Source
Juarrero (2023), LIT-1995, pp. 68, 72, 77 and 183–191; read in NOTE-1532.
What was actually shown
Nothing is derived; the chapter states and illustrates.
Rate demarcation. “Boundaries between levels of organization and constraint are therefore typically marked by sharp discontinuities in order parameters and average process and relaxation rates”, and “overarching hierarchical levels of organization are usually slower than their components or realizations. The smaller the ‘average rate constants’ that define a set of interdependencies (Salthe 1985, 72), the higher its organizational level” (p. 183). Earlier: entrained pendulums trace a pattern “longer and slower than the swings of the individual pendulums” (p. 68), and rate differences between predator–prey cycles and lifespans “constitute the boundaries between parts and wholes” (p. 77).
Why the relation is constraint. Quoting Salthe: processes at one level cannot interact energetically with another “because [faster] lower-level dynamics would have been completed before feedback from the [slower] upper level arrived” (p. 187). Whole-to-part relations are “rate independent”: governing constraints “inform and influence” components “without participating in them dynamically” (p. 188).
Loss on convergence. The asymmetry “can be destroyed by either excessively accelerating the dynamics of an embedding environment or slowing down the rates of the focal-level system beyond its tolerance range” (p. 189, after Allen, O’Neill and Hoekstra 1984). “Lack of asymmetry in cycling rates between focal level and the context in which it is embedded, or between the focal level and its components, reflects the absence of control constraint by one on the other, regardless of signal amplitude” (p. 190). A component sped up becomes “invisible” to its embedding context, the tumour being the example (p. 190).
Inside a level, coupling is fast. A coherent dynamic’s interactions have “feedback loops and relaxation times shorter, faster, and more regular” than the environment’s (p. 72).
What could have come out otherwise: a case in which a whole controls parts that run at its own rate, or a slower context that exerts no control. The chapter offers none of either and tests neither.
What this does not say
- That slowness makes a constraint. The book’s constraint (p. 40) has no time-scale condition; rate separation here marks levels and is a condition of control, not a mechanism by which a relation becomes a constraint. That mechanism, the slow manifold, is CLAIM-478’s, from LIT-1292 and LIT-582, not this book’s.
- That organization makes the separation by an instability. The pendulums’ slower wave (p. 68) is a slower whole, but the book does not treat critical slowing, and Haken appears only for “slaving” (p. 81).
- That near-decomposability is the general case. The book calls the nested-doll picture “misleading” where closure and hypercycles cut across layers (p. 183).
- Anything quantitative. No ratio, threshold or measure is given.