Timing diagrams are popular in hardware design. They have been formalized for use in reasoning tasks, such as computer-aided verification. These efforts have largely treated timing diagrams as interfaces to established notations for which verification is decidable; this has restricted timing diagrams to expressing only regular language properties. This paper presents a timing diagram logic capable of expressing certain context-free and context-sensitive properties. It shows that verification is decidable for properties expressible in this logic. More specifically, it (...) shows that containment of -regular languages generated by Büchi automata in timing diagram languages is decidable. The result relies on a correlation between timing diagram and reversal bounded counter machine languages. (shrink)

In his reflections on inner time consciousness written in the years 1917–1918, Husserl makes use of an illustrative device he apparently developed in fits and starts between 1905–1911 2: the so-called “time-diagram.” It proves to be an important instrument for several of the texts published in Husserliana XXXIII, in particular Text Nr. 2: “Die Komplexion von Retention und Protention. Gradualitäten der Erfüllung und das Bewusstsein der Gegenwart. Graphische Darstellung des Urprozesses”. More, the diagram appears in these texts in (...) a much more refined and complete manner than anything found in Husserliana X, which in turn allows us to sharpen a number of questions that had already arisen with original 1928 publication of Husserl’s 1905 Zeitvorlesungen. (shrink)

When the German mathematician Hermann Minkowski first introduced the space-time diagrams that came to be associated with his name, the idea of picturing motion by geometric means, holding time as a fourth dimension of space, was hardly new. But the pictorial device invented by Minkowski was tailor-made for a peculiar variety of space-time: the one imposed by the kinematics of Einstein’s special theory of relativity, with its unified, non-Euclidean underlying geometric structure. By plo tting two or (...) more reference frames in relative motion on the same picture, Minkowski managed to exhibit the geometric basis of such relativistic phenomena as time dilation, length contraction or the dislocation of simultaneity. These disconcerting effects were shown to result from arbitrary projections within four-dimensional space-time. In that respect, Minkowski diagrams are fundamentally different from ordinary space-time graphs. The best way to understand their specificity is to realize how productively ambiguous they are. (shrink)

The “origins” of (geometric) space is examined from the perspective of the so-called “conceptual space” or “semantic space”. Semantic space is characterized by its fundamental “locality” that generates an “implicit” mode of geometrizing. This view is examined from within three perspectives. First, the role that various diagrammatic entities play in the everyday life and pragmatic activities of selected ethnic groups is illustrated. Secondly, it is shown how conceptual spaces are fundamentally linked to the meaning effects of particular natural languages and (...) these are very different from the global and universal aspects of Euclidean spaces. Thirdly, it is contended that these modes of creating body and culture-based spatial frameworks and related cosmogonies and cosmologies can be described as forms of “latent geometry” that initially appear unexplainable in any rational way. Nonetheless, and thanks to the deep mathematical reflections provided by René Thom, it is illustrated how the various ways of generating space can be further analyzed as distortions of mainstream spatialization furnished by Euclidean geometry that established the dominant universality of the ideas of space (and time). (shrink)

The usual metaphor for time is a flow. Edmund Husserl, in describing experience of our inner temporality, uses the term often: Fluss. In the final three decades of his life (1900s to 1930s), he gives us a well-articulated theory of time, especially the experience of its ongoingness and of our- selves in the processing of time. He refers to this latter, our immanent temporality, as a "flux" or flow and thus calls up the image of the river (...) moving along with its contents comprised in that flowing, gaining their fluent qualities from it. Yet Husserl's theory is not limited to a mechanistic understanding of flow as pure series, but in fact incorporates both a serial- ized aspect and a decentering, highly complex aspect of inner time-con- sciousness. The theory, then, requires a new metaphor, a re-mapping from serialistic diagrams to more dynamic ones. The challenge lies not only in achieving this re-mapping, but in showing the relation of dynamic diagrams to the serialistic ones that are still vital to the full descriptions of inner time- consciousness. (shrink)

Some very good arguments can be given in favor of the Augustinean wisdom, according to which it is impossible to provide a satisfactory definition of the concept of time. However, even in the absence of a proper definition, it is possible to deal with conceptual problems regarding time. It can be done in terms of analogies and metaphors. In particular, it is attractive to make use of Peirce's diagrams by means of which various kinds of conceptual experimentation (...) can be carried out. This paper investigates how Peircean diagrams can be used within the study of time. In particular, we discuss 1) the topological properties of time, 2) the implicative structure in tense logic, 3) the notions of open future and branching time models, and finally 4) tenselogical alternatives to branching time models. (shrink)

Cartesian method both organizes and impoverishes the domains to which Descartes applies it. It adjusts geometry so that it can be better integrated with algebra, and yet deflects a full-scale investigation of curves. It provides a comprehensive conceptual framework for physics, and yet interferes with the exploitation of its dynamical and temporal aspects. Most significantly, it bars a fuller unification of mathematics and physics, despite Descartes' claims to quantify nature. The work of his contemporaries Galileo and Torricelli, and of his (...) successor Newton, illustrates conceptual possibilities Descartes left aside, due to his attachment to method. (shrink)

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of (...) most importance for a taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)

There are two important ways in which, when dealing with documents, we go beyond the boundaries of linear text. First, by incorporating diagrams into documents, and second, by creating complexes of intermeshed documents which may be extended in space and evolve and grow through time. The thesis of this paper is that such aggregations of documents are today indispensable to practically all complex human achievements from law and finance to orchestral performance and organized warfare. Documents provide for what (...) we can think of as a division of intellectual, instructional, and deontic labour, allowing plans, orders, and obligations to be enmeshed together in a way that often involves the use of diagrammatic elements, as for example in a musical score. (shrink)

Why are diagrams sometimes so useful, while other times unhelpful and even misguiding? There are systematic reasons for this. Drawing on modern research in logic, Artificial Intelligence, cognitive psychology, and graphic design, "Semantic Properties of Diagrams and their Cognitive Potentials" shows that diagrams' cognitive functions are rooted in the characteristic ways they carry information about their targets. The analysis leads to an answer for the deeper question of What makes a diagram a diagram?, which is of crucial (...) importance to the foundation of a collective science of diagrams. ". (shrink)

Abstract The artwork of Joseph Beuys was provocative in his time. Although he was very successful on the international art scene and on the art market, the larger The public is still bewildered by his Fat Chair or his installations and his performances. The article shows the evolution of his artwork from classical materials (stone, steel) to soft materials (animals, products of animals) and further to his concept of “social sculpture” and to programmatic diagrams (with words and graphics). (...) A special point of interest is the transition towards language (phonic and conceptual), the philosophy of art exposed in his drawings, and diagrams and the relation between art and science in his artwork. (shrink)

Hans Reichenbach’s posthumous book The Direction of Time ends somewhere between Socratic aporia and historical irony. Prompted by Feynman’s diagrammatic formulation of quantum electrodynamics, Reichenbach eventually abandoned the delicate balancing between the macroscopic foundation of the direction of time and microscopic descriptions of time order undertaken throughout the previous chapters in favor of an exclusively macroscopic theory that he had vehemently rejected in the 1920s. I analyze Reichenbach’s reasoning against the backdrop of the history of Feynman (...) class='Hi'>diagrams and the current practice of particle physics. Building upon the debates about processes and conserved quantities between Wesley Salmon and Phil Dowe in the 1990s, and the exchange between Reichenbach and the gestalt theorist Kurt Lewin during the 1920s about topology and genidentity, I investigate whether the aporia about local time order could be avoided by following a strategy that Reichenbach adopted elsewhere in the book and develop a notion of functional genidentity that captures the practice of present-day elementary particle physics and the fact that Feynman diagrams have to be understood in the context of a complex mathematical description of scattering processes. (shrink)

This book investigates a number of central problems in the philosophy of Charles Peirce grouped around the realism of his semiotics: the issue of how sign systems are developed and used in the investigation of reality. Thus, it deals with the precise character of Peirce's realism; with Peirce's special notion of propositions as signs which, at the same time, denote and describe the same object. It deals with diagrams as signs which depict more or less abstract states-of-affairs, facilitating (...) reasoning about them; with assertions as public claims about the truth of propositions. It deals with iconicity in logic, the issue of self-control in reasoning, dependences between phenomena in their realist descriptions. A number of chapters deal with applied semiotics: with biosemiotic sign use among pre-human organisms: the multimedia combination of pictorial and linguistic information in human semiotic genres like cartoons, posters, poetry, monuments. All in all, the book makes a strong case for the actual relevance of Peirce's realist semiotics. (shrink)

From the mid-1600s to the beginning of the eighteenth century, there were two main circles of German scholars which focused extensively on diagrammatic reasoning and representation in logic. The first circle was formed around Erhard Weigel in Jena and consists primarily of Johann Christoph Sturm and Gottfried Wilhelm Leibniz; the second circle developed around Christian Weise in Zittau, with the support of his students, particularly Samuel Grosser and Johann Christian Lange. Each of these scholars developed an original form of using (...) geometric diagrams in logic. In this paper, I will trace the historical notes of John Venn and other modern logicians back to the original works published in the Weigel and Weise circles and describe the development of using geometric figures for logical reasoning and representation in that period of time. (shrink)

The aim of this article is to clarify how Husserl applies his formal ontology to the constitution of immanent temporality. By doing so, my objective is to unravel the relationships between the phases of this temporality that make up a unit—that is, the relationship between protentions and retentions and a proto-impression that gives rise to the temporal moment “now” in an experience of the immanent consciousness. In connection with this reconstruction, I will attempt to clarify Husserl’s definition of time (...) as a “one-dimensional orthoid multiplicity,” the roots of which lie in Riemann’s work. I interpret Husserl’s description as a model for the description of the phenomenon of time. Its nature as a model seems to unfold with the problem of the time diagram. Which diagram best represents the constitution of immanent temporality? Larrabee has discussed this issue, and I propose that the best interpretation of the diagram is to consider it as applying to a spherical surface rather than a flat one. This interpretation allows us to account for the multiple relationships among presentations, memories, and other presentifications in an empirically appropriate manner while at the same time providing us with another vision of Husserl’s consciousness, which allows us to reconsider the relationship between subjectivity and objectivity. (shrink)

This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. 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. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician. (shrink)

Jean-Pierre Dupuy argues that our failure to prevent the looming climate catastrophe results from a faulty metaphysics of time: because we believe the present can proceed down one of the many branches that extend into the future, some of which bypass the catastrophe, we do not think it is absolutely urgent to take drastic action now. His solution to this problem of demotivation is “enlightened doomsaying” in “projected time”, which means that we affirm the coming catastrophe as something (...) real in the future rather than being a mere possibility; thus, we regard it seriously enough that we are motivated to take the needed actions to prevent it. One potential obstacle to this proposal is that it requires the forming of consensus and coordination with the powerful players who benefit from our current path and whose apparently near-total grip on this catastrophic future may itself discourage action. We then consider an alternative model based on Gilles Deleuze’s philosophy of the present–future relation. Although it has the branching structure that Dupuy is wary of, it may not suffer from the same problem of demotivation on account of the way it conceives the complex structure of the present event. For this reason, the Deleuzian model may be more suited to motivating action in a world where the future must be fought for rather than unanimously agreed upon. (shrink)

In this chapter the author examines the idea of time's motion, or flow, more carefully, by comparing it to the motion of ordinary objects. Ordinary objects move with respect to time. So if time itself moves, it must move with respect to some other sort of time. But what would that other time be? Most motion takes place with respect to the familiar timeline, but time itself moves with respect to another timeline, hypertime. Hypertime (...) is supposed to be a sort of time. Hypertime must move with respect to yet another sort of time, hyper‐hyper time. Space‐time diagrams can be used to represent all of history; everything that has ever happened or ever will happen can be fit into a space‐ time diagram somewhere. According to the space‐time theory, time and space are analogous in many ways. Finally the author argues against the space‐time theory. (shrink)

There are two distinct interpretations of the role that Feynman diagrams play in physics: (i) they are calculational devices, a type of notation designed to keep track of complicated mathematical expressions; and (ii) they are representational devices, a type of picture. I argue that Feynman diagrams not only have a calculational function but also represent: they are in some sense pictures. I defend my view through addressing two objections and in so doing I offer an account of representation (...) that explains why Feynman diagrams represent. The account that I advocate is a version of that defended by Kendall Walton, which provides us with a basic characterization of the way that representations in general work and is particularly useful for understanding distinctively pictorial representations - in Walton's terms, depictions. The question of the epistemic function of Feynman diagrams as pictorial representations is left for another time. (shrink)

This paper aims, on the one hand, to determine the valid span of the diagram of unequal hours and, on the other, to find a mathematical expression for the error. It is found that the diagram is valid for the two days of the equinoxes and for the times when the sun is on the horizon or on the meridian. This subject has previously been treated by Delambre in 1819 and Drecker in 1925, but not comprehensively.

CL diagrams – the abbreviation of Cubus Logicus – are inspired by J.C. Lange’s logic machine from 1714. In recent times, Lange’s diagrams have been used for extended syllogistics, bitstring semantics, analogical reasoning and many more. The paper presents a method for testing statistical syllogisms (also called proportional syllogisms or inductive syllogisms) by using CL diagrams.

It is little known that Schopenhauer (1788–1860) made thorough use of Euler diagrams in his works. One specific diagram depicts a high number of concepts in relation to Good and Evil. It is, hence, uncharacteristic as logicians of that time seldom used diagrams for more than three terms (the number demanded by syllogisms). The objective of this paper is to make sense of this diagram by explaining its function and inquiring whether it could be viewed as an (...) early serious attempt to construct complex diagrams. (shrink)

Mario Savio is widely known as the first spokesman for the Free Speech Movement. Having spent the summer of 1964 as a civil rights worker in segregationist Mississippi, Savio returned to the University of California at a time when students throughout the country were beginning to mobilize in support of racial justice and against the deepening American involvement in Vietnam. His moral clairty, his eloquence, and his democratic style of leadership inspired thousands of fellow Berkeley students to protest university (...) regulations that had severely limited political speech and activity on campus. The nonviolent campaign culminated in the largest mass arrest in American history, drew widespread faculty support, and resulted in a revision of university rules to permit political speech and organizing. This significant advance for student freedom rapidly spread to countless other colleges and universities across the country. Mario Savio went on to become a college teacher of physics, logic, and philosophy, to speak and organize in favor of immigrant rights and affirmative action and against U.S. intervention in Central America. He died on November 6, 1996, in the middle of a struggle against California State University fee hikes that hurt working-class students. Savio had submitted this article to the Notre Dame Journal of Formal Logic before he died. Final revisions were made by Philip Clayton with the assistance of Mario's colleagues at Sonoma State University. As reader for the Journal, George Englebretsen not only provided an extensive commentary on the article--much of which has been incorporated here--but also assisted in the difficult task of making revisions without changing the substance of Mario's style or thought. It is fitting that this, Savio's final publication, would be pedagogical in orientation. For him, moral considerations were no less pertinent in logic than in philosophy's less abstract fields. The usual student confusion with Venn diagrams led him to develop the new pictorial device presented in the following pages, which he believed was more sensitive to user psychology. It is hard to miss the political overtones in Savio's closing worry that in Venn diagrams "information of real significance may occasionally appear hidden and distorted." The decision by the Notre Dame Journal of Formal Logic to publish this piece posthumously is a testimony that logic, no less than other fields of philosophy, can be a tool of free speech and political change--as powerful in its way as the rhetorical brilliance of that young man standing on top of a police car who launched a worldwide movement with the words, "There is a time when the operation of the machine becomes so odious, makes you so sick at heart, you can't take part.". (shrink)

Using matrix iterations of ccc posets, we prove the consistency with ZFC of some cases where the cardinals on the right hand side of Cichon’s diagram take two or three arbitrary values (two regular values, the third one with uncountable cofinality). Also, mixing this with the techniques in J Symb Log 56(3):795–810, 1991, we can prove that it is consistent with ZFC to assign, at the same time, several arbitrary regular values on the left hand side of Cichon’s diagram.

The paper is a study of how graphic narratives (graphic novels and the comics) represent time in external visual space as well as in inner (mental) representations. Peirce’s semiotics is the main tool of research. After a survey of various approaches to the study of time in narratives in general and in graphic narratives in particular, an outline of the various aspects of the embodiment of time in space in general is given before the forms of the (...) embodiment of time in the space of graphic narratives is examined in detail. Signs of time are signs that represent time as their object and create mental representations of time as their interpretant. On this semiotic premise, the paper proposes a reinterpretation of Genette’s theory of time in narratives. A comparison with narratives in prose reveals that narrative time in graphic narratives evinces marked discontinuities in their spatial representation. The paper distinguishes between time as continuity, time as age, and points in time. It concludes that time as continuity is typically embodied in the form of spatial diagrams whereas time as age and points in time are mainly of the nature of indexical signs. The insights into the forms of embodiment of time in space derived from these premises are applied to examples from recent graphic novels and some traditional comics. (shrink)

This chapter shows that the combination of mathematical and chemical thinking in particular, as evidenced by Charles Sanders Peirce’s chemical training at Harvard, formed a solid conceptual basis for his account of diagrams. The connection between the Lawrence school and the chemical tradition established by Justus von Liebig in Giessen is of crucial importance to understand the context of Peirce’s own chemistry training. A completely different picture emerges if one pays greater attention to the nature of the chemistry curriculum (...) in Harvard at the time, and in particular to the pedagogical innovations introduced by Peirce’s chemistry teacher, Josiah Parsons Cooke. Historians of science have investigated the rise of institutional scientific laboratories from a range of perspectives. The chapter concludes with some suggestions for further investigation into the role of chemistry in Peirce’s philosophical system more broadly and the potential this new avenue of inquiry might have for the direction of Peirce scholarship. (shrink)

This chapter will examine two puzzles that percolate Husserl’s On the Phenomenology of the Consciousness of Internal Time (PITC). They concern: (1) whether or not memory is pictorial and (2) whether or not the temporal determinations (past, now, future, etc.) are categories. Considering these aporetic discussions helps us to understand the time diagrams Husserl uses, as well as some of the motivation behind Husserl’s talk of the two intentionalities of retention and his talk of the time-constituting (...) flow. Moreover, this approach to PITC helps to highlight the role that aporetic considerations play in phenomenological investigation more generally. (shrink)

This collection focuses on the ontology of space and time. It is centred on the idea that the issues typically encountered in this area must be tackled from a multifarious perspective, paying attention to both a priori and a posteriori considerations. Several experts in this area contribute to this volume: G. Landini discusses how Russell’s conception of time features in his general philosophical perspective;D. Dieks proposes a middle course between substantivalist and relationist accounts of space-time;P. Graziani argues (...) that it is necessary to provide an account of the “synthetic procedures” implicit in the recourse to diagrams in Euclid’s Elements, while E. Mares comes to the conclusion that in Euclid’s Elements we should treat the parallel postulate as empirical and the postulate that space is continuous as a priori. M. Arsenijevi?/M. Adži? present an important formal result concerning two theories of the infinite two-dimensional continua, which sheds new light on the current dispute between gunkologists and pointilists; F. Orilia discusses two problems for presentism, one regarding the duration of the present and the other related to Zeno’s paradoxes. A. Iacona delves deep into logical matters by focusing on the so-called T×W modal frames in order to deal with the deteterminism-indeterminism controversy. D. Mancuso outlines a non-standard temporal model compatible with time travel, andV. Fano/G. Macchia discuss time travels in the light of an important foundational principle of modern cosmology, Weyl’s Principle. (shrink)

Barry Dainton wrote Time and Space “to provide an introduction to the contemporary philosophical debate that presupposes little or nothing by way of prior exposure to the subject, but that will also take the interested and determined reader quite a long way”. He has achieved much of what he intended in this difficult enterprise. He covers the major arguments in a fair-minded way, writes clearly, and has found a good illustrator to provide a host of diagrams that his (...) student readers in particular will find helpful. The book also has a helpful glossary and list of web resources, as well as a brief bibliography and index. (shrink)

My first aim in this paper is to use time diagrams in the style of Brentano to analyze constructions in Brouwer's separable mathematics more precisely. I argue that constructions must involve not only pairing and projecting as basic operations guaranteed by the intuition of twoity, as sometimes assumed in the literature, but also a recalling operation. My second aim is to argue that Brouwer's views on the intuition of twoity and arithmetic lead to an ontological explosion. Redeveloping the (...) constructions of natural numbers and systems sketched in an appendix to Brouwer's Cambridge lectures, I observe that the only plausible way he can make some elementary arithmetic in his separable mathematics is by allowing for the same canonical number to be determined by multiple separable entities, resulting in an overabundant mathematical ontology. (shrink)

Outline by Section: I. INTRODUCTION: METHOD OF PHENOMENOLOGY II. REDUCTION FROM DOGMAS III. EXAMPLES OF PHENOMENOLOGICAL DESCRIPTION OF A. SENTENCE B. MELODY C. DIAGRAM OF TIME IV. MODIFICATIONS AS MODES OF TEMPORAL STRUCTURE V. RETENTION VI. CONSTITUTION OF EXTERNAL TIME Time present and time past.

A naive introduction of a dependency of the mass of a black hole on the Schwarzschild time coordinate results in singular behavior of curvature invariants at the horizon, violating expectations from complementarity. If instead a temporal dependence is introduced in terms of a coordinate akin to the river time representation, the Ricci scalar is nowhere singular away from the origin. It is found that for a shrinking mass scale due to evaporation, the null radial geodesics that generate the (...) horizon are slightly displaced from the coordinate singularity. In addition, a changing horizon scale significantly alters the form of the coordinate singularity in diagonal (orthogonal) metric coordinates representing the space-time. A Penrose diagram describing the growth and evaporation of an example black hole is constructed to examine the evolution of the coordinate singularity. (shrink)

In an effort to reassess the status of Phenomenology of Perception and its relation to The Visible and the Invisible, this essay argues that Merleau-Ponty's engagement with Husserl's text and his discussion of the “field of presence” in La temporalité are intended to think through the field in which time makes its appearance as one of passage. Time does not show itself as presence or in the present but manifests itself as Ablauf, as lapse or flow, an écoulement (...) that is simultaneously an explosion, an éclatement. Merleau-Ponty's account of temporality in these pages is thus legible as recovering the primordial experience of time as a self-differentiating déhiscence in its dual power of articulation and erosion. Time is thus simultaneously the vehicle of the world's appearance and of its “disarticulation”, the passage of a rhythm of affirmation and disintegration. Merleau-Ponty's account of temporality in Phenomenology of Perception is oblique, somewhat fragmentary and circuitous.11 References to Merleau-Ponty's works cite the French followed by the English translation. I will use the abbreviation PhP for Phenomenology of Perception and VI for The Visible and the Invisible. Other texts by Merleau-Ponty will be referenced by the title. References to Husserl and Heidegger use the German followed by the translation. I will use the abbreviations ZB for the Zeitbewußtsein lectures; FT for Formale und transzendentale Logik; EU for Erfahrung und Urteil; and SZ for Sein und Zeit. View all notes While of course this phenomenon comes under close scrutiny in La temporalité, a brief inspection of this text as a whole finds it to be virtually everywhere.22 The theme of temporality is introduced as early as the Preface to Part I, “Experience and Objective Thought” and appears again in almost every subsequent chapter: the first chapter of Part I ; in his discussion on number blindness and Goldstein's patient known as Schneider in La spatialité du corps et la motricité ; in the sexuality chapter ; in the discussion of memory in La corps comme expression et la parole ; in Le sentir ; in the discussion of depth in L'espace ; in La chose et le monde naturel ; in Autrui et le monde humain and in Le cogito. Rather than providing the perhaps much called for synopsis of these scattered accounts of time or trying to locate a unified account in Phenomenology of Perception through such a synopsis, this essay will focus only on La temporalité, particularly the discussion of Husserl's diagram from the Zeitbewußtsein and the “champ de présence”. View all notes It is this apparent ubiquity that will motivate scholars such as Renaud Barbaras to claim that “… the entire structure of Phenomenology of Perception rests on a chapter devoted to temporality”.33 Barbaras The Being of the Phenomenon, 218. View all notes In spite of this ubiquity and apparent centrality, however, the treatment of temporality seems to neglect a systematic and thoroughgoing approach, and whether this work manages to address this theme with a sufficient degree of rigor remains open to debate. Furthermore, beyond the scattered and fragmented appearance of temporality in the text, the chapter devoted to its exploration contains numerous, well-recognized problems.44 Merleau-Ponty's misinterpretation of Bergson in this chapter has received much warranted attention. Alia Al-Saji, for example, has criticized Merleau-Ponty's account of temporality in this chapter of Phenomenology of Perception for this misreading as well as its perhaps too uncritical infatuation with Husserl and his emphasis on presence. See Lawlor Thinking Through French Philosophy, Al-Saji “The Temporality of Life” and “A Past Which Has Never Been Present” and Barbaras “The Turn of Experience”. View all notes Among these difficulties, Merleau-Ponty's engagement with Husserl's lectures on time-consciousness, the Vorlesungen zur Phänomenologie des inneren Zeitbewußtseins,55 The 1928 publication of the Zeitbewußtsein, edited by Heidegger, is what appears in the bibliography of Phenomenology of Perception. This version, from the Jahrbuch für Philosophie und phänomenologishe Forschung, as Brough notes, appears as “Part A” of Husserliana X. The notes that constitute this version of the text, furthermore, as Heidegger mentions in his preface to the Jahrbuch version and which Brough repeats were heavily edited by Husserl's assistant at the time, Edith Stein. Merleau-Ponty's references to the Zeitbewußtsein cut across various moments of the text and do not focus on one section in particular, and in fact, he actually references section 11, “Urimpression und retentionale Modifikation”/“Primal impression and retentional modification” in his discussion of the field of presence. As Al-Saji has noted, the extent to which Merleau-Ponty's account of time in La temporalité centres the account of time on “the living present” can be shown to be at play behind the misreading of Bergson. While I do not wish to dispute the specifics of her compelling reading, it is nonetheless worth noting that Al-Saji's reading of the Zeitbewußtsein only focuses on Appendix V, “Gleichzeitigkeit von Wahrnehmung und Wahrgenommenem”/“Simultaneity of Perception and the Perceived”. View all notes looms large, as it seems that his discussion of what he designates as le champ de présence or “field of presence” commits him to the ontological primacy of the present in his account of time. As a result, this earlier work appears to confine itself to a metaphysics organized around the privilege and authority of the present in establishing the structure of time.66 Leonard Lawlor has convincingly argued against this interpretation. Following the famous remark at the end of Le Sentir about “a past which has never been present”, Lawlor argues that precisely because Merleau-Ponty's critique of Bergson is a straw man – that is, because his critique of Bergson is based on a misreading – a closer inspection of Le Sentir and La temporalité shows Merleau-Ponty to be committed to the ontological primacy of an “originary” past. See Lawlor Thinking Through French Philosophy, 89. Marratto, following Lawlor, takes up the charge of a metaphysics of presence in Phenomenology of Perception in dialogue with Derrida. Marratto argues that Derrida's reading selectively overlooks “the very imporant dimensions of difference, discontinuity, and delay and non-self-presence in Merleau-Ponty's descriptions”, located particularly in the latter's theory of subjectivity. I agree with Marratto's assessment, and my aim here is to deepen it by turning in more detail to La temporalité. View all notes This apparent commitment to the ontological primacy of the present, for some readers, has also functioned as an index for tracking the revision of Phenomenology of Perception that is said to figure in The Visible and the Invisible, where a metaphysics of the present is replaced with a commitment to the primacy of an original past, signalling a significant break in the development of Merleau-Ponty's thought.77 This has bearing on the debate mentioned above as the question of temporality and Merleau-Ponty's evolving relationship with Bergson are also cited as part of the index for tracking the differences between Phenomenology of Perception and The Visible and the Invisible. What we see, according to this reading, is Merleau-Ponty move away from a more strictly phenomenological orientation of Phenomenology of Perception, an orientation that is said to adversely mediate his early, critical stance with respect to Bergson, toward a progressively less Husserlian and more Bergsonian stance in The Visible and the Invisible. While he does not specifically address Merleau-Ponty's engagement with Bergson, Marratto's reading also places a special emphasis on the significance of the past, specifically Merleau-Ponty's reference to a “past which has never been present”. It is also not my intention to enter into the question of Merleau-Ponty's relationship with Bergson. Rather, I will restrict my remarks specifically to Merleau-Ponty's engagement with Husserl and the Zeitbewußtsein in La temporalité in order to show that there are grounds for at least questioning one of the premises of the interpretation mentioned above, namely that Phenomenology of Perception is unequivocally legible as committed to the ontological primacy of the present. As will become clear later in the essay, I also dispute interpretations that would place the emphasis on the ontological primacy of an original past. For my own views on the significance of a “past which has never been present”, see Whitmoyer “The Primary Silence of the Past”. View all notes In considering the manner in which the Zeitbewußtsein figures in La temporalité and Merleau-Ponty's discussion of the field of presence, it will do to think about the parameters in which his engagement with Husserl is staged more generally. It seems that Merleau-Ponty never considered his task in terms of the perhaps false alternative of fidelity and heresy, because “any commemoration is also a betrayal”, and because the task of the interpreter is, as he famously notes, thinking through that “unthought-of element … which is wholly his [Husserl's] and yet opens out on something else”.88 Merleau-Ponty, Signes, 203/160. This methodological dictum is developed in more detail in the notes to the course offered on Husserl's Origin of Geometry in 1959–1960. “We are saying not that Husserl was that, but that Husserl was not only what they say, was also another, bearer of an unthought”. View all notes Following Merleau-Ponty's own indications, we could suggest that Husserl's text, rather than a source of orthodoxy, functions as a point of orientation through which Merleau-Ponty marks out his own theory of temporality.99 I will not, therefore, address the question of the “accuracy” of his interpretation of Husserl because, according to Merleau-Ponty himself, this question presupposes that the author, in this case Husserl, has a privileged access to his thought, as if there is some kernel or essence of what a philosopher thought that interpreters can either get right or wrong. As the remarks in “The Philosopher and His Shadow” make clear, interpretation can never really avail itself of this presupposition and in this manner the question of accuracy is precisely the wrong question. View all notes This essay argues that his discussion of the Zeitbewußtsein in Phenomenology of Perception does not offer an account of time that “centers around the living present”, as some have argued,1010 Al-Saji “A Past Which Has Never Been Present”, 42–44. View all notes but that the discussion of the field of presence and what follows are rather intended to account for the field of temporal phenomenalization – not as a presence – but as écoulement, passage and flux. Time, therefore, does not appear in the present or as presence, but manifests itself as a flow and movement that is simultaneously an éclatement, an eruption, and a self-differentiating “dehiscence”.1111 A favorite word of Merleau-Ponty, borrowed from botany, where it designates the splitting open of a seed-pod or flower as well as medicine, where it refers to the splitting open of a healed or partially healed wound. The idea here is that, in its flow and passage, time splits open in a process of differentiation – which is simultaneously a process of degeneration, decay, and what Merleau-Ponty will term in The Visible and the Invisible, “disarticulation”. View all notes Time's passage is not determined, organized and oriented in advance in accordance with a transcendental synthesis that would give it shape and form, privileging one temporal dimension over another, so much as it is understood in terms of a splitting open, or to use another favoured locution of Merleau-Ponty, a “deflagration”.1212 In Eye and Mind, Merleau-Ponty speaks of the “deflagration of being”. Metaphors of explosiveness and dissonance populate his attempt to think being otherwise than as structure, form, and stability. Here I will focus particularly on écoulement, flux and éclatement, eruption, because these are the terms he uses in his discussion of time in La temporalité. See Merleau-Ponty L’Œil et l'esprit, 64/369. View all notes To this extent, Merleau-Ponty's account of temporality in Phenomenology of Perception cannot be said to orient itself in terms of the ontological primacy of any one temporal dimension – past, present, or future – but is more accurately understood as an attempt to recover the primordial experience of time as the simultaneity of écoulement and éclatement – an account that thinks time in its dual power of phenomenalization and erosion, the “pulse [pulsation] of my existence, its systole and diastole”.1313 Merleau-Ponty PhP, 337/332. View all notes Time is the vehicle of the world's appearance, and at the same time of its “disarticulation” [désarticulation],1414 This is a term Merleau-Ponty uses in The Visible and the Invisible in a well-known working note entitled “ Transcendence – forgetting – time”. See Merleau-Ponty VI, 247/197. View all notes the vehicle through which “becoming” – rather than being – shows itself. This process of phenomenalization, precisely because it is temporal, never achieves the density of fully realized being – the sense of this becoming is never fully articulate – but is perpetually subject to a temporal erasure that necessitates its repetition and reiteration. Time, in other words, is the principle of the world's eloquence – it is that thanks to which things have and make sense and simultaneously the principle of the world's murmuring stutter, the principle through which the sense of things remains incomplete and even erodes, decays, and degenerates. To begin, I will turn to Merleau-Ponty's reading of Husserl's diagram from the Zeitbewußtsein, which opens his attempt to “arrive at authentic time”.1515 Merleau-Ponty PhP, 477/483. View all notes Rather than simply rehearsing Husserl's discussion of primal impression, retention and protention, Merleau-Ponty's analysis of the diagram provides an opportunity for raising two problems: the problem of time's representability and the problem of its synthesis. Rather than through an “act intentionality” carried out by a transcendental subjectivity, time appears in accordance with an “operative intentionality” always already under way. Turning to the section of La temporalité aptly entitled “Passive Synthesis”, we see that Merleau-Ponty's analysis of the diagram leads him to the paradox of passive synthesis and what he calls, following Husserl, “transition synthesis”. Time does not show itself punctually – time appears neither as presence nor in the present – but only in the dual movement of its flux, its écoulement, and its éclatement, its explosive, self-differentiating unfurling. These reflections, finally, bring Merleau-Ponty into dialogue with Heidegger on what the latter called the Zusammenhang des Lebens. The “unity of a life”, accordingly, is not a question of any “resolution”, but is a function of our immersion in this temporal dehiscence. The important lesson to be learned from Merleau-Ponty's engagement with Husserl's Zeitbewußtsein is not something about the ontological primacy of one temporal dimension over another but what Merleau-Ponty famously calls in The Visible and the Invisible the “passivity of our activity”1616 Merleau-Ponty VI, 270/221. View all notes and our immersion in time's power of disarticulation. (shrink)

When all sorts of material entities from atoms to people and from bacilli to stars are plotted on a scale of time and a scale of mass some very interesting alignments and symmetries emerge. It is observed that the data of the physical, biological, psychological, and social sciences form a neat isosceles triangle as shown in Figure 1 below. The facts are simple as graphed in Figure 1 on logarithmic scales; their explanation or interpretation is not apparent. Is Figure (...) 1 merely an interesting diagram useful in teaching the masses and evolutionary ages of the phenomena of various classes of science, or has it some more fundamental scientific significance? The graph will be first described and then its uncertainties and possible implications will be discussed. (shrink)

Neurons encode and transmit signals through chemical synaptic or electrical synaptic connections in the actual nervous system. Exploring the biophysical properties of coupling channels is of great significance for further understanding the rhythm transitions of neural network electrical activity patterns and preventing neurological diseases. From the perspective of biophysics, the activation of magnetic field coupling is the result of the continuous release and propagation of intracellular and extracellular ions, which is very similar to the activation of chemical synaptic coupling through (...) the continuous release of neurotransmitters. In this article, an induction coil is used to connect two HR neurons to stimulate the effect of magnetic field coupling. It is inevitable that time delays can affect the coupling process in the transmission of information, and it should be considered in the coupled model. Firstly, the firing characteristics and bifurcation modes of two coupled HR neurons are studied by using one parameter and two parameters bifurcation. With the increase of propagation delay and coupling gain, the chaotic state of neurons disappears and the high-period window decreases due to the influence of energy transfer between neurons. Then, the synchronization patterns of two HR neurons with different stimulation are analyzed by error diagrams and time series diagrams. It is confirmed that the synchronous pattern has certain regularity and is related not only to the neurons with large stimulation current but also to the time delay and coupling gain. The research conclusions of this article will provide the corresponding theoretical basis for medical experiments. (shrink)

Multimedia learning theories suggest presenting associated pieces of information in spatial and temporal contiguity. New technologies like Augmented Reality allow for realizing these principles in science laboratory courses by presenting virtual real-time information during hands-on experimentation. Spatial integration can be achieved by pinning virtual representations of measurement data to corresponding real components. In the present study, an Augmented Reality-based presentation format was realized via a head-mounted display and contrasted to a separate display, which provided a well-arranged data matrix in (...) spatial distance to the real components and was therefore expected to result in a spatial split-attention effect. Two groups of engineering students performed six experiments exploring fundamental laws of electric circuits. Cognitive load and conceptual knowledge acquisition were assessed as main outcome variables. In contrast to our hypotheses and previous findings, the Augmented Reality group did not report lower extraneous load and the separate display group showed higher learning gains. The pre- and posttest assessing conceptual knowledge were monitored by eye tracking. Results indicate that the condition affected the visual relevancy of circuit diagrams to final problem completion. The unexpected reverse effects could be traced back to emphasizing coherence formation processes regarding multiple measurements. (shrink)

Based on the existing financial system risk models, a set of time-lag financial system risk models is established considering the influence brought by time-lag factors on the financial risk system, and the dynamical behavior of this system is analyzed by using chaos theory. Through Matlab simulation, the bifurcation diagram and phase diagram of time-lag risk intensity and control intensity are plotted. The analysis shows that this kind of time-lag financial system risk model has complex dynamic behavior, (...) different motion states will appear when different parameter values are selected, and the time-lag risk intensity parameter also has a very strong influence on the system motion. To ensure the operation of the financial system in a stable state, measures with certain delay effects must be taken to control the risk and to choose the appropriate time-lag control intensity, and too much or too little time-lag control intensity is not conducive to the benign operation of the system. (shrink)

We propose a new relational direction in higher education that acknowledges external and internal images as integrated in thinking and learning. We expand educational theory and practice that commonly rely on discrete conceptual developments that exclude images. Our argument epistemologically relies on certain semiotic views that consider the role of iconic signs and iconicity (meaning making by the virtue of similarity) as significant in relation to knowledge and learning. The analogical and imaginative work required to discover similarity between external pictures (...) and any educational concept is a form of iconic mind work that opens a space for transformational thinking and creative solutions. The novelty of our argument lies in the schematic philosophy of mind by C.S. Peirce, and specifically, an adaptation of Peirce’s triadic sign diagram for learning, exemplified via an ‘inquiry graphic’ sign and reflective method. This outlook seeks connections in diversity, arguing for an education that acknowledges and teaches intrinsic human relatedness to other humans, beings and things in the environment, thus challenging any notions of anthropocentrism and superiority. It calls for a reaction in international higher education to acknowledge the iconicity of concepts and thinking and embrace integrated image-concept signs for deep and critical teaching-learning, towards a modest educational contribution to counteracting social and environmental crises. (shrink)

We propose a new relational direction in higher education that acknowledges external and internal images as integrated in thinking and learning. We expand educational theory and practice that commonly rely on discrete conceptual developments that exclude images. Our argument epistemologically relies on certain semiotic views that consider the role of iconic signs and iconicity (meaning making by the virtue of similarity) as significant in relation to knowledge and learning. The analogical and imaginative work required to discover similarity between external pictures (...) and any educational concept is a form of iconic mind work that opens a space for transformational thinking and creative solutions. The novelty of our argument lies in the schematic philosophy of mind by C.S. Peirce, and specifically, an adaptation of Peirce’s triadic sign diagram for learning, exemplified via an ‘inquiry graphic’ sign and reflective method. This outlook seeks connections in diversity, arguing for an education that acknowledges and teaches intrinsic human relatedness to other humans, beings and things in the environment, thus challenging any notions of anthropocentrism and superiority. It calls for a reaction in international higher education to acknowledge the iconicity of concepts and thinking and embrace integrated image-concept signs for deep and critical teaching-learning, towards a modest educational contribution to counteracting social and environmental crises. (shrink)

Toegye Yi Hwang is the most renowned Neo-Confucian thinker of Korea’s Joseon dynasty. The first three sections of this chapter describe his early life, the violent “literati purges” that preceded and extended tragically into his early career, and his career in office, from which he sought retirement only to be recalled repeatedly. The fourth section looks into the primary sources, the books from which he became steeped in the learning of the Cheng-Zhu school of Neo-Confucian thought. His own major written (...) works are briefly described. The fifth section is devoted to the most famous controversy in the history of Korean Neo-Confucian thought, the Four-Seven Debate, which originated between Toegye and a younger scholar, Gobong. This is followed by a section of description and analysis of the work that is considered his masterwork, the Ten Diagrams on Sage Learning. A brief conclusion sums up his contribution and imprint on Korean Neo-Confucian thought. (shrink)

A book review of 'Diagrams of Sensation: Deleuze and Aesthetics Pli,' by Darren Ambrose and Wahida Khandker, The Warwick Journal of Philosophy Volume 16 ISBN 1897646127.

This paper discusses the stability and Hopf bifurcation analysis of the diffusive Kaldor–Kalecki model with a delay included in both gross product and capital stock functions. The reaction-diffusion domain is considered, and the Galerkin analytical method is used to derive the system of ordinary differential equations. The methodology used to determine the Hopf bifurcation points is discussed in detail. Furthermore, full diagrams of the Hopf bifurcation regions considered in the stability analysis are shown, and some numerical simulations of the (...) limit cycle are used to confirm the theoretical outcomes. The delay investment parameter and diffusion coefficient can have great impacts on the Hopf bifurcations and stability of the business cycle model. The investment parameters for the gross product and capital stock as well as the adjustment coefficient of the production market are also studied. These parameters can cause instability in, and the stabilization of, the business cycle model. In addition, we point out that, as the delay investment parameter increases, the Hopf bifurcation points for the diffusion coefficient values decrease considerably. When the delay investment parameter has a very small value, the solution of the business cycle model tends to become steady. (shrink)

A new description of gravitational motion will be proposed. It is part of the proper time formulation of physics as presented on the IARD 2000 conference. According to this formulation the proper time of an object is taken as its fourth coordinate. As a consequence, one obtains a circular space–time diagram where distances are measured with the Euclidean metric. The relativistic factor turns out to be of simple goniometric origin. It further follows that the Lagrangian for gravitational (...) dynamics does not require an interpretation in terms of curvature of space–time. The flat space model for gravitational dynamics leads to the correct predictions for the bending of light, the perihelion shift of Mercury and gravitational red-shift. The new theory is free of singularities. More important, the new formulation of gravitational dynamics restores the validity of the principle of addition of potentials. One therefore can find solutions for static gravitational configurations for which it is difficult to find the solution of the corresponding Einstein equations. The method will be illustrated by means of the orbital precession for non-spherical stellar mass distributions. In case of the bipole mass distribution the agreement with the predictions of the general theory of relativity is very striking. Nevertheless, the new model is far more simple. (shrink)