Pioneers of the Ice Age Models: A Brief History from Agassiz to Milankovitch

It is currently known that astronomical factors trigger the emergence of glacial and interglacial periods. However, nearly two centuries ago, the overall situation was not as apparent as it was with today’s scientists. In this article, I briefly discuss the astronomical model of ice ages put forward between the 19th and 20th centuries. This century was indeed annus mirabilis for scientists to understand the ice age phenomenon. Agassiz, Adhémar and Croll laid the foundation stones for understanding the dynamics of ice ages. But it was Milankovitch who combined empirical geology with mathematical astronomy. To put specifically, he identified the shortcomings of the preceding ice age models and modified his model accordingly. In what follows, I review former approaches to the ice age problem and show how they failed to meet their objectives. Next, I show how Milankovitch’s model managed to capture all sufficient astronomical elements. Last sections focus on Milutin Milankovitch’s genuine approach, including his accomplishment of tackling the problem mathematically.

The Tabulae Eclypsium by Giovanni Bianchini

The Tabulae eclypsium by Giovanni Bianchini (d. after 1469) was part of a larger work, the Flores Almagesti, on mathematical astronomy. In his work on eclipses, which hitherto has not been studied in depth, Bianchini compiled new tables, strictly adhering to Ptolemy’s procedures, and explained their use by means of worked examples to facilitate the task of computers. Bianchini’s works were influential among his contemporaries, especially Peurbach and his student Regiomontanus, with whom Bianchini corresponded. For a variety of reasons, Regiomontanus’ works have eclipsed Bianchini’s. In this article, we present one of Bianchini’s major works, with the aim of restoring a more balanced perspective on 15th-century mathematical astronomy in Europe. Published Online (2021-08-31)Copyright © 2021 by José Chabás and Bernard R. Goldstein Article PDF Link: https://jps.library.utoronto.ca/index.php/aestimatio/article/view/37699/28698 Corresponding Author: José Chabás, Universitat Pompeu FabraE-Mail: [email protected]

Ephemerides in high medieval Europe: The textual evidence

A common aspect of the practice-oriented side of pre- and early modern mathematical astronomy was the computation of ephemerides, that is, tables that displayed the daily positions of the planets in a synoptic and calendrical format. Even though medieval Europe was no exception in this regard, the existence of ephemerides in this period and region has gone largely unnoticed, owing both to terminological difficulties and the low survival rate of actual specimens. What exists in significant numbers, however, are texts describing different approaches to constructing ephemerides and computing their various entries. The article demonstrates this by discussing ten such texts dating from approximately the middle of the 12th century to just after 1300. Taken in its entirety, this hitherto neglected corpus provides conclusive evidence against a view according to which ephemerides entered European astronomical practice only in the 15th century.

The Moon and Planets in Ancient Mesopotamia

In ancient Mesopotamia, all five planets visible to the naked eye were known and studied, along with the Moon, the Sun, the stars, and other celestial phenomena. In all Mesopotamian sources concerning the Moon and the planets, be they textual or iconographical, the astronomical, astrological, and religious aspects are intertwined. The term “astral science” covers all forms of Mesopotamian scholarly engagement with celestial entities, including celestial divination and astrology. Modern research on Mesopotamian astral science began in the 19th century. Much research remains to be done, because important sources remain unpublished and new questions have been posed to published sources. From ca. 3000 bce onward, Mesopotamians used a calendar with months and years, which indicates that the Moon was studied at that early age. In cuneiform writing, the Sumerian and Akkadian names of the Moongod, Nanna/Sin, are attested since ca. 2500 bce. The most common Akkadian names of the five planets, Šiḫṭu (Mercury), Dilbat (Venus), Ṣalbatānu (Mars), White Star (Jupiter), and Kayyāmānu (Saturn), are attested first in 1800–1000 bce. The Moon, the Sun, and the planets were viewed as gods or manifestations of gods. From ca. 1800 bce onward, the phenomena of the Moon, the Sun, and the planets were studied as signs that were produced by the gods to communicate with humankind. Between ca. 600 bce and 100 ce, Babylonian scholars reported lunar and planetary phenomena in astronomical diaries and related texts. Their purpose was to enable predictions of the reported phenomena with period-based, so-called Goal-Year methods. After the end of the 5th century bce Babylonian astronomers introduced the zodiac and developed new methods for predicting lunar and planetary phenomena known as mathematical astronomy At about the same time they developed horoscopy and other forms of astrology that use the zodiac, the Moon, the Sun, and the planets to predict events on Earth.

4. Identities, and more identities

The world of trigonometry is full of identities: some of them extremely useful, others beautiful, and a few that are simply bizarre. ‘Identities, and more identities’ takes a tour of the menagerie of identities, viewing a little from each of these categories. The first two examples are known as triangle identities, because they refer to angles and lengths in a given triangle. The Law of Sines and the Law of Cosines are discussed, along with Mollweide’s formulas, the Law of Tangents, Morrie’s Law, and the introduction of logarithms, which became the preferred computing tool in mathematical astronomy, and then in practical disciplines like surveying and architecture in the early 17th century.

New Astronomy in Service of Old Astrology: Close Planetary Conjunctions in Pre-Modern China

This article introduces various definitions and criteria for the astronomical phenomena of “encroachments” (close lunar and planetary conjunctions) in pre-modern China. With improvements in observations and mathematical astronomy, the standard of encroachments began to undergo many changes leading to more precise explanations of the phenomena. Before the adoption of Huihui Lifa (Islamic-Chinese calendrical astronomy), traditional Chinese methods could not predict the phenomena of encroachments, and records of encroachments were mainly based on actual observations. These records abound in Chinese dynastic histories, and they play an essential role in the interpretation of astrological omens. In the first half of the seventeenth century, the prediction of encroachments became an effective approach for examining the accuracy of different elements of calendrical astronomy besides solar and lunar eclipses. In the meantime, with the introduction of western astronomical knowledge into China, people had a better understanding of the principle of encroachments, and they began to question its rationality in astrology. Moreover, new knowledge of encroachments also brought new insights and inspired some philosophical discussions on the structure of the cosmos. However, these new astronomical methods still served the old astrology, due to the continued requirements that astronomers interpret astrological omens.

Indian Sine Table of 36 Entries

Trigonometry is an indispensable tool of Indian mathematical astronomy. The concept of trigonometry originated in Greece and it was transmitted to India together with astronomy.

A Chinese Innovation Based on Western Methods: The Double-Epicycle Solar Model in the Lixiang kaocheng, 1722

This article attempts to show how an effort was made by Chinese astronomers to improve on the solar model under the auspice of Emperor Kangxi, in circumstances of the merging of Western and Chinese mathematical astronomy. The result of this effort is the Lixiang kaocheng. Different from the eccentric solar model in the previous calendars, Lixiang kaocheng invented a double-epicycle model to describe the solar motion, aiming at bringing computations into agreement with observation. The observational data used for determining the parameters of solar model might be obtained with Tychonic instruments. But it is also possible that these “observational data” might have been derived from Western astronomical tables. Although actual observations did become more accurate, it did not reflect upon the revision of the solar model. The accuracy of the solar model in the Lixiang kaocheng did not increase very much compared with the previous models.

Knowledge Production

The chapter traces the non-European roots of specialized knowledge production in the ancient times as illustrated by the civilizations of the Indian and the Chinese regions. Examining the archaeology and ethno-archaeology of remains of the civilizations in the valleys of the Indus and Yellow rivers, we try and capture the earliest knowledge in crafts production technology such as architecture, metallurgy, lapidary, and ceramics. Orally transmitted Vedic knowledge, eschatology, metaphysics, grammar, phonetics, astronomy, the post-Vedic systems of thought, Ayurvedic knowledge, architecture, nature of metallurgical texts, the Indian and Chinese textual traditions, and epistemological traces constitute other contents of the chapter. This chapter underscores the early India’s methodologically distinct aphoristic structure of stating truth as astute observations generalized as self-validated principles, the logic of which corresponds to that of mathematical equations or formulas. It discusses the history of mathematical astronomy. A distinct epistemic shift is explicit in India’s astronomy of fourteenth to sixteenth centuries CE. Mādhava of Sangamagrāma (c. 1340–1425 CE) in Kerala marks the beginnings of this shift through his path-breaking mathematical advances in conceptualizing infinite series. The chapter ends with a concise discussion of the Chinese history of knowledge systems across the material cultures