Akado-Sammarru toplumlarındaki matematik birikimini gösteren M.Ö 19., 17. yüzyıl döneminden kalma bir çalışma kil tableti...
Pisagor Teoreminden yaklaşık 2500 yıl önce, kare kökü bulma üzerine bir çalışma.....
Yale Babil Kolleksiyonu. YBC 7289 .
Ancient Tablets Reveal Mathematical Achievements of Ancient Babylonian Culture
Old Babylonian “hand tablet” illustrating Pythagoras’ Theorem and an approximation of the square root of two. Clay, 19th-17th century BCE. Yale Babylonian Collection YBC 7289. Photo: West Semitic Research.
NEW YORK, NY.- An illuminating exhibition of thirteen ancient Babylonian tablets, along with supplemental documentary material, opens at New York University’s Institute for the Study of the Ancient World (ISAW) on November 12, 2010. Before Pythagoras: The Culture of Old Babylonian Mathematics reveals the highly sophisticated mathematical practice and education that flourished in Babylonia—present-day Iraq—more than 1,000 years before the time of the Greek sages Thales and Pythagoras, with whom mathematics is traditionally said to have begun.
The tablets in the exhibition, at once beautiful and enlightening, date from the Old Babylonian Period (ca. 1900–1700 BCE). They have been assembled from three important collections: the Columbia Rare Book and Manuscript Library, Columbia University; the University of Pennsylvania Museum of Archaeology and Anthropology; and the Yale Babylonian Collection, Yale University.
Before Pythagoras has been curated by Alexander Jones, ISAW Professor of the History of the Exact Sciences in Antiquity, and ISAW visiting scholar Christine Proust, historian of mathematics and ancient sciences at the Institut Méditerranéen de Recherches Avancées, in Marseille. The exhibition remains on view at ISAW through December 17, 2010.
Jennifer Chi, ISAW director for exhibitions and public programs, states, “It has long been widely recognized that many of the critical achievements of Western Civilization, including writing and the code of law that is the basis for our present-day legal system, developed in ancient Mesopotamia. However, the stunningly advanced state of mathematics in this region has largely been known only to scholars. By demonstrating the richness and sophistication of ancient Mesopotamian mathematics, Before Pythagoras adds an important dimension to the public knowledge of the history of historic cultures and attainments of present-day Iraq.”
Babylonian mathematics is known to the modern world through the work of scribes, primarily young men who, coming from wealthy families in which literacy and professional expertise were handed down through generations, were formally trained in reading and writing. Destined to work in such fields as accounting, building-project planning, and other professions in which mathematics is essential, the scribes learned and practiced mathematics by copying symbols and solving problems—some practical, others theoretical—such as those seen in the tablets in the exhibition.
Alexander Jones notes, “The evidence we have for Old Babylonian mathematics is amazing not only in its abundance, but also in its range, from basic arithmetic to really challenging problems and investigations. And since the documents are the actual manuscripts of the scribes, not copies selected and edited by later generations, we feel as if we were looking over their shoulders as they work; we can even see them getting confused and making mistakes. Recent research has made this human dimension very vivid, using archeological evidence to re-imagine the schools and the process of teaching and learning. Moreover, the contents of the tablets are still recognizable, as they continue to be taught in contemporary mathematics.”
The tablets in Before Pythagoras, inscribed in cuneiform script, cover the full spectrum of mathematical activity, from arithmetical tables copied by scribes-in-training to sophisticated work on topics that today would be classified as number theory and algebra. In so doing, they illuminate three major themes: arithmetic exploiting a notation of numbers based entirely on two basic symbols; the scribal schools of Nippur, which was the most prestigious center of scribal education; and advanced mathematical training.
Many of the problems solved by scribes at the advanced level of training were in fact much more difficult than any they would have to deal with in their careers, and their solutions depended on principles that, before the rediscovery of the Babylonian tablets, were believed to have been discovered by the Greeks of the sixth century BCE and later. One of the tablets, for example, is an extremely unusual diagram showing a square with its two diagonals and three numbers that demonstrate that what we call the Pythagorean Theorem existed 1,000 years before Pythagoras lived. The content of other tablets ranges from mathematical tables for training, to practical calculations for professionals, to abstract algebraic problems.
The meaning of these and other tablets from the Old Babylonian Period were first elucidated by mathematician and historian of science Otto Neugebauer (1899–1990), who spent some two decades, beginning in the 1920s, transcribing and interpreting tablets that had come to light in ancient Mesopotamia since the nineteenth century. It is his pioneering research, as well as the work of his associates, rivals, and successors, that revealed to modern scholars the period’s rich culture of mathematics. Before Pythagoras includes a selection of manuscripts and correspondence, on loan from the Institute for Advanced Study (Princeton, New Jersey), that offers a glimpse of Neugebauer’s methods and his central role in this “heroic age” of scientific discovery.
In order to enable visitors to appreciate the cuneiform tablets more fully, ISAW has developed an extended exhibition pamphlet that will guide viewers in reading cuneiform numbers. In addition, a content-rich website devoted to the exhibition may be found at:
www.nyu.edu/isaw/exhibitions/before-pythagoras/.
http://www.archaeologydaily.com/news/201011125530/Ancient-Tablets-Reveal-Mathematical-Achievements-of-Ancient-Babylonian-Culture.html
*********
Révéler tablettes anciennes réalisations de la culture mathématique babylonienne antique
Paléo-babylonienne "tablette main" illustrant théorème de Pythagore et une approximation de la racine carrée de deux. Clay, 19e-17e siècle avant notre ère. Yale Collection babylonienne YBC 7289. Photo: Ouest recherche sémitiques.
NEW YORK, NY .- Une exposition éclairante de treize anciennes tablettes babyloniennes, ainsi que du matériel documentaire complémentaire, s'ouvre à l'Institut de la New York University pour l'étude du monde antique (ISAW) sur Novembre 12, 2010. Avant de Pythagore: La culture de la paléo-babylonienne mathématiques révèle la pratique hautement sophistiqué mathématiques et de l'éducation qui ont prospéré en Babylonie-Irak actuel-plus de 1.000 ans avant l'époque de la Grèce Thales et Pythagore sages, avec lesquels les mathématiques sont traditionnellement aurait commencé.
Les comprimés de l'exposition, à la date fois belle et instructive, de la période paléo-babylonienne (ca. 1900-1700 BCE). Ils ont été assemblés à partir de trois collections importantes: la Colombie-livres rares et manuscrits, l'Université de Columbia, l'Université de Pennsylvanie, musée d'archéologie et d'anthropologie et de la Yale Babylonian Collection, Yale University.
Avant de Pythagore a été organisée par Alexander Jones, ISAW professeur d'histoire des sciences exactes dans l'Antiquité, et ISAW chercheur invité Christine Proust, historien des mathématiques et de sciences anciennes à l'Institut Méditerranéen de Recherches Avancées, à Marseille. L'exposition reste à l'affiche au ISAW à Décembre 17, 2010.
Jennifer Chi, directeur ISAW pour les expositions et programmes publics, déclare: «Il a longtemps été largement reconnu que bon nombre des réalisations essentielles de la civilisation occidentale, y compris la rédaction et le code de droit qui est le fondement de notre système juridique actuel, mis au point dans l'ancienne Mésopotamie. Toutefois, l'état étonnamment avancée des mathématiques dans cette région a été largement connue seulement pour les érudits. En démontrant la richesse et la sophistication de l'ancienne Mésopotamie mathématiques, avant Pythagore ajoute une dimension importante à la connaissance du public de l'histoire des cultures historiques et des acquis de l'Irak actuel. "
mathématiques babyloniennes est connu dans le monde moderne grâce au travail des scribes, principalement des hommes jeunes qui, venant de familles aisées pour lesquelles l'alphabétisation et les compétences professionnelles ont été transmises depuis des générations, ont été officiellement formé en lecture et écriture. Destiné à travailler dans des domaines tels que la comptabilité, planification de la construction-projet, et d'autres professions dans lesquelles les mathématiques sont essentielles, les scribes ont appris et pratiqué par des symboles mathématiques pour résoudre des problèmes de copie et-une pratique, d'autres théoriques, tels que ceux observés dans les comprimés dans l'exposition.
Alexander Jones notes, «Les preuves que nous avons pour les mathématiques babyloniennes Vieux est étonnant, non seulement dans l'abondance, mais aussi dans sa gamme, de l'arithmétique de base pour bien des problèmes difficiles et des enquêtes. Et puisque les documents sont des manuscrits réelle des scribes, pas de copies sélectionné et édité par les générations plus tard, nous nous sentons comme si nous étions à la recherche sur leurs épaules, comme ils travaillent; on peut même les voir se confondre et faire des erreurs. Des recherches récentes ont fait de cette dimension humaine très vif, en utilisant des preuves archéologiques de ré-imaginer les écoles et les processus d'enseignement et d'apprentissage. En outre, le contenu des comprimés sont encore reconnaissables, comme ils continuent à être enseignée dans les mathématiques contemporaines. "
Les comprimés en avant Pythagore, inscrite en écriture cunéiforme, couvrent tout le spectre de l'activité mathématique, de tables arithmétiques copiés par des scribes en formation pour travailler sur des sujets complexes qui aujourd'hui seraient classés comme la théorie des nombres et l'algèbre. Ce faisant, ils éclairent trois grands thèmes: l'exploitation d'une notation arithmétique des nombres repose entièrement sur deux symboles de base, les écoles des scribes de Nippur, qui était le centre le plus prestigieux de l'enseignement des scribes, et la formation avancée en mathématiques.
Bon nombre des problèmes résolus par les scribes au niveau avancé de formation ont été en fait beaucoup plus difficile que n'importe quel qu'ils auraient à traiter dans leur carrière, et leurs solutions sur des principes qui dépendait, avant le redécouverte de l'tablettes babyloniennes, que l'on croit ont été découvertes par les Grecs du VIe siècle avant notre ère et, plus tard. Un des comprimés, par exemple, est un schéma extrêmement rare montrant un carré avec ses deux diagonales et de trois chiffres qui démontrent que ce que nous appelons le théorème de Pythagore existait 1.000 ans avant Pythagore a vécu. Le contenu de comprimés varie d'autres tables mathématiques pour la formation, les calculs de pratique pour les professionnels, de faire abstraction des problèmes algébriques.
Le sens de ces comprimés et autres de la période paléo-babylonienne ont d'abord été élucidé par le mathématicien et historien des sciences Otto Neugebauer (1899-1990), qui a passé près de deux décennies, en commençant dans les années 1920, la transcription et l'interprétation des comprimés qui était venu à la lumière de l'ancienne Mésopotamie depuis le XIXe siècle. C'est sa recherche de pointe, ainsi que le travail de ses collaborateurs, rivaux, et ses successeurs, qui a révélé aux savants modernes riche culture de l'époque des mathématiques. Avant de Pythagore comprend une sélection de manuscrits et la correspondance, prêté par l'Institute for Advanced Study, Princeton (New Jersey), qui offre un aperçu des méthodes de Neugebauer et son rôle central dans cet «âge héroïque» de la découverte scientifique.
Afin de permettre aux visiteurs d'apprécier les tablettes cunéiformes plus pleinement, ISAW a mis au point une brochure d'exposition prolongée qui guidera les téléspectateurs de lire les nombres cunéiformes. En outre, un site Web riche en contenu consacré à l'exposition peut être consulté à:
www.nyu.edu/isaw/exhibitions/before-pythagoras/.
***
1
1 2
2 3
3 4
4 5
5 6
6 7
7 8
8
9
9
..........
44 = Babylonian 40.svgBabylonian 4.svg
85 = Babylonian 8.svgBabylonian 5.svg
327 = Babylonian 3.svgChiffre-babylonien-100.pngBabylonian 20.svgBabylonian 7.svg
60'lık sisteme göre açılımı
1 1 1 x 1
17 107 17(10+7) x 1
44 404 44(40+4) x 1
60 1 60 = 1 x 60 + 0 x 1
85 1 205 1 × 60 + 25 x 1
3600 1 3600 = 1 x 60² + 0 x 60 + 0 x 1
11327 3 8 407 3 × 60² + 8 × 60 + 47 x 1
7000,2525 1 506 40 105 9 1 x 60² + 56 x 60 + 40 x 1 + 15/60 + 9/60²
***********************
1 = 60 = 3600 = 1
Tablodan da görüldüğü gibi 60'lık sistemde 1, 60 ve 3600 rakamları tamamen aynı biçimde tek şekil ile ifade edilebiliyordu.
Bu durum ise, tabletlerin rakam yazımlarının okunmasında "... tanrı beni 36.000 kişi arasından seçti... " vb. olarak yapılan "tercüme"lerin ve bu tür "tercüme"lerden yola çıkarak , tablette adı geçen o dönemdeki ilgili yerleşim "nüfusunu saptama"nın ne denli hatalı olabileceğini gösteriyor.
........
10'lık sisteme göre
= 2 x 10+ 5 =60
biçiminde yazılan şekilleri
aynı zamanda, 60'lık sisteme göre,
= 2.60+10+5 biçiminde okuyarak 135 değerine ulaşmak da mümkün..
Çünkü, 2
işareti 2 değerini anlatabileceği gibi 2×60=120 veya 2/60 değerlerini de verebilmektedir.
[[ ....örneğin ondalık sistemde 439 olarak yazılan sayı
(4 x 10²) + (3 x 10) +9'un karşılığı [=(400+3+9 ] iken,
Altmışlık sistemde aynı sayı (4 x 60²) + (3 x 60) +9'un, yani 14.589’ un karşılığıdır. ]]
Burada okuyucunun yorumu çok büyük önem taşıyor.
Musevi takvimine göre "Dünya'nın,Gökyüzü'nün, Adam'ın ve öteki varlıkların yaratılması"nın tarihi ("Yaratılış") 5768 yıl kadar bir değerdir. Şimdi artık anlıyoruz ki, bu tarihleme gerçekten de kendisine Mezopotamya'da, İÖ.3750 yıl önceki olay veya olayları "milat" kabul eden bir değerlendirme tarzından kaynaklanıyordu.
Musevi imanlılarının "Yaratılış" dedikleri bu olay, Mezopotamya'da çok büyük ve köklü bir "ittifak" ve "yeniden düzenleniş" toplantısının "milad" kabul edilmesi ile ilgiliydi.
Arkeolojik bakımdan da artık yeterince tanınan bu tarihlerin Mezopotamyasının toplumlarının ilişkileri ve ilişki düzenleri bu nedenle bir "Yaratılış", "Yeniden biçimleniş" olarak yorumlanmış olmalıydı.
Gelgelelim, daha sonraki tapınak görevlileri veya katipler, eski kronoloji tabletlerini okurken( örneğin "Sümer Kıraliyet Listesi"ni) kıral yaşamlarına veya bazı dönemlere "onbinlerce" hatta, "yüzbinlerce yıl"lık değerler atfetmişlerdi ve bizim bazı tarih uzmanlarımız da bunlara "fantastik rakamlar" diye burun kıvırmışlardı.
Oysa farklı takvim değerlerinin kullanılması (ay, gün, ay yılı,..vb. ) bir yana, daha büyük olasılıkla, eski Akado-Sammaru rakam çizimleri farklı değerler temelinde yorumlanmış olmalıydı ki, bunun açıklamasını artık tam bir bilimsellik ölçüsünde biliyoruz.
*****
http://christine.proust.pagesperso-orange.fr/Publications.htm
***
http://toplumvetarih.blogcu.com/zaman-olcum-degerleri-1/646810
