IAB and D remain high, a highly overfocused, poorly linked
pattern of behavior which will require significant intervention
to alter once it reaches such a quasi-stable resilience mode.
The structure’s cognitive capacity, measured by H in figure
1a, is the lowest of all for this condition of pathological re-
silience, and attempts to correct the problem - to return to
condition A, will be met with very high barriers in S, accord-
ing to figure 1b. That is, mode C is very highly resilient,
although pathologically so, much like the eutrophication of a
pure lake by sewage outflow. See Wallace (2008a, b) for a
discussion of resilience and literature references.
We can argue that the three quasi-equilibrium configura-
tions of figure 1b represent different dynamical states of the
system, and that the possibility of transition between them
represents the breaking of the associated symmetry groupoid
by external forcing mechanisms. That is, three manifolds rep-
resenting three different kinds of system dynamics have been
patched together to create a more complicated topological
structure. For cognitive phenomena, such behavior is likely
to be the rule rather than the exception. ‘Pure’ groupoids
are abstractions, and the fundamental questions will involve
linkages which break the underlying symmetry.
In all of this, as in equation (19), system convergence is not
to some fixed state, limit cycle, or pseudorandom strange at-
tractor, but rather to some appropriate set of highly dynamic
information sources, i.e., behavior patterns constituting, here,
developmental trajectories, rather than to some fixed ‘answer
to a computing problem’ (Wallace, 2009).
What this model suggests is that sufficiently strong exter-
nal perturbation can force a highly parallel real-time cogni-
tive epigenetic structure from a normal, almost homeostatic,
developmental path into one involving a widespread, comor-
bid, developmental disorder. This is a well studied pattern
for humans and their institutions, reviewed at some length
elsewhere (Wallace and Fullilove, 2008; Wallace, 2008b). In-
deed, this argument provides the foundation of a fairly com-
prehensive model of chronic developmental dysfunction across
a broad class of cognitive systems, including, but not limited
to, cognitive epigenetic control of gene expression. One ap-
proach might be as follows:
A developmental process can be viewed as involving a se-
quence of surfaces like figure 1, having, for example, ‘criti-
cal periods’ when the barriers between the normal state A
and the pathological states B and C are relatively low. This
might particularly occur under circumstances of rapid growth
or long-term energy demand, since the peaks of figure 1 are in-
herently energy maxima by the duality between information
source uncertainty and free energy density. During such a
time the peaks of figure 1 might be relatively suppressed, and
the system would become highly sensitive to perturbation,
and to the onset of a subsequent pathological developmental
trajectory.
To reiterate, then, during times of rapid growth, embryonic
de- and re- methylation, and/or other high system demand,
metabolic energy limitation imposes the need to focus via
something like a rate distortion manifold. Cognitive process
requires energy through the homologies with free energy den-
sity, and more focus at one end necessarily implies less at some
other. In a distributed zero sum developmental game, as it
were, some cognitive or metabolic processes must receive more
free energy than others, and these may then be more easily
affected by external chemical, biological, or social stressors,
or by simple stochastic variation. Something much like this
has indeed become a standard perspective (e.g., Waterland
and Michels, 2007).
A structure trapped in region C might be said to suffer
something much like what Wiegand (2003) describes as the
loss of gradient problem, in which one part of a multiple pop-
ulation coevolutionary system comes to dominate the others,
creating an impossible situation in which the other partici-
pants do not have enough information from which to learn.
That is, the cliff just becomes too steep to climb. Wiegand
(2003) also characterizes focusing problems in which a two-
population coevolutionary process becomes overspecialized on
the opponent’s weaknesses, effectively a kind of inattentional
blindness.
Thus there seems some consonance between our asymptotic
analysis of cognitive structural function and current studies
of pathologies affecting coevolutionary algorithms (e.g. Ficici
et al., 2005; Wallace, 2009). In particular the possibility of
historic trajectory, of path dependence, in producing individ-
ualized failure modes, suggests there can be no one-size-fits-all
amelioration strategy.
Equation (21) basically enables a kind of environmental
catalysis to cognitive gene expression, in a sense closely sim-
ilar to the arguments of Section 6. This is analogous to, but
more general than, the ‘mesoscale resonance’ invoked by Wal-
lace and Wallace (2008): during critical periods, according to
these models, environmental signals can have vast impact on
developmental trajectory.
14.4 A simple probability model
Again, critical periods of rapid growth require energy, and
by the homology between free energy density and cognitive
information source uncertainty, that energy requirement may
be in the context of a zero-sum game so that the barriers of
figure 1 may be lowered by metabolic energy constraints or
high energy demand. In particular the groupoid structure of
equation (5) changes progressively as the organism develops,
with new equivalence classes being added to A = ∪α. If
metabolic energy density remains capped, then
P [Hβ] =
exp[-Hβ K ]
pα exp[-HαK]
must decrease with increase in α, i.e., with increase in the
cardinality of A. Thus, for restricted K, barriers between
different developmental paths must fall as the system becomes
more complicated.
A precis of these results can be more formally captured us-
ing methods closely similar to recent algebraic geometry ap-
proaches to concurrent, i.e., highly parallel, computing (Pratt,
1991; Goubault and Raussen, 2002; Goubault, 2003).
16