Policy and Complex Systems
The quantity of creation is determined by knowledge and creation rate positively reinforcing one another , and the size of knowledge is determined by the size of creation . In other words , the larger the knowledge the larger the creation , the larger the creation rate the larger the creation capacity , and the larger the creation capacity the larger the knowledge quantity . This feedback structure makes a self-reinforcing loop that grows scientific knowledge continuously .
There is a negative feedback loop ( B1 ) to control the pace of knowledge growth . The negative feedback structure is the feedback loop from knowledge through normal obsolescence and obsolescence back to knowledge . Knowledge can and does become obsolescent at some point . When scientific knowledge is obsolete , articles are no longer cited . The obsolete scientific knowledge negatively influences knowledge growth . The pace of obsolescence is influenced by the normal obsolescent rate positively . In other words , the larger the normal obsolescence rate , the larger the amount of obsolescent material . However , the normal obsolescence rate is influenced by the average lifetime of scientific knowledge negatively ; that is , the longer average lifetime of knowledge the fewer the normal obsolescence rate . In this respect , this negative feedback structure tends to set the pace of knowledge growth .
The size of obsolescence is also influenced by the effect of knowledge crowding on obsolescence as seen in the negative feedback loop ( B2 ). This loop is formed by causal relationships among knowledge , normalized knowledge , effect of knowledge crowding on obsolescence , and obsolescence . Through the loop , we can see how scientific knowledge becomes obsolescent . Normalized scientific knowledge is determined by the function ( f )= knowledge / carrying capacity . In other words , scientific knowledge and carrying capacity influence the formation of normalized knowledge positively and negatively , respectively . Kuhn ( 1962 ) suggested that within the structure of scientific revelations , the stock of scientific knowledge is normalized . We accept this view ; the stock is the carrying capacity of knowledge among scientists in the system plus codified knowledge . Thus , in our model , we assume that scientific knowledge repeats this process over time with an accumulation . In addition , the normalized knowledge is assumed to have a nonlinear relationship with its effect on obsolescence over time . Obsolescence is expected to increase more quickly than knowledge as knowledge grows to a level of quantity ( that we do not determine in this experiment ). In measurable systems , it is difficult to express the relationship between them as a constant value and it may be that the value is not constant , although we did not test for this fact .
The type of feedback loop ( positive or negative feedback loop ) will determine the direction of the growth of the scientific knowledge system . The dynamics will determine whether the system displays exponential growth or s-shape growth . In other words , when the positive feedback structure ( R1 ) dominates the other two negative feedback structures ( B1 and B2 ) in our knowledge system , it creates an exponential growth mode . The s-shape growth that Price ( 1963 ) anticipated in his scientific knowledge growth model would require negative feedback dominating at least one of the two positive feedback structures . To test the model , we constructed a simulation setting based on a stock-flow model . The simulation uses empirical data of the actual number of published articles per year between 1990 and 2010 7 as drawn from the Web of Science . Information of each parameter is described in the appendix .
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