This project investigates how new knowledge emerges from the originally separate traditions of astronomy, astrology and mathematics in a transformation and innovation process. The investigations are based on the research results obtained in research group (D-1) Space of Nature.

### Research

In three sub-projects, the aim was to analyse which procedural, theoretical or empirical knowledge resources are involved in innovation and how innovations are created through new combinations and applications of existing procedures and knowledge in ancient astronomy and astrology. What the case studies have in common is that they deal with transformation and innovation processes in knowledge resources involving at least two separate astronomical, astrological or mathematical traditions.

##### Late Babylonian mathematics in the context of astronomy

*Mathieu Ossendrijver*

Along with mathematical astronomy, Late Babylonian (LB) scholars (400-50 BCE) also pursued a range of more narrowly mathematical topics. Partly due to the small size of the LB mathematical corpus (ca. 60 tablets and fragments), mathematics remains a badly understood area of LB scholarship. Research in the project (D-1-1) Mathematical astronomy in Babylonia has revealed that LB mathematics and astronomy were more intricately connected than previously thought, in particular due to the discovery of geometrical methods within the astronomical procedures. The purpose of this project was to shed further light on the interaction between LB mathematical and astronomical practices by focussing on the mathematical corpus. In D-1-1 a few accidentally discovered unknown LB mathematical tablets were studied and published. However, a dedicated search for unpublished LB mathematical texts has recently become possible due to the availability, since October 2016, of an unpublished digital catalogue of the “Babylon collection” of the British Museum, which is the main repository of LB scholarly texts. A preliminary search in this catalogue has already yielded about a dozen unpublished and previously unknown LB mathematical tablets.

A selection of unpublished LB mathematical tablets were edited, investigated and will be published. The purpose is (1) to identify areas of change with regard to Old Babylonian mathematical practices (1800-1600 BCE), (2) to explore if and how these changes can be correlated to developments in LB astronomy, and (3) to identify possible astronomical applications of the methods that are attested in the mathematical texts.

##### The hermeneutics of sign and number in Late Babylonian astrology

*Marvin Schreiber*

Some features of cuneiform texts from the 1st Millennium, mostly astrological, are the use of astrological-numerological calculation schemes, the writing of specific signs and words with numerals, and a system which offers new interpretations of signs by means of the numerical writing, and also adding further associations and links. This mixture of astrology, numerology and lexicography still awaits a complete description and an explanation of its underlying hermeneutics of numerals and signs. It seems partly linked to Late Babylonian zodiology. In this form of astral science it was possible to read a certain number either as a sign for a month of the calendar or as a sign for the corresponding zodiac sign. New texts which promise a better understanding of this barely studied field were found during the work on the dissertation “(D-1-5-1) Die Astrologische Medizin der spätbabylonischen Zeit” about astrological medicine.

A study of the new material should shed further light on Late Babylonian scholarship and worldview, and the astrological influence on it. Other related text groups that are already known are the so-called ‘number-syllabaries’, the explanatory text i-nam-giš-ḫur-an-ki-a and some divinatory texts that express the omens in numbers. Relations of these texts with the new ones were also explored.

##### Byzantine astronomy between tradition and innovation: Leontius´ treatis *On the construction of an Aratean globe *

*Fabio Guidetti*

Fabio Guidetti works on the history of ancient astronomy, particularly on the transmission of Graeco-Roman scientific knowledge into the Western and Byzantine middle ages, and on the interaction between written (descriptive) and visual (cartographical) information in astronomical manuscripts. Within this project he examined the coexistence of tradition and innovation in mediaeval science through the study of a middle-Byzantine astronomical text, the treatise *On the construction of a celestial sphere* by Leontius Mechanicus. This text, of which Guidetti prepared a new commented edition and translation, aims at integrating the prestigious tradition of Hellenistic astronomy, as transmitted in the Phenomena of Aratus, with the new information derived by the contact with Arab and Persian astronomers, and the new observations of the sky carried out by them. The publication will make available to scholars a hitherto neglected text, which shows a remarkable awareness of the historical development of scientific knowledge, as well as an effort toward the integration between traditional authorities and newly improved information.