 Okay. I wonder if I might call us to order. Good afternoon. I'm Ben Hermelin. I am the Executive Vice Chancellor and Provost here at UC Berkeley. It's my great privilege and honor to welcome you to the first of this year's 110th annual Martin Meyerson Berkeley Faculty Research Lectures. For more than a century, Berkeley's Academic Senate has singled out distinguished members of our faculty whose research has changed the trajectory of their disciplines and of our understanding. These lectures shine a light on the essential part of our mission, creating new knowledge. The curiosity and creativity that fuel the quest to learn and understand are at the heart of our commitment to making the world a better place through what we discover and what we teach and the public service we provide. This year's lectures represent the continuation of a treasured tradition that has occurred annually with one exception. In the wake of World War I and the influenza pandemic, the faculty research lectures were suspended in 1919. In 2020, when virtual events were in vogue and Zoom kept us together, these lectures went on. I should note that today's lecture will be recorded and available to view on YouTube or from the Faculty Research Lectures website. Being selected to deliver a faculty research lecture is rightfully seen as a high honor. The standout among peers to exemplify academic excellence is no small thing. For students, members of the campus community and the public, this is a wonderful way to experience scholarly research of the highest caliber. Sorry about that. Join me in welcoming the past recipients who are here with us today. Professors, please stand when I read your name and let's hold our applause until everyone has been recognized. Robert Alter, John Clark, Eric Grun, Tony Long, Barbara Omanowich, Jan DeVries, Vicky Kahn, Catherine Gallagher, Tom LeCour, Marty Jay, and Jatendra Malik. And I apologize if this list is incomplete and I missed anyone. Who did I miss? Okay, I apologize. Okay, so the two individuals chosen by our Academic Senate to give this year's Faculty Research Lectures are Francesca Rookberg, today's speaker, and Jatendra Malik, who is presenting on March 20th. Francesca Rookberg is a serialogist and a historian of science who focuses on the science of nature or nature of science rather in antiquity. Her research materials are the Kinea-formed sciences, especially Babylonian astronomy and related sciences and their transmission, transformation, and legacy in ancient Greece and the Greco-Roman world. She is the Catherine and William L. Magistretti Distinguished Professor of Near Eastern Studies, Emerita, in the Department of Middle Eastern Languages and Cultures, the Graduate Group in Ancient History and Mediterranean Archaeology, and the Office for the History of Science and Technology. She is a John D. and Catherine T. MacArthur Fellow, the Guggenheim Fellow, and a member of the American Philosophical Society. She received the Society's John Frederick Lewis Award for her book, Babylonian Horoscopes. Among her other publications are Before Nature, Kinea-formed Knowledge, and the History of Science and Hellenistic Astronomy, The Science in its Context, which she co-edited with Alan Bowen. And that received the Choice Award as an outstanding academic title. Rookberg has been a member of the Institute for Advanced Study at Princeton and a fellow at Maudlin College, Oxford. She's a senior fellow at the Institute for the Study of the Ancient World at New York University. Most recently she was awarded the California Institute of Technology's prestigious Frances Bacon Award in the History and Philosophy of Science and Technology. Please join me in welcoming Professor Francesca Rookberg, who will speak to us about the history and transmission of a Babylonian astronomical idea. Thank you very much, Ben. It is such a pleasure to be here today and I want to thank Executive Vice Chancellor and Provost Hermelin for his most kind introduction. It is a great privilege and an honor to participate in the tradition of the Meyerson Faculty Research Lectures, and I thank the Academic Senate for giving me this wonderful opportunity. I also thank Susan Parish for her expert organizing and help with the PowerPoint. And last but certainly not least, I thank my Department of Middle Eastern Languages and Cultures colleagues for setting the ball in motion with their nomination. I am deeply grateful for that and for their intellectual generosity and friendship over the years. Ideas begin in the heaven of contemplation, but they end in the sublunary realm of historical experience. That is the opening sentence of Donald R. Kelly's The Descent of Ideas, and it perfectly suits my subject today. Not for Kelly's metaphor, but in a rather literal way. I wish to link the heaven of contemplation, that is literally the contemplation of heaven, to the sublunary realm of historical experience in taking up the question of the history and transmission of an astronomical idea from ancient Babylonia into many of the regions, languages, and cultures of the vast Hellenistic world. It's spread from Mesopotamia, which sits nicely in the center of the map you see here, to the Eastern Mediterranean, South and West, to Egypt and the Western Mediterranean, and also East to India from circa 300 BCE, well into the period of late antiquity, and into the Middle Ages. Can everyone hear me okay? The transmission and integration of astronomical ideas from the cuneiform world is one of the principal historical developments of ancient intellectual history. The Hellenistic period and the geocultural realm unifying its regions played a unique role in the sciences, precisely because it provided the cultural and intellectual means for the astronomy and astrology of Babylonia to enter the tradition of astral science that would come to dominate the West until the dissolution of the geocentric cosmos in approximately 1500 of the common era. To speak of pre-modern astronomy and astrology is really to speak of one complex science of the heavens in which all the ancient cultures from whence we have written sources for astral science participated. That is to say, the Babylonians, Egyptians, Greeks, Romans, Judeans, Indians, Chinese, and the European heirs to Greco-Roman intellectual culture each developed a certain kind of knowledge of the heavens, and all with the exception of the Chinese were heavily indebted to the Babylonians for their methods and ideas. Babylonian forms of astral science, therefore, played a decisively creative role in the development of methods of astronomical prediction, as well as astrological prognostication throughout antiquity. To show some of the ways Babylonian astronomical ideas shaped new Hellenistic traditions in the astral sciences, I shall focus on only one subject, that of the problem of the variable length of the day throughout the year. This subject and its various ramifications was of surprising consequence, as I hope to show. Almost everyone experiences variability in the length of the day, except if one lives on the equator, but the variation in length of daylight is not only different depending on where one is, but cultural diversity abounds in how this experience was understood and expressed. In spite of all this diversity, it was the Babylonian parameters of, first, the ratio of longest to shortest daylight, second, the rising times of the zodiacal signs, which I will come to a little later, and third, the placement of the vernal equinox at degrees of Aries that mark the indelible traces of Babylonian ideas in relation to the length of the day across the intellectual landscape of the Hellenistic Oikumine. The parameters and calculation methods associated with the phenomenon of the variable daylight demonstrate the fact of widespread influence from Babylonian astronomical tradition to new traditions of astronomy, astrology, calendrix, and geography in Hellenistic contexts. The widespread adoption of Babylonian numbers and methods had little to do with their accuracy. Indeed, they were not accurate, but that is a complex question. This is worth underscoring because the story of the transmission of science, especially of the exact or mathematical sciences, is usually about excellent parameters being passed along on the sheer force of their accuracy. But that is not the story I want to tell today. To tell my story, I shall spend a little time on the Babylonian evidence for the variable daylight and its associated parameters and where it was adopted in other contexts. Then I want to turn to the broader historiographical importance of this and the reason for my interest in it, which is the question of accounting for such a phenomenon in the transmission of ancient science and what sort of historiographical methods we have to best address it. What is at stake is not simply how we approach the transmission of the Babylonian method of calculating the variable length of the day or the values of the so-called rising times, but how we view science in history more generally and understand its various cultural forms and diverse contexts over time. To follow the Babylonian parameters associated with the idea of the variable daylight is to follow a historical marker of identity best likened to a bit of Babylonian genetic code discernible within distinct and even apparently disconnected contexts. This genealogy of ideas suggests that quantitative elements, that is, numbers and calculation methods as a language of ideas, very like qualitative ideas expressed in verbal language, had the ability to transcend boundaries of politics and culture through translation and transformation into new contexts and horizons of meaning. Much as the evidence compels us to see the travel or transport of the parameters and methods associated with the idea of the variable length of the day, the contexts and traditions in which these parameters appear, far from their point of origin, also testify to powerful stabilizing forces of new intellectual and cultural norms for which these parameters and methods were repurposed. Where the transfer and intermixing of scientific ideas across geographical and temporal boundaries is evident, the relationship between transcontextual movement of ideas on one hand and the stability even static nature of ideas on the other poses attention of historiographical ideals classified by historian Peter Gordon as movement versus containment. As fixed ideal types, Gordon cautioned against their unqualified and unrefined use. Movement alone cannot explain how local conditions transform and even expand upon transmitted ideas or why they preserve certain ideas and not others. Containment alone over emphasizes the stabilizing force and cultural wholism of local communities or textual traditions, which makes historical change difficult to explain. I will return to these methodological issues in the historiography of science in relation to the question of transmission, but now turn to the subject at hand that of the variable length of the day. Two elemental building blocks underpin the idea of the variable length of the day over the course of a year. First is the ratio of the longest to shortest day, a parameter originally formulated in Babylonia during the second millennium BCE. And second is the zodiac, which appeared over a thousand years later, also in Babylonia. Once the zodiac was invented in the mid first millennium BCE, it became the sine qua non, not only for a solution to the question of the variation in the length of the day, but many other essential aspects of ancient astronomy. The convention of the 12 zodiacal signs of 30 degrees each marked the yearly path of the sun against the fixed stars. Its sex adjustable units of measure for time and arc were rooted in the fundamentals of Babylonian sex adjustable or base 60 counting, mathematics and metrology and resulted in the 360 degree circle we all know. The variable length of the day over the course of a year was the subject of the very first known mathematical description of a periodic phenomenon in Babylonian astronomy. Beginning in the old Babylonian period, circa 1800 BCE, this numerical scheme treated the length of the day as a function of the calendar month of a schematic year in which 12 30-day months totaled 360 schematic or ideal days. The variable length of the day was modeled as a series of rising and falling values of constant difference between two extrema, the maximum and the minimum, according to which the longest day or maximum was assigned a value twice that of the shortest day and the ratio of longest to shortest day was two to one. Accordingly, the period around which the length of day varied was 12 months or one ideal year of 360 schematic or ideal days. In this model, the length of the day shifts by one sex adjustable unit each 90 day season. Accordingly, from vernal equinox to summer solstice, the length of day increased by one, which stands for 60 degrees or four hours in our money. From summer solstice to autumnal equinox, the day decreased by one and so on, producing the model for the change in the length of the day throughout the ideal year as you see on the slide. This old Babylonian scheme, which is rather beautifully simple, is arguably more about defining the year, that is the ideal year rather than creating a method for calculating the length of any given actual, that is, civil calendar day. Each day of an ideal month was for the purpose of the scheme taken to have the same length and thus the daily variation was not a goal of the scheme. Needless to say, the ratio of longest to shortest day of two to one is the outcome of the scheme and was never meant to represent the actual ratio of longest to shortest day experienced at Babylon. Much later in the Hellenistic Babylonian astronomical tables of what we now call lunar systems A and B, and what you see here is a system B lunar ephemeris, the variable length of day was understood to depend not on a date in the schematic year, but as dependent on the position of the sun in the zodiac at the time of new or full moon. In this particular table written at Babylon on December 22nd, 103 BCE, consecutive day lengths are generated in the third column of the table from the longitudes of the sun at new moon listed in the second column, themselves derived from what are degrees of longitudinal progress in the first column. So the first column gives us the second column with the zodiacal longitudes, which in turn is used to derive these are the lengths of the day in the third column. It's actually the fourth column, but the first column is broken. The late Babylonian lunar tables thus introduced a new conception of the length of day as an astronomical rather than a calendrical phenomenon, generating values for the length of daylight from solar longitudes by means of a clever scheme based on the idea of the rising times of the zodiacal signs, which I am coming to. In addition to having a new astronomical purpose for calculating the variable daylight, the ephemerities of the late Babylonian period replaced the old ratio of the longest to shortest day of two to one with a new parameter three to two. The late lunar tables therefore used the calculated lengths of the day as an essential component in the complex procedures for predicting the moment of the first visibility of the moon with reference to sunset. That moment, as we know, is the very definition of the first day of the lunar month used by cultures that have a lunar or a lunar solar calendar. And it was the principal goal of the Babylonian lunar theory. The scheme I mentioned a moment ago that underpinned the new calculation of the length of the day in the late Babylonian ephemerities was the result of the idea that the values for the length of the day were tied to what we call the rising times of the zodiacal signs. The rising times are defined as the time required for one zodiacal sign along the red circle to cross the horizon, which is the green circle in this diagram. If on a certain day the sun rises in a certain degree of a zodiacal sign by sunset of that day, one half of the zodiac will have risen. That is from the point of the sun's rising to a point of longitude, 180 degrees from the sun's initial position. The signs do not rise in equal times, however, because the zodiac is inclined to the plane of the celestial equator, here the blue circle. As the sun progresses around the red circle of the zodiac then, the sum of the six rising times from sunrise to sunset will be different each day. The length of daylight on any given day, as diagrammed on the slide, equals the rising time of the half of the zodiacal circle to rise from the rising point of the sun or longitude sun to longitude sun plus 180 degrees and is the length of time from sunrise to sunset. It follows that if the rising time of each individual zodiacal sign is known and one has a solar longitude as an initial position, the length of the day for any day of the year can also be known. In spite of the difference in the construction of the column for the length of the day in systems A and B, and the different values assigned to the rising times in each system, as you see here, both had a maximum day length of 3,36 time degrees, which is 14 hours and 24 minutes, again in our money, and a minimum of 2,24 time degrees or 9 hours and 36 minutes. And the mean value still as in the old Babylonian scheme of 3,0 time degrees or 12 hours, which is 3 times 60 or 180 and is half is the length of the day on the equinox. The extrema and mean values of the two systems are the same, as is the ratio of maximum to minimum of 3 to 2, except that system A assumed the vernal equinox at 10 degrees of Aries, system B at 8 degrees of Aries. The key components of the Babylonian approach to the length of the day. First, the ratio of maximum to minimum of 3 to 2, second, the idea of the rising times, and third, the use of the system B norm for the vernal equinox at 8 degrees of Aries are all attested in later sources from the Greek, Greco-Egyptian and Greco-Roman traditions. A principal text is the second century BCE treatise of Hipsicles of Alexandria, which using the Babylonian linear methods calculates rising times based on the ratio of longest to shortest day at Alexandria of 7 to 5. The goal in this text was the calculation of each individual degree of rising around the zodiacal circle and therefore represents the first Greek attestation to the 360 degrees zodiac. By the first century BCE, as shown by Menelaus's spherica, the rising times were solved by trigonometric methods. And indeed, the problem of the rising times, or oblique ascensions as they would be called, was one of the main reasons for the development of trigonometry. If we look beyond the Hellenistic period into late antiquity, we see the system A Babylonian rising times quoted by the self-professed lapsed Chaldean, the Christian convert Bardisan of Edessa in the second century CE, and by George I of Antioch, known as the Syriac Bishop of the Arabs in the late eighth century CE. The system B rising times are applied by Cleomides, the stoic philosopher of the early third century CE, then quoted by the Latin writer and founder of the Trivium and Quadrivium, Martianus Capella, in the first half of the fifth century CE in his marriage of philology and Mercury, from which Gerber, later Pope Sylvester II at the end of the ninth century, quoted Capella's rising times as did the 12th century scholar Gerard of Cremona. On the other side of the late antique world, Varaha Mahira used the Babylonian system A rising times in the Sanskrit astronomical treatise, the Brihat Jataka of the sixth century CE. Although in Babylonia, neither of the two sets of rising times, nor the parameter of maximum to minimum of three to two, gave any consideration to the difference in what we would now call geographical latitude because there was as yet no conception of the celestial sphere or the idea that earth was spherical. The significance of both these ideas for geography was developed by Greek astronomers who did conceive of the celestial sphere and the spherical earth and introduced other ratios of longest to shortest day derived to account for other locales, hence the seven klimata of Hellenistic astrology and astronomy. We should recall that the original meaning of clima or climb was geometric. It meant inclination, namely of the earth's axis to the local horizon and observable by the elevation of the pole. For this one needs the conception of the earth's sphericity, which was certainly not available to Babylonian astronomers. The system of the seven klimata, for which there are a number of attested variants, adopted the Babylonian parameter three to two and the maximum as three comma 36 or four hours, 24 minutes to apply to the second clima identified with Syria in various Valens horoscopes of the second century CE. The Babylonian ratio of three to two was very likely the point of departure for the Hellenistic Greek system of defining geographical latitude in terms of the characteristic ratio of longest to shortest day for a given locality. The ratio of maximum to minimum was thus an important parameter in ancient astronomy because it served the same purpose we assign to geographical latitude. In addition to the use of the Babylonian rising times, both Babylonian norms for the position of the vernal equinox, but more often that of system B in eight degrees of Aries, are attested in Greek and Greco-Roman sources. For the two centuries surrounding the turn of the common era, the value of eight degrees Aries as the vernal point is found in Roman calendrical works, for example of Varro in 40 BCE and Columella in 65 CE. Also Vitruvius at the end of the first century BCE and Pliny in the first century CE also put the cardinal points of the year at the eighth degree of their signs. This system B Babylonian norm persisted for over 500 more years in other Greek and Latin literature from Geminis in the first century BCE to Manilius circa first century CE to Vettius Valens to George the Syriac Bishop and was then carried over into medieval texts and the Easter Computus. Outside of the Greco-Latin tradition, Biruni's chronology of the 10th century remarks that quote the Chaldeans are said to have commenced the seasons eight degrees after the equinoxes and solstices. To the wealth of Greek and Greco-Roman astronomical and astrological texts and contexts for the continuation of the Babylonian ideas of the ratio maximum to minimum, the rising times and the norming of the zodiac at eight degrees of Aries, the intellectual communities of second temple period Jewish scholars also adopted a Babylonian style scheme for reckoning the length of the day in the excuse me in the Enochic tradition. In this case, however, they applied the earlier parameter of maximum to minimum of two to one and the old zigzag function for calculating the increase and decrease of the day that is preserved in the fragmentary pieces of the Aramaic astronomical book from Qumran, a forlaga of the later Ethiopic text of 1st Enoch, chapters 72 to 82, also known as the Ethiopic astronomical book. 1st Enoch 72, or book of the luminaries, employed a zigzag function in the Babylonian manner but based it upon a different calendar structure from that of the 2nd millennium old Babylonian scheme we saw before and used different units for dividing the day over the course of the year. The variation in the length of day and night during the solar year in the Ethiopic 1st Enoch 72 is a linear sequence of numbers fixed between a maximum and a minimum and separated by a constant difference which is what constructs a linear zigzag function as seen on the slide because daylight and night according to this scheme always adds up to 18 parts. The unit part is one 18th of a day or one and a third hours. The monthly constant difference is one part and so the maximum is 12 parts and the minimum is six parts. The resulting ratio of longest to shortest day is two to one as in the early Babylonian daylight scheme although unlike the old Babylonian scheme with its ideal 360 day year and 90 day seasons Enoch's is a 364 day year divided into four seasons of 91 days each which makes for a significant departure from Babylonian tradition. For the source of the parameters in the Ethiopic astronomical book the environment of Hellenistic Egypt in which astral knowledge from Babylonia had made well attested inroads not to mention the geographical proximity and connection between Ethiopic and Egyptian cultures suggest that the early Babylonian parameter two to one for longest to shortest daylight came to Ethiopia via Egypt. Indeed an Egyptian parchment codex of the seventh or eighth century CE contains a scheme for the lengths of daytime and nighttime for the 12 months of the Alexandrian calendar where the values vary with constant difference each month in exactly the manner of the old Babylonian scheme. The text assigns the values for the longest day of 16 hours and for the shortest day of eight hours hence the ratio two to one as in the original old Babylonian scheme more than 2,500 years before. How are we to account for the incredible spread and acceptance of this Babylonian astronomical idea and its related parameters and methods of calculation not only across the vast geographical area of the Hellenistic world and beyond into Europe but over an equally incredible chronological span. Regardless of whether our focus is on quantitative or qualitative ideas one cannot talk about the transmission transit or transfer of ideas without making mention of what represents something of an or text namely Arthur Lovejoy's 1936 book The Great Chain of Being a study of the history of an idea. In the inaugural volume of the Journal for the History of Ideas which he founded in 1940 Lovejoy proclaimed ideas to be the most migratory things in the world. In Lovejoy's analysis what he called unit ideas were perennial and continuous conceptual elements which he cautiously compared to the chemical elements traveling through history and taking on various meanings in time. A phenomenon he called metaphysical semantics. A few of Lovejoy's unit ideas for example the principle of plenitude or indeed the idea of the Great Chain of Being itself were firmly embedded in the history of science. The former in both classical and medieval cosmology the latter in 18th century biology but Lovejoy's unit ideas migrating through world history were repudiated in the 1960s from a number of sources. Maurice Mondelbaum was an early critic in particular to Lovejoy's claim of the continuous life histories of these unit ideas and their supposed imminence in history. Although Mondelbaum did not take Lovejoy's unit ideas as platonic ideals disembodied from authors and periods this nevertheless became somewhat of a stereotype of the history of ideas in its Lovejoyan form. More well known criticisms came from the emergent method of historical contextualism associated with Quentin Skinner and others at Cambridge who in 1969 like Mondelbaum preferred to speak of intellectual history rather than the history of ideas. Also a few years ahead of Skinner and the Cambridge School Thomas Coons structure of scientific revolutions already prefigured in his 1957 the Copernican Revolution argued for a similar contextualist approach by attaching science to communities rather than to trans historical truths. Although Coons and Skinner's contextualism had been foreshadowed 30 years before in Ludwig Fleck's idea of the Denk Kollektiv Coon was the one to galvanize a wide embrace of the historicity of scientific knowledge which eventually in the form of the sociology of scientific knowledge and science and technology studies went in the direction of social construction, scientific practice and an interest in certain non empirical sometimes called external factors that influence the formation of scientific knowledge. Accordingly and in terms of the historiography of the transmission of science especially in its Anglo-American form the emphasis on migrating dislocated scientific ideas pre Coon often associated with lovejoy was replaced by an emphasis on contained local scientific knowledge and practice. What contextualism afforded was not simply a shift in perspective from above to below where historically contextualized scientific ideas would still be taken to represent a notion of science measured by the standards of the modern West but a more thoroughgoing historicization of scientific ideas always infused with cultural purpose. These aspects of the lived life of science can better account for the longevity of certain scientific ideas in spite of in many cases they're highly inaccurate nature as was the case in the Babylonian idea of the variable daylight its parameters and methods or some of them again this is a complex question reclaiming the idea that a rehabilitated context oriented history of ideas has a role to play in the history of science emphasizes that ideas are as much a lived part of science as practice indeed cannot be separated from it and for historical sciences it is especially important to reinstate scientific ideas into their contextualized life whether as in our present case that means Greek Greco-Roman Greco-Egyptian or Sanskrit astronomy astrology and geography or Judean religious cosmography and calendrix astronomical parameters as ideas are therefore as much a part of intellectual history and the history of ideas as they are of the history of science although rarely does one see quantitative evidence taken up by intellectual historians relevant I would say to the question of the transmission of science across the intercultural and multi linguistic Hellenistic world is another kind of shift within intellectual history that responded to implications of thinking trans nationally in a in a globalized world David armadages the intellectual turn in intellectual history in the volume rethinking modern European intellectual history of 2014 and Edward Bering's ideas on the move context in transnational intellectual history in the journal of the history of ideas of 2016 both saw a rapprochement between a revised history of ideas and historical contextualism Bering stated that today love joys words speak to an essential affinity between transnational study and intellectual history ideas and the texts that are their vehicles are by nature mobile and it is the task of the historian to follow them wherever they might go although Hellenistic antiquity lacked nation states the global analogy works well as does the analogy of texts as the vehicles of ideas in ancient astronomy indeed the global turn in historiography has a corollary in the German school of visions geschichte where the question of transmission is seen as recontextualizing knowledge within new knowledge economies as developed by Jurgen Ren and Sonja branches in their globalization of knowledge in the post antique Mediterranean 700 to 1500 from 2016 this wide ranging scholarship offers a trifecta of historiographical approaches to the transmission of ideas that of ideas in migration by means of texts and traditions or love joys view from above that of ideas in local micro context or let's call it the Cambridge view from below and that of ideas in macro context of a global nature or the view from a distance of the globalists and of business geschichte movement containment and cultural intellectual globalism are all relevant to our understanding of how a quantitative language of Babylonian astronomical ideas came to be translated and repurposed in a great many parts of the Hellenistic intellectual world where context can be viewed not only in terms of single authors single text exemplars and single places but as textual traditions representing intellectual philosophical scientific or even religious traditions that span any given author text or place how and why Babylonian astronomical ideas are evident across the intellectual landscape of the Hellenistic world requires exactly the sort of project involving integration of all three historiographical views movement containment and some form of globalism the Hellenistic Oikumene provides the global context as it spanned the lands from India across Mesopotamia to the eastern and western Mediterranean and Egypt within this enormous geocultural framework there is the matter of the selection of influence which speaks to why Babylonian ideas were so highly valued the fact that Greek Greco-Egyptian and ultimately Greco-Roman intellectuals were aware and exceedingly respectful of the heritage of cuneiform traditions of learning especially the astronomical knowledge of the Chaldeans is as I have tried to show writ large across diverse corpora of Greek and Latin literature and from the Hellenistic period to late antiquity and even into the 16th century and early modernity where Isaac Newton spoke of good Caldean astronomy I want to close with a statement of Coons from the Copernican Revolution in which he found the combination of science and intellectual history to be of the essence and questioned whether indeed the two were really distinct he said quote scientific concepts are ideas and as such they are the subject of intellectual history they have seldom been treated that way but I am myself quite certain that the techniques developed by historians of ideas can produce a kind of understanding that science will receive in no other way unquote I hope I have been able to illustrate here that when we classify numbers and quantitative methods as ideas ancient astronomy can be seen to belong at the center and nexus of the history of science intellectual history and the history of ideas the story of how the Babylonian idea of the variable length of the day became a fundamental source for astronomy astrology geography cosmography and calendrix across the Hellenistic world and into the Middle Ages neatly depicts this as it also depicts Kelly's evocative line with which I began namely and if I might paraphrase a little that the heaven of contemplation is fully and inextricably embedded in the sub-lunary realm of historical experience thank you