Our perceptual experience of quantity means that without counting, we recognize quantities up to about three or four rapidly and unambiguously, and we appreciate quantities larger than this range as bigger or smaller in groups when differences are big enough to be noticeable. These ranges correspond exactly to the first numbers to emerge across cultures and languages, even those widely separated by distance and time: one, two, (maybe) three, (occasionally) four, and many, with many often further specified as big many and small many. In other words, the first numbers are consistent with the functions of numerosity, subitizing, and magnitude appreciation.

We turn now to technologies that can be moved and rearranged, like pebbles and cowrie shells. These material forms and practices both accumulate and group (Fig. 12.1). Accumulation adds like the tally does: one, two, three, four, five, and so on; adjacent markers differ by one. Grouping makes numerical information more concise: One kind of pebble – perhaps one with a certain size, shape, or color – might represent a group of ten, and a pebble with a different appearance might represent one. This reduces the number of pebbles by replacing multiple units of lower value with one of higher value. Alternatively, pebbles might take their value from their spatial placement – their literal place value as units or tens. This reduces the total number of elements needed because ten is represented by a single pebble in the tens place. These strategies bring new relations into the number system, as for example, ten of a lower value make one of the next higher value.

The Conclusions explore the consequences of our arguments for the study of late antiquity more generally and the patterns of Roman military organization. The Roman military was among the most important institutions in the ancient world, and revising its history has ramifications for such perennial questions as imperial decision-making and Roman identity. Moreover, our reconstruction creates new questions, in particular about the economy of the fifth-century east Roman empire and its ability to mobilize and sustain the armies described by the Notitia. This chapter concludes by situating our revised narrative within the longe durée of Roman military history from Augustus to Byzantium and identifying the major considerations, including many non-military considerations, that motivated the empire’s various military configurations.

At the beginning of the second book of Cicero’s De re publica (54–51 BC) we find a remarkable passage: Scipio Aemilianus, one of the dialogue’s interlocutors, cites Cato the Elder’s statement on the superiority of the res publica. Cato attributes the success of the Roman Republic to its gradual evolution thanks to the combined wisdom of many Romans through many generations. Cato rates the Roman constitution much more highly than the ones of Crete, Sparta and Athens because the laws and institutions of these Greek polities have been crafted by only a few, albeit ingenious, persons.

Cultural memory theory is a framework which elucidates the relationship between the past and the present. At its most basic level, it explains why, how, and with what results certain pieces of information are remembered. Despite its origins in historiographical scholarship, however, in recent years cultural memory has been applied with increasing frequency to the study of the Classics, most notably in Gowing’s (2005) and Gallia’s (2012) exploration of memory under the Principate as well as the edited volumes by Galinsky (2014), (2016a), and (2016b). As the organisers of the ‘Roman Cultural Memory’ project, we are glad to count ourselves part of this emerging wave. We held three conferences to promote intersections between memory theory and Classics research, the first in November 2016 at King’s College London, the second in June 2017 at the Université Paris-Est Créteil, and the third in March 2018 at the University of São Paulo.

At the mouth of the Tiber river lies Ostia, Rome’s port town. Legend has it that Ostia was founded as Rome’s first citizen colony (a colonia civium Romanorum) back in the 600s BC, but the archaeological evidence dates the first structured settlement, which was protected by a wall of tufa blocks, to the 300s BC.1

Soon the settlement outgrew the small castrum (as the area surrounded by the early wall is called today) and both private and public buildings spread out in every direction. The Roman Late Republic (c. 133–31 BC) brought hardship on several occasions. During the first four decades of the last century BC, the inhabitants of Ostia suffered both from troops involved in civil warfare and from a raid by daring pirates from the eastern Mediterranean.2 The town was unable to protect itself adequately, since it lacked a proper town wall.

In 211 BC, the Romans were embroiled in a multi-front war with the great Carthaginian general Hannibal, and despite surviving the disastrous battles of the early years of the war, the Romans continued to face significant setbacks. In the Iberian Peninsula that year, the last-minute defection of Rome’s Celtiberian allies led to the deaths in battle of Publius and Gnaeus Cornelius Scipio, along with many of their soldiers. This was a disastrous blow to Rome’s war with Carthage, since the campaign in Iberia had been the only successful front in recent years.1 It is perhaps surprising, then, that the Romans minted a coin in Iberia that year that was stamped with symbols of Roman victory (Figure 19.1). The coin shows the Roman god Jupiter on the obverse (front) wearing a laurel wreath on his head, and the goddess Victory standing before a Roman trophy on the reverse (back).