Dioptrique Research Articles

Yves Le Grand on matrices in optics with application to vision: Translation and critical analysis

An appendix to Le Grand’s 1945 book, Optique Physiologique: Tome Premier: La Dioptrique de l’Œil et Sa Correction, briefly dealt with the application of matrices in optics. However the appendix was omitted from the well-known English translation, Physiological Optics, which appeared in 1980. Consequently the material is all but forgotten. This is unfortunate in view of the importance of the dioptric power matrix and the ray transference which entered the optometricliterature many years later. Motivated by the perception that there has not been enough care in optometry to attribute concepts appropriately this paper attempts a careful analysis of Le Grand’s thinking as reflected in his appendix. A translation into English is provided in the appendix to this paper. The paper opens with a summary of the basics of Gaussian and linear optics sufficient for the interpretation of Le Grand’s appendix which follows. The paper looks more particularly at what Le Grand says in relation to the transference and the dioptric power matrix though many other issues are also touched on including the conditions under which distant objects will map to clear images on the retina and, more particularly, to clear images that are undistorted. Detailed annotations of Le Grand’s translated appendix are provided. (S Afr Optom 2013 72(4) 145-166)

Jeu de Paume & Jeux de la Raison in Seventeenth-Century Optics

In La Dioptrique (1637) René Descartes elucidated his derivation of the sine law of refraction by means of a comparison of light rays with the motion of tennis balls. In terms of a mathematical-physical model this comparison was quite problematic, as his critics then and now did not hesitate to point out. However, they misread Descartes’ intention, which was to appeal in a clarifying way to the imagination of his readers in order to render his discoveries comprehensible. These readers were in the first place the circle of supporters around Constantijn Huygens. In his comparisons Descartes drew directly on the cultural meanings and the practice of tennis in the urban culture of the Dutch Republic. The tennis metaphor entered Descartes’ writing in this cultural setting, providing him with a clue to understanding the rainbow. Later, however, in the Météores it figured much less prominently than in La Dioptrique.

On the Conceptual and Civilization Frames in René Descartes’ Physical Works

The paper try to provide a contribution to the scientific—historiographic debate concerning the relations between experiments, metaphysics and mathematics in Descartes’ physics. The three works on which the analysis is focused are the Principia philosophiae and the two physical essays: La Dioptrique and Les Météores. The authors will highlight the profound methodological and epistemological differences characterizing, from one side, the Principia and, from the other side, the physical essays. Three significant examples will be dealt with: 1) the collision rules in the Principia philosophiae; 2) the refraction law in La Dioptrique; 3) the rainbow in Les Météores. In the final remarks these differences will be interpreted as depending upon the different role Descartes ascribed to the three books inside his whole work. The concepts of intensity and gradation of the physical quantities used by Descartes will provide an important interpretative means. In this paper, we compare the aprioristic approach to physics typical for Descartes’ Principia with the experimental and mathematical one characterizing Descartes’ Essays.

BECKETT’S : A POLYCENTRIC PARODIC PICTORIAL PARABLE FOR PERENNIAL PARADOXES

We put forth the proposition that Beckett's Film adroitly parodies Russell's paradox in order to call into question the normative claims of metaphysical posturing and to disrupt the prevalent philosophical paradigms. Film instantiates the pitfalls of dogmatic certainties by dint of humor, which the sole set that contains itself.At the epicenter of the design of Stephen Hawking's Grand Design there are grand epistemological and ontological conundrums, as evidenced by the questions Hawking poses right off the bat: How can we understand the world in which we find ourselves?, What the nature of reality? or Did the universe need a creator? (5). It a philosopher, Nietzsche, who first proclaimed the demise of (a shared belief in) God. It a scientist, Hawking, who embarks upon endeavor to answer the aforementioned questions by stipulating that only scientists be assigned this task, as (ontotheology would have been more precise in this context) is dead owing to the fact that it has not kept up with modem developments in science, particularly physics (5), and he arrives at the conclusion that the primum movens not God, but gravity (180). It a literary figure (erudite in both philosophy and science), Beckett, who accords emphasis to the fallacies inherent in the interpretations executed by the trifecta, namely philosophy, science and literature. We contend that Film the work wherein Beckett's humotopia, an immanent topos at one remove from immanence, with humor as its emergent property [...] whose contingent flux reflects the differentiated multiplicity which the resultant of the interactions between concretely existent human beings, attains its apogee (Tsakalakis, 7). We pursue the hypothesis that Beckett proffers a cinematic variation on Bertrand Russell's paradox, which pertains to the problematic character of the set of all sets that are not elements of themselves, inasmuch as a member of itself if and only if it's not a member of itself' (Gold- stein, 91). Beckett thereby stages a parodie game wherein the object/subject of the movie the self-perception of a bifurcated subject/object, which to say that the camera, qua a Panopticon, substantialized as active subject (E), whereas the assumed subject (O) both de-subjectified and objectified via intersubjective perception that occurs within a framework delimited by a concatenation of recursions.Beckett's atypical anti-ocularcentrim takes many shapes. Martin Jay explicates how the advent of perspective in art during the Renaissance, and the attendant denarrativation of the ocular (51), led to a rationalization of sight (49). Film sternly contradicts the naturalistic conventions of linear perspective; in the movie, the outlook may be perspectivist but the vision anything but perspectival insofar as depth perception rendered unattainable on account of O's (and E's) monocular vision; and the photographs eloquently narrate the adventures of /'/rational sight. Aside from the fact that Beckett specifies that the goings-on of the film take place in the period about 1929 (1967, 164), the year Un chien andalou was released, there may also be intertextual affinity between the opening scenes of the two short movies (see Brater, 76); yet Beckett does not slice through the eye as Bunuel and Dali, and also Descartes, while working on his La Dioptrique (Jay, 75) had done. Applicable to the point at issue Rudy Rucker's notion of the hypersphere, which he introduces in his exploration of spatial infinities: The reason that the two-dimensional surface of the Earth finite but unbounded that it bent, in three-dimensional space, into the shape of a sphere. In the same way, it possible to imagine the three-dimensional space of our universe as being bent, in some fourdimensional space, into the shape of a hypersphere (17). Rucker correctly indicates that the precursor of this concept a saying ascribed to Hermes Trismegistus: God intelligible sphere whose center everywhere and whose circumference nowhere (17). …

Huygens at work: Annotations in his rediscovered personal copy of Hooke's Micrographia

Summary It is well known that Hooke's wave theory of light, set forth in his Micrographia of 1665, is viewed as a step towards Huygens's famous theory of light. This view depends mostly on some short remarks given by Huygens in his Traite de la Lumi`ere (1690) and the earlier Projet du Contenu de la Dioptrique (1673). Huygens's personal copy of Micrographia was believed to be lost until found at Braunschweig (Brunswick) University Library by the author three years ago. It is annotated at Observ. IX (pp. 47–67) only, where Hooke deals with his wave theory of light and colours. This article provides a short review of Hooke's theory, and an interpretation of Huygens's annotations, which show clearly the first steps towards the opinions he was to express in his Traite de la lumi`ere, particularly methodological ones. Furthermore, a short comparison is here drawn with Huygens's annotations in his copy of Ango's L'optique divisee en trois livres, which show similar patterns of reasoning.

Representationalism, judgment and perception of distance: further to Yolton and McRae

The recent literature has seriously challenged, and in my view defeated, the traditional representationalist interpretation of Descartes. One contributor to it, John Yolton, has recently extended its arguments to argue that the traditional representationalist interpretation of Locke must be relinquished as well, that Locke, following the Cartesian path of Arnauld, held a semiotic theory of ideas which “de-ontologized” them and construed them as signs or cues in the direct perception of physical objects. The Cartesian support for this view, especially in La Dioptrique, has been questioned by R.F. McRae, who argues that “if Locke accepts Descartes' theory of vision, then Descartes' conception of sensations as signs provides no support for the direct realist interpretation of Locke.” My aim here is not to resolve the representationalism issue, but to show the irrelevance to it of the kinds of questions the Yolton-McRae exchange raises concerning sense perception. I shall try to show that there stems from Descartes a single account of those questions the essentials of which are embedded in theories falling on both sides of the representationalism issue. That single account involves a theory of judgment and vision, especially of distance, which in the case of Malebranche and Berkeley, even involves the same confusions.

Revisions of Descartes's Matter Theory in Le Monde

There are several differences between the theories of matter published by René Descartes in 1637 and 1644 which deserve attention. The differences follow from Descartes's well-known identification of substance with spatial extension, and his consequent rejection of the void. Since there was no void space, Descartes argued, a very finely divided subtle matter must extend throughout the universe in order to fill all space not otherwise occupied by the less finely divided ordinary matter. In the 1637 treatises La dioptrique and Les météores Descartes described only one kind of subtle matter, the primary function of which was to transmit the action of light. Yet when he came to write Principia philosophiae (1644), he believed that the subtle matter was divided into two separate elements. One of these remained an aether for light transmission, but the other had lost this property and was believed instead to be active in magnetic effects and in the electrification of glass, and to form part of the substance of flame.

Light, pressure, and rectilinear propagation: Descartes' celestial optics and Newton's hydrostatics

NEWTON’S early encounter with the Cartesian scientific corpus-La Dioptrique, La Glomtbie and Principia philosophiae’--left a permanent mark on his later scientific development. If Newton’s contemporaries interpreted his work largely as a rejection of the Cartesian system of philosophy, today we understand the Cartesian influence to have been so pervasive and complex that Newton could not overcome it simply by refuting it. We still recognize the ultimate rejection of the Cartesian system, but we also see the many Cartesian concepts which Newton accepted, further developed, and finally incorporated into his own work. Broadly speaking, we can characterize the Cartesian influence in the following way. While still an undergraduate Newton read Descartes’ scientific works and took from them primarily specific scientific concepts and techniques. We can, for example, see this in his optics, by his treatment of refraction from La Dioptrique; in his mathematics, by his researches in algebra, analytic geometry and calculus from La Ge’omt?trie; and in his mechanics, by his formulation of the law of inertia and calculation

Reproductions of Prints, Drawings, and Paintings of Interest in the History of Physics. 52. Frontispiece and Vignette from Chérubin's La dioptrique oculaire

Chérubin's La dioptrique oculaire (Paris 1671) is an unusually beautiful scientific work. The frontispiece and a vignette engraved by Edelinck are here reproduced and commented upon.