To develop cyber-physical system behaviour is to program the whole bipartite system—both the software machine and the physical world whose behaviour it governs. To ensure desired behaviour of the machine, programmers must know its given properties—the hardware architecture and instruction set and the programming language semantics. This knowledge amounts to an axiomatic model of the machine: the axioms state those properties that determine the machine's behaviour in executing its software.
What axioms ensure desired behaviour in the governed world in its interaction with the machine? At first sight, they must be sought in the laws of physics. The natural laws discovered by scientists—from particle physics to chemistry, mechanics, and thermodynamics—describe what is physically possible in the world. But in fact physics is not nearly enough to provide the necessary axioms. Why not?
A cyber-physical system is what the physicist and chemist Michael Polanyi [1,2] calls a contrivance; its components—the machine and the physical domains of the governed world—work together to serve human purposes. Possible behaviour is restricted at two levels. The lower level reflects the physical laws that restrict possible behaviour by equations relating natural phenomena at many granularities—from particle interactions to conservation laws. The upper level reflects the system's purposes and the designed operational principles by which those purposes are achieved. At this upper level the shapes and combinations and interactions of the system's physical domains further restrict behaviour by determining temporal and spatial configurations within which the effects of distinct natural laws are combined, and by setting boundary conditions for applying their equations.
Nature's laws are not flouted: the upper level does not introduce anarchy, and the laws of physics continue to hold. But what happens within those laws is constrained by the implemented operational principles of the contrivance expressed in terms of the upper level. Those principles must be devised—and reasoned about—in terms of concepts that are foreign to the discourse of the laws of physics. First, because the operational principles of physical contrivances rest on the concept of causality. Newton expressly rejected causal explanation of his gravitational law: he insisted that he was describing only what happens, not why or how it happens .
Second, because reasoning about operational principles in terms of the laws of physics and of the boundary conditions for each local and each combined application of each law would be impossibly complex and voluminous. The physical domains of the governed world—whether natural, or engineered, or evolved by chance processes—are typically heterogeneous, mutable, very irregularly shaped, deeply structured, and richly interconnected both horizontally and vertically. For devising, exploring, and reasoning about these domains it is necessary to adopt informal abstractions at the scale and granularity of the operational principles. Certainly, natural laws limit what the operational principles can hope to achieve; and they may often be invoked to explain particular failures. But the necessary axiomatic models of the governed world must be sought elsewhere, in more than physics.
 Michael Polanyi; The Tacit Dimension, pp39-40; U Chicago Press, 2009.
 Michael Polanyi; Personal Knowledge, pp331-332; U Chicago Press, 1974.
 Richard Feynman; The Character of Physical Law, pp55-6; Penguin Books, 1992.
Links to other posts:
↑ Cyber-Physical Systems: The essential character of a cyber-physical system
→ More than Physics: Finding and structuring axioms for the governed world behaviour
→ Axiomatic Models: Capturing basic assumptions for a behaviour