Coming Anarchy has an interesting PNM Theory related post entitled Neo-Medievalism II that used historical examples and the idea of ungoverned spaces:
The nexus thereof, ungoverned space, creates a network of internationally connected fiefdoms which engage in smuggling, trafficking, terrorism and other forms of organized crime. The Coming Anarchy meets Global Guerillas.
I think the idea of ungoverned spaces (or little mini-gaps) throughout the world is a better description of the world then the macro level old-core/new-core/gap description with standard PNM Theory.
Recently TDAXP published a series of articles testing how well the core/gap and other common geographic models describe the world based on: poverty, nastiness, shortness, brutality, and solitariness. The results were is bit surprising. Barnett oldcore-newcore-gap wasn't the best fit. One problem may have been that the geographic units used in the models are too large.
A better description of the world may be networks of mini-cores and mini-gaps that also have some inter-connectivity.
For instance China-as-new-core is too broad. Parts of China are old-core (Hong Kong), parts are new-core and parts are gap. The distinction between new-core nodes and old-core nodes is just how strongly they are connected to other core nodes. New-core nodes are not as strongly connected (they are still transitioning, and they have lots of connectivity with the mini-gap networks they are transitioning from).
None of this invalidates the prescriptive parts of PNM Theory – Shrinking the Gap ("The GAP" as a network on mini-gaps or ungoverned spaces) is still the goal.
The Core-networks/Gap-networks idea also transitions nicely to domestic applications of PNM theory. Lesson from Network Science could also be added to expanding PNM Theory.
Update: An earlier Coming Anarchy post on Ungoverned Spaces
Update: Related at Phatic Communion
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