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”.