DOCSLIB.ORG

Improving Event Causality Recognition with Multiple Background Knowledge Sources Using Multi-Column Convolutional Neural Networks

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Improving Event Causality Recognition with Multiple Background Knowledge Sources Using Multi-Column Convolutional Neural Networks Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence (AAAI-17) Improving Event Causality Recognition with Multiple Background Knowledge Sources Using Multi-Column Convolutional Neural Networks Canasai Kruengkrai, Kentaro Torisawa, Chikara Hashimoto, Julien Kloetzer, Jong-Hoon Oh, Masahiro Tanaka National Institute of Information and Communications Technology, Kyoto, 619-0289, Japan {canasai, torisawa, ch, julien, rovellia, mtnk}@nict.go.jp Abstract keizaikankyou-ga akkasuru → shijoukinri-ga gerakusuru (“economic environment deteriorates” → “markets decline”) We propose a method for recognizing such event causalities as “smoke cigarettes” → “die of lung cancer” using back- bukka-wa gerakusuru → defure-ni naru ground knowledge taken from web texts as well as original (“prices of commodities decline” → “become deflation”) sentences from which candidates for the causalities were ex- kubi-ni naru → sitsugyouhoken-o morau tracted. We retrieve texts related to our event causality candi- → dates from four billion web pages by three distinct methods, (“get fired” “get unemployment insurance”) including a why-question answering system, and feed them chiyuryoku-o takameru → atopii-o kokufukusu to our multi-column convolutional neural networks. This al- (“enhance healing power” → “defeat atopic syndrome”) lows us to identify the useful background knowledge scat- tered in web texts and effectively exploit the identified knowl- bitamin-ga fusokusuru → koukakuen-ni naru edge to recognize event causalities. We empirically show that (“lack vitamin” → “cause angular cheilitis”) the combination of our neural network architecture and back- ground knowledge significantly improves average precision, while the previous state-of-the-art method gains just a small Table 1: Japanese examples of event causalities successfully benefit from such background knowledge. recognized by our proposed method 1 Introduction This work develops a method that recognizes event → Event causality, such as “smoke cigarettes” “die of lung causalities from sentences regardless whether they have cancer,” is critical knowledge for many NLP applications, such explicit clues as “because.” The novelty of this work including machine reading and comprehension (Richard- lies in that we exploit a wide range of background knowledge son, Burges, and Renshaw 2013; Berant et al. 2014), pro- (written in web texts) using convolutional neural networks. cess extraction (Scaria et al. 2013), and future event/scenario In other words, given an event causality candidate, our neu- prediction (Radinsky, Davidovich, and Markovitch 2012; ral network analyzes descriptions in web texts that are some- Hashimoto et al. 2014). However, the state-of-the-art meth- how related to the given causality candidate and judges ods for event causality recognition still suffer from low pre- whether the candidate is a proper causality. The web texts cision and coverage because event causality is expressed in are retrieved by three distinct methods from our 4-billion- a wide range of forms that often lack explicit clues indicat- page web archive. We target such event causalities as “global ing the existence of event causality. Consider the following warming worsens” → “typhoons strengthen,” in which each sentences: cause phrase (“global warming worsens”) and effect phrase 1. Typhoons have strengthened because global warming has (“typhoons strengthen”) consists of a noun (“global warm- worsened. ing”) and a verb (“worsens”). Our experimental results 2. Global warming worsened, and typhoons strengthened. showed that our neural network-based method outperforms the state-of-the-art method based on SVMs (Hashimoto et The first sentence includes “because,” which explic- al. 2014) and its variants augmented with the background itly indicates the event causality between effect “typhoons knowledge sources introduced in this work. This suggests strengthen” and cause “global warming worsens.” On the that our neural network architecture is more suitable for other hand, the second sentence has no such clues. Nonethe- dealing with background knowledge. Table 1 shows ex- less, many people would infer that this sentence expresses amples of event causalities successfully recognized by our the same event causality as that in the first sentence. This is method but not by Hashimoto et al.’s method. possible because people have background knowledge about As one method to extract background knowledge from “typhoons” and “global warming.” web archives, we use a why-question answering (why-QA) Copyright c 2017, Association for the Advancement of Artificial system following (Oh et al. 2013) that retrieves seven- Intelligence (www.aaai.org). All rights reserved. sentence passages as answers to a given why-type ques- Softmax ist, they are encoded in the features of their SVM classifier. Note that the set of short binary patterns they prepared in- cludes not only CAUSE (“A causes B”) relations but also Pooling Pooling Pooling Pooling Pooling such relations as MATERIAL (“A is made of B”) and USE . A B Convolution Convolution Convolution Convolution Convolution (“ is used for ”), which are not directly related to causal- Column 1 Column 2 Column 5 Column 6 Column 8 ity. They showed that such patterns actually improved the performance, suggesting that a wide range of texts can be effective clues for judging causality. Causality candidate Context "smoke cigarettes" "He <CAUSE> too Patterns extracted from related texts, We extend Hashimoto et al.’s method by introducing MC- "die of lung cancer" often and <EFFECT>." which are retrieved from the web by NNs to effectively use a wider range of background knowl- three distinct methods edge expressed in a wider range of web texts. By “back- Original sentence Web ground knowledge,” we refer to any type of information that "He smoked cigarettes too often and died of lung cancer." is useful to generally recognize event causalities. Our as- sumption is that a wide range of dependency paths between Figure 1: Our MCNN architecture nouns can be used as background knowledge, not just the short binary patterns that Hashimoto et al. proposed to ex- ploit. In this work, we did not start from pre-specified pat- tion. We automatically generate a question from the ef- terns, but designed our method so that it can automatically fect part of an event causality candidate and extract back- learn/identify a wide range of paths as background knowl- ground knowledge from its answers. For recognizing the edge in extra texts, such as why-QA system’s answers. Our event causality candidate, “global warming worsens” → “ty- method is given those paths even if they are long and com- phoons strengthen” as a proper causality, our method gen- plex. We also even extend the notion of dependency paths erates the question, “Why do typhoons strengthen?”, and to inter-sentential ones so that they can capture the inter- retrieves such answers as one that includes the following sentential relations between two nouns that appear in con- two sentences: “Typhoons are becoming more powerful than secutive sentences. before. This is probably an effect of recent global warm- In addition to the above why-QA system’s answers, we ing.” Useful background knowledge here might be the causal tried the following two types of texts as sources of back- relation between “Typhoons are becoming more powerful” ground knowledge: and “global warming,” which somehow resembles the event A. A wider range of short binary patterns than those used in causality candidate. A problem is that the why-QA system’s Hashimoto et al. (2014). Contrary to their work, we did answers have a wide variety of forms, and the recognition not pose any semantic restrictions on the patterns. of such relations and their similarity to our target causality B. One or two (consecutive) sentences that include such clue candidates is not a trivial task. Furthermore, not all of the terms for causality as “reason” and “because” and the two answers necessarily express any useful background knowl- nouns in a target event causality, like “Recently powerful edge. Even proper answers to a given question may not pro- typhoons have been reported. One reason is global warm- vide any useful knowledge (e.g., “The paper reported that ing.” Note that we do not use any sophisticated mech- typhoons are becoming powerful due to high sea tempera- anism such as a why-QA system to retrieve these sen- ture. Another paper addressed the issues caused by global tences. We just retrieve all the texts including the clue warming.”). Extracting useful knowledge from such noisy terms and the nouns. texts itself is challenging. To perform this difficult task, we use multi-column con- Although our target language is Japanese, we believe that volutional neural networks (MCNNs) (Ciresan, Meier, and our method is extendable to other languages without much Schmidhuber 2012), which are a variant of convolutional cost. Note that we use English examples for the sake of read- neural networks (Lecun et al. 1998) with several indepen- ability throughout this paper. dent columns. Each column has its own convolutional and pooling layers, and the outputs of all the columns are com- 2 Related work bined in the last layer to provide a final prediction (Fig. 1). For event causality recognition, researchers have exploited In our architecture, we use five columns to process the event various clues, including discourse connectives and word causality candidates and their surrounding contexts in the sharing between cause and effect (Torisawa 2006; Abe, Inui, original sentence and three other columns to deal with web and Matsumoto 2008; Riaz and Girju 2010). Do, Chan, and texts retrieved by different methods. Roth (2011) proposed cause-effect association (CEA) statis- Our work was inspired by the research of Hashimoto et tics. Radinsky, Davidovich, and Markovitch (2012) used ex- al. (2014). They improved the performance of event causal- isting ontologies, such as YAGO (Suchanek, Kasneci, and ity recognition using a carefully selected set of short binary Weikum 2007). Hashimoto et al. (2012) introduced a new se- patterns that connect pairs of nouns, like “A causes B” and mantic orientation of predicates, and Hashimoto et al.
Load more

Recommended publications
  • Parts of Persons Identity and Persistence in a Perdurantist World
    UNIVERSITÀ DEGLI STUDI DI MILANO Doctoral School in Philosophy and Human Sciences (XXXI Cycle) Department of Philosophy “Piero Martinetti” Parts of Persons Identity and persistence in a perdurantist world Ph.D. Candidate Valerio BUONOMO Tutors Prof. Giuliano TORRENGO Prof. Paolo VALORE Coordinator of the Doctoral School Prof. Marcello D’AGOSTINO Academic year 2017-2018 1 Content CONTENT ........................................................................................................................... 2 ACKNOWLEDGMENTS ........................................................................................................... 4 INTRODUCTION ................................................................................................................... 5 CHAPTER 1. PERSONAL IDENTITY AND PERSISTENCE...................................................................... 8 1.1. The persistence of persons and the criteria of identity over time .................................. 8 1.2. The accounts of personal persistence: a standard classification ................................... 14 1.2.1. Mentalist accounts of personal persistence ............................................................................ 15 1.2.2. Somatic accounts of personal persistence .............................................................................. 15 1.2.3. Anti-criterialist accounts of personal persistence ................................................................... 16 1.3. The metaphysics of persistence: the mereological account .........................................
    [Show full text]
  • Presentism/Eternalism and Endurantism/Perdurantism: Why the Unsubstantiality of the First Debate Implies That of the Second1
    1 Presentism/Eternalism and Endurantism/Perdurantism: why the 1 unsubstantiality of the first debate implies that of the second Forthcoming in Philosophia Naturalis Mauro Dorato (Ph.D) Department of Philosophy University of Rome Three [email protected] tel. +393396070133 http://host.uniroma3.it/dipartimenti/filosofia/personale/doratoweb.htm Abstract The main claim that I want to defend in this paper is that the there are logical equivalences between eternalism and perdurantism on the one hand and presentism and endurantism on the other. By “logical equivalence” I mean that one position is entailed and entails the other. As a consequence of this equivalence, it becomes important to inquire into the question whether the dispute between endurantists and perdurantists is authentic, given that Savitt (2006) Dolev (2006) and Dorato (2006) have cast doubts on the fact that the debate between presentism and eternalism is about “what there is”. In this respect, I will conclude that also the debate about persistence in time has no ontological consequences, in the sense that there is no real ontological disagreement between the two allegedly opposite positions: as in the case of the presentism/eternalism debate, one can be both a perdurantist and an endurantist, depending on which linguistic framework is preferred. The main claim that I want to defend in this paper is that the there are logical equivalences between eternalism and perdurantism on the one hand and presentism and endurantism on the other. By “logical equivalence” I mean that one position is entailed and entails the other. As a consequence of this equivalence, it becomes important to inquire into the question whether the dispute between endurantists and perdurantists is authentic, given that Savitt (2006) Dolev (2006) and Dorato (2006) have cast doubts on the fact that the debate between presentism and eternalism is about “what there is”.
    [Show full text]
  • Taking Tense Seriously’ Dean W
    W. Zimmerman dialectica Vol. 59, N° 4 (2005), pp. 401–457 The A-Theory of Time, The B-Theory of Time, and ‘Taking Tense Seriously’ Dean W. Zimmerman† ABSTRACT The paper has two parts: First, I describe a relatively popular thesis in the philosophy of propositional attitudes, worthy of the name ‘taking tense seriously’; and I distinguish it from a family of views in the metaphysics of time, namely, the A-theories (or what are sometimes called ‘tensed theories of time’). Once the distinction is in focus, a skeptical worry arises. Some A- theorists maintain that the difference between past, present, and future, is to be drawn in terms of what exists: growing-block theorists eschew ontological commitment to future entities; pre- sentists, to future and past entities. Others think of themselves as A-theorists but exclude no past or future things from their ontology. The metaphysical skeptic suspects that their attempt to articulate an ‘eternalist’ version of the A-theory collapses into merely ‘taking tense seriously’ – a thesis that does not imply the A-theory. The second half of the paper is the search for a stable eternalist A-theory. It includes discussion of temporary intrinsics, temporal parts, and truth. 1. Introduction Sadly, the great metaphysician J. McT. E. McTaggart is now remembered mainly for what must be his worst argument: the infamous argument for ‘the unreality of time’. But even this ‘philosophical “howler” ’ (as C. D. Broad rightly called it1) includes enough insightful analysis to have made it a natural starting point for most subsequent work on the metaphysics of time.
    [Show full text]
  • Endurantism Or Perdurantism?
    The embodied self: Endurantism or perdurantism? Saskia Heijnen Contents Contents ...................................................................................................................................... 1 Abstract ...................................................................................................................................... 2 Introduction ................................................................................................................................ 2 1. Endurantism versus perdurantism in metaphysics .............................................................. 5 1.1 Particulars ......................................................................................................................... 5 1.2 Persisting particulars ......................................................................................................... 7 1.3 Temporal parts: a closer look ......................................................................................... 10 1.4 Wholly present: a closer look ......................................................................................... 14 1.5 Perdurantism and endurantism in action ........................................................................ 17 1.5.1 Fusion ....................................................................................................................... 17 1.5.2 Fission ...................................................................................................................... 19 2. Endurantism versus
    [Show full text]
  • Temporal Parts and Spatial Location
    Temporal parts and spatial location Damiano Costa Abstract. The literature offers us several characterizations of temporal parts via spatial co-location: by these accounts, temporal parts are roughly parts that are of the same spatial size as their wholes. It has been argued that such definitions would fail with entities outside space. The present paper investigates the extent to which such criticism works. Keywords: temporal parts, spatial location, events, four-dimensionalism, perdurance. § 0. Introduction Temporal parts of an entity – according to current vulgate – incorporate “all of that entity” for as long as they exist (Heller 1984; Sider 2001; Olson 2006). For example, a temporal part of Sam incorporates “all of Sam” for as long as it exists. One immediate consequence of this fact is that some “smaller parts” of Sam, like his brain and hearth, do not count as temporal parts of Sam, because they do not incorporate “all of Sam” at a certain time. A suitable definition for temporal parts must exclude such “smaller parts”. In this regard, two approaches have been put forward, a mereological one (Simons 1987; Sider 1997; Parsons 2007) and a spatial one (Thomson 1983; Heller 1984; McGrath 2007). On the one hand, the mereological approach says that such “smaller parts” of Sam are not temporal parts because they don’t overlap every part of Sam at a certain time. On the other hand, the spatial approach roughly says that such “smaller parts” of Sam are not temporal parts because a temporal part is of the same spatial size as its whole for as long as that part exists.
    [Show full text]
  • Nietzsche's Doctrine of Eternal Return
    University of Rhode Island DigitalCommons@URI Senior Honors Projects Honors Program at the University of Rhode Island 2007 Nietzsche’s Doctrine of Eternal Return David R. Gadon University of Rhode Island, [email protected] Follow this and additional works at: http://digitalcommons.uri.edu/srhonorsprog Part of the Philosophy Commons Recommended Citation Gadon, David R., "Nietzsche’s Doctrine of Eternal Return" (2007). Senior Honors Projects. Paper 47. http://digitalcommons.uri.edu/srhonorsprog/47http://digitalcommons.uri.edu/srhonorsprog/47 This Article is brought to you for free and open access by the Honors Program at the University of Rhode Island at DigitalCommons@URI. It has been accepted for inclusion in Senior Honors Projects by an authorized administrator of DigitalCommons@URI. For more information, please contact [email protected]. Nietzsche’s Doctrine of Eternal Return David Ray Gadon Honors Senior Thesis Spring 2007 Sponsor: Dr. Galen A. Johnson Gadon 2 Nietzsche’s Doctrine of Eternal Return “Six thousand feet beyond man and time.” 1 In the Western world, we have a pronounced affinity for understanding time as something ultimately simple. Despite our recognition of the differences in subjective perception of the passing of intervals, we tacitly affirm that time itself must objectively follow a comprehensible structure of unidirectional flow which, like the commonly cited river metaphor, begins at one point and is definitively moving towards another. Thanks especially to the Judeo-Christian model of history plowing inevitably towards a conclusion at the end of days, even in the absence of direct religious influence, our intuitive understanding of time remains linear. We see this model addressed and contested by metaphysicians throughout the ages, but only rarely do we glimpse a philosophy that is able to cogently upturn this intuitively correct ideal.
    [Show full text]
  • Relativity and Three Four Dimensionalism
    Relativity and Three Four-Dimensionalisms Abstract: Relativity theory is often said to support something called ‘the four-dimensional view of reality’. But there are at least three different views that sometimes go by this name. One is the B-theory of time, according to which the past, present, and future are all equally real and there is nothing metaphysically special about the present. A second is ‘spacetime unitism’ (as we call it), according to which there is a spacetime manifold, and if there are such things points of space or instants of time, these are just spacetime regions of different sorts: thus space and time are not separate manifolds. A third is perdurantism, according to which persisting material objects (rocks, trees, human beings) are made up of different temporal parts located at different times. We sketch routes from relativity to the B-theory and to unitism. We then discuss some routes to perdurantism, via the B-theory and via unitism. Introduction Relativity theory1 is often said to support something called ‘the four-dimensional view’ of reality. But there are three independent views that go by this name: (i) spacetime unitism, as we call it, according to which spacetime is more fundamental than space or time, and points of space and instants of time, if they exist at all, are just spacetime regions of different sorts; (ii) the B-theory of time, according to which the past, present and future are all equally real and there is nothing objectively special about the present; and (iii) perdurantism, according to which material objects are four-dimensional wholes made up of different temporal parts.
    [Show full text]
  • Three Readings of the Eternal Return Michael James Maclaggan Louisiana State University and Agricultural and Mechanical College, [email protected]
    Louisiana State University LSU Digital Commons LSU Master's Theses Graduate School 2014 Three Readings of the Eternal Return Michael James MacLaggan Louisiana State University and Agricultural and Mechanical College, [email protected] Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_theses Part of the Arts and Humanities Commons Recommended Citation MacLaggan, Michael James, "Three Readings of the Eternal Return" (2014). LSU Master's Theses. 861. https://digitalcommons.lsu.edu/gradschool_theses/861 This Thesis is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Master's Theses by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. THREE READINGS OF THE ETERNAL RETURN A Thesis Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Master of Arts in The Department of Philosophy and Religious Studies by Michael James MacLaggan B.S., University of Texas at Austin, 2004 August 2014 To the greatest of them all: Sanford L. “Sandy” Bauman, ordinary philosopher. ii TABLE OF CONTENTS ABSTRACT ..................................................................................................................................................................................... iv INTRODUCTION ........................................................................................................................................................................
    [Show full text]
  • WHO-UMC System for Standardised Case Causality Assessment
    The use of the WHO-UMC system for standardised case causality assessment Why causality assessment? An inherent problem in pharmacovigilance is that most case reports concern suspected adverse drug reactions. Adverse reactions are rarely specific for the drug, diagnostic tests are usually absent and a rechallenge is rarely ethically justified. In practice few adverse reactions are ‘certain’ or ‘unlikely’; most are somewhere in between these extremes, i.e. ‘possible’ or ‘probable’. In an attempt to solve this problem many systems have been developed for a structured and harmonised assessment of causality (1). None of these systems, however, have been shown to produce a precise and reliable quantitative estimation of relationship likelihood. Nevertheless, causality assessment has become a common routine procedure in pharmacovigilance. The advances and limitations of causality assessment are reviewed in Table 1 (2). Table 1. Advances and limitations of standardised case causality assessment What causality assessment can do What causality assessment cannot do Decrease disagreement between assessors Give accurate quantitative measurement of relationship likelihood Classify relationship likelihood Distinguish valid from invalid cases Mark individual case reports Prove the connection between drug and event Improvement of scientific evaluation; Quantify the contribution of a drug to the educational development of an adverse event Change uncertainty into certainty The WHO-UMC causality assessment system The WHO-UMC system has been developed in consultation with the National Centres participating in the Programme for International Drug Monitoring and is meant as a practical tool for the assessment of case reports. It is basically a combined assessment taking into account the clinical-pharmacological aspects of the case history and the quality of the documentation of the observation.
    [Show full text]
  • Student Understanding of Time in Special Relativity: Simultaneity and Reference Frames
    Student understanding of time in special relativity: simultaneity and reference frames Rachel E. Scherr, Peter S. Shaffer, and Stamatis Vokos Department of Physics, University of Washington, Seattle, WA This article reports on an investigation of student understanding of the concept of time in special relativity. A series of research tasks are discussed that illustrate, step-by-step, how student reasoning of fundamental concepts of relativity was probed. The results indicate that after standard instruction students at all academic levels have serious difficulties with the relativity of simultaneity and with the role of observers in inertial reference frames. Evidence is presented that suggests many students construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity harmoniously co-exist. relativistic kinematics in the laboratory I. INTRODUCTION frame.1 We wanted to expand this research There is growing national interest in base to relativity in order to provide a guide increasing the exposure of students in for the development of instructional 2,3 introductory courses to modern physics materials by ourselves and others. topics, such as relativity. Proponents of This article reports on an investigation enlarging the scope of the curriculum argue of student understanding of time in special that in the beginning of the 21st century the relativity. A major purpose is to identify content of introductory classes should reflect and characterize the conceptual and some of the major intellectual breakthroughs reasoning difficulties that students at all of the 20th century. Others hold that the list levels encounter in their study of special of topics that must be covered is already too relativity.
    [Show full text]
  • Temporal Parts and Timeless Parthood
    Temporal Parts and Timeless Parthood Eric T. Olson University of Sheffield abstract: What is a temporal part? Most accounts explain it in terms of timeless parthood: a thing's having a part without temporal qualification. Some find this hard to understand, and thus find the view that persisting things have temporal parts--four- dimensionalism--unintelligible. T. Sider offers to help by defining temporal parthood in terms of a thing's having a part at a time. I argue that no such account can capture the notion of a temporal part that figures in orthodox four-dimensionalism: temporal parts must be timeless parts. This enables us to state four-dimensionalism more clearly. 1. “Four-dimensionalists” say that things persist by having temporal parts spread out across time. A thing exists at a time, they say, by having a temporal part located just at that time. So I exist in 1975 by having a temporal part that exists throughout that year and only then; I exist now by having another temporal part that exists only now. “Three- dimensionalists,” by contrast, say that at least some things persist without having temporal parts. The event that is the history of a person or a dog might have temporal parts, but people and dogs themselves have none. Better, three-dimensionalism says that some persisting things lack proper temporal parts: maybe anything that exists at some time is a temporal part of itself, just as anything whatever a part of itself. Three- and four-dimensionalists disagree about whether persisting things have temporal parts other than themselves.
    [Show full text]
  • Symmetry in Classical Mechanics
    Symmetries and Conservation Laws: 1 J. Hanc, S. Tuleja, M. Hancova Consequences of Noether’s Theorem 1 2 Symmetries and Conservation Laws: 3 Consequences of Noether’s Theorem 4 5 Jozef Hanca) 6 Technical University, Vysokoskolska 4, 042 00 Kosice, Slovakia 7 8 Slavomir Tulejab) 9 Gymnazium arm. gen. L. Svobodu, Komenskeho 4, 066 51 Humenne, Slovakia 10 11 Martina Hancovac) 12 University of Pavol Jozef Safarik, Jesenna 5, 040 11 Kosice, Slovakia 13 14 We derive conservation laws from symmetry operations using the principle of least 15 action. These derivations, which are examples of Noether’s theorem, require only 16 elementary calculus. They help provide physical understanding of the relation be- 17 tween symmetry and fundamental mechanics for introductory university physics stu- 18 dents. We extend these arguments to the transformation of coordinates due to uniform 19 motion to show that a symmetry argument applies more elegantly to the Lorentz 20 transformation than to the Galilean transformation. 21 22 23 I. INTRODUCTION 24 It is increasingly clear that the symmetry group of nature is the deepest thing that we un- 25 derstand about nature today. 26 Steven Weinberg1 27 28 Many of us have heard statements like: For each symmetry operation there is a corre- 29 sponding conservation law. The conservation of momentum is related to the homogeneity of 30 space. Invariance under translation in time means that law of conservation of energy is valid. 31 Such statements come from one of the most amazing and useful theorems in physics, called 32 Noether’s theorem. 33 When the German mathematician Emmy Noether proved her theorem in 19182,3, she un- 34 covered the most fundamental justification for conservation laws.
    [Show full text]