Comparing Methods in Systems Research
Embracing Intuition and Deduction
Last week I was reading Bertalanffy’s General System Theory when I came across a section focused on comparing and contrasting two distinct methods in general systems research — the empirico-intuitive and deductive approaches.1
Empirical Intuition
The discussion begins by citing Ross Ashby’s description of the “essentially empirical” method of Bertalanffy and his co-workers:
“[It] takes the world as we find it, examines the various systems that occur in it—zoological, physiological, and so on—and then draws up statements about the regularities that have been observed to hold. This method is essentially empirical.” — General System Theory (p.94)
The advantage of this “empirico-intuitive” approach is that it can be easily illustrated and verified by examples taken from the individual fields of sciences since it “remains so close to reality.”
Bertalanffy used this approach to identify several general systems principles based on his work in theoretical biology — centralization, differentiation, closed and open systems, growth in time, and competition. These general principles proved useful for researchers across disciplines from systems engineering and chemical reaction networks, to social work and organizational growth.
However, the downside of this approach is that it lacks mathematical elegance and deductive strength. It may even “appear naive and unsystematic to the mathematically minded.”
Mathematical Deduction
The alternative method is the one of deductive systems theory proposed by Ross Ashby. Rather than starting with the observation of several real world systems, the researcher begins by considering, in the abstract realm of mathematics, the set of all conceivable systems. They then proceed to reduce the set to a more “reasonable size.” 2
Ashby points to crystallography, the science which studies crystals, as an example of a field where the deductive approach has proven especially effective. Mathematical crystallography studies all types of crystals which are conceptually possible, or which might exist. It reveals that there are certain laws which must apply to the set of all conceivable crystals. Even though it is largely founded upon imaginary constructs which have never been observed in nature, it still makes confident predictions about what we can find in the real world.
Similarly, mathematical physics considers a number of constructs which don’t actually exist — particles with mass but no volume, frictionless pulleys, massless springs — in order to produce reliable predictions about real world physical systems.
Ashby argues that general system theory requires its own sound logical framework in order to effectively relate various real world systems to each other so that higher relations and laws can be discovered.
Dynamic Interplay
Responding to Ashby, Bertalanffy acknowledges that the intuitive approach lacks logical rigor and completeness. However, he also argues that the deductive approach struggles with the issue of correctly choosing fundamental terms.
In reality, science often advances as the result of a dynamic interplay between the two. To provide a concrete example he references the historical debate over which magnitude should be considered as a constant in physical transformations — force, or energy?
A brief review of some highlights in this debate will help illustrate his point.
Vis Viva
In 1686, Leibniz introduced the concept of “vis viva” (living force) based on a deductive philosophical approach with some mathematical formalism. He formulated vis viva as proportional to mv^2, indicating the conservation of energy.
Many physicists, unaware of his work and influenced by the work of Isaac Newton and Rene Descartes, advocated instead for the conservation of momentum as a guiding principle. 3
Coriolis Effect
In 1829, Gaspard-Gustave Coriolis used a rigorous mathematical approach grounded in engineering to refine Leibniz’s concept by introducing the factor of 1/2 and the associated term “kinetic energy.”
His work helped ground the debate in more modern conceptions of energy.
Faraday Cages
Michael Faraday’s experimental work on electromagnetism between 1821 and 1845 provided crucial empirical evidence which demonstrated the interconversion of mechanical to electrical energy. This supported the emerging idea of energy conservation.
Many of Faraday’s ideas were initially ignored because he was not very comfortable with the symbolic language of mathematics and he couldn’t back them up with rigorous proofs.
Lord Kelvin’s Laws
In 1851, Lord Kelvin published On the Dynamical Theory of Heat, synthesizing previous work including Faraday’s laboratory results. Using a primarily mathematical deductive approach, he formalized thermodynamics and the concept of kinetic energy quantified as mv^2/2.
Kelvin’s work was instrumental in establishing the principle of energy conservation and resolving the long-standing debate initiated by Leibniz nearly two centuries earlier.
Synthesis
Bertalanffy reasonably concludes that “there is no royal road to general systems theory.” Systems theory, like other branches of science, must ultimately develop by an interplay of empirical, intuitive and deductive procedures.
While I personally feel much more comfortable with Bertalanffy’s empirico-intuitive approach, I hope to gain a greater appreciation for the deductive approach during my independent study in mathematical systems theory this fall.
I believe that by bringing greater awareness to our own preferences and how they might complement those of people who don’t share them, systems researchers of all stripes might be able to collaborate more effectively.
Bertalanffy, L. v. (1969). General System Theory: Foundations, Development, Applications. (p. 94)
Ashby, W. R. (1991). General Systems Theory as a New Discipline. In G. J. Klir (Ed.), Facets of Systems Science (pp. 249–257). Springer US. https://doi.org/10.1007/978-1-4899-0718-9_16
Iltis, C. (1971). Leibniz and the Vis Viva Controversy. Isis, 62(1), 21–35. https://doi.org/10.1086/350705