On the First Assignment for History of Science and Technology: Basic Features of Hellenistic Science Seen Through Ptolemaic Astronomy

The first assignment has basically been graded; let me summarize it.

First, about the scores. This semester each assignment is worth only 10 points, and I was thinking of grading in 0.5-point increments. The highest score, 9.5, should be kept to a very small number—about one per class on average, and it can even be left unused; the teaching assistants can compare the best papers and then decide. Excellent papers get 9; good ones, 8 or 8.5; passing ones, 7 or 7.5; rather poor ones, around 6; abysmal ones, below 5; and plagiarism or failure to submit, 0.

As for late submissions—strictly speaking, this course does not even have the concept of late work. Late work and no submission are both 0 points. But in individual cases where a late submission was caused by an oversight on the part of the teaching assistants or by other force majeure, we can be flexible. For later assignments, the teaching assistants will reply promptly with confirmation; students who do not receive a timely reply after sending their email should contact the teaching assistant through other channels as soon as possible to confirm. For this assignment, the deadline had originally been set for before 6 p.m., but a few students sent their emails after 6, even during class; this time we were lenient, and I hope it won’t happen again.

As for the format of the assignment, I hope everyone will uniformly use doc or docx format. html files are also allowed, but I would prefer not to receive pdfs. pdf files interfere with the teaching assistants’ work of counting word totals, extracting text for search purposes (to identify plagiarism), and adding comments and replies. There is no need to compress and package the files; as far as possible, please include your name and student ID both in the email and in the attachment name to make record-keeping easier.

I gave feedback on all the assignments I received. The amount of feedback varied, more or less, depending on the problems in the paper and my mood. For the last few papers I received, including a few rescued from the spam folder, I replied with less comment; for the papers submitted earlier, I gave more detailed replies. The first two papers I received happened both to be very poor, so I sent them back for revision with suggestions for improvement. Of course, for the sake of fairness, I do exercise some restraint in sending papers back for revision after pointing things out, and I also won’t reveal too much… In any case, submitting early always has some advantages, and I hope everyone won’t wait until the very last moment to turn things in.

Below I’ll first explain the main points of this assignment, and at the same time summarize some of the typical problems that commonly appeared in students’ papers.

The requirements for this assignment were as follows:

Title: The Basic Features of Hellenistic Science Seen through Ptolemaic Astronomy

Prompt: Briefly describe the basic content and historical sources of Ptolemaic astronomy

Discuss which features of Ptolemaic astronomy reflect the characteristics of Hellenistic science

Requirements: 1000–1500 Chinese characters; neither too short nor too long; learn to think clearly and express yourself concisely

First of all, the first key point in the title is “Ptolemaic astronomy,” not Ptolemy himself. Apart from the Almagest, at most one should mention the Planetary Hypotheses and the Tetrabiblos; as for the Geography and the like, there is no need to bring them up much. Biographical introductions can also be omitted if possible (except for noting that he was in Alexandria in the later Hellenistic period). Since the paper has a limited length, every word should be precious, and the discussion should focus on the content of Ptolemy’s astronomy.

Second, what must be brought out is “Hellenistic science.” The Hellenistic period differs from classical Greek antiquity: it inherited things, but it also changed them. It retained the characteristics of the purity and freedom of Greek science, while also adding the features of Eastern pragmatism and support from royal power. A very small number of students failed to distinguish Hellenistic science from Greek science and simply discussed the characteristics of Greek science; such papers had to receive low marks. More students (myself included back then) paid attention only to the new features of Hellenistic science, without explaining that it still inherited the characteristics of classical Greece.

The characteristics of Greek science are nothing more than freedom and purity, an emphasis on mathematics, the pursuit of perfection, rational inference, and so on; the changes in Hellenistic science are nothing more than specialization and centralization supported by royal power, Eastern pragmatism, and an emphasis on observation and calculation, and so forth. Some students said these things more completely and expressed them more accurately, but the majority did manage to grasp the basic points. However, merely covering all the points was not enough to earn a high grade.

Wu teacher especially gave two hints: first, briefly describe the basic content and historical sources of Ptolemaic astronomy; then “discuss” which “features” of Ptolemaic astronomy reflect the characteristics of Hellenistic science.

In other words, the assignment is not asking you to divide the paper into two parts and simply list: first list the content and sources of Ptolemaic astronomy, then list what characteristics Hellenistic science has. The key is that the connection between these two parts is what you are supposed to “discuss.” Some students did not understand why they had to write the first part on “basic content,” as if it were merely a simple listing exercise. In fact, that is not so. This assignment is prompting you to pay attention to the correspondence among “content,” “source,” and “feature.” “Seen through…” first of all requires a full grasp of the case at hand, and that it be developed as a “case.” In many students’ papers, the two halves were disconnected and they failed to combine the content with the features effectively.

At the end of my paper from that time I added some hints, namely that one must pay attention to the correspondence between “content” and “feature.” When writing each item of content, one can note whether its source was inherited from Greece or newly added in the Hellenistic period, and then consider what characteristic of Greek or Hellenistic science it may reflect; when stating each feature, one should also keep in mind which basic item of content might serve as an example. Listing the basic content and listing the basic features are both not difficult; the difficulty lies in connecting them.

The most crucial content of Ptolemaic astronomy is his three mathematical tools for dealing with planetary problems: the eccentric circle, the epicycle-deferent, and the equant (the off-center equal-speed point, the balancing point, the point of equality…). Among these, the equant is the most typical, because in a certain sense it violates Plato’s demand to save the phenomena, symbolizing a compromise or turning point from perfection to reality, from ideas to observation, and from qualitative explanation to quantitative prediction. A few students did not mention the equant at all; many mentioned the equant but did not explain in the slightest what sort of device it was; some students pointed out that the addition of the equant had the character of a compromise with practicality, but since they still did not explain what the equant actually was, they still did not provide a clear “argument.”

By the way, there are countless translations for the equant. Wu teacher uses “偏心匀速点” here, but I don’t think it is necessarily the best; perhaps “等点” or “均衡点” would be better. In any case, students could use any of these translations in their papers. The problem is that some students used several different translations in the same paper: in one place they said “balancing point,” and later they said “equant,” without any explanation or note. That kind of thing suggests that they never really understood the concept at all.

Many students’ papers had similar problems, which reflects an insufficiently coherent reading of the literature. Since there are now many ready-made assignments online, students can directly quote certain concluding or judgmental statements from them. But because they have not done enough reading themselves, and have merely hauled in second-hand or even third-hand materials, this inevitably leads to the situation where they quote a few isolated words and phrases without understanding what they mean.

In addition, although I emphasized on BBS that when you cite a work quoted in someone else’s article, you cannot directly cite that original work (unless you have personally consulted it), but should indicate that it is a secondary citation, many students still cited Wu Xinji and Wen Xueshi’s Modern Astronomy in Fifteen Lectures. That book is practically a telltale sign: anyone citing it is definitely citing either the sentence on page 6 or page 7, and definitely has read the assignment with “Crystal Jinghong!” found by searching on Baidu. Of course, besides that book, many students’ papers were actually citing books that had themselves only been cited in predecessors’ assignments, books they had not actually read, and without noting that these were secondary citations. I know this, because the articles you can find, the teaching assistants can also find, and I myself have been grading assignments for two years now. It’s just that in other ordinary cases I tend to turn a blind eye, whereas Wu Xinji’s book is especially conspicuous, because that passage is simply too awful; it is completely not worth citing and should not be cited. That passage says:

The main point of Ptolemaic astronomy is: “The earth is at the center of the universe and remains motionless; the planets, the sun, the moon, and the stars revolve around the earth from east to west once each day. The first orbit nearest the earth is the moon, followed in order by Mercury, Venus, the sun, Mars, Jupiter, and Saturn. Outside them is the sphere of the fixed stars. The sun, moon, and sphere of the fixed stars move directly around the earth.”[11]

Perhaps because Jinghong student added wording like “the main point is,” later students flocked to it and insisted on citing this passage. But how can this be the main point? Think carefully: what is so clever about this sentence? Why has it been cited so much? And the sentence is not even correct, because Ptolemy’s moon also has an epicycle.

As for the “saving the phenomena” of classical Greek science, many people mentioned it, but some students did not understand what it meant. Some even said that saving the phenomena means using theoretical models to explain phenomena, and that this therefore reflects Eastern pragmatism—by that logic, was Plato an Easterner? In fact, saving the phenomena implies the idea of a perfect world of forms, while the imperfect “phenomena” need to be saved. But what Plato required by saving the phenomena was a qualitative explanation: roughly what is going on, not a quantitatively exact correspondence. For example, the concentric-sphere model could not explain the variation in planetary brightness, but Plato did not care, because phenomena are after all a “mimicry” of the forms; as long as they look roughly right, that is fine, and small deviations need not be worried about. Ptolemy, by contrast, went to every length to adjust theory so that it would fit the phenomena precisely, even being forced to adopt an awkward device like the equant. That kind of demand is no longer saving the phenomena.

Of course, besides its several major mathematical models, Ptolemaic astronomy also had some implicit background conditions, which likewise reflect the characteristics of Hellenistic science. For example, a preference for circles, a belief in natural order, a belief that the heavens are “unchanging,” and a concern with planetary problems, and so on (I saw no one mention this, that is to say: why is Ptolemy’s astronomy centered on “planetary astronomy”? By contrast, the main task of astronomy in ancient China was the recording of changes in celestial phenomena). In addition, the organically integrated relation between astronomy and cosmology in Greek science as a whole is also worth mentioning (unfortunately, no one seems to have mentioned this either). The relation between astronomy and astrology is also worth mentioning. Many students, when mentioning Ptolemy’s astrology, spoke only of his pragmatic tendency and the like; but on the other hand one can also notice something else (which no one noticed): although Western ancient astronomers often worked on both astronomy and astrology, there was still a conscious distinction between the two disciplines. The Almagest discusses astronomy and not a word of astrology, whereas in the East the disciplinary boundaries were relatively blurred, and the division between astronomy and the humanities was lacking.

Another major background condition is the accumulation of data. The construction of the Ptolemaic system required massive data support and a great deal of computational work. Although ancient Greece had already inherited some astronomical records from the East, it is obvious that the materials available in the Hellenistic period were more comprehensive and richer. In addition, before Arabic numerals and convenient notation for operations existed, the difficulty of large-scale numerical calculation was beyond what people today can imagine. From this one may speculate that Ptolemy may have relied on an institutionalized support apparatus, which can be linked to new things such as the Mouseion of Alexandria,

In addition, the Almagest is clearly a work that gathers the achievements of the past in one place, reflecting the Hellenistic-period characteristic of collecting earlier knowledge and systematizing it. Of course, the existence of libraries and research institutes supported by royal power made the accumulation of scholarship possible.

As for literature, a relatively good source is the History of Astronomy with an Introduction by Cambridge, translated by Jiang Xiaoyuan. Jiang Xiaoyuan’s own biographical study of Ptolemy is also easy to find online and may be consulted. Thomas Kuhn’s The Copernican Revolution—Planetary Astronomy in the Development of Western Thought, translated by Wu teacher and others, is also an important reference; the ancient section in its first chapter is relevant to this assignment, and the later sections can still be consulted when we get to the period of the Scientific Revolution. In the same series there are also some good translated works in the history of science, mostly related to the Scientific Revolution, though they may be rather specialized and not necessarily suitable for all students to consult. Those with the ability can certainly find and read them. The two general histories by McClellan III and Lindberg are of course also worth consulting. Wu teacher’s The Course of Science is relatively less authoritative, but it can help with understanding. Some students cited materials on the history of mathematics such as History of Mathematical Thought in Ancient and Modern Times, which is good; but if someone only reads materials on the history of mathematics and ignores the history of astronomy or general history of science, that is not really enough.

As for citation conventions, there is, in principle, no need to say much. As long as you are willing to, you can imitate the pattern and figure it out; the first few papers found online were in fact fairly standardized in their notes and citations (of course, there are many forms of standardization, and for undergraduates choosing an appropriate style is enough). But there were still quite a few students whose citations were not very standard. Some people like to use italics in the body text (which looks awful in Chinese), and some do not use quotation marks. Direct quotations must be enclosed in quotation marks and accompanied by a footnote or endnote indicating the source; indirect quotations (that is, paraphrasing someone else’s view in your own words) should not use quotation marks, but should still have a footnote or endnote. Long quotations may be set off as separate paragraphs with indentation or a change of font (in which case quotation marks are not necessary). Citations of books should indicate the author, translator, publisher, year of publication, and page number; citations of online sources should indicate the URL and the date accessed. It is recommended to use Word’s built-in “footnotes and endnotes” function to add notes automatically, which makes formatting easier.

Translated from the Chinese original with AI assistance. The original text is authoritative.