DOCSLIB.ORG

Antikythera Mechanism

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Antikythera Mechanism Timeline for Laws of Mathematics, Astronomy, Physics , and Newton's Parliamentary Procedure. Principia Watt's 1687 Steam Engine Lunar Earliest Archedemes 1778 Antikythera Copernicus Babylonian Pythagorus -249 Landing Mechanism 1543 1969 star catalogues -530 -87 -1200 Enuma Hipparchus Columbus Great Anu Euclid -155 1492 -300 Ptolemy Pyramid of Enlil Thales 129 Giza -650 -575 Gutenberg -2559 1903 1450 Wright Flyer -3000 -2500 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 Dark Age Industrial Golden Age Roman Rennaisance Revolution of Greece Republic Magna Fulk's Hammurabi Pericles Carta -1772 -462 1215 Written Montfort's Motions Parliament Robert's 2013 1265 Rules Rules written into rules of the British House of Commons 1876 -One subject should be discussed at a time (1581) U.S. -Personal attacks are to be avoided in debate (1604) Constitution -Debate must be limited to the merits of the question (1610) 1787 -Division of a question when some seem to be for one part but not the other (1640) We begin with the Great Pyramid of Giza to establish that the set (41 BC). Also, Cleopatra was closer to our time, today, than ancient Egyptians had some knowledge of geometry. It is worth Cleopatra was to the time when the Great Pyramid of Giza was built. noting that today is closer to Shakespeare’s time (1600), than In many respects, we is still part of the European Renaissance. […must Shakespeare’s time was to when his play Anthony and Cleopatra was insert footnote or paragraph on Arab contributions to all this.] The Saros cycle was apparently discovered by ancient Babylonians, calculations. Gutenberg’s invention was significant because it helped and can be used to predict lunar eclipses. The oldest known change the world, not because it solved challenging engineering Babylonian known star catalogues date back to 1200 BC. The Greek problems. Those who made the Antikythera Mechanism could easily astronomer Thales probably used Babylonian Enuma Anu Enlil tablets have invented Gutenberg’s press, had they considered the mass in to predict a solar eclipse. production of books to be important. Pythagoras, Euclid, Archimedes, Hipparchus, and Ptolemy were Copernicus proposal that the Sun was the center of the Solar famous ancient Greek thinkers. While Pythagoras did not invent the System was published after his death in 1543. Soon afterwards, Pythagorean theorem (a2+b2=c2), he or one of his colleagues Tycho and Kepler constructed mathematical formulas that tracked apparently discovered a proof of it. Euclid’s textbook on geometry the motion of the planets with greater precision than was achieved by serves as the basis for Euclidean Geometry we learn today, although Ptolemy. Meanwhile Galileo and Newton invented a successful effort Euclid’s emphasis was as much on construction using straight edge to find a simple mathematical model for the motion of all objects and compass as on rigorous “proof”. It has been speculated that under the force of gravity. Soon afterwards, Watt improved the Euclid postponed introduction his “5th Postulate” because he steam engine, as one of a countless number of small steps towards suspected that it could be proven, thus foreshadowing the industrialization. Then the Wright brothers constructed the first abandonment by that postulate in the 19th century non-Euclidean engine powered airplane, and two astronauts walked on the Moon. geometry that eventually evolved into Einstein’s Theory of General Relativity in 1916. Recent manuscripts suggest that Archimedes Had this pause in scientific progress not occurred, someone like developed mathematical methods often credited to Newton and Newton might have invented calculus and physics circa 400 AD. And Leibniz in order to solve problems typically associated with calculus. the engineering and scientific skills available to the ancient Greeks Hipparchus has been credited with discovering precession of the and Romans could easily have led to a person walking on the Moon equinoxes, and he probably relied heavily on prior efforts by the well before Columbus was born Babylonians. Hipparchus also developed what we now know as Virtually none of the Greco-Roman accomplishments occurred in a trigonometry. The Antikythera Mechanism was an intricate assembly political environment that resembles what we would call of 30 or more gears was used to predict the motion and eclipses of “democracy”. Nevertheless, it is clear that scientific and technical the Moon. Ptolemy used available data on planetary motion to make progress requires a nourishing environment. The Dark Ages and precise predictions of the motion of the planets. recent history both show how political disruption can stop progress. Then a European Dark Age interrupted progress. The scientific For this reason, progress in government and parliamentary procedure accomplishments are placed on an exponential curve, with a “pause” are also charted on the same timeline. It must be kept in mind that of zero growth between the years 400-1000 AD. We offer no metric for much of history, there has been little or no causal correlation by which scientific growth would follow such an exponential curve, or between advances in technology and progress towards pluralistic that the growth in Europe was at or near zero during the Dark Age. democracy. But it might be worth noting that there is something mundane about the two events marking the beginning and end of the Dark Age. The Antikythera Mechanism ‘s use of gears to describe the motion of the Moon seems more impressive than Ptolemy’s heroic but tedious .
Load more

Recommended publications
  • COPYRIGHT NOTICE: for COURSE PACK and Other PERMISSIONS
    COPYRIGHT NOTICE: Jean-Louis and Monique Tassoul: A Concise History of Solar and Stellar Physics is published by Princeton University Press and copyrighted, © 2004, by Princeton University Press. All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher, except for reading and browsing via the World Wide Web. Users are not permitted to mount this file on any network servers. For COURSE PACK and other PERMISSIONS, refer to entry on previous page. For more information, send e-mail to [email protected] Chapter One The Age of Myths and Speculations And God said, Let there be light, and there was light. —Genesis 1:3 For thousands of years men have looked up into the star-filled night sky and have wondered about the nature of the “fixed” stars as opposed to that of the five planets wandering among the constellations of the zodiac. The daily course of the sun, its brilliance and heat, and the passing of the seasons are among the central problems that have concerned every human society. Undoubtedly, the appearance of a comet or a shooting star, the passing phenomena of clouds and rain and lightning, the Milky Way, the changing phases of the moon and the eclipses—all of these must have caused quite a sense of wonder and been the source of endless discussions. Faced with this confusing multiplicity of brute facts, beyond their physical power to control, our ancestors sought to master these unrelated phenomena symbolically by picturing the universe in terms of objects familiar to them so as to make clear the unfamiliar and the unexplained.
    [Show full text]
  • Positional Notation Or Trigonometry [2, 13]
    The Greatest Mathematical Discovery? David H. Bailey∗ Jonathan M. Borweiny April 24, 2011 1 Introduction Question: What mathematical discovery more than 1500 years ago: • Is one of the greatest, if not the greatest, single discovery in the field of mathematics? • Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? • Was fiercely resisted in Europe for hundreds of years after its discovery? • Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, to- gether with the basic arithmetic computational schemes, which were discov- ered in India prior to 500 CE. ∗Bailey: Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Email: [email protected]. This work was supported by the Director, Office of Computational and Technology Research, Division of Mathematical, Information, and Computational Sciences of the U.S. Department of Energy, under contract number DE-AC02-05CH11231. yCentre for Computer Assisted Research Mathematics and its Applications (CARMA), University of Newcastle, Callaghan, NSW 2308, Australia. Email: [email protected]. 1 2 Why? As the 19th century mathematician Pierre-Simon Laplace explained: It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very sim- plicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appre- ciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.
    [Show full text]
  • Canada Archives Canada Published Heritage Direction Du Branch Patrimoine De I'edition
    Rhetoric more geometrico in Proclus' Elements of Theology and Boethius' De Hebdomadibus A Thesis submitted in Candidacy for the Degree of Master of Arts in Philosophy Institute for Christian Studies Toronto, Ontario By Carlos R. Bovell November 2007 Library and Bibliotheque et 1*1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A0N4 Ottawa ON K1A0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-43117-7 Our file Notre reference ISBN: 978-0-494-43117-7 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par Plntemet, prefer, telecommunication or on the Internet, distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, electronique commercial purposes, in microform, et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in et des droits moraux qui protege cette these. this thesis. Neither the thesis Ni la these ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent etre imprimes ou autrement may be printed or otherwise reproduits sans son autorisation. reproduced without the author's permission.
    [Show full text]
  • Archimedes' Principle
    General Physics Lab Handbook by D.D.Venable, A.P.Batra, T.Hubsch, D.Walton & M.Kamal Archimedes’ Principle 1. Theory We are aware that some objects oat on some uids, submerged to diering extents: ice cubes oat in water almost completely submerged, while corks oat almost completely on the surface. Even the objects that sink appear to weigh less when they are submerged in the uid than when they are not. These eects are due to the existence of an upward ‘buoyant force’ that will act on the submerged object. This force is caused by the pressure in the uid being increased with depth below the surface, so that the pressure near the bottom of the object is greater than the pressure near the top. The dierence of these pressures results in the eective ‘buoyant force’, which is described by the Archimedes’ principle. According to this principle, the buoyant force FB on an object completely or partially submerged in a uid is equal to the weight of the uid that the (submerged part of the) object displaces: FB = mf g = f Vg . (1) where f is the density of the uid, mf and V are respectively mass and the volume of the displaced uid (which is equal to the volume of the submerged part of the object) and g is the gravitational acceleration constant. 2. Experiment Object: Use Archimedes’ principle to measure the densities of a given solid and a provided liquid. Apparatus: Solid (metal) and liquid (oil) samples, beaker, thread, balance, weights, stand, micrometer, calipers, PASCO Science Workshop Interface, Force Sensors and a Macintosh Computer.
    [Show full text]
  • Great Inventors of the Ancient World Preliminary Syllabus & Course Outline
    CLA 46 Dr. Patrick Hunt Spring Quarter 2014 Stanford Continuing Studies http://www.patrickhunt.net Great Inventors Of the Ancient World Preliminary Syllabus & Course Outline A Note from the Instructor: Homo faber is a Latin description of humans as makers. Human technology has been a long process of adapting to circumstances with ingenuity, and while there has been gradual progress, sometimes technology takes a downturn when literacy and numeracy are lost over time or when humans forget how to maintain or make things work due to cataclysmic change. Reconstructing ancient technology is at times a reminder that progress is not always guaranteed, as when Classical civilization crumbled in the West, but the history of technology is a fascinating one. Global revolutions in technology occur in cycles, often when necessity pushes great minds to innovate or adapt existing tools, as happened when humans first started using stone tools and gradually improved them, often incrementally, over tens of thousands of years. In this third course examining the greats of the ancient world, we take a close look at inventions and their inventors (some of whom might be more legendary than actually known), such as vizier Imhotep of early dynastic Egypt, who is said to have built the first pyramid, and King Gudea of Lagash, who is credited with developing the Mesopotamian irrigation canals. Other somewhat better-known figures are Glaucus of Chios, a metallurgist sculptor who possibly invented welding; pioneering astronomer Aristarchus of Samos; engineering genius Archimedes of Siracusa; Hipparchus of Rhodes, who made celestial globes depicting the stars; Ctesibius of Alexandria, who invented hydraulic water organs; and Hero of Alexandria, who made steam engines.
    [Show full text]
  • Squaring the Circle a Case Study in the History of Mathematics the Problem
    Squaring the Circle A Case Study in the History of Mathematics The Problem Using only a compass and straightedge, construct for any given circle, a square with the same area as the circle. The general problem of constructing a square with the same area as a given figure is known as the Quadrature of that figure. So, we seek a quadrature of the circle. The Answer It has been known since 1822 that the quadrature of a circle with straightedge and compass is impossible. Notes: First of all we are not saying that a square of equal area does not exist. If the circle has area A, then a square with side √A clearly has the same area. Secondly, we are not saying that a quadrature of a circle is impossible, since it is possible, but not under the restriction of using only a straightedge and compass. Precursors It has been written, in many places, that the quadrature problem appears in one of the earliest extant mathematical sources, the Rhind Papyrus (~ 1650 B.C.). This is not really an accurate statement. If one means by the “quadrature of the circle” simply a quadrature by any means, then one is just asking for the determination of the area of a circle. This problem does appear in the Rhind Papyrus, but I consider it as just a precursor to the construction problem we are examining. The Rhind Papyrus The papyrus was found in Thebes (Luxor) in the ruins of a small building near the Ramesseum.1 It was purchased in 1858 in Egypt by the Scottish Egyptologist A.
    [Show full text]
  • 15 Famous Greek Mathematicians and Their Contributions 1. Euclid
    15 Famous Greek Mathematicians and Their Contributions 1. Euclid He was also known as Euclid of Alexandria and referred as the father of geometry deduced the Euclidean geometry. The name has it all, which in Greek means “renowned, glorious”. He worked his entire life in the field of mathematics and made revolutionary contributions to geometry. 2. Pythagoras The famous ‘Pythagoras theorem’, yes the same one we have struggled through in our childhood during our challenging math classes. This genius achieved in his contributions in mathematics and become the father of the theorem of Pythagoras. Born is Samos, Greece and fled off to Egypt and maybe India. This great mathematician is most prominently known for, what else but, for his Pythagoras theorem. 3. Archimedes Archimedes is yet another great talent from the land of the Greek. He thrived for gaining knowledge in mathematical education and made various contributions. He is best known for antiquity and the invention of compound pulleys and screw pump. 4. Thales of Miletus He was the first individual to whom a mathematical discovery was attributed. He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry. 5. Aristotle Aristotle had a diverse knowledge over various areas including mathematics, geology, physics, metaphysics, biology, medicine and psychology. He was a pupil of Plato therefore it’s not a surprise that he had a vast knowledge and made contributions towards Platonism. Tutored Alexander the Great and established a library which aided in the production of hundreds of books.
    [Show full text]
  • Theon of Alexandria and Hypatia
    CREATIVE MATH. 12 (2003), 111 - 115 Theon of Alexandria and Hypatia Michael Lambrou Abstract. In this paper we present the story of the most famous ancient female math- ematician, Hypatia, and her father Theon of Alexandria. The mathematician and philosopher Hypatia flourished in Alexandria from the second part of the 4th century until her violent death incurred by a mob in 415. She was the daughter of Theon of Alexandria, a math- ematician and astronomer, who flourished in Alexandria during the second part of the fourth century. Information on Theon’s life is only brief, coming mainly from a note in the Suda (Suida’s Lexicon, written about 1000 AD) stating that he lived in Alexandria in the times of Theodosius I (who reigned AD 379-395) and taught at the Museum. He is, in fact, the Museum’s last attested member. Descriptions of two eclipses he observed in Alexandria included in his commentary to Ptolemy’s Mathematical Syntaxis (Almagest) and elsewhere have been dated as the eclipses that occurred in AD 364, which is consistent with Suda. Although originality in Theon’s works cannot be claimed, he was certainly immensely influential in the preservation, dissemination and editing of clas- sic texts of previous generations. Indeed, with the exception of Vaticanus Graecus 190 all surviving Greek manuscripts of Euclid’s Elements stem from Theon’s edition. A comparison to Vaticanus Graecus 190 reveals that Theon did not actually change the mathematical content of the Elements except in minor points, but rather re-wrote it in Koini and in a form more suitable for the students he taught (some manuscripts refer to Theon’s sinousiai).
    [Show full text]
  • 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.
    [Show full text]
  • Chapter Two Democritus and the Different Limits to Divisibility
    CHAPTER TWO DEMOCRITUS AND THE DIFFERENT LIMITS TO DIVISIBILITY § 0. Introduction In the previous chapter I tried to give an extensive analysis of the reasoning in and behind the first arguments in the history of philosophy in which problems of continuity and infinite divisibility emerged. The impact of these arguments must have been enormous. Designed to show that rationally speaking one was better off with an Eleatic universe without plurality and without motion, Zeno’s paradoxes were a challenge to everyone who wanted to salvage at least those two basic features of the world of common sense. On the other hand, sceptics, for whatever reason weary of common sense, could employ Zeno-style arguments to keep up the pressure. The most notable representative of the latter group is Gorgias, who in his book On not-being or On nature referred to ‘Zeno’s argument’, presumably in a demonstration that what is without body and does not have parts, is not. It is possible that this followed an earlier argument of his that whatever is one, must be without body.1 We recognize here what Aristotle calls Zeno’s principle, that what does not have bulk or size, is not. Also in the following we meet familiar Zenonian themes: Further, if it moves and shifts [as] one, what is, is divided, not being continuous, and there [it is] not something. Hence, if it moves everywhere, it is divided everywhere. But if that is the case, then everywhere it is not. For it is there deprived of being, he says, where it is divided, instead of ‘void’ using ‘being divided’.2 Gorgias is talking here about the situation that there is motion within what is.
    [Show full text]
  • Can One Design a Geometry Engine? on the (Un) Decidability of Affine
    Noname manuscript No. (will be inserted by the editor) Can one design a geometry engine? On the (un)decidability of certain affine Euclidean geometries Johann A. Makowsky Received: June 4, 2018/ Accepted: date Abstract We survey the status of decidabilty of the consequence relation in various ax- iomatizations of Euclidean geometry. We draw attention to a widely overlooked result by Martin Ziegler from 1980, which proves Tarski’s conjecture on the undecidability of finitely axiomatizable theories of fields. We elaborate on how to use Ziegler’s theorem to show that the consequence relations for the first order theory of the Hilbert plane and the Euclidean plane are undecidable. As new results we add: (A) The first order consequence relations for Wu’s orthogonal and metric geometries (Wen- Ts¨un Wu, 1984), and for the axiomatization of Origami geometry (J. Justin 1986, H. Huzita 1991) are undecidable. It was already known that the universal theory of Hilbert planes and Wu’s orthogonal geom- etry is decidable. We show here using elementary model theoretic tools that (B) the universal first order consequences of any geometric theory T of Pappian planes which is consistent with the analytic geometry of the reals is decidable. The techniques used were all known to experts in mathematical logic and geometry in the past but no detailed proofs are easily accessible for practitioners of symbolic computation or automated theorem proving. Keywords Euclidean Geometry · Automated Theorem Proving · Undecidability arXiv:1712.07474v3 [cs.SC] 1 Jun 2018 J.A. Makowsky Faculty of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel E-mail: [email protected] 2 J.A.
    [Show full text]
  • 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.
    [Show full text]