Terrance J. Quinn
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One of my ongoing interests has been the interdisciplinary nature of progress in mathematics and the sciences. My Ph.D. (1992) was in Operator Theory (C*-algebras), the origins of this area of mathematics being quantum mechanics, and later quantum physical chemistry. Since 1992 I have published in pure and applied mathematics, mathematics for the biosciences, mathematics education and mathematics pedagogy. I have gradually been increasing my work on the foundations of mathematics and the empirical sciences. More recently (2011), foundations of the sciences has become a main focus.
There is of course tremendous activity, ongoing advances throughout the many disciplines, emerging sub-disciplines and hybrid disciplines. If we include the full sweep of scholarship to include past oriented studies as well as future oriented work such as directions, policies, plannings, communications, and so on, various questions can arise: How can we better collaborate, in more effective ways? What is the dynamical structure of progress in the mathematical and empirical sciences? Physics has had several centuries to work out a basic stability in some of its methods. So, within the present context of a Standard Model, specialists in high energy labs (http://www.er.doe.gov/hep/universities/index.shtml) look for anomalies in data, while theoreticians look for interpretations through, e.g., various gauge field theories. This is not to say that there are not individuals who do both, but that experimental research and theoretical development have emerged as two distinct but functionally related types of expertise.
In 1965, Bernard Lonergan made a fundamental breakthrough in identifying an eightfold structure, a “general dynamics” of progress, consistent with development in physics, but reaching across disciplines. His result points to a unity in the sciences that embraces spontaneous interdisciplinary developments. He called this general dynamics “functional specialization”.
At present, I am interested in better understanding the potential of “functional specialization”, and in particular how adverting to the emergent differentiations within the general dynamics may, in particular, help increase and implement collaborative potential across the mathematical and empirical sciences. Basic leads on this have been provided by Phil McShane (http://www.philipmcshane.ca/ ). There is a growing international awareness of the significance of “functional specialization”. See, e.g., SGEME (http://www.sgeme.org/). I am working on various collaborative projects in this area, and welcome queries.