K , and a renormalization symmetry representing the global structure of the
system coupling. This may be much different from the renormalization be-
havior of the individual components. If K < KC , where KC is a critical point
(or surface), the two information sources will be closely coupled enough to
be characterized as condensed.
Wallace and Wallace [51, 52] use this technique to address speciation,
coevolution and group selection in a relatively unified fashion. These papers,
and [56, 59], further describe how biological or social systems might respond
to gradients in information source uncertainty and related quantities when
the system is away from phase transition. Language-on-network systems, as
opposed to physical systems, appear to diffuse away from concentrations of an
‘instability’ construct related to a Legendre transform of information source
uncertainty. This is much the same way entropy is the Legendre transform
of free energy density in a physical system. The parametized ‘instability’,
Q[K], is defined from the principal splitting criterion by the relation
Q[K] = -KdH[K]/dK
Q[K] = -KdI[K]/dK.
(5)
H [K] is the information source uncertainty in the Asymptotic Equipar-
tition Theorem and I [K] the mutual information in the Rate Distortion and
Joint Asymptotic Equipartition Theorems, describing the cross-talk between
two information sources.
Universality class tuning
We suppose that a structured environment, which we take itself to be
an appropriately regular information source Y, ‘engages’ a modifiable sys-
tem through selection pressure, and begins to write itself on that system’s
genetic sequences or other internal structures in a distorted manner permit-
ting definition of a mutual information I [K] splitting criterion according to
16
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