I found a timeline script that I really like. I've plugged a few dates in and a few pictures. More work to be done, but you should get the idea. Eventually I want to compare this to the start of philosophy in Greece, then the current state of things in America.
Timeline of Abbasid dynasty
The difficulty of presenting history is that the only way to paint the complete picture is to tell the entire story of the human race. Any partial story shows your bias. History is usually told as the story of a country or of a life. The history of the philosophy of science spans many lives and many countries. Important inventions were lost at the bottom of the sea for 2,000 years. Writings were hidden then lost then found then misunderstood then expanded upon then argued over.
In this timeline, I take a parts of many stories that usually occur in the middle of other stories. The story is usually told of how something was discovered or first written about in one part of the world, how it passed through Baghdad, then came to its modern form in Europe during the Renaissance. It seems Baghdad just happened to be at the hub of trade, like the central processing station for FedEx. There must of course be more to the story.
For the human race to come up with something as unlikely and counter intuitive as the scientific method required financing, some level of peace and cooperation, and the willingness of people to acknowledge each's others value and admit their own faults. How often do you see those factors come together in one person, let alone an entire empire? Religion plays a role in this story. In the beginning it encouraged the search for knowledge but in the end it became a tool to suppress reason. But as always, I'm getting ahead of myself.