I recently wrote a brief letter to the editors of Isis, a leading peer reviewed journal in the history of science, to call attention to a fatal error in a recent article they published on the sociology of ancient science, “Ancient Greek Mathêmata from a Sociological Perspective: A Quantitative Analysis” by Leonid Zhmud and Alexei Kouprianov, Isis 109.3 (September 2018). Here I will expand that into a full article explaining the problem and why it matters.

Summary of the Issue

In that article a pair of researchers attempted to work up some sociological statistics on ancient science using extant references to named scientists and their published books. They overlooked the fact that all their data represents Medieval choices of preservation and not the actual activity of ancient scientists. They look through the lens of what Medieval Christians liked or by accident didn’t completely throw away, and mistakenly think they are learning things about the rate of scientific publication in antiquity. Which mistake shoots down their paper’s entire thesis.

It’s otherwise a neat article, albeit with some weird choices made. For instance, they don’t really give a good reason to completely ignore the biological sciences (like, say, medicine, physiology, pharmacology) and even many physical sciences (like, say, geology, climatology, oceanography), focusing instead on just “astronomy” and “physics” (with specific subdivision into optics, mechanics, and harmonics). This is reflected even in their selection of their search term, mathêmata, “mathematics,” often in antiquity a metonym for sciences that relied a lot on math (hence, “physics and astronomy”). In reality, physika, “physics” (or more aptly “natural philosophy”) was the more common and inclusive word for scientists in antiquity (on this point see Chapter 2 of my book The Scientist in the Early Roman Empire). That word covered both astronomy as well as biology, for example. True, it also included nonscientific philosophy, which makes it harder to use indiscriminately as a search term. But if you only look for mathêmata you are narrowing your search too far. Whereas using physika would broaden your search too far—unless you do the hard work of manually discerning which of its uses apply to what we today mean by science: empirical research into the nature of things.

And there is nothing Whiggish about that; the origin and rise of such activity, activity going beyond mere philosophizing, is precisely the phenomenon we want to explain. So we had better be looking for its earliest instantiations, and tracing its development. And just looking at the most mathematical of its instantiations doesn’t fully accomplish that. But even within their narrowed approach of only looking at the most mathematized of sciences (“physics and astronomy,” with one nod to geography), their methodology is fatally flawed.

Causal & Statistical Error

Zhmud and Kouprianov graph the location in time of every known scientist by their narrow definition and base all their conclusions off that. They also do this by city, but since we know the working location of only few ancient scientists, their results in this respect are automatically of little use, and their confident conclusions there should simply be rejected without further argument. I will continue discussing only their chronological data, from which they draw fallacious conclusions about the rise and fall of scientific activity in antiquity.

This is their key figure:

From this Zhmud and Kouprianov conclude science “declined” after 100 BC—and all but vanished after 500 AD, even in the Eastern, Byzantine Empire. This works for the latter period, because we really do see precipitous decline in scientific activity and references to it in the Middle Ages, corresponding with an equal decline in scientific knowledge and thought, and there is no other way to explain this. But this doesn’t work for the earlier period, because there the numbers remain quite high, and yet their reasoning is entirely dependent on the implausible assumption that our list of surviving names of scientists is a random or representative sample of all ancient scientists. Since instead the surviving record is highly distorted, containing material chosen for survival on a basis neither random nor representative, that assumption is wholly unsound.

Moreover, their graph shows a steady representation of scientific activity by a count of “named scientists” between 100 BC and 500 AD (hovering around 30 or 40), and yet all significant advances in the sciences ceased after 250 AD, so merely counting by “name” is actually not indicative of scientific progress at all. What we see instead is an increasing fossilization of science, as advances cease, and what used to be empirical researchers are replaced with bookworms and tutors who merely used, taught, or commented on the scientific findings of bygone times. Eventually even that ceased to be popular, and scientific knowledge almost entirely died out in the Dark Ages (and the concurring but less drastic period of decline in the East). On the other side of the graph, though, we see a rise in surviving names of scientists after or around the time of Aristotle to about 60 or 70, again steadily for centuries, up to about 100 BC. So, it looks like there were twice as many scientists in the Hellenistic era, than in the Roman era to follow. But that’s actually not indicative of anything either, for more than one reason.

First, since later scientists cite earlier scientists, whose work they are building on, it is already going to be the case that we will have twice as many names from a prior era, than a subsequent one. Precisely because progress ceased after 250, we are no longer getting scientists citing predecessors to the same extent, but bookworms and tutors singling out just the few treatises they taught from or retained interest in. So most scientists of the Roman era were forgotten (I adduce considerable evidence supporting this conclusion in Scientist, in Chapter 3). Secondly, the “first” to do things are more likely to get mentioned in memory or singled out for preservation, than later technical improvers (for instance, everyone knows who Einstein is, but how many scientists who improved on his work do you know the name of?), and Aristotle’s systematization of science as a subject field launched a boom in the sciences, so most of the “firsts” are crowded into the Hellenistic period. That does not mean there were more scientists in that period; rather, that there were more “first scientists” in that period. Thirdly, a disparity in which authors Medieval Christians chose to preserve exacerbates both sources of counting error.

A more careful method would be to check where these names come from, and then check if comparable sources exist for the other centuries being compared. For example, we get a few names from Archimedes (and a few other like sources), whose treatises almost didn’t even survive the Middle Ages at all (most were in fact destroyed and had to be recovered using a modern particle accelerator). Why? Because Archimedes was a little more chatty about his colleagues in the physical sciences. Do we have any comparable source for the first or second century? We do not. Apart from a few minor treatises too brief to contain much information of that kind, for the first century we pretty much only have Hero; the second, Ptolemy. Neither was at all chatty about their colleagues. They address arguments without naming who they came from; they didn’t address their writings to named persons; and unlike Galen for the medical sciences, they almost never discussed their interactions and rivalries and travels, or anything that often evoked mentions of fellow scientists, past or present. And it is only by accident that we even have Archimedes. As any statistician can explain, this situation will create enormous statistical disparities in the data, rendering the counts on Zhmud & Kouprionov’s graph essentially useless for what they are trying to do.

My mention of Galen here illustrates this point especially well. It’s only by accident that we have a lot of Galen’s work. In fact, by count, almost half of all scientific treatises Medieval Christians chose to preserve are by Galen. And not because Galen wrote half of all ancient scientific books. Indeed, we can demonstrate he wrote only a minute fraction of what then existed (I survey countless examples in Scientist; notably, Christians did not even preserve all of Galen, either). And yet just by accident Galen was a very chatty author. So we are merely lucky that Christians liked him. Because Galen digresses often and a lot on his social network and social life, on rival scientists and colleagues, we get a lot of names from him in the biological sciences, particularly medical science. But Zhmud and Kouprionov chose to simply not even count medical or biological scientists. Thus skewing their graph for that reason alone. If we were to graph “medical scientists” we might see a flat curve of name counts across the whole Hellenistic and Roman era simply because of Galen alone. Galen did for medical science in the Roman era what the likes of Archimedes did for physical science in the Hellenistic era. But these are single author sources, whose survival was accidental, and whose chattiness was accidental. I hardly need explain further why the precariousness of our sources for the names of scientists therefore cannot generate reliable sociological data. This is not random sampling. A variance in name counts in surviving sources is simply not going to correspond to the variance in name counts in actual history. This fact alone nullifies every argument Zhmud and Kouprionov make.

In short, they are assuming that what caused the name counts in their data, is the actual number of scientists in any given century. When in fact, what caused the name counts in their data, are the accidental decisions of Medieval Christians as to what sources to preserve, our accidental ability to recover only a scant few sources the Christians even destroyed, and the equally accidental tendency of one author or another to chat a lot about the names of other scientists, contemporary or historical. Because these surviving sources are so extremely scarce, they have an extremely disproportionate impact on the resulting data Zhmud and Kouprionov chart. It’s not like we have hundreds of books by scientists in any given century (and there were at least as many), such that accidental selection would have less effect on results because enough examples of useful sources would survive that selection process to keep our results representative. No. We get, say, one source, or two, or none, in any given century, and maybe a single chance mention in some random unrelated source here and there, and that’s it. So we cannot trust that the resulting data is representative.

The Mythical Decline of the Life Sciences

A similar error plagues one of Zhmud and Kouyprionov’s reasons for excluding life sciences from their study. As they put it:

Aristotle and Theophrastus, exploring a wide range of natural problems, laid the first foundations of zoology and botany, but these studies were not further developed in antiquity and became classic examples of abortive sciences.

This is completely false. But it’s a common myth still repeated in textbooks and other works in the study of ancient science. And it’s a myth born of the same mistake: simply because Medieval Christians chose not to preserve hardly any works in biology after Theophrastus, this has confused modern historians like Zhmud and Kouprionov (and their source here, James Lennox) into falsely believing there weren’t any such works. Thus, again, they confuse source survival with source existence. We are lucky to know there were in fact a lot of such treatises, continuing well into the Roman era, because of scattered, chance mentions of them in other sources. Most of which themselves are not scientific, e.g. Plutarch is not a scientist, but he discusses many scientists at random places across his Moralia, an encyclopedia of essays on diverse topics that survives for us to read it solely because a scant few Medieval librarians liked it enough to keep some of it around. Indeed, almost all of it survives in just one single manuscript. So it barely survived at all. And that’s just an example.

In The Scientist in the Early Roman Empire I document numerous treatises in biological subjects that we don’t have and yet that were continuously produced afterward and highly respected, by the hand of such researchers as Dioscorides, Oppius, Metrodorus of Alexandria, Leonidas of Byzantium, Nicolaus of Damascus, Demostratus, Antonius Castor, Sostratus of Alexandria, Philumenus of Alexandria, Galen, and many others, leaving the conclusion that these sciences were “abortive” untenable (see Scientist, pp. 107-29 and 175-83 for scholarship and source citations on that and everything to follow).

Much of this information is already in the Encyclopedia of Ancient Natural Scientists that Zhmud and Kouprionov use as their database. There you’ll learn that, though essentially nothing survives, nevertheless long after Theophrastus a certain Oppius had written detailed treatises on trees and insects, including anatomical observations. The Roman Antonius Castor cultivated his own botanical garden and wrote scientific treatises on botany for which he was regarded as the foremost authority in the field. Pamphilus wrote a treatise On Botany; Nicolaus of Damascus, On Plants; Trebius Niger, on zoology. Posidonius published on scientific geology and mineralogy as part of his observational research on volcanology. Apuleius was dissecting fish and publishing his research. Oppian wrote an epic poem called Fishing, surveying details on all creatures of the sea, frequently displaying enough scientific accuracy that modern ichthyologists regard it as “the most accurate and comprehensive ichthyological treatise up to” the 16th century; he was evidently versifying lost scientific treatises. We have scattered references to his likely sources: the scientific works of Metrodorus of Alexandria, Leonidas of Byzantium, and Demostratus of Athens, which we hear included scientific observations, dissections, and experiments. All published centuries after Theophrastus. All lost. Galen tells us he wrote a book on the physiology of plants. Despite their love of his medical work, Medieval Christians evidently found botanical physiology too uninteresting to preserve. But even what of his they did preserve exhibits extensive experimental and anatomical studies on animals that far rival Aristotle’s. And that was at the height of the Roman Empire.

We also know of Sostratus, a surgeon and zoologist at Alexandria whose early 1st century work on animals was so extensive, and remained impressive enough in quotations by later authors, for William David Ross to conclude that “in zoology he perhaps ranks next after Aristotle.” His treatises we hear of include On Animals, On the Nature of Animals, and On Striking and Biting Animals. All lost. Gaius Iulius Hyginus wrote a lost treatise On Bees. Agathinus wrote on numerous medical subjects, including an empirical treatise determining the dosage requirements of hellebore in medical application that reported his own controlled experiments performed on animals in order to derive a table matching dose to body mass. Galen tells us he admired the scientific quality of Lucius Calpurnius Piso’s treatise On Animals, which we know was published in the late second century, but don’t get to read hardly a single line from (indeed, only a single quotation survives). Galen also studied under Pelops, who we’re told wrote many scientific treatises on the dissection and anatomy of animals. The list goes on. We have the authors’ names and sometimes titles of countless works published between Theophrastus and Galen on horticulture, agriculture, veterinary science, and botany, zoology, even meteorology, geology, mineralogy. All lost. We also have mentions of scientific work without the titles or names. For instance, Plutarch mentions treatises on the excavation of anthills; he gives no names or titles. Galen and Pliny both mention an anatomical study of fleas; they give no names or titles. Clearly, a lot more work existed than survives or that we’re even told about.

So even Zhmud and Kouprionov’s belief that biological sciences “died out” after Theophrastus is completely unfounded and wholly contrary to the actual evidence. How then do they make this mistake? By confusing source survival with source existence—and doing no legwork to check how much we know about what was lost. This is the exact same mistake that dooms their attempt to “count” scientists in the fields of physics and astronomy.

Conclusion

In Logic and the Imperial Stoa (Brill 1997) Jonathan Barnes demonstrated a similar point with regard to modern historians’ (mis)understanding of Roman-era Stoicism. He shows how the choices and preferences of Medieval Christian scribes and librarians created the false impression that Roman Stoics were obsessed with ethics and had abandoned their previously hailed interest in logic and science—because early Medieval Christians loved ethics and hated science and logic. In actual fact, the reality in the Roman period was exactly the reverse: the Stoics were actually far more obsessed with making advances in logic and science, than in composing treatises in moral philosophy (Barnes thoroughly covers the point for logic; for the sciences, see Peter Barker and Bernard Goldstein, “Is Seventeenth Century Physics Indebted to the Stoics?” Centaurus 27.2 (1984): 148–64). But since the Christians preserved all those, but none of others, we came to falsely believe the opposite. Nearly every Stoic scientific treatise we know about was destroyed, tossed in the trash; and there would necessarily have been many more we don’t have a chance mention of.

Likewise all their sophisticated advances in logic, which far surpassed Aristotle. Might similar distortion have affected the record in mathematics and physics? It seems likely. As Peter Rosumek documents in Technischer Fortschritt und Rationalisierung im antiken Bergbau (RH 1982), there is “so much consistency in Roman mining operations across the empire” as to conclude “the Romans must have had engineering schools with an established body of texts or instruction,” none of which we happen to have—evidently owing to Medieval disinterest in them, not ancient. The more so for biology, mineralogy, climatology, and so on. So, too, mathematics itself. We have hints and references in many writers to advances in such fields as combinatorics and isoperimetrics, too, and only by accident recovered lost works in non-Euclidean geometries from Herculaneum. Other treatises we have—again only by accident, such as by Geminus and Pappus—likewise allude to a lot of mathematical work we don’t have. And we don’t have them, quite honestly, because Medieval Christians found them boring and threw them away.

How many treatises in math, science, and logic were there that we didn’t get a lucky mention or burial of so as to even know about them? How many scientists’ names have been entirely lost to history because Medieval Christians had the barest interest in the subject, and yet made all choices as to what would survive? Zhmud and Kouprionov’s thesis is simply unsustainable, because they have no relevant data. They are simply counting the wrong thing: Medieval Christian interests, not ancient; and accidents of source survival, not real counts of ancient scientists.

Zhmud and Kouprionov do adduce more than enough evidence to establish another of their conclusions, however:

If the social role [of a profession] is defined as “a pattern of actions, sentiments and beliefs thought by those who perform and experience that pattern and by other persons who perceive it as a distinctive one with a distinctive function of its own and a distinctive appropriateness in particular situations,” then the scientist’s role as producer of knowledge has emerged in ancient Greece. … All this and much more would have been impossible if engagement in mathêmata was not [then] recognized as a socially legitimate, indeed prestigious, activity worthy of pursuit.

This is likewise the result I document, far more extensively, in The Scientist in the Early Roman Empire. Especially for the Roman period.