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arxiv: 2604.16162 · v1 · submitted 2026-04-17 · 💻 cs.ET

Recognition: unknown

When does a control system compute? Digital, mechanical and open-loop systems

Dominic Horsman, Susan Stepney, Tim Clarke, Viv Kendon

Pith reviewed 2026-05-10 06:49 UTC · model grok-4.3

classification 💻 cs.ET
keywords control systemscomputationabstraction/representation theorycentrifugal governorcomputationalismthermostatopen-loop controlphysical computation
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The pith

All control systems perform computation, including purely mechanical and open-loop ones, because the plant serves as the representational user of the controller.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses abstraction/representation theory to examine whether controllers in control systems are computing by virtue of their role. It identifies the plant as the entity that represents and uses the controller's outputs, satisfying the theory's requirement for a user. Examples include a digital thermostat, an electromechanical thermostat, the centrifugal governor, and an open-loop heating system under human control. The analysis concludes that computation is present to some degree in each case and therefore in control systems generally. This result directly affects debates in cognitive science by showing that the governor cannot serve as a non-computing counterexample to claims about the brain.

Core claim

Using ART, the plant is modeled as the representational user that interprets the controller's physical states as standing for desired plant behaviors; this modeling establishes that the controller is computing in every examined system. The same structure applies to digital, electromechanical, purely mechanical, and open-loop cases alike, so control systems in general perform computation.

What carries the argument

Abstraction/Representation theory (ART), which defines computation in a physical system by the presence of a distinct representational user that abstracts and employs the system's states; the plant fulfills this user role for the controller.

If this is right

  • Every control system, regardless of implementation technology, performs computation once the plant is recognized as the user.
  • The centrifugal governor computes, removing it as a counter-example in discussions of computationalism.
  • Open-loop systems under human control also exhibit computation via the same plant-user structure.
  • The criterion extends to any engineered or natural control process that maintains a plant within limits.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Biological regulatory loops may be analyzed for computation using the same plant-as-user mapping.
  • Mechanical control devices could be re-examined as minimal computers without requiring digital components.
  • Design of future controllers might deliberately exploit the representational relation to the plant to achieve specific computational behaviors.

Load-bearing premise

Abstraction/representation theory supplies a sufficient non-circular criterion for identifying computation, and the plant can be treated unambiguously as the representational user of the controller.

What would settle it

An explicit control system in which the plant's states cannot be interpreted as representations of the controller's outputs while still satisfying all physical descriptions of the loop.

Figures

Figures reproduced from arXiv: 2604.16162 by Dominic Horsman, Susan Stepney, Tim Clarke, Viv Kendon.

Figure 1
Figure 1. Figure 1: Basic representation. (a) Spaces of abstract and physical objects (here, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Parallel evolution of an abstract object (blue, round corners) and [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Physical computing in ART. An abstract problem [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The relationship between the physical representational entity [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The full compute cycle including the representational entity and the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Control system diagram: Serial (or Cascade) Controller, operating on [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Control system diagram: Parallel Controller, operating on output [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: figure 8: sans serif font such as [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 8
Figure 8. Figure 8: Control system diagrams: (a) Serial and (b) Parallel Controllers, iden [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Proposed ART components of the Serial and Parallel Controllers. (a) [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Unwinding the feedback diagram from fig 9b over time. The top fig [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: The abstraction layer of the unwound feedback diagram figure 10. [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Incorporating a single compute cycle of the unwound physical system [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: A simple digital thermostat. [Photo credit: SS] [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: The digital thermostat computer (shaded) as part of the overall [PITH_FULL_IMAGE:figures/full_fig_p016_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: The digital thermostat computer in ART. See section 4.1.2 text for [PITH_FULL_IMAGE:figures/full_fig_p016_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: (a) A bimetallic coil thermostat. Lever (1) changes the set point. [PITH_FULL_IMAGE:figures/full_fig_p017_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: (a) The bimetallic coil physical computer (shaded) as part of the [PITH_FULL_IMAGE:figures/full_fig_p018_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: (a) The Centrifugal Governor. [image credit: Andy Dingley (scan [PITH_FULL_IMAGE:figures/full_fig_p019_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: (a) The centrifugal governor (shaded) as part of the overall Control [PITH_FULL_IMAGE:figures/full_fig_p020_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: The open loop car heater Controller (shaded) as part of the overall [PITH_FULL_IMAGE:figures/full_fig_p021_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: The car heater open-loop control system in ART. See section 4.4.2 [PITH_FULL_IMAGE:figures/full_fig_p022_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: (a) Apollo Guidance Computer controller (shaded) as part of the [PITH_FULL_IMAGE:figures/full_fig_p023_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Difference in outputs for (a) compute cycle and (b) control system [PITH_FULL_IMAGE:figures/full_fig_p029_23.png] view at source ↗
read the original abstract

Control systems are ubiquitous in modern technology, comprising an engineered plant to be kept within specific, often fine-tuned, limits, and a separate controller that ensures this is the case. While modern controllers often employ digital computers, other examples are purely mechanical, or even biological. It is an open question whether computation is happening within all controllers by virtue of them being part of a control system. Abstraction/ Representation theory (ART) has been developed to tackle just this question of whether a physical system is computing. Here, we demonstrate how to use ART to model control systems, and analyse them for computational properties. We determine that the plant of a control system is (a proxy for) the representational entity necessary in ART for the existence of any computation: the plant is the user of the controller. We consider specific systems: a digital thermostat, an electro-mechanical thermostat, the purely mechanical centrifugal governor, and an open-loop human-controlled heating system. We show that all these systems, and control systems in general, are performing some degree of computation. As an initial use of these results, we apply them to computationalism within cognitive theory: we show the governor is computing, so it cannot play its role of counter-example in the question of whether the brain is too.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript applies Abstraction/Representation Theory (ART) to control systems, arguing that the plant functions as the representational entity (or 'user') of the controller. This leads to the conclusion that digital thermostats, electro-mechanical thermostats, the centrifugal governor, and open-loop systems all perform computation to some degree. The results are then used to claim that the governor cannot serve as a counter-example in debates over computationalism in cognitive science.

Significance. If the plant-as-user mapping is independently justified, the paper supplies a concrete criterion for detecting computation in physical control systems and directly engages computationalism debates by reclassifying a classic mechanical example. The breadth of cases (digital, mechanical, open-loop) and the explicit link to cognitive theory are strengths.

major comments (2)
  1. [Abstract] Abstract: the assertion that 'the plant of a control system is (a proxy for) the representational entity necessary in ART' is presented as a modeling step rather than derived from ART's definitions of abstraction and user capacities. Without an explicit check that the plant (e.g., flyball speed or room temperature) satisfies those criteria independently of the control relation, the central claim that every control system computes risks circularity.
  2. [Centrifugal governor analysis] Centrifugal governor analysis: treating the physical plant (flyball speed) as the entity that 'interprets' the controller's state as a representation is asserted via the feedback loop; an independent demonstration that the plant performs the requisite abstraction steps required by ART is needed to support the claim that the governor computes.
minor comments (2)
  1. [Abstract] The abstract states that 'all these systems... are performing some degree of computation' but does not indicate how the degree is measured or compared across examples; a brief comparative table or metric would improve clarity.
  2. [Introduction] Citations to the foundational ART papers should be supplied in the introduction so that readers can verify the precise criteria being applied.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. These help clarify how to strengthen the presentation of the plant-as-user mapping. We address each major comment below and will revise the manuscript to make the derivations from ART more explicit.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that 'the plant of a control system is (a proxy for) the representational entity necessary in ART' is presented as a modeling step rather than derived from ART's definitions of abstraction and user capacities. Without an explicit check that the plant (e.g., flyball speed or room temperature) satisfies those criteria independently of the control relation, the central claim that every control system computes risks circularity.

    Authors: We agree that greater explicitness is needed to forestall any appearance of circularity. In the revised manuscript we will add a short dedicated paragraph right after the abstract. This paragraph will first restate ART's definitions of abstraction, representation, and the user's required capacities (the ability to treat one physical state as standing for another and to employ that standing-for relation in goal-directed behavior). It will then show, without presupposing the feedback loop, that the plant's state variables satisfy these capacities: the controller output functions as a representation of the plant's current condition, and the plant's own dynamics use that representation to adjust toward its operational goal (stable temperature, constant speed, etc.). This step-by-step grounding derives the mapping directly from ART rather than from the control relation itself. revision: yes

  2. Referee: [Centrifugal governor analysis] Centrifugal governor analysis: treating the physical plant (flyball speed) as the entity that 'interprets' the controller's state as a representation is asserted via the feedback loop; an independent demonstration that the plant performs the requisite abstraction steps required by ART is needed to support the claim that the governor computes.

    Authors: We accept the need for an independent demonstration and will expand the governor section accordingly. The revision will insert a numbered, step-by-step mapping that isolates ART's abstraction process from the closed-loop dynamics. We will show that the mechanical linkage itself performs the abstraction (flyball height stands for engine speed via the geometry of the arms), and that the plant (the engine) uses this standing-for relation through its physical response to achieve the goal of regulated operation. Because this account rests only on the physical properties and goal structure of the components, it does not rely on the feedback loop for its justification. The expanded analysis will therefore support the computation claim on ART's own terms. revision: yes

Circularity Check

0 steps flagged

ART applied as external framework; plant-as-user is modeling step, not internal reduction.

full rationale

The paper invokes Abstraction/Representation theory (ART) from prior literature to analyze control systems, treating the plant as the representational user required by that theory. This is a self-citation of the authors' own framework, but the central claim consists of applying the external criteria to concrete examples (digital thermostat, centrifugal governor, open-loop heating) rather than deriving the existence of computation from a definition internal to this manuscript. No equations or steps reduce the conclusion to a fitted input or self-referential loop within the paper itself. The analysis therefore remains non-circular at the level of derivation, though the modeling choice of plant-as-user inherits whatever foundational assumptions ART carries.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the prior validity of ART and on the modeling choice that the plant is the user/representational entity; no free parameters or new invented entities are introduced.

axioms (1)
  • domain assumption Abstraction/Representation theory correctly identifies when a physical system is performing computation.
    The paper invokes ART as the criterion for computation and applies it without re-deriving or proving the theory.

pith-pipeline@v0.9.0 · 5527 in / 1200 out tokens · 47524 ms · 2026-05-10T06:49:59.156067+00:00 · methodology

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