The Mathematics of Collision and the Collision of Mathematics in the 17th Century

Thesis (Ph.D.) - Indiana University, History and Philosophy of Science, 2015This dissertation charts the development of the quantitative rules of collision in the 17th century. These were central to the mathematization of nature, offering natural philosophy a framework to explain all the changes of nature in terms of the size and speed of bodies in motion. The mathematization of nature is a classic thesis in the history of early modern science. However, the significance of the dynamism within mathematics should not be neglected. One important change was the emergence of a new language of nature, an algebraic physico-mathematics, whose development was intertwined with the rules of collision. The symbolic equations provided a unified system to express previously diverse kinds of collision with a new representation of speed with direction, while at the same time collision provided a practical justification of the otherwise "impossible" negative numbers. In private manuscripts, Huygens criticized Descartes's rules of collision with heuristic use of Cartesian symbolic algebra. After he successfully predicted the outcomes of experiments using algebraic calculations at an early meeting of the Royal Society, Wallis and Wren extended the algebraic investigations in their published works. In addition to the impact of the changes in mathematics itself, the rules of collision were shaped by the inventive use of principles formulated by 'thinking with objects,' such as the balance and the pendulum. The former provided an initial framework to relate the speeds and sizes of bodies, and the latter was key both in the development of novel conservation principles and made possible experimental investigations of collision. This dissertation documents the formation of concepts central to modern physical science, and re-evaluates the mathematics of collision, with implications for our understanding of major figures in early modern science, such as Descartes and Huygens, and repercussions for the mathematization of nature

Generalized Volterra-Wiener and surrogate data methods for complex time series analysis

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (leaves 133-150).This thesis describes the current state-of-the-art in nonlinear time series analysis, bringing together approaches from a broad range of disciplines including the non-linear dynamical systems, nonlinear modeling theory, time-series hypothesis testing, information theory, and self-similarity. We stress mathematical and qualitative relationships between key algorithms in the respective disciplines in addition to describing new robust approaches to solving classically intractable problems. Part I presents a comprehensive review of various classical approaches to time series analysis from both deterministic and stochastic points of view. We focus on using these classical methods for quantification of complexity in addition to proposing a unified approach to complexity quantification encapsulating several previous approaches. Part II presents robust modern tools for time series analysis including surrogate data and Volterra-Wiener modeling. We describe new algorithms converging the two approaches that provide both a sensitive test for nonlinear dynamics and a noise-robust metric for chaos intensity.by Akhil Shashidhar.M.Eng

Visualizing Set Relations and Cardinalities Using Venn and Euler Diagrams

In medicine, genetics, criminology and various other areas, Venn and Euler diagrams are used to visualize data set relations and their cardinalities. The data sets are represented by closed curves and the data set relationships are depicted by the overlaps between these curves. Both the sets and their intersections are easily visible as the closed curves are preattentively processed and form common regions that have a strong perceptual grouping effect. Besides set relations such as intersection, containment and disjointness, the cardinality of the sets and their intersections can also be depicted in the same diagram (referred to as area-proportional) through the size of the curves and their overlaps. Size is a preattentive feature and so similarities, differences and trends are easily identified. Thus, such diagrams facilitate data analysis and reasoning about the sets. However, drawing these diagrams manually is difficult, often impossible, and current automatic drawing methods do not always produce appropriate diagrams. This dissertation presents novel automatic drawing methods for different types of Euler diagrams and a user study of how such diagrams can help probabilistic judgement. The main drawing algorithms are: eulerForce, which uses a force-directed approach to lay out Euler diagrams; eulerAPE, which draws area-proportional Venn diagrams with ellipses. The user study evaluated the effectiveness of area- proportional Euler diagrams, glyph representations, Euler diagrams with glyphs and text+visualization formats for Bayesian reasoning, and a method eulerGlyphs was devised to automatically and accurately draw the assessed visualizations for any Bayesian problem. Additionally, analytic algorithms that instantaneously compute the overlapping areas of three general intersecting ellipses are provided, together with an evaluation of the effectiveness of ellipses in drawing accurate area-proportional Venn diagrams for 3-set data and the characteristics of the data that can be depicted accurately with ellipses

Hegel’s Theory of Quantity

Prior to Hegel\u27s time, no philosopher had ever tried to state what quantity or number was. Hegel undertakes a monumental definition in some of his longest chapters in the Science of Logic. In this paper, the author describes the nature of Hegel\u27s project and how Hegel derives quantity from the more primitive concept of quality. The author also reviews Hegel\u27s critique of calculus, which hereto has received very little attention in English. Finally the author shows how, according to Hegel, the concept of measure derives from the unity of quality and quantity. This is the second in a planned nine-part series that explicates how Hegel\u27s logic functions, using a specially designed series of graphic illustrations that memorialize each and every official progression in the Science of Logic

The Physicist - Philosophers: The Legacy of James Clerk Maxwell and Herrmann von Helmholtz

One of the most effective, and most mysterious, tools of modern theoretical physics is a mathematical method including what is here called “field theory.” The success of this procedure in unraveling the “zoology” of fundamental particles and their behavior is a marvel. The philosophical context of this marvel is the source of endless academic controversy. The core of the method is a blend of mathematics and description created by “physicist-philosophers,” from Maxwell and Helmholtz to Einstein and Schrödinger. This book tries to unravel the mystery, or at least chronicle it.https://digitalcommons.bard.edu/facbooks/1000/thumbnail.jp

Nihilism Inc.: Environmental Destruction and the Metaphysics of Sustainability

The spectre of global environmental destruction is before us, the legacy of the expansion and domination of the world by European civilization. Not even the threat to the continued existence of humanity is enough to move the members of this civilization to alter its trajectory. And Marxism, which had held out the possibility of creating a new social order, has been swept from the historical stage by the failure of Eastern European communism. Nihilism Inc. is an attempt to overcome this crisis. Examining the relationship between metaphysical assumptions, ideas, social practices, institutions and economic processes in the formation and evolution of European civilization, it offers a genealogy of its current nihilism. The theory and practice of Marxism are analysed to show why the Soviet Union proved even more environmentally destructive and even less responsive to the environmental crisis than the West. These analyses reveal the need for a radical cultural transformation, a transformation which can only be effected on the foundation of a new metaphysics. The final part of this work offers the required metaphysics, clearing the way for the creation of an environmentally sustainable civilization

Technology 2002: The Third National Technology Transfer Conference and Exposition, volume 2

Proceedings from symposia of the Technology 2002 Conference and Exposition, December 1-3, 1992, Baltimore, MD. Volume 2 features 60 papers presented during 30 concurrent sessions

Relationships amongst science, ethics and polis in pre-modern times

The emergence of the Modern Age is depicted as a replacement of a long standing political philosophy by a distinctly new one. Foundational meanings are attributed to key terms Science, Ethics and Polis, nuance in these terms is traced against those attributed meanings, and the integrating impact of that nuance on relationships amongst key terms is interpreted as changing political philosophy. Speculative questioning reflection is expressed about the nature of the next Polis

Beyond European Civilization: Marxism, Process Philosophy, and the Environment

Beyond European Civilization is the sequel to Nihilism Incorporated, a work in which I described how European civilization came to embody a nihilistic world-orientation and to conquer the world, and how, through the expansion of capitalism, it continues to impose its environmentally destructive culture on the rest of humanity. Through a critical analysis of the failure of Marxism to overcome the defects of European culture, Beyond European Civilization elaborates the foundations for a culture to transcend European civilization