A few days ago, I heard about Henri Pirenne’s book Mohammed and Charlemagne, which I will summarize below, as I’m reading the book so you don’t have to. Over the past week, I have become quite interested in how the barbarian invasions and the rise of the Umayyad Caliphate affected Western Europe. Bryan Ward-Perkins [excellent quality pirate version of his medium-quality book The Fall of Rome and the End of Civilization here] considers the barbarian invasions to have severely degraded economic and cultural activity in the Roman cultural sphere in Western Europe (though less than in Britain) and does not mention the conquests of the Caliphs as having any impact on Western Europe at all. Over the next few days, I will attempt to coherently sum up the evidence relating to the transformation of the Roman Empire from a unified Mediterranean-wide naval power to the small monarchy we find in the early 9th century AD and the economic processes that relate to this political decline.
Chapter I of Mohammed and Charlemagne:
*By the mid-5th century AD, the Western Roman Empire had ceased to exist as a serious political entity and its entirety had been split up among the barbarian kingdoms and their puppets.
*By 500 AD, the barbarians in the present-day Roman cultural sphere in Western Europe ruled in the name of the Roman Empire. They did not seek to conquer its entirety or replace it with their own culture or empire. No barbarian claimed to be Emperor from the Fall of Rome to the rise of Charlemagne.
*The barbarians were not contemptuous of Rome, nor did they think themselves superior to the Romans. The Roman cultural sphere only retrenched along the Rhine and some of northern Gaul. While there was some barbarian looting, the barbarians only wanted to enjoy the benefits of Roman rule.
*The barbarians had little to no long-term influence on the culture and language of the Roman cultural sphere.
*Barbarian law in the Roman cultural sphere eventually became assimilated into Roman law. Arianism disappeared by 600 AD.
*The barbarians were at least as corrupt and amoral as the Romans.
* Though there was clear intellectual and artistic decline in the barbarian-controlled Roman cultural sphere, the Roman cultural sphere survived due to lack of superior alternatives and the power of the Latin church.
* The Ostrogoth administration attempted to preserve Roman culture. The Vandals lived as an extractive elite that expropriated the population and persecuted Catholics, but even the Vandal kingdom quickly abandoned Germanic culture and adopted the manners and customs of the old Roman administration. The Burgrundians were almost completely Romanized soon after their invasions.
[comment by me: The nature of the economic situation in Tunisia and southern Gaul between the 2nd and 9th centuries AD must be settled through archaeology.]
* The barbarians were not at all culturally innovative.
* The Frank kingdom preserved less of Roman administration than the other barbarian kingdoms, but introduced no new Germanic cultural features. The Frank population merged easily with the Gallo-Roman, and the Gallo-Romans quickly became a part of the Frankish ruling class.
* The tax system under the barbarians drew in massive amounts of revenue.
* Under the barbarians, bishops played no part in the government and the king was the state, with the church being subservient to him. The church played no formal part in confirming the king. This is a contrast with the later strength of the church’s influence on the state in Western Europe.
* Under the barbarians, the church remained socially prestigious and a massive recipient of government subsidies.
* All the barbarian kingdoms, with the sole exception of that of the Vandals, recognized the legitimacy of the current eastern Emperor. The Vandals struck coins in the name of the Emperor Honorius, thus recognizing the legitimacy of past Roman emperors.
* Justinian’s conquest of North Africa was quick and complete; the conquest of Italy was hindered by Ostrogoth resistance after an initial quick surrender of the Ostrogothic kingdom, but by 554, after much spilled blood, the conquest of Italy was complete. The Ostrogoths and Franks never allied.
* The Visigoth kingdom continued to recognize Justinian as legitimate even after his armies took the entirety of the kingdom’s coastline.
* Justinian’s Spanish and North Italian conquests were very short-lived.
* The Lombards were the first barbarians to enter Italy to rule like barbarians.
* In the second half of the 6th century AD, the Pope was still subservient to the Emperor.
* Were not for the Empire’s break with the Frankish kingdom in the sixth century AD, the Lombard kingdom would have been destroyed.
* By 600 AD, the Lombards had begun a process of Romanization, the cultural influence of the East was continuing its expansion, and the Empire was still the most powerful political entity in the Mediterranean.
Against Jebel al-Lawz 
You use “BC” where you surely mean “AD.”
“By 500 BC, the barbarians in the present-day Roman cultural sphere in Western Europe ruled in the name of the Roman Empire.”
“Arianism disappeared by 600 BC.”
Yes, I know. I have a tendency to do this since I’ve read much more about Josiah and Nebuchadnezzar than Justinian and Muhammad.