The Antikythera Mechanism, the Oldest Known Astronomical Device and Mechanical Universe
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Plato As "Architectof Science"
Plato as "Architectof Science" LEONID ZHMUD ABSTRACT The figureof the cordialhost of the Academy,who invitedthe mostgifted math- ematiciansand cultivatedpure research, whose keen intellectwas able if not to solve the particularproblem then at least to show the methodfor its solution: this figureis quite familiarto studentsof Greekscience. But was the Academy as such a centerof scientificresearch, and did Plato really set for mathemati- cians and astronomersthe problemsthey shouldstudy and methodsthey should use? Oursources tell aboutPlato's friendship or at leastacquaintance with many brilliantmathematicians of his day (Theodorus,Archytas, Theaetetus), but they were neverhis pupils,rather vice versa- he learnedmuch from them and actively used this knowledgein developinghis philosophy.There is no reliableevidence that Eudoxus,Menaechmus, Dinostratus, Theudius, and others, whom many scholarsunite into the groupof so-called"Academic mathematicians," ever were his pupilsor close associates.Our analysis of therelevant passages (Eratosthenes' Platonicus, Sosigenes ap. Simplicius, Proclus' Catalogue of geometers, and Philodemus'History of the Academy,etc.) shows thatthe very tendencyof por- trayingPlato as the architectof sciencegoes back to the earlyAcademy and is bornout of interpretationsof his dialogues. I Plato's relationship to the exact sciences used to be one of the traditional problems in the history of ancient Greek science and philosophy.' From the nineteenth century on it was examined in various aspects, the most significant of which were the historical, philosophical and methodological. In the last century and at the beginning of this century attention was paid peredominantly, although not exclusively, to the first of these aspects, especially to the questions how great Plato's contribution to specific math- ematical research really was, and how reliable our sources are in ascrib- ing to him particular scientific discoveries. -
Alexander Jones Calendrica I: New Callippic Dates
ALEXANDER JONES CALENDRICA I: NEW CALLIPPIC DATES aus: Zeitschrift für Papyrologie und Epigraphik 129 (2000) 141–158 © Dr. Rudolf Habelt GmbH, Bonn 141 CALENDRICA I: NEW CALLIPPIC DATES 1. Introduction. Callippic dates are familiar to students of Greek chronology, even though up to the present they have been known to occur only in a single source, Ptolemy’s Almagest (c. A.D. 150).1 Ptolemy’s Callippic dates appear in the context of discussions of astronomical observations ranging from the early third century B.C. to the third quarter of the second century B.C. In the present article I will present new attestations of Callippic dates which extend the period of the known use of this system by almost two centuries, into the middle of the first century A.D. I also take the opportunity to attempt a fresh examination of what we can deduce about the Callippic calendar and its history, a topic that has lately been the subject of quite divergent treatments. The distinguishing mark of a Callippic date is the specification of the year by a numbered “period according to Callippus” and a year number within that period. Each Callippic period comprised 76 years, and year 1 of Callippic Period 1 began about midsummer of 330 B.C. It is an obvious, and very reasonable, supposition that this convention for counting years was instituted by Callippus, the fourth- century astronomer whose revisions of Eudoxus’ planetary theory are mentioned by Aristotle in Metaphysics Λ 1073b32–38, and who also is prominent among the authorities cited in astronomical weather calendars (parapegmata).2 The point of the cycles is that 76 years contain exactly four so-called Metonic cycles of 19 years. -
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. -
94 Erkka Maula
ORGANON 15 PROBLÊMES GENERAUX Erkka Maula (Finland) FROM TIME TO PLACE: THE PARADIGM CASE The world-order in philosophical cosmology can be founded upon time as well as .space. Perhaps the most fundamental question pertaining to any articulated world- view concerns, accordingly, their ontological and epistemological priority. Is the basic layer of notions characterized by temporal or by spatial concepts? Does a world-view in its development show tendencies toward the predominance of one set of concepts rather than the other? At the stage of its relative maturity, when the qualitative and comparative phases have paved the way for the formation of quantitative concepts: Which are considered more fundamental, measurements of time or measurements of space? In the comparative phase: Is the geometry of the world a geometry of motion or a geometry of timeless order? In the history of our own scientific world-view, there seems to be discernible an oscillation between time-oriented and space-oriented concept formation.1 In the dawn, when the first mathematical systems of astronomy and geography appear, shortly before Euclid's synthesis of the axiomatic thought, there were attempts at a geometry of motion. They are due to Archytas of Tarentum and Eudoxus of Cnidus, foreshadowed by Hippias of Elis and the Pythagoreans, who tend to intro- duce temporal concepts into geometry. Their most eloquent adversary is Plato, and after him the two alternative streams are often called the Heraclitean and the Parmenidean world-views. But also such later and far more articulated distinctions as those between the statical and dynamic cosmologies, or between the formalist and intuitionist philosophies of mathematics, can be traced down to the original Greek dichotomy, although additional concepts entangle the picture. -
Meet the Philosophers of Ancient Greece
Meet the Philosophers of Ancient Greece Everything You Always Wanted to Know About Ancient Greek Philosophy but didn’t Know Who to Ask Edited by Patricia F. O’Grady MEET THE PHILOSOPHERS OF ANCIENT GREECE Dedicated to the memory of Panagiotis, a humble man, who found pleasure when reading about the philosophers of Ancient Greece Meet the Philosophers of Ancient Greece Everything you always wanted to know about Ancient Greek philosophy but didn’t know who to ask Edited by PATRICIA F. O’GRADY Flinders University of South Australia © Patricia F. O’Grady 2005 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Patricia F. O’Grady has asserted her right under the Copyright, Designs and Patents Act, 1988, to be identi.ed as the editor of this work. Published by Ashgate Publishing Limited Ashgate Publishing Company Wey Court East Suite 420 Union Road 101 Cherry Street Farnham Burlington Surrey, GU9 7PT VT 05401-4405 England USA Ashgate website: http://www.ashgate.com British Library Cataloguing in Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask 1. Philosophy, Ancient 2. Philosophers – Greece 3. Greece – Intellectual life – To 146 B.C. I. O’Grady, Patricia F. 180 Library of Congress Cataloging-in-Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask / Patricia F. -
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. -
Mathematics and Cosmology in Plato's Timaeus
apeiron 2021; aop Andrew Gregory* Mathematics and Cosmology in Plato’s Timaeus https://doi.org/10.1515/apeiron-2020-0034 Published online March 18, 2021 Abstract: Plato used mathematics extensively in his account of the cosmos in the Timaeus, but as he did not use equations, but did use geometry, harmony and according to some, numerology, it has not been clear how or to what effect he used mathematics. This paper argues that the relationship between mathematics and cosmology is not atemporally evident and that Plato’s use of mathematics was an open and rational possibility in his context, though that sort of use of mathematics has subsequently been superseded as science has progressed. I argue that there is a philosophically and historically meaningful space between ‘primitive’ or unre- flective uses of mathematics and the modern conception of how mathematics relates to cosmology. Plato’s use of mathematics in the Timaeus enabled the cosmos to be as good as it could be, allowed the demiurge a rational choice (of which planetary orbits and which atomic shapes to instantiate) and allowed Timaeus to give an account of the cosmos (where if the demiurge did not have such a rational choice he would not have been able to do so). I also argue that within this space it is both meaningful and important to differentiate between Pythagorean and Platonic uses of number and that we need to reject the idea of ‘Pythagorean/ Platonic number mysticism’. Plato’s use of number in the Timaeus was not mystical even though it does not match modern usage. -
Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley
Arfstarchus of Samos and Graeco-Babylonian Astronomy Huxley, George Greek, Roman and Byzantine Studies; Summer 1964; 5, 2; ProQuest pg. 123 Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley N THE HALF CENTURY following the death of Alexander the Great the I history of astronomy amongst the Greeks is dominated by Aris tarchus the Samian, who is best known for his theory of the earth's revolution about the sun. His life cannot be dated exactly, but it is clear that he was already of mature age by 280 B.C., for Ptolemy states that "the men around Aristarchus," that is to say his pupils, observed the summer solstice in that year, the 50th of the first Callippic period [Ptolemy, Almagest 3.1]. He was a pupil of Strato the Lampsacene, who succeeded Theophrastus as head of the Lyceum in ca. 288/7 B.C. [Apollodorus 244 F 40] and remained in that post for eighteen years till his death not later than 269 B.C. [Apollodorus 244 F 350]. The date of the publication of Aristarchus's heliocentric theory is not known, but the doctrine was attacked by Cleanthes the Stoic land so must have been well known by 232 B.C., when Cleanthes died; but the helio centric hypothesis may have been formulated much earlier than that. Vitruvius spoke highly of the versatility of Aristarchus in geometry, astronomy, and music [De Architectura 1.1.16], and ascribes to him the invention of two kinds of sundial-the hemispherical uKac/>T} and the disc in the plane [9.8.1].2 He perhaps made use of these improved instruments in his observations of the solstices. -
The Antikythera Mechanism: the Ancient Computer That Mapped The
Sign In | Register Home Space The Antikythera Mechanism: the ancient Greek computer that mapped the stars Built over 2,000 years ago, the Antikythera mechanism calculated the movement of the Sun, Moon and planets using a system of dials and gears. 18th September, 2019 at 00:00 Imagine, in an age long before miniaturised electronics, a portable machine, the size and shape of a shoebox, that showed a moving picture of the cosmos, with the Sun, the Moon, and the planets orbiting at greatly accelerated speed, so that with a few twists of a knob, you could see where they would be in the sky on some chosen date years in the future or past. It sounds like something in a fantasy story, but the mysterious Antikythera Mechanism shows that these devices were indeed being built, over 2,000 years ago. Ad Try the Bike for 30 Days Exquisite devices like this were being crafted in a GTrey ethek w Bikorkesh forop 30 days, worry-free. somewhere in the eastern Mediterranean about 2,100 years ago or more. One of them met an unfortunate accident—for its owner, aLnEywARNay M, bOuRtE fortunate for us since from its shattered remains we can learn a great deal about ancient Greek science and its public face. The accident happened around 60 BC, off the island of Antikythera in the straits between Crete and the Peloponnese: a ship laden with bronze and marble statuary and other luxury objects, en route from the Aegean Sea to destinations in the western Mediterranean, was violently wrecked. ADVERTISING Replay inRead invented by Teads A team of Greek sponge divers discovered the shipwreck in 1900, and over the next year they salvaged what they could under the Greek government’s supervision.