1. Science in the “Dark Ages”
The world is still largely undiscovered. People in one country or continent know little or nothing about people or ideas elsewhere. Much of the flourishing of scientific thought is taking place in China and what is now known as the Middle East.

2. One Possible Waveform
Oops …
The Barbarian
Hole

3. Important Conditions
Barbarians, hordes, warrior-kings and empire building is a major aspiration of some cultures.
Translation of ancient latin/greek texts into Arabic becomes very important for the transmission of knowledge

4. More Maps http://www.worldology.com/Europe/dark_ages_lg.htm

5. Algebra circa 800
Muslim Spain becomes one of the principal centers of learning and discussion in all of Europe. This activity was mostly located in Cordoba.

6. Nasir al-Din al-Tusi
Most significant alteration of Ptolemy model – replaced epicycles with complex nesting of circles
Copernicus knows about this work
But fails to improve the accuracy of prediction of planetary positions

7. More Highlights
About 1000, Ibn al-Haitam, or al-Hazen, in Opticae Thesaurus, introduced the idea that light rays emanate in straight lines in all directions from every point on a luminous surface.
1079: Omar Khayyam, computed the length of the year as days
1086: Shen Kua, a Chinese scientist, writes his Dream Pool Essays in In these he outlines the principles of erosion, sedimentation and uplift
1088 (approximate). The University of Bologna is founded

9. New Methodologies
In 1267 and 1268, Roger Bacon published proposals for educational reform, arguing for the study of nature, using observation and exact measurement, and asserting that the only basis for certainty is experience, or verification
“Reasoning draws a conclusion, but does not make the conclusion certain, unless the mind discovers it by the path of experience”
What would Aristotle say to this?