Greek angles from Babylonian numbers

Models of planetary motion as observed from Earth must account for two principal anomalies: the nonuniform speed of the planet as it circles the zodiac, and the correlation of the planet’s position with the position of the Sun. In the context of the geometrical models used by the Greeks, the practical difficulty is to somehow isolate the motion of the epicycle center on the deferent from the motion of the planet on its epicycle. One way to isolate the motion of the epicycle center is to determine the longitude and time of oppositions of the planet with the mean Sun. A Greek astronomer might have realized that the predictions of mean oppositions by Babylonian models could serve as useful proxies for real empirical observations. It is shown that a Greek astronomer with a reasonable understanding of Babylonian System A models for the outer planets and the Sun–Moon could have used those models to estimate approximate values for the eccentricity e and longitude of apogee A required for geometrical models. The same method would work for the inner planets if conjunctions were observable, but they are not, and the variation of the observable synodic events—first and last morning and evening visibilities—is dominated more by the motion of the planet in latitude than the nonuniform motion of the epicycle center.     

Celestial Measurement in Babylonian Astronomy

Late Babylonian astronomical texts contain frequent measurements of the positions of the Moon and planets. These measurements include distances of the Moon or a planet from a reference star and measurements of the position of celestial bodies within a sign of the zodiac. In this paper, I investigate the relationship between these two measurement systems and propose a new understanding of the concepts of celestial longitude and latitude in Babylonian astronomy. I argue that the Babylonians did not define latitude using the ecliptic but instead considered the Moon and each planet to move up or down within its own band as it travelled around the zodiac.     

A consideration of Babylonian astronomy within the historiography of science

This paper traces the reception of Babylonian astronomy into the history of science, beginning in early to mid twentieth century when cuneiform astronomical sources became available to the scholarly public. The dominant positivism in philosophy of science of this time influenced criteria employed in defining and demarcating science by historians, resulting in a persistently negative assessment of the nature of knowledge evidenced in cuneiform sources. Ancient Near Eastern astronomy (and astrology) was deemed pre- or non-scientific, and even taken to reflect a stage in the evolution of thought before the emergence of science (in ancient Greece). Two principal objections are examined: first, that the Near East produced merely practical as opposed to theoretical knowledge and, second, that astronomy was in the service of astrology and religion. As the notion of a universal scientific method has been dismantled by post-positivists and constructivists of the second half of the twentieth century, an interest in varieties of intellectual and cultural contexts for science has provided a new ground for the re-consideration of Babylonian astronomical texts as science developed here.     

A Study of Babylonian Observations of Planets Near Normal Stars

The present paper is an attempt to describe the observational practices behind a large and homogeneous body of Babylonian observation reports involving planets and certain bright stars near the ecliptic (Normal Stars). The reports in question are the only precise positional observations of planets in the Babylonian texts, and while we do not know their original purpose, they may have had a part in the development of predictive models for planetary phenomena in the second half of the first millennium B.C. The paper is organized according to the following topics: (I) Sections 1–3 review the format of the observations and the texts in which they are found; (II) Sections 4–6 discuss the composition of the Normal Star list; (III) Sections 7–8 concern the orientation of the reported celestial directions from star to planet; (IV) Sect. 9 concerns the relationship between the reported distances and the actual angular distances between planet and star; and (V) Sect. 10 discusses the reports of planetary stations, which are the most common reports giving precise locations of planets when they are not near their closest approach to stars, and draws some brief general conclusions about the utility of the Babylonian observations for estimating planetary longitudes and calibrating models in antiquity.I wish to thank Lis Brack-Bernsen, John Britton, Peter Huber, Hermann Hunger, Teije de Jong, Norbert Roughton, John Steele, and Noel Swerdlow for comments on drafts of the paper, for access to work before publication, and for help in various forms.     

Reconstruction of a Greek table of chords

Summary R. R. Newton has shown that Ptolemy's table of solar declinations (Almagest I, 15) was not computed from Ptolemy's own table of chords. Newton explains this by assuming that Ptolemy copied his table of declinations from an earlier source, and that originally the table has been computed by means of a less accurate table of chords.In the present paper I shall venture a tentative reconstruction of the method of computation of this ancient table of chords. The clue to this reconstruction is a recursion formula which allows a rapid calculation of the chords belonging to arcs of 1°, 2°, ... in a circle. This recursion formula, which was suggested to me by a verse in the ryabhtya of ryabhata, can be deduced from a theorem of Archimedes concerning a certain sum of chords in a circle. I suppose that this recursion formula was used by Apollonius of Perga in order to obtain a table of chords, and that this table of chords was used by a Greek author (possibly Apollonios himself or Hipparchos) to calculate the table of solar declinations used by Ptolemy. If this hypothesis is adopted, the errors in Ptolemy's table can be explained.     

Studies in Babylonian lunar theory: part III. The introduction of the uniform zodiac

This paper is the third of a multi-part examination of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton, AHES 61:83–145, 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies, accomplished in the construction of the System A lunar theory early in the fourth century B.C. Part II (Britton, AHES 63:357–431, 2009) examines the accomplishment of this separation by the construction of a successful theory depicting the variations due to lunar anomaly in System A and its subsequent adaptation in System B. The present paper examines the introduction of the uniform zodiac, necessary for any theory depicting variations depending on the position of syzygy. It addresses three questions: (1) In light of all available evidence, what is the magnitude of the constant term in the expression Δλ* = C ? 1.3828°Y, describing the difference between the Babylonian sidereal longitudes and modern tropical longitudes? (2) What considerations governed the placement of the Babylonian sidereal zodiac relative to the fixed stars? (3) When was the uniform zodiac introduced? To the first question it finds C = 3.20° ± 0.1°, scarcely different from Huber’s (Centaurus 5:192–208, 1958) estimate of 3.08°, essentially confirming Huber’s result obtained from much less data. For the second it shows that accommodating the three asterisms comprising Taurus limited the placement of the zodiac to within 3°, while the prominence of half sign multiples among the measured intervals between prominent Normal Stars led irresistibly to the choice adopted. Finally, it finds that the zodiac was introduced between ?408 and ?397 and probably within a very few years of ?400.     

一种新型统一潮流控制器

本文提出一种基于奇异值分解（SVD）的统一潮流控制器。该控制器通过解耦直轴与交轴控制变量的交互作用,可有效减小有功和无功之间的动态交互影响。故其性能与静态解耦（sD）控制器和比例积分（PI）控制器相比,具有明显优势。     

饮用水源水质评价的模糊聚类模型的研究

考虑到饮用水源样本并没有严格的属性,以及它们在形态和类属方面存在看中介性,确定了对人类生理健康影响较大的高锰酸盐指数、生化需氧量、总氮、氨氮、氟化物、总磷、溶解氧等9项评价因子;将特征空间中一组没有类别标记的矢量按某种相似性准则划分到若干个子集中,实现每个子集代表整个样本集的某个或者某些特征和性质;建立起基于模糊聚类法的饮用水源水质评价模型。最后,将所建模型应用到阜新市目前饮用水源地水质评价中,应用效果表明：所建模型既能有效地判断饮用水源水质类别,又能确定水体中主要污染物和主要污染源,通过不同评价方法结果的比较分析,体现了所建模型的良好有效性和适用性。     

清洁生产：海水养殖业持续发展的新模式

清洁生产（Cleaner Production)是20世纪70年代兴起的新型工业生产模式,实践证明这种模式有助于产业实现可持续发展,海水养殖业具有明显的特殊性,如对海洋系统水环境赞成直接的影响,养殖水产品对污染物的富集,养殖生和的病害严重等,清洁生产是实现海水养殖业持续高效发展的先决条件,本文在较为系统地论述海水养殖业开展清洁生产必要性的基础上,阐述了我国海水养殖业开展汪有洁生产的基本思路,如立足生态养殖,发展工程化养殖等,并提出亟待解决的离岸设施生态养殖,养殖用水高效处理关键技术.     

复杂能源系统结构演化和评价的新模型

能源系统作为开放的有机整体,是一个无确定边界的、与环境耦合的实体。定义了描述该实体的新物理量,由此建立了能源系统演化和评价的新模型,对“参考情景”、“可选择情景”以及“高经济增长情景”三种模式下的中国能源系统结构演化进行了案例分析,得到了合理的结果。该模型也为一般的社会经济系统发展提供了比笛卡尔一牛顿式的机械模型和熵增的热寂模型更合理的图景。     

一种基于模糊聚类的新型入侵防御攻击系统模型

本文从降低传统入侵防御系统检测引擎的虚警率、漏警率与增强主动防御能力方面入手,给出了一种基于模糊聚类的入侵防御系统检测引擎实现方案;并探讨了将蜜罐技术与入侵防御系统相结合的可行性;进而提出了一个全新的入侵攻击防御系统模型。在这个模型中,入侵防御系统同时具有了实时防御与攻击防御的能力。     

经济-资源-环境系统自组织演化的新模型

经济-资源-环境（ERE）系统是个典型的开放复杂自组织系统,将广义信息熵的概念引入复杂ERE系统,建立其普适的结构自组织演化方程,形成了复杂系统建模新方法,可揭示复杂ERE系统中多主体作用动力学及结构自组织演化过程。以国家可持续发展实验区ERE发展模式为例,根据1994～2005年指标数据,对其发展演化过程做了具体的模拟研究,揭示了实验区规划的实施对可持续发展系统的改进和完善是一个复杂的自组织过程.