How Many Layers, and How Concentrated Each One What would falsify "the more complex, the more centralised": one decomposition and a test design for three propositions

Abstract

Abstract That rising complexity requires more centralisation is a claim used repeatedly in cybernetics, organisation theory and complexity science, and it has never been taken apart. Because it has not, it can be neither falsified nor turned into an executable prescription. This paper does not argue that the claim is true. It asks what would count as showing it false. The argument runs in two steps. The first shows that “centralisation” is not one dial but at least four separately adjustable quantities: the number of layers, the concentration of coordination load within a layer, the strength of authorisation, and enforceability. None of the four determines any other, and collapsing them into a single word is the main reason the claim is unfalsifiable. This yields a two-axis reading that replaces the single axis: layer count read vertically, within-layer concentration read horizontally. The second step splits the claim into three separately testable propositions. Proposition 1: the number of layers a system requires is no fewer than the number of separable characteristic scales in its environment’s screening-length spectrum. This follows from the law of requisite variety together with the fact that one layer screens one screening-length band; it is tier B, because the judgement of “separable” itself carries a threshold that has no independent calibration. Proposition 2: when a function is conjunctive, so that the thinnest component determines the whole and the aggregation operator is the minimum, the coordination load of that function must be concentrated, while additive functions are under no such constraint; this is tier A, and what it delivers is a list of which things to centralise, answerable item by item, rather than a verdict on how centralised a system should be overall. Proposition 3: within-layer coordination concentration has an interior optimum, fixed by the lower envelope of three mutually independent constraints, namely identification delay, maintenance power, and conjunctive collapse; this is tier B, and the paper takes no position on which side the optimum moves toward. Each of the three carries its own falsification condition and its own non-overlapping data source. Section 7 treats this separately, because if the three shared one body of evidence they would collapse back into one claim. Section 6 walks a concrete system through the four quantities and the three propositions; Section 7 sets out why the three must be falsified separately; Section 8 handles four classes of case unfavourable to the paper; Section 9 states the domain gate; Section 10 lists what the paper does not claim.