Barney Ricca's Complexity Page

Barney Ricca
Director, Graduate Program in Mathematics, Science and Technology Education
Associate Professor
Department of Mathematical and Computing Sciences
Saint John Fisher College
3690 East Avenue
Rochester, NY 14618

Phone: 585-899-3866
FAX: 585-899-3872
email: bricca (all Fisher e-mails are "at sjfc dot edu")

To me, a complex system is one that has three interrelated hallmarks; I will call these three growth, mutual influence, and topology.

First, complex systems grow; they cannot be assembled piece by piece as a car on an assembly line. This notion has many important consequences, including:

  • Because the actual state of existence of a complex system is "the result of a series of highly contingent events that would not happen again if we could rewind the tape" (Gould, quoted in Rosenberg, 1990), complex systems always bring their pasts with them.
  • Complex systems are autopoietic (Maturana & Varela, 1992) and cannot easily be directed (or predicted!) by external entities.
  • In such a growing system all action is creative action (Kampis, 1991). Even the maintenance of a complex system entails ongoing acts of creation (as, for example, the cells that compose a body today are not the same cells that composed the body yesterday). Creative systems often bring forth new entities, and so not only is prediction impossible: the creation of new entities may also require the creation of new interpretations and meanings .

Second, although all systems can be considered to be in relationship to all other systems – even if the relationship is a null one – complex relationships are those that exhibit a mutual influence of each system on the other (Kaneko, 2009). Hence, the complex interaction of two systems may provokes changes in both systems, and not merely the adaptation of one system to the other.

Third, complex systems possess a topology that is markedly different from non-complex systems.

  • Most complex systems simultaneously exist both as themselves and inside themselves (Kampis, 1994).
  • Most complex systems are enmeshed with (and not merely embedded in or part of) other systems

These create a sort of Klein bottle topology which does not permit classical reductionism. Attempts to reduce a complex system to its parts generally result in fragmentation of the system and disconnection rather than insight.


  • Complexity: Foundations and Applications
  • Teacher preparation and professional development
  • Science Learning


  • Inquiry-Based Chemistry Institute. (Workshop grant from the Rochester Area Colleges Center for Excellence in Mathematics and Science.)
  • Fisher Scholars for Rural Schools (Robert Noyce Scholarship Grant from the National Science Foundation)
  • Problem solving approaches to student learning


  • Green, K & Ricca, B. (2010). If Mowat & Davis are correct, then teaching is hard. Complicity 7(1) 63-69. Edmonton, Alberta, Canada: University of Alberta.
  • Ricca, B. (2009). The imposition of boundaries. Complicity. 6(1) 56-60. . Edmonton, Alberta, Canada: University of Alberta.
  • Ricca, B. (2008). Enframing: The view from inside. Complicity 5(1) 115-120. Edmonton, Alberta, Canada: Univers
  • Ricca, B. (2009). Refining models of complex systems. In N. Kellam & D. Stanley (Eds.), Proceedings of the Fifth Complexity Sciences and Educational Research Conference. Vancouver, British Columbia, Canada: University of British Columbia.


  • “Does self-organization exist in education?” Presented at the Annual Meeting of the American Educational Research Association, Denver, CO, May 2010.
  • “Observers and Autopoietic Systems.” Presented at the Annual Meeting of the American Educational Research Association, New York, April, 2008.
  • “Refining Models of Complex Systems.” Presented at the Fifth Complexity Sciences and Educational Research Conference. Athens, GA, February, 2008.
  • “Learning, Learning Environments, and Complexity Theories: Domains of Applicability.” Presented at the Annual Meeting of the American Educational Research Association, San Francisco, April, 2006.
  • “Boundaries, Components, and Education.” Paper presented at the Third Complexity Sciences and Educational Research Conference, Loranger, LA, November, 2005.
  • “Complexity and learning processes.” Presented at the meeting of the American Educational Research Association, San Diego, CA, April, 2004
  • “Complexity sciences and implications for schools.” Presented at the Complexity Sciences and Educational Research conference, Edmonton, Alberta, Canada, October, 2003.
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