Critique: Control Causality vs. Mechanical Causality

Critique and response context for Control Causality vs. Mechanical Causality in AffineDrift’s control-affine golf-swing framework.

Critique: Control Causality vs. Mechanical Causality

Summary of Concern

Assumption 5 defends the model against reflex-loop objections by distinguishing “Control Causality” (neural intent) from “Mechanical Causality” (force origin). The Weakness: This distinction is technically valid but functionally useless for analyzing human movement. In biological systems, the “Mechanical Causality” is downstream of the “Control Causality” in a way that makes separating them arbitrary. If a reflex loop (\(u = -Kx\)) is fast enough, the system mechanically behaves like a spring. Insisting on calling it “Input” because it comes from a muscle, rather than “Drift” because it acts like a spring, misclassifies the functional behavior of the system.

Location

• Page: articles/affine-nature-golf-swing.qmd
• Section: Limitations -> Mechanical vs. Control Causality
• Claim: “The ZTCF answers the question: ‘Regardless of the complex sensory-motor loops… what would the system have done if that input were instantaneously removed?’”

Nature of the Issue

• The “So What?” Problem: If the “input” (\(u\)) is effectively a feedback law (\(u(x)\)) determining the system’s impedance, then removing it (\(u=0\)) creates a counterfactual that never happens and cannot happen.
• Arbitrary Boundary: Why is the tendon (passive) part of Drift, but the short-latency reflex (active but automatic) part of Input? Both are “spring-like” to the conscious brain.
• Identifiability: We cannot measure \(u\) separate from passive mechanics in vivo without invasive nerve blocks. The model assumes we can know \(u\), but we only know \(\tau_{net}\).

Why This Is a Problem

• It makes the theory “physically true but biologically irrelevant.”
• It ignores the concept of synergy and impedance control (Hogan, 1985), which are foundational in modern motor control.
• A control theorist would say: “You are analyzing the open-loop plant, but the human is a closed-loop system. Your ‘Drift’ is the plant, but the effective plant includes the reflexes.”

Evidence / References

• Todorov, E. (2004). Optimality principles in sensorimotor control. (Feedback laws define the dynamics).
• Latash, M. L. (2008). Synergy. (Uncontrolled manifold hypothesis).

Severity

• High: It threatens the applicability of the framework to real human data.

Suggested Remedies

1. Impedance Term: Ideally, split dynamics into \(\dot{x} = f(x) + h(x, u_{stiffness}) + G(x)u_{torque}\).
2. Reflex Admission: Explicitly state that “Drift” includes only physics, not reflexes. “Input” includes all neural activity, reflexive or voluntary.
3. Functional Grouping: Acknowledge that for the golfer, high impedance feels like “Drift” (stability), even if the model labels it “Input” (cost). The taxonomy should perhaps distinguish “Stabilizing Input” vs “Driving Input”.

Cite this page