Sunday, August 01, 2010

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.

The Christian Delusion: Why Faith FailsThis 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.


Andrew G. said...

typo/thinko: "angles" should be "areas" in reference to Kepler, no?

Loren said...

Nice work. It also suggests an interesting counterfactual: what if the Roman leaders had worked out how to avoid the strife of the third century and thereabouts? They might have had to sacrifice some of their outlying territories, but it would have been worth it. But as the saying goes, hindsight is 20/20.

Another thing: Kepler proposed that the planets have elliptical, not parabolic orbits.

Unknown said...

Smashing work again, especially the smashing.

As already noted, for Kepler I think you wanted to refer to his equal areas in equal times rather than angles. As for the parabolic orbits of Kepler, I'm not sure if that is a mistake. Solutions for orbits included circles and ellipses (circles are a subset of ellipses) as well as parabolas and hyperbolas; it's a matter of initial position and kinetic energy. Since I don't know about the exact history, I don't know if this is a mistake by Richard.

Speaking of errors when it comes to ancient science--Richard, do you know of any good medievalists that do get the history of science right, at least in your area of expertise? When I read E. Grant's "Science and Religion" I was just shocked when he said that gunpowder and the printing press were invented by medieval Europeans, among other things.

Richard Carrier said...

Andrew: Yes, thanks. Fixed.

Loren: Yes, you're right. An ellipse is what happens when a parabola connects to itself. But ellipse is the more precise term for a double focus curve, so I fixed that. I was thinking in terms of the physical of motion (from which the elliptical orbit is derived from a parabolic motion).

Formally, "A parabola can also be obtained as the limit of a sequence of ellipses where one focus is kept fixed as the other is allowed to move arbitrarily far away in one direction. In this sense, a parabola may be considered an ellipse that has one focus at infinity." Conversely, an ellipse is a parabola that does not have one focus at infinity (which is why the orbits are elliptical: planets fall toward the sun in parabolic motion, but when that motion is sufficiently curved, the parabola extends all the way around the sun, becoming an ellipse).

Richard Carrier said...

Loren said... What if the Roman leaders had worked out how to avoid the strife of the third century and thereabouts? They might have had to sacrifice some of their outlying territories, but it would have been worth it.

They wouldn't have had to sacrifice any territories. In fact, had they worked out an effective constitution (such as the Greek Federations had done before the successors of Alexander and then the Romans destroyed them in the 3rd century B.C.), they might have even gained territory (as then being a part of their empire would actually have been attractive to many tribes and nations). But even if not, their problem wasn't external. It was internal. Had they solved that, they would have been able to keep external enemies at bay without as much difficulty. In effect, barbarians took advantage of the internal strife and collapse of the empire. Had there been none, the barbarians couldn't have taken advantage of it, and would never have made inroads.

I discuss this a little in chapter eighteen of Not the Impossible Faith, but in short, what they needed was a system that guaranteed a peaceful succession of power, a reduction of corruption in their system of administration, and a more cognizant economic policy. No doubt key to all three would have been anything comparable to a Bill of Rights. The concept was not alien to them, as the philosophy of rights (including such things as a right to freedom of speech and a right to freedom from oppression) was much discussed even before, and also during, the rise of the Empire. It's just that no one with the political will to implement them ever gained power (and in hindsight, it's really rather a fluke that that even happened in 1776).

Richard Carrier said...

Gilgamesh said... Do you know of any good medievalists that do get the history of science right, at least in your area of expertise? When I read E. Grant's "Science and Religion" I was just shocked when he said that gunpowder and the printing press were invented by medieval Europeans, among other things.

Those aren't Greco-Roman inventions, but I see what you mean. I'm sure Grant knows the background. His treatment of science is generally sound, as far as can be expected from a non-expert in ancient science. So if he said what you say (I only read his treatment of Greco-Roman science), he was probably just not wording carefully. Or he was eliding the debate and picking sides without argument

Though gunpowder and the printing press are ancient Chinese inventions, it's not simply a given that they weren't independently invented in Europe.

For gunpowder there is a plausible chain of transmission through the Muslims to Europe via the Silk Road (the sequence of acquiring gunpowder follows the trade route), a curious coincidence, yet it still could have been invented independently. The history of the development of pyrotechnics and incendiaries already in the early Roman period was tracking a trajectory that would inevitably have ended in the formula for gunpowder. So though it's always correct to say the Chinese invented it first, it's at least arguable whether the Muslims or Byzantines figured it out on their own many centuries later, though IMO it's both (the diffusion dovetailed with existing R&D).

For the printing press the story is similar: while Muslims started with wood block printing conveniently a few centuries after China, and then Europe started with with it a few centuries after that, a sequence that tracks the diffusion pattern, there is some evidence block printing was used in late Roman times. Meanwhile, Gutenberg's machine combined two existing technologies, wood block printing (already centuries old; possibly an independent Muslim invention, although diffusion from China is likely; but not yet adapted for book production by Muslims or Europeans) and the paper press (which for a century had been used to make paper for book production, but not for printing). Seen in that light, it's development seems so obvious that Gutenberg's particular device must have been an independent invention; just its inspiration was undeniably foreign.

For example, movable type was invented four centuries earlier in China, but there is no evidence of diffusion. IMO Gutenberg thought of that himself. But the paper press was definitely diffused Chinese technology (paper was a common silk substitute, and its diffusion tracks the Silk Road as expected). Yet it had been adapted in Europe by applying ancient Roman press technology to the same task (the Chinese had a different press).

So the full story is more complicated. The Chinese got there first in every essential respect, and all the essential component ideas diffused from China to Europe, inspiring Europeans to adapt them to ancient Roman and Muslim technologies, which eventually inspired Gutenberg.

It's impossible to convey all this in a quick sentence or two, so I don't begrudge historians who take a shortcut, as long as they don't build an invalid argument on it (e.g. if Grant were to argue that Gutenberg's invention proved the unique genius of Christians or the power of Christianity to inspire useful technologies, that would be fallacious; but to merely say the introduction of the printing press in the 15th century changed Western society is valid, regardless of how it came to be introduced).

Unknown said...

Actually, I reread the passage from Grant, and I must correct myself. He seems to only claim innovations with things in firearms and printing as improvements, not the whole-sale creations. His examples were also to convey the innovative spirit and abilities of medieval peoples--he also agrees that the period between 500 to 1000 wasn't that great. I maligned him unfairly.

However, his thesis that science did well in Western Europe over the Islamic world or Eastern Europe in part because the West had a separation of church and state seems harder to defend.

Nonetheless, thank you for giving info about various theories on these inventions.

Richard Carrier said...

Update: I have now seen the film. It's excellent. And some reviewers have misrepresented what it contains. See my review here.

Richard Carrier said...

Does Grant actually argue "separation of church and state" helped science anytime between 400 and 1400 A.D.?

Even after that it's a bit specious, but I can at least imagine him arguing it, whereas before that, not at all. After 1400 the churches' loss of institutional power certainly mattered. It was a necessary cause of the revival of real science, since it restored the intellectual freedom the ancient Romans already had before Christianity took over. But that's not the same thing as separation of church and state, which in actual reality never existed before 1791 (see my remarks on this in Flynn's Pile of Boners).

And of course separation of church and state was never a distinctly Christian idea; nor was intellectual freedom.

Unknown said...

Grant does think church-state separation helped (pp. 102-3, 246-8). Unfortunately, his argument consists of reading one verse of the gospels, Matt 22:21. Grant is also confused by the Byzantine Empire being a theocracy, considering it ironic again because of how he read that one verse.

He may be using a different definition of church-state separation than is normally meant in modern parlance, but he doesn't specify such a difference. He makes no contrast between his statements and, say, the 1st Amendment.

Unknown said...

Thanks for the clarifications. I've studied (as an amateur) these times and characters, but primarily from the political and religious history, not science. I've added links to both your post and Killings from my blog where I have a series of "reel vs. real" discussions about the movie Agora. The piece on Hypatia's science was skimpy, so I'm pleased to point any readers in your direction.

Pikemann Urge said...

Nice post. Will have to read again, but more slowly.

I always assumed, apparently incorrectly, that the essence of 'empirical evidence' was that it was available to any and all persons. Objectivity is a different thing. I checked Wiki and the only definition of 'empiricism' is 'practical experience'.

I don't get it though, because it makes sense that 'empire', a political entity not limited to one nation, matches up with my seemingly incorrect understanding of 'empirical', evidence available to all.

Richard Carrier said...

Gilgamesh said... Grant does think church-state separation helped (pp. 102-3, 246-8). Unfortunately, his argument consists of reading one verse of the gospels, Matt 22:21.

That's irresponsible. Nothing is said in that verse about separating the legal authority of state and church (the remark is solely about paying taxes to both institutions).

Does he even try to find any author before the 18th century who cites that verse in any way that shows they were taking it as an instruction to deny the state the power to enforce the church's will?

...or even to deny the state the power to meddle in the church's affairs? (which is a far weaker one-sided principle, yet even that was never adopted as far as I can tell--from Constantine to King Henry, the state always fully and freely meddled in church affairs without anyone citing Matthew 22:21 that I know of).

Richard Carrier said...

Pikemann Urge said... I always assumed, apparently incorrectly, that the essence of 'empirical evidence' was that it was available to any and all persons. Objectivity is a different thing. I checked Wiki and the only definition of 'empiricism' is 'practical experience'.

The essence of empirical method is that it relies on evidence available to all disputants, which principle is explicitly defended by Roman scientists like Galen. Perhaps that's what you're thinking of.

Unknown said...

Grant gives no secondary sources or really any other arguments other than his personal exegesis of this verse. He also admits meddling between church and state, such as who gets to be bishop and the like.

Again, he may have a different view of separation between church and state than that found in the 1st amendment, but he doesn't specify. Best I can guess (and without much merit to my guess) is that church and state were not the same entity, such as the biblical kingdom of David and Solomon. I must admit I don't truly understand his argument, especially when he admits the Eastern Roman Empire exists as a contradiction to his reading of the Gospel, especially since he gives no other sources or scholarship to explain or fall back on.

Give his book a read if need be; I supplied the necessary pages. Also, you have read the book before; you cited it in The Christian Delusion, I think even the same pages.

Richard Carrier said...

As I remarked earlier here, I only read Grant's sections on ancient science and Byzantine science. I didn't read the rest--which evidently is where this "separation of church and state caused modern science" argument appears. It sounds like a muddle to me. Either he means intellectual liberty was necessary (which is true, but not a Christian invention, but a belated return to pagan ideals) or a separation of powers was necessary (which isn't true, nor did such a condition ever obtain) or...what?