Final answer:
The hadith encourages seeking knowledge even as far as China, exemplifying the emphasis on innovation and exchange during the Islamic Golden Age, and aligns with the promotion of learning and scholarship within Dar al-Islam.
Step-by-step explanation:
The hadith stating "The Prophet said: 'Seek knowledge even in China'" best explains the historical development in the Islamic world of the sponsorship of innovation and exchange in Dar al-Islam (A). This encouragement of learning represents the Islamic Golden Age, a period marked by extensive trade, travel, and the amalgamation of different cultural wisdoms, including the translation of Greek and Persian texts into Arabic.
During this time, scholars in the Islamic world were not restricted to religious studies alone and frequently engaged with a range of scientific, technological, and philosophical pursuits. The sponsorship of innovation was facilitated by the caliphs and other wealthy patrons, who provided the financial backing necessary for scholars to study and translate a variety of works, which fostered a rich culture of learning.