64th RAI in Innsbruck 2018

In a fragment ascribed to Theophrastus (ca. 370-287 BC) this author very likely alludes to the Mesopotamian tradition of the fish-apkallu, which would be the oldest attestation in Greek texts. Elsewhere in his extant writings Theophrastus provides information on the date cultivation in Babylonia.
In this paper I would like to present what Theophrastus writes about Babylonia and investigate how he could have had access to this information. Furthermore, I would like to elaborate on the wider context of the Peripatetic school and its scholarly activities.

When we think of the first scientific developments in botany and pharmacology, we usually think of Theophrastus (ca. 370 - ca. 287 BCE), who, for many good reasons, earned the epithet “Father of Botany”. His treatise, the Historia plantarum (including one book on medicinal plants, ca. 300 BCE), is considered the earliest fully-surviving example of Pre-Linnaean plant taxonomy. But to what degree are the principles and reasoning behind this remarkable achievement an exclusive product of Greek culture and the Peripatetic school to which Theophrastus owed so much?
In this talk, I will argue that the specific method adopted by Theophrastus to think about and systematize information regarding medicinal plants, is to be related, to a surprising level of detail, to the same conceptual method devised by Assyro-Babylonian academics half a millennium earlier, as evinced from an analysis of their work on plants Šammu šikinšu. The implications of this finding are multifold. For example, it suggests the distinct possibility that Theophrastus’ formal application of standard rules in the description and identification of plant elements (as from Hist. pl. IX) developed within the same normative tradition common to Šammu šikinšu. It also seems reasonable to assume that such a tradition would have more likely circulated through formal (and technical) education than through casual communication.

Babylonian mathematical astronomy appears founded on an understanding of iterated maps—a technology utilized by modern methods of non-linear dynamics capable of describing deterministic chaos.
The iterated maps appear to model visibility phenomena such as first or last appearance using Poincaré sections describing close recurrence in position among the stars in terms of sidereal ecliptic longitude. Babylonian astronomers were careful to define stable one-dimensional periodic maps addressed by terminating sexagesimal fractions and partitioned according to resonances, which strongly suggests at least empirical knowledge of mode-locking for which the simplest rationals have the largest steps in winding number.
Although the “music of the spheres” is widely associated with Kepler’s musical expression of planetary angular velocities in Harmonices Mundi (1699) and Plato’s cosmic harmony in Timaeus (ca. 360 BCE), musical intervals based on 5-limit just intonation appear in Babylonian mathematical astronomy whose cuneiform texts comprise predictions for years SE 15-150 with few exceptions (ca. 295/396-160/161 BCE according to the Seleucid Empire).
The longitudes of Babylonian Normal Stars are well-described by a model in which the ratio of successive longitudes is either 16/15 (minor second) or 8/5 (perfect fifth plus a minor second).
As noted by Aaboe in 1964, many System A models are based on zones for which a fundamental angular frequency is related to the others by regular 5-limit fractions based on superparticular ratios i.e., first order resonances. The just intervals expressed in Babylonian astronomy include minor semitone, minor whole tone, major whole tone, minor third, major third, perfect fourth, perfect fifth and diapason. The range of angular frequencies may be clipped to robustify the model by eliminating rarely-observed extreme values, while the zigzag functions of System B models are shown to be lifts of circle maps including the tent map.
The paper concludes by applying mathematical methods of Babylonian astronomy to a modern problem of cardiac arrhythmia based on chaotic circle maps that describe the competition of two natural pacemakers for control of the heart.

The expression “lunar six” was first used by Sachs in the general presentation of Late Babylonian astronomical texts he gave in 1948. These items, namely, NA, ME, ŠÚ, GI₆, NA, and KUR, point to lunar phenomena, two of which occur around the moon’s disappearance at the end of the month, with the other four occurring before and after the full moon. The astronomical meaning of the “lunar six” was already well-established at the time of Sachs’ publication, though scholars have devoted many pages since then to the precise description of these phenomena, and especially to understanding the way the “lunar six” were measured and what these measurements help to accomplish. For example, Lis Brack-Bernsen has argued quite strongly that the measurement and determination of the “lunar six” played a leading role in the development of mathematical astronomy in Achaemenid and Seleucid Babylonia, even if other scholars have not followed her on this matter. While “lunar six” measurements from as early as the Neo-Assyrian period give us access to the Mesopotamian study of the moon's behavior, no literal interpretation, however, of the Sumerian and Akkadian terms for these items has been established. Indeed, it is only in the last decades that the social and linguistic aspects of Mesopotamian astronomy have become points of emphasis for modern scholar.
In this presentation, I propose a unified interpretation of the “lunar six” terms. I characterize this interpretation as unified because I developed my understanding of these terms not only through separate inquiries into each item, but by considering the “lunar six” as a system and taking their mutual relations in to account. Moreover, I will endeavor to show that analyzing the names of technical astronomical terms does not have to be limited to the philological realm, and can yield important insights that help us understand the principals that guided the creation of Mesopotamian scientific knowledge. I will conclude by sharing a problem I have encountered in literally interpreting the “lunar six” term NA, my resolution of which strengthens the hypothesis that choices like those between Sumerian and Akkadian names for terms are intentional and meaningful.