Final answer:
Considering the historical context and contributions, Dar-al Islam was more inventive and innovative between the eighth and eleventh centuries, particularly in commerce, law, and cultural integration compared to Byzantium, which upheld Roman cultural practices.
Step-by-step explanation:
To determine whether Byzantium or Dar-al Islam was more inventive/innovative during the period from the eighth to the eleventh century, we need to consider the contributions and societal development of each region in that historical context.
In Byzantium, particularly during the Macedonian dynasty, there was a period of cultural production called the Macedonian Renaissance. This era saw a revival in art and culture that eventually influenced the Italian Renaissance. The Byzantine Empire was also a beacon of stability in the Mediterranean, upholding Roman cultural practices for centuries. However, by the eleventh century, the Byzantines were challenged by Turkic tribes and would eventually lose their last remnants of power to the Ottomans.
In contrast, Dar-al Islam, particularly during the rule of the Muslims, demonstrated an advanced currency-based market economy, rich scholarship, and superior quality of goods compared to Europe at the time. They inherited Roman-Byzantine culture and innovatively integrated it with Islamic influences, leading to developments in architecture, visual arts, and more. The legal framework of Shariah law provided a sophisticated system for business transactions, putting the Muslim kingdoms at the forefront of commerce and military prowess.
Considering these facts, it can be argued that Dar-al Islam was more inventive and innovative, particularly in the domains of commerce, law, and cultural fusion. They played a pivotal role in the transference of knowledge and culture to Europe, which would later fuel the Renaissance.