Based on the provided sources, W. Ross Ashby distinguishes between variables and parameters functionally and relationally, rather than by their physical nature. This distinction is central to his definition of a “machine” or a state-determined system.
Here is how Ashby distinguishes the two:
1. Functional Role: Operands vs. OperatorsThe most fundamental distinction lies in the role each plays in the system’s transformation (the change from one state to the next).
• Variables are Operands: Variables are the measurable quantities that define the state of the system at any given instant[1],[2]. They are the entities acted upon; as time passes, the variables change from one value to another (e.g., from state a to state b)[3]. This change of state constitutes the system’s behavior[1].
• Parameters are Operators: Parameters determine which transformation is applied to the variables[1]. A parameter acts as a constraint or a condition that fixes the laws governing the system’s behavior[4],[5]. While a change in variables represents a movement along a line of behavior (a trajectory), a change in a parameter causes a change in the way of behaving[3].
**2. Relationship to the “Field”**Ashby uses the concept of a “field” (or phase-space) to visualize the set of all possible behaviors of a system.
• Variables define the position: The values of the variables determine the system’s location within a specific field (its current state)[6].
• Parameters define the field itself: A specific set of parameter values generates a specific field (a specific set of trajectories). If a parameter changes, the system’s field changes—meaning the rules governing the system’s transitions have changed[1],[7]. Consequently, a system has as many different fields (ways of behaving) as its parameters have combinations of values[8].
3. Mathematical IdentificationIn the mathematical representation of a system (canonical equations), Ashby provides a simple visual test to distinguish them:
• Variables appear on the left side of the equation as quantities changing with time (e.g., dx/dt or x′), indicating they are the result of the transformation[1],[9],[10].
• Parameters appear only on the right side of the equation. They contribute to the calculation of the next state but are not themselves the subject of the differential or difference equation in that specific system definition[1],[10].
4. Interaction and CouplingAshby uses the distinction between variables and parameters to rigorously define how two systems (such as an organism and its environment) interact.
• Coupling: To join two systems, the variables of one system are made to act as the parameters of the other[11],[12].
• Feedback: For example, in an organism-environment relationship, the organism’s output (variables) acts as the environment’s input (parameters). Simultaneously, the environment’s output (variables) acts as the organism’s input (parameters). This reciprocal relationship creates a single state-determined system with feedback[12],[13].
5. Relativity to the ObserverAshby emphasizes that the distinction is not inherent to the physical object but depends on the observer’s definition of the system.
• Observer Choice: An observer selects a specific set of quantities to observe; these become the variables[11],[14]. All other quantities that affect the system but are not included in this set are classified as parameters[15].
• Changing Definitions: If a quantity originally defined as a parameter begins to change and the observer decides to study its changes, it must be re-classified as a variable. This effectively redefines the system into a larger one[16]. Conversely, if a variable is held constant, it effectively becomes a parameter for the remaining variables[17].
In summary, for Ashby, variables are the changing parts inside the system being studied, while parameters are the “inputs” or surrounding conditions that determine how those variables relate to one another[18],[19].
References
[1] Ashby’s Cybernetic Framework_ System, Parameter, and Environment.pdf [2] [Book] Ashby - Design for a Brain The origin of adaptive behaviour.pdf [3] [Book] Ashby - Introduction to Cybernetics.pdf [4] Ashby-Mechanisms_of_intelligence_ocr.pdf [5] [Book] Ashby - Introduction to Cybernetics.pdf [6] [Book] Ashby - Design for a Brain The origin of adaptive behaviour.pdf [7] [Book] Ashby - Design for a Brain The origin of adaptive behaviour.pdf [8] [Book] Ashby - Design for a Brain The origin of adaptive behaviour.pdf [9] [Book] Ashby - An Introduction to Cybernetics.pdf [10] [Book] Ashby - Introduction to Cybernetics.pdf [11] Adaptive Systems work of ashby and ultrastability version 2.pdf [12] Ashby’s Cybernetic Framework_ System, Parameter, and Environment.pdf [13] [Book] Ashby - Design for a Brain The origin of adaptive behaviour.pdf [14] Ashby’s Cybernetic Framework_ System, Parameter, and Environment.pdf [15] [Book] Ashby - Design for a Brain The origin of adaptive behaviour.pdf [16] [Book] Ashby - Design for a Brain The origin of adaptive behaviour.pdf [17] [Book] Ashby - Design for a Brain The origin of adaptive behaviour.pdf [18] [Book] Ashby - An Introduction to Cybernetics.pdf [19] [Book] Ashby - Introduction to Cybernetics.pdf