Complexity Modeling: Solving Modern Problems and Confronting Real Issues
Author: Chris Arney & Amanda Beecher
Applied mathematics and science have made substantial progress in
modeling methodologies that have resulted in the advancement of knowledge
and improvement of solutions to important problems. Until the mid-
20th century, modeling-accessible problems primarily involved the physical
and technical world.
Hardin  suggested a broader strategy of using modeling to solve
also complex human problems. There is a shifting paradigm for solving these
problems called complexity modeling (see West and Deering ). The
utility of new forms of complexity modeling in disciplines such as sociology
and decision science shows the great benefit of this methodology.
Kuhn  proposed an episodic model in which paradigm shifts are
the driving forces for scientific advancement. According to Kuhn, paradigm
shifts are more important than the normal, steady, incremental progress of scientific methodology. The success of modern sociology and the introduction
of humanism into many science and engineering disciplines are
During the 20th century, a number of significant interdisciplinary scientific
disciplines emerged from paradigm shifts in modeling: information
science, computer science, network science, operations research, computational
linguistics, mathematical sociology, and data science (see Arney et
al. ). These interdisciplines have relied heavily on complexity modeling
for their progress (see Arney ). As the 20th century unfolded,
more and more modelers found the traditional reductive modeling approach
limiting for many of the most cogent and capricious problems, and
the foundation for the new paradigm of complexity modeling emerged in
the 21st century as a more powerful problem-solving tool.
COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.