Geometry and Meaning

Geometry and Meaning

This text explores the computational techniques necessary to represent meaning and their basis in conceptual space.

Author: Dominic Widdows

Publisher: Center for the Study of Language & Information - Lecture Notes

ISBN: 1575864487

Category: Mathematics

Page: 319

View: 543

Geometric models similar to those of Pythagoras and Einstein are now being applied to the conceptual space of information and meaning, for example in the arrangement of Internet documents. This text explores the computational techniques necessary to represent meaning and their basis in conceptual space.
Categories: Mathematics

The Geometry of Meaning

The Geometry of Meaning

In The Geometry of Meaning, Peter Gärdenfors proposes a theory of semantics that bridges cognitive science and linguistics and shows how theories of cognitive processes, in particular concept formation, can be exploited in a general ...

Author: Peter Gardenfors

Publisher: MIT Press

ISBN: 9780262319591

Category: Language Arts & Disciplines

Page: 356

View: 429

A novel cognitive theory of semantics that proposes that the meanings of words can be described in terms of geometric structures. In The Geometry of Meaning, Peter Gärdenfors proposes a theory of semantics that bridges cognitive science and linguistics and shows how theories of cognitive processes, in particular concept formation, can be exploited in a general semantic model. He argues that our minds organize the information involved in communicative acts in a format that can be modeled in geometric or topological terms—in what he terms conceptual spaces, extending the theory he presented in an earlier book by that name. Many semantic theories consider the meanings of words as relatively stable and independent of the communicative context. Gärdenfors focuses instead on how various forms of communication establish a system of meanings that becomes shared between interlocutors. He argues that these “meetings of mind” depend on the underlying geometric structures, and that these structures facilitate language learning. Turning to lexical semantics, Gärdenfors argues that a unified theory of word meaning can be developed by using conceptual spaces. He shows that the meaning of different word classes can be given a cognitive grounding, and offers semantic analyses of nouns, adjectives, verbs, and prepositions. He also presents models of how the meanings of words are composed to form new meanings and of the basic semantic role of sentences. Finally, he considers the future implications of his theory for robot semantics and the Semantic Web.
Categories: Language Arts & Disciplines

The Geometry of Love

The Geometry of Love

A “delightful” tour of Rome’s St. Agnes Outside the Walls, examining the stories, rituals, and architecture of this seventeen-hundred-year-old building (The Christian Science Monitor).

Author: Margaret Visser

Publisher: Open Road Media

ISBN: 9781504011709

Category: Architecture

Page: 328

View: 446

A “delightful” tour of Rome’s St. Agnes Outside the Walls, examining the stories, rituals, and architecture of this seventeen-hundred-year-old building (The Christian Science Monitor). In The Geometry of Love, acclaimed author Margaret Visser, the preeminent “anthropologist of everyday life,” takes on the living history of the ancient church of St. Agnes. Examining every facet of the building, from windows to catacombs, Visser takes readers on a mesmerizing tour of the old church, covering its social, political, religious, and architectural history. In so doing, she illuminates not only the church’s evolution but also its religious legacy in our modern lives. Written as an antidote to the usual dry and traditional studies of European churches, The Geometry of Love is infused with Visser’s unmatched warmth and wit, celebrating the remarkable ways that one building can reveal so much about our history and ourselves.
Categories: Architecture

Giordano Bruno and the Geometry of Language

Giordano Bruno and the Geometry of Language

Paris: Hachette, 1978. PérezLlantada Auria, Carmen. “On Fractal Geometry and
Meaning Dissemination: Rethinking Pynchon's The Crying of Lot 49.” Atlantis 17 (
1995): 229–243. Pieri, Marzia. “Fra scrittura e scena: La cinquecentina teatrale.

Author: Arielle Saiber

Publisher: Routledge

ISBN: 9781351933674

Category: Literary Criticism

Page: 200

View: 403

Giordano Bruno and the Geometry of Language brings to the fore a sixteenth-century philosopher's role in early modern Europe as a bridge between science and literature, or more specifically, between the spatial paradigm of geometry and that of language. Arielle Saiber examines how, to invite what Bruno believed to be an infinite universe-its qualities and vicissitudes-into the world of language, Bruno forged a system of 'figurative' vocabularies: number, form, space, and word. This verbal and symbolic system in which geometric figures are seen to underlie rhetorical figures, is what Saiber calls 'geometric rhetoric.' Through analysis of Bruno's writings, Saiber shows how Bruno's writing necessitates a crafting of space, and is, in essence, a lexicon of spatial concepts. This study constitutes an original contribution both to scholarship on Bruno and to the fields of early modern scientific and literary studies. It also addresses the broader question of what role geometry has in the formation of any language and literature of any place and time.
Categories: Literary Criticism

Geometry and Topology

Geometry and Topology

It is the central activity and main driving force in many branches of math and
physics , and offers a whole range of views on the nature and meaning of the
universe . This book treats geometry in a wide context , including a wealth of
relations ...

Author: Miles Reid

Publisher: Cambridge University Press

ISBN: 052184889X

Category: Mathematics

Page: 196

View: 672

Geometry provides a whole range of views on the universe, serving as the inspiration, technical toolkit and ultimate goal for many branches of mathematics and physics. This book introduces the ideas of geometry, and includes a generous supply of simple explanations and examples. The treatment emphasises coordinate systems and the coordinate changes that generate symmetries. The discussion moves from Euclidean to non-Euclidean geometries, including spherical and hyperbolic geometry, and then on to affine and projective linear geometries. Group theory is introduced to treat geometric symmetries, leading to the unification of geometry and group theory in the Erlangen program. An introduction to basic topology follows, with the Möbius strip, the Klein bottle and the surface with g handles exemplifying quotient topologies and the homeomorphism problem. Topology combines with group theory to yield the geometry of transformation groups,having applications to relativity theory and quantum mechanics. A final chapter features historical discussions and indications for further reading. With minimal prerequisites, the book provides a first glimpse of many research topics in modern algebra, geometry and theoretical physics. The book is based on many years' teaching experience, and is thoroughly class-tested. There are copious illustrations, and each chapter ends with a wide supply of exercises. Further teaching material is available for teachers via the web, including assignable problem sheets with solutions.
Categories: Mathematics

Language and Meaning in Cognitive Science

Language and Meaning in Cognitive Science

What is probably the world's first psychological experiment is described in the
Platonic dialogues, when Socrates undertakes to demonstrate that a slave boy,
who has had no instruction in geometry, nevertheless knows the truths of

Author: Andy Clark

Publisher: Routledge

ISBN: 9781136525391

Category: Philosophy

Page: 312

View: 103

Summarizes and illuminates two decades of research Gathering important papers by both philosophers and scientists, this collection illuminates the central themes that have arisen during the last two decades of work on the conceptual foundations of artificial intelligence and cognitive science. Each volume begins with a comprehensive introduction that places the coverage in a broader perspective and links it with material in the companion volumes. The collection is of interest in many disciplines including computer science, linguistics, biology, information science, psychology, neuroscience, iconography, and philosophy. Examines initial efforts and the latest controversies The topics covered range from the bedrock assumptions of the computational approach to understanding the mind, to the more recent debates concerning cognitive architectures, all the way to the latest developments in robotics, artificial life, and dynamical systems theory. The collection first examines the lineage of major research programs, beginning with the basic idea of machine intelligence itself, then focuses on specific aspects of thought and intelligence, highlighting the much-discussed issue of consciousness, the equally important, but less densely researched issue of emotional response, and the more traditionally philosophical topic of language and meaning. Provides a gamut of perspectives The editors have included several articles that challenge crucial elements of the familiar research program of cognitive science, as well as important writings whose previous circulation has been limited. Within each volume the papers are organized to reflect a variety of research programs and issues. The substantive introductions that accompany each volume further organize the material and provide readers with a working sense of the issues and the connection between articles.
Categories: Philosophy

Architecture Mentalities and Meaning

Architecture  Mentalities and Meaning

That geometry is matched by a condition that exists within the mind as an
established pattern of neural energy. Its recognition is dependent on the
existence of corresponding sets of environmental and cognitive states, and on
the human ...

Author: Patrick Malone

Publisher: Taylor & Francis

ISBN: 9781351675369

Category: Social Science

Page: 240

View: 521

In order to function, architectural theory and practice must be shaped to suit current cultural, economic, and political forces. Thus, architecture embodies reductive logic that conditions the treatment of human and social processes – which raises the question of how to define objectivity for architectural mentalities that must conform to a set of immediate conditions. This book focuses on meaning, and on the physical and mental processes that define life in built environments. The potential to draw knowledge from aesthetics, psychology, political economy, philosophy, geography, and sociology is offset by the fact that architectural logic is inevitably reductive, cultural, socio-economic, and political. However, despite the duty to conform, it is argued that the treatment of human processes, and the understanding of architectural mentalities, can benefit from interdisciplinary linkages, small freedoms, and cracks in a system of imperatives that can yield the means of greater objectivity. This is valuable reading for students and researchers interested in architectural theory as a working reality, and in the relationships between architecture and other fields.
Categories: Social Science

David Hilbert and the Axiomatization of Physics 1898 1918

David Hilbert and the Axiomatization of Physics  1898   1918

... both arithmetic and geometry, Dedekind only stressed the epistemological
dimension for the case of his definition of ... the role and meaning of axioms for
these two mathematical disciplines, geometry and arithmetic, his method for
abstractly ...

Author: L. Corry

Publisher: Springer Science & Business Media

ISBN: 140202777X

Category: Science

Page: 513

View: 718

David Hilbert (1862-1943) was the most influential mathematician of the early twentieth century and, together with Henri Poincaré, the last mathematical universalist. His main known areas of research and influence were in pure mathematics (algebra, number theory, geometry, integral equations and analysis, logic and foundations), but he was also known to have some interest in physical topics. The latter, however, was traditionally conceived as comprising only sporadic incursions into a scientific domain which was essentially foreign to his mainstream of activity and in which he only made scattered, if important, contributions. Based on an extensive use of mainly unpublished archival sources, the present book presents a totally fresh and comprehensive picture of Hilbert’s intense, original, well-informed, and highly influential involvement with physics, that spanned his entire career and that constituted a truly main focus of interest in his scientific horizon. His program for axiomatizing physical theories provides the connecting link with his research in more purely mathematical fields, especially geometry, and a unifying point of view from which to understand his physical activities in general. In particular, the now famous dialogue and interaction between Hilbert and Einstein, leading to the formulation in 1915 of the generally covariant field-equations of gravitation, is adequately explored here within the natural context of Hilbert’s overall scientific world-view. This book will be of interest to historians of physics and of mathematics, to historically-minded physicists and mathematicians, and to philosophers of science.
Categories: Science

Meaning Agency and the Making of a Social World

Meaning  Agency and the Making of a Social World

If this connection is not seen then science behaves like a machine operating on
an algorithm which is to be followed in a routine manner without having any
understanding of meaning. In this respect, Husserl's work, Origin of Geometry, ...

Author: Amitabha Das Gupta

Publisher: Routledge

ISBN: 9780429534379

Category: Philosophy

Page: 340

View: 678

This book explores a vital but neglected element in the philosophy of social science – the complex nature of the social world. By a systematic philosophical engagement, it conceives the social world in terms of three basic concerns: epistemic, methodological and ethical. It examines how we cognize, study and ethically interact with the social world. As such, it demonstrates that a discussion of ethics is epistemically indispensable to the making of the social world. The book presents a new interpretation of philosophy of social science and addresses a series of related topics, including the role of the human subject in the context of scientific knowledge, objectivity, historicity, meaning and nature of social reality, social and literary theory, scientific methodology and fact/value dichotomy, human and collective agency and the limits to relativism. Examining each in turn, it argues that the social world is constructed through human actions and becomes significant because we ascribe meaning to it. This is organized around discussions on the meaning, agency and the making of a social world. The book will be useful to scholars and researchers of philosophy of social science, political philosophy and sociology.
Categories: Philosophy

Elements of Analytical Geometry and of the Differential and Integral Calculus

Elements of Analytical Geometry and of the Differential and Integral Calculus

INTRODUCTION , COMMON TERMS must always be employed in definitions ,
because a definition refers to a class of things in which each enjoys at least one
property common to all the others . Each individual of a class , so defined , is
called ...

Author: Charles Davies


ISBN: IND:30000153294172

Category: Calculus

Page: 398

View: 237

Categories: Calculus

Mathematics Its Content Methods and Meaning

Mathematics  Its Content  Methods  and Meaning

Lobačevskii geometry consequently has a perfectly real meaning : It is nothing
but an abstract account of the geometry on the pseudosphere . We ought to
mention that , thirty years before Beltrami ' s discovery , the intrinsic geometry of
the ...

Author: Matematicheskiĭ institut im. V.A. Steklova


ISBN: UOM:39015017378194

Category: Mathematics


View: 351

Categories: Mathematics

The Geometry of Meaning

The Geometry of Meaning

The fourfold division - The measure formulae - The threefold division - Generating other measure formulae - The rosetta stone of meaning - The roots of unity - Comparison of threefold and fourfold operators - Substance and form - Purposive ...

Author: Arthur M. Young

Publisher: Anodos Foundation

ISBN: 0960985050

Category: Knowledge, Theory of

Page: 169

View: 175

Categories: Knowledge, Theory of

Riemannian Geometry and Geometric Analysis

Riemannian Geometry and Geometric Analysis

I have selected that proof because it elucidates the interplay between the
geometric meaning of the energy functional and its approximations and the
geometric features of nonpositively curved manifolds. Finally, the proofs of
Theorems 7.6.3 ...

Author: Jürgen Jost

Publisher: Springer Science & Business Media

ISBN: 354077341X

Category: Mathematics

Page: 590

View: 272

This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. This new edition introduces and explains the ideas of the parabolic methods that have recently found such spectacular success in the work of Perelman at the examples of closed geodesics and harmonic forms. It also discusses further examples of geometric variational problems from quantum field theory, another source of profound new ideas and methods in geometry.
Categories: Mathematics

Foundations of Geometry and Induction

Foundations of Geometry and Induction

the only test of the truth of particular ... Writers most occupied withthe empirical
meaning of propositions about the material world give us, in fact,only the most ...

Author: Jean Nicod

Publisher: Routledge

ISBN: 9781317830689

Category: Philosophy

Page: 292

View: 166

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.
Categories: Philosophy

Discrete Geometry and Topology

Discrete Geometry and Topology

Similar meaning will be attached to the notions of crowns of the polyhedron of the
partition . To begin with , let us take any vertex A of the initial polyhedron M ,
consider the m - hedral angle ( m - gonohedron ) defined by this vertex , and
choose ...

Author: Boris Nikolaevich Delone

Publisher: American Mathematical Soc.

ISBN: 082183147X

Category: Mathematics

Page: 193

View: 537

This collection of papers honors the 100th anniversary of the birth of Boris Nikolaevich Delone, whose mathematical interests centered on the geometry of positive quadratic forms. After an initial paper presenting an account of Delone's life, including his scientific work, the book centers on discrete geometry and combinatorics. The book presents new methods that permit a description of the structure of some $L$-bodies and $L$-partitionings and that, in many cases, provide a definitive description. Also studied are combinatorial-topological problems arising in the statistical Ising model, the disposition of finite point sets in convex bodies of high dimension under certain conditions, and investigations of regular partitionings of spaces of constant curvature.
Categories: Mathematics

The Search for the Meaning of Space Time and Matter

The Search for the Meaning of Space  Time  and Matter

From the time of Euclid, the Greek mathematician, (around 300 BC), it was
assumed that the geometry of the space in which our world is embedded is a
Euclidean space that follows the rules of the geometry that Euclid had shown in
his ...

Author: Kai Woehler

Publisher: Xlibris Corporation

ISBN: 9781469101989

Category: Science

Page: 447

View: 896

The book gives a comprehensive introduction for interested general readers, into the development and structure of concepts, ideas and theory formation about the elementary building blocks of matter, the forces with which these particles interact and about the fundamental nature of space itself. Einsteins theory of the cosmos and the recent discovery of the presence of a dark energy which leads to an accelerated expansion of cosmic space, provide the background for the most astonishing recent developments in the search for the origin of space and matter. The String-Theory revolution has led to the notion that nature may not follow one unique set of laws to build worlds, but that innumerable many possible universes may exist, that worlds may be emerging and disappearing like biological species and that our existence may be extraordinarily rare and therefore precious. An introduction to the concept of emergence in self-organizing systems is given to make the connection to the idea that Emergence may be the inherent creative property of space and matter at the quantum level.
Categories: Science

Nonfiction Writing Prompts for Geometry

Nonfiction Writing Prompts for Geometry

Consistently uses paragraph breaks that reinforce organization and meaning.
Reasonable control of standard writing conventions. Occasional errors in
capitalization, punctuation, and spelling do not interfere with readability.
Grammar and ...

Author: Center for Performance Assessment

Publisher: Lead + Learn Press

ISBN: 1933196084

Category: Education

Page: 128

View: 191

The positive effect of writing is counterintuitive to what many educators believe to be true. However, when shown the data, teachers and administrators who start using nonfiction writing are quickly convinced of its value.
Categories: Education

An Introduction to Geometry and the Science of Form

An Introduction to Geometry and the Science of Form

Meaning of terms plane surface ; face and edge or side of a solid ; and plane and
solid angles , 1 2. Comparison of the parts of a cube . Meaning of terms
quadrilateral ; perpendicular ; parallel ; horizontal ; vertical . Definition of a square
; and ...



ISBN: HARVARD:32044097044879

Category: Geometry

Page: 161

View: 664

Categories: Geometry

Geometry and Chronometry in Philosophical Perspective

Geometry and Chronometry in Philosophical Perspective

... the distinction between preserving a particular geometry (e.g., the Euclidean
one) by a remetrizational change in the congruence definition, on the one hand,
and intending to retain a particular geometry without change in that definition (or
in ...

Author: Adolf Grunbaum

Publisher: U of Minnesota Press

ISBN: 9780816604906

Category: Science

Page: 378

View: 350

Geometry and Chronometry in Philosophical Perspective was first published in 1968. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. In this volume Professor Grünbaum substantially extends and comments upon his essay "Geometry, Chronometry, and Empiricism," which was first published in Volume III of the Minnesota Studies in the Philosophy of Science. Commenting on the essay when it first appeared J. J. C. Smart wrote in Mind (England): "In my opinion Adolf Grünbaum's paper ... supersedes nearly all that has been written on the logical status of physical geometry and chronometry." The full text of the essay is given here with the author's extension of it and his discussion of some of the critical comment it has evoked, particularly, a critique published by Hilary Putnam. Adolph Grünbaum is Andrew Mellon Professor of Philosophy at the University of Pittsburgh and the current president of the Philosophy of Science Association.
Categories: Science

Modern Geometry Methods and Applications

Modern Geometry    Methods and Applications

Part II: The Geometry and Topology of Manifolds B.A. Dubrovin, A.T. Fomenko,
S.P. Novikov ... M under the action of G are "discretely distributed" (meaning that
around each point y of M there exists a neighbourhood U containing no other
point ...

Author: B.A. Dubrovin

Publisher: Springer Science & Business Media

ISBN: 0387961623

Category: Mathematics

Page: 432

View: 647

Up until recently, Riemannian geometry and basic topology were not included, even by departments or faculties of mathematics, as compulsory subjects in a university-level mathematical education. The standard courses in the classical differential geometry of curves and surfaces which were given instead (and still are given in some places) have come gradually to be viewed as anachronisms. However, there has been hitherto no unanimous agreement as to exactly how such courses should be brought up to date, that is to say, which parts of modern geometry should be regarded as absolutely essential to a modern mathematical education, and what might be the appropriate level of abstractness of their exposition. The task of designing a modernized course in geometry was begun in 1971 in the mechanics division of the Faculty of Mechanics and Mathematics of Moscow State University. The subject-matter and level of abstractness of its exposition were dictated by the view that, in addition to the geometry of curves and surfaces, the following topics are certainly useful in the various areas of application of mathematics (especially in elasticity and relativity, to name but two), and are therefore essential: the theory of tensors (including covariant differentiation of them); Riemannian curvature; geodesics and the calculus of variations (including the conservation laws and Hamiltonian formalism); the particular case of skew-symmetric tensors (i. e.
Categories: Mathematics