Humor me for a moment. There is a pi (π) that some may be less aware of – the theoretical formalism of pi calculus in process algebra. Thank Robin Milner, a part of the brain trust with Joachim Parrow, David Walker who is behind the theory of pi calculus, for approaching systems as fundamentally able to reorganize and reconstitute themselves through interactions (see Milner, 1999). Pi (π) calculus is algebra of concurrent processes. Jeannette Wing (2002) explained the utility of pi calculus in a way that I found highly approachable (or as cuddly as process calculus can be). The process is that mysterious force based on inputs that control a system (see Wing, 2002). First, there are processes that hold control in the systems which are acted upon by channels. The channels tie together through some mode of communication (or relationship) (see Wing, 2002). Systems are made of components that are interdependent which make sense by looking at protocols. Also the process can involve any number of balancing and reinforcing factors that loop together.

Displaying a recognized connection to another agent is, at its center, systemic. For example, when using pi calculus theory within computer code modeling, what is of interest is the process calculus of the messaging (connections) that may be measured asynchronously (with a time delay) or synchronously (at the same time). The computer code using pi (π) calculus is an approximation, replicating the nature of the concurrent inputs/outputs into the system. According to Wing’s (2002) summation, “the syntax of π-calculus lets you represent processes, parallel composition of processes, synchronous communication between processes through channels, creation of fresh channels, replication of processes, and nondeterminism.”

Specifically, health policies cross into people’s lives very intimately. I strongly believe that any discussion of health policy must identify the dueling private welfare and the health of the collective. I explored this more fully in an earlier Hippo Reads commentary, “Blooming History, private lives and dissent in the public sphere.” In an expansion of that commentary, I offer three kinds of “wicked” expectations that are intrinsic to any public acting under a policy:
1. Social expectations- how the world expects a citizen to act under the policy
2. Ethical expectations- individual and collective moral decisions and actions that are tied to compliance or noncompliance to the policy
3. Behavioral expectations- what behaviors keeps a person in compliance with a policy (Battle-Fisher, 2015)

Pi (π) calculus plays in the syntax, reaction, actions, and transitions sandbox. The values in the system (called “names”) intrinsically have no structure. In this calculus, structure shows up when values are linked together and undergo a process over time. An individual agent in a social system and measurement of his actions add little evidence to how the policy is informing the welfare of the collective. Bringing all of the agents together then mapping “syntax, reaction, actions, and transitions” of the social agents under a policy is the goal. A policy becomes meaningfully understood when inputs and outputs across agents are explored. There is this cool component of a “silent action” in Pi (π) which denotes internal, unobservable actions in a process. This is an important issue to acknowledge when reading systemic factors in a policy as well.

What can policy learn from pi calculus?

1. There should be an accounting of the systemic process underlying the policy. This may include looking at the interdependence and feedbacks among elements of the system, ongoing assessments of the past policy successes and failures, as well as changing landscape of epidemiological evidence.
2. Dynamic changes in inputs/outcomes are debated beyond the mental models offered around the table (e.g. use of formal modeling).
3. Overlap (concurrence) of different systems at play in the policy should be explored.

In a process evaluation of a policy, we cannot have complete certainty that we have caught everything that is happening in a social system. But we sure had better try to find as many observable values to have a fighting chance of capturing the truest nature of the system at work.


Battle-Fisher, M. (2015) Application of Systems thinking to health policy and public health ethics- public health and private illness. Springer: New York.

Milner, R. (1999). Communication and Mobile Systems: The Pi Calculus. Cambridge: Cambridge University Press.

Wing, J. (2002). FAQ on pi-calculus. Retrieved on August 17, 2016 from .

This post extends an argument by the author in the Orgcomplexity Blog called “Time to get a piece of the modeling pi,” published on February 18, 2014.

About The Author

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Adjunct Assistant Professor, Wright State University Boonshoft School of Medicine

Michele Battle-Fisher is an Adjunct Assistant Professor at the Wright State University Boonshoft School of Medicine and the author of Application of Systems Thinking to Health Policy and Public Health Ethics: Public Health and Private Illness (Springer), a 2016 Doody's Core Title. Ms. Battle-Fisher is a Health Systems/Complexity scholar and bioethicist. She has researched and taught in the medical and policy fields, ranging from public health, science and technology, bioethics, systems theory and its application to health. She was a speaker at TEDxDartmouth 2018 where she discussed the "Paradigm Shift" of Health Systems Science curriculum in health and clinical medicine. She was selected as a finalist in the 1st annual MIT Press “Pitchfest”, the “Shark Tank” of book publishing.