The relation (ratio) between humankind and infinity. The Logos.

RENÉ DESCARTES: UMA BIOGRAFIA -/- RENÉ DESCARTES: A BIOGRAPHY -/- Emanuel Isaque Cordeiro da Silva - CAP-UFPE, IFPE-BJ e UFRPE. E-mails: [email protected] e [email protected]. WhatsApp: (82)98143-8399. -/- -/- Nascido em 1596 em Haia, nas fronteiras de Touraine e Poitou, em uma família nobre, René Descartes vem ao mundo ao mesmo ano em que Johannes Kepler (1671-1630), em seu primeiro trabalho publicado (Mysterium cosmographicum), prova a superioridade da astronomia moderna (a de Nicolau Copérnico (1473-1543)) da astronomia antiga (a de Ptolomeu (90-168 (...) d.C.)). Ao mesmo tempo, Galileu Galilei (1564-1642), que detém a cadeira de matemática da Universidade de Pádua, funda o método experimental. As descobertas de Galileu tiveram forte impacto sobre o Colégio Real de La Fleche, realizado pelos jesuítas e onde Descartes recebeu, a partir de 1606, uma forte educação. Ele menciona, no Discurso do Método, seu “desejo extremo” em aprender, seguido, no final de seus estudos, de uma grande decepção: decepção com a filosofia ensinada, cujas controvérsias perpétuas revelam um caráter questionável, e que não pode fornecer um alicerce, em seu estado atual, para outras ciências. Também é proferido um desapontamento, mas esse desapontamento é inverso e diz respeito às matemática, capaz de fornecer esse fundamento que a filosofia não confere, mediante sua certeza e evidências, mas sobre o qual ainda não construímos nada. -/- -/- Numa Europa marcada pelo choque do tradicionalismo católico e do mercantilismo protestante, o lento declínio do poder espanhol e a luta dos Países Baixos pela sua independência, Descartes escolheu, primeiramente, após a graduação, a carreira militar. Engajado no exército do Príncipe Maurício de Nassau, ele é retirado da ociosidade da vida da guarnição pelo encontro, em 1618, de um jovem cientista holandês, Isaac Beeckman (1588-1637), que se tornou seu amigo íntimo por algum tempo. Conhecedor de todas as pesquisas científicas do momento e partidário da nova concepção “mecanicista” da natureza, Beeckman compartilhou com Descartes um entusiasmo que foi acompanhado, segundamente, da ambição de realizar a ciência universal por si mesma, mediante um método único: na noite de 10 de novembro de 1619, ele concebe em três “sonhos”, “os alicerces de uma ciência admirável”. -/- Nos anos seguintes a essa iluminação decisiva, Descartes viajou por toda a Europa, estimando, como Michel de Montaigne (1533-1592), que a demonstração de boas maneiras e costumes diferentes podem gerar muitos preconceitos. Toda sua vida, além disso, esteve vagando, isto é, foi marcada por múltiplas mudanças de residências, e a recusa de estabelecer um vínculo muito de perto com alguém. Foi na Holanda que ele, finalmente, buscará a tranquilidade que não encontrara na França ainda abalada pelas guerras religiosas, antes de ser assim pelas convulsões da Fronda. Todavia, mesmo na Holanda, ele não pôde evitar os ataques de calvinistas e polemicas teológicas que o repugnaram, como evidenciado em suas discussões com a Universidade de Utrecht entre 1643 à 1645 e a Universidade de Leiden em 1647. -/- -/- Além de sua amizade com Beeckman, outro encontro teve uma influência indubitavelmente decisiva sobre o destino de Descartes: o encontro com o cardeal de Bérulle. Fundador da congregação do Oratório (ao qual pertencem Nicolas Malebranche (1638-1715) e Jean-Baptiste Massillon (1663-1742)), o cardeal de Bérulle enxerga na nova física mecanicista, um meio de lutar contra o naturalismo resultante do Renascimento e seu paganismo latente: em uma longa entrevista com Descartes, no outono de 1647, ele fez dessa última uma obrigação de consciência para se dedicar, nesse sentido, à filosofia. -/- Em 1628, Descartes começa a escrever as Regras para a direção do espírito, um tratado inacabado e que não foi publicado durante a vida do autor. Em 1631, desenvolvera a geometria analítica que combina curvas geométricas com equações algébricas. Em 1633 escreveu O Tratado do Homem e preparava-se para publicar O Tratado do Mundo quando a notícia da condenação de Galileu Galilei pelo Santo Ofício (a Inquisição) o deixou receoso e decide, por prudência, não publicar o seu Tratado no qual a tese do movimento da Terra ao redor do Sol é apoiada. Alguns anos depois, foi divulgado em público cultivada de algumas de suas descobertas científicas: além da geometria, a dioptria (a teoria da refração da luz) e meteoros (teoria dos fenômenos atmosféricos luminosos). Esses três tratados aparecem no apêndice do Discurso do Método, e como “ensaios” desse método, em 1637. No século XIX, Victor Cousin (1792-1867) publicou pela primeira vez o Discurso sozinho, sem os ensaios. -/- Então vem a principal obra de Descartes no ramo da metafísica: as seis Meditações, aumentadas pelas objeções dos mais famosos filósofos da época (incluindo Thomas Hobbes (1588-1679), Antoine Arnauld (1612-1694) e Pierre Gassendi (1592-1655)), e as respostas a essas objeções, apareceram em 1641. Ansioso para expor sua filosofia para que pudesse ser ensinada, ele também a caracteriza em forma de manual com os Princípios da Filosofia de 1644. -/- Além dos trabalhos publicados, foi por meio das cartas trocadas com personalidades do mundo erudito que Descartes encontrou a oportunidade de esclarecer vários pontos de sua filosofia. Seus principais correspondentes foram o Prade Marin Mersenne (1588-1648), o Padre Denis Mesland (1615-1672), Pierre Chanut (1601-1662), Claude Clerselier (1614-1684), Christiaan Huygens (1629-1695) e Henry More (1614-1687). A partir de 1643, Descartes sustentou, com a Princesa Isabel da Boêmia (1596-1662), uma correspondência dedicada essencialmente a questões morais, que lhe permitiu a formulação de suas ideias nesse campo: esse esforço conduziu, em 1649, ao tratado das Paixões da alma. -/- Nesse mesmo ano, 1649, a Rainha Cristina da Suécia (1626-1689) o convida para ir a Estocolmo, que ele aceitou após muita hesitação. Recebido com todas as honras, mas forçado a um modo de vida bastantemente distinto daquele que era acostumado, e submetido a um clima do qual não se adequou, ele sucumbiu a pneumonia em fevereiro de 1650. -/- Descartes deixou-nos uma espécie de autobiografia intelectual na primeira parte do Discurso do Método: em seus anos de treinamento, seus entusiasmos e suas decepções. O discurso é, também, o primeiro livro para quem busca compreender o projeto filosófico cartesiano desde sua gênese até sua realização. Existem expostos, o método claro (na segunda parte), mas também a moral (terceira parte), a metafísica (quarta parte) e finalmente a física (quinta e sexta partes). (shrink)

The objective of this doctoral dissertation is to interpret the explanation of akrasia that the Dutch philosopher Benedictus Spinoza (1632-1677) gives in his work The Ethics. One is said to act acratically when one intentionally performs an action that one judges to be worse than another action which one believes one might perform instead. In order to interpret Spinoza’s explanation of akrasia, a large part of this dissertation investigates Spinoza’s theory of emotion. The first chapter is introductory and outlines Spinoza’s (...) categorisation of mental states and his conception of the relation between the mind and the body. The second chapter deals with Spinoza’s epistemology and the relation between cognitive mental states and states of the brain. The third chapter argues that Spinoza holds that emotions are non-cognitive mental states that are caused by cognitive mental states. The fourth chapter interprets Spinoza’s discussion of the emotions of Joy and Sadness insofar as they are mental states. The fifth chapter suggests that when Spinoza says that the power of our body is increased or decreased when we are joyful or sad, he means that when we are joyful or sad then, at the same time, our heart and perhaps the organs of our digestive system are affected in such a way that our bodily health is increased or decreased. The sixth chapter points to three problems that concern Spinoza’s definitions of the psychophysical states of pleasure, pain, cheerfulness and melancholy, and offers slightly altered definitions of these states. The seventh chapter interprets the various aspects of Spinoza’s conception of the emotion of Desire, both insofar as it is a state of the mind and insofar it is a state of the body, as well as the relation between the emotion of Desire and man’s striving for self-preservation. The eighth chapter discusses what Spinoza writes on the strength of emotions and the way in which we make value judgments in order to finally interpret why it is, according to Spinoza, that ‘we so often see the better for ourselves but follow the worse’. (shrink)

This article’s guiding thesis is that the theory of radical democratic citizenship is built on a tension between a radical, conflictual element and a democratic element. As radical democrats, these philosophers point to the intimate relation between conflict and both emancipation and democracy. But as radical democrats, they also propose different methods that prevent conflict from breaking up the polis—the common ground that makes democratic conflict possible. I look at two radical democrats’ way of dealing with this tension: Chantal Mouffe (...) and Étienne Balibar. My claim is that the former ends up overemphasising the danger of division in her later democratic works and is therefore unable to account for more intense forms of democratic resistance (such as riots). In the work of Balibar, however, we find a way of dealing with this tension. (shrink)

In response to critiques of rights as moralistic and depoliticising, a literature on the political nature and contestability of rights has emerged. In this view, rights are not merely formal, liberal and moralistic imperatives, but can also be invoked by the excluded in a struggle against domination. This article examines the limits to this practice of rights-claiming and its implication in forms of domination. It does this by returning to Marx’s blueprint for the critique of subjective rights. This engagement with (...) Marx will, however, take a particular form. I will read Marx first through the eyes of Claude Lefort and thereafter against Lefort. The latter’s critique of Marx still constitutes the strongest case against the dismissal of subjective rights. Introducing a reading of Lefort into the argument allows us to discover what is dead and what is well alive in the Marxist theory of rights. What is dead, I will argue, is Marx’s early conception of subjective rights as ideology and illusion. However, the more mature Marx developed a theory and critique of the legal form that is able to explain why the politics of rights—despite its undeniable advances—has not been able to overcome certain forms of domination. (shrink)

In an effort to inform the discussion surrounding existential risks from AI, we formulate Extinction-level Goodhart’s Law as “Virtually any goal specification, pursued to the extreme, will result in the extinction of humanity”, and we aim to understand which formal models are suitable for investigating this hypothesis. Note that we remain agnostic as to whether Extinction-level Goodhart’s Law holds or not. As our key contribution, we identify a set of conditions that are necessary for a model that aims to be (...) informative for evaluating specific arguments for Extinction-level Goodhart’s Law. Since each of the conditions seems to significantly contribute to the complexity of the resulting model, formally evaluating the hypothesis might be exceedingly difficult. This raises the possibility that whether the risk of extinction from artificial intelligence is real or not, the underlying dynamics might be invisible to current scientific methods. (shrink)

In this paper, we criticize the current focus of the bio-based economy (BBE) on efficiency and control and demonstrate the contradictions that this causes. We elucidate these tensions by comparing the BBE to alternative conceptions of economy that emphasise the relevance of both the human condition and unfathomable nature in the macro ecological transition project. From Emmanuel Levinas’s philosophy, we take and extrapolate two major concepts—il y a and enjoyment—that help to re-evaluate the status of both nature and the human (...) subject involved in environmental instability. From this analysis, we evaluate current economic practice in close relation to the deteriorating environment to contribute to a conception of an economy that is truly based on principles of the biosphere. We conclude that humankind and nature are notions that must be always considered in this encompassing and topical effort and explain how they have been fundamentally overlooked in current thought on the bio-based and circular economy. (shrink)

Proceedings of Philosophical Festival Drift 2014. Theme: Under Influence. Includes lectures by Katrien Schaubroeck, Philippe Descola, Markus Gabriel, Ray Brassier, Francesco Berto, Henk Oosterling, and Tomáš Sedlácek (among others). Lectures are in Dutch or English.

This paper explores the possibility of constructing a Cartesian space-time that can resolve the dilemma posed by a famous argument from Newton's early essay, De gravitatione. In particular, Huygens' concept of a center-of-mass reference frame is utilized in an attempt to reconcile Descartes' relationalist theory of space and motion with both the Cartesian analysis of bodily impact and conservation law for quantity of motion. After presenting a modern formulation of a Cartesian space-time employing Huygens' frames, a series of (...) Newtonian counter-replies are developed in order to estimate the viability of this relationalist project. (shrink)

I explain and assess here Huygens’ concept of relative motion. I show that it allows him to ground most of the Law of Inertia, and also to explain rotation. Thereby his concept obviates the need for Newton’s absolute space. Thus his account is a powerful foundation for mechanics, though not without some tension.

Článek se zabývá vybranými aspekty dvou známých publikací o mnohosti světů a mimozemském životě, které vyšly na konci 17. století. Jedná se o Entretiens sur la pluralité des mondes Bernarda de Fontenelle a Cosmotheoros Christiaana Huygense. V první části se článek soustředí především na to, jak oba autoři chápou postavení člověka v obydleném a neohraničeném univerzu. Fontenelle a Huygens poskytují ve svých textech přesvědčivé vyvrácení často opakované představy, že idea neohraničeného vesmíru probouzela v novověkých lidech hrůzu a obavy. Ve (...) skutečnosti pro ně neohraničený vesmír znamenal oslavu rozumu, který se dokáže vymanit z geocentrické pověry a antropocentrismu. Současně se v protoosvícenském duchu jednalo i o oslavu vesmírné všudypřítomnosti rozumu. Ve druhé části se článek zabývá tzv. kognitivními vášněmi: zejména strachem, úžasem a zvědavostí. Analýza děl Huygense a Fontenella potvrzuje některé poznatky Lorraine Dastonové a prohlubuje je. Ukazuje se, že na konci 17. století strach i obdiv byly již jednoznačně chápány jako projev nevědomosti a zaostalosti, ačkoliv dříve byly spojovány se zbožností a počátkem filosofování. Proti tomu dříve odsuzovaná zvědavost se stala legitimní, ba dokonce žádoucí vlastností opravdového badatele. (shrink)

This essay explores Kant’s concept of absolute space in the Metaphysical Foundations from the perspective of the development of the relationist interpretation of bodily interactions in the center-of-mass reference frame, a strategy that Huygens had originally pioneered and which Mach also endorsed. In contrast to the interpretations of Kant that stress a non-relationist, Newton-inspired orientation in his critical period work, it will be argued that the content and function of Kant’s utilization of this reference frame strategy places him much (...) closer to Huygens’ relationism than the absolute notions of space and motion favored by Newton and Euler. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Newton's Metaphysics: Essays by Eric SchliesserMarius StanEric Schliesser. Newton's Metaphysics: Essays. Oxford: Oxford University Press, 2021. Pp. 328. Hardback, $99.90.Newton owes his high regard to the quantitative science he left us, but his overall picture of the world had some robustly metaphysical threads woven in as well. Posthumous judgment about the value of these threads has varied wildly. Christian Wolff thought him a metaphysical rustic, as did Hans (...) Reichenbach some two centuries later ("Die Bewegungslehre bei Newton, Leibniz und Huygens," Kant-Studien 29 [1924]: 416–38). In the 1960s, the tide would turn, as Howard Stein and James Edward McGuire separately began to show that Newton's metaphysics was not just sophisticated, but often more compelling than its early modern alternatives (see respectively "Newtonian Spacetime," Texas Quarterly 10 [1967]: 174–200; and Tradition and Innovation: Newton's Metaphysics of Nature [Dordrecht: Kluwer Academic Publishers, 1995]). Eric Schliesser's book unfolds in that same register of appreciative, high scholarship, and it attests to the enduring attraction of its subject.The book grew out of previous discrete papers, to which he added a few more for this occasion. Accordingly, it does not come with a master argument. Rather, it is an in-depth exploration of some key metaphysical themes in Newton. As such, it befits its subject figure, who reflected on themes and concepts while stopping short of working out systems.The first major theme is Newton and Spinozism. The latter does not denote Spinoza's metaphysics. In fact, Schliesser explains, Newton shared with Spinoza some weighty commitments, for example, to space being actually infinite, and to substance monism: "for Newton, there is strictly speaking only one genuine substance," namely, God (33). Rather, "Spinozism" is an interpreter's category for a bundle of three theses: identifying God and nature; denying final causation in the physical world; and the assumption of "blind" metaphysical necessity. Some counted Hobbes and John Toland as Spinozist in this sense, and even Epicurus, avant la lettre. Newton and his followers argued vehemently against this package, as Schliesser shows in chapters 4, 5, and 8. Their chief complaint was that Spinozism is unable to account for the "origin of motion," for a certain type of order, and for the stability of cosmological structure—and to do so in a way that "meets the standards of Newtonian mechanics" (122). This interpretive lens allows Schliesser to draw Kant in, by reading his youthful Theory of Heaven as a possible Spinozist reply to their objections (chapter 3). [End Page 157]A second theme is the metaphysics of mechanics, where Schliesser weaves together several strands. One is the ontology of gravity, for which he offers a novel construal: for Newton, gravity counts as real, but in a qualified sense. Namely, it is not essential and not intrinsic: "even after creation, a lonely partless particle of matter in the universe would not be said to gravitate." And gravity is relational: a "shared quality" of two or more bits of matter, which obtains in virtue of their sharing a nature (19). Another strand is Newton's ontology of time—really, a subtle, difficult topic long neglected. Famously, Newton in Principia defends absolute, true, and mathematical time. The question is what these three qualifiers denote, and whether Newton thought they were synonymous. Schliesser in chapter 7 argues for the provocative view that "absolute" and "true" time are not identical concepts; rather, they pick out different entities. These entities share a common structure, namely, metric and topological. That makes them species of "mathematical" time (179). But, Schliesser contends, Newton has unequal warrant for his two concepts of time.Yet another theme is formal causation. It comes to the fore in chapter 5, which grapples with Newton's opaque idea that space is an "emanative effect." Schliesser explains that here, "emanation picks out a species of formal causation" (147), but in a novel, early modern sense that comes from Bacon, not Aristotle. If space has a formal cause, then so has its twin brother, time, the topic of chapter 7. God is their common formal cause. Then in chapter 6 (coauthored with Zvi Biener) Schliesser adds that, for Newton, laws... (shrink)

This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in the (...) sciences, Spinoza sided with those that criticized the aspirations of those (the physico-mathematicians, Galileo, Huygens, Wallis, Wren, etc) who thought the application of mathematics to nature was the way to make progress. In particular, he offers grounds for doubting their confidence in the significance of measurement as well as their piece-meal methodology (see section 2). Along the way, this chapter offers a new interpretation of common notions in the context of treating Spinoza’s account of motion (see section 3). (shrink)

Since the dawn of philosophy, the paradoxical interconnection between the continuous and the discrete plays a central rôle in attempts to understand the ontology of the world, while defying all attempts at consistent formulation. I investigate the relation between (classical) logic and concepts of “space” and “time” in physical and metaphysical theories, starting with the Greeks. An important part of my research consists in exploring the strong connections between paradoxes as they appear and are dealt with in ancient philosophy, and (...) their re-appearance in early modern natural philosophy, as well as in the foundations of contemporary science and mathematics. The way paradoxes are dealt with sheds light on a theory’s hidden metaphysical assumptions, especially with respect to matter, space, time and causation, it defines its ontological signature. This conclusion led me to the in-depth study of early modern natural philosophy, the origin of natural science, especially the influences ancient thinkers had on the new conceptions of space, time and causation developed by Newton, Huygens and Leibniz. (shrink)

This item is a chapter from a book in progress, entitled "True Motion". Leibniz’s mechanics was, as we shall see, a theory of elastic collisions, not formulated like Huygens’ in terms of rules explicitly covering every possible combination of relative masses and velocities, but in terms of three conservation principles, including (effectively) the conservation of momentum and kinetic energy. That is, he proposed what we now call (ironically enough) ‘Newtonian’ (or ‘classical’) elastic collision theory. While such a theory is, (...) for instance, vital to the foundations of the kinetic theory of gases, it is not applicable to systems – like gravitational systems – in which fields of force are present. Thus, Leibniz’s mechanical principles never led to developments of the order of Newton’s in the Principia (additionally, he hamstrung their application by embedding them in a baroque philosophical system). (shrink)

The roots of the problem of vis-viva or the living forces are potentially from the ancient Greek philosophy, more specifically Aristotle. He wanted to know, What is motion?, Why things move?, Is movement 'real' or 'not-real'?. Answer to this question never came until 16 th century. Philosophers and scientists such as Galileo, Descartes, Huygens, Leibniz, D'Alambert found an approach to this problem that seems rigorously to our observations. Even though, we do not know if that was the intention of (...) Aristotle? (shrink)

Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with (...) its main contributors: Archimedes, Cavalieri, Wallis, Hobbes, Pascal, Huygens, Bernoulli, and Nieuwentijt. Many of us know and probably have used the Leibnizian formula: to .. (shrink)

Alhazen problem of reflection at a concave spherical surface is one of the most discussed problems in optics. It was solved by Alhazen, The number of solution points vary from zero to a maximum of four. However, his solution is known to be prolix. Huygens solved the problem and identified the solution points to be points of intersection of the given circle and a hyperbola. Many other lines of attack were attempted with their solutions. New solutions are offered from (...) time to time. In this paper we offer a solution based on the criterion to be satisfied by reflection of a ray of light at a concave spherical surface. Based on that criterion we show that it is impossible for a circle containing both end points of the path of the ray inside it, to reflect rays from one point to the other. However, for every point on the given circle, we can construct two orthogonal circles (orthogonal conics in general) which reflect rays from one given point to the other, while the given circle is a non-reflector. (shrink)

Une présentation de la monographie de 1674 de Hooke présentant l'idée de la gravitation universelle est apparue dans Philosophical Transactions de 1674, et puis plusieurs lettres contenant des observations, dont celle de Huygens. Mais évidemment, après la publication du Principia en 1687, la priorité de Hooke dans la proposition de la gravitation universelle a été oubliée. Après avoir entendu parler de la demande de Hooke de reconnaître sa priorité, Newton a supprimé les nombreuses références à Hooke dans Principia. DOI: (...) 10.13140/RG.2.2.27734.40009. (shrink)

A presentation of Hooke’s 1674 monograph introducing the idea of universal gravity was included in the Philosophical Transactions (Royal Society 1775) and subsequently several letters containing observations, including one of Huygens. But obviously, after the publication of Principia in 1687, Hooke’s priority in proposing universal gravitation was forgotten. Hooke, considered as a “mechanical genius” rather than a scientist, was often at a social disadvantage to Newton, the noble theorist, or Huygens. Hooke’s inferior social status did not allow him (...) to identify with “free and unconfin’d” gentlemen such as Boyle, for example. DOI: 10.13140/RG.2.2.13746.45763. (shrink)

The philosopher René Descartes wrote the Compendium musicæ in 1618. Even though he was not known for his music production, he maintained a long correspondence around the subject in dialogue with Marin Mersenne, Constantjin Huygens, Isaac Beeckman and Joan-Albert Ban. However, his musical propositions appear as a marginal subject in his intellectual journey. To understand whether the musical theme relates to the development of his ideas, first, the organization of his correspondence about music and the citations to it in (...) his works was necessary, either in smaller texts or in the works published by the author. We analyzed the hypotheses about the forgetfulness of music in studies about the development of Descartes´ ideas. With these materials, we analyzed and historically contextualized the trajectory of the author's musical conceptions with the development of his main themes. Thus, it is possible to verify Descartes' musical dialogues with his own work and with his historical context. (shrink)

In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converg-ing series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz’s various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper answers the (...) question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world. (shrink)

Twenty-first century science faces a dilemma. Two of its well-verified foundation stones - relativity and quantum theory - have proven inconsistent. Resolution of the conflict has resisted improvements in experimental precision leaving some to believe that some fundamental understanding in our world-view may need modification or even radical reform. Employment of the wave-front model of electrodynamics, as a propagation process with a Markov property, may offer just such a clarification.