Local covariant quantum field theory over spectral geometries

A framework which combines ideas from Connes' noncommutative geometry, or spectral geometry, with recent ideas on generally covariant quantum field theory, is proposed in the present work. A certain type of spectral geometries modelling (possibly noncommutative) globally hyperbolic spacetimes is introduced in terms of so-called globally hyperbolic spectral triples. The concept is further generalized to a category of globally hyperbolic spectral geometries whose morphisms describe the generalization of isometric embeddings. Then a local generally covariant quantum field theory is introduced as a covariant functor between such a category of globally hyperbolic spectral geometries and the category of involutive algebras (or *-algebras). Thus, a local covariant quantum field theory over spectral geometries assigns quantum fields not just to a single noncommutative geometry (or noncommutative spacetime), but simultaneously to ``all'' spectral geometries, while respecting the covariance principle demanding that quantum field theories over isomorphic spectral geometries should also be isomorphic. It is suggested that in a quantum theory of gravity a particular class of globally hyperbolic spectral geometries is selected through a dynamical coupling of geometry and matter compatible with the covariance principle.Comment: 21 pages, 2 figure

Mathematics in the work of Spinoza and Guarini

During the seventeenth century mathematics and the exact sciences brought about a scientific revolution, and seemed to be involved in all novel social developments of the time. To give just a few examples, Newton (1643-1727) used mathematical principles to explain the philosophy of nature in his Principia, and, prior to that, Descartes (1569-1650) used mathematics as a model for his metaphysics, his main concern for many years. His greatest legacy, for the purposes and framing of this paper, has to do with moving classical geometry within the reach of algebra, putting into connection Euclid's and Vitruvius’s theories. This has great relevance within the field of architecture, translating these theories to the building experience of that period. Baroque architecture indeed shares with mathematics a spatial structure which combines the arts and the sciences. Space is controlled by the possible variations of mathematical laws — which is the cause of the way in which architects struggle to work within pre-established rules.The aim of this paper, intended as research from a history of architectural points of view, is to find relations between the idea of mathematics used by Spinoza (Ethics) and Guarini (Placita philosophica; Architettura civile) in their metaphysics, and the outcomes they had in architecture. In addition, if it is difficult to establish whether Spinoza had any influence on Guarini — their most relevant texts were published posthumously — the role of mathematics in the work of these two figures, whose similarities and differences are worth enumerating, is particularly interesting when related to the architectural period of Baroque, a period when the use of mathematics in architecture might be said to have reached a peak.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The representation selection problem: Why we should favor the geometric-module framework of spatial reorientation over the view-matching framework

Many species rely on the three-dimensional surface layout of an environment to find a desired goal following disorientation. They generally do so to the exclusion of other important spatial cues. Two influential frameworks for explaining that phenomenon are provided by geometric-module theories and view-matching theories of reorientation respectively. The former posit a module that operates only on representations of the global geometry of three-dimensional surfaces to guide behavior. The latter place snapshots, stored representations of the subject’s two-dimensional retinal stimulation at specific locations, at the heart of their accounts. In this paper, I take a fresh look at the debate between them. I begin by making a case that the empirical evidence we currently have does not clearly favor one framework over the other, and that the debate has reached something of an impasse. Then, I present a new explanatory problem—the representation selection problem—that offers the prospect of breaking the impasse by introducing a new type of explanatory consideration that both frameworks must address. The representation selection problem requires explaining how subjects can reliably select the relevant representation with which they initiate the reorientation process. I argue that the view-matching framework does not have the resources to address this problem, while a certain type of theory within the geometric-module framework can provide a natural response to it. In showing this, I develop a new geometric-module theory

The development of local solar irradiance for outdoor computer graphics rendering

Atmospheric effects are approximated by solving the light transfer equation, LTE, of a given viewing path. The resulting accumulated spectral energy (its visible band) arriving at the observer’s eyes, defines the colour of the object currently on the line of sight. Due to the convenience of using a single rendering equation to solve the LTE for daylight sky and distant objects (aerial perspective), recent methods had opt for a similar kind of approach. Alas, the burden that the real-time calculation brings to the foil had forced these methods to make simplifications that were not in line with the actual world observation. Consequently, the results of these methods are laden with visual-errors. The two most common simplifications made were: i) assuming the atmosphere as a full-scattering medium only and ii) assuming a single density atmosphere profile. This research explored the possibility of replacing the real-time calculation involved in solving the LTE with an analytical-based approach. Hence, the two simplifications made by the previous real-time methods can be avoided. The model was implemented on top of a flight simulator prototype system since the requirements of such system match the objectives of this study. Results were verified against the actual images of the daylight skies. Comparison was also made with the previous methods’ results to showcase the proposed model strengths and advantages over its peers

D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck

We review first Azumaya geometry and D-branes in the realm of algebraic geometry along the line of Polchinski-Grothendieck Ansatz from our earlier work and then use it as background to introduce Azumaya $C^{\infty}$-manifolds with a fundamental module and morphisms therefrom to a projective complex manifold. This gives us a description of D-branes of A-type. Donaldson's picture of Lagrangian and special Lagrangian submanifolds as selected from the zero-locus of a moment map on a related space of maps can be merged into the setting. As a pedagogical toy model, we study D-branes of A-type in a Calabi-Yau torus. Simple as it is, it reveals several features of D-branes, including their assembling/disassembling. The 4th theme of Sec. 2.4, the 2nd theme of Sec. 4.2, and Sec. 4.3 are to be read respectively with G\'omez-Sharpe (arXiv:hep-th/0008150), Donagi-Katz-Sharpe (arXiv:hep-th/0309270), and Denef (arXiv:hep-th/0107152). Some string-theoretical remarks are given at the end of each section.Comment: 58+2 pages, 7 figure

Can Rats Reason?

Since at least the mid-1980s claims have been made for rationality in rats. For example, that rats are capable of inferential reasoning (Blaisdell, Sawa, Leising, & Waldmann, 2006; Bunsey & Eichenbaum, 1996), or that they can make adaptive decisions about future behavior (Foote & Crystal, 2007), or that they are capable of knowledge in propositional-like form (Dickinson, 1985). The stakes are rather high, because these capacities imply concept possession and on some views (e.g., Rödl, 2007; Savanah, 2012) rationality indicates self-consciousness. I evaluate the case for rat rationality by analyzing 5 key research paradigms: spatial navigation, metacognition, transitive inference, causal reasoning, and goal orientation. I conclude that the observed behaviors need not imply rationality by the subjects. Rather, the behavior can be accounted for by noncognitive processes such as hard-wired species typical predispositions or associative learning or (nonconceptual) affordance detection. These mechanisms do not necessarily require or implicate the capacity for rationality. As such there is as yet insufficient evidence that rats can reason. I end by proposing the ‘Staircase Test,’ an experiment designed to provide convincing evidence of rationality in rats

Design and Development of a Geometric Calculator in CATIA

In this article, an application in the field of engineering graphics is presented for the design of a geometric calculator generated as a macro in CATIA V5. The code of this macro is written in the CATVBA language and utilizes the CATIA internal editor while taking advantage of the capabilities offered by Visual Basic for Applications (VBA). The principal purpose of this application lies in the possibility of creating the three main geometric elements (point, line, and plane) and in solving five types of general geometric problems, and then comparing the results obtained with their equivalent problems from analytical geometry. In particular, within these types of general geometric problems, 34 possible cases are solved: definition of lines (nine cases), definition of planes (12 cases), intersection points (three cases), angles (three cases), and distances (seven cases). These new entities defined with the geometric calculator can serve as support for the generation of new three-dimensional volumes, the creation of auxiliary symmetries, and the dimensioning of various elements. It was verified that the results of the designed macro and the solutions of the analytical equations coincided; therefore, the procedure was validated. Likewise, the module employed herein in the CATIA V5 environment is “Wireframe and Surface Design”, since it enables handling the three basic geometric elements (point, line, and plane), which form the basis of the geometric calculator. Lastly, it is verified how the geometric calculator allows their integration with three-dimensional solids, which represents a notable advance as an aid in its geometric definition

Where Am I? The Cognitive Architecture of Spatial Reorientation

Navigation is of fundamental importance to humans, just as it is for other species. And, like most other animal species, we possess a number of distinct navigational processes. This thesis examines navigation, focusing particularly on the widely studied phenomenon of reorientation following disruption to spatial behavior. In typical reorientation experiments, subjects rely on the three-dimensional surface layout of an environment to find a desired goal following disorientation, and they do so to the exclusion of other important spatial cues. An influential explanatory framework aims to account for such findings by holding that subjects possess a modular mechanism known as the geometric module, which only operates on geometric information about three-dimensional extended surfaces. This thesis provides a sustained defense of this framework and develops a new type of geometric-module theory of reorientation. I begin by making the case that, if the general geometric-module framework is right, it has deep implications for two foundational debates in philosophy of psychology: the debate about the nature of mental representations and the debate about the structure of the mind. I then address the two most pressing challenges against the framework. The first challenge comes from what I call ‘the explanatory inflexibility objection’, which holds that the geometric-module framework simply does not have the required flexibility to deal with evidence that non-geometric cues can affect subjects’ search behavior in some experimental contexts. The second challenge arises from an alternative explanatory framework, the view-matching framework, which aims to explain subjects’ behavior in reorientation experiments by appealing to snapshots, stored representations of the subjects’ two-dimensional retinal stimulation at specific locations. In answering these two challenges, I put forward a new type of geometric-module theory which has stronger implications for debates in philosophy of psychology than standard geometric-module models

`Electronic Publishing' -- Practice and Experience

Electronic Publishing -- Origination, Dissemination and Design (EP-odd) is an academic journal which publishes refereed papers in the subject area of electronic publishing. The authors of the present paper are, respectively, editor-in-chief, system software consultant and senior production manager for the journal. EP-odd's policy is that editors, authors, referees and production staff will work closely together using electronic mail. Authors are also encouraged to originate their papers using one of the approved text-processing packages together with the appropriate set of macros which enforce the layout style for the journal. This same software will then be used by the publisher in the production phase. Our experiences with these strategies are presented, and two recently developed suites of software are described: one of these makes the macro sets available over electronic mail and the other automates the flow of papers through the refereeing process. The decision to produce EP-odd in this way means that the publisher has to adopt production procedures which differ markedly from those employed for a conventional journal