Nomen et Numerus: Quantitative Reasoning in the Field of Classics

C. L. H. Barnes

Upon first consideration, courses on Greco-Roman antiquity would seem to offer few opportunities to bring numeracy into the classroom. The texts of Homer, Herodotus, Cicero and Vergil, whether in translation or the original language, hold few if any theorems or mathematical formulae. Data sets are not readily available nor do our students normally spend their time solving problems which involve mathematics or statistics. And while archaeological field surveys and excavations do involve active data collection, sorting, analysis and issues of statistical sampling, the realities of our geographical circumstances, not too mention a host of other factors, dictate other avenues must be sought if we are to integrate quantitative reasoning successfully into the Classics curriculum.

One possible means would be through stylometry, currently being practiced with spectacular success by scholars like Don Foster (see, for example, Author Unknown: On the Trail of Anonymous, [New York, 2000]. His analyses of vocabulary, style, and meter have allowed him to attribute the poem of a formerly unknown author to Shakespeare, to identify correctly the anonymous author of Primary Colors (Newsweek columnist Joe Klein) and to demonstrate that Clement Moore was not the author of " 'Twas the Night Before Christmas." However, while such computer-based research works well in the field of English, one might notice that the identification of a papyrus in Cologne as the work of Archilochus has not generated a similar buzz in the media. To engage in such studies requires a thorough knowledge of both a text's original language and of genre, and a singular dedication to what might often be incredibly dull, tedious work. To illustrate, let us imagine we are trying to identify the fragment of an unknown Roman author (a task already highly unlikely). Given that there are at least four different ways to say "and" in Latin (et, -que, atque, ac), we could compile statistics on the usage of author x and compare the results to those of other known authors. In short, a study of this kind would be excellent punishment for hardened criminals were it not for the fact that someone would have to do the same tasks to check their work. I cannot imagine subjecting myself to such analyses in Greek or Latin, never mind undergraduates, most of whom encounter the ancient world in translation.

A more engaging possibility might involve designing a project around the preparations for the Trojan War. Agamemnon and Menelaos had to travel throughout the Greek world to enlist support for their attempts to recover Helen from Ilion. Had they been able to draw upon the services of Leonhard Euler, William Rowan Hamilton, or any of the experts engaged today in designing telecommunications networks or the most efficient routes for salesmen to travel, they doubtless would have been stuck at Aulis, unable to attack Troy until the sacrifice of Iphigeneia, in a much more efficient manner. Thus, an exercise in Euler circuits would be a wonderful way to get a large number of students in Core 1: The Classical Origins of Western Culture to gain a more thorough understanding of Homer's Iliad, networking issues, the geography of Greece and the Mediterranean, and the logistics of leadership. Unfortunately, given the current syllabus for the course, the introduction of such an assignment would be awkward. Furthermore, considerations of time would make it difficult if not impossible.

Numeracy finds a more satisfactory fit in a course like Classics 0.11, Vocabulary Building: The Greek and Latin element in English. In chapter 8 of Tamara Green's Greek and Latin, the Roots of English, students learn the Greek and Latin names for the numbers one to ten (cardinal and some ordinal), 100, and 1000. Words like primary, cent, millimeter, and mile, help them to see how much our daily language reflects the necessity of being comfortable with numbers. The word uniform encourages them to think about how "one appearance" can also mean "even," "free from fluctuation", or the "distinctive dress of an organization." As they learn the Greek words for one and only, hen and monos respectively, they then ponder the difference between henotheism and monotheism, both of which mean "the belief in one god" (the former implies that other divinities exist). Finally, students learn how to generate and use Roman numerals, which involves the practice of simple addition and subtraction. Through homework, quizzes and exams, they convert numbers like MCMXCVIII into1998 or 1442 into its Roman equivalent (MCDXLII). Any attempts at multiplication or division lead to the realization that there is one very good reason to be glad about the fall of Rome, the coming of Islam and the spread of the numerals which the latter civilization transmitted to Europeans. Of course, this phenomenon does not fall under the purview of a Classics department. Thus, we might look to the Roman world for other ways to incorporate numeracy in the classroom.

Within the topics covered in Classics 16, Rome: City of Empire, there are plenty of opportunities for exercises in quantitative reasoning. The complex political system of the Roman Republic (divided into tribes, curiae and centuries) raises the question of how one organizes a populace for voting and why. Looking at passages such as the following by Velleius Paterculus, students gain an understanding of how politicians attempted to manipulate the vote to curry favor and acquire power, influence and wealth:

Non erat Mario Sulpicioque Cinna temperantior. Itaque cum ita civitas Italiae data esset, ut in octo tribus contribuerentur novi cives, ne potentia eorum et multitudo veterum civium dignitatem frangerent, Cinna in omnibus tribubus eos se distributurum pollicitus est.

Cinna was no more moderate than Marius and Sulpicius. Thus, when citizenship was granted to Italians so that the new citizens were enrolled in eight tribes, lest their power and numbers diminish the influence of the old cities, Cinna promised that he would distribute them among all the tribes.

The number of Roman tribes, once it reached 35 in 241 B.C., remained stable, although new citizens were constantly being admitted. Since the tribes voted on a one vote one tribe basis, created most legislation and elected a number of important public officials, control of their assembly was a serious matter and enrollment of new citizens in only eight of the pre-existing tribes guaranteed that they could not influence elections in any significant way. Such gerrymandering today, albeit one hopes to promote fairness, is clearly visible on the maps distributed in New York City voter guides.

The Romans were well-known for their engineering and architecture. Thus, study of the aqueducts at Rome raises questions not only about their technical aspects, their size, length, construction methods, materials, and capacity, but also about their maintenance. Marcus Agrippa, the emperor Augustus' right hand man, bequeathed the Roman people 240 public slaves to oversee this work upon his death at the end of the first century B.C. One could draw upon this information to pose a problem such as the following:

Along the Anio Vetus aqueduct, 12 slaves on a loaded oxcart are traveling 2 m.p.h. on their way out of Rome while 10 slaves on foot moving an average of 3 mph are headed back into the city from the aqueduct's source 20 miles outside the city. Assuming they all start at the same time, when and where would they meet. Of course, we're dealing with Roman miles so you'll need to convert. Roman miles consisted of 1000 paces of 5 feet each. The Roman foot was either 11.6496 or 11.62 English inches.

However, I prefer to have the students ponder what the number of aqueducts can tell us about the population of the city, what their distribution might suggest about their uses and the political and social implications of erecting such structures.

Another possibility for the study of early Rome would be to consider what the numbers and distribution of particular kinds of vases can tell us about economic conditions in Italy in the fifth century B. C. The decline in imports of Attic Black and Red Figure Vases has been used to argue that a recession affected much of the central peninsula for a significant stretch of time. However, more recent studies have been able to challenge such a position based on the number and types of finds at various sites. Instead of a recession, what we see is apparently a change in consumer preference in the cities of Etruria and Latium.

The field of Classics already has a strong inclination to bring the material culture of Greco-Roman antiquity into the classroom for a variety of pedagogical reasons. Quantitative reasoning plays an essential role in the interpretation of that evidence. We might admire how the Romans managed to build their roads and aqueducts without the benefits of calculus, gasoline-powered engines or computer generated models. At the same time, we gain an increased appreciation for the benefits in our own world which numeracy has made possible.