Emergence of Euclidean geometrical intuitions in hierarchical generative models

In this study, we aim to understand the origins of human intuitions about Euclidean geometry by simulating geo-metric concepts acquisition with unsupervised learning in hierarchical generative models. Specifically, we build a deep neuralnetwork that learns a hierarchical generative model of sensory inputs. The results show that hidden layer activities can supportthe categorization of different geometric objects and distinguish among various spatial relationships between geometric figures.Specifically, hidden layer activities can be decoded to compare line orientations, detect right triangles, and judge whether twotriangles are similar or not. We further analyze the response profiles of hidden layers units and find some units resembling pari-etal neurons in the brain. Using unsupervised deep learning, the current modeling work provides a possible explanation of howEuclidean geometrical intuitions might emerge from daily visual experience, which has significant implications for cognitivepsychology and computational neuroscience

Design operators

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture, 2004.Includes bibliographical references (leaves 58-61).Design operators is a thesis that investigates the nature and characteristics of the design process by examining the interaction of computation with architectural design. The effects of the introduction of these media in design are traced and their quantitative and qualitative characteristics are identified. The thesis hints for an emerging design mentality delineated by the implementation, documentation and critical evaluation of a series of experimental projects in computational design.by Stylianos Dritsas.S.M

The Translocal Event and the Polyrhythmic Diagram

This thesis identifies and analyses the key creative protocols in translocal performance practice, and ends with suggestions for new forms of transversal live and mediated performance practice, informed by theory. It argues that ontologies of emergence in dynamic systems nourish contemporary practice in the digital arts. Feedback in self-organised, recursive systems and organisms elicit change, and change transforms. The arguments trace concepts from chaos and complexity theory to virtual multiplicity, relationality, intuition and individuation (in the work of Bergson, Deleuze, Guattari, Simondon, Massumi, and other process theorists). It then examines the intersection of methodologies in philosophy, science and art and the radical contingencies implicit in the technicity of real-time, collaborative composition. Simultaneous forces or tendencies such as perception/memory, content/ expression and instinct/intellect produce composites (experience, meaning, and intuition- respectively) that affect the sensation of interplay. The translocal event is itself a diagram - an interstice between the forces of the local and the global, between the tendencies of the individual and the collective. The translocal is a point of reference for exploring the distribution of affect, parameters of control and emergent aesthetics. Translocal interplay, enabled by digital technologies and network protocols, is ontogenetic and autopoietic; diagrammatic and synaesthetic; intuitive and transductive. KeyWorx is a software application developed for realtime, distributed, multimodal media processing. As a technological tool created by artists, KeyWorx supports this intuitive type of creative experience: a real-time, translocal “jamming” that transduces the lived experience of a “biogram,” a synaesthetic hinge-dimension. The emerging aesthetics are processual – intuitive, diagrammatic and transversal

Intrinsic Dimension Estimation for non-Euclidean manifolds: from metagenomics to unweighted networks

Within the field of unsupervised manifold learning, Intrinsic Dimension estimators are among the most important analysis tools. The Intrinsic Dimension provides a measure of the dimensionality of the hidden manifold from which data are sampled, even if the manifold is embedded in a space with a much higher number of features. The present Thesis tackles the still unanswered problem of computing the Intrinsic Dimension (ID) of spaces characterised by non-Euclidean metrics. In particular, we focus on datasets where the distances between points are measured by means of Manhattan, Hamming or shortest-path metrics and, thus, can only assume discrete values. This peculiarity has deep consequences on the way datapoints populate the neighbourhoods and on the structure on the manifold. For this reason we develop a general purpose, nearest-neighbours-based ID estimator that has two peculiar features: the capability of selecting explicitly the scale at which the Intrinsic Dimension is computed and a validation procedure to check the reliability of the provided estimate. We thus specialise the estimator to lattice spaces, where the volume is measured by means of the Ehrhart polynomials. After testing the reliability of the estimator on artificial datasets, we apply it to genomics sequences and discover an unexpectedly low ID, suggesting that the evolutive pressure exerts strong restraints on the way the nucleotide basis are allowed to mutate. This same framework is then employed to profile the scaling of the ID of unweighted networks. The diversity of the obtained ID signatures prompted us into using it as a signature to characterise the networks. Concretely, we employ the ID as a summary statistics within an Approximate Bayesian Computation framework in order to pinpoint the parameters of network mechanistic generative models of increasing complexity. We discover that, by targeting the ID of a given network, other typical network properties are also fairly retrieved. As a last methodological development, we improved the ID estimator by adaptively selecting, for each datapoint, the largest neighbourhoods with an approximately constant density. This offers a quantitative criterion to automatically select a meaningful scale at which the ID is computed and, at the same time, allows to enforce the hypothesis of the method, implying more reliable estimates

Spatial Aspects of Metaphors for Information: Implications for Polycentric System Design

This dissertation presents three innovations that suggest an alternative approach to structuring information systems: a multidimensional heuristic workspace, a resonance metaphor for information, and a question-centered approach to structuring information relations. Motivated by the need for space to establish a question-centered learning environment, a heuristic workspace has been designed. Both the question-centered approach to information system design and the workspace have been conceived with the resonance metaphor in mind. This research stemmed from a set of questions aimed at learning how spatial concepts and related factors including geography may play a role in information sharing and public information access. In early stages of this work these concepts and relationships were explored through qualitative analysis of interviews centered on local small group and community users of geospatial data. Evaluation of the interviews led to the conclusion that spatial concepts are pervasive in our language, and they apply equally to phenomena that would be considered physical and geographic as they do to cognitive and social domains. Rather than deriving metaphorically from the physical world to the human, spatial concepts are native to all dimensions of human life. This revised view of the metaphors of space was accompanied by a critical evaluation of the prevailing metaphors for information processes, the conduit and pathway metaphors, which led to the emergence of an alternative, resonance metaphor. Whereas the dominant metaphors emphasized information as object and the movement of objects and people through networks and other limitless information spaces, the resonance metaphor suggests the existence of multiple centers in dynamic proximity relationships. This pointed toward the creation of a space for autonomous problem solving that might be related to other spaces through proximity relationships. It is suggested that a spatial approach involving discrete, discontinuous structures may serve as an alternative to approaches involving movement and transportation. The federation of multiple autonomous problem-solving spaces, toward goals such as establishing communities of questioners, has become an objective of this work. Future work will aim at accomplishing this federation, most likely by means of the IS0 Topic Maps standard or similar semantic networking strategies

Logic and intuition in architectural modelling: philosophy of mathematics for computational design

This dissertation investigates the relationship between the shift in the focus of architectural modelling from object to system and philosophical shifts in the history of mathematics that are relevant to that change. Particularly in the wake of the adoption of digital computation, design model spaces are more complex, multidimensional, arguably more logical, less intuitive spaces to navigate, less accessible to perception and visual comprehension. Such spatial issues were encountered much earlier in mathematics than in architectural modelling, with the growth of analytical geometry, a transition from Classical axiomatic proofs in geometry as the basis of mathematics, to analysis as the underpinning of geometry. Can the computational design modeller learn from the changing modern history, philosophy and psychology of mathematics about the construction and navigation of computational geometrical architectural system model space? The research is conducted through a review of recent architectural project examples and reference to three more detailed architectural modelling case studies. The spatial questions these examples and case studies raise are examined in the context of selected historical writing in the history, philosophy and psychology of mathematics and space. This leads to conclusions about changes in the relationship of architecture and mathematics, and reflections on the opportunities and limitations for architectural system models using computation geometry in the light of this historical survey. This line of questioning was motivated as a response to the experience of constructing digital associative geometry models and encountering the apparent limits of their flexibility as the graph of dependencies grew and the messiness of the digital modelling space increased. The questions were inspired particularly by working on the Narthex model for the Sagrada Família church, which extends to many tens of thousands of relationships and constraints, and which was modelled and repeatedly partially remodelled over a very long period. This experience led to the realisation that the limitations of the model were not necessarily the consequence of poor logical schema definition, but could be inevitable limitations of the geometry as defined, regardless of the means of defining it, the ‘shape’ of the multidimensional space being created. This led to more fundamental questions about the nature of Space, its relationship to geometry and the extent to which the latter can be considered simply as an operational and notational system. This dissertation offers a purely inductive journey, offering evidence through very selective examples in architecture, architectural modelling and in the philosophy of mathematics. The journey starts with some questions about the tendency of the model space to break out and exhibit unpredictable and not always desirable behaviour and the opportunities for geometrical construction to solve these questions is not conclusively answered. Many very productive questions about computational architectural modelling are raised in the process of looking for answers

Scientific Coordination beyond the A Priori: A Three-dimensional Account of Constitutive Elements in Scientific Practice

In this dissertation, I present a novel account of the components that have a peculiar epistemic role in our scientific inquiries, since they contribute to establishing a form of coordination. The issue of coordination is a classic epistemic problem concerning how we justify our use of abstract conceptual tools to represent concrete phenomena. For instance, how could we get to represent universal gravitation as a mathematical formula or temperature by means of a numerical scale? This problem is particularly pressing when justification for using these abstract tools comes, in part or entirely, from knowledge which is not independent from them, thus leading to threats of circularity. Achieving coordination between some abstract conceptual tools and the concrete phenomena that they are supposed to represent is usually a complex process, which involves several epistemic components. Some of these components eventually provide stable conditions for applying those abstract representations to concrete phenomena. It is in this sense of providing certain conditions of applicability that different philosophical traditions, as well as some contemporary reappraisals, view these components as constitutive or a priori. In this work, I present a new gradualist, contextualist, and relational approach to understand these constitutive components of scientific inquiry. It is gradualist inasmuch as the degree to which some component is constitutive depends on three quantifiable features: quasi-axiomaticity, generative potential, and empirical shielding. Since the quantification of these three features impinges on the history and practice of using these components in a scientific context, my approach is a contextualist one. Finally, my approach is relational in a double sense: first, it identifies ordinal relationships among epistemic components with respect to their constitutive character; second, these relationships are relative to a scientific framework of inquiry. After introducing my account and a classic example of constitutively a priori principles, i.e., Friedman’s (2001) analysis of Newtonian mechanics, I turn to my own case studies to demonstrate the advantages of my approach. Firstly, I discuss Okasha’s (2018) view of endogenization as a pervasive theoretical strategy in evolutionary biology and suggest that the constitutive character of the core Darwinian principles progressively increases with endogenization. Secondly, I apply a conceptual distinction between two varieties or scopes of coordination – general coordination and coordination in measurement – to Ohm’s work on electrical conductivity. This distinction allows me to pinpoint to what extent components along different dimensions (e.g., instrumentation, measurement, theorising, etc.) were constitutive of the forms of coordination which Ohm relied on. Thirdly, I discuss the epistemic function of the Hardy-Weinberg principle in the history and practice of population genetics. I assess this principle in terms of my account and identify approximation and stability as two components that are highly constitutive, in that they contribute to justifying its use in population genetics. Finally, applying my account to these case studies enables me to identify at least three qualitatively different types of constitutive components: domain-specific theoretical principles, material components, and domain-independent assumptions underlying reasoning abilities. In the light of my results, I draw some general conclusions on epistemic justification and scientific knowledge

Digital architecture and difference: a theory of ethical transpositions towards nomadic embodiments in digital architecture

This thesis contributes to histories and theories of digital architecture of the past two decades, as it questions the narratives of its novelty. The main argument this thesis puts forward is that a plethora of methodologies, displacing the centrality of the architect from the architectural design process, has folded into the discipline in the process of its rewriting along digital protocols. These steer architecture onto a post-human path. However, while the redefinition of the practice unfolds, it does so epistemically only without redefining the new subject of architecture emerging from these processes, which therefore remains anchored to humanist-modern definitions. This unaccounted-for position, I argue, prevents novelty from emerging. Simultaneously, the thesis unfolds a creative approach – while drawing on nomadic, critical theory concepts, there surfaces an alternative genealogy already underpinning digital methodologies that enable a reconceptualization of novelty framed with difference to be articulated through nomadic digital embodiment. Regarding the first claim, I turn to the narratives as well as to the mechanisms of digital discourse emerging in two modes of production – mathematical and biological – in exploration of the ways perceptions of novelty are articulated: a) through close readings of its narratives as they consolidate into digital architectural theory (Carpo 2011; Lynn 2003, 2012; Terzidis 2006; Migayrou 2004, 2009); b) through an analysis of the two digital methodologies that support these narratives – parametric architecture and biodigital architecture. In parallel, this thesis draws on twentieth-century critical theory and twenty-firstcentury nomadic feminist theory to rethink two thematic topics: difference and subjectivity. Specifically, these are Gilles Deleuze’s non-essentialist, nonrepresentational philosophy of difference (1968, 1980, 1988) and Rosi Braidotti’s nomadic feminist reconceptualization of post-human, nonunitary subjectivity (2006, 2011, 2015). Nomadic feminist theory also informs my methodology. I draw on Rosi Braidotti’s cartographing and transposing (2006, 2011) because they engender a non-dualist approach to research itself that is dynamic and affirmative, insisting on grounding techniques – grounding in subject positions that are nevertheless post-human and nonunitary. This leads to a redefinition of novel digital practices with ethical ones