Eclipse Prediction on the Ancient Greek Astronomical Calculating Machine Known as the Antikythera Mechanism
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{"title"=>"Eclipse prediction on the ancient Greek astronomical calculating machine known as the Antikythera Mechanism", "type"=>"journal", "authors"=>[{"first_name"=>"Tony", "last_name"=>"Freeth", "scopus_author_id"=>"15131192200"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"doi"=>"10.1371/journal.pone.0103275", "scopus"=>"2-s2.0-84904962140", "pui"=>"373645978", "pmid"=>"25075747", "issn"=>"19326203", "sgr"=>"84904962140"}, "id"=>"cfcbf746-dd71-3590-9fed-c0e023b9654d", "abstract"=>"The ancient Greek astronomical calculating machine, known as the Antikythera Mechanism, predicted eclipses, based on the 223-lunar month Saros cycle. Eclipses are indicated on a four-turn spiral Saros Dial by glyphs, which describe type and time of eclipse and include alphabetical index letters, referring to solar eclipse inscriptions. These include Index Letter Groups, describing shared eclipse characteristics. The grouping and ordering of the index letters, the organization of the inscriptions and the eclipse times have previously been unsolved. A new reading and interpretation of data from the back plate of the Antikythera Mechanism, including the glyphs, the index letters and the eclipse inscriptions, has resulted in substantial changes to previously published work. Based on these new readings, two arithmetical models are presented here that explain the complete eclipse prediction scheme. The first model solves the glyph distribution, the grouping and anomalous ordering of the index letters and the structure of the inscriptions. It also implies the existence of lost lunar eclipse inscriptions. The second model closely matches the glyph times and explains the four-turn spiral of the Saros Dial. Together, these models imply a surprisingly early epoch for the Antikythera Mechanism. The ancient Greeks built a machine that can predict, for many years ahead, not only eclipses but also a remarkable array of their characteristics, such as directions of obscuration, magnitude, colour, angular diameter of the Moon, relationship with the Moon's node and eclipse time. It was not entirely accurate, but it was an astonishing achievement for its era.", "link"=>"http://www.mendeley.com/research/eclipse-prediction-ancient-greek-astronomical-calculating-machine-known-antikythera-mechanism", "reader_count"=>10, "reader_count_by_academic_status"=>{"Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>4, "Student > Master"=>1, "Student > Bachelor"=>2, "Professor"=>1}, "reader_count_by_user_role"=>{"Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>4, "Student > Master"=>1, "Student > Bachelor"=>2, "Professor"=>1}, "reader_count_by_subject_area"=>{"Engineering"=>1, "Design"=>1, "Arts and Humanities"=>2, "Physics and Astronomy"=>2, "Social Sciences"=>1, "Computer Science"=>1, "Earth and Planetary Sciences"=>2}, "reader_count_by_subdiscipline"=>{"Design"=>{"Design"=>1}, "Engineering"=>{"Engineering"=>1}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>2}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>2}, "Computer Science"=>{"Computer Science"=>1}, "Arts and Humanities"=>{"Arts and Humanities"=>2}}, "reader_count_by_country"=>{"United States"=>1}, "group_count"=>0}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1615077"], "description"=>"<p>EYM’s predictions <i>North of the node</i> are first arranged in <i>month order</i>, including: <i>month number</i>, <i>index letter</i>, <i>EYu from eclipse year start</i>, <i>Ascending or Descending node</i> and <i>EYu from node point</i> (NP EYu). Similarly for predictions <i>At the node/South of the node</i>, with a negative sign attached to their NP EYu to match their negative <i>ecliptic latitude</i> (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275.s028\" target=\"_blank\">Note S1</a>). They are then re-ordered by <i>EYu from node point</i> in <i>descending order</i>. This generates the observed Index Letter Groups (in red) and the ordering of the letters within each group (with one exception). It also shows how EYM completes the picture with two conjectural solar Index Letter Groups (in black).</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "eym"], "article_id"=>1122412, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g007", "stats"=>{"downloads"=>1, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Generation_by_EYM_of_the_Index_Letter_Groups_/1122412", "title"=>"Generation by EYM of the Index Letter Groups.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615071"], "description"=>"<p>(A) Part of a spreadsheet (shown in full in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275.s009\" target=\"_blank\">Figure S9</a>) illustrating how EYM maps syzygies onto eclipse years. EYM is based on mean months. Each month is divided into 38 EYu. The 19 <i>eclipse years</i> are numbered on the left, with 446 EYu in each eclipse year. Eclipses are clustered in <i>eclipse seasons</i> around the <i>node points</i>: here at the <i>Descending Node Point</i> (DNP) (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275.s028\" target=\"_blank\">Note S1</a>). Observed glyphs are in bright blue for lunar and bright orange for solar; glyphs reconstructed by EYM in paler colours; observed index letters in red; index letters reconstructed by EYM in blue. The two alphabets of index letters are distinguished here by subscripts, though the original index letters were distinguished by bars on the second alphabet. The superimposed Saros Dial shows how glyphs are mapped onto eclipse years. The grey vertical line is the DNP at 66 EYu from the Saros start. The blue dotted line is one side of the symmetrical limits for lunar glyphs; the orange dotted lines are the asymmetrical limits for solar glyphs as well as the lunar limit North of the node, as described in the text. Months start at <i>First Crescent Moon</i> (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275.s028\" target=\"_blank\">Note S1</a>), 2 EYu (1.55 days) after New Moon. Full Moon is at 17 EYu from the start of each Month; and New Moon at 36 EYu. (B) Part of a spreadsheet (shown in full in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275.s010\" target=\"_blank\">Figure S10</a>), which calculates the glyphs generated by EYM, with <i>index letter</i>; <i>EYu from eclipse year start</i>; <i>Descending or Ascending node</i>; <i>North or South of the node</i>; <i>EYu from node point</i>.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "Spreadsheets"], "article_id"=>1122406, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g006", "stats"=>{"downloads"=>0, "page_views"=>26, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Detail_of_spreadsheets_showing_EYM_/1122406", "title"=>"Detail of spreadsheets showing EYM.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615082"], "description"=>"<p>This uses the same colour conventions as described in the legend for <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone-0103275-g009\" target=\"_blank\">Figure 9</a>.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis"], "article_id"=>1122417, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g009", "stats"=>{"downloads"=>4, "page_views"=>19, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Conjectural_arrangement_of_back_plate_inscriptions_/1122417", "title"=>"Conjectural arrangement of back plate inscriptions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615063"], "description"=>"<p>(A) Fragment A, PTM of back plate with specular enhancement. (B) Fragment A, PTM of back plate with diffuse gain. (C) Fragment A, PTM of back plate with specular enhancement. (D) Fragment A, PTM of impression of back cover with luminance unsharp masking. (E) Fragment A, X-ray CT slice of back plate. (F) Fragment F, X-ray CT slice of back plate. (G) Fragment E, X-ray CT slice of back plate. (H) Fragment E, X-ray CT slice of accretion layer. (I) Fragment E, orthogonal X-ray CT slice of back plate and accretion layer.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis"], "article_id"=>1122402, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g005", "stats"=>{"downloads"=>1, "page_views"=>20, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Inscriptions_data_from_the_back_plate_/1122402", "title"=>"Inscriptions data from the back plate.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615080"], "description"=>"<p>(A) Text that is traced from the data is in red; text reconstructed from the context in blue; uncertain text in green. The Index Letter Groups, underlined in white and with white line numbers, refer to the lines of inscription above them. (B) Transcription using Leiden conventions. (C) Translation.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "eclipse"], "article_id"=>1122415, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g008", "stats"=>{"downloads"=>3, "page_views"=>31, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_solar_eclipse_inscriptions_/1122415", "title"=>"The solar eclipse inscriptions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615021"], "description"=>"<p>On the <i>left</i>, the front plate includes zodiac and calendar dials <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-PriceDde1\" target=\"_blank\">[6]</a> and a conjectural reconstruction of the ancient Greek <i>Cosmos </i><a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth3\" target=\"_blank\">[5]</a>. In the middle is an exploded reconstruction of the gears. The input contrate gear is in the centre, with a keyway to turn the Mechanism. The planetary gearing at the front is conjectural <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth3\" target=\"_blank\">[5]</a>, but the gearing behind the main plate for the lunar anomaly mechanism and the back dials is now firmly established <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth1\" target=\"_blank\">[1]</a>, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-PriceDde1\" target=\"_blank\">[6]</a>. On the upper right is the 19-year Metonic calendar dial <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth1\" target=\"_blank\">[1]</a>, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth2\" target=\"_blank\">[4]</a>, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Wright1\" target=\"_blank\">[7]</a> and on the lower right, the 223-month Saros eclipse prediction dial <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth1\" target=\"_blank\">[1]</a>.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "reconstruction", "antikythera"], "article_id"=>1122365, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g003", "stats"=>{"downloads"=>53, "page_views"=>960, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Exploded_computer_reconstruction_of_the_Antikythera_Mechanism_/1122365", "title"=>"Exploded computer reconstruction of the Antikythera Mechanism.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615042"], "description"=>"<p>Red text is traced from data; blue reconstructed from context; green is uncertain. Eclipse predictions–strictly speaking <i>predictions of eclipse possibilities</i> (EPs) <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth1\" target=\"_blank\">[1]</a>–are specified by <i>glyphs</i>, numbered by their month round the dial <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth2\" target=\"_blank\">[4]</a>: two examples are inset. Σ for ΣEΛΗΝΗ (<i>the goddess of the Moon</i>) indicates a lunar eclipse; Η for ΗΛΙΟΣ (<i>the god of the Sun</i>) a solar eclipse. In Glyph 137, Η under Μ, denoted by H<sup>\\M</sup>, means ΗΜEΡΑΣ (<i>of the day</i>): a lunar eclipse during the day, which is therefore not visible. In other glyphs Ν under Υ, denoted by N<sup>\\Υ</sup>, means NYKTOΣ (<i>of the night</i>): a solar eclipse during the night, which is therefore not visible. The eclipse time follows, with a ligature of ω and ρ, abbreviating ωρα (<i>hour</i>), followed by a letter for a number of hours <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth2\" target=\"_blank\">[4]</a>. At the bottom of the glyphs are <i>index letters</i> in alphabetic order, using two alphabets, plus three additional symbols. This alphabetic ordering previously established <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth2\" target=\"_blank\">[4]</a> that there were fewer solar than lunar eclipse predictions. The index letters in the glyphs reference inscriptions to the right of the dial, where the same index letters appear in groups, which are underlined in white and have white line numbers. These <i>Index Letter Groups</i> all reference <i>solar</i> eclipse inscriptions (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275.s022\" target=\"_blank\">Table S1</a>). They are written in a perplexing non-alphabetic ordering. Conjectural inscriptions (in yellow) and conjectural <i>Index Letter Groups</i> (in blue) are predicted by the <i>Eclipse Year Model</i> (EYM). Inside the Saros Dial is the subsidiary Exeligmos Dial, which adds eight hours to the eclipse times for successive Saros periods <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Freeth2\" target=\"_blank\">[4]</a>.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "223-lunar", "saros"], "article_id"=>1122385, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g004", "stats"=>{"downloads"=>7, "page_views"=>146, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_223_lunar_month_Saros_Dial_/1122385", "title"=>"The 223-lunar month Saros Dial.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615105", "https://ndownloader.figshare.com/files/1615106", "https://ndownloader.figshare.com/files/1615107", "https://ndownloader.figshare.com/files/1615108", "https://ndownloader.figshare.com/files/1615109", "https://ndownloader.figshare.com/files/1615110", "https://ndownloader.figshare.com/files/1615111", "https://ndownloader.figshare.com/files/1615112", "https://ndownloader.figshare.com/files/1615113", "https://ndownloader.figshare.com/files/1615115", "https://ndownloader.figshare.com/files/1615116", "https://ndownloader.figshare.com/files/1615117", "https://ndownloader.figshare.com/files/1615118", "https://ndownloader.figshare.com/files/1615119", "https://ndownloader.figshare.com/files/1615121", "https://ndownloader.figshare.com/files/1615122", "https://ndownloader.figshare.com/files/1615123", "https://ndownloader.figshare.com/files/1615125", "https://ndownloader.figshare.com/files/1615126", "https://ndownloader.figshare.com/files/1615127", "https://ndownloader.figshare.com/files/1615128", "https://ndownloader.figshare.com/files/1615129", "https://ndownloader.figshare.com/files/1615130", "https://ndownloader.figshare.com/files/1615131", "https://ndownloader.figshare.com/files/1615132", "https://ndownloader.figshare.com/files/1615133", "https://ndownloader.figshare.com/files/1615134", "https://ndownloader.figshare.com/files/1615135", "https://ndownloader.figshare.com/files/1615136", "https://ndownloader.figshare.com/files/1615137", "https://ndownloader.figshare.com/files/1615138", "https://ndownloader.figshare.com/files/1615139"], "description"=>"<div><p>The ancient Greek astronomical calculating machine, known as the <i>Antikythera Mechanism</i>, predicted eclipses, based on the 223-lunar month <i>Saros cycle</i>. Eclipses are indicated on a four-turn spiral <i>Saros Dial</i> by <i>glyphs</i>, which describe type and time of eclipse and include alphabetical <i>index letters</i>, referring to <i>solar eclipse inscriptions</i>. These include <i>Index Letter Groups</i>, describing shared eclipse characteristics. The grouping and ordering of the index letters, the organization of the inscriptions and the eclipse times have previously been unsolved. A new reading and interpretation of data from the back plate of the Antikythera Mechanism, including the glyphs, the index letters and the eclipse inscriptions, has resulted in substantial changes to previously published work. Based on these new readings, two arithmetical models are presented here that explain the complete eclipse prediction scheme. The first model solves the glyph distribution, the grouping and anomalous ordering of the index letters and the structure of the inscriptions. It also implies the existence of lost <i>lunar eclipse inscriptions.</i> The second model closely matches the glyph times and explains the four-turn spiral of the Saros Dial. Together, these models imply a surprisingly early epoch for the Antikythera Mechanism. The ancient Greeks built a machine that can predict, for many years ahead, not only eclipses but also a remarkable array of their characteristics, such as <i>directions of obscuration</i>, <i>magnitude</i>, <i>colour</i>, <i>angular diameter of the Moon, relationship with the Moon’s node</i> and <i>eclipse time</i>. It was not entirely accurate, but it was an astonishing achievement for its era.</p></div>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "greek", "astronomical", "antikythera"], "article_id"=>1122434, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0103275.s001", "https://dx.doi.org/10.1371/journal.pone.0103275.s002", "https://dx.doi.org/10.1371/journal.pone.0103275.s003", "https://dx.doi.org/10.1371/journal.pone.0103275.s004", "https://dx.doi.org/10.1371/journal.pone.0103275.s005", "https://dx.doi.org/10.1371/journal.pone.0103275.s006", "https://dx.doi.org/10.1371/journal.pone.0103275.s007", "https://dx.doi.org/10.1371/journal.pone.0103275.s008", "https://dx.doi.org/10.1371/journal.pone.0103275.s009", "https://dx.doi.org/10.1371/journal.pone.0103275.s010", "https://dx.doi.org/10.1371/journal.pone.0103275.s011", "https://dx.doi.org/10.1371/journal.pone.0103275.s012", "https://dx.doi.org/10.1371/journal.pone.0103275.s013", "https://dx.doi.org/10.1371/journal.pone.0103275.s014", "https://dx.doi.org/10.1371/journal.pone.0103275.s015", "https://dx.doi.org/10.1371/journal.pone.0103275.s016", "https://dx.doi.org/10.1371/journal.pone.0103275.s017", "https://dx.doi.org/10.1371/journal.pone.0103275.s018", "https://dx.doi.org/10.1371/journal.pone.0103275.s019", "https://dx.doi.org/10.1371/journal.pone.0103275.s020", "https://dx.doi.org/10.1371/journal.pone.0103275.s021", "https://dx.doi.org/10.1371/journal.pone.0103275.s022", "https://dx.doi.org/10.1371/journal.pone.0103275.s023", "https://dx.doi.org/10.1371/journal.pone.0103275.s024", "https://dx.doi.org/10.1371/journal.pone.0103275.s025", "https://dx.doi.org/10.1371/journal.pone.0103275.s026", "https://dx.doi.org/10.1371/journal.pone.0103275.s027", "https://dx.doi.org/10.1371/journal.pone.0103275.s028", "https://dx.doi.org/10.1371/journal.pone.0103275.s029", "https://dx.doi.org/10.1371/journal.pone.0103275.s030", "https://dx.doi.org/10.1371/journal.pone.0103275.s031", "https://dx.doi.org/10.1371/journal.pone.0103275.s032"], "stats"=>{"downloads"=>53, "page_views"=>34, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Eclipse_Prediction_on_the_Ancient_Greek_Astronomical_Calculating_Machine_Known_as_the_Antikythera_Mechanism_/1122434", "title"=>"Eclipse Prediction on the Ancient Greek Astronomical Calculating Machine Known as the Antikythera Mechanism", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614945"], "description"=>"<p>The fragments of the Antikythera Mechanism as seen from both sides. In addition to the seven lettered fragments A–G, there are also seventy-five small fragments 1–75. The fragments are seen here using <i>Polynomial Texture Mapping</i> (PTM) <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Malzbender1\" target=\"_blank\">[2]</a>, with specular enhancement, which emphasizes small surface details.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "lettered", "fragments", "antikythera"], "article_id"=>1122327, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g001", "stats"=>{"downloads"=>4, "page_views"=>26, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_PTM_of_the_seven_lettered_fragments_A_8211_G_of_the_Antikythera_Mechanism_/1122327", "title"=>"PTM of the seven lettered fragments A–G of the Antikythera Mechanism.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615087"], "description"=>"<p>Computer reconstruction of the Saros and Exeligmos Dials.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "reconstruction", "saros", "exeligmos"], "article_id"=>1122422, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g011", "stats"=>{"downloads"=>8, "page_views"=>44, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Computer_reconstruction_of_the_Saros_and_Exeligmos_Dials_/1122422", "title"=>"Computer reconstruction of the Saros and Exeligmos Dials.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1615084"], "description"=>"<p>(A) Detail of spreadsheet (described in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275.s031\" target=\"_blank\">Note S4</a>), showing the first few rows of calculation out of 223, with parameters optimized and final errors rounded to whole numbers. The graphs at the top show the generated month lengths and the graphs in the middle show the close match of the model with the glyph times, with a lunar rms error of 1.4 hours and a solar rms error of 1.9 hours, giving a total rms error of 1.7 hours. The apparently large errors in the fifth and tenth solar times are much smaller than they seem, since the <i>clock distance</i> error is the relevant measure (<a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275.s031\" target=\"_blank\">Note S4</a>). (B) Optimization of the solar anomaly parameter: rms error of model times vs glyph times, dependent on solar anomaly, with lunar anomaly fixed when <i>lunar apogee</i>, L<sub>apo</sub> = FM<sub>1</sub>. Optimal value is 346 days before <i>solar apogee</i>, S<sub>apo</sub>. (C) Optimization of the lunar anomaly parameter: rms error of model times vs glyph times, dependent on lunar anomaly, with solar anomaly fixed at 346 days before S<sub>apo</sub>. Optimal value is at zero when L<sub>apo</sub> = FM<sub>1</sub>.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "zigzag"], "article_id"=>1122419, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g010", "stats"=>{"downloads"=>3, "page_views"=>44, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_ZigZag_model_ZZM_/1122419", "title"=>"The ZigZag model, ZZM.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/1614997"], "description"=>"<p>(A) Polynomial Texture Mapping (PTM) with specular enhancement <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Malzbender1\" target=\"_blank\">[2]</a>. (B) High-resolution Microfocus X-ray Computed Tomography (X-ray CT) <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0103275#pone.0103275-Ramsey1\" target=\"_blank\">[3]</a>.</p>", "links"=>[], "tags"=>["Computing methods", "Mathematical computing", "Computing systems", "Analog computing", "Information technology", "text mining", "Astronomical sciences", "astronomy", "Astronomical instruments", "Celestial objects", "planets", "jupiter", "mars", "Mercury (planet)", "Saturn", "venus", "stars", "sun", "Planetary sciences", "solar system", "mathematics", "Discrete mathematics", "Computational systems", "Numerical analysis", "gathered", "2005", "antikythera"], "article_id"=>1122340, "categories"=>["Biological Sciences"], "users"=>["Tony Freeth"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0103275.g002", "stats"=>{"downloads"=>1, "page_views"=>11, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Examples_of_data_gathered_in_2005_on_the_Antikythera_Mechanism_/1122340", "title"=>"Examples of data gathered in 2005 on the Antikythera Mechanism.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-07-30 03:06:05"}

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