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Galileo's Search for the Laws of Fall
Phys. Perspect. 21 (2019) 194–221 Ó 2019 Springer Nature Switzerland AG 1422-6944/19/030194-28 https://doi.org/10.1007/s00016-019-00243-y Physics in Perspective What the Middle-Aged Galileo Told the Elderly Galileo: Galileo’s Search for the Laws of Fall Penha Maria Cardozo Dias, Mariana Faria Brito Francisquini, Carlos Eduardo Aguiar and Marta Feijo´ Barroso* Recent historiographic results in Galilean studies disclose the use of proportions, graphical representation of the kinematic variables (distance, time, speed), and the medieval double distance rule in Galileo’s reasoning; these have been characterized as Galileo’s ‘‘tools for thinking.’’ We assess the import of these ‘‘tools’’ in Galileo’s reasoning leading to the laws of fall (v2 / D and v / t). To this effect, a reconstruction of folio 152r shows that Galileo built proportions involving distance, time, and speed in uniform motions, and applied to them the double distance rule to obtain uniformly accelerated motions; the folio indicates that he tried to fit proportions in a graph. Analogously, an argument in Two New Sciences to the effect that an earlier proof of the law of fall started from an incorrect hypothesis (v µ D) can be recast in the language of proportions, using only the proof that v µ t and the hypothesis. Key words: Galileo Galilei; uniformly accelerated fall; double distance rule; theorem of the mean speed; kinematic proportions in uniform motions. Introduction Galileo Galilei stated the proof of the laws of fall in their finished form in the Two New Sciences,1 published in 1638, only a few years before his death in 1642, and shortly before turning 78. -
2-Minute Stories Galileo's World
OU Libraries National Weather Center Tower of Pisa light sculpture (Engineering) Galileo and Experiment 2-minute stories • Bringing worlds together: How does the story of • How did new instruments extend sensory from Galileo exhibit the story of OU? perception, facilitate new experiments, and Galileo and Universities (Great Reading Room) promote quantitative methods? • How do universities foster communities of Galileo and Kepler Galileo’s World: learning, preserve knowledge, and fuel • Who was Kepler, and why was a telescope Bringing Worlds Together innovation? named after him? Galileo in Popular Culture (Main floor) Copernicus and Meteorology Galileo’s World, an “Exhibition without Walls” at • What does Galileo mean today? • How has meteorology facilitated discovery in the University of Oklahoma in 2015-2017, will History of Science Collections other disciplines? bring worlds together. Galileo’s World will launch Music of the Spheres Galileo and Space Science in 21 galleries at 7 locations across OU’s three • What was it like to be a mathematician in an era • What was it like, following Kepler and Galileo, to campuses. The 2-minute stories contained in this when music and astronomy were sister explore the heavens? brochure are among the hundreds that will be sciences? Oklahomans and Aerospace explored in Galileo’s World, disclosing Galileo’s Compass • How has the science of Galileo shaped the story connections between Galileo’s world and the • What was it like to be an engineer in an era of of Oklahoma? world of OU during OU’s 125th anniversary. -
Galileo's Two New Sciences: Local Motion
b. Indeed, notice Galileo’s whole approach here: put forward a hypothesis, develop a mathe- matical theory yielding striking predictions that are amenable to quasi-qualitative tests! c. But the experiments were almost certainly too difficult to set up in a way that would yield meaningful results at the time G. Mersenne's Efforts and the Lacuna: 1633-1647 1. Mersenne, perhaps provoked by a remark in Galileo's Dialogue, sees a different way of bridging any lacuna in the evidence for claims about free-fall: measure the distance of fall in the first second -- in effect g/2 -- the constant of proportionality in s î t2 a. Galileo's remark: objects fall 4 cubits in first sec, which Mersenne knew to be way too small b. Galileo himself calls attention to a lacuna in the argument for the Postulate in the original edition of Two New Sciences [207] c. If stable value regardless of height, and if it yields reasonable results for total elapsed times, then direct evidence for claim that free fall uniformly accelerated 2. Fr. Marin Mersenne (1588-1648) a professor of natural philosophy at the University of Paris, a close friend of Gassendi and Descartes, and a long time correspondent and admirer of Galileo's a. Deeply committed to experimentation, and hence naturally tried to reproduce Galileo's exper- iments, as well as to conduct many further ones on his own, in the process discovering such things as the non-isochronism of circular pendula b. Relevant publications: Les Méchanique de Galilée (1634), Harmonie Universelle (1636), Les nouevelles pensées de Galilée (1639), Cogitata Physico-Mathematica, Phenomena Ballistica (1644), and Reflexiones Physico-Mathematica (1647) c. -
Galilei-1632 Dialogue Concerning the Two Chief World Systems
Galileo di Vincenzo Bonaulti de Galilei ([ɡaliˈlɛːo ɡaliˈlɛi]; 15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath, from Pisa. Galileo has been called the "father of observational astronomy", the "father of modern physics", the "father of the scientific method", and the "father of modern science". Galileo studied speed and velocity, gravity and free fall, the principle of relativity, inertia, projectile motion and also worked in applied science and technology, describing the properties of pendulums and "hydrostatic balances", inventing the thermoscope and various military compasses, and using the telescope for scientific observations of celestial objects. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the observation of the four largest satellites of Jupiter, the observation of Saturn's rings, and the analysis of sunspots. Galileo's championing of heliocentrism and Copernicanism was controversial during his lifetime, when most subscribed to geocentric models such as the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism because of the absence of an observed stellar parallax. The matter was investigated by the Roman Inquisition in 1615, which concluded that heliocentrism was "foolish and absurd in philosophy, and formally heretical since it explicitly contradicts in many places the sense of Holy Scripture". Galileo later defended his views in Dialogue Concerning the Two Chief World Systems (1632), which appeared to attack Pope Urban VIII and thus alienated him and the Jesuits, who had both supported Galileo up until this point. He was tried by the Inquisition, found "vehemently suspect of heresy", and forced to recant. -
Redalyc.The International Pendulum Project
Revista Electrónica de Investigación en Educación en Ciencias E-ISSN: 1850-6666 [email protected] Universidad Nacional del Centro de la Provincia de Buenos Aires Argentina Matthews, Michael R. The International Pendulum Project Revista Electrónica de Investigación en Educación en Ciencias, vol. 1, núm. 1, octubre, 2006, pp. 1-5 Universidad Nacional del Centro de la Provincia de Buenos Aires Buenos Aires, Argentina Available in: http://www.redalyc.org/articulo.oa?id=273320433002 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative Año 1 – Número 1 – Octubre de 2006 ISSN: en trámite The International Pendulum Project Michael R. Matthews [email protected] School of Education, University of New South Wales, Sydney 2052, Australia The Pendulum in Modern Science Galileo in his final great work, The Two New Sciences , written during the period of house arrest after the trial that, for many, marked the beginning of the Modern Age, wrote: We come now to the other questions, relating to pendulums, a subject which may appear to many exceedingly arid, especially to those philosophers who are continually occupied with the more profound questions of nature. Nevertheless, the problem is one which I do not scorn. I am encouraged by the example of Aristotle whom I admire especially because he did not fail to discuss every subject which he thought in any degree worthy of consideration. (Galileo 1638/1954, pp.94-95) This was the pendulum’s low-key introduction to the stage of modern science and modern society. -
A Phenomenology of Galileo's Experiments with Pendulums
BJHS, Page 1 of 35. f British Society for the History of Science 2009 doi:10.1017/S0007087409990033 A phenomenology of Galileo’s experiments with pendulums PAOLO PALMIERI* Abstract. The paper reports new findings about Galileo’s experiments with pendulums and discusses their significance in the context of Galileo’s writings. The methodology is based on a phenomenological approach to Galileo’s experiments, supported by computer modelling and close analysis of extant textual evidence. This methodology has allowed the author to shed light on some puzzles that Galileo’s experiments have created for scholars. The pendulum was crucial throughout Galileo’s career. Its properties, with which he was fascinated from very early in his career, especially concern time. A 1602 letter is the earliest surviving document in which Galileo discusses the hypothesis of pendulum isochronism.1 In this letter Galileo claims that all pendulums are isochronous, and that he has long been trying to demonstrate isochronism mechanically, but that so far he has been unable to succeed. From 1602 onwards Galileo referred to pendulum isochronism as an admirable property but failed to demonstrate it. The pendulum is the most open-ended of Galileo’s artefacts. After working on my reconstructed pendulums for some time, I became convinced that the pendulum had the potential to allow Galileo to break new ground. But I also realized that its elusive nature sometimes threatened to undermine the progress Galileo was making on other fronts. It is this ambivalent nature that, I thought, might prove invaluable in trying to understand crucial aspects of Galileo’s innovative methodology. -
ANNUAL REPORT 2010 11 a VISION for a BETTER FUTURE What Our Clients Are Saying
ANNUAL REPORT 2010 11 A VISION FOR A BETTER FUTURE What Our Clients Are Saying... Our community’s Financial Management System Certifi cation will support our reputation as an entrepreneurial Band... the community’s Financial Performance Certifi cation will prove that we have the systems in place and that those systems are working eff ectively and effi cient- “ly. Credibility in business and strong fi nancial support can only benefi t members, councillors, staff and the South Okanagan. Raising the bar as this process has been described, enhances the Osoyoos Indian Band’s reputation and credibility while providing the needed fi nancial support for continued growth and success in First Nations terms. Our Community wants access to longer term, lower interest fi nancing options that better match the large infrastructure projects that the Osoyoos Indian Band has been building and will be building over the next years... Multi-year fi nancial planning and longer term, lower interest rate fi nancing will allow the Band to manage and sustain their development as a more cohesive whole, rather than having more traditional lender preferences determine the development agenda. Katherine MacNeill, CMA OSOYOOS INDIAN BAND” Chief Financial Offi cer I believe that the combination of the FMB fi nancial certifi cation and the requirement to establishment a Financial Administration Law within a First Nation community will provide a solid foundation for those communities seeking to be part of the borrowing pool off ered “by the First Nation Financial Authority. Th is is the most promising opportunity that I have seen in a long time whereby a community can achieve its vision of a better future for its members—the possibility is very real and I am pleased to have been a part of the process to achieve fi nancial certifi cation for this community. -
Computational Intelligence in Communications and Business
Communications in Computer and Information Science 1406 Editorial Board Members Joaquim Filipe Polytechnic Institute of Setúbal, Setúbal, Portugal Ashish Ghosh Indian Statistical Institute, Kolkata, India Raquel Oliveira Prates Federal University of Minas Gerais (UFMG), Belo Horizonte, Brazil Lizhu Zhou Tsinghua University, Beijing, China More information about this series at http://www.springer.com/series/7899 Paramartha Dutta • Jyotsna K. Mandal • Somnath Mukhopadhyay (Eds.) Computational Intelligence in Communications and Business Analytics Third International Conference, CICBA 2021 Santiniketan, India, January 7–8, 2021 Revised Selected Papers 123 Editors Paramartha Dutta Jyotsna K. Mandal Visva-Bharati University University of Kalyani Santiniketan, India Kalyani, India Somnath Mukhopadhyay Assam University Silchar, India ISSN 1865-0929 ISSN 1865-0937 (electronic) Communications in Computer and Information Science ISBN 978-3-030-75528-7 ISBN 978-3-030-75529-4 (eBook) https://doi.org/10.1007/978-3-030-75529-4 © Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. -
15. Galileo and Aristotle on Motion. II
I. Aristotle's Theory. 15. Galileo and Aristotle on Motion. II. Galileo's Theory. I. Aristotle's Theory of Motion • Two basic principles: I. No motion without a mover in contact with moving body. II. Distinction between: (a) Natural motion: mover is internal to moving body (b) Forced motion: mover is external to moving body • Forced motion: - Non-natural (results in removal of object from its natural place). - Influenced by two factors: motive force F, and resistance of medium R. • Aristotle's "Law of Motion": V ∝ F/R, V = speed. Qualifications: - Assumes F > R. When F ≤ R, Aristotle says no motion occurs. - V represents speed, not velocity. Question: Which hits ground first: 1 lb ball or 10 lb ball? • Claim: Aristotle's "law" predicts 1 lb ball will take 10 times longer to fall than 10 lb ball. ! Let T = time required to travel a given distance. ! Assume: V ∝ 1/T (the greater the speed, the less the time of fall). ! Let V1 = speed of 1 lb ball, T1 = time for 1 lb ball to hit ground V2 = speed of 10 lb ball, T2 = time for 10 lb ball to hit ground. ! Then: V1/V2 = T2/T1. ! Or: F1/F2 = T2/T1 (V ∝ F). ! So: 1/10 = T2/T1 or T1 = 10T2. Projectile Motion • Big Problem: What maintains the motion of a projectile after it's left the thrower's hand? Antiparistasis ("mutual replacement"): • Medium is the required contact force. air flow • Medium flows around object to fill in space left behind. • Result: Object is pushed foward. Aristotle's Explanation: • Initial motive force transfers to the medium initially surrounding the power transfer object a "power" to act as a motive force. -
Excerpts from Galileo Galilei Dialogues Concerning Two New Sciences [1638]
Excerpts from Galileo Galilei Dialogues Concerning Two New Sciences [1638] THIRD DAY: CHANGE OF POSITION. [De Motu Locali] INTRODUCTION MY purpose is to set forth a very new science dealing with a very ancient subject. There is, in nature, perhaps nothing older than motion, concerning which the books written by philosophers are neither few nor small; nevertheless I have discovered by experiment some properties of it which are worth knowing and which have not hitherto been either observed or demonstrated. Some superficial observations have been made, as, for instance, that the free motion [naturalem motum] of a heavy falling body is continuously accelerated [Natural motion of the author has here been translated into free motionsince this is the term used to-day to distinguish the natural from the violent motions of the Renaissance]; but to just what extent this acceleration occurs has not yet been announced; for so far as I know, no one has yet pointed out that the distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity [A theorem demonstarted in the text]. It has been observed that missiles and projectiles describe a curved path of some sort; however no one has pointed out the fact that this path is a parabola. But this and other facts, not few in number or less worth knowing, I have succeeded in proving; and what I consider more important, there have been opened up to this vast and most excellent science, of which my work is merely the beginning, ways and means by which other minds more acute than mine will explore its remote corners. -
TWO NEW SCIENCESBY GALILEO ° O°
TWO NEW SCIENCESBY GALILEO °_o° THE MACMILLAN COMPANY _W YORJK• BOSTON• CItlCAGO• DALLAS ATLANTA• SANyP.ANCISCO MACMILLAN & CO., Lmrr_ LONDON• BOMBAY• CALCUTTA _T,_ OUP._NE T_L_; MACMILLAN CO. OF CANADA, LTD. TORONTO GALILEOGALILEI. Subterman'pors trait,paintedaboutI64O;nowin the Galler_dra ' Pittiat Florence. DIALOGUES CONCERNING TWO NEW SCIENCES BY GALILEOGALILEI Translatedfromthe Italianand Latin intoEnglishby HENRY CREWAND ALFONSODE SALVIO of Northwestern University WITH AN INTRODUCTION BY ANTONIOFAVARO of the University of Padua. "I think with your friend that it has been of late too much the mode to slight the learning of the ancients." Benjamin Franklin, Phil. Trans. 64,445.(I774.) N_ _ork THE MACMILLAN COMPANY I914 All rightsreserved COPX_IGBTX.914 B_ THEMACMILLANCOMPANY Set upande[ectrotyped. PublishedMay_I914. "La Dynamiqueest lasciencedesforcesaccN6ra- tricesor retardatriceset, des mouvemensvaries qu'ellesdoiventproduire.Cette scienceest due enti_rementauxmodernes,et Galileeest cduiqui denaadj.Iet_. zlzl,es premierfsondemens."LagrangeMec. TRANSLATORS' PREFACE OR morethana centuryEnglishspeaking studentshavebeenplacedin theanomalous positionof hearingGalileoconstantlyre- ferredto asthefounderofmodernphysical science,withouthavinganychanceto read, in theirownlanguagewhat, Galileohimself has to say. Archimedehass beenmade availablebyHeath;HuygensLight' hasbeen turnedinto Englishby Thompson,whileMotte has put the Principiaof Newtonbackintothe languagein whichit was conceived.To renderthe Physicsof Galileoalsoaccessibleto EnglishandAmericanstudentsis -
Dialogues Concerning Two New Sciences
BOUGHT WITH THE INCOME FROM THE SAGE ENDOWMENT FUND THE GIFT OF iienrs M. Sage 1891 ({MA0..±1.. ^iH"f. 3777 Cornell University Library QC 17.G15 Dialogues concerning two new sciences, 3 1924 012 322 701 TWO NEW SCIENCES BY GALILEO THE MACMILLAN COMPANY HEW YORK - BOSTON • CHICAGO - DALLAS ATLANTA • SAN FRANCISCO MACMILLAN & CO., Limited LONDON • BOMBAY • CALCUTTA MELBOURNE THE MACMILLAN CO. OF CANADA, Ltd. TORONTO Cornell University Library The original of tinis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924012322701 DIALOGUES CONCERNING TWO NEW SCIENCES BY GALILEO GALILEI Translated from the Italian and Latin into English by HENRY CREW AND ALFONSO DE SALVIO of Northwestern Uni\'ersity WITH AN INTRODUCTION BY ANTONIO FAVARO of the University of Padua. ' I think with vour friend that it has been of late too much the mode to slight the learning of the ancients." Benjamin FrankHn, Phil. Trans. (>4< 445- (1774) Nrm fnrk THE MACMILLAN COMPANY 1914 All rights reserved // Copyright, 1914 By the MACMILLAN COMPANY Set up and electrotyped. Published May, 1914- "La Dynamique est la science des forces accelera- trices or retardatrices, et des mouvemens vanes qu'elles doivent produire. Cette science est due entierement aux modernes, et Galilee est celui qui en a jete les premiers fondemens." Lagrange Mec. Anal. L 221. TRANSLATORS' PREFACE 30R more than a century English speaking students have been placed in the anomalous position of hearing Galileo constantly re- ferred to as the founder of modem physical science, without having any chance to read, in their own language, what Galileo himself has to say.