Malka Rappaport Hovav and Beth Levin
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199544325
- eISBN:
- 9780191720536
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199544325.003.0002
- Subject:
- Linguistics, Historical Linguistics
This chapter investigates the observed complementarity of manner and result as components of lexicalized verb meaning. We provide a precise characterization of these meaning components: results ...
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This chapter investigates the observed complementarity of manner and result as components of lexicalized verb meaning. We provide a precise characterization of these meaning components: results involve scalar changes, while manners involve nonscalar changes. We propose a verb may only lexicalize one type of change, giving rise to manner/result complementarity.Less
This chapter investigates the observed complementarity of manner and result as components of lexicalized verb meaning. We provide a precise characterization of these meaning components: results involve scalar changes, while manners involve nonscalar changes. We propose a verb may only lexicalize one type of change, giving rise to manner/result complementarity.
Ken Safir
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780195166132
- eISBN:
- 9780199788460
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195166132.003.0003
- Subject:
- Linguistics, Syntax and Morphology
Unlike theories that stipulate complementary distribution of anaphors and pronouns, the theory of competition between dependent forms proposed here predicts that complementary distribution of ...
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Unlike theories that stipulate complementary distribution of anaphors and pronouns, the theory of competition between dependent forms proposed here predicts that complementary distribution of anaphors, pronouns and referring expressions should hold, unless two forms tie. Apparent empirical counterexamples to the complementary distribution of pronouns and anaphors are addressed. A variety of arguments are given to show that competition between dependent forms to represent dependent identity relations as established by the Form-to-Interpretation Principle, derives Principles B and C, and is the only theory that provides natural explanations for apparent violations of principles (like Principle B) when a morphological paradigm does not include an anaphor (as in Old English) while at the same time the competitive theory predicts the distribution of Principle C effects whenever pronouns are available and the antecedent c-commands. Conditions ranking the forms in competition, scalar intervention effects that eliminate competitors in certain contexts, and other conditions on the nature of the competition between forms are explored. Earlier competition theories are evaluated in light of this one and pragmatic competition theories are rejected in favor of the syntactic-interpretive principle proposed here.Less
Unlike theories that stipulate complementary distribution of anaphors and pronouns, the theory of competition between dependent forms proposed here predicts that complementary distribution of anaphors, pronouns and referring expressions should hold, unless two forms tie. Apparent empirical counterexamples to the complementary distribution of pronouns and anaphors are addressed. A variety of arguments are given to show that competition between dependent forms to represent dependent identity relations as established by the Form-to-Interpretation Principle, derives Principles B and C, and is the only theory that provides natural explanations for apparent violations of principles (like Principle B) when a morphological paradigm does not include an anaphor (as in Old English) while at the same time the competitive theory predicts the distribution of Principle C effects whenever pronouns are available and the antecedent c-commands. Conditions ranking the forms in competition, scalar intervention effects that eliminate competitors in certain contexts, and other conditions on the nature of the competition between forms are explored. Earlier competition theories are evaluated in light of this one and pragmatic competition theories are rejected in favor of the syntactic-interpretive principle proposed here.
Regine Eckardt
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199262601
- eISBN:
- 9780191718939
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199262601.003.0006
- Subject:
- Linguistics, Semantics and Pragmatics
This chapter traces the development of intensifying selbst (self) to the focus particle selbst (even) in German. Starting from a semantic analysis of the intensifier, it surveys German literary data ...
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This chapter traces the development of intensifying selbst (self) to the focus particle selbst (even) in German. Starting from a semantic analysis of the intensifier, it surveys German literary data from when this development emerged (c.1550-1600) and traces passages which shift between old and new use of selbst. It is shown that such contexts of use do not support the presuppositions of selbst in its older sense and create a ‘pragmatic overload’ for the hearer. Striving for pragmatic simplicity and plausibility, hearers hypothesize a new possible use for the item, initiating the emergence of the new selbst/even entry.Less
This chapter traces the development of intensifying selbst (self) to the focus particle selbst (even) in German. Starting from a semantic analysis of the intensifier, it surveys German literary data from when this development emerged (c.1550-1600) and traces passages which shift between old and new use of selbst. It is shown that such contexts of use do not support the presuppositions of selbst in its older sense and create a ‘pragmatic overload’ for the hearer. Striving for pragmatic simplicity and plausibility, hearers hypothesize a new possible use for the item, initiating the emergence of the new selbst/even entry.
Aman Ullah
- Published in print:
- 2004
- Published Online:
- August 2004
- ISBN:
- 9780198774471
- eISBN:
- 9780191601347
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198774478.003.0004
- Subject:
- Economics and Finance, Econometrics
This chapter presents the finite sample analysis of estimators and test statistics in the case of regression models, where the errors have a scalar covariance matrix. Most of the results of the ...
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This chapter presents the finite sample analysis of estimators and test statistics in the case of regression models, where the errors have a scalar covariance matrix. Most of the results of the normal distribution have been obtained in econometrics textbooks. The results for the nonnormal cases are presented, which have been rarely discussed in literature.Less
This chapter presents the finite sample analysis of estimators and test statistics in the case of regression models, where the errors have a scalar covariance matrix. Most of the results of the normal distribution have been obtained in econometrics textbooks. The results for the nonnormal cases are presented, which have been rarely discussed in literature.
Yvonne Choquet-Bruhat
- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0016
- Subject:
- Mathematics, Applied Mathematics
This chapter begins with a discussion of Gowdy cosmological models. It then covers S1 invariant Einsteinian universes, equations; invariant Einstein universes, the Cauchy problem; the ...
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This chapter begins with a discussion of Gowdy cosmological models. It then covers S1 invariant Einsteinian universes, equations; invariant Einstein universes, the Cauchy problem; the Andersson–Moncrief theorem, and Einstein non-linear scalar field system.Less
This chapter begins with a discussion of Gowdy cosmological models. It then covers S1 invariant Einsteinian universes, equations; invariant Einstein universes, the Cauchy problem; the Andersson–Moncrief theorem, and Einstein non-linear scalar field system.
Adrienne Lehrer
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195307931
- eISBN:
- 9780199867493
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195307931.003.0006
- Subject:
- Linguistics, Theoretical Linguistics
A semantic theory must account for both how words are related to other words (intralinguistic connections) and how words connect to the world. Semantic field theory, which is appropriate for ...
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A semantic theory must account for both how words are related to other words (intralinguistic connections) and how words connect to the world. Semantic field theory, which is appropriate for intralinguistic relations, is applied to wine words in this chapter. The semantic relationships most commonly found among wine descriptors are synonymy, antonymy, hyponymy (class inclusion), and incompatibility. Association, a weaker connection, also plays a role in understanding words. Four classes of descriptors are discussed: natural kind terms, gradable adjectives, evaluative words, and metaphors. The role of experts is discussed, but there are different kinds of wine experts, not all of whom use the same terminology. For example, wine writers use and generate metaphors (brawny, decadent) which the wine scientists consider silly or meaningless.Less
A semantic theory must account for both how words are related to other words (intralinguistic connections) and how words connect to the world. Semantic field theory, which is appropriate for intralinguistic relations, is applied to wine words in this chapter. The semantic relationships most commonly found among wine descriptors are synonymy, antonymy, hyponymy (class inclusion), and incompatibility. Association, a weaker connection, also plays a role in understanding words. Four classes of descriptors are discussed: natural kind terms, gradable adjectives, evaluative words, and metaphors. The role of experts is discussed, but there are different kinds of wine experts, not all of whom use the same terminology. For example, wine writers use and generate metaphors (brawny, decadent) which the wine scientists consider silly or meaningless.
Adrienne Lehrer
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780195307931
- eISBN:
- 9780199867493
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195307931.003.0008
- Subject:
- Linguistics, Theoretical Linguistics
Subjects in the Stanford group had not drunk or discussed wine with one another before the experiments. At some sessions subjects worked alone to describe (usually) three different wines of the same ...
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Subjects in the Stanford group had not drunk or discussed wine with one another before the experiments. At some sessions subjects worked alone to describe (usually) three different wines of the same color but from different countries and different grape varietals. Tasks included free descriptions, selecting words from a list of 145 descriptors, and deciding if a descriptor was appropriate for each wine. At other sessions subjects had partners where they had to agree on wine descriptions or each subject tried to match the same wines with the partner's descriptions. Results showed little consensus on all the tasks. Two contributing factors were differences in liking or disliking the wine and the differences in norms used for scalar judgments.Less
Subjects in the Stanford group had not drunk or discussed wine with one another before the experiments. At some sessions subjects worked alone to describe (usually) three different wines of the same color but from different countries and different grape varietals. Tasks included free descriptions, selecting words from a list of 145 descriptors, and deciding if a descriptor was appropriate for each wine. At other sessions subjects had partners where they had to agree on wine descriptions or each subject tried to match the same wines with the partner's descriptions. Results showed little consensus on all the tasks. Two contributing factors were differences in liking or disliking the wine and the differences in norms used for scalar judgments.
Katalin É. Kiss
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199570959
- eISBN:
- 9780191721786
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199570959.003.0004
- Subject:
- Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics
In chapter 4 ‘Structural focus and exhaustivity’, Katalin É. Kiss claims that the structural focus of the Hungarian sentence, occupying Spec,FocP, and structural focus (e.g. the English cleft), in ...
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In chapter 4 ‘Structural focus and exhaustivity’, Katalin É. Kiss claims that the structural focus of the Hungarian sentence, occupying Spec,FocP, and structural focus (e.g. the English cleft), in general, encodes the feature [+exhaustive]. After reviewing the standard arguments for the exhaustivity of structural focus, a new argument against it, proposed by Wedgwood (2005), is examined, and is shown to be based on a false premise. Finally, a new type of evidence is presented. It is argued (following van Kuppevelt (1996), and Wedgwood (2005)) that the ‘exactly n’ reading of a focussed numeral (as opposed to its basic, ‘at least n’ meaning) is a manifestation of its exhaustivity. It is shown that the ‘exactly n’ meaning of focussed numerals is grammaticalized in Hungarian; it is associated with the preverbal focus position, causing obligatory focus movement in the case of certain types of scalar elements, and predictable, structurally determined meaning differences in the case of others.Less
In chapter 4 ‘Structural focus and exhaustivity’, Katalin É. Kiss claims that the structural focus of the Hungarian sentence, occupying Spec,FocP, and structural focus (e.g. the English cleft), in general, encodes the feature [+exhaustive]. After reviewing the standard arguments for the exhaustivity of structural focus, a new argument against it, proposed by Wedgwood (2005), is examined, and is shown to be based on a false premise. Finally, a new type of evidence is presented. It is argued (following van Kuppevelt (1996), and Wedgwood (2005)) that the ‘exactly n’ reading of a focussed numeral (as opposed to its basic, ‘at least n’ meaning) is a manifestation of its exhaustivity. It is shown that the ‘exactly n’ meaning of focussed numerals is grammaticalized in Hungarian; it is associated with the preverbal focus position, causing obligatory focus movement in the case of certain types of scalar elements, and predictable, structurally determined meaning differences in the case of others.
Satoshi Tomioka
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199570959
- eISBN:
- 9780191721786
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199570959.003.0006
- Subject:
- Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics
Contrastive Topics are known to elicit a kind of pragmatic effect that is characterized as incompleteness, partiality, and/or uncertainty. Chapter 5 ‘Contrastive Topics Operate on Speech Acts’ by ...
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Contrastive Topics are known to elicit a kind of pragmatic effect that is characterized as incompleteness, partiality, and/or uncertainty. Chapter 5 ‘Contrastive Topics Operate on Speech Acts’ by Satoshi Tomioka presents an analysis of this effect that makes appeal to contrasted speech acts. The majority of the empirical data discussed in the chapter come from Japanese, in which contrastive topics receive proto‐typical focus accents and the particle (‐wa) that signals a sentence topic must be employed. The proposed analysis derives the pragmatic effect of contrastive topics by making use of the contribution of focus accents, the function of the topic particle, and pragmatic inference based on the Gricean reasoning. A variety of consequences and implications of the analysis are also addressed.Less
Contrastive Topics are known to elicit a kind of pragmatic effect that is characterized as incompleteness, partiality, and/or uncertainty. Chapter 5 ‘Contrastive Topics Operate on Speech Acts’ by Satoshi Tomioka presents an analysis of this effect that makes appeal to contrasted speech acts. The majority of the empirical data discussed in the chapter come from Japanese, in which contrastive topics receive proto‐typical focus accents and the particle (‐wa) that signals a sentence topic must be employed. The proposed analysis derives the pragmatic effect of contrastive topics by making use of the contribution of focus accents, the function of the topic particle, and pragmatic inference based on the Gricean reasoning. A variety of consequences and implications of the analysis are also addressed.
Zachary Horton
- Published in print:
- 2021
- Published Online:
- January 2022
- ISBN:
- 9780226742304
- eISBN:
- 9780226742588
- Item type:
- book
- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226742588.001.0001
- Subject:
- History, History of Ideas
The Cosmic Zoom develops a cross-disciplinary theory of scale as mediated difference by examining the history of a trope that has influenced multiple media forms during the past seventy years: the ...
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The Cosmic Zoom develops a cross-disciplinary theory of scale as mediated difference by examining the history of a trope that has influenced multiple media forms during the past seventy years: the cosmic zoom, a flight through the many scales of the universe. What, it asks, are the origins of our received notions about scale? What role does scale play in fundamental processes of mediation? How does scalar mediation function differently in analog and digital modes? How have cosmic zoom media influenced both scientific and popular understandings of the unseen world? This book’s primary aim is to establish a much-needed interdisciplinary framework for theorizing scale at a moment defined on one hand by “big data” and on the other by climate change. Scalar mediation, this book argues, is a process of stabilization between multiple surfaces that enables and constrains the human encounter with other milieus. This is trans-scalar ecology. Analyzing numerous cosmic zoom media, from books to films to databases, The Cosmic Zoom unravels the paradoxical nature of scale: it appears to be an arbitrary human construct, and yet the universe itself seems to be fundamentally defined by different rules for different scales. Unraveling this scalar paradox reveals the extent to which human subjectivity is bound up in constructions of scale as both cause and effect, with profound implications for knowledge-making itself.Less
The Cosmic Zoom develops a cross-disciplinary theory of scale as mediated difference by examining the history of a trope that has influenced multiple media forms during the past seventy years: the cosmic zoom, a flight through the many scales of the universe. What, it asks, are the origins of our received notions about scale? What role does scale play in fundamental processes of mediation? How does scalar mediation function differently in analog and digital modes? How have cosmic zoom media influenced both scientific and popular understandings of the unseen world? This book’s primary aim is to establish a much-needed interdisciplinary framework for theorizing scale at a moment defined on one hand by “big data” and on the other by climate change. Scalar mediation, this book argues, is a process of stabilization between multiple surfaces that enables and constrains the human encounter with other milieus. This is trans-scalar ecology. Analyzing numerous cosmic zoom media, from books to films to databases, The Cosmic Zoom unravels the paradoxical nature of scale: it appears to be an arbitrary human construct, and yet the universe itself seems to be fundamentally defined by different rules for different scales. Unraveling this scalar paradox reveals the extent to which human subjectivity is bound up in constructions of scale as both cause and effect, with profound implications for knowledge-making itself.
François Recanati
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199226993
- eISBN:
- 9780191710223
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199226993.003.0006
- Subject:
- Philosophy, Philosophy of Language, General
Conversational implicatures do not normally fall within the scope of operators because they arise at the speech act level, not at the level of sub-locutionary constituents. Yet in some cases they do, ...
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Conversational implicatures do not normally fall within the scope of operators because they arise at the speech act level, not at the level of sub-locutionary constituents. Yet in some cases they do, or so it seems. ‘Embedded implicatures’ are seeming implicatures that arise locally, at a sub-locutionary level, without resulting from an inference in the narrow sense. The phenomenon has received a good deal of attention recently and has led many researchers to cast doubt on the traditional division of labour between semantics and pragmatics. This chapter discusses the relation between various possible approaches to the phenomenon, including Truth-Conditional Pragmatics.Less
Conversational implicatures do not normally fall within the scope of operators because they arise at the speech act level, not at the level of sub-locutionary constituents. Yet in some cases they do, or so it seems. ‘Embedded implicatures’ are seeming implicatures that arise locally, at a sub-locutionary level, without resulting from an inference in the narrow sense. The phenomenon has received a good deal of attention recently and has led many researchers to cast doubt on the traditional division of labour between semantics and pragmatics. This chapter discusses the relation between various possible approaches to the phenomenon, including Truth-Conditional Pragmatics.
Gary E. Bowman
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228928
- eISBN:
- 9780191711206
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228928.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials
The quantum state is the fundamental entity in quantum mechanics. This chapter develops the basic mathematical structure of quantum states by developing the correspondence between states and ordinary ...
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The quantum state is the fundamental entity in quantum mechanics. This chapter develops the basic mathematical structure of quantum states by developing the correspondence between states and ordinary vectors. The familiar scalar or dot product of vectors is used to develop the concepts of projection, orthonormality, linear independence, and expansion over a complete set of basis vectors. These ideas are then extended from vectors in a vector space to functions in a function space. Dirac's bra-ket notation is introduced, and the concepts developed for ordinary vectors are revisited in the context of quantum states and Dirac notation. The central quantum concept of a representation is then explored, and the relation between representations and superpositions is illustrated with the infinite potential well. The final topic is representational freedom: the fact that quantum mechanics remains valid regardless of the representation chosen for calculation.Less
The quantum state is the fundamental entity in quantum mechanics. This chapter develops the basic mathematical structure of quantum states by developing the correspondence between states and ordinary vectors. The familiar scalar or dot product of vectors is used to develop the concepts of projection, orthonormality, linear independence, and expansion over a complete set of basis vectors. These ideas are then extended from vectors in a vector space to functions in a function space. Dirac's bra-ket notation is introduced, and the concepts developed for ordinary vectors are revisited in the context of quantum states and Dirac notation. The central quantum concept of a representation is then explored, and the relation between representations and superpositions is illustrated with the infinite potential well. The final topic is representational freedom: the fact that quantum mechanics remains valid regardless of the representation chosen for calculation.
Gary E. Bowman
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199228928
- eISBN:
- 9780191711206
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199228928.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter introduces the matrix-mechanics formulation of quantum mechanics, emphasizing both calculational techniques and conceptual understanding. Parallels between matrix mechanics and ordinary ...
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This chapter introduces the matrix-mechanics formulation of quantum mechanics, emphasizing both calculational techniques and conceptual understanding. Parallels between matrix mechanics and ordinary vectors and matrices are extensively utilized. Starting with the representation of ordinary vectors as rows or columns of numbers, the scalar product is discussed, followed by the transformation of vectors by matrices, as illustrated by rotations. The vector representation of quantumstates, the inner product of two such states, and the matrix representation of operators are then introduced. The simple forms assumed in matrix mechanics by a basis state, and by an operator, when either is written in its eigenbasis, are discussed, as are the specific forms of adjoint, Hermitian, and unitary operators. The chapter concludes with a brief exposition of eigenvalue equations in matrix mechanics.Less
This chapter introduces the matrix-mechanics formulation of quantum mechanics, emphasizing both calculational techniques and conceptual understanding. Parallels between matrix mechanics and ordinary vectors and matrices are extensively utilized. Starting with the representation of ordinary vectors as rows or columns of numbers, the scalar product is discussed, followed by the transformation of vectors by matrices, as illustrated by rotations. The vector representation of quantumstates, the inner product of two such states, and the matrix representation of operators are then introduced. The simple forms assumed in matrix mechanics by a basis state, and by an operator, when either is written in its eigenbasis, are discussed, as are the specific forms of adjoint, Hermitian, and unitary operators. The chapter concludes with a brief exposition of eigenvalue equations in matrix mechanics.
Pier A. Mello and Narendra Kumar
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter examines the linear response theory of Kubo and its specialization to calculating the conductance of a narrow constriction connected adiabatically to reservoirs through widening horns. ...
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This chapter examines the linear response theory of Kubo and its specialization to calculating the conductance of a narrow constriction connected adiabatically to reservoirs through widening horns. The Landauer two-probe conductance formula that treats the entire sample as a single scatterer and relates its conductance to the total transmission coefficient is derived and discussed. In order to make the discussion self-contained, a brief account of the time-dependent perturbation theory in quantum mechanics is presented. A distinction is made between the mesoscopic sample-specific conductance and the macroscopic material-specific conductivity in the bulk. Damping (dephasing) is introduced and discussed as being provided by the dissipative environment — the bath and the reservoirs. The contents of this chapter include a discussion of the scalar- and the vector- potential gauges; the charge-density and the current-density profile; and the KSL theorem on the conductivity tensor.Less
This chapter examines the linear response theory of Kubo and its specialization to calculating the conductance of a narrow constriction connected adiabatically to reservoirs through widening horns. The Landauer two-probe conductance formula that treats the entire sample as a single scatterer and relates its conductance to the total transmission coefficient is derived and discussed. In order to make the discussion self-contained, a brief account of the time-dependent perturbation theory in quantum mechanics is presented. A distinction is made between the mesoscopic sample-specific conductance and the macroscopic material-specific conductivity in the bulk. Damping (dephasing) is introduced and discussed as being provided by the dissipative environment — the bath and the reservoirs. The contents of this chapter include a discussion of the scalar- and the vector- potential gauges; the charge-density and the current-density profile; and the KSL theorem on the conductivity tensor.
Dennis Sherwood and Jon Cooper
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199559046
- eISBN:
- 9780191595028
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199559046.003.0002
- Subject:
- Physics, Crystallography: Physics
This chapter introduces the essential mathematics of diffraction. Initially the concept of a vector is presented along with the mathematical operations which we can perform on vector quantities ...
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This chapter introduces the essential mathematics of diffraction. Initially the concept of a vector is presented along with the mathematical operations which we can perform on vector quantities including addition, subtraction, and multiplication by a scalar. The important methods for multiplying two or more vector quantities (scalar or dot product and the vector or cross product) are then covered. Next the chapter describes the concept of complex numbers and their graphical representation in the form of an Argand diagram. Mathematical operations such as addition and multiplication of complex numbers are then covered, followed by the concepts of the complex conjugate and the complex exponential — both of utmost importance in understanding the mathematics of diffraction. The chapter then introduces briefly some of the mathematics of determinants.Less
This chapter introduces the essential mathematics of diffraction. Initially the concept of a vector is presented along with the mathematical operations which we can perform on vector quantities including addition, subtraction, and multiplication by a scalar. The important methods for multiplying two or more vector quantities (scalar or dot product and the vector or cross product) are then covered. Next the chapter describes the concept of complex numbers and their graphical representation in the form of an Argand diagram. Mathematical operations such as addition and multiplication of complex numbers are then covered, followed by the concepts of the complex conjugate and the complex exponential — both of utmost importance in understanding the mathematics of diffraction. The chapter then introduces briefly some of the mathematics of determinants.
Osamu Sawada
- Published in print:
- 2017
- Published Online:
- December 2017
- ISBN:
- 9780198714224
- eISBN:
- 9780191782633
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198714224.001.0001
- Subject:
- Linguistics, Semantics and Pragmatics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics
This book investigates pragmatic aspects of scalar modifiers. Through a detailed analysis of the semantics and pragmatics of comparatives with indeterminate pronouns, positive polarity minimizers, ...
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This book investigates pragmatic aspects of scalar modifiers. Through a detailed analysis of the semantics and pragmatics of comparatives with indeterminate pronouns, positive polarity minimizers, intensifiers, and expectation-reversal adverbs in Japanese and other languages, the book shows that scalarity is utilized not just for measuring a thing/event in the semantic level, but also for expressing various kinds of pragmatic information, including politeness, priority of utterance, the speaker’s attitude, and unexpectedness, at the level of conventional implicature (CI). The similarities and differences between at-issue and CI scalar meanings are analyzed using a multidimensional composition system (Potts 2005; McCready 2010). Two types of pragmatic scalar modifiers are proposed: a higher-level pragmatic scalar modifier, which utilizes an implicit pragmatic scale, and a lower-level pragmatic scalar modifier, which recycles the scale of an at-issue gradable predicate. The book also investigates the interpretations of pragmatic scalar modifiers that are embedded in the complement of an attitude predicate, and claims that there is a semantic shift from a CI to a secondary at-issue entailment in the case of non-speaker-oriented readings. It will also show that there is a phenomenon of “projection of not-at-issue meaning via modal support” in lower-level pragmatic scalar modifiers. Finally, the historical development of pragmatic scalar modifiers is also discussed. This book claims that although semantic scalar meanings and pragmatic (CI) scalar meanings are compositionally different, there is a relationship between the two, and it is important to look at both kinds of meaning in a uniform/flexible fashion.Less
This book investigates pragmatic aspects of scalar modifiers. Through a detailed analysis of the semantics and pragmatics of comparatives with indeterminate pronouns, positive polarity minimizers, intensifiers, and expectation-reversal adverbs in Japanese and other languages, the book shows that scalarity is utilized not just for measuring a thing/event in the semantic level, but also for expressing various kinds of pragmatic information, including politeness, priority of utterance, the speaker’s attitude, and unexpectedness, at the level of conventional implicature (CI). The similarities and differences between at-issue and CI scalar meanings are analyzed using a multidimensional composition system (Potts 2005; McCready 2010). Two types of pragmatic scalar modifiers are proposed: a higher-level pragmatic scalar modifier, which utilizes an implicit pragmatic scale, and a lower-level pragmatic scalar modifier, which recycles the scale of an at-issue gradable predicate. The book also investigates the interpretations of pragmatic scalar modifiers that are embedded in the complement of an attitude predicate, and claims that there is a semantic shift from a CI to a secondary at-issue entailment in the case of non-speaker-oriented readings. It will also show that there is a phenomenon of “projection of not-at-issue meaning via modal support” in lower-level pragmatic scalar modifiers. Finally, the historical development of pragmatic scalar modifiers is also discussed. This book claims that although semantic scalar meanings and pragmatic (CI) scalar meanings are compositionally different, there is a relationship between the two, and it is important to look at both kinds of meaning in a uniform/flexible fashion.
Jay David Atlas
- Published in print:
- 2005
- Published Online:
- October 2011
- ISBN:
- 9780195133004
- eISBN:
- 9780199850181
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195133004.003.0003
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
The parallel between saying something and articulating a more informative statement and saying something and articulating the more informative implies that such can apply for both positive and ...
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The parallel between saying something and articulating a more informative statement and saying something and articulating the more informative implies that such can apply for both positive and negative statements. Examining the parallelism of the implications brought about by scalar items and negation proves to be, however, somewhat deceptive since such examination may seem more informative than merely looking into the logical consequences of “what is said.” This chapter also looks into the “Horn Scale” which involves a condition in sentence construction that concerns the ordering of the words. Also, the chapter provides examples of sentences that exemplify the use of Grice's First Maxim of Quantity and the other Maxims of Quality.Less
The parallel between saying something and articulating a more informative statement and saying something and articulating the more informative implies that such can apply for both positive and negative statements. Examining the parallelism of the implications brought about by scalar items and negation proves to be, however, somewhat deceptive since such examination may seem more informative than merely looking into the logical consequences of “what is said.” This chapter also looks into the “Horn Scale” which involves a condition in sentence construction that concerns the ordering of the words. Also, the chapter provides examples of sentences that exemplify the use of Grice's First Maxim of Quantity and the other Maxims of Quality.
Spyros Alexakis
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691153476
- eISBN:
- 9781400842728
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691153476.001.0001
- Subject:
- Mathematics, Geometry / Topology
This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ...
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This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? This book asserts that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern–Gauss–Bonnet integrand. The book provides a proof of this conjecture. The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants—such as the classical Riemannian invariants and the more recently studied conformal invariants—and the study of global invariants, in this case conformally invariant integrals.Less
This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? This book asserts that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern–Gauss–Bonnet integrand. The book provides a proof of this conjecture. The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants—such as the classical Riemannian invariants and the more recently studied conformal invariants—and the study of global invariants, in this case conformally invariant integrals.
Zachary Horton
- Published in print:
- 2021
- Published Online:
- January 2022
- ISBN:
- 9780226742304
- eISBN:
- 9780226742588
- Item type:
- chapter
- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226742588.003.0001
- Subject:
- History, History of Ideas
This introductory chapter explores the current historical moment, marked by climate change and “big data,” as animated by new scalar processes in ways that are analogous to those faced by Alice in ...
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This introductory chapter explores the current historical moment, marked by climate change and “big data,” as animated by new scalar processes in ways that are analogous to those faced by Alice in Lewis Carroll’s Alice’s Adventures in Wonderland. Arguing that the human race finds itself in a paradoxical position of unprecedented scalar access but unable to change to become compatible with the new scales that confront it, this chapter suggests that a more robust understanding of scale across disciplines is necessary to avoid “scalar collapse,” or the negation of scalar difference by speculative media. It examines various meanings, histories, and implications of scale from different disciplines and argues for a combination of their insights into a new, trans-disciplinary conception of scale based upon difference and mediation. This chapter introduces the cosmic zoom as a trans-medial form that engages scale itself in an attempt to characterize how scale and knowledge affect each other, and to construct a particular model of the cosmos. This cosmic zoom is a paradoxical medial form that reveals that scales are products of mediation, but also that media are a fundamental expression of scalar difference. These processes form the two sides of the “circuit” of scalar mediation.Less
This introductory chapter explores the current historical moment, marked by climate change and “big data,” as animated by new scalar processes in ways that are analogous to those faced by Alice in Lewis Carroll’s Alice’s Adventures in Wonderland. Arguing that the human race finds itself in a paradoxical position of unprecedented scalar access but unable to change to become compatible with the new scales that confront it, this chapter suggests that a more robust understanding of scale across disciplines is necessary to avoid “scalar collapse,” or the negation of scalar difference by speculative media. It examines various meanings, histories, and implications of scale from different disciplines and argues for a combination of their insights into a new, trans-disciplinary conception of scale based upon difference and mediation. This chapter introduces the cosmic zoom as a trans-medial form that engages scale itself in an attempt to characterize how scale and knowledge affect each other, and to construct a particular model of the cosmos. This cosmic zoom is a paradoxical medial form that reveals that scales are products of mediation, but also that media are a fundamental expression of scalar difference. These processes form the two sides of the “circuit” of scalar mediation.
Zachary Horton
- Published in print:
- 2021
- Published Online:
- January 2022
- ISBN:
- 9780226742304
- eISBN:
- 9780226742588
- Item type:
- chapter
- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226742588.003.0003
- Subject:
- History, History of Ideas
This chapter considers the aesthetic, epistemological, ontological, and political implications of media that animate radical perspectival shifts across scales. Its objects are 1950s and 1960s ...
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This chapter considers the aesthetic, epistemological, ontological, and political implications of media that animate radical perspectival shifts across scales. Its objects are 1950s and 1960s trans-scalar films by Eva Szasz and iconic designers Charles and Ray Eames. These projects culminate in the Eameses’ Rough Sketch in 1968. From the history of science and optical technology to questions of interface and temporality, this chapter focuses on the aesthetics of the zoom as a medial process and trope, as well as the attendant politics of animating trans-scalar encounter. Building on the scalar stabilizations enacted by Boeke’s book, it argues that the animation process primarily engages its own techniques of mediation in order to obscure the seams between distinct scalar milieus. Central to this process is the manipulation of temporal scale to fix scalar coordinates for the viewer of the film. This mediated experience exchanges time for space, a scalar shell game that is analyzed here as a form of scalar collapse particular to cinema. This chapter argues that the film serves as a model of equidistant optics, a topology of knowledge production in which all scales are medially positioned as equidistant from the human knowledge producer.Less
This chapter considers the aesthetic, epistemological, ontological, and political implications of media that animate radical perspectival shifts across scales. Its objects are 1950s and 1960s trans-scalar films by Eva Szasz and iconic designers Charles and Ray Eames. These projects culminate in the Eameses’ Rough Sketch in 1968. From the history of science and optical technology to questions of interface and temporality, this chapter focuses on the aesthetics of the zoom as a medial process and trope, as well as the attendant politics of animating trans-scalar encounter. Building on the scalar stabilizations enacted by Boeke’s book, it argues that the animation process primarily engages its own techniques of mediation in order to obscure the seams between distinct scalar milieus. Central to this process is the manipulation of temporal scale to fix scalar coordinates for the viewer of the film. This mediated experience exchanges time for space, a scalar shell game that is analyzed here as a form of scalar collapse particular to cinema. This chapter argues that the film serves as a model of equidistant optics, a topology of knowledge production in which all scales are medially positioned as equidistant from the human knowledge producer.
