2026 DRAFT - Ideas in Progress
Cybernetics, as developed by W. Ross Ashby and others, is often presented in terms of systems, feedback loops, and control mechanisms. Central to this tradition is the distinction between “trivial” and “non-trivial” machines, where a trivial machine maps input to output via a fixed function, and a non-trivial machine introduces internal state, rendering behavior dependent on history.
In practice, this distinction is often used operationally, and not always taken as a literal claim about physical systems.
Still, this framing can obscure a more fundamental structure. It can conflate three distinct layers: the physical substrate, the relational pattern observed, and the conceptual model used by the observer. The result is a language in which properties of models are easily attributed to machines themselves.
A cleaner formulation emerges if we replace the machine-centric view with a selector-based one.
At face value, the idea is straightforward. A “trivial machine” is one where a given input produces a predictable output—essentially, a stable input–output relation. A “non-trivial machine” is one where the output depends not only on the input, but also on internal state. The problem is that no real system is actually trivial — triviality is something the observer assumes by selecting a stable relation and ignoring everything else. This is a sound basis for reasoning, but it must be understood as an abstraction, not a property of the system itself.
A ripple adder makes this concrete. At the level of reasoning, we describe it with the relation:
A = B + CThis is what cybernetics would call a “trivial machine”: a stable mapping from inputs to outputs. It is a constraint we assume holds, and from which we derive further reasoning.
But the physical ripple adder is not that relation. It is a chain of gates whose behavior depends on, for example:
In other words, it is a stateful, embedded process. By any literal reading, it is a non-trivial machine.
The only reason we can treat it as “trivial” is that we have engineered it so that, within certain bounds, the relation A = B + C remains statistically stable.
The trivial description is therefore not describing the machine—it is describing a selected invariant we expect the machine to satisfy.
This is the key point:
The “trivial machine” is not the implementation, but a constraint we reason with.
All reasoning derived from A = B + C is valid only insofar as the physical system continues to satisfy that constraint.
When the underlying conditions drift—noise, thermal effects, timing violations—the relation breaks, and the reasoning no longer applies.
So in practice:
This exposes the issue with the terminology. Calling A = B + C a “machine” conflates:
The same structure applies broadly: any engineered system is treated as “trivial” only insofar as its behavior remains within a selected envelope of stability.
The former is a model used for reasoning. The latter is an implementation that may or may not satisfy that model.
In that sense, the trivial/non-trivial machine dichotomy is not really a classification of machines at all. It is a distinction between:
Framed as a distinction between machines, it risks conflating distinct levels of description.
The distinction between “trivial” and “non-trivial” machines can therefore be restated without appealing to machines at all.
What is called a “trivial machine” is not a property of a system, but a relation selected by an observer and assumed to hold. It is a constraint over possible values — for example, A = B + C — that remains stable enough to support reasoning.
The physical system is then treated as if it instantiates that relation, so long as the conditions required for its stability are maintained.
This suggests a clearer formulation:
A “trivial machine” is not a machine, but a selected invariant — a relation over a system that has been isolated for the purpose of reasoning and treated as if it remains stable.
This selection can be understood as a selector: a relation that filters the behavior of a system down to those configurations that satisfy the constraint. Formally, a selector can be understood as a constraint over a space of possible system states, identifying those configurations that satisfy a given relation.
In the case of A = B + C, the selector isolates only those states of the system consistent with addition.
The crucial step is idealization. The selected relation is not merely identified, but assumed to hold, allowing reasoning to proceed within its bounds.
The physical system is then treated as if it instantiates this relation, so long as the conditions required for its stability are maintained.
All reasoning proceeds within this assumption.
When the underlying conditions drift beyond the bounds in which the relation holds, the invariant breaks, and the reasoning derived from it ceases to apply.
On this view, the machine itself is not intrinsically trivial. Only the relation we select from it is.
In this framework, the distinction introduced by Ashby can be restated without reference to “machines.”
A trivial selector extracts a constrained relation:
R(x, y)A non-trivial selector extracts a constrained relation that includes a carried coordinate:
R(x, s, y)
Here, s is not “state” in a temporal sense, but a shared component linking successive applications of the relation. What appears as memory or history is simply the propagation of this coordinate across a chain of relations.
Crucially, a non-trivial selector is not a fundamentally different kind of entity. It is a composition of trivial selectors, linked by this carried coordinate. The apparent complexity arises not from a new category of system, but from the chaining of relations.
This reduces the need to treat time as a primitive in the model. Temporal behavior becomes an indexing over relation applications, rather than a foundational dimension of the model.
Once selectors are understood as relations, a further consequence follows: selectors themselves can be selected.
Once relations are treated as primary, they can be composed and operated on in the same way as other objects of analysis.
This produces a recursive structure:
There is no privileged level at which this process terminates. Observers, models, and systems all occupy positions within the same recursive grammar.
This aligns with Ashby’s deeper insight: that regulation and control depend on the capacity of a system to match the variety of its environment. In selector terms, this becomes:
A structure can only stabilize patterns that lie within the expressive capacity of its selectors.
In this framework, idealization is no longer a vague notion of approximation. It is a precise claim:
The selected pattern will remain stable under the assumed conditions.
Failures of prediction—whether in engineering, finance, or natural systems—occur when unmodeled patterns, previously suppressed by the selector, become relevant.
Thus, the limits of prediction are not merely computational. They arise from the partiality of selection itself. Every model is a projection; every projection excludes.
If taken as more than a modeling framework, the selector perspective suggests a shift away from object-centered ontology toward a pattern-centered one.
Whether this shift is ontological or merely methodological is left open.
Rather than beginning with systems that exhibit behavior, we begin with:
Cybernetics then becomes a special case: the study of selectors that maintain pattern stability under disturbance—feedback, control, adaptation.
This reframing preserves the operational insights of Ashby while removing some of the conceptual ambiguities introduced by machine-based language.
It emphasizes relation over hierarchy. It reframes causation in terms of selection. It treats system boundaries as domains of pattern stability.
The open question—left deliberately unresolved—is what constrains the space of possible selectors. That question moves beyond cybernetics into the domain of coherence, structure, and ultimately, ontology itself.