There is ample evidence demonstrating the transmission of mathematical and astronomical/astrological knowledge from the Babylonian context to that of Greece, as well as the transmission of Greek celestial sciences and mathematics from Greece to other civilizations, including the Roman Empire.138 While this is beyond our scope, it is
138 On some of the key supporting evidence, see F. Rochberg-Halton, 1988, "Elements of the Babylonian
Contribution to Hellenistic Astrology.” Journal of the American Oriental Society 108:1, 51-62; J. M. Steele, 2011, "Visual Aspects of the Transmission of Babylonian Astronomy and its Reception into Greek Astronomy."
sufficient for our purposes to note that the studies conducted to date establish the transmission of mathematics and astronomy of a high degree of sophistication to Hellenistic Greece and its territories, and thence, to Rome.
The Roman context and its scientific inheritance have been debated in the scholarly literature, and here, we note the often reiterated perception that the Romans were merely the inheritors of Greek mathematical and astronomical wisdom. This view, generally speaking, locates the Roman sciences in the applied realm – encompassing engineering and practical calculation. (Lehoux, Romans, passim; S. Cuomo, 143-211) This may be likened to the history of scholarship related to the astronomy of ancient Egypt, which initially made the claim that no such science existed, but which has more recently broken very different ground in the literature, arriving at new conclusions regarding Egyptian astronomy.139 It should be of no small interest, then, that we note a remarkably similar unexamined assumption throughout history of science and rabbinic scholarship that the rabbis of late antiquity used mathematics and science for the purely practical, applied ends required by halakhah.
Annals of Science 68:4, 453-465; Jan P. Hogendijk, 1996. "Transmission, Transformation, and Originality: The
Relation of Arabic to Greek Geometry." In F. Jamil Ragep, Sally P. Ragep, and Steven Livesey, Eds.,
Transmission, Transformation. Leiden and New York: E.J. Brill, 31-64; Bill M. Mak, 2013, "The transmission of
Greek Astral Science Into India Reconsidered-Critical Remarks on the Contents and the Newly Discovered Manuscript of the Yavanajātaka.” History of Science in South Asia 1, 1-20; O. Neugebauer, 1969, The Exact
Sciences in Antiquity. Mineola, New York: Dover Publications, 172-76.
139 See R. A. Parker, 1974, “Ancient Egyptian Astronomy.” Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 276, No. 1257. The Place of Astronomy in the Ancient World, 51–65;
Hugh Thurston, 1994, Early Astronomy. New York: Springer-Verlag, 82-83; Compare Gregg De Young, 2000, “Astronomy in Ancient Egypt.” In Helaine Selin, ed. Astronomy Across Cultures: The History of Non-Western
However, as scholars including Daryn Lehoux and S. Cuomo have demonstrated, though the Romans were indeed focused on the engineering feats necessary for the expansion of the Empire, they were by no means mere applied scientists.140 Indeed, while many practical uses of mathematics and astronomy such as sundials, land-surveying, military strategy, and accounting were part of Roman life, advanced astronomical and mathematical writings from Rome are attested. Moreover, such expertise, which included Greek geometry, was extolled. We note this in the Astronomy, by the author Hyginus (ca. second century C.E.), which was addressed to Marcus Fabius, whom Hyginus praised owing to his knowledge of astronomy. The celestial knowledge in this work is profound, encompassing precise definitions and a catalogue of stars based in part on the work of Eratosthenes. Hyginus also takes pains to make a pointed distinction between experts and amateurs in the field of astronomy. (Cuomo, 173) This latter point underscores the high value assigned to mathematical and astronomical expertise and hence, to epistemic authority in the Roman context. S. Cuomo describes astronomical interest among the elite of Roman society as follows:
Astronomical expertise implies that one is able to recognize the stars, even those which are not very bright, assign them to the right constellation, and express their precise number. Apart from Hyginus, we have extensive literary evidence of the astronomical interests of many illustrious Romans: Cicero translated Aratus into Latin, and Germanicus wrote a commentary on the same text. Manilius chose Augustus as dedicatee of his Astronomy, which, as well as detailed arithmetical and geometrical procedures, contains an explicit parallel between the hierarchy of the stars and that of human society. (Cuomo, 174)
140 For a more thoroughgoing look at the Roman sciences, see Daryn Lehoux, 2012, What Did the Romans Know? An Inquiry Into Science and Worldmaking. Chicago: The University of Chicago Press; S. Cuomo, 2001, Ancient Mathematics. London and New York: Routledge, 143-211.
Turning to the matter of deontic authority, ever-present in Roman politics, there is also evidence that Augustus (63 B.C.E.-14 C.E.) used mathematics to bolster his own
prestige. For example, he created numerical records of account prior to his death,
including his expenditures for the empire, the number of territories and people within it, as well the number of elite participants in Roman society. Augustus also arranged for the installation of an immense sundial in Rome “whose pediment reminded the public of Augustus’ victory over Antony and Cleopatra.” (Cuomo, 151) Archeologists have since discovered elements dating from the time of Domitian (ca. 51-96 C.E.), which suggests a later restoration. (Ibid.)141 Here, we see but one point of interconnection between
epistemic and deontic authority. Each form of authority – and its possessor – had the power to either support or override the agenda of the other, depending upon the epistemological and political contexts of their usage. In the above example, Augustus is said to have supported his authority with empirical wisdom and technology
demonstrating the knowledge found in his empire. In the rabbinic context of b. Bava Metzi’a 59b, empirical truth is overturned by deontic authority. Moreover, as we have seen in chapter two, there is evidence that Greco-Roman wisdom could also be used to establish perceived rabbinic authority both within the ranks of Jewish scholarship and among Roman authorities.
Our primary focus on the Bavli also highlights its Sasanian context, well described in the research of Yaakov Elman, as well as that of Shai Secunda, and M.J. Geller.
141 According to Pliny the Elder (23–79 C.E.) the sundial of Augustus was created by the mathematician
Numerous scientific and mathematical texts survive from the period following the Arab conquest of Sasanian Persia, with some Arabic translations of earlier Sasanian texts also coming down to us. As the next greatest power in western Eurasia after Rome itself between ~226 and 654 C.E., the Sasanian Empire has been shown to have been a
transmission hub for scientific knowledge between cultures. Far more is known about the elites of Persia during the Sasanian period than about everyday administrative matters and the history of science.142 Nevertheless, there is sufficient evidence to make it clear both that Greek and Roman science and mathematics made their way to Persia during this period, and that Persian mathematics and astronomy were themselves flourishing.
Moving onto what we know of scientific transmission in Persia, Otto Neugebauer traced the transmission of the sciences between Mesopotamia and India, suggesting an indirect route via Greece and Sasanian Persia. His arguments are well constructed and demonstrate the presence of Greek loan words in Hindu astrology, as well as the
presence of Greek epicyclic models in Indian astronomy. Neugebauer also points to the importance of understanding Roman trade routes and the commercial transactions engaged in between India and Egypt during the first century C.E. This contact, which was particularly active between the first and fourth centuries, he points out, is also
142 Some of this comes from the fourth century Roman writer, Ammianus Marcellinus, who had joined the
Emperor Julian in an ill-fated campaign in the 360s C.E. against the Persians. In the extant books (spanning 353-378 C.E.) of his Res Gestae, Marcellinus described their kings, artistocrats, courts, feasts, and other matters of importance to the elite of Persian society. However, other than military details, everyday life and
government administration in Sasanian Persia were not covered, and Marcellinus presented his portrait using Hellenistic tropes, portraying Persian culture through a Greco-Roman lens. See Ammianus Marcellinus, 1935- 39, Res Gestae. Translated by John Carew Rolfe. Three vols. London and Cambridge: Loeb Classical Library; E. A. Thompson, 1947, The Historical Work of Ammianus Marcellinus. Cambridge: Cambridge University Press. (Reprinted: Groningen 1969); J. den Boeft, J.W. Drijvers, D. den Hengst, H.C. Teitler, 1995-2013. Philological
supported by archeological evidence, as well as internal references to “the Ionians” in Hindu astronomical texts. This expression, however, referred to both the Greeks and the Romans. (Neugebauer 1969, 166-67) In brief, his conclusion is that Babylonian science was transmitted “through the medium of Hellenistic astronomy and astrology” and found its way to India either via Persia or Roman maritime trade routes. (167)143 Moreover, Neugebauer sees astrology as a key tool in tracing the transmission of Hellenistic thought. (171)
Also central to a fuller understanding of the transmission of astronomy and astronomical mathematics is awareness of the trend toward the reception of Hellenistic texts directly from the Sasanian Persian context, circa 226-652 C.E. Circa 260 C.E., Shahpuhr I (241-272 C.E.) founded Jund-i-Shapur in south-western Iran to house Roman prisoners including engineers, doctors, and other learned experts who had been captured in the war with Valerian. These almost certainly included those familiar with Egyptian, Mesopotamian, and Greek mathematics. (Joseph 2011, 26) Later, in 489 C.E., when the Persian school in Edessa was closed by Zeno, the centre of learning relocated to Nisibis, in Persia. Greek medical expertise, and through it, earlier Egyptian and Babylonian remedies, were also brought to Jund-i-Shapur, a medical training centre.
143 Neugebauer also comments on the linkage between astronomy and astrology in the Late Antique context,
asserting: “One of the main reasons for the transmission of astronomical knowledge from one nation to another was undoubtedly the spread of the belief in astrology as the one science which gave insight into the causes of the events on earth. It has often been said that astronomy originated from astrology. I see no evidence for this theory. It seems to me much more plausible to assume that one major incentive for the development of astronomy consisted in attempts to achieve regularity in the intercalation of the lunar calendars.” (Neugebauer 1956, 168) Key here is not the question of where or how astronomy originated, but the fact that astronomy and astrology were frequently transmitted together in antiquity. I will further examine the taxonomical implications of this dual transmission in the conclusion.
Later, during the reign of the Persian king Khusro I, a group of Greek Neoplatonist philosophers and other refugees from the Byzantine Empire, persecuted under the rule of Justinian I, who had closed their academy of learning, were invited to settle in Persia when they fled Athens in 529 C.E. Indeed, Khusro I welcomed the influx of Greek philosophy and science. (26-27) As a result numerous Pahlavi translations of Greek and Syriac texts were made, including Neoplatonic works. Beginning with the rule of
Shahpuhr I, onward through the reign of Khusro I, there is evidence of these translations, as well as from Sanskrit texts, into Pahlavi, or Middle Persian, some of which likely included astronomical and mathematical texts. (27)
Also notable in the Sasanian context in which the Bavli was composed and
compiled would have been the composition of indigenous Persian works of mathematics in Pahlavi, including a handbook of astronomical tables known as the Zij-I Shah.144 Of equal note was the composition, ca. 531-579 C.E., of The Denkard, an encyclopedic collection of scientific and mathematical works, including a section classifying six types of healers, including magi, alchemists, and physicians.
On a related point of interest, Neugebauer describes one such transmission later, in the ninth century, by Abu Ma’shar (d. 886) of the 542 C.E. Persian translation of the Hellenistic text Sphaera Barbarica, by Teukros of Babylon (circa the first century C.E.). These writings had been translated into several languages, including Hebrew.
144 On this important Pahlavi work, later preserved in Arabic, see E.S. Kennedy, 1958, “The Sasanian
Astronomical Handbook Zij-I Shah and The Astrological Doctrine of ‘Transit’ (Mamarr).” This work, which demonstrates Indian mathematical influence according to Kim Plofker (2008. Mathematics in India. Princeton: Princeton University Press, 255), predates Kharazmi’s Algebra and his Trigonometric Planetary Tables (circa 830-5 C.E.).
(Neugebauer 1969, 171-72) In 2002, Antonio Panaino further examined this particular transmission of Teukros of Babylon, confirming its translation into Pahlavi, likely during the third century C.E. While the Pahlavi translation vanished, fragments were preserved in Arabic. The Sphaera was a key work that served to transmit knowledge of the 36 subdivisions of the zodiac, known as decans, consisting of 10 degrees each, with three decans comprising each constellation. Also transmitted in this work was knowledge concerning the constellations rising on the horizon at the same time as a given decan, known as the paranatellonta. (Panaino, 4; Popović, Reading, 138) As Neugebauer describes the importance of such transmission of scientific knowledge via Sasanian Persia:
Following the unmistakable traces of very specific astrological doctrines, one can reconstruct the road which connected Hellenistic Mesopotamia with Hellenistic Egypt, with pre-Islamic Persia, and with India. We are obviously entitled to assume that the same road was followed by the transmission of mathematical astronomy even if no more is available to us than the two external ends in Mesopotamia and India. (Neugebauer 1969, 172)
Demonstrating the transmission, translation, and indigenous creation, of
mathematical and other scientific texts within the Roman and Sasanian contexts is merely the first step, complemented by the presentation of evidence for this transmission in the rabbinic texts themselves in section 3.1.2.