some driven systems tune themselves to a critical point with no parameter set by hand. the sandpile of Bak, Tang and Wiesenfeld (1987) relaxes into a state where avalanche sizes follow a power law and a single grain can trigger a slide of any scale
the biological instance is the one that matters here: cortical activity propagates in avalanches whose size distribution follows $P(s) \sim s^{-3/2}$ with branching ratio near one (Beggs & Plenz 2003). brains appear to sit at criticality, where dynamic range, information transmission and susceptibility are all maximal
the cybergraph has the same tension built into its economics. superadditivity rises with connectivity $\lambda_2$ while syntropy falls with it — measured, not conjectured — so there is an interior optimum, and the reward law is a control loop that should drive the network toward it
falsifiable: cascade sizes of $\Delta\phi^*$ on a healthy graph should be power-law with exponent near $-3/2$ and branching ratio approaching one. a subcritical graph is fragmented and cheap; a supercritical one is a mob
see superadditivity · syntropy · dissipative structures · physical analogies
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