the arena of many–body physics and second quantisation and, at least superficially, return to single–particle quantum mechanics. By establishing the path integral approach for ordinary quantum mechanics, we will set the stage for the introduction of functional field integral methods for many–body theories explored in the next chapter. We will see that the path integral not only represents a gateway to higher dimensional functional integral methods but, when viewed from an appropriate perspective, already represents a field theoretical approach in its own right. Exploiting this connection, various techniques and concepts of field theory, viz. stationary phase analyses of functional integrals, the Euclidean formulation of field theory, instanton techniques, and the role of topological concepts in field theory will be motivated and introduced in this chapter. 3.1 The Path Integral: General Formalism Broadly speaking, there are two basic approaches to the formulation of quantum mechan- ics: the ‘operator approach’ based on the canonical quantisation of physical observables Concepts in Theoretical Physics 64 CHAPTER 3.