TOWARD CULTURAL ONCOLOGY: THE EVOLUTIONARY INFORMATION DYNAMICS OF CANCER

for real systems, since Q[K], in this model, represents a kind of barrier for
information systems.

On the other hand, smaller values of α mean that the system is far more
efficient at responding to the adaptive demands imposed by the embedding
structured ecosystem, since the mutual information which tracks the match-
ing of internal response to external demands, I[K], rises more and more
quickly toward the maximum for smaller and smaller α as the inverse cou-
pling parameter K declines below K_C = 1. That is, systems able to attain
smaller α are more adaptive than those characterized by larger values, in this
model, but smaller values will be hard to reach, and can probably be done
so only at some considerable physiological or other cost.

Again, more biologically realistic renormalization strategies - based on
different forms of f (R) - are given in the Appendix. These produce sets of
several parameters defining the ‘universality class’, one of whose tuning gives
behavior much like that of α in this simple example.

We iterate the phase transition argument on this calculation to obtain
our version of the mutator, focusing on ‘paths’ of universality classes.

The adaptive mutator and cognitive mutation control

Suppose the renormalization properties of a biological or social language-
on-a network system at some ‘time’ k are characterized by a set of parameters
Ak ≡ α₁^k, ..., α_m^k . Fixed parameter values define a particular universality class
for the renormalization. We suppose that, over a sequence of ‘times’, the uni-
versality class properties can be characterized by a path x_n = A₀, A₁, ..., A_n-1
having significant serial correlations which, in fact, permit definition of an
adiabatically piecewise memoryless ergodic information source associated
with the paths xn . We call that source X.

We further suppose, in the usual manner [56, 57], that external selection
pressure is also highly structured, and forms another information source Y
which interacts not only with the system of interest globally, but specifically
with its universality class properties as characterized by X. Y is necessarily
associated with a set of paths yn .

We pair the two sets of paths into a joint path, z_n ≡ (x_n, y_y) and invoke
an inverse coupling parameter, K , between the information sources and their
paths. This leads, by the arguments above, to phase transition punctuation
of I [K], the mutual information between X and Y, under either the Joint
Asymptotic Equipartition Theorem or under limitation by a distortion mea-
sure, through the Rate Distortion Theorem [14]. Again, see [56, 57] for more

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