What\u27s in a Name? The Matrix as an Introduction to Mathematics

In my classes on the nature of scientific thought, I have often used the movie The Matrix (1999) to illustrate how evidence shapes the reality we perceive (or think we perceive). As a mathematician and self-confessed science fiction fan, I usually field questions related to the movie whenever the subject of linear algebra arises, since this field is the study of matrices and their properties. So it is natural to ask, why does the movie title reference a mathematical object? Of course, there are many possible explanations for this, each of which probably contributed a little to the naming decision. First off, it sounds cool and mysterious. That much is clear, and it may be that this reason is the most heavily weighted of them all. However, a quick look at the definitions of the word reveals deeper possibilities for the meaning of the movie’s title. Consider the following definitions related to different fields of study taken from Wikipedia on January 4, 2010: • Matrix (mathematics), a mathematical object generally represented as an array of numbers. • Matrix (biology), with numerous meanings, often referring to a biological material where specialized structures are formed or embedded. • Matrix (archeology), the soil or sediment surrounding a dig site. • Matrix (geology), the fine grains between larger grains in igneous or sedimentary rocks. • Matrix (chemistry), a continuous solid phase in which particles (atoms, molecules, ions, etc.) are embedded. All of these point to an essential commonality: a matrix is an underlying structure in which other objects are embedded. This is to be expected, I suppose, given that the word is derived from the Latin word referring to the womb — something in which all of us are embedded at the beginning of our existence. And so mathematicians, being the Latin scholars we are, have adapted the term: a mathematical matrix has quantities (usually numbers, but they could be almost anything) embedded in it. A biological matrix has cell components embedded in it. A geological matrix has grains of rock embedded in it. And so on. So a second reason for the cool name is that we are talking, in the movie, about a computer system generating a virtual reality in which human beings are embedded (literally, since they are lying down in pods). Thus, the computer program forms a literal matrix, one that bears an intentional likeness to a womb. However, there are other ways to connect the idea of a matrix to the film’s premise. These explanations operate on a higher level and are explicitly relevant to the mathematical definition of a matrix as well as to the events in the trilogy of Matrix movies. They are related to computer graphics, Markov chains, and network theory. This essay will explore each of these in turn, and discuss their application to either the events in the film’s story-line or to the making of the movie itself

The rock: points of view in Bart De Clercq's painting

Images are of the order of monsters. They are beautiful in the same way that they are shocking to the eye. In Édouard Manet’s own words: “Un des plus beaux, des plus curieux, et des plus terribles spectacles que l’on puisse voir, c’est une course de taureaux. J’espère, à mon retour, mettre sur la toile l’aspect brillant, papillotant et en même temps dramatique de la corrida à laquelle j’ai assisté.” In the bullfighting occurring at the moment of looking at images (any image), the fight between the beholder’s eye and the painting’s gaze, in Lacan’s sense, is won by the latter. The toreros, the embodiment of modern warriors for the bourgeois spectators in the second half of the European XIX century, are always destined to symbolic death: the power of the (self-) annihilating gaze of the picture itself wins over the eye in the ritual of exchange between subjects and objects of looking, whose roles mingle, interchange and constantly shift during the realistic and also hallucinatory act of seeing images

Change That Abides: A Retrospective Look at Five Community and Family Stengthening Projects and Their Enduring Results

Examines the interactions among funders, grantees, and community groups, and outlines the results of three different types of foundation grants for projects in Savannah, Little Rock, Dayton, Alameda County, and Boston. Includes recommendations

Teaching Paleontology

This guide is designed to be used by teachers as an aid for teaching principles of fossils and past life to elementary school students. The activities and labs provided include topics such as fossilization, sedimentation, trace fossils, the importance of fossils, ancient environments, changes in environments, paleontology as a science, biodiversity, food webs, ecosystems, and human influences. The lessons provide pre- and post-questions, procedures, vocabulary, materials, and field trip ideas. This curriculum guide for paleontology was developed by Fossil Butte National Monument as part of its growing environmental education program. Educational levels: Intermediate elementary, Primary elementary

Marnda Gardairri: Facilitation of an Indigenous Ranger Rock Art Workshop

The Marnda Gardairri Indigenous Rangers Workshop was held from 3–5 October 2017 on the Burrup Peninsula in the Pilbara region of Western Australia. The event, which was hosted by the Murujuga Aboriginal Corporation (MAC), brought together rangers from across Australia to discuss rock art conservation and management. The workshop was given the title ‘Marnda Gardairri’ as this means rock scratching/engraving on the Burrup Peninsula. The workshop was developed by MAC in collaborative partnership with Rio Tinto Iron Ore-Pilbara Operations and the Nulungu Research Institute (The University of Notre Dame Australia). Rio Tinto and Woodside Petroleum funded the workshop, with Mel Marshall and Lynley Wallis of Nulungu engaged to coordinate and facilitate the event, assisted by Kate Golson.https://researchonline.nd.edu.au/nulungu_insights/1002/thumbnail.jp

An Analysis of the Impact of Charter Schools on Desegregation Efforts in Little Rock, Arkansas

The aim of this report is to address the challenge by the Little Rock School District (LRSD) that open-enrollment charter schools in Pulaski County (PC) are impeding the efforts of the three PC school districts (Little Rock, North Little Rock (NLRSD), and Pulaski County Special (PCSSD)) to become racially integrated. A key motivation for this analysis is the ongoing debate about how expanded school choice, in this case charter schools, impacts racial segregation. Critics of charter schools argue that these schools lead to greater racial segregation, whereas proponents of charter schools suggest that there is no necessary link between racial segregation and the existence of charter schools. Indeed, some charter advocates contend that charters and parental choice can actually lead to more racial integration for students

Eliciting Expertise

Since the last edition of this book there have been rapid developments in the use and exploitation of formally elicited knowledge. Previously, (Shadbolt and Burton, 1995) the emphasis was on eliciting knowledge for the purpose of building expert or knowledge-based systems. These systems are computer programs intended to solve real-world problems, achieving the same level of accuracy as human experts. Knowledge engineering is the discipline that has evolved to support the whole process of specifying, developing and deploying knowledge-based systems (Schreiber et al., 2000) This chapter will discuss the problem of knowledge elicitation for knowledge intensive systems in general

Space Math: Lunar Math

This booklet includes 17 problems relating to the Moon and its exploration. Images from NASA are analyzed to determine image scales and the physical sizes of various crates and features. The probability of meteor impacts near a lunar colony are calculated, and the horizon distance is determined using simple geometry. Also covered are: determining the mass of the Moon, a simple model for the lunar interior, heat flow rates, extracting oxygen from lunar rock, and lunar transits and eclipses. (8.5 x11, 28 pages, 11 color images, PDF file) Educational levels: Intermediate elementary, Middle school, High school