Hilbert, Completeness and Geometry

This paper aims to show how the mathematical content of Hilbert’s Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert’s conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play inHilbert’s foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert’s position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert’s for the completeness of set theory.

Hilbert, completeness and geometry

This paper aims to show how the mathematical content of Hilbert's Axiom of Completeness consists in an attempt to solve the more general problem of the relationship between intuition and formalization. Hilbert found the accordance between these two sides of mathematical knowledge at a logical level, clarifying the necessary and sufficient conditions for a good formalization of geometry. We will tackle the problem of what is, for Hilbert, the definition of geometry. The solution of this problem will bring out how Hilbert's conception of mathematics is not as innovative as his conception of the axiomatic method. The role that the demonstrative tools play in Hilbert's foundational reflections will also drive us to deal with the problem of the purity of methods, explicitly addressed by Hilbert. In this respect Hilbert's position is very innovative and deeply linked to his modern conception of the axiomatic method. In the end we will show that the role played by the Axiom of Completeness for geometry is the same as the Axiom of Induction for arithmetic and of Church-Turing thesis for computability theory. We end this paper arguing that set theory is the right context in which applying the axiomatic method to mathematics and we postpone to a sequel of this work the attempt to offer a solution similar to Hilbert's for the completeness of set theory

Idealist and Realist Aspirations for Just Peace

This PhD thesis analyzes the following three ethical questions: 1) When and how, if at all, is it reasonable to use military force that potentially brings suffering and destruction to land and property, body and mind? 2) How do contemporary ideologies argue for the use of military force and are their arguments reasonable? 3) How have responsible political actors argued for the use of military force in contemporary conflicts and have their arguments been reasonable? The thesis develops an ethic of military force within the framework of a global ethic of just peace. It analyzes in depth predominant ideologies and the political arguments behind the Iraq war (2003) and the intervention in Kosovo (1999). The thesis argues that just peace is a significant realist and idealist global ethical ideology, and there is no other political strategy to achieve just peace than by practicing it

An initial assessment of the environmental impact of grocery products

This report presents a series of analyses with the common purpose of establishing which grocery products are likely to contribute most to the environmental impacts (carbon footprint or embodied carbon, embodied energy, water, materials use and waste) associated with UK household consumption. Understanding and prioritising these has enabled reduction actions, interventions and further research to be directed more effectively at those products with the greatest potential to influence overall consumption impacts.The report includes a systematic review of 1,900 grocery carbon footprint data points for 191 products; believed to be the largest assessment of its kind at the time of publication

Incorporating AI-assisted Sensing into the Metaverse: Opportunities for Interactions, eSports, and Security Enhancement

With the rapid growth and development of Virtual Reality (VR) and Augmented Reality (AR), extensive research has been carried out in the domain of the Metaverse, including immersive gaming, human-computer interaction, eSports, and the associated security & privacy concerns. My research explores the potential of incorporating Artificial Intelligence (AI)-assisted sensing technologies to facilitate a more immersive, convenient, authentic, and secure virtual experience. This dissertation mainly focus on the following topics: (1) how to perform facial expression tracking to improve the users\u27 awareness in the Metaverse; (2) fitness tracking for immersive eCycling; (3) running gait analysis for immersive indoor running, and (4) the potential privacy leakages through unrestricted sensors in the Metaverse. We first propose a single-earpiece lightweight biosensing system, BioFace-3D, that can unobtrusively, continuously, and reliably sense the entire facial movements, track 2D facial landmarks, and further render 3D facial animations. In addition, to revolutionize the current state of eCycling and address a series of deficiencies related to the user’s virtual experience, we propose SmarCyPad, an innovative smart seat pad that can continuously and unobtrusively track five cycling-specific metrics. Moreover, we design a running gait analysis system by utilizing the acoustic sensors to reconstruct the runner\u27s cadence, ground contact time, pressure distribution, and center of pressure. Finally, we conduct a comprehensive study to assess the trustworthiness of the embedded sensors on VR, which embed various forms of sensitive data that may put users’ privacy at risk. We validate this vulnerability through developing malware programs and malicious websites and specifically explore to what extent it exposes the user’s information in the context of keystroke snooping. By exploring these opportunities, this dissertation aim to facilitate a more immersive, convenient, authentic, and secure virtual experience in the Metaverse

Women's experience of laparoscopic surgery in endometrial cancer: A phenomenological study.

Aim: This study aimed to develop a description of the experience of laparoscopic surgery for endometrial cancer from the patient perspective. Background: Laparoscopic surgery is increasingly used to treat early endometrial cancer where there are surgeons trained to perform the procedure. It is generally associated with low levels of morbidity and considered safe for cancer surgery but research is limited on quality of life and patient experience. Method: Heideggerian hermeneutic phenomenology was used to explore the experiences of 14 women who had undergone the procedure in two South of England cancer centres. Unstructured taped interviews were transcribed and analysed using Colaizzi's (1978) framework, which included returning to the participants for a validation interview. Findings: A phenomenological description emerged from the five identified themes: having cancer, information and support, independence, normality and transfer of responsibility to the surgeon. The experience of laparoscopic surgery was shown to be overshadowed by the presence of endometrial cancer. Fear of cancer and lack of knowledge played a significant role in the need to trust the surgeon with the responsibility for decision making. Information needs were unique to the individual but focused on what would be done, what to expect and the practicalities of being in an unfamiliar situation and environment rather than treatment choices. Loss of control, vulnerability and dependence are associated with illness and surgery but early postoperative mobility and minimal pain facilitated a rapid return to independence and normality with the potential to significantly enhance wellbeing. Conclusion: The findings of this study represent a phenomenological description of the essence of the experience of laparoscopic surgery for endometrial cancer. Understanding the significance of the cancer diagnosis and the role of the surgeon in decision making will enable healthcare professionals to deliver care that is responsive to the patient experience and entourage the use of treatments that maintain independence and normality

Evaluation of Multi-frequency Synthetic Aperture Radar for Subsurface Archaeological Prospection in Arid Environments

The discovery of the subsurface paleochannels in the Saharan Desert with the 1981 Shuttle Imaging Radar (SIR-A) sensor was hugely significant in the field of synthetic aperture radar (SAR) remote sensing. Although previous studies had indicated the ability of microwaves to penetrate the earth’s surface in arid environments, this was the first applicable instance of subsurface imaging using a spaceborne sensor. And the discovery of the ‘radar rivers’ with associated archaeological evidence in this inhospitable environment proved the existence of an earlier less arid paleoclimate that supported past populations. Since the 1980’s SAR subsurface prospection in arid environments has progressed, albeit primarily in the fields of hydrology and geology, with archaeology being investigated to a lesser extent. Currently there is a lack of standardised methods for data acquisition and processing regarding subsurface imaging, difficulties in image interpretation and insufficient supporting quantitative verification. These barriers keep SAR technology from becoming as integral as other remote sensing techniques in archaeological practice The main objective of this thesis is to undertake a multi-frequency SAR analysis across different site types in arid landscapes to evaluate and enhance techniques for analysing SAR within the context of archaeological subsurface prospection. The analysis and associated fieldwork aim to address the gap in the literature regarding field verification of SAR image interpretation and contribute to the understanding of SAR microwave penetration in arid environments. The results presented in this thesis demonstrate successful subsurface imaging of subtle feature(s) at the site of ‘Uqdat al-Bakrah, Oman with X-band data. Because shorter wavelengths are often ignored due to their limited penetration depths as compared to the C-band or L-band data, the effectiveness of X-band sensors in archaeological prospection at this site is significant. In addition, the associated ground penetrating radar and excavation fieldwork undertaken at ‘Uqdat al-Bakrah confirm the image interpretation and support the quantitative information regarding microwave penetration