1,847 research outputs found
Computational universes
Suspicions that the world might be some sort of a machine or algorithm
existing ``in the mind'' of some symbolic number cruncher have lingered from
antiquity. Although popular at times, the most radical forms of this idea never
reached mainstream. Modern developments in physics and computer science have
lent support to the thesis, but empirical evidence is needed before it can
begin to replace our contemporary world view.Comment: Several corrections of typos and smaller revisions, final versio
Clifford Algebra: A Case for Geometric and Ontological Unification
Robert Battermanâs ontological insights (2002, 2004, 2005) are apt: Nature abhors singularities. âSo should we,â responds the physicist. However, the epistemic assessments of Batterman concerning the matter prove to be less clear, for in the same vein he write that singularities play an essential role in certain classes of physical theories referring to certain types of critical phenomena. I devise a procedure (âmethodological fundamentalismâ) which exhibits how singularities, at least in principle, may be avoided within the same classes of formalisms discussed by Batterman. I show that we need not accept some divergence between explanation and reduction (Batterman 2002), or between epistemological and ontological fundamentalism (Batterman 2004, 2005).
Though I remain sympathetic to the âprinciple of charityâ (Frisch (2005)), which appears to favor a pluralist outlook, I nevertheless call into question some of the forms such pluralist implications take in Robert Battermanâs conclusions. It is difficult to reconcile some of the pluralist assessments that he and some of his contemporaries advocate with what appears to be a countervailing trend in a burgeoning research tradition known as Clifford (or geometric) algebra.
In my critical chapters (2 and 3) I use some of the demonstrated formal unity of Clifford algebra to argue that Batterman (2002) equivocates a physical theoryâs ontology with its purely mathematical content. Carefully distinguishing the two, and employing Clifford algebraic methods reveals a symmetry between reduction and explanation that Batterman overlooks. I refine this point by indicating that geometric algebraic methods are an active area of research in computational fluid dynamics, and applied in modeling the behavior of droplet-formation appear to instantiate a âmethodologically fundamentalâ approach.
I argue in my introductory and concluding chapters that the model of inter-theoretic reduction and explanation offered by Fritz Rohrlich (1988, 1994) provides the best framework for accommodating the burgeoning pluralism in philosophical studies of physics, with the presumed claims of formal unification demonstrated by physicists choices of mathematical formalisms such as Clifford algebra. I show how Battermanâs insights can be reconstructed in Rohrlichâs framework, preserving Battermanâs important philosophical work, minus what I consider are his incorrect conclusions
Overcoming the Newtonian Paradigm: The Unfinished Project of Theoretical Biology from a Schellingian Perspective
Defending Robert Rosenâs claim that in every confrontation between physics and biology it is physics that
has always had to give ground, it is shown that many of the most important advances in mathematics
and physics over the last two centuries have followed from Schellingâs demand for a new physics that
could make the emergence of life intelligible. Consequently, while reductionism prevails in biology, many
biophysicists are resolutely anti-reductionist. This history is used to identify and defend a fragmented but
progressive tradition of anti-reductionist biomathematics. It is shown that the mathematicoephysico
echemical morphology research program, the biosemiotics movement, and the relational biology of
Rosen, although they have developed independently of each other, are built on and advance this antireductionist tradition of thought. It is suggested that understanding this history and its relationship to the broader history of post-Newtonian science could provide guidance for and justify both the integration of these strands and radically new work in post-reductionist biomathematics
The Problem of Women and Mathematics
Reviews relevant research to determine the reasons for the limited participation of women in advanced mathematics and related fields. Explores options for improving women's mathematics skills and increasing their participation in related fields
Non-Smooth Spatio-Temporal Coordinates in Nonlinear Dynamics
This paper presents an overview of physical ideas and mathematical methods
for implementing non-smooth and discontinuous substitutions in dynamical
systems. General purpose of such substitutions is to bring the differential
equations of motion to the form, which is convenient for further use of
analytical and numerical methods of analyses. Three different types of
nonsmooth transformations are discussed as follows: positional coordinate
transformation, state variables transformation, and temporal transformations.
Illustrating examples are provided.Comment: 15 figure
Rational series and asymptotic expansion for linear homogeneous divide-and-conquer recurrences
Among all sequences that satisfy a divide-and-conquer recurrence, the
sequences that are rational with respect to a numeration system are certainly
the most immediate and most essential. Nevertheless, until recently they have
not been studied from the asymptotic standpoint. We show how a mechanical
process permits to compute their asymptotic expansion. It is based on linear
algebra, with Jordan normal form, joint spectral radius, and dilation
equations. The method is compared with the analytic number theory approach,
based on Dirichlet series and residues, and new ways to compute the Fourier
series of the periodic functions involved in the expansion are developed. The
article comes with an extended bibliography
Illinois Science Academy: A Proposal to the State of Illinois
There is a widely recognized perception that the nation facing a crisis in fulfilling its needs for citizens trained in the fields of science, mathematics and technology. In particular, the State of Illinois has an obligation toward this national issue and to .its own need to develop these human resources that are so intimately coupled to economic leadership in a post-industrial society. This is a very broad challenge; here we propose to address only one important aspect: the nurturing of creative excellence in students of science and mathematics. We are concerned with the extraordinarily gifted person--the upper few tenths of one percent of the secondary-school population of Illinois. It is our conviction that, in spite of the existence of many excellent schools in this state, this special breed of student is too often insufficiently challenged, with a consequent loss of potential to the individual and to the society that he or she might have served. The brilliant child is a rare blessing and, at the same time, represents a great responsibility. Over the past decade, our system of education has not met the needs of this group of students.
We propose to remedy this by the creation of an Illinois Science Academy, a three-year residential public school which bridges the conventional 10th, 11th and 12th grades of high school and the first year of college. The Science Academy will search throughout the state to identify young students exceptionally talented in science and mathematics. They will be provided with a uniquely challenging education in mathematics and science, as well as a superior program in English, foreign languages, social studies, and the humanities. The Academy will also act as a catalyst for the improvement of teaching of science and mathematics in all Illinois schools. We propose the governance to be by an independent Board of Trustees, appointed by the appropriate State authorities
Undergraduate Curriculum and Academic Policy Committee Minutes, October 17, 2012
Minutes from the Wright State University Faculty Senate Undergraduate Curriculum and Academic Policy Committee meeting held on October 17, 2012
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