Decoding the Antikythera Mechanism
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Mathematical Discourse in Philosophical Authors: Examples from Theon of Smyrna and Cleomedes on Mathematical Astronomy
Mathematical discourse in philosophical authors: Examples from Theon of Smyrna and Cleomedes on mathematical astronomy Nathan Sidoli Introduction Ancient philosophers and other intellectuals often mention the work of mathematicians, al- though the latter rarely return the favor.1 The most obvious reason for this stems from the im- personal nature of mathematical discourse, which tends to eschew any discussion of personal, or lived, experience. There seems to be more at stake than this, however, because when math- ematicians do mention names they almost always belong to the small group of people who are known to us as mathematicians, or who are known to us through their mathematical works.2 In order to be accepted as a member of the group of mathematicians, one must not only have mastered various technical concepts and methods, but must also have learned how to express oneself in a stylized form of Greek prose that has often struck the uninitiated as peculiar.3 Be- cause of the specialized nature of this type of intellectual activity, in order to gain real mastery it was probably necessary to have studied it from youth, or to have had the time to apply oneself uninterruptedly.4 Hence, the private nature of ancient education meant that there were many educated individuals who had not mastered, or perhaps even been much exposed to, aspects of ancient mathematical thought and practice that we would regard as rather elementary (Cribiore 2001; Sidoli 2015). Starting from at least the late Hellenistic period, and especially during the Imperial and Late- Ancient periods, some authors sought to address this situation in a variety of different ways— such as discussing technical topics in more elementary modes, rewriting mathematical argu- ments so as to be intelligible to a broader audience, or incorporating mathematical material di- rectly into philosophical curricula. -
From Ancient Greece to Byzantium
Proceedings of the European Control Conference 2007 TuA07.4 Kos, Greece, July 2-5, 2007 Technology and Autonomous Mechanisms in the Mediterranean: From Ancient Greece to Byzantium K. P. Valavanis, G. J. Vachtsevanos, P. J. Antsaklis Abstract – The paper aims at presenting each period are then provided followed by technology and automation advances in the accomplishments in automatic control and the ancient Greek World, offering evidence that transition from the ancient Greek world to the Greco- feedback control as a discipline dates back more Roman era and the Byzantium. than twenty five centuries. II. CHRONOLOGICAL MAP OF SCIENCE & TECHNOLOGY I. INTRODUCTION It is worth noting that there was an initial phase of The paper objective is to present historical evidence imported influences in the development of ancient of achievements in science, technology and the Greek technology that reached the Greek states from making of automation in the ancient Greek world until the East (Persia, Babylon and Mesopotamia) and th the era of Byzantium and that the main driving force practiced by the Greeks up until the 6 century B.C. It behind Greek science [16] - [18] has been curiosity and was at the time of Thales of Miletus (circa 585 B.C.), desire for knowledge followed by the study of nature. when a very significant change occurred. A new and When focusing on the discipline of feedback control, exclusively Greek activity began to dominate any James Watt’s Flyball Governor (1769) may be inherited technology, called science. In subsequent considered as one of the earliest feedback control centuries, technology itself became more productive, devices of the modern era. -
The Geodetic Sciences in Byzantium
The geodetic sciences in Byzantium Dimitrios A. Rossikopoulos Department of Geodesy and Surveying, Aristotle University of Thessaloniki [email protected] Abstract: Many historians of science consider that geodeasia, a term used by Aristotle meaning "surveying", was not particularly flourishing in Byzantium. However, like “lo- gistiki” (practical arithmetic), it has never ceased to be taught, not only at public universi- ties and ecclesiastical schools, as well as by private tutors. Besides that these two fields had to do with problems of daily life, Byzantines considered them necessary prerequisite for someone who wished to study philosophy. So, they did not only confine themselves to copying and saving the ancient texts, but they also wrote new ones, where they were ana- lyzing their empirical discoveries and their technological achievements. This is the subject of this paper, a retrospect of the numerous manuscripts of the Byzantine period that refer to the development of geodesy both in teaching and practices of surveying, as well as to mat- ters relating to the views about the shape of the earth, the cartography, the positioning in travels and generally the sciences of mapping. Keywords: Geodesy, geodesy in Byzantium, history of geodesy, history of surveying, history of mathematics. Περίληψη: Πολλοί ιστορικοί των επιστημών θεωρούν ότι η γεωδαισία, όρος που χρησι- μοποίησε ο Αριστοτέλης για να ορίσει την πρακτική γεωμετρία, την τοπογραφία, δεν είχε ιδιαίτερη άνθιση στο Βυζάντιο. Ωστόσο, όπως και η “λογιστική”, δεν έπαψε ποτέ να διδά- σκεται όχι μόνο στα κοσμικά πανεπιστήμια, αλλά και στις εκκλησιαστικές σχολές, καθώς επίσης και από ιδιώτες δασκάλους. Πέρα από το ότι οι δύο αυτοί κλάδοι είχαν να κάνουν με προβλήματα της καθημερινής ζωής των ανθρώπων, οι βυζαντινοί θεωρούσαν την διδα- σκαλία τους απαραίτητη προϋπόθεση ώστε να μπορεί κανείς να παρακολουθήσει μαθήμα- τα φιλοσοφίας. -
The Magic of the Atwood Sphere
The magic of the Atwood Sphere Exactly a century ago, on June Dr. Jean-Michel Faidit 5, 1913, a “celestial sphere demon- Astronomical Society of France stration” by Professor Wallace W. Montpellier, France Atwood thrilled the populace of [email protected] Chicago. This machine, built to ac- commodate a dozen spectators, took up a concept popular in the eigh- teenth century: that of turning stel- lariums. The impact was consider- able. It sparked the genesis of modern planetariums, leading 10 years lat- er to an invention by Bauersfeld, engineer of the Zeiss Company, the Deutsche Museum in Munich. Since ancient times, mankind has sought to represent the sky and the stars. Two trends emerged. First, stars and constellations were easy, especially drawn on maps or globes. This was the case, for example, in Egypt with the Zodiac of Dendera or in the Greco-Ro- man world with the statue of Atlas support- ing the sky, like that of the Farnese Atlas at the National Archaeological Museum of Na- ples. But things were more complicated when it came to include the sun, moon, planets, and their apparent motions. Ingenious mecha- nisms were developed early as the Antiky- thera mechanism, found at the bottom of the Aegean Sea in 1900 and currently an exhibi- tion until July at the Conservatoire National des Arts et Métiers in Paris. During two millennia, the human mind and ingenuity worked constantly develop- ing and combining these two approaches us- ing a variety of media: astrolabes, quadrants, armillary spheres, astronomical clocks, co- pernican orreries and celestial globes, cul- minating with the famous Coronelli globes offered to Louis XIV. -
The Dark Shades of the Antikythera Mechanism
Journal of Radioanalytical and Nuclear Chemistry https://doi.org/10.1007/s10967-018-6255-9 (0123456789().,-volV)(0123456789().,-volV) The dark shades of the Antikythera Mechanism 1 2 3 Aristeidis Voulgaris • Christophoros Mouratidis • Andreas Vossinakis Received: 19 June 2018 Ó Akade´miai Kiado´, Budapest, Hungary 2018 Abstract In this work we analyze the dark shades which are evident on the AMRP X-ray positive Computed Tomographies and Radiographies of the Antikythera Mechanism ancient prototype. During 2000 years under the sea, the Mechanism bronze parts were totally corroded. The decreased X-ray absorption of the corroded bronze, allowed the CTs capture even in the thick large side of Fragment A. During the photometric analysis of the CTs, apart from corroded bronze, at least two other different (corroded) metal materials were detected, which were used by the ancient manufacturer during the construction of the Antikythera Mechanism. From our analysis and correlating with the mechanical evidence resulting by the use of our functional reconstruction models of the Antikythera Mechanism, we conclude that the existing design of the Antikythera Mechanism is probably the first of such a sophisticated design of the ancient manufacturer. Keywords Metals of Antikythera Mechanism Á Bronze corrosion Á Atacamite X-ray absorption Introduction Mechanism via the 2D X-ray and Thulium 170 radiation began by C. Karakalos of National Centre of Scientific The Antikythera Mechanism was found in 1901, in a Research ‘‘Demokritos’’ (Greece), in the 1970s. Karakalos shipwreck at 50 m depth, on a gulf of Antikythera island, took several film radiographies @160 keV [3]. The first Greece, by Symian sponge divers. -
Kytherian Newsletter November 2011
Page 888 The KYTHERIAN, NOVEMBER 2011 ANCIENT GREEK TECHNOLOGY: THE ANTIKYTHERA MECHANISM Dr Amelia R Brown looks at ancient technology, and how it's affected modern technology The last two decades are generally described as an era of technology, characterised by the rapid development and global distribution of new technologies, especially in relation to transportation, by land or by sea. The ancient Greeks, however, are often described as overly traditional when it comes to technology, as they did not achieve modern levels of industrialisation. However the Antikythera Mechanism has been influential in changing opinions about ancient technology, as it is the most sophisticated geared machine to survive from Antiquity: a veritable primitive computer. Before its discovery on a shipwreck off the island of Antikythera in 1900, the existence of devices like it was hardly dreamed of, and in recent years it has been subjected to a battery of modern tests, though it is surely hiding secrets still (see Marchant's Decoding the Heavens. Three things seem clear, however, about ancient Greek technology, and about the Antikythera Mechanism. First, the Greeks knew how to work in bronze to a very high level of sophistication. Second, the Antikythera Mechanism derives from a context related to the city of Corinth, the origin for the names of the months on its dials, and the Greek city most famous for its bronze work. Finally, the mechanism was created to fulfil a perceived need in Greek society of its time, surely through incremental developments in technology, and NOT necessarily to fulfil the 'needs' which we perceive in our society today and which can be fulfilled by our technology. -
Decoding the Antikythera Mechanism: Investigation of an Ancient Astronomical Calculator
Decoding the Antikythera Mechanism: Investigation of an Ancient Astronomical Calculator 2 Supplementary Notes T. Freeth 1,2 , Y. Bitsakis 3,5 , X. Moussas 3, J.H. Seiradakis 4, A.Tselikas 5, E. Magkou 6, M. Zafeiropoulou 6, R. Hadland 7, D. Bate 7, A. Ramsey 7, M. Allen 7, A. Crawley 7, P. Hockley 7, T. Malzbender 8, D. Gelb 8, W. Ambrisco 9 and M.G. Edmunds 1 1 Cardiff University, School of Physics andAstronomy, Queens Buildings, The Parade, Cardiff CF24 3AA, UK. Mike Edmunds Mike.Edmunds @ astro.cf.ac.uk 2 Images First Ltd10 HerefordRoad, South Ealing, London W5 4SE, UK. Tony Freeth tony @ images- first.com 3 National & Kapodistrian University of Athens, Department of Astrophysics, Astronomy andMechanics, Panepistimiopolis, GR15783, Zographos, Greece. Xenophon Moussas, xmoussas @ phys.uoa.gr 4 Aristotle University of Thessaloniki, Department of Physics, Section of Astrophysics, Astronomy and Mechanics, GR-54124 Thessaloniki, Greece. John Seiradakis jhs @ astro.auth.gr 5 Centre for History andPalaeography, National Bank of Greece Cultural Foundation, P. Skouze 3, 10560 Athens, Greece. Yanis Bitsakis bitsakis @ gmail.com 6 National Archaeological Museum of Athens, 44 Patission Str, 106 82 Athens, Greece. 7 X-Tek Systems Ltd, Tring Business Centre, IcknieldWay, Tring, Herts HP23 4JX, UK. 8 Hewlett-PackardLaboratories, 1501 Page Mill Road, Palo Alto, CA 94304, USA. 9 Foxhollow Technologies Inc., 740 Bay Road, RedwoodCity, CA 94063, USA. Decoding the Antikythera Mechanism , published in Nature, Volume 444, Issue 7119, pp. 587-591 (2006). 1 Supplementary Information Guide There are three Supplementary Information sections: Supplementary Notes 1 (Fragments ) giving a key to fragment identification for Figure 1 of the main text andthe dimensions of the fragments. -
Volgei Nescia: on the Paradox of Praising Women's Invisibility*
Matthew Roller Volgei nescia: On the Paradox of Praising Women’s Invisibility* A funerary plaque of travertine marble, originally from a tomb on the Via Nomentana outside of Rome and dating to the middle of the first century BCE, commemorates the butcher Lucius Aurelius Hermia, freedman of Lucius, and his wife Aurelia Philematio, likewise a freedman of Lucius. The rectangular plaque is divided into three panels of roughly equal width. The center panel bears a relief sculpture depicting a man and woman who stand and face one another; the woman raises the man’s right hand to her mouth and kisses it. The leftmost panel, adjacent to the male figure, is inscribed with a metrical text of two elegiac couplets. It represents the husband Aurelius’ words about his wife, who has predeceased him and is commemorated here. The rightmost panel, adjacent to the female figure, is likewise inscribed with a metrical text of three and one half elegiac couplets. It represents the wife Aurelia’s words: she speaks of her life and virtues in the past tense, as though from beyond the grave.1 The figures depicted in relief presumably represent the married individuals who are named and speak in the inscribed texts; the woman’s hand-kissing gesture seems to confirm this, as it represents a visual pun on the cognomen Philematio/Philematium, “little kiss.”2 This relief, now in the British Museum, is well known and has received extensive scholarly discussion.3 Here, I wish to focus on a single phrase in the text Aurelia is represented as speaking. -
Hermes and Dionysos at Olympia and the Antikythera Shipwreck
Hermes and Dionysos at Olympia and the Antikythera Shipwreck Since its discovery in 1877 at Olympia, the marble group of Hermes and baby Dionysos has generated controversy. Is the composition Classical, an original work by the fourth-century sculptor Praxiteles (according to Pausanias), is it a Hellenistic or later copy of his lost original, or is it a Roman statue with no connection to the Athenian sculptor ? Right now, the pendulum of opinion appears to be swinging back to the fourth-century scenario. This argument rests in part on the assumption that the sculpture is made of Parian marble, although no scientific testing has been done. According to Palagia, the work would then be fourth-century or early Hellenistic, because Parian marble was not used much at Olympia after this time, supporting the Praxitelean attribution. Furthermore Stewart has argued that the baby god resembles Classical parallels. There may be another approach to this problem. Hermes’ body, highly polished in front, was originally finished smooth but matte in back. The drapery cascading over the tree trunk on the god’s left side is plastically dimpled. A thick square strut connects the trunk to the figure’s left leg. The marble may be Parian. A look at marbles retrieved from the Antikythera shipwreck may provide clues to the origins of Hermes and Dionysos. Carved from Parian marble, statues preserving their original surface, like a crouching boy (Athens, NM inv. no. 2773) were highly polished in front, with a matte finish in back. Large square struts supported the boy’s pose. A drapery fragment from the wreck (Athens, NM inv. -
Pos(Antikythera & SKA)018
Building the Cosmos in the Antikythera Mechanism Tony Freeth1 Antikythera Mechanism Research Project 10 Hereford Road, South Ealing, London W54 4SE, United Kingdom E-mail: [email protected] PoS(Antikythera & SKA)018 Abstract Ever since its discovery by Greek sponge divers in 1901, the Antikythera Mechanism has inspired fascination and fierce debate. In the early years no-one knew what it was. As a result of a hundred years of research, particularly by Albert Rehm, Derek de Solla Price, Michael Wright and, most recently, by members of the Antikythera Mechanism Research Project, there has been huge progress in understanding this geared astronomical calculating machine. With its astonishing lunar anomaly mechanism, it emerges as a landmark in the history of technology and one of the true wonders of the ancient world. The latest model includes a mechanical representation of the Cosmos that exactly matches an inscription on the back cover of the instrument. We believe that we are now close to the complete machine. From Antikythera to the Square Kilometre Array: Lessons from the Ancients, Kerastari, Greece 12-15 June 2012 1 Speaker Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence. http://pos.sissa.it Building the Cosmos in the Antikythera Mechanism Tony Freeth 1. Ancient Astronomy Astronomy? Impossible to understand and madness to investigate... Sophocles Since astronomy is so difficult, I will try to keep everything as simple as possible! As all astronomers know well, the stars are fixed! When the ancients looked at the sky, they saw a number of astronomical bodies that moved relative to the stars. -
The Antikythera Mechanism, Rhodes, and Epeiros
The Antikythera Mechanism, Rhodes, and Epeiros Paul Iversen Introduction I am particularly honored to be asked to contribute to this Festschrift in honor of James Evans. For the last nine years I have been engaged in studying the Games Dial and the calendar on the Metonic Spiral of the Antikythera Mechanism,1 and in that time I have come to admire James’s willingness to look at all sides of the evidence, and the way in which he conducts his research in an atmosphere of collaborative and curious inquiry combined with mutual respect. It has long been suggested that the Antikythera Mechanism may have been built on the is- land of Rhodes,2 one of the few locations attested in ancient literary sources associated with the production of such celestial devices. This paper will strengthen the thesis of a Rhodian origin for the Mechanism by demonstrating that the as-of-2008-undeciphered set of games in Year 4 on the Games Dial were the Halieia of Rhodes, a relatively minor set of games that were, appro- priately for the Mechanism, in honor of the sun-god, Helios (spelled Halios by the Doric Greeks). This paper will also summarize an argument that the calendar on the Metonic Spiral cannot be that of Syracuse, and that it is, contrary to the assertions of a prominent scholar in Epirote stud- ies, consistent with the Epirote calendar. This, coupled with the appearance of the extremely minor Naan games on the Games Dial, suggests that the Mechanism also had some connection with Epeiros. The Games Dial and the Halieia of Rhodes The application in the fall of 2005 of micro-focus X-ray computed tomography on the 82 surviv- ing fragments of the Antikythera Mechanism led to the exciting discovery and subsequent publi- cation in 2008 of a dial on the Antikythera Mechanism listing various athletic games now known as the Olympiad Dial (but which I will call the Games or Halieiad Dial—more on that below), as well as a hitherto unknown Greek civil calendar on what is now called the Metonic Spiral.3 I begin with my own composite drawing of the Games Dial (Fig. -
The Draconic Gearing of the Antikythera Mechanism: Assembling the Fragment D, Its Role and Operation
The Draconic gearing of the Antikythera Mechanism: Assembling the Fragment D, its role and operation A.Voulgaris1, C.Mouratidis2, A.Vossinakis3, G.Bokovos4 (Submitted 14 January 2020) 1Municipality of Thessaloniki, Directorate Culture and Tourism, Thessaloniki, GR-54625, Greece 2Hellenic Ministry of Education, Research and Religious Affairs, Kos, GR-85300, Greece 3Thessaloniki Astronomy Club, Thessaloniki, GR-54646, Greece 4Thessaloniki Science Center and Technology Museum-Planetarium, Thermi, GR-57001, Greece Abstract The unplaced Fragment D of the Antikythera Mechanism with an unknown operation was a mystery since the beginning of its discovery. The gear-r1, which was detected on the Fragment radiographies by C. Karakalos, is preserved in excellent condition, but this was not enough to correlate it to the existing gear trainings of the Mechanism. The suggestion that this gear could be a part of the hypothetical planet indication gearing is still a hypothesis since no mechanical evidence has been preserved. After the analysis of AMRP tomographies of Fragment D and its mechanical characteristics revealed that it could be part of the Draconic gearing. Although the Draconic cycle was well known during the Mechanism’s era as represents the fourth Lunar cycle, it seems that it is missing from the Antikythera Mechanism. The study of Fragment D was supported by the bronze reconstruction of the Draconic gearing by the authors. The adaptation of the Draconic gearing on the Antikythera Mechanism improves its functionality and gives answers on several questions. 1. Introduction. The Antikythera Mechanism, a geared machine based on the lunar cycles The Antikythera Mechanism a creation of an ingenious manufacturer of the Hellenistic era was a geared machine capable of performing complex astronomical calculations, mostly based on the lunar periodic cycles.