My first response was that no society retains the leading edge in science for very long. Some societies have had their “day” - Greece, Rome, Caliphate Baghdad, India, China, Italy, France, England, Scotland, Germany, Sweden,Russia, Japan, the United States. Some societies never have had a “day”, while a few lose out and later return to the forefront.
I then got to thinking about what makes for a society's leadership in science. Here are some of the cross-cultural and long-term historical parameters that seem essential.
1)Every society has smart young people but the education system must direct some of them into science. It must value the search for understanding the natural world. It must value hands-on involvement in, for example, medicine, fabricating equipment and tools, and observation.
2) There must be patronage and employment for practitioners of science. This not only provides the conditions for discoveries, but also provides role models for upcoming generations of scientists. The “leading” scientific society frequently attracts practitioners from long distances.
3) There must be some consensus on how to discuss and prove or disprove thinking about a natural process. This can refer to observed results or more formal hypothesis and data collection. Also useful is a way to challenge recognized authorities.
4) The results of experiments must circulate to other scientists. The obvious example is the extensive correspondence between scientists during the Renaissance. Consider also gun-casting. The big scientific breakthroughs in England and France in the eighteenth century were made in national arsenals where experimental results were recorded, discussed and used in subsequent experiments. This is a long way from gun-casting as a closely guarded family secret.
5) Experimental results need to be written down and somehow become part of a semi-public historical record of attempts to understand the natural world.
It’s easy to see how vulnerable and fragile is maintaining leading-edge science. Political changes could end scientific patronage. Slight changes in the education system could orient bright students away from science. War could end the public exchange of knowledge. Archives could be destroyed. News of declining opportunities might mean that bright foreign scientists no longer sought out a particular court.
Some people today are concerned that the patronage of science is rapidly growing in China, India and Korea. This bid for leading-edge science is a very, very old process and one that will continue. Whoever develops these five difficult and fragile factors will keep the leading edge of science as long as they can.
So, to answer to the teacher’s question. Which of these five factors did the Islamic world lose? Actually, several of them. Education turned away from the Neo-Platonism and science of an earlier period toward literature and religious studies. Patronage moved away from science. Islamic courts less attracted scientific talent from far-away places. The network of scientists communicating by letter shrunk.
One of major courts that was heir to Islamic science was that of Alfonso X in Spain. It was in his court that Muslims and Jews translated so many Islamic science books into Latin, thence to Italy to become basis for the Renaissance.
It’s worth considering what would have happened if the Pope had prevailed over Venice. Perhaps the Renaissance would never have happened.