Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility)

It is shown that there are significant conceptual differences between QM and QFT which make it difficult to view the latter as just a relativistic extension of the principles of QM. At the root of this is a fundamental distiction between Born-localization in QM (which in the relativistic context changes its name to Newton-Wigner localization) and modular localization which is the localization underlying QFT, after one separates it from its standard presentation in terms of field coordinates. The first comes with a probability notion and projection operators, whereas the latter describes causal propagation in QFT and leads to thermal aspects of locally reduced finite energy states. The Born-Newton-Wigner localization in QFT is only applicable asymptotically and the covariant correlation between asymptotic in and out localization projectors is the basis of the existence of an invariant scattering matrix. In this first part of a two part essay the modular localization (the intrinsic content of field localization) and its philosophical consequences take the center stage. Important physical consequences of vacuum polarization will be the main topic of part II. Both parts together form a rather comprehensive presentation of known consequences of the two antagonistic localization concepts, including the those of its misunderstandings in string theory.Comment: 63 pages corrections, reformulations, references adde

Gödel’s Cantorianism

Gödel’s philosophical conceptions bear striking similarities to Cantor’s. Although there is no conclusive evidence that Gödel deliberately used or adhered to Cantor’s views, one can successfully reconstruct and see his “Cantorianism” at work in many parts of his thought. In this paper, I aim to describe the most prominent conceptual intersections between Cantor’s and Gödel’s thought, particularly on such matters as the nature and existence of mathematical entities (sets), concepts, Platonism, the Absolute Infinite, the progress and inexhaustibility of mathematics

The Web of Corruption:A Tardean Analysis of the Shifting Constructions of the Elios Scandal in the Hungarian Online News Media

Although corruption portrayals within the news media have become a regularly analysed topic in Organisation and Management Studies, the construction of scandals within the online realm is still under-researched. Organisational scholars call for studies to analyse corruption in online media due to the highly participatory sense- making processes that distinguish this context from traditional press. Analysing scandalisation online is important because interactions in this realm define and curb corruption.This thesis responds to these points by exploring the co-production of corruption scandals within online news articles as occurring through narrative developments and hyperlink relations. To address the processual and participatory aspects of online corruption scandalisation, it engages with the theories of Gabriel Tarde. Particularly, the Tardean lens allows this thesis to analyse articles with their embedded hyperlinks as sense-making crossroads of information flows that accumulate into the rhythmical meanderings of scandal narratives.Empirically, the thesis focuses on the Hungarian organisational and political Elios scandal. It investigates the articles of the news outlets of Origo and Index, and their hyperlinks. Thematic analysis is used for studying the textual data, and argumentation analysis for the hyperlink interactions.This results in the identification of three narrative-construction periods: (1) scandalisation, (2) anti-scandalisation and moderation, and (3) counter- scandalisation. The thesis shows that hyperlinks play an important role in these meaning constructions. On the one hand, hyperlinks represent online sense-making channels, leading to reliable and relevant sources. However, through the avoidance of hyperlinking opposing arguments, these contribute to one-sided, meaning- constructions. Furthermore, the thesis demonstrates how the corruption scandal is gradually diverted and replaced with the sensationalist counter-scandalising Soros- narrative that provokes social currents, such as Antisemitism. Overall, this thesis contributes to the literature on corruption within the media by illustrating how hyperlinks and gradual narrative-developments are strategically used to shape the meaning-constructions around scandals

The idea of evolution in digital architecture: Toward united ontologies?

Humans have always sought to grasp nature’s working principles and apply acquired intelligence to artefacts since nature has always been the source of inspiration, solution and creativity. For this reason, there is a comprehensive interrelationship between the philosophy of nature and architecture. After Charles Darwin’s revolutionary work, living beings have started to be comprehended as changing, evolving and developing dynamic entities. Evolution theory has been accepted as the interpretive power of biology after several discussions and objections among scientists. In time, the working principles of evolutionary mechanisms have begun to be explained from genetic code to organism and environmental level. Afterwards, simulating nature’s evolutionary logic in the digital interface has become achievable with computational systems’ advancements. Ultimately, architects have begun to utilise evolutionary understanding in design theories and methodologies through computational procedures since the 1990s. Although several studies about technical and pragmatic elements of evolutionary tools in design, there is still little research on the historical, theoretical and philosophical foundations of evolutionary understanding in digital architecture. This paper fills this literature gap by critically reviewing the evolutionary understanding embedded in digital architecture theories and designs since the beginning of the 1990s. The original contribution is the proposed intellectual framework seeking to understand and conceptualise how evolutionary processes were defined in biology and philosophy, then represented through computational procedures, to be finally utilised by architectural designers. The network of references and concepts is deeply connected with the communication between natural processes and their computational simulations. For this reason, another original contribution is the utilisation of theoretical limits and operative principles of computation procedures to shed light on the limitations, shortcomings and potentials of design theories regarding their speculations on the relationship between natural and computational ontologies

Formally justified and modular Bayesian inference for probabilistic programs

Probabilistic modelling offers a simple and coherent framework to describe the real world in the face of uncertainty. Furthermore, by applying Bayes' rule it is possible to use probabilistic models to make inferences about the state of the world from partial observations. While traditionally probabilistic models were constructed on paper, more recently the approach of probabilistic programming enables users to write the models in executable languages resembling computer programs and to freely mix them with deterministic code. It has long been recognised that the semantics of programming languages is complicated and the intuitive understanding that programmers have is often inaccurate, resulting in difficult to understand bugs and unexpected program behaviours. Programming languages are therefore studied in a rigorous way using formal languages with mathematically defined semantics. Traditionally formal semantics of probabilistic programs are defined using exact inference results, but in practice exact Bayesian inference is not tractable and approximate methods are used instead, posing a question of how the results of these algorithms relate to the exact results. Correctness of such approximate methods is usually argued somewhat less rigorously, without reference to a formal semantics. In this dissertation we formally develop denotational semantics for probabilistic programs that correspond to popular sampling algorithms often used in practice. The semantics is defined for an expressive typed lambda calculus with higher-order functions and inductive types, extended with probabilistic effects for sampling and conditioning, allowing continuous distributions and unbounded likelihoods. It makes crucial use of the recently developed formalism of quasi-Borel spaces to bring all these elements together. We provide semantics corresponding to several variants of Markov chain Monte Carlo and Sequential Monte Carlo methods and formally prove a notion of correctness for these algorithms in the context of probabilistic programming. We also show that the semantic construction can be directly mapped to an implementation using established functional programming abstractions called monad transformers. We develop a compact Haskell library for probabilistic programming closely corresponding to the semantic construction, giving users a high level of assurance in the correctness of the implementation. We also demonstrate on a collection of benchmarks that the library offers performance competitive with existing systems of similar scope. An important property of our construction, both the semantics and the implementation, is the high degree of modularity it offers. All the inference algorithms are constructed by combining small building blocks in a setup where the type system ensures correctness of compositions. We show that with basic building blocks corresponding to vanilla Metropolis-Hastings and Sequential Monte Carlo we can implement more advanced algorithms known in the literature, such as Resample-Move Sequential Monte Carlo, Particle Marginal Metropolis-Hastings, and Sequential Monte Carlo squared. These implementations are very concise, reducing the effort required to produce them and the scope for bugs. On top of that, our modular construction enables in some cases deterministic testing of randomised inference algorithms, further increasing reliability of the implementation.Engineering and Physical Sciences Research Council, Cambridge Trust, Cambridge-Tuebingen programm

Seeing all things in space : Kant and the reality of space in the context of early modern philosophy

One of the basic concepts of the metaphysics of the pre-critical Kant is the early modern, Leibnizian concept of the world as a synthetic whole of simple substances. Space is the order according to which these simple substances coexist, in the presence of God. Kant’s turn to critical philosophy contained a re-evaluation of Leibnizian metaphysics. Space is an ideal form of sensibility, not a real order of coexisting simple substances. This dissertation argues that Kant’s critical turn inspired him to outline a new science of subjective space – the Transcendental Aesthetic. Leibnizians argued that our knowledge of space is innate, but still abstracted from the common sense idea of extension. In the Critique of Pure Reason Kant responded that this misrepresents our knowledge of the subjective space, which is the topic of the Transcendental Aesthetic. An exposition of the marks of the concept of subjective space not only shows that space is a form of sensibility, but that it is a continuous, actually infinite whole, which precedes its potentially infinite parts. In Kant’s terminology space is an analytic whole, which gives a key to the ideality of space, according to this dissertation. One important topic in the literature concerns Kant’s awareness of the Leibnizian alternative that space might be both a form of sensibility and an order of coexistence. This dissertation claims that Kant could not rule out this alternative completely. However, in one aspect, Kant was successful: Leibnizians had to admit that continuity belongs to space, not as an order of coexistence, but as a form of sensibility. We see all things in continuous space, not in God. However, seeing things in space is analogous to seeing them in God.Kantin niin sanotun esikriittisen metafysiikan yksi leibnizilaisista peruskäsityksistä on, että maailma on yksinkertaisten substanssien muodostama synteettinen kokonaisuus. Tässä näkemyksessä avaruus on järjestys, jonka mukaisesti yksinkertaiset substanssit ovat yhdessä olemassa Jumalan läsnäollessa. Kantin kriittiseen filosofiaan sisältyy leibnizilaisen metafysiikan uudelleen arviointi. Sen sijaan, että avaruus olisi yhdessä olemassa olevien yksinkertaisten substanssien reaalinen järjestys, avaruus on aistimellisuuden ideaali muoto. Tässä väitöskirjassa esitetään, kuinka Kantin kriittinen käänne sai hänet hahmottelemaan uuden subjektiivisen avaruuden tieteen – transsendentaalisen estetiikan. Leibnizilaiset väittivät, että tietomme avaruudesta on sisäsyntyistä, joskin abstrahoitu arkiajatteluunkin kuuluvasta ulotteisuuden ideasta. Puhtaan järjen kritiikissä Kant puolestaan väittää, että leibnizilaiset vääristävät tietomme subjektiivisesta avaruudesta, joka on aiheena transsendentaalisessa estetiikassa. Subjektiivisen avaruuden käsitteen erittely osoittaa, että avaruus on paitsi aistimellisuuden muoto, myös jatkuva, aktuaalisesti ääretön kokonaisuus, joka edeltää sen potentiaalisesti äärettömiä osia. Kantin terminologiassa avaruus on analyyttinen kokonaisuus, joka tässä väitöskirjassa esitetyn perusteella toimii avaimena avaruuden ideaalisuuteen. Tutkimuskirjallisuudessa tärkeä aihe on, miten tietoinen Kant oli leibnizilaisesta vaihtoehdosta, että avaruus saattaisi olla sekä aistimellisuuden muoto että yhdessä olemisen järjestys. Tässä väitöskirjassa esitetään, ettei Kant voinut kokonaan sulkea pois tätä vaihtoehtoa. Yhdessä mielessä Kant kuitenkin onnistui: leibnizilaiset olivat pakotettuja myöntämään, että jatkuvuus kuuluu avaruuteen aistimellisuuden muotona eikä yhdessä olemisen järjestyksenä. Näemme kaikki oliot jatkumollisessa avaruudessa, emme Jumalassa. Niiden näkeminen avaruudessa on kuitenkin analogista niiden näkemiselle Jumalassa

Relations and Folds in Leibniz: Monadological Intimacy

My goal is to provide a clear explanation of Leibniz’s notoriously difficult system of relations. Relations among ‘windowless’ substances that exert no causal power over one another seems like a pipe dream that should be abandoned. However, I demonstrate that each substance expresses its relations only through the unique representation of all other substances. That is, any relation a substance expresses is due to this unique, perspectival, non-causal, representation of others. Because this is the case for all substances, this means that this relation of representation is an ongoing process of interconnection for all substances. This representation is not merely a cognitive copy of the universe (i.e. all other substances); it is the expression of all other substances from a distinct perspective. By taking a holistic approach, I show that Leibniz is not contradicting himself when he claims that substances are windowless, relations are ideal, all substances are interconnected, and there are no such things as purely extrinsic denominations

Developing and Measuring Parallel Rule-Based Systems in a Functional Programming Environment

This thesis investigates the suitability of using functional programming for building parallel rule-based systems. A functional version of the well known rule-based system OPS5 was implemented, and there is a discussion on the suitability of functional languages for both building compilers and manipulating state. Functional languages can be used to build compilers that reflect the structure of the original grammar of a language and are, therefore, very suitable. Particular attention is paid to the state requirements and the state manipulation structures of applications such as a rule-based system because, traditionally, functional languages have been considered unable to manipulate state. From the implementation work, issues have arisen that are important for functional programming as a whole. They are in the areas of algorithms and data structures and development environments. There is a more general discussion of state and state manipulation in functional programs and how theoretical work, such as monads, can be used. Techniques for how descriptions of graph algorithms may be interpreted more abstractly to build functional graph algorithms are presented. Beyond the scope of programming, there are issues relating both to the functional language interaction with the operating system and to tools, such as debugging and measurement tools, which help programmers write efficient programs. In both of these areas functional systems are lacking. To address the complete lack of measurement tools for functional languages, a profiling technique was designed which can accurately measure the number of calls to a function , the time spent in a function, and the amount of heap space used by a function. From this design, a profiler was developed for higher-order, lazy, functional languages which allows the programmer to measure and verify the behaviour of a program. This profiling technique is designed primarily for application programmers rather than functional language implementors, and the results presented by the profiler directly reflect the lexical scope of the original program rather than some run-time representation. Finally, there is a discussion of generally available techniques for parallelizing functional programs in order that they may execute on a parallel machine. The techniques which are easier for the parallel systems builder to implement are shown to be least suitable for large functional applications. Those techniques that best suit functional programmers are not yet generally available and usable