Reading the Texture of Reality : Chaos Theory, Literature and the Humanist Perspective

Tutkimuksessa analysoidaan kaaosteorian vaikutusta kaunokirjallisuudessa ja kirjallisuudentutkimuksessa ja esitetään, että kaaosteorian roolia kirjallisuuden kentällä voidaan parhaiten ymmärtää sen avaamien käsitteiden kautta. Suoran soveltamisen sijaan kaaosteorian avulla on käyty uudenlaisia keskusteluja vanhoista aiheista ja luonnontieteestä ammennetut käsitteet ovat johtaneet aiemmin tukkeutuneiden argumenttien avaamiseen uudesta näkökulmasta käsin. Väitöskirjassa keskitytään kolmeen osa-alueeseen: kaunokirjallisen teoksen rakenteen teoretisointiin, ihmisen (erityisesti tekijän) identiteetin hahmottamiseen ja kuvailemiseen sekä fiktion ja todellisuuden suhteen pohdintaan. Tutkimuksen tarkoituksena on osoittaa, kuinka kaaosteorian kautta näitä aiheita on lähestytty niin kirjallisuustieteessä kuin kaunokirjallisissa teoksissakin. Väitöskirjan keskiössä ovat romaanikirjailija John Barthin, dramatisti Tom Stoppardin ja runoilija Jorie Grahamin teosten analyysit. Nämä kirjailijat ammentavat kaaosteoriasta keinoja käsitteellistää rakenteita, jotka ovat yhtä aikaa dynaamisia prosesseja ja hahmotettavia muotoja. Kaunokirjallisina teemoina nousevat esiin myös ihmisen paradoksaalisesti tunnistettava ja aina muuttuva identiteetti sekä lopullista haltuunottoa pakeneva, mutta silti kiehtova ja tavoiteltava todellisuus. Näiden kirjailijoiden teosten analyysin sekä teoreettisen keskustelun kautta väitöskirjassa tuodaan esiin aiemmassa tutkimuksessa varjoon jäänyt, koherenssia, ymmärrettävyyttä ja realismia painottava humanistinen näkökulma kaaosteorian merkityksestä kirjallisuudessa.

Contributions to the Theory of Finite-State Based Grammars

This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing. Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammars

Konstrukcija mnimosti : K poètike "Voskovoj persony" Ju. Tynjanova

The subject of this work is the poetics of «The Wax Effigy», a short novel or novella by Jurii Tynianov, Russian writer, literary critic, historian of literature and prominent literary theoretician. The plot structure of the novel is based upon a real event, the creation by Bartolomeo Carlo Rastrelli in 1725 of a wax sculpture of the first Russian emperor, Peter the Great. «Construction of the Sham» consists of three chapters, an introduction and a conclusion. Due to the fact that Tynianov was at the same time a prose writer and theoretician of literature it seemed important to consider the reception of his prose and his works on literary theory in relationship to each other. The introduction is devoted to this task. The first chapter is about the history of the creation of the novel and its reception. Tynianov stopped writing one short story in order to write the novel; these two works have some common traits. It seems almost obvious that his work on the first text was a real step toward the creation of the second. In the first story there is an opposition of dead/alive which is semantic prefiguring of a central motif in «The Wax Effigy». An analysis of the reception of the novel demonstrated that almost every critic writing about the novel has described it as nonsense. Critics considered Tynianov's work in terms of «devices» and «content» and could not understand how devices are related to the content of the novel: the novel was thought as a signifier without any signified. Implicitly, critics thought the signified of the novel as a traditional one of the historical novel, as the historiosophical «idea», embodied in the system of literary devices. In this case literature becomes something instrumental, a kind of expression of extraliterary content. In contradistinction to that Tynianov considered literary semantics as an effect of the literary structure. From his point of view the literary sense is immanent to the process of signification accomplished inside the literary text. The second chapter is devoted to a rhetorical analysis of the opposition dead/alive. Tynianov systematically compares both terms of the opposition. As a result of this strategy the wax effigy of the dead emperor becomes «as if» alive and the world of living people «as if» dead. The qualifier «as if» refers to the fact that Tynianov creates an ambiguous semantic system. This rhetoric is related to European Romanticism and his «fantastic literature» (Merimé, Hoffmann, Maupassant etc.). But Tynianov demonstrates a linguistic origin of the strange fantoms created by romantics; he demystifies these idols by parodying the fantastic literature, that is, showing «how it was done». At the same time, the opposition mentioned above refers to his idea of «incongruity» which plays a prominent role in Tynianov s theory but has never been conceptualised. The incongruity is a inner collision of the literary text; from Tynianov's point of view the meaning of the work of literature is always a dynamic collision of semantically heterogeneous elements struggling with each other. In «The Wax Effigy» Tynianov creates a metalevel of the work demonstrating the process of creation of the literary sense. The third chapter is a reconstruction of Tynianov's conception of the historical prose, specifically of the mechanisms by which historical facts are transformed into literary events. Tynianov thought that the task of the historical novelist is to depict his hero as an actor, to demonstrate that as a wearer of many masks he is a creator of appearances, ambiguities. Here, in the «figure of fiction» (Andrei Belyi), the very idea of the historical prose and rhetoric employed in «The Wax Effigy», history and literature meet each other. In his last theoretical work, «On parody» Tynianov writes about the so-called sham structure of parody. In his opinion every parody is a text about other texts and «serious» work which could be read at the same time as a text about «reality». This twofold structure of parody is that of «The Wax Effigy»: that text speaks about ambiguities of the history and about ambiguities of the literary sense, about social reality of the past and - about the working of the literature itself. «The Wax Effigy» is written as a autoreflective text, as an experiment in literary semantics, as a system of literary ambiguities - of hero, rhetoric and the text itself. The meaning of the novel is created not by the embodiment extraliterary idea, but by the process of signification accomplished inside the work of literature. In this sense Tynianov's novel is parody, a break with the tradition of the historical novel preceding «The Wax Effigy».

Space in Musical Semiosis : An Abductive Theory of the Musical Composition Process

Space in musical semiosis is a study of musical meaning, spatiality and composition. Earlier studies on musical composition have not adequately treated the problems of musical signification. Here, composition is considered an epitomic process of musical signification. Hence the core problems of composition theory are core problems of musical semiotics. The study employs a framework of naturalist pragmatism, based on C. S. Peirce’s philosophy. It operates on concepts such as subject, experience, mind and inquiry, and incorporates relevant ideas of Aristotle, Peirce and John Dewey into a synthetic view of esthetic, practic, and semiotic for the benefit of grasping musical signification process as a case of semiosis in general. Based on expert accounts, music is depicted as real, communicative, representational, useful, embodied and non-arbitrary. These describe how music and the musical composition process are mental processes. Peirce’s theories are combined with current morphological theories of cognition into a view of mind, in which space is central. This requires an analysis of space, and the acceptance of a relativist understanding of spatiality. This approach to signification suggests that mental processes are spatially embodied, by virtue of hard facts of the world, literal representations of objects, as well as primary and complex metaphors each sharing identities of spatial structures. Consequently, music and the musical composition process are spatially embodied. Composing music appears as a process of constructing metaphors—as a praxis of shaping and reshaping features of sound, representable from simple quality dimensions to complex domains. In principle, any conceptual space, metaphorical or literal, may set off and steer elaboration, depending on the practical bearings on the habits of feeling, thinking and action, induced in musical communication. In this sense, it is evident that music helps us to reorganize our habits of feeling, thinking, and action. These habits, in turn, constitute our existence. The combination of Peirce and morphological approaches to cognition serves well for understanding musical and general signification. It appears both possible and worthwhile to address a variety of issues central to musicological inquiry in the framework of naturalist pragmatism. The study may also contribute to the development of Peircean semiotics.

A Literary Turn : Rethinking the Roles of Generalization and Theory in Anglo-American Moral Philosophy

This work investigates the role of narrative literature in late-20th century and contemporary Anglo-American moral philosophy. It aims to show the trend of reading narrative literature for purposes of moral philosophy from the 1970 s and early 80 s to the present day as a part of a larger movement in Anglo-American moral philosophy, and to present a view of its significance for moral philosophy overall. Chapter 1 provides some preliminaries concerning the view of narrative literature which my discussion builds on. In chapter 2 I give an outline of how narrative literature is considered in contemporary Anglo-American moral philosophy, and connect this use to the broad trend of neo-Aristotelian ethics in this context. In chapter 3 I connect the use of literature to the idea of the non-generalizability of moral perception and judgment, which is central to the neo-Aristotelian trend, as well as to a range of moral particularisms and anti-theoretical positions of late 20th century and contemporary ethics. The joint task of chapters 2 and 3 is to situate the trend of reading narrative literature for the purposes of moral philosophy in the present context of moral philosophy. In the following two chapters, 4 and 5, I move on from the particularizing power of narrative literature, which is emphasized by neo-Aristotelians and particularists alike, to a broader under-standing of the intellectual potential of narrative literature. In chapter 4 I argue that narrative literature has its own forms of generalization which are enriching for our understanding of the workings of ethical generalizations in philosophy. In chapter 5 I discuss Iris Murdoch s and Martha Nussbaum s respective ways of combining ethical generality and particularity in a philosophical framework where both systematic moral theory and narrative literature are taken seriously. In chapter 6 I analyse the controversy between contemporary anti-theoretical conceptions of ethics and Nussbaum s refutation of these. I present my suggestion for how the significance of the ethics/literature discussion for moral philosophy can be understood if one wants to overcome the limitations of both Nussbaum s theory-centred, equilibrium-seeking perspective, and the anti-theorists repudiation of theory. I call my position the inclusive approach .

On the Origin of Ideas : An Abductivist Approach to Discovery

The purpose of this study is to analyze and develop various forms of abduction as a means of conceptualizing processes of discovery. Abduction was originally presented by Charles S. Peirce (1839-1914) as a "weak", third main mode of inference -- besides deduction and induction -- one which, he proposed, is closely related to many kinds of cognitive processes, such as instincts, perception, practices and mediated activity in general. Both abduction and discovery are controversial issues in philosophy of science. It is often claimed that discovery cannot be a proper subject area for conceptual analysis and, accordingly, abduction cannot serve as a "logic of discovery". I argue, however, that abduction gives essential means for understanding processes of discovery although it cannot give rise to a manual or algorithm for making discoveries. In the first part of the study, I briefly present how the main trend in philosophy of science has, for a long time, been critical towards a systematic account of discovery. Various models have, however, been suggested. I outline a short history of abduction; first Peirce's evolving forms of his theory, and then later developments. Although abduction has not been a major area of research until quite recently, I review some critiques of it and look at the ways it has been analyzed, developed and used in various fields of research. Peirce's own writings and later developments, I argue, leave room for various subsequent interpretations of abduction. The second part of the study consists of six research articles. First I treat "classical" arguments against abduction as a logic of discovery. I show that by developing strategic aspects of abductive inference these arguments can be countered. Nowadays the term 'abduction' is often used as a synonym for the Inference to the Best Explanation (IBE) model. I argue, however, that it is useful to distinguish between IBE ("Harmanian abduction") and "Hansonian abduction"; the latter concentrating on analyzing processes of discovery. The distinctions between loveliness and likeliness, and between potential and actual explanations are more fruitful within Hansonian abduction. I clarify the nature of abduction by using Peirce's distinction between three areas of "semeiotic": grammar, critic, and methodeutic. Grammar (emphasizing "Firstnesses" and iconicity) and methodeutic (i.e., a processual approach) especially, give new means for understanding abduction. Peirce himself held a controversial view that new abductive ideas are products of an instinct and an inference at the same time. I maintain that it is beneficial to make a clear distinction between abductive inference and abductive instinct, on the basis of which both can be developed further. Besides these, I analyze abduction as a part of distributed cognition which emphasizes a long-term interaction with the material, social and cultural environment as a source for abductive ideas. This approach suggests a "trialogical" model in which inquirers are fundamentally connected both to other inquirers and to the objects of inquiry. As for the classical Meno paradox about discovery, I show that abduction provides more than one answer. As my main example of abductive methodology, I analyze the process of Ignaz Semmelweis' research on childbed fever. A central basis for abduction is the claim that discovery is not a sequence of events governed only by processes of chance. Abduction treats those processes which both constrain and instigate the search for new ideas; starting from the use of clues as a starting point for discovery, but continuing in considerations like elegance and 'loveliness'. The study then continues a Peircean-Hansonian research programme by developing abduction as a way of analyzing processes of discovery.

Theory and Analysis of Classic Heavy Metal Harmony

This thesis explores melodic and harmonic features of heavy metal, and while doing so, explores various methods of music analysis; their applicability and limitations regarding the study of heavy metal music. The study is built on three general hypotheses according to which 1) acoustic characteristics play a significant role for chord constructing in heavy metal, 2) heavy metal has strong ties and similarities with other Western musical styles, and 3) theories and analytical methods of Western art music may be applied to heavy metal. It seems evident that in heavy metal some chord structures appear far more frequently than others. It is suggested here that the fundamental reason for this is the use of guitar distortion effect. Subsequently, theories as to how and under what principles heavy metal is constructed need to be put under discussion; analytical models regarding the classification of consonance and dissonance and chord categorization are here revised to meet the common practices of this music. It is evident that heavy metal is not an isolated style of music; it is seen here as a cultural fusion of various musical styles. Moreover, it is suggested that the theoretical background to the construction of Western music and its analysis can offer invaluable insights to heavy metal. However, the analytical methods need to be reformed to some extent to meet the characteristics of the music. This reformation includes an accommodation of linear and functional theories that has been found rather rarely in music theory and musicology.

Evaluation of driving ability of the disabled persons in the context of the psychological activity theory

In the future the number of the disabled drivers requiring a special evaluation of their driving ability will increase due to the ageing population, as well as the progress of adaptive technology. This places pressure on the development of the driving evaluation system. Despite quite intensive research there is still no consensus concerning what is the factual situation in a driver evaluation (methodology), which measures should be included in an evaluation (methods), and how an evaluation has to be carried out (practise). In order to find answers to these questions we carried out empirical studies, and simultaneously elaborated upon a conceptual model for driving and a driving evaluation. The findings of empirical studies can be condensed into the following points: 1) A driving ability defined by the on-road driving test is associated with different laboratory measures depending on the study groups. Faults in the laboratory tests predicted faults in the on-road driving test in the novice group, whereas slowness in the laboratory predicted driving faults in the experienced drivers group. 2) The Parkinson study clearly showed that even an experienced clinician cannot reliably accomplish an evaluation of a disabled person’s driving ability without collaboration with other specialists. 3) The main finding of the stroke study was that the use of a multidisciplinary team as a source of information harmonises the specialists’ evaluations. 4) The patient studies demonstrated that the disabled persons themselves, as well as their spouses, are as a rule not reliable evaluators. 5) From the safety point of view, perceptible operations with the control devices are not crucial, but correct mental actions which the driver carries out with the help of the control devices are of greatest importance. 6) Personality factors including higher-order needs and motives, attitudes and a degree of self-awareness, particularly a sense of illness, are decisive when evaluating a disabled person’s driving ability. Personality is also the main source of resources concerning compensations for lower-order physical deficiencies and restrictions. From work with the conceptual model we drew the following methodological conclusions: First, the driver has to be considered as a holistic subject of the activity, as a multilevel hierarchically organised system of an organism, a temperament, an individuality, and a personality where the personality is the leading subsystem from the standpoint of safety. Second, driving as a human form of a sociopractical activity, is also a hierarchically organised dynamic system. Third, in an evaluation of driving ability it is a question of matching these two hierarchically organised structures: a subject of an activity and a proper activity. Fourth, an evaluation has to be person centred but not disease-, function- or method centred. On the basis of our study a multidisciplinary team (practitioner, driving school teacher, psychologist, occupational therapist) is recommended for use in demanding driver evaluations. Primary in a driver’s evaluations is a coherent conceptual model while concrete methods of evaluations may vary. However, the on-road test must always be performed if possible.

Widening Perspectives of Teacher Education : Studies on theory-practice relationship, reflection, research and professional development

This dissertation examined the research-based teacher education at the University of Helsinki from different theoretical and practical perspectives. Five studies focused on these perspectives separately as well as overlappingly. Study I focused on the reflection process of graduating teacher students. The data consisted of essays the students wrote as their last assignment before graduating, where their assignment was to examine their development as researchers during their MA thesis research process. The results indicated that the teacher students had analysed their own development thoroughly during the process and that they had reflected on theoretical as well as practical educational matters. The results also pointed out that, in the students’ opinion, personally conducted research is a significant learning process. -- Study II investigated teacher students’ workplace learning and the integration of theory and practice in teacher education. The students’ interviews focused on their learning of teacher’s work prior to education. The interviewees’ responses concerning their ‘surviving’ in teaching prior to teacher education were categorized into three categories: learning through experiences, school as a teacher learning environment, and case-specific learning. The survey part of the study focused on integration of theory and practice within the education process. The results showed that the students who worked while they studied took advantage of the studies and applied them to work. They set more demanding teaching goals and reflected on their work more theoretically. -- Study III examined practical aspects of the teacher students’ MA thesis research as well as the integration of theory and practice in teacher education. The participants were surveyed using a web-based survey which dealt with the participants’ teacher education experiences. According to the results, most of the students had chosen a practical topic for their MA thesis, one arising from their work environment, and most had chosen a research topic that would develop their own teaching. The results showed that the integration of theory and practice had taken place in much of the course work, but most obviously in the practicum periods, and also in the courses concerning the school subjects. The majority felt that the education had in some way been successful with regards to integration. -- Study IV explored the idea of considering teacher students’ MA thesis research as professional development. Twenty-three teachers were interviewed on the subject of their experiences of conducting research about their own work as teachers. The results of the interviews showed that the reasons for choosing the MA thesis research topic were multiple: practical, theoretical, personal, professional reasons, as well as outside effect. The objectives of the MA thesis research, besides graduating, were actual projects, developing the ability to work as teachers, conducting significant research, and sharing knowledge of the topic. The results indicated that an MA thesis can function as a tool for professional development, for example in finding ways for adjusting teaching, increasing interaction skills, gaining knowledge or improving reflection on theory and/or practice, strengthening self-confidence as a teacher, increasing researching skills or academic writing skills, as well as becoming critical and being able to read scientific and academic literature. -- Study V analysed teachers’ views of the impact of practitioner research. According to the results, the interviewees considered the benefits of practitioner research to be many, affecting teachers, pupils, parents, the working community, and the wider society. Most of the teachers indicated that they intended to continue to conduct research in the future. The results also showed that teachers often reflected personally and collectively, and viewed this as important. -- These five studies point out that MA thesis research is and can be a useful tool for increasing reflection doing with personal and professional development, as well as integrating theory and practice. The studies suggest that more advantage could be taken of the MA thesis research project. More integration of working and studying could and should be made possible for teacher students. This could be done in various ways within teacher education, but the MA thesis should be seen as a pedagogical possibility.

Microclimate and gas emissions in dairy buildings : Instrumentation, theory and measurements

The aim of this thesis was to develop measurement techniques and systems for measuring air quality and to provide information about air quality conditions and the amount of gaseous emissions from semi-insulated and uninsulated dairy buildings in Finland and Estonia. Specialization and intensification in livestock farming, such as in dairy production, is usually accompanied by an increase in concentrated environmental emissions. In addition to high moisture, the presence of dust and corrosive gases, and widely varying gas concentrations in dairy buildings, Finland and Estonia experience winter temperatures reaching below -40 ºC and summer temperatures above +30 ºC. The adaptation of new technologies for long-term air quality monitoring and measurement remains relatively uncommon in dairy buildings because the construction and maintenance of accurate monitoring systems for long-term use are too expensive for the average dairy farmer to afford. Though the documentation of accurate air quality measurement systems intended mainly for research purposes have been made in the past, standardised methods and the documentation of affordable systems and simple methods for performing air quality and emissions measurements in dairy buildings are unavailable. In this study, we built three measurement systems: 1) a Stationary system with integrated affordable sensors for on-site measurements, 2) a Wireless system with affordable sensors for off-site measurements, and 3) a Mobile system consisting of expensive and accurate sensors for measuring air quality. In addition to assessing existing methods, we developed simplified methods for measuring ventilation and emission rates in dairy buildings. The three measurement systems were successfully used to measure air quality in uninsulated, semi-insulated, and fully-insulated dairy buildings between the years 2005 and 2007. When carefully calibrated, the affordable sensors in the systems gave reasonably accurate readings. The spatial air quality survey showed high variation in microclimate conditions in the dairy buildings measured. The average indoor air concentration for carbon dioxide was 950 ppm, for ammonia 5 ppm, for methane 48 ppm, for relative humidity 70%, and for inside air velocity 0.2 m/s. The average winter and summer indoor temperatures during the measurement period were -7º C and +24 ºC for the uninsulated, +3 ºC and +20 ºC for the semi-insulated and +10 ºC and +25 ºC for the fully-insulated dairy buildings. The measurement results showed that the uninsulated dairy buildings had lower indoor gas concentrations and emissions compared to fully insulated buildings. Although occasionally exceeded, the ventilation rates and average indoor air quality in the dairy buildings were largely within recommended limits. We assessed the traditional heat balance, moisture balance, carbon dioxide balance and direct airflow methods for estimating ventilation rates. The direct velocity measurement for the estimation of ventilation rate proved to be impractical for naturally ventilated buildings. Two methods were developed for estimating ventilation rates. The first method is applicable in buildings in which the ventilation can be stopped or completely closed. The second method is useful in naturally ventilated buildings with large openings and high ventilation rates where spatial gas concentrations are heterogeneously distributed. The two traditional methods (carbon dioxide and methane balances), and two newly developed methods (theoretical modelling using Fick s law and boundary layer theory, and the recirculation flux-chamber technique) were used to estimate ammonia emissions from the dairy buildings. Using the traditional carbon dioxide balance method, ammonia emissions per cow from the dairy buildings ranged from 7 g day-1 to 35 g day-1, and methane emissions per cow ranged from 96 g day-1 to 348 g day-1. The developed methods proved to be as equally accurate as the traditional methods. Variation between the mean emissions estimated with the traditional and the developed methods was less than 20%. The developed modelling procedure provided sound framework for examining the impact of production systems on ammonia emissions in dairy buildings.

Noncommutative Gravitation as a Gauge Theory of Twisted Poincaré Symmetry

Gravitaation kvanttiteorian muotoilu on ollut teoreettisten fyysikkojen tavoitteena kvanttimekaniikan synnystä lähtien. Kvanttimekaniikan soveltaminen korkean energian ilmiöihin yleisen suhteellisuusteorian viitekehyksessä johtaa aika-avaruuden koordinaattien operatiiviseen ei-kommutoivuuteen. Ei-kommutoivia aika-avaruuden geometrioita tavataan myös avointen säikeiden säieteorioiden tietyillä matalan energian rajoilla. Ei-kommutoivan aika-avaruuden gravitaatioteoria voisi olla yhteensopiva kvanttimekaniikan kanssa ja se voisi mahdollistaa erittäin lyhyiden etäisyyksien ja korkeiden energioiden prosessien ei-lokaaliksi uskotun fysiikan kuvauksen, sekä tuottaa yleisen suhteellisuusteorian kanssa yhtenevän teorian pitkillä etäisyyksillä. Tässä työssä tarkastelen gravitaatiota Poincarén symmetrian mittakenttäteoriana ja pyrin yleistämään tämän näkemyksen ei-kommutoiviin aika-avaruuksiin. Ensin esittelen Poincarén symmetrian keskeisen roolin relativistisessa fysiikassa ja sen kuinka klassinen gravitaatioteoria johdetaan Poincarén symmetrian mittakenttäteoriana kommutoivassa aika-avaruudessa. Jatkan esittelemällä ei-kommutoivan aika-avaruuden ja kvanttikenttäteorian muotoilun ei-kommutoivassa aika-avaruudessa. Mittasymmetrioiden lokaalin luonteen vuoksi tarkastelen huolellisesti mittakenttäteorioiden muotoilua ei-kommutoivassa aika-avaruudessa. Erityistä huomiota kiinnitetään näiden teorioiden vääristyneeseen Poincarén symmetriaan, joka on ei-kommutoivan aika-avaruuden omaama uudentyyppinen kvanttisymmetria. Seuraavaksi tarkastelen ei-kommutoivan gravitaatioteorian muotoilun ongelmia ja niihin kirjallisuudessa esitettyjä ratkaisuehdotuksia. Selitän kuinka kaikissa tähänastisissa lähestymistavoissa epäonnistutaan muotoilla kovarianssi yleisten koordinaattimunnosten suhteen, joka on yleisen suhteellisuusteorian kulmakivi. Lopuksi tutkin mahdollisuutta yleistää vääristynyt Poincarén symmetria lokaaliksi mittasymmetriaksi --- gravitaation ei-kommutoivan mittakenttäteorian saavuttamisen toivossa. Osoitan, että tällaista yleistystä ei voida saavuttaa vääristämällä Poincarén symmetriaa kovariantilla twist-elementillä. Näin ollen ei-kommutoivan gravitaation ja vääristyneen Poincarén symmetrian tutkimuksessa tulee jatkossa keskittyä muihin lähestymistapoihin.

The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.