Quasi-Empirical Fictionalism as an Approach to the Philosophy of Geometry

<p>The central claim of this thesis is that geometry is a quasi-empirical science based on the idealisation of the elementary physical operations that we actually perform with pen and paper. This conclusion is arrived at after searching for a theory of geometry that will not only explain the epistemology and ontology of mathematics, but will also fit with the best practices of working mathematicians and, more importantly, explain why geometry gives us knowledge that is relevant to physical reality. We will be considering all the major schools of thought in the philosophy of mathematics. Firstly, from the epistemological side, we will consider apriorism, empiricism and quasi-empiricism, finding a Kitcherian style of quasi-empiricism to be the most attractive. Then, from the ontological side, we will consider Platonism, formalism, Kitcherian ontology, and fictionalism. Our conclusion will be to take a Kitcherian epistemology and a fictionalist ontology. This will give us a kind of quasiempirical-fictionalist approach to mathematics. The key feature of Kitcher's thesis is that he placed importance on the operations rather than the entities of arithmetic. However, because he only dealt with arithmetic, we are left with the task of developing a theory of geometry along Kitcherian lines. I will present a theory of geometry that parallels Kitcher's theory of arithmetic using the drawing of straight lines as the most primitive operation. We will thereby develop a theory of geometry that is founded upon our operations of drawing lines. Because this theory is based on our line drawing operations carried out in physical reality, and is the idealisation of those activities, we will have a connection between mathematical geometry and physical reality that explains the predictive power of geometry in the real world. Where Kitcher uses the Peano postulates to develop his theory of arithmetic, I will use the postulates of projective geometry to form the foundations of operational geometry. The reason for choosing projective geometry is due to the fact that by taking it as the foundation, we may apply Klein's Erlanger programme and build a theory of geometry that encompasses Euclidean, hyperbolic and elliptic geometries. The final question we will consider is the problem of conventionalism. We will discover that investigations into conventionalism give us further reason to accept the Kitcherian quasi-empirical-fictionalist approach as the most appealing philosophy of geometry available.</p>

Quasi-Empirical Fictionalism as an Approach to the Philosophy of Geometry

<p>The central claim of this thesis is that geometry is a quasi-empirical science based on the idealisation of the elementary physical operations that we actually perform with pen and paper. This conclusion is arrived at after searching for a theory of geometry that will not only explain the epistemology and ontology of mathematics, but will also fit with the best practices of working mathematicians and, more importantly, explain why geometry gives us knowledge that is relevant to physical reality. We will be considering all the major schools of thought in the philosophy of mathematics. Firstly, from the epistemological side, we will consider apriorism, empiricism and quasi-empiricism, finding a Kitcherian style of quasi-empiricism to be the most attractive. Then, from the ontological side, we will consider Platonism, formalism, Kitcherian ontology, and fictionalism. Our conclusion will be to take a Kitcherian epistemology and a fictionalist ontology. This will give us a kind of quasiempirical-fictionalist approach to mathematics. The key feature of Kitcher's thesis is that he placed importance on the operations rather than the entities of arithmetic. However, because he only dealt with arithmetic, we are left with the task of developing a theory of geometry along Kitcherian lines. I will present a theory of geometry that parallels Kitcher's theory of arithmetic using the drawing of straight lines as the most primitive operation. We will thereby develop a theory of geometry that is founded upon our operations of drawing lines. Because this theory is based on our line drawing operations carried out in physical reality, and is the idealisation of those activities, we will have a connection between mathematical geometry and physical reality that explains the predictive power of geometry in the real world. Where Kitcher uses the Peano postulates to develop his theory of arithmetic, I will use the postulates of projective geometry to form the foundations of operational geometry. The reason for choosing projective geometry is due to the fact that by taking it as the foundation, we may apply Klein's Erlanger programme and build a theory of geometry that encompasses Euclidean, hyperbolic and elliptic geometries. The final question we will consider is the problem of conventionalism. We will discover that investigations into conventionalism give us further reason to accept the Kitcherian quasi-empirical-fictionalist approach as the most appealing philosophy of geometry available.</p>

Cotranscriptional kinetic folding of RNA secondary structures

Computational prediction of RNA structures is an important problem in computational structural biology. Studies of RNA structure formation often assume that the process starts from a fully synthesized sequence. Experimental evidence, however, has shown that RNA folds concurrently with its elongation. We investigate RNA structure formation, taking into account also the cotranscriptional effects. We propose a single-nucleotide resolution kinetic model of the folding process of RNA molecules, where the polymerase-driven elongation of an RNA strand by a new nucleotide is included as a primitive operation, together with a stochastic simulation method that implements this folding concurrently with the transcriptional synthesis. Numerical case studies show that our cotranscriptional RNA folding model can predict the formation of metastable conformations that are favored in actual biological systems. Our new computational tool can thus provide quantitative predictions and offer useful insights into the kinetics of RNA folding.

Channel Simulation in Quantum Metrology

In this review we discuss how channel simulation can be used to simplify the most general protocols of quantum parameter estimation, where unlimited entanglement and adaptive joint operations may be employed. Whenever the unknown parameter encoded in a quantum channel is completely transferred in an environmental program state simulating the channel, the optimal adaptive estimation cannot beat the standard quantum limit. In this setting, we elucidate the crucial role of quantum teleportation as a primitive operation which allows one to completely reduce adaptive protocols over suitable teleportation-covariant channels and derive matching upper and lower bounds for parameter estimation. For these channels,wemay express the quantum Cramér Rao bound directly in terms of their Choi matrices. Our review considers both discrete- and continuous-variable systems, also presenting some new results for bosonic Gaussian channels using an alternative sub-optimal simulation. It is an open problem to design simulations for quantum channels that achieve the Heisenberg limit.

Efficient Shared Execution Processing of k-Nearest Neighbor Joins in Road Networks

We investigate the k-nearest neighbor (kNN) join in road networks to determine the k-nearest neighbors (NNs) from a dataset S to every object in another dataset R. The kNN join is a primitive operation and is widely used in many data mining applications. However, it is an expensive operation because it combines the kNN query and the join operation, whereas most existing methods assume the use of the Euclidean distance metric. We alternatively consider the problem of processing kNN joins in road networks where the distance between two points is the length of the shortest path connecting them. We propose a shared execution-based approach called the group-nested loop (GNL) method that can efficiently evaluate kNN joins in road networks by exploiting grouping and shared execution. The GNL method can be easily implemented using existing kNN query algorithms. Extensive experiments using several real-life roadmaps confirm the superior performance and effectiveness of the proposed method in a wide range of problem settings.

Composite-Level Conflict Detection in UML Model Versioning

At present, model-driven engineering plays an essential role in software development. Model versioning systems perform the task of conflict detection when merging parallel-developed model versions. However, conflict detection is typically conducted at the primitive operation level in operation-based systems. This situation implies that the overall intention of model developers may be disregarded, which results in unsatisfactory performance. In this study, we present an approach to conflict detection at the composite level in model versioning systems for Unified Modeling Language. This approach has two main stages. During the preprocessing stage, redundant operations are removed from the originally recorded operation lists to increase efficiency. During the conflict detection stage, a fragmentation procedure is conducted with only potentially conflicted operations allocated into the same fragment. Then, a pattern-matching strategy is applied to help indicate conflicts.

Ultrasound in Lund —three world premieres

In the historical section of the monograph Ultrasound in Medical Diagnosis, published in 1976, one can read that a substantial part of the early development of the ultrasound-echo method took place in the little university town of Lund in Sweden. It is not without pride that the Lundensians Inge Edler and Hellmuth Hertz comment upon this in a later review article. They also describe what happened in Lund in the 1950s which they thought contributed in a decisive way to diagnostics in cardiology, neurosurgery, and obstetrics and gynaecology. Apart from the cardiologist Edler and the physicist Hertz the pioneers were the neurosurgeon Lars Leksell and the obstetrician Bertil Sundén. Hertz and his pupils were to a high degree responsible for the technical development and the application in all three specialities. During the late 1940s and the early 1950s surgery of the heart was started in Lund. The first common lesion to be corrected in adults was mitral stenosis. The valve was opened by forced dilatation. Results were often good but there was a diagnostic problem. In some patients the symptoms were not due simply to a small valve opening. There was also a leakage of blood ‘backwards’, mitral insufficiency. This condition of course could not be improved by such a primitive operation. Instead, the procedure might make the condition worse. There was thus a great need for improved diagnostics before operation. This was when the young internist Inge Edler entered the scene. Born in 1911 he had started his career in internal medicine in Malmö but in 1950 he moved to Lund where he became responsible for the preoperative heart evaluations. He immediately focused his interest on the possibilities of making a quantitative diagnosis of mitral stenosis and to determine the existence of mitral insufficiency. Edler’s nurse was married to a physicist, Jan Cederlund. Hence it was natural for Edler to ask Cederlund if the radar technique developed during world war II could be used for examination of the heart. Cederlund forwarded the question to his friend Hellmuth Hertz, also a physicist.

Grasping Operation Based on Functional Cooperation of Fingers

When we observe human grasping, some grasping operations consist of multiple cooperative primitive operations. Performing individual movements by different fingers in a grasping operation are generally called “partitioning of fingers.” Our interest is not in the individual movement of each finger, but in functional units of operations constituting entire grasping operations realized by fingers working together. We define such functional unit operation as a “primitive operation.” When one grasping operation consists of multiple cooperative primitive operations and fingers are used in different primitive operations, we call this “functional partitioning of fingers.” By assigning different primitive operations to functional partitioning of fingers, robot can realize various grasping operations. This paper shows that primitive operations can be described in software modules running in multifingered robot hand system, and demonstrates that various grasping operations are achieved by cooperation of primitive operations.

Sideward Movement

Assuming the general framework of the Minimalist Program of Chomsky 1995, this article argues that Move is not a primitive operation of the computational system, but rather the output of the interaction among the independent operations Copy, Merge, Form Chain, and Chain Reduction (deletion of chain links for purposes of linearization). The crucial aspect of this alternative model is that it permits constrained instances of sideward movement, whereby a given constituent “moves” from a syntactic object K to an independent syntactic object L. This version of the copy theory of movement (a) provides an explanation for why (some) traces must be deleted in the phonological component, (b) provides a cyclic analysis for standard instances of noncyclic movement, and (c) accounts for the main properties of parasitic gap and across-the-board extraction constructions.

Illicit Remnant Movement: An Argument for Feature-Driven Movement

This article discusses previously unnoticed empirical effects of the operation Attract/Move F. Certain illicit cases of so-called remnant movement are accounted for if the primitive operation inducing move-ment is feature movement and all category movement is feature-driven, as is claimed by the Attract/Move F hypothesis. Since the relevant cases of illicit remnant movement remain unaccounted for under the traditional Move a hypothesis, which claims that the primitive opera-tion is category movement, the present discussion lends new empirical support to the feature-driven view of movement.