Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics

Mind out of matter: topics in the physical foundations of consciousness and cognition

This dissertation begins with an exploration of a brand of dual aspect monism and some problems deriving from the distinction between a first person and third person point of view. I continue with an outline of one way in which the conscious experience of the subject might arise from organisational properties of a material substrate. With this picture to hand, I first examine theoretical features at the level of brain organisation which may be required to support conscious experience and then discuss what bearing some actual attributes of biological brains might have on such experience. I conclude the first half of the dissertation with comments on information processing and with artificial neural networks meant to display simple varieties of the organisational features initially described abstractly.While the first half begins with a view of conscious experience and infers downwards in the organisational hierarchy to explore neural features suggested by the view, attention in the second half shifts towards analysing low level dynamical features of material substrates and inferring upwards to possible effects on experience. There is particular emphasis on clarifying the role of chaotic dynamics, and I discuss relationships between levels of description of a cognitive system and comment on issues of complexity, computability, and predictability before returning to the topic of representation which earlier played a central part in isolating features of brain organisation which may underlie conscious experience.Some themes run throughout the dissertation, including an emphasis on understanding experience from both the first person and the third person points of view and on analysing the latter at different levels of description. Other themes include a sustained effort to integrate the picture offered here with existing empirical data and to situate current problems in the philosophy of mind within the new framework, as well as an appeal to tools from mathematics, computer science, and cognitive science to complement the more standard philosophical repertoire

L'information algorithmique en physique : émergence, sophistication et localité quantique

Cette thèse explore des aspects du monde naturel par la lentille de l'information algorithmique. La notion de l'émergence, intuitivement reliée à tant de phénomènes naturels, se voit offrir une définition cadrée dans le domaine plus spécifique des statistiques algorithmiques. Capturant toutes deux l'organisation non triviale d'un objet, la sophistication et la profondeur logique sont relativisées à un objet auxiliaire puis remises en relation. Enfin, des modèles proposant une description locale des systèmes quantiques sont démontrés équivalents, ont leur coût de description quantifié et sont généralisés aux systèmes continus.This thesis explores aspects of the physical world through the lens of algorithmic information. The notion of emergence, intuitively linked to many natural phenomena, is offered a definition framed in the field of algorithmic statistics. Both capturing non-trivial organization of an object, sophistication and logical depth are compared once relativized to an auxiliary object. Finally, models proposing a local description of the quantum systems are shown equivalent, have their description cost quantified and are generalized to continuous systems