Most people nowadays have a rough idea of what everyday life was like in the kingdoms of medieval Europe. Popular media and folk tales, have painted a picture, though sometimes an inaccurate one, of what the daily life of nobility and knights or townsmen and peasants was like in the post-Carolignian feudal states. However, the life of commoners(peasants, merchants, etc.) in the Byzantine Empire during the same period is largely a mystery to many laymen, including myself. So my question to you, historians of reddit, is: How was life for the common people in the medieval Eastern Roman Empire and how was their way of life different than that of the people in European kingdoms.
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This is a difficult question to answer completely for several reasons. First, the Byzantine Empire has no clear start date, it exists within a continuum with the Roman Empire. While there are generally accepted thresholds, none are really better than one another as they are all arbitrary in one sense or another. Without going too far down that rabbit hole, there is easily a millennia of Byzantine history so making any single description of daily life in Byzantium an impossible task. Because of this I'm going to only cover a specific time period with Byzantine history, but like I said, this is just the tip of the iceberg, there is so much more that I won't be able to share with you. Second, being able to compare Byzantium with Western European kingdoms would require knowledge of both, and unfortunately, I am unable to speak to the workings of Medieval Western Europe at anything more than a superficial level. Third, daily life during the medieval period is a difficult topic to fully know. So few of the common folk were literate and so we have precious little with which to know them. That being said, the Byzantine period does have a large amount of legal, financial, and administrative documents that have survived, and do give us some insight to how common people lived. While not my primary area of study I hope to share what I can on how common people lives, and also interacted with their Government.
You mention post-Carolingian so I am going to talk about Byzantium in the middle Byzantine period, roughly the 8th through 11th centuries. During the end of this period the middle Byzantine state is at its height of power and prosperity. After centuries of contending with strong hostile neighbors on all sides, the Byzantines are beset by favorable conditions and the internal strength to make the most of this advantageous position. From the Byzantine-Sassanian wars of the 6th and 7th centuries, through the Arab conquests shortly after and all the way through to the 10th century Byzantine Anatolia (modern day Turkey) was the victim of almost constant raiding and hostile activity. The Byzantines adopted a defense in depth strategic outlook, investing in a combination of intelligence, scouting, and observation to track enemy movements. Anatolia is a largely mountainous region and so there are not many routes from Syria, the staging ground of most Arab attacks, into Byzantine territory. As invading forces would begin moving, the Byzantines would sound the alarm to run, to hide, and to prepare the local soldiers for action. Most of these warnings were carried practically by runners and riders throughout the Themes (Byzantine provinces), however, the Byzantines also had several systems of beacons. My favorite being one that could transmit a warning of invasion from the cicilian gates in south eastern Anatolia, all the way to Constantinople 450 miles away (this is likely what the beacons between Gondor and Rohan are based on in The Lord of the Rings). While these attack became more infrequent during the 10th and 11th century, millions of Byzantine citizens across Anatolia had to be ready for a raid at any time. Most of the population would retreat to, and fortify, local forts, but some created more elaborate plans to evade attack. A good example being Derinkuyu underground city, a Byzantine town with an underground complex underneath. Derinkuyu was able to house all the inhabitants of the town, and possibly even the surrounding towns, in the event of a hostile action. These types of raids were on an almost annual basis during different periods of Byzantine history, so most Anatolian Byzantines would have a plan of what supplies and valuables to grab, and where to seek refuge in the event of an attack. Once the attackers were satisfied with their exploits they would retreat back to Syria which is when the Byzantine army would attempt to ambush and counterattack the weary raiders slowed by booty and slaves. Something I've always wondered myself, is what happened to booty recovered during these counterattacks or ambushes? It's likely that it couldn't be returned to its original owners and so damage, while minimized through preparation, was probably done to the common folk either way.
On the economic side the vast majority of Byzantine common folk were farmers, working on small plots of land either that they owned, or at the permission of a landlord. It seems that most plots worked on by a single peasant family were smaller than 100 modii (20 acres), a poor family may work a plot as small of 25 modii. A typical price during this period was roughly a half nomisma for a modius of farmable land (1 modius being roughly .2 acres). To put this in perspective, a soldier during this time period might make between 5 and 10 nomisma in a year. By Leo III (8th century) property worth 2 pounds of gold (72 nomisma to 1 pound of gold) was the dividing line between rich and poor. Leo's Ecloga fined the seducer of a virgin a pound of gold if he was wealthy, but half his fortune if he was poor by this definition. Although the numbers are extremely hard to calculate, Warren Treadgold suggests that a modius of land yielded between four and five modii of wheat. Treadgold also calculates a modius of wheat to be worth about a tenth of a nomisma. While I wouldn't put too much thought into how exact these numbers are, I think they are useful from a more general perspective. Now before you say a peasant with 100 modii of land could make 400 modii of wheat and sell it for 40 nomisma then reinvest that nomisma in land and almost double his holding in 1 season, keep in mind a considerable amount of the wheat was consumed by the family, or by taxes. By the late 10th century and through the 11th century the small independent landholder became increasingly reliant of local powerful individuals referred to as Dynatoi in Byzantine legal documents. This shift from small independent landholders who payed taxes to the state and who served as the majority of the domestic army to large private estates worked by bound laborers owned by the privileged classes who were not subjected to the same fiscal and service obligation ended up dooming the middle Byzantine state but that is a topic for another day.
As far as taxes were concerned, this was one of the primary interactions between citizen and state. By the 8th and 9th centuries, Byzantine officials (epoptai or anagrapheis) would go out into the countryside to evaluate individual property and assets to asses an individualized tax rate. Once the assessments were complete, the state would send out tax collectors (dioiketes or praktor for example) to actually do the tax collecting which is made complicated by the necessity to collect, look after, then transfer large amounts of gain around the countryside. Because of the difficulties associate with collecting taxes in kind, there were several efforts to move to collection in currency which were met with varying degrees of success. In parts of the empire close to the capitol, or urban areas, currency was more prevalent and this form of taxation doesn't seem to have faced major resistance. However, payment in kind was largely preferred by farmers, and in fact an attempt to move to taxation in currency sparked a revolt in the 11th century. We don't know much about rates but it does seem that taxation was proportionally heavier on the poorest citizens. State and religious officials as well as military personnel were given different forms of exception form taxes making these occupations desirable to those able to pursue them. The Byzantine state was also rather sophisticated in its record keeping, able to track who had paid what amount of tax and when. An example of this is when the Byzantine army was on the move, provisions would be collected and stockpiled along the route of march. These provisions would be collected from the local tax but if that year's tax wasn't sufficient the state would ask (demand if we're being honest) for an advance on next year's taxes. While this no doubt caused hardship on those taxed in this way, I do find it interesting that a medieval state was able to keep track of who paid more tax than assessed last year, and was therefore not obligated to provide that tax this year.