The division of the world system into the periphery and core is a very useful and commonly accepted explanation. It represents a relationship between all the relevant actors in the world, be it nation-state or multinational corporations. In the age of Pax Mongolica, this system was more static. A lack of technology hindered the abilities of traders to quickly exchange goods. I think the slower nature of trade in this time is not as closely linked with the phenomenon of core & periphery trading. Tracking the Black Death across Eurasia shows how long it took to cross that landmass in the 14th century. The lack of any hegemonic power also distances the example of Pax Mongolica from this theory. Alternatively the trade relationships of today clearly involve the extraction of cheap resources, labor and products from the periphery and that wealth being sent to the core.
When discussing the issue of the center of the world, the lecture looked at different maps that different cultures created. Each had its own civilization at the center. It has taken thousands of years to develop “good” world maps. It is technically hard to create truly representative maps. E.g. some maps over represent certain land masses like Greenland while dwarfing the southern hemisphere. The best representation is an actual globe. However, it strikes me that problems with maps continue today because you can have a globe perfectly represent the physical world but maps today are often outdated or even mislabeled (maps of Europe for instance often have Yugoslavia and the U.S.S.R. still on them. All this aside, many people cannot locate many things on a globe or atlas besides where they are located. Personally, I have tutored high school students in social studies and often have to point out where countries like France, England and Germany are located. When I ask them where they are on the globe they can quickly point to western Pennsylvania on the atlas. A persons frame of reference is very important to their understanding of the world.