��������������������������
displacement of a single electron by a billionth of a centimeter at one moment might make the difference between a man being killed by an avalanche a year later , or escaping . ( Turing , 1950 , p . 440 )
Lastly , May states that “ Not only in research , but also in the everyday world of politics and economics , we would all be better off if more people realized that simple nonlinear systems do not necessarily possess simple dynamical properties ” ( May , 1976 , p . 467 , our emphasis ).
In the realm of economics and finance , a precursor and prolific contributor to complexity is Brian Arthur . He consolidates the ideas of path-dependence ( Arthur , 1988 , 1994a ) and feedback ( Arthur , 1990 ); helps along with others open-up the area of finance ( Palmer , Brian Arthur , Holland , LeBaron , & Tayler , 1994 ); while proposing alternative views on traditional economic concepts ( Arthur , 1991 , 1994b ) and establishing epistemologically the ideas of complexity within economics ( Arthur , 1999 , 2005 , 2013 ).
V - On the Need of Models
The scientist does not have full methodological knowledge of their object of investigation . However , according to Rosenblueth and Wiener , they should have a clear view of their research questions . These could be defined hierarchically from the most general to the most specific . The general question possibly contains more relevant answers , but they are less precise and , especially , less susceptible to experimentation .
Rosenblueth and Wiener ( 1945 ) departing point is the premise that science follows a dual rite that goes from the understanding of reality to the action upon it . The authors say that if one intends to act upon the scientific phenomenon , thus exerting control , it is necessary to abstract reality , work with similar elements which are simpler , but which contain the essence .
Then , Rosenblueth and Wiener define closed and open box models . Closed box models are defined as those in which a fixed finite number of input variables determine a fixed number of output variables , independently of the transition structures . As the model demands a greater number of variables for its full comprehension , it becomes more and more open . Actually , “ scientific progress consists in a progressive opening of those boxes ” ( Rosenblueth & Wiener , 1945 , p . 319 ), leading into more elaborated , sophisticated , and hierarchically superior models ; both abstract and complex ones . Finally , Rosenblueth and Wiener argue that imperfection is intrinsically of the nature of models . That is , a one-to-one model would be redundant .
Still on the debate over models , Conant and Ashby ( 1970 ) develop a theorem according to which the regulator ( of a system ) who aims at simplicity and effectiveness should necessarily have a model . “ A model ���� be needed ” ( Conant & Ashby , 1970 , p . 90 , emphasis in the original ). Besides , the regulator must know exactly how the structure of the system works , and continuing effectiveness is dependent upon the deepening of his knowledge of the system .
In order to fully develop the theorem , Conant and Ashby ( 1970 ) define ( a ) regulation , ( b ) model , and ( c ) system . Regulation is defined in the context of events in a system . The system contains all events that can occur . The events may be separated into regulated or unregulated ones . Regulated events represent pursued goals , are generated by the regulator and are a subset of all possible events . Unregulated events are disturbances , that is , events happening out of the control of the regulator but within the system . Unregulated events can also influence regulated events .
14