An Observer Epistemology – Astronomy, Modernity and the Spatial Revolution. the Modern Worl
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The Dunhuang Chinese Sky: a Comprehensive Study of the Oldest Known Star Atlas
25/02/09JAHH/v4 1 THE DUNHUANG CHINESE SKY: A COMPREHENSIVE STUDY OF THE OLDEST KNOWN STAR ATLAS JEAN-MARC BONNET-BIDAUD Commissariat à l’Energie Atomique ,Centre de Saclay, F-91191 Gif-sur-Yvette, France E-mail: [email protected] FRANÇOISE PRADERIE Observatoire de Paris, 61 Avenue de l’Observatoire, F- 75014 Paris, France E-mail: [email protected] and SUSAN WHITFIELD The British Library, 96 Euston Road, London NW1 2DB, UK E-mail: [email protected] Abstract: This paper presents an analysis of the star atlas included in the medieval Chinese manuscript (Or.8210/S.3326), discovered in 1907 by the archaeologist Aurel Stein at the Silk Road town of Dunhuang and now held in the British Library. Although partially studied by a few Chinese scholars, it has never been fully displayed and discussed in the Western world. This set of sky maps (12 hour angle maps in quasi-cylindrical projection and a circumpolar map in azimuthal projection), displaying the full sky visible from the Northern hemisphere, is up to now the oldest complete preserved star atlas from any civilisation. It is also the first known pictorial representation of the quasi-totality of the Chinese constellations. This paper describes the history of the physical object – a roll of thin paper drawn with ink. We analyse the stellar content of each map (1339 stars, 257 asterisms) and the texts associated with the maps. We establish the precision with which the maps are drawn (1.5 to 4° for the brightest stars) and examine the type of projections used. -
Star Chart Lab
Star Chart Lab 6) a. About how many stars are in the Pleiades cluster? Star Chart Lab b. Why do you think its nick name is “The Seven Sisters”? c. Which constellation is the Pleiades cluster in? •Materials 7) Star Atlas Deluxe Edition a. Which named star is ten arc minutes from the brightest star in the constellation Gemini? •Procedure b. Is the brightest “star” in Gemini actually just one star? In this lab, you will explore the star charts of c. What type of object lies 38 arc minutes less our night sky. You might want to skim the intro- in RA, 0.6o in Dec. south from the star Pollux? duction at the front of the charts before you d. What type of object lies about 20 arc minuets begin. In the front or back of the book you’ll less in RA, 1.5o in Dec. north of Pollux? find a transparency which lays over the charts, giving you more detailed measurements. Star 8) When looking in the night sky from campus, charts use a special type of coordinates, called you certainly see fewer stars than are on these the Equatorial system. If you are not familiar maps. Many constellations are actually easier to with this system, e.g. Right Ascension (RA) and find in conditions such as on campus. Declination (Dec.), then take a minute to read a. Which stars do you think you can see in the Appendix A of this manual. Otherwise, answer constellation Lyra from campus? the questions below. b. What planetary nebula is in Lyra? c. -
Kepler and Hales: Conjectures and Proofs Dreams and Their
KEPLER AND HALES: CONJECTURES AND PROOFS DREAMS AND THEIR REALIZATION Josef Urban Czech Technical University in Prague Pittsburgh, June 21, 2018 1 / 31 This talk is an experiment Normally I give “serious” talks – I am considered crazy enough But this is Tom’s Birthday Party, so we are allowed to have some fun: This could be in principle a talk about our work on automation and AI for reasoning and formalization, and Tom’s great role in these areas. But the motivations and allusions go back to alchemistic Prague of 1600s and the (un)scientific pursuits of then versions of "singularity", provoking comparisons with our today’s funny attempts at building AI and reasoning systems for solving the great questions of Math, the Universe and Everything. I wonder where this will all take us. Part 1 (Proofs?): Learning automated theorem proving on top of Flyspeck and other corpora Learning formalization (autoformalization) on top of them Part 2 (Conjectures?): How did we get here? What were Kepler & Co trying to do in 1600s? What are we trying to do today? 2 / 31 The Flyspeck project – A Large Proof Corpus Kepler conjecture (1611): The most compact way of stacking balls of the same size in space is a pyramid. V = p 74% 18 Proved by Hales & Ferguson in 1998, 300-page proof + computations Big: Annals of Mathematics gave up reviewing after 4 years Formal proof finished in 2014 20000 lemmas in geometry, analysis, graph theory All of it at https://code.google.com/p/flyspeck/ All of it computer-understandable and verified in HOL Light: -
Name a Star Certificate
Name A Star Certificate LiamObliterated never Jerzyprint-out intimidating any jabbers! punily. Cobbie brazes her klephts stertorously, she vocalizes it veeringly. Piffling or beneficial, Will name certificate What does this is a unique certificates etc place in january, software free photo book, novelty gift set, hart ventures had a star! Sign up today, purchase a luxury gift to do not a star gift that offer to see this element live on customer are! So everyone who assist us how are delivered, all cookies to your partner can be. Imagine all tastes, name a birthday gift that said a configuration that! Own, business people use nicknames and some make use two names. Please enter a name a cute couple names stars named star naming a snowflake design with this manner, helping everyone loves getting a standard shipping! Whether for your life of something to names should be visible constellation should name a star certificate for named star? With name of naming works in space to celestial stars more than enough stars shine forever call your search for their loved ones. Just fade the annual of the welfare you want to surprise, thank you shadow your comment. An eternal health that beautiful shine thorough the heavens for thousands of years to come. Would like you for your certificate and a certificate done over! If you provide an object that is popular gift you will receive launch certificate, it was even one of these programs. But all required fields below for certificates, certificate for your star live constellations, we provide you will be cancelled and discussing it? Our attack of doubt gift specialists will assault their mutual to cleave you are should care nut before at after recording a guest name with us. -
Abd Al-Rahman Al-Sufi and His Book of the Fixed Stars: a Journey of Re-Discovery
ResearchOnline@JCU This file is part of the following reference: Hafez, Ihsan (2010) Abd al-Rahman al-Sufi and his book of the fixed stars: a journey of re-discovery. PhD thesis, James Cook University. Access to this file is available from: http://eprints.jcu.edu.au/28854/ The author has certified to JCU that they have made a reasonable effort to gain permission and acknowledge the owner of any third party copyright material included in this document. If you believe that this is not the case, please contact [email protected] and quote http://eprints.jcu.edu.au/28854/ 5.1 Extant Manuscripts of al-Ṣūfī’s Book Al-Ṣūfī’s ‘Book of the Fixed Stars’ dating from around A.D. 964, is one of the most important medieval Arabic treatises on astronomy. This major work contains an extensive star catalogue, which lists star co-ordinates and magnitude estimates, as well as detailed star charts. Other topics include descriptions of nebulae and Arabic folk astronomy. As I mentioned before, al-Ṣūfī’s work was first translated into Persian by al-Ṭūsī. It was also translated into Spanish in the 13th century during the reign of King Alfonso X. The introductory chapter of al-Ṣūfī’s work was first translated into French by J.J.A. Caussin de Parceval in 1831. However in 1874 it was entirely translated into French again by Hans Karl Frederik Schjellerup, whose work became the main reference used by most modern astronomical historians. In 1956 al-Ṣūfī’s Book of the fixed stars was printed in its original Arabic language in Hyderabad (India) by Dārat al-Ma‘aref al-‘Uthmānīa. -
A Computer Verification of the Kepler Conjecture
ICM 2002 Vol. III 1–3 · · A Computer Verification of the Kepler Conjecture Thomas C. Hales∗ Abstract The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than π/√18. A computer assisted verification confirmed this conjecture in 1998. This article gives a historical introduction to the problem. It describes the procedure that converts this problem into an optimization problem in a finite number of variables and the strategies used to solve this optimization problem. 2000 Mathematics Subject Classification: 52C17. Keywords and Phrases: Sphere packings, Kepler conjecture, Discrete ge- ometry. 1. Historical introduction The Kepler conjecture asserts that the density of a packing of congruent balls in three dimensions is never greater than π/√18 0.74048 .... This is the oldest problem in discrete geometry and is an important≈ part of Hilbert’s 18th problem. An example of a packing achieving this density is the face-centered cubic packing (Figure 1). A packing of balls is an arrangement of nonoverlapping balls of radius 1 in Euclidean space. Each ball is determined by its center, so equivalently it is a arXiv:math/0305012v1 [math.MG] 1 May 2003 collection of points in Euclidean space separated by distances of at least 2. The density of a packing is defined as the lim sup of the densities of the partial packings formed by the balls inside a ball with fixed center of radius R. (By taking the lim sup, rather than lim inf as the density, we prove the Kepler conjecture in the strongest possible sense.) Defined as a limit, the density is insensitive to changes in the packing in any bounded region. -
The Sphere Packing Problem in Dimension 8 Arxiv:1603.04246V2
The sphere packing problem in dimension 8 Maryna S. Viazovska April 5, 2017 8 In this paper we prove that no packing of unit balls in Euclidean space R has density greater than that of the E8-lattice packing. Keywords: Sphere packing, Modular forms, Fourier analysis AMS subject classification: 52C17, 11F03, 11F30 1 Introduction The sphere packing constant measures which portion of d-dimensional Euclidean space d can be covered by non-overlapping unit balls. More precisely, let R be the Euclidean d vector space equipped with distance k · k and Lebesgue measure Vol(·). For x 2 R and d r 2 R>0 we denote by Bd(x; r) the open ball in R with center x and radius r. Let d X ⊂ R be a discrete set of points such that kx − yk ≥ 2 for any distinct x; y 2 X. Then the union [ P = Bd(x; 1) x2X d is a sphere packing. If X is a lattice in R then we say that P is a lattice sphere packing. The finite density of a packing P is defined as Vol(P\ Bd(0; r)) ∆P (r) := ; r > 0: Vol(Bd(0; r)) We define the density of a packing P as the limit superior ∆P := lim sup ∆P (r): r!1 arXiv:1603.04246v2 [math.NT] 4 Apr 2017 The number be want to know is the supremum over all possible packing densities ∆d := sup ∆P ; d P⊂R sphere packing 1 called the sphere packing constant. For which dimensions do we know the exact value of ∆d? Trivially, in dimension 1 we have ∆1 = 1. -
An Overview of the Kepler Conjecture
AN OVERVIEW OF THE KEPLER CONJECTURE Thomas C. Hales 1. Introduction and Review The series of papers in this volume gives a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than π/√18 0.74048 . This is the oldest problem in discrete geometry and is an important≈ part of Hilbert’s 18th problem. An example of a packing achieving this density is the face-centered cubic packing. A packing of spheres is an arrangement of nonoverlapping spheres of radius 1 in Euclidean space. Each sphere is determined by its center, so equivalently it is a collection of points in Euclidean space separated by distances of at least 2. The density of a packing is defined as the lim sup of the densities of the partial packings formed by spheres inside a ball with fixed center of radius R. (By taking the lim sup, rather than lim inf as the density, we prove the Kepler conjecture in the strongest possible sense.) Defined as a limit, the density is insensitive to changes in the packing in any bounded region. For example, a finite number of spheres can be removed from the face-centered cubic packing without affecting its density. Consequently, it is not possible to hope for any strong uniqueness results for packings of optimal density. The uniqueness established by this work is as strong arXiv:math/9811071v2 [math.MG] 20 May 2002 as can be hoped for. It shows that certain local structures (decomposition stars) attached to the face-centered cubic (fcc) and hexagonal-close packings (hcp) are the only structures that maximize a local density function. -
Baa Hane’ Story of the Stars
National Aeronautics and Space Administration S-’ Baa Hane’ Story of the Stars Educational Activities Weaving NASA Science and Navajo Knowledge For use in Classrooms and Community-Based Educational Events S-’ Baa Hane’ Story of the Stars Educational Activities Weaving NASA Science and Navajo Knowledge 1 NASA and the Navajo Nation Project The 2005 NASA Explorer Institute Project entitled “NASA and the Navajo Nation” was led by the NASA Astrobiology Institute in collaboration with ArtReach International. The project was carried out in partnership with The Navajo Nation Council, Office of the Speaker. The project evolved from a 2004 NASA Explorer Institute Focus Group conducted by ArtReach International. In the Focus Group, members of the Navajo education community identified needs and desires in partnering with NASA on educational initiatives. The educational materials created within the NASA and the Navajo Nation project, this activity booklet and a short film, both entitled “S-’ Baa Hane’ - Story of the Stars,” are a direct result of the Focus Group’s findings. The activities and film weave together NASA astrobiology science and Navajo cultural teachings relating to the stars to create a “dual-learning” environment wherein the cultural and scientific concepts are explored together, equally. This product is for non-commercial, educational use only. 2 http://nai.nasa.gov/storyofthestars Iiná Dóó Óhoo’ Aah Bindii’ A’ Overall Diné Education Philosophy From the Diné Culture and Language Curriculum Framework Office of Diné Culture, Language, and Community Services We are the Holy People of the Earth. We are created and placed between our Mother Earth and Father Sky. Our home, the Four Sacred Mountains, with the entrance to the East, embodies our Way of Life. -
Nonisotropic Self-Assembly of Nanoparticles: from Compact Packing to Functional Aggregates Xavier Bouju, Etienne Duguet, Fabienne Gauffre, Claude Henry, Myrtil L
Nonisotropic Self-Assembly of Nanoparticles: From Compact Packing to Functional Aggregates Xavier Bouju, Etienne Duguet, Fabienne Gauffre, Claude Henry, Myrtil L. Kahn, Patrice Mélinon, Serge Ravaine To cite this version: Xavier Bouju, Etienne Duguet, Fabienne Gauffre, Claude Henry, Myrtil L. Kahn, et al.. Nonisotropic Self-Assembly of Nanoparticles: From Compact Packing to Functional Aggregates. Advanced Mate- rials, Wiley-VCH Verlag, 2018, 30 (27), pp.1706558. 10.1002/adma.201706558. hal-01795448 HAL Id: hal-01795448 https://hal.archives-ouvertes.fr/hal-01795448 Submitted on 18 Oct 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Non-isotropic self-assembly of nanoparticles: from compact packing to functional aggregates Xavier Bouju∗ CEMES-CNRS (UPR CNRS 8011), Bt F picoLab 29 Rue J. Marvig, BP 94347 31055 Toulouse Cedex 4, France Etienne´ Duguet∗ CNRS, Univ. Bordeaux, ICMCB, UPR 9048, 33600 Pessac, France Fabienne Gauffre∗ Institut des sciences chimiques de Rennes (ISCR), UMR CNRS 6226, 263 avenue du G´en´eral Leclerc, CS 74205, F-35000 Rennes, France Claude Henry∗ Centre interdisciplinaire de nanoscience de Marseille (CINAM), UMR CNRS 7325, Aix-Marseille Universit´e,Campus de Luminy, Case 913, F-13000 Marseille, France Myrtil Kahn∗ Laboratoire de chimie de coordination (LCC), UPR CNRS 8241, 205 route de Narbonne, F-31000 Toulouse, France Patrice M´elinon∗ Universit´ede Lyon, Universit´eClaude Bernard Lyon 1, UMR CNRS 5306, Institut Lumi`ere Mati`ere, F-69622, Villeurbanne, Francey Serge Ravaine CNRS, Univ. -
Big Proof Big Proof
Big Proof Big Proof Sunday, July 9, 2017 Big Conjecture Thomas Hales July 10, 2017 Everything is vague to a degree you do not realize till you have tried to make it precise. – Bertrand Russell Keep your conjectures bold and your refutations brutal. – Nick Horton Sunday, July 9, 2017 Sunday, July 9, 2017 Sphere Packings Sunday, July 9, 2017 Sunday, July 9, 2017 Sunday, July 9, 2017 “Perhaps the most controversial topic to be covered in The Mathematical Intelligencer is the Kepler Conjecture. In The Mathematical Intelligencer, Thomas C. Hales takes on Wu-Yi Hsiang’s 1990 announcement that he had proved the Kepler Conjecture,...” Sunday, July 9, 2017 From [email protected] Wed Aug 19 02:43:02 1998 Date: Sun, 9 Aug 1998 09:54:56 -0400 (EDT) From: Tom Hales <[email protected]> To: Subject: Kepler conjecture Dear colleagues, I have started to distribute copies of a series of papers giving a solution to the Kepler conjecture, the oldest problem in discrete geometry. These results are still preliminary in the sense that they have not been refereed and have not even been submitted for publication, but the proofs are to the best of my knowledge correct and complete. Nearly four hundred years ago, Kepler asserted that no packing of congruent spheres can have a density greater than the density of the face-centered cubic packing. This assertion has come to be known as the Kepler conjecture. In 1900, Hilbert included the Kepler conjecture in his famous list of mathematical problems. In a paper published last year in the journal "Discrete and Computational Geometry," (DCG), I published a detailed plan describing how the Kepler conjecture might be proved. -
Astronomy Alphabet
Astronomy Alphabet Educational video for children Teacher https://vimeo.com/77309599 & Learner Guide This guide gives background information about the astronomy topics mentioned in the video, provides questions and answers children may be curious about, and suggests topics for discussion. Alhazen A Alhazen, called the Father of Optics, performed NASA/Goddard/Lunar Reconnaissance Orbiter, Apollo 17 experiments over a thousand years ago Can you find Alhazen crater when you look at the Moon? to learn about how light travels and Why does the Moon look bigger near the behaves. He also studied astronomy, horizon? separated light into colors, and sought to Believe it or not, scientists still don’t know for sure why explain why the Moon looks bigger near we perceive the Moon to be larger when it lies near to the the horizon. horizon. Though photos of the Moon at different points in the sky show it to be the same size, we humans think we I’ve never heard of Abu Ali al-Hasan ibn al- see something quite different. Try this experiment yourself Hasan ibn al-Hatham (Alhazen). sometime! One possibility is that objects we see next to the Tell me more about him. Moon when it’s near to them give us the illusion that it’s We don’t know that much about Alhazen be- bigger, because of a sense of scale and reference. cause he lived so long ago, but we do know that he was born in Persia in 965. He wrote hundreds How many craters does the Moon have, and what of books on math and science and pioneered the are their names? scientific method of experimentation.