The Exact Sciences in Antiquity

Neugebauer, O.; Boyer, Carl B.

doi:10.1119/1.1933313

Cited by 54 publications

(44 citation statements)

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“…Neugebauer, 1969' Just as in the case of the decans, the crudeness of the underlying procedures is so great that only under severely restrictive assumptions could numerical conclusions be abstracted from the given lists. If we add the fact of obvious errors and carelessness in details in the execution of the texts as we have them, one would do best to avoid all hypothetical structures designed to identify Egyptian constellations from the analysis of the Ramesside star clocks.…”

Section: Discussionmentioning

confidence: 99%

A Firmament above Thebes: Uncovering the Constellations of Ancient Egyptians

Lull¹,

Belmonte

2006

Journal for the History of Astronomy

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The study of ancient sacred sources permits us to say that the ancient Egyptians had a complete set of constellations covering the whole sky that could be seen from Egyptian latitudes. There were two dominant groups, one (probably) in the southern sky and another for northern declinations. The northern sky, as beautifully represented in some New Kingdom tomb ceilings, was full of constellations. These took the form of a lion, a crocodile, a bull's foreleg (sometimes a complete Bull), or a female hippopotamus. The southern group was essentially formed by a belt of 'constellations' known as the decans, individual stars or asterisms whose heliacal rising was presumably used for time-keeping, at least from the end of the Old Kingdom (c. 2200 B.C.), if not earlier, since some decanal stars or constellations, such as sJI} (Sah) or spdt (Sopdet), are already mentioned in the Pyramid Texts. We know this group from the diagonal star-clocks decorating coffin lids (17 have so far come to light) of the First Intermediate Period and the Middle Kingdom, and also from later tombs and temple ceilings, including the famous Zodiac of Denderah (c. 50 B.C.). The system needed to be updated during the Middle Kingdom (c. 1850 B.C.) when the decanal star-clocks were presumably developed, although information about them has been obtained only from a later source known as the Cosmology ofNut, with two relevant extant copies in the cenotaph of Sethy I at Abydos and in the tomb of Ramesses IV (Kings'Valley 2, hereafter KV2).However, in the New Kingdom (c. 1500 B.C.), the decans were no longer useful for time-keeping, due to the wandering character of the civil year, and a new system was developed, using only the meridian (or near-meridian) transit of certain stars, belonging in some cases to huge constellations, such as the Female Hippopotamus (rrt) or the Giant (nb.t), and in others to asterisms. These star charts have been found in the tombs of the last Ramesside pharaohs (c. 1100 B.C.; hence the name "Ramesside clocks or star-charts") in the Valley of the Kings (notably Ramesses VI, VII and IX; KV9, I and 6, respectively), where they were painted for the benefit of the deceased king.The number and variety of documents of astronomical character substantially increases during the New Kingdom and after. As we have mentioned, astronomical ceilings began to depict a complicated pattern, or 'celestial diagram' as it is frequently called, in which lists of stars were combined with actual representations of both southern constellations, such as Sah, Sopdet, sit/srt (Sit or Seret, the Sheep) or wiJ (Wia, the Boat), and northern ones such as mshtyw (Meskhetyu, the Foreleg), msi (the Lion) or rnw(Anu, a falcon-head god). The best preserved, which could be considered masterpieces of Egyptian art, are those found at Thebes in the tomb of Senenmut

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Section: Discussionmentioning

confidence: 99%

A Firmament above Thebes: Uncovering the Constellations of Ancient Egyptians

Lull¹,

Belmonte

2006

Journal for the History of Astronomy

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“…The work on medieval optics, illuminating as it is for medieval doctrines of perception, has straightforward philosophical relevance (see, e.g., Lindberg 1970). The work of Neugebauer and his group on ancient mathematics and astronomy has been equally spectacular (Neugebauer 1957). History of science is by now a significant portion of the American university scene, with several fullscale university departments, several history and philosophy of science departments, and a very large number of individual historians of science as members of history, philosophy, or science departments.…”

Section: B History Of Sciencementioning

confidence: 99%

Diskussion/Discussion. Richard Rorty and the American Philosophical Scene

Turnbull¹

1982

Analyse &Amp; Kritik

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Richard Rorty's assessment of the American philosophical scene is unduly cynical. Part of the reason for this seems to lie in his recognition (in Philosophy and the Mirror of Nature) of the incoherence of "grounding" a linguistic or conceptual scheme on a "given", but proceeding, nevertheless, to think of representation and truth as requiring conformity to a "·given". He, therefore, fails to appreciate the unity and seriousness of American philosophers who, abandoning the "given", are working with some success·on plausible accounts of representation and truth. Surprisingly, neither in his article nor his book does he attend to the remarkable increase in sophistication and serious research on the part of historians of philosophy and historians of science. Both in serious work on representation and truth and in historical research there is more rapprochement between American and Continental philosophers than Rorty seems prepared to credit.

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“…Precise descriptions of multiplication methods close to the ones that we learn at school appeared in Europe during the late Middle Ages. For historical references, we refer to [49,Section II.5] and [37,5].…”

Section: Brief History and Related Workmentioning

confidence: 99%

Even faster integer multiplication

Harvey

Hoeven

Lecerf

2016

Journal of Complexity

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We give a new proof of Fürer's bound for the cost of multiplying n-bit integers in the bit complexity model. Unlike Fürer, our method does not require constructing special coecient rings with fast roots of unity. Moreover, we prove the more explicit bound O(n logn K log n ) with K = 8. We show that an optimised variant of Fürer's algorithm achieves only K = 16, suggesting that the new algorithm is faster than Fürer's by a factor of 2 log n . Assuming standard conjectures about the distribution of Mersenne primes, we give yet another algorithm that achieves K = 4.

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The Exact Sciences in Antiquity

Cited by 54 publications

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A Firmament above Thebes: Uncovering the Constellations of Ancient Egyptians

A Firmament above Thebes: Uncovering the Constellations of Ancient Egyptians

Diskussion/Discussion. Richard Rorty and the American Philosophical Scene

Even faster integer multiplication

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