Kindness also may have an attractor, or due to discreteness have a volume > 0 in weight space.
The question is if the attractor is big enough. And given how there’s various impossibility theorems related to corrigibility & coherence I anticipate that the attractor around corrigibility is quite small, bc one has to evade various obstacles at once. Otoh proxies that flow into a non-corrigible location once we ramp up intelligence, aren’t obstructed by the same theorems, so they can be just as numerous as proxies for kindness.
Wrt your concrete attractor: if the AI doesn’t improve its world model and decisions aka intelligence, then it’s also not useful for us. And a human in the loop doesn’t help if the AI’s proposals are inscrutable to us bc then we’ll just wave them through and are essentially not in the loop anymore. A corrigible AI can be trusted with improving its intelligence bc it only does so in ways that preserve the corrigibility.
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Disclosure: Written by ChatGPT on 2025-09-16 at my request.
Energy use in isometric holds
Abstract. Standard physiology; no novelty. When an object is held stationary, static equilibrium (∑F=0, ∑τ=0) sets the joint torque needed to counter gravity. Muscle fibers generate that torque. Force in skeletal muscle is produced by continuous actomyosin cross-bridge cycling; each cycle uses one ATP. Calcium must be kept high to permit attachment and then pumped back into the sarcoplasmic reticulum; the Na+/K+ pump maintains excitability. External mechanical work is approximately zero, but chemical energy is consumed continuously and dissipated as heat. Example: holding a 5kg bag at the hand (forearm r≈0.35m, elbow 90∘) requires T≈17Nm. Relative to typical maximum elbow-flexion torque (≈70Nm in young men, ≈35Nm in young women), this corresponds to ≈24–49% MVC. Forearm ˙VO2 in that range is ≈20–30mLmin−1, i.e., ≈7–10W of local heat; two minutes dissipates ≈0.8–1.2kJ.
Model
Static equilibrium (mechanics). Gravity exerts a force mg at a horizontal distance r from the elbow. The required elbow torque is Treq≈mgr (simple forearm model).
Torque to muscle force (anatomy). Elbow flexors act through an effective moment arm reff. The muscle force satisfies T≈Fmreff. Holding a constant torque implies a near-constant average Fm (ignoring co-contraction and passive tissues for this shortform).
Force generation (molecular). Each muscle fiber contains many myosin heads that attach to actin briefly, pull, and detach. Only a fraction are attached at any instant, so maintaining force requires continuous replacement of attached heads; each replacement hydrolyzes one ATP. Attachment requires elevated Ca2+; relaxation requires pumping Ca2+ back into the sarcoplasmic reticulum.
Energy balance (physiology). External work is ≈0 at zero velocity, but internal processes consume ATP: PATP=Pxb+Pact. Reviews place activation at roughly 25–45% of ATP turnover in isometric contractions (muscle-dependent). At higher %MVC and longer holds, intramuscular pressure restricts blood flow, limiting oxygen delivery and accelerating fatigue.[1][2][3]
Worked example
Setup. m=5kg; r≈0.35m; elbow 90∘.
Torque required: T≈mgr=5×9.81×0.35≈17Nm.
Relative intensity: MVC≈70Nm (young men, ∼120∘) or 35Nm (young women, ∼90∘) ⇒ 24% or 49% MVC.[4]
Metabolic cost (from oxygen): around 20–30% MVC, forearm ˙VO2≈20–30mLmin−1. With ≈20.9kJL−1 O2: ≈7–10W locally; two minutes ≈0.8–1.2kJ.[5][6]
Predictions
Micro-breaks extend endurance. Alternating 1 s on / 1 s off at the same mean force allows reperfusion and reduces activation cost during the off phases.
Geometry reduces cost. Shortening r or shifting load to passive structures (bone, ligament, tendon) lowers Treq and the required ATP use.
Perceived effort rises during a hold. As some fibers fatigue, additional motor units are recruited to keep T constant, so effort increases before failure.
References
Barclay CJ (2023). Advances in understanding the energetics of muscle contraction. Activation ≈25–45% of ATP in isometric contraction. Journal page: https://www.sciencedirect.com/science/article/pii/S0021929023002385 ↩︎
Lind AR (1979). Forearm blood flow in isometric contractions. Flow rises to ≈60% MVC then plateaus. PubMed: https://pubmed.ncbi.nlm.nih.gov/469732/ ↩︎
McNeil CJ et al. (2015). Blood flow and muscle oxygenation during isometric contractions. J Appl Physiol (Regul Integr Comp Physiol). Abstract: https://journals.physiology.org/doi/abs/10.1152/ajpregu.00387.2014 ↩︎
Tsunoda N et al. (1993). Elbow flexion strength curves in untrained men and women and male bodybuilders. ≈70Nm (men), ≈35Nm (women). PubMed: https://pubmed.ncbi.nlm.nih.gov/8477679/ ↩︎
Nyberg SK et al. (2018). Reliability of forearm oxygen uptake during handgrip exercise. Rest ≈6.5mLmin−1; rises with intensity. PMC: https://pmc.ncbi.nlm.nih.gov/articles/PMC5974736/ ↩︎
Gill PK et al. (2023). It is time to abandon single-value oxygen uptake energy equivalents. Common 20.1–20.9kJL−1 O2 and caveats. PubMed: https://pubmed.ncbi.nlm.nih.gov/36825641/ ↩︎