According to the received view, the first spyglass was assembled without any theory of how the instrument magnifies. Galileo, who was the first to use the device as a scientific instrument, improved the power of magnification up to 30 times. How did he accomplish this feat? Galileo does not tell us what he did. We hold that such improvement of magnification is too intricate a problem to be solved by trial and error, accidentally stumbling upon a complex procedure. We construct (...) a plausibility argument and submit that Galileo had a theory of the telescope. He could develop it by analogical reasoning based on the phenomenon of reflection in mirrors—as it was put to use in surveying instruments—and applied to refraction in sets of lenses. Galileo could appeal to this analogy and assume Della Porta’s theory of refraction. He could thus turn the spyglass into a revolutionary scientific instrument—the telescope. (shrink)

In 1646, Francesco Fontana (1580–1656) published his Novae Coelestium Terresriumque Rerum Observationes which includes discussions of optical properties of systems of lenses, e.g., telescope and microscope. Our study of the Novae Coelestium shows that the advance Fontana made in optics could not have been accomplished on the basis of the traditional spectacle optics which was the dominant practice at his time. Though spectacle and telescope making share the same optical elements, improving eyesight and constructing telescope are different practices based on (...) different principles. The production of powerful astronomical telescopes demanded objective lenses with much longer focal length and eyepiece lenses with much shorter focal length than the range of focal length of lenses used for spectacles, respectively. Moreover, higher standard of precision and purity of the glass was required. The transition from the practice by which optical components were chosen from ready-made spectacle lenses to lenses which were produced according to predetermined specifications (e.g., calculation of focal length) was anything but straight forward. We argue that Fontana developed the optical knowledge necessary for improving the performance of optical systems. Essentially, he formulated—based on rich practical experience—a set of rules of calculation by which optical properties of a lens system could be determined and adjusted as required. (shrink)

This volume contains essays that examine the optical works of Giambattista Della Porta, an Italian natural philosopher during the Scientific Revolution. Coverage also explores the science and technology of early modern optics. Della Porta's groundbreaking book, Magia Naturalis, includes a prototype of the camera. Yet, because of his obsession with magic, Della Porta's scientific achievements are often forgotten. As the contributors argue, his work inspired such great minds as Johanes Kepler and Francis Bacon. After reading this book, researchers, historians, and (...) students will have a better appreciation of this influential scientist. They will also gain a greater understanding of an important period in the history of optics. Readers will learn about Della Porta's experimental method, a process governed by the protocols, aims, and theoretical assumptions of natural magic. Coverage also discusses the material properties and limitations of optical technology in the early 17th century, based on a recently discovered Dutch spyglass. It also demonstrates how diagrams were instrumental in the discovery of the sine law of refraction. In addition, the book includes an in-depth analysis of previously untranslated Latin sources. This makes the material useful to historians of optics unfamiliar with the language. More than 70 illustrations complement the text. (shrink)

: Scientific observation is determined by the human sensory system, which generally relies on instruments that serve as mediators between the world and the senses. Instruments came in the shape of Heron's Dioptra, Levi Ben Gerson's Cross-staff, Egnatio Danti's Torqvetto Astronomico, Tycho's Quadrant, Galileo's Geometric Military Compass, or Kepler's Ecliptic Instrument. At the beginning of the seventeenth century, however, it was unclear how an instrument such as the telescope could be employed to acquire new information and expand knowledge about the (...) world. To exploit the telescope as a device for astronomical observations Galileo had to: 1. establish that telescopic images are not optical defects, imperfections in the eye of the observer, or illusions caused by lenses; 2. develop procedures for systematically handling errors that may occur during observation and measurement and methods of processing data. Galileo made it clear that in order to measure and interpret natural phenomena accurately, a suitable method and instrument would need to be developed. It is intriguing, therefore, to regard the Galilean telescope in this light and to discover the linkage established by Galileo among theory, method, and instrument—the telescope. Although the telescope was not invented through science, it is instructive to see how Galileo used optics to employ a theory-laden instrument for bridging the gulf between picture and scientific language, between drawing and reporting physical facts, and between merely sketching the world and actually describing it. (shrink)

The claim that Galileo Galilei transformed the spyglass into an astronomical instrument has never been disputed and is considered a historical fact. However, the question what was the procedure which Galileo followed is moot, for he did not disclose his research method. On the traditional view, Galileo was guided by experience, more precisely, systematized experience, which was current among northern Italian artisans and men of science. In other words, it was a trial-and-error procedure—no theory was involved. A scientific analysis of (...) the optical properties of Galileo’s first improved spyglass shows that his procedure could not have been an informed extension of the traditional optics of spectacles. We argue that most likely Galileo realized that the objective and the eyepiece form a system and proceeded accordingly. (shrink)

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated , was (...) to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

Summary In his Theoremata de lumine, et umbre (1521), Francesco Maurolyco (1494–1575) discussed, inter alia, the problem of the pinhole camera. Maurolyco outlined a framework based on Euclidean geometry in which he applied the rectilinear propagation of light to the casting of shadow on a screen behind a pinhole. We limit our discussion to the problem of how the image behind an aperture is formed, and follow the way Maurolyco combined theory with instrument to solve the problem of the projection (...) of light through small apertures. We show that Maurolyco not only reformed the classical sources which, he thought, were no longer the authoritative code of textual knowledge, but also established with the dioptra a novel linkage of method, theory, and instrument. He thereby demonstrated the importance of optics to the science of astronomy. (shrink)

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated, was to (...) solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

"...A monográfia célja, hogy tanárképzésben és a tanártovábbképzésben résztvevők megismerkedjenek az intézményes és nem-intézményes nevelés aktuális és megoldandó feladataival, valamint a hazai és nemzetközi törekvésekkel ezen feladatok megoldására. A nemzetközi és összehasonlító megközelítésű kötet számos témája közé tartozik a nevelés (pedagógiai) antropológiai megközelítése, történeti-filozófiai előzményei, kapcsolódásai más tudományterületekkel, a nevelés stílusai, valamint a nevelő- és a tanulószerep." (@bookline.hu).

Rabbi Mattisyahu Salomon'sinfluence radiates far beyond his headquarters as Mashgiach of Lakewood's Beth Medrash Govoha. Thinker, speaker, guide, and inspirational leader, Rabbi Salomon has.

We give a geometric realization of space-time spinors and associated representations, using the Jordan triple structure associated with the Cartan factors of type 4, the so-called spin factors. We construct certain representations of the Lorentz group, which at the same time realize bosonic spin-1 and fermionic spin- $${\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-0em}\!\lower0.7ex\hbox{$2$}}$$ wave equations of relativistic field theory, showing some unexpected relations between various low-dimensional Lorentz representations. We include a geometrically and physically motivated introduction to Jordan triples and spin factors.

Contextualist scholars working on the rhetoric of corporeal presence in seventeenth-century English religious lyrics have naturally focused their attention on sacramental discourse of the Reformation era. As part of the Common Knowledge symposium on the future of contextualism, this full-length monograph, serialized in installments, argues that the contextualist focus on a single and time-limited “epistemic field” has resulted in a less than adequately ramified understanding of the poetry of John Donne, George Herbert, Aemilia Lanyer, and John Milton. What the contextualist (...) approach misses is that even the religious discourses of the period were tied to a long and in no way local epistemological debate about signs and their meaning, whose roots are to be found in Greek and Latin rhetorical theory. This first installment of “Tokens of Love” commences a discussion of the role of classical pagan sign-theory in the development of Reformation sacramental discourse. (shrink)

In the second installment of this contribution to the Common Knowledge symposium “Contextualism—the Next Generation,” Donne's religious poetry is set in dialogue not only with the “Great Controversy” of the 1560s over the nature of the eucharistic sign but also with pre-Christian semiotic discourses. From the perspective of contextualist scholarship, which recognizes in any temporal context a limited number of discourses available, Donne's religious poems of the period from about 1607 to 1620 register many contradictory conceptions, but contradictory only in (...) the sense that no contextualist map of religious identities allows for their miscibility or even collocation. Notoriously resistant to psychological and phenomenological interests, contextualism has no place for an early seventeenth-century Christian writer whose concern is less to join a school of thought on the Real Presence in the Eucharist than to dismiss the issue as vexingly trivial in comparison with the question of whether God thinks that each or any of us adequately loves him. For the questions that concern Donne, there are no determinate answers available, and no standard vocabulary. But the poet's alternating acquiescence in and fretfulness about indeterminacy and incomprehensibility constitute an intellectual and affective identity as much as does the attachment to any one or other more recognizable set of arguments and ways of framing them. (shrink)

The current study addresses how information whose processing was not part of task requirement is represented in memory. Using a novel measure, recognition memory for unattended material was assessed twice, once when it appeared with the same attended study target and once with a new target. The data reveal memory for unattended study information only in the old target condition. Results suggest that the entire study event is encoded and represented in a memory trace, which contains both attended target information (...) along with unattended context information. In conclusion, manifestation of unattended memory may be dependent on the presence of old target information at test. (shrink)

When two agents of unequal strength compete, the stronger one is expected to always win the competition. This expectation is based on the assumption that evaluation of performance is complete, hence flawless. If, however, the agents are evaluated on the basis of only a small sample of their performance, the weaker agent still stands a chance of winning occasionally. A theoretical analysis indicates that, to increase the chance of this happening the weaker agent ought to give up on enough occasions (...) so that he or she can match the stronger agent on the remaining ones. We model such a competition in a game, present its game‐theoretic solution, and report an experiment, involving 144 individuals, in which we tested whether players (both weak and strong) are actually sensitive to their relative strengths and know how to allocate their resources accordingly. Our results indicate that they do. (shrink)

The third and final installment of this book-length contribution to the Common Knowledge symposium “Contextualism—the Next Generation” treats two further writers in seventeenth-century England whose work is not representative of any stance or discourse that contextualist historians have recognized as available in that era. In Aemelia Lanyer's poetry, we find a resistance to established perspectives that is related to her sense that divine signification is always incomplete and that, therefore, the diffidence of female cognition is superior, when approaching religious texts, (...) to the assertive mentality that she associates with men. Despite his sex, however, and his reputation for theological and political radicalism, Milton too explicitly contends that the interpretation of scripture should always be “non-committal” because its signification is always incomplete. The “very magnitude” of the “great mystery” of the Incarnation, Milton argues in De Doctrina Christiana, should encourage the reader's mind to stand on “guard from the outset” against the tendency to make “rash or hasty assertions.” The urge to tamper with, pry into, add to, or hasten to understand the signifiers of divine meaning is shown, in Paradise Lost, to be the original sin of the first human couple. As much as for Lanyer, then, sex is for Milton bound up with hermeneutics—and, for both poets, the individual's relationship with God is a consuming passion, about which one may report a phenomenology of affects but can offer no contentions or arguments. (shrink)

Usually the Lorentz transformations are derived from the conservation of the spacetime interval. We propose here a way of obtaining spacetime transformations between two inertial frames directly from symmetry, the isotropy of the space and principle of relativity. The transformation is uniquely defined except for a constant e, that depends only on the process of synchronization of clocks inside each system. Relativistic velocity addition is obtained, and it is shown that the set of velocities is a bounded symmetric domain. If (...) e=0, Galilean transformations are obtained. If e>0, the speed 1/√e and a spacetime interval are conserved. By assuming constancy of the speed of light, we get e=1/c 2 and the transformation between the frames becomes the Lorentz transformation. If e<0, a proper speed and a Hilbertian norm are conserved. (shrink)

Jüdische Gelehrte reagierten auf Bruno Bauers antisemitisches Pamphlet Die Judenfrage (1842) auf ganz verschiedene Weise. Gemeinsam war allen Antworten jedoch die Annahme, dass die Mission des Judentums an Kultur und Humanität noch nicht erfüllt ist und auch nicht vom Christentum allein erfüllt werden kann. Nur der mosaische Monotheismus war dazu bestimmt, „den zivilisierten Nationen eine moralische Grundlage zu geben“, wie Gotthold Salomon, einer der in diesem Aufsatz behandelten Denker, gegen Bauer schrieb. Andere Disputanten, wie Hermann Jellinek, behaupteten sogar eine absolute (...) theologische Überlegenheit des Judentums gegenüber der halb-paganen christlichen Religion, wieder andere, wie der Luxemburger Oberrabbiner Samuel Hirsch, sahen im Judentum zumindest das bessere, das essentiellere Christentum. Keiner der jüdischen Gegner Bauers jedoch war mit dessen These einverstanden, dass es sich beim Judentum um ein überholtes Religionsmodell handelte, das nur noch künstlich von einigen halsstarrigen Traditionalisten am Leben gehalten wird. Ob die jüdischen Theologen Bauer als moralisch gefährlichen Atheisten oder eher als Hegelianischen Wiederbeleber der alten christlichen Substitutionslehre sahen, die hier besprochene öffentliche Debatte mit Bauer gab ihnen eine willkommene Gelegenheit – möglicherweise sogar zum allerersten Mal – den genauen Ort des Judentums innerhalb der Entwicklung der kulturellen Idee der Religion in der Weltgeschichte zu bestimmen. (shrink)