Grapheus Was Here

Synthese

pballew.blogspot.com, 2009

Some history notes and observations about the once ubiquitous math class favorite, Graph Paper.

Diagrams, Graphs, and Visual Imagination in Mathematics, 2023

This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. As we know from Kant, vision (as a part of human sensibility) and responsiveness to reasons (as supported by our overall conceptual capacities) are related with one another through the imagination. Mathematics is an expression of this relation based on our most fundamental intuitions about space and time. Peirce went a long way to develop Kant’s take on the nature of mathematics, and central to his interpretation of it was the idea of diagrammatic reasoning. According to Peirce, in practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. As thinking, in this case, is actually performed by means of manipulating images, seeing and understanding become one. Defining diagrammatic reasoning as a fusion of vision and thought helped Peirce find some intriguing answers to questions concerning the nature of mathematical knowledge, many of which could not even be as much as formulated by Kant. What is the role of observation in mathematics? How can we explain the fact that mathematical reasoning is deductive and, at the same time, capable of the discovery of new truths? How is mathematical necessity reconciled with the essential incompleteness and indeterminacy of our ordinary visual experience? What exactly is the relationship between the particularity of a mathematical diagram and the generality of the meaning it conveysand what is the difference (if any) between mathematics and natural languages in this respect? Etc. Peirce’s life-long, if unsystematic, work on the issues that are associated with the questions above created an intricate conceptual puzzle. The driving motivation of the research this book represents is to show that tackling this puzzle requires something more than sifting through the wealth of available historical and philosophical material. While the histories of science and philosophy do provide separate bits of the puzzle, Peirce’s theoretical interests, by his own admission, appear to be closely intertwined with certain facts of his personal history. In light of this, without considering relevant biographical data, in Peirce’s case, there is no way to understand how the pieces of the puzzle actually fit together. Due to the plurality of data impelled by the task, this book is addressed both to those specializing in philosophy, mathematics, and intellectual history, and to a wider audience that might be interested in what all those areas have in common in Peirce’s case. Last but not least, this book could not have been written without the support of family, friends, and colleagues. I am especially grateful to Eric Bredo, Marcel Danesi, Paul Forster, Nathan Houser, Henry Jackman, Steven Levine, Mark Migotti, and James O’Shea. Of great importance for the book were my conversations with Kathleen Hull and Thomas L. Short. As to the biographical part of the study, I am indebted to Joseph Brent, the author of the most comprehensive biography of Charles Peirce to date. Finally, I owe much more than I can tell to my constant companions and interlocutors, Zina Uzdenskaya and Gleb Kiryushchenko.

1543 and All That: Image and Word, Change and Continuity in the Proto-Scientific Revolution, ed. G. Freeland and A. Corones, 2000

In the early, more mathematical, phase of the Scientific Revolution (up to about 1610, before forces, experiments ...) a crucial role was played by diagrams, both on paper and in the imagination. Medieval culture had made full use of diagrams - family trees, wheels of fortune, machine diagrams, memory theatres ... That gave training in the kind of thought experiments that allowed Galileo to make his breakthroughs in the science of motion. From 1600, philosophy too moved "inside", with the Cartesian emphasis on the inner point of view.

Journal of Visual Art Practice

Exploratory diagrams can be distinguished from statistical and explanatory diagrams in that they do not merely communicate what already exists, but provide a method of discovery, experiment and creative invention. As such, they are recommended as productive modes which can be utilized for art, education and philosophy. This paper seeks to draw out a number of key concepts and approaches to exploratory diagramming by examining three powerful diagram theories. First, A.J. Greimas' invention of the 'semiotic square'; second, C.S. Peirce's semiotic account of the diagram as icon; and third, Gilles Châtelet's retelling of scientific and mathematical discovery through diagrammatic devices. Respectively, these theories can each be identified according to a primary operative principle: opposition, relation and gesture.

Nuncius, 2016

2011

Index of Figures. - Drawing a Hypothesis (Preface), Nikolaus Gansterer. - A Line with Variable Direction, which Traces No Contour, and Delimits No Form, Susanne Leeb. - I Must Be Seeing Things, Clemens Krummel. - Subjective Objectivities, Jorg Piringer. - Grapheus Was Here, Anthony Auerbach. - Asynchronous Connections, Kirsten Matheus. - Distancing the If and Then, Emma Cocker. - Drawing Interest / Recording Vitality, Karin Harrasser. - Nonself Compatibility in Plants, Monika Bakke. - Hypotheses non Fingo or When Symbols Fail, Andreas Schinner, - Wiry Fantasy, Ferdinand Schmatz. - Reading Figures, Helmut Leder. - Collection of Figures of Thoughts, Gerhard Dirmoser. - Radical Cartographies, Philippe Rekacewicz. - 3 Elements, Axel Stockburger. - Dances of Space, Marc Boeckler. - Collection of Emotions and Orientation, Christian Reder. - On the Importance of Scientific Research in Relation to Humanities, Walter Seidl. - Interpersonal Governance Structures, Katja Mayer. - The Afterthoug...

Drawing: Research, Theory, Practice, Volume 5, Number 2, pg. 311 - 317, Intellect Books, UK, 2020, 2020

The drawing and modelling of diagrammatic images provides unique aesthetic, semiotic and philosophical overlap between science and art. This project report considers the diagrammatic artwork ‘Model for the origins of movement’, which was created using a hybrid drawing process. The drawing is one of thirty new works which I presented during the solo exhibition ‘Portraits of Thought: diagrams in art and science’ at the Kyoto University Museum, between 2018 and 2019. This body of work is part of an ongoing project to ‘poeticize the sciences’, and to enter in to a dialogue with scientists and the nature of their research, and transfigure their data and diagrams by means of visual metaphor and poetic associations. In doing so, new creative connections can be drawn between not only art and science, but amongst the hyper-specialised and fragmented fields of the scientific project itself.

Since the 1980s, interdisciplinary research crossing literature and the sciences has gone through substantial development through the stimulating input of both historians of the sciences and literary scholars. Research, which generally positions itself at the level of discourse, attaches priority to two paths, either by focussing on the use that literary texts make of scientific discourse, or by examining " literary technologies " employed by sciences as supports of " poetics " or a " rhetoric " of sciences. My perspective here will be somewhat different, to the extent that the aim is not to identify borrowings or influences between these two fields but instead to distinguish a common field, the shared use of intellectual resources that bring visual imagination into play. The hypothesis that will guide me is that mathematics and literature share an iconic character which is crucial for their specific semiotic regime and that can be attributed to the implication of diagrammatic properties both in natural and formal language (Batt, 2007).