A Complex Adaptive Systems Analysis of Shaka Zulu and the Mfecane
dynamics modeling , i . e ., Kosko ’ s fuzzy cognitive map ( FCM ) as expressed in Kiel and Elliot ’ s spreadsheet modeling method , to test commonly adduced theories of whether , how , why , and in what sequence the contributing elements of the Mfecane coalesced ( Kiel & Elliot 1997a , 1997b ). Such theories could be modeled and falsifiable predictions tested by running the model to see the result ( Wilensky & Rand , 2015 ). System dynamics is a form of model employed when considering elements , which do not have clearly measurable quantities ( Borshchev , 2013 ). Kosko ’ s fuzzy cognitive maps , a subset of system dynamics , is a modeling technique that can represent accommodation of coarse-grained ( uncertain ) CAS schemata to the real world ( Kosko , 1993 ; McNeill & Freiberger , 1993 ). Fuzzy cognitive maps connect nodes of concepts ( either entities or functions ) with fuzzy rules represented by arrows , their interactions , and adjustments reflected in successive iterations ( Kosko , 1993 ). In contrast to the combination of many individual decisions represented by agent-based modeling , system dynamics charts thus capture the relations of large elements in a process . Douglas and Elliot ( 1997 ) illustrated the actual execution of the process by a spreadsheet method that they developed to explore non-linear systems . Their “ logistic map ” illustrated chaotic functions , but can be adapted to show the operations of CAS . The technique calls for entering the initial conditions and operations in the first row of cells . Then it calls for applying a cumulative formula in the second row and copying the operative formula through enough rows to provide as many iterations as time periods under consideration , allowing operations to be tracked as they work themselves out in the computer model ( Axelrod , 1997 ; Douglas & Elliot , 1997 ). The system dynamics method permits actors and their qualities to interact in an imprecise fashion , with general tendencies indicated by linguistic expressions describing qualities rather than precise values calculated ( Yen & Langari , 1999 ).
The models represent Zulu society and its environment and the Nguni populace generally . Various nodes to test the proposed models for the Mfecane possess initial values of 100 sets in all variables . Individual components of a model are modifiable . The model can be run a number of times with the modification to see what results to test the validity of proposed explanations of Zulu and Nguni development against the archeological and historical record . If a given explanation is correct , its corresponding model should yield the same results as the actual record . This concept of theory assessment was initially employed in the context of agent-based modeling to analyze settlement patterns of the Anasazi in the prehistoric American Southwest , allowing researchers to “ rewind and replay the tape of history ” to assess causational theories ( Dean et al ., 2000 , p . 205 ).
The large number of proposed theories of the cause ( or even existence ) of the Mfecane presents an excellent opportunity to test the theories by CAS modeling ( Axelrod , 1997 ; Chorafas , 1994 ; Eldredge , 2001 . The historic record of the Mfecane is limited to oral traditions recorded some years after the actual events . The physical record , although it contains some gaps , has considerable details as to climate , location , and production of peoples . Levels and subjects of trade are discernable by the size and activities of the European populations at the trading colonies , primarily Delagoa Bay and Natal . Thus , more or less quantifiable data is extractable from the material record and used to assess the proposed causes of the Mfecane .
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