TOWARD CULTURAL ONCOLOGY: THE EVOLUTIONARY INFORMATION DYNAMICS OF CANCER

To reiterate, the ‘adiabatic’ nature of the information source means that
probabilities defining H closely track parameter changes, remaining as ‘mem-
oryless’ as is necessary for the mathematics to work, along a ‘piece’ of un-
derlying structure. Between such pieces, we impose ‘phase transition’ regu-
larities described by renormalization dynamics.

While information systems do not have ‘Hamiltonians’ allowing definition
of a ‘partition function’ and a free energy density, they may have a source
uncertainty obeying a limiting relation like that of free energy density. Im-
porting ‘renormalization’ symmetry gives phase transitions at critical points
(or surfaces), and importing a Legendre transform gives dynamic behavior
far from criticality.

As neural networks demonstrate so well, it is possible to build larger pat-
tern recognition systems from assemblages of smaller ones. We abstract this
process in terms of a generalized linked array of subcomponents that ‘talk’ to
each other in two different ways. These we take to be ‘strong’ and ‘weak’ ties
between subassemblies. ‘Strong’ ties are, following arguments from sociol-
ogy [25], those which permit disjoint partition of the system into equivalence
classes. The strong ties are associated with some reflexive, symmetric, and
transitive relation between components. ‘Weak’ ties do not permit such dis-
joint partition. In a physical system these might be viewed, respectively, as
‘local’ and ‘mean field’ coupling.

We are, thus, concerned with languages ‘spoken’ on an underlying net-
work, be it chemical, neural, social, ecological, or some mix of these. The
network will be manifest in the properties of any language ‘spoken’ on it,
and vice versa, if language process can affect network properties. It is this
composite, interactive phenomenon we wish to model.

We fix the magnitude of strong ties, but vary the index of weak ties
between components, which we call P, taking K = 1/P.

We assume the ergodic information source depends on three parameters,
two explicit and one implicit. The explicit are K as above and an ‘external
field strength’ analog J, which gives a ‘direction’ to the system. We may, in
the limit, set J = 0.

The implicit parameter, which we call r, is an inherent generalized ‘length’
on which the phenomenon, including J and K , are defined. That is, we can
write J and K as functions of averages of the parameter r, which may be
quite complex, having nothing at all to do with conventional ideas of space;
for example the degree of niche partitioning in ecosystems or separation in
social structures.

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