Requisite Hierarchy – What carries the load instead

Keywords: internal model principle, Francis & Wonham, Aulin, requisite hierarchy, requisite knowledge, multiscale variety

Detail page for the cheat sheet. Legend: ✓ read · ◐ secondary/abstract · † unread · ✗ no source.

Introduction. Where the tradition cites C&A, stronger or cleaner results exist, and they come from outside it. Each has stated conditions. The chapter’s rule is to keep those conditions in view, since dropping them is the habit being criticised.

Francis & Wonham: the internal model principle

  • Francis, B. A. & Wonham, W. M. (1976). The internal model principle of control theory. Automatica 12(5): 457–65. doi:10.1016/0005-1098(76)90006-6.
  • The result: a controller that achieves asymptotic regulation robustly against parameter perturbation must contain a copy of the dynamics that generate the exogenous signals.
  • Scope: linear multivariable systems with stated signal classes. An organisation is not obviously such a system.
  • Extensions worth listing (from the Stress Test cheat sheet reading list, all †):
    • Sontag, E. D. (2003). Adaptation and regulation with signal detection implies internal model. Systems & Control Letters 50(2): 119–126. The principle beyond linear systems.
    • Yi, Huang, Simon & Doyle (2000). PNAS 97(9): 4649–53. Integral feedback in bacterial chemotaxis, where the principle yields a tested prediction.

Virgo et al. 2025: the reconstruction. See page 2. Being versus having a model, and trivial attributable models ✓.

Wentworth’s repair. See page 2. The minimal optimal regulator is isomorphic to the Bayesian posterior ✓. It is not peer-reviewed; cite it as a forum post.

Aulin: the law of requisite hierarchy

  • Aulin-Ahmavaara, A. Y. (1979). The law of requisite hierarchy. Kybernetes 8(4): 259–66. doi:10.1108/eb005528.
  • Hierarchy compensates when regulatory ability is limited. It is the derivation Beer’s recursion never had.
  • OpenAlex, 7 Aug 2026: Aulin ~43 citations, C&A ~1,040, F&W ~2,838. Use only as an order of magnitude, and refresh before print.
  • Whether Aulin actually establishes recursion in the form the VSM needs is left open in the chapter †.

Heylighen & Joslyn: requisite knowledge

  • Heylighen, F. & Joslyn, C. (2001). Cybernetics and second-order cybernetics. In R. A. Meyers (ed.), Encyclopedia of Physical Science & Technology, 3rd ed., vol. 4, pp. 155–170. Academic Press ✓ (preprint; printed pages unchecked).
  • It gives the law with buffering: V(E) ≥ V(D) − V(R) − K.
  • It adds the law of requisite knowledge: H(E) ≥ H(D) + H(R|D) − H(R) − K. Having many actions is not enough; the regulator must know which one to select.
  • It presents Aulin’s requisite hierarchy and the good regulator theorem side by side.

Bar-Yam: multiscale variety

  • Bar-Yam, Y. (2004). Multiscale variety in complex systems. Complexity 9(4): 37–45. doi:10.1002/cplx.20014. Citation ✓, content ◐.
  • Siegenfeld, A. F. & Bar-Yam, Y. (2020). An introduction to complex systems science and its applications. Complexity 2020: 6105872. It restates the law as “at least as complex as the environmental behaviors to which it must differentially react… at all scales for which these behaviors occur” ✓.
  • Siegenfeld & Bar-Yam (2025). Entropy 27(8): 835 (arXiv 2206.04896). This is the formal multi-scale law, with a sum rule trading small-scale against large-scale degrees of freedom. The profile depends on the chosen coarse-graining ✓.

Galbraith. Treated in Ch 12: a variety argument for organisation design made without citing Ashby.

Importance for the chapter. Section “A derivation that went almost uncited”, and the receipt: cite F&W and Virgo et al., not C&A as proved.

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