Killings Hypatia

A while ago I blogged about a coming film on Hypatia of Alexandria (Weisz Is Hypatia). I've heard reviews from people who've seen it (still hasn't come to where I am, and might never), and they've reassured me it isn't as loose with historical facts as it at first sounded. It does engage in fictional "what ifs" apparently, but that's fine.

One review of note is by a medievalist who posted at the website of Skeptic magazine (Was Hypatia of Alexandria a Scientist? by S. James Killings). His area of expertise is not Late Antiquity, or ancient science, so he gets a lot wrong. Nevertheless, he's right about a lot, so in case you'd like to benefit from reading his brief commentary but not get misled by the errors in it, I've composed the following corrective, which is also informative and educational in its own right. You won't likely have known a lot of this stuff.

This blog entry adds to the running series I've had going for a while now addressing misrepresentations of ancient science in the media (the latest being Flynn's Pile of Boners). An extensive bibliography of references are already provided in my chapter on ancient science in The Christian Delusion (TCD). I'll start with the minor errors (in Killings' blog, not the movie) and progress to the more serious.


(1) Apollonius (of Perga) was only one of Ptolemy's major predecessors in planetary epicyclic theory; Hipparchus figured much more prominently, having already advanced on the work of Apollonius (their lives possibly just barely overlapping around 200 B.C., Hipparchus the younger, Apollonius the elder). There were many other astronomers working on the problem in antiquity between Apollonius and Ptolemy, only some of whom we know by name (but next to nothing about their writings or discoveries).

(2) Quadratic equations are not "necessary to determine the properties of curves." Though they can be used as a convenient computational tool in that respect, Diophantus doesn't discuss that aspect of their use, his interest is more in the field of logistics (such as calculations made in commercial industries or by army supply officers) and abstract arithmetical theory (developing a clumsy but sophisticated algebraic system for finding unknown quantities in complex equations, which led him on numerous flights of mathematical curiosity, one of which being the quadratic equation, e.g. ax^2 + bx + c = k). But curves weren't his interest. Apollonius of Perga provided the entire apparatus for determining the properties of curves in his Conics at least a century earlier, and all he needed was geometry.

(3) Empiricism ("theoretical knowledge drawn from observation and experiment") did not begin with Avicennna in the 11th century. It actually began with Aristotle (in his zoological treatises it's already evident) and was first formalized by Strato (Aristotle's second successor, in the early 3rd century B.C.), and we can see it in practice in Hero's introduction to the Pneumatics in the 1st century A.D. (drawing heavily, it's widely believed, on Strato),  and of course all throughout scientific writings after Aristotle (I give many examples and references in TCD).

So the method Killings refers to would not have been "completely alien" to Hypatia. It's just that by all accounts and background evidence, Hypatia almost certainly did not adopt it. Neoplatonists were notably hostile to the methodology, and on that point Killings is right. But he's wrong to say she would have had to create those empirical methods ex nihilo. Though those methods had evidently been abandoned since the 3rd century A.D. (see the final paragraphs of my chapter in TCD), they were available. We still have some of the works attesting and describing those methods even now, so there must have been a great deal more still available then (at the very least, those works were available then--otherwise we couldn't have them now). Their epistemology just wasn't being heeded or used anymore. 

Indeed, we have an extant excerpt from Strato where he makes almost exactly the same inferences from almost exactly the same observations: carefully observing water poured from a tall building, Strato notices that it starts as a continuous body but separates into drops of increasingly small size that part ways the more as it falls, which he rightly adduced as proof of Aristotle's theory that falling bodies accelerate. Unfortunately the quote ends at that point. It seems natural to infer that Aristotle's (incorrect) mass-law of fall, whereby heavier bodies fall faster than light, is just as plainly refuted by the very thing Strato observed, as the smaller drops were falling faster than the larger mass as a whole. 

Did Strato make that inference, too? It seems incredible he wouldn't. But unfortunately none of the treatises on gravity written after Aristotle survive (including Strato's), so we don't know exactly what was in them. We have a similar frustrating clip from Hipparchus, describing a correct theory of projectile motion (clearly implying parabolic trajectories and the time-based dissipation of imparted energy)--thus proving Aristotle's theory had already by then been abandoned by many, no doubt due to the rise of artillery as a science in the generation immediately after Aristotle (to which entire institutes were devoted to research, as reported and explained by Hero centuries later in his brief history of the early development of catapults). Nevertheless, we find the Roman scientist Hero still saying that heavier bodies fall faster (unless the passage concerned has been mistranslated--see below--it survives only in Arabic), so we don't know how far the debate had gone. But it was evidently proceeding empirically.

From another quote we know Strato likewise proved that falling bodies gain energy from their fall, by measuring the impact craters they made when dropped from different elevations. Which again makes it unlikely that Strato didn't also notice heavier objects fall as fast as light. But which also leaves me to wonder if this is what Hero actually was speaking of, and "harder" became mistranslated as "faster" in the Arabic. There is a definite clue to this in the surrounding text (of the Mechanics) where Hero speaks of flat plates falling "faster" than stacked columns, which makes no sense on Aristotelian mass-law, but is exactly correct on Strato's force-law. That is, he would then be simply stating a basic law of differential ground pressure. It's the same reason American tanks sank faster in mud than Nazi tanks in WWII even when they weighed the same: they had narrower tracks and thus concentrated more weight at the point of contact with the ground, thereby delivering more pounds per square inch. Hero uses almost exactly that wording, hence my suspicion.

At any rate, Hero describes observing actual falling objects and inferring physical principles therefrom. Galen likewise used observations from the deck of a ship to demonstrate the principles of relative motion, in a manner almost identical to what the film imagines Hypatia did (a similar observation appears in Lucretius 4.387-90). Hypatia didn't reason like that (it's very unlikely for her and in that degenerate time), but as a "what if" it's far more plausible than Killings claims.

(4) Killings says "the real Hypatia would have been more likely to attribute the physical properties of the falling grain sack to the god Seraphis, than to the possibility that it meant the Earth was moving in the heavens in contradiction to Aristotle," which I hope is just a joke, since divine causation was not embraced as a valid scientific explanation even by Platonists (and certainly Serapis wouldn't be the divinity responsible, even in popular imagination).

There were several naturalistic explanations of falling bodies accepted in antiquity that she could have appealed to, some of which did support the theory of inertia that the "cinematic Hypatia" is imagined to conceive, and some not. The principle of relativity of motion is articulated already by Galen in the 2nd century, for example (as just noted), so her doing the same and making the extra step to objects in space is not implausible (just unlikely by that point in history, when no one was thinking like that anymore).  

Likewise, a theory of universal gravitation in which the moon is held aloft by its inertia (with the actual, and partly correct, analogy of a stone in a twirled sling) is described by Plutarch in the 1st century. In fact he describes that theory as being widely known and discussed at the time. So had Hypatia lived then, her reasoning would've fit right in. Indeed, Lucretius already describes her reasoning as a standard theory among the atomists in the 1st century B.C.: in De Rerum Natura the earth is indeed falling through space at constant velocity and no one notices (1.1068-82, 2.203-24), and all atoms maintain constant velocity until struck (and, contra Aristotle, fall at the same speed regardless of weight, when we discount friction with the air: 2.225-42), which all entails a basic principle of inertia.

In addition to those concepts floating around, there was of course Aristotle's theory, but by Roman times more popular was the Stoic theory, which the scientist Ptolemy (2nd century A.D.) appears to have supported, and possibly Hero, too, in which falling objects were being pushed down by atmospheric pressure, in accordance with Archimedean fluid dynamics. The universe was imagined by them as contained within a kind of cosmic diving bell under intense pressure, causing material to be sorted out by density, the ether pushing in on the air, and the air on the ground and water, and the ground and water on the rest of the ground pressed together at the center. The theory doesn't quite work (it sneaks in an element of directionality that wouldn't actually emerge), but it's cleverly conceived.

More importantly, in the first section of his Almagest Ptolemy had to argue against two sets of opponents: heliocentrists and dynamic geocentrists (for whom we have more evidence than just Ptolemy's arguments against them), the latter arguing that the earth spins (thus efficiently explaining all diurnal motion) but everything else rotates around it. Both groups obviously must have accepted the observation Killings is insisting Hypatia couldn't have made. Perhaps she would not have made that observation or inference (Killings' characterization of her and her unempirical philosophy is accurate in all other respects), but clearly someone before her already had.

Again, in general scientists of the period from 300 B.C. to 300 A.D. were every bit as empirical as this fictional Hypatia is depicted to be, in fact far more so. The examples are endless, and I give many in TCD, and references there contain countless more. But we can treat a closer parallel: there is one actual empirical scientist in antiquity who was a woman. But because she wasn't horribly murdered by Christians, almost no one knows about her. The Roman Ptolemais was a female expert in acoustic science in the 1st century whose work on the subject was highly respected, but of course not preserved (just like Hypatia). From the one fragment we have from her, she particularly called for unifying mathematical and empirical schools of thought in the sciences (and her method was subsequently followed in Ptolemy's Harmonics). 

Ptolemais thus reflects a trend seen in all scientific writings of the Roman Empire. Even in attempts to make divination scientific, as in Artemidorus' effort to empirically gather statistical data with which to construct a reliable system of dream interpretation. His preface to On Interpretation of Dreams even explains that such empirical methodologies were the only ones reliable and respectable enough to use. We find the same harangues in Galen and Dioscorides and Hero, all scientists of the Roman period. And like Artemidorus, Cicero describes how Stoic scientists gathered an impressive array of empirical evidence of astral influences on terrestrial bodies in order to give theoretical support to physical theories of astrology. And they discovered real examples, too, e.g. shellfish grow and shrink with the lunar cycle, the position of the sun and moon directly influence the tides, etc. Indeed, a complete mathematical lunisolar tide theory had already been worked out by Seleucus, a then-renowned (but now forgotten) student of the heliocentrist Aristarchus, in the 3rd century B.C., and as later writings attest, he theorized that a gravitational force projected by the sun and moon was responsible. So the fictional Hypatia is not so anachronistic after all.

Indeed, the contrafactual posed is actually correct in pointing out that all the elements were in place: a complete mathematics of parabolas (from Apollonius), concepts of inertia (known from Lucretius and Plutarch), parabolic motion (attested from Hipparchus) and universal gravitation (attested in Plutarch, with similar notions from Seleucus), empirical methods and insights (Archimedes' famous "realization" of the law of hydrostatics while observing his body displacing water in a bath may be as legendary as this movie, but the empirical insight actually did occur, in whatever actual context, because we have his results from it in writing--and since that tale comes from them, the ancients certainly understood the idea of sudden empirical insights, even well enough to dramatize them), the idea of planetary laws (Ptolemy's law of equal angles in equal times described the inconstant velocity of the planets and clearly inspired Kepler's law of equal areas in equal times, and Hypatia certainly knew of Ptolemy's law--she also must have known his system of equants, which are almost identical to the foci of ellipses in Kepler's solution to planetary motion; in fact I have no doubt that's where Kepler got the idea), and the heliocentric theory (widely known even then, and must have been known to Hypatia, as Ptolemy argues against it in the very work she edited). That all makes for a more than plausible "what if" scenario. It's just two centuries too late.

(5) Killings concludes by declaring that "making too much of her legend does great disservice to the multitude of men and women throughout history who have made modern science possible." I don't think that's true. Fiction is just fiction, and it doesn't do scientists a disservice to celebrate them and their struggles against hostility in mythical form. But Killings isn't writing fiction. He's actually trying to educate. And unfortunately in his attempt to unveil Hypatia's legend Killings did a great disservice to the multitude of men (and a few women, too) of the earlier Greco-Roman period who were already doing science of the very kind he is sure Hypatia didn't do. He's probably right she didn't. But he's wrong to claim none before her did.