66 research outputs found
Qualia and the Formal Structure of Meaning
This work explores the hypothesis that subjectively attributed meaning constitutes the phenomenal content of conscious experience. That is, phenomenal content is semantic. This form of subjective meaning manifests as an intrinsic and non-representational character of qualia. Empirically, subjective meaning is ubiquitous in conscious experiences. We point to phenomenological studies that lend evidence to support this. Furthermore, this notion of meaning closely relates to what Frege refers to as "sense", in metaphysics and philosophy of language. It also aligns with Peirce's "interpretant", in semiotics. We discuss how Frege's sense can also be extended to the raw feels of consciousness. Sense and reference both play a role in phenomenal experience. Moreover, within the context of the mind-matter relation, we provide a formalization of subjective meaning associated to one's mental representations. Identifying the precise maps between the physical and mental domains, we argue that syntactic and semantic structures transcend language, and are realized within each of these domains. Formally, meaning is a relational attribute, realized via a map that interprets syntactic structures of a formal system within an appropriate semantic space. The image of this map within the mental domain is what is relevant for experience, and thus comprises the phenomenal content of qualia. We conclude with possible implications this may have for experience-based theories of consciousness
A Cosine Rule-Based Discrete Sectional Curvature for Graphs
How does one generalize differential geometric constructs such as curvature
of a manifold to the discrete world of graphs and other combinatorial
structures? This problem carries significant importance for analyzing models of
discrete spacetime in quantum gravity; inferring network geometry in network
science; and manifold learning in data science. The key contribution of this
paper is to introduce and validate a new estimator of discrete sectional
curvature for random graphs with low metric-distortion. The latter are
constructed via a specific graph sprinkling method on different manifolds with
constant sectional curvature. We define a notion of metric distortion, which
quantifies how well the graph metric approximates the metric of the underlying
manifold. We show how graph sprinkling algorithms can be refined to produce
hard annulus random geometric graphs with minimal metric distortion. We
construct random geometric graphs for spheres, hyperbolic and euclidean planes;
upon which we validate our curvature estimator. Numerical analysis reveals that
the error of the estimated curvature diminishes as the mean metric distortion
goes to zero, thus demonstrating convergence of the estimate. We also perform
comparisons to other existing discrete curvature measures. Finally, we
demonstrate two practical applications: (i) estimation of the earth's radius
using geographical data; and (ii) sectional curvature distributions of
self-similar fractals
Ruliology: Linking Computation, Observers and Physical Law
Stephen Wolfram has recently outlined an unorthodox, multicomputational
approach to fundamental theory, encompassing not only physics but also
mathematics in a structure he calls The Ruliad, understood to be the entangled
limit of all possible computations. In this framework, physical laws arise from
the the sampling of the Ruliad by observers (including us). This naturally
leads to several conceptual issues, such as what kind of object is the Ruliad?
What is the nature of the observers carrying out the sampling, and how do they
relate to the Ruliad itself? What is the precise nature of the sampling? This
paper provides a philosophical examination of these questions, and other
related foundational issues, including the identification of a limitation that
must face any attempt to describe or model reality in such a way that the
modeller-observers are include
Spectral Modes of Network Dynamics Reveal Increased Informational Complexity Near Criticality
What does the informational complexity of dynamical networked systems tell us
about intrinsic mechanisms and functions of these complex systems? Recent
complexity measures such as integrated information have sought to
operationalize this problem taking a whole-versus-parts perspective, wherein
one explicitly computes the amount of information generated by a network as a
whole over and above that generated by the sum of its parts during state
transitions. While several numerical schemes for estimating network integrated
information exist, it is instructive to pursue an analytic approach that
computes integrated information as a function of network weights. Our
formulation of integrated information uses a Kullback-Leibler divergence
between the multi-variate distribution on the set of network states versus the
corresponding factorized distribution over its parts. Implementing stochastic
Gaussian dynamics, we perform computations for several prototypical network
topologies. Our findings show increased informational complexity near
criticality, which remains consistent across network topologies. Spectral
decomposition of the system's dynamics reveals how informational complexity is
governed by eigenmodes of both, the network's covariance and adjacency
matrices. We find that as the dynamics of the system approach criticality, high
integrated information is exclusively driven by the eigenmode corresponding to
the leading eigenvalue of the covariance matrix, while sub-leading modes get
suppressed. The implication of this result is that it might be favorable for
complex dynamical networked systems such as the human brain or communication
systems to operate near criticality so that efficient information integration
might be achieved
A Black Hole Levitron
We study the problem of spatially stabilising four dimensional extremal black
holes in background electric/magnetic fields. Whilst looking for stationary
stable solutions describing black holes kept in external fields we find that
taking a continuum limit of Denef et al's multi-center solutions provides a
supergravity description of such backgrounds within which a black hole can be
trapped in a given volume. This is realised by levitating a black hole over a
magnetic dipole base. We comment on how such a construction resembles a
mechanical Levitron.Comment: 5 pages, 1 figur
Beyond neural coding? Lessons from perceptual control theory
Pointing to similarities between challenges encountered in today's neural coding and twentieth-century behaviorism, we draw attention to lessons learned from resolving the latter. In particular, Perceptual Control Theory posits behavior as a closed-loop control process with immediate and teleological causes. With two examples, we illustrate how these ideas may also address challenges facing current neural coding paradigms
Pregeometry, Formal Language and Constructivist Foundations of Physics
How does one formalize the structure of structures necessary for the foundations of physics? This work is an attempt at conceptualizing the metaphysics of pregeometric structures, upon which new and existing notions of quantum geometry may find a foun- dation. We discuss the philosophy of pregeometric structures due to Wheeler, Leibniz as well as modern manifestations in topos theory. We draw attention to evidence suggesting that the framework of formal language, in particular, homotopy type theory, provides the conceptual building blocks for a theory of pregeometry. This work is largely a synthesis of ideas that serve as a precursor for conceptualizing the notion of space in physical theories. In particular, the approach we espouse is based on a constructivist philosophy, wherein “structureless structures” are syntactic types realizing formal proofs and programs. Spaces and algebras relevant to physical theories are modeled as type-theoretic routines constructed from compositional rules of a formal language. This offers the remarkable possibility of taxonomizing distinct notions of geometry using a common theoretical framework. In particular, this perspective addresses the crucial issue of how spatiality may be realized in models that link formal computation to physics, such as the Wolfram model
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