rapidity: typically the global broadcasts of consciousness oc-
cur in a matter of a few hundred milliseconds, limiting the
number of processes that can operate simultaneously. Slower
cognitive dynamics can, therefore, be far more complex than
individual consciousness. One well known example is institu-
tional distributed cognition that encompasses both individual
and group cognition in a hierarchical structure typically op-
erating on timescales ranging from a few seconds or minutes
in combat or hunting groups, to years at the level of major
governmental structures, commercial enterprises, religious or-
ganizations, or other analogous large scale cultural artifacts.
Wallace and Fullilove (2008) provide the first formal mathe-
matical analysis of institutional distributed cognition.
Clearly cognitive gene expression is not generally limited
to a few hundred milliseconds, and something much like the
distributed cognition analysis may be applied here as well.
Extending the analysis requires recognizing an individual cog-
nitive actor can participate in more than one ‘task’, syn-
chronously, asynchronously, or strictly sequentially. Again,
the analogy is with institutional function whereby many in-
dividuals often work together on several distinct pro jects:
Envision a multiplicity of possible cognitive gene expression
dual ‘languages’ that themselves form a higher order network
linked by crosstalk.
Next, describe crosstalk measures linking different dual lan-
guages on that meta-meta (MM) network by some character-
istic magnitude ω, and define a topology on the MM network
by renormalizing the network structure to zero if the crosstalk
is less than ω and set it equal to one if greater or equal to
it. A particular ω , of sufficient magnitude, defines a giant
component of network elements linked by mutual information
greater or equal to it, in the sense of Erdos and Renyi (1960),
as more fully described in Wallace and Fullilove (2008, Section
3.4).
The fundamental trick is, in the Morse Theory sense (Mat-
sumoto, 2002), to invert the argument so that a given topol-
ogy for the giant component will, in turn, define some critical
value, ωC , so that network elements interacting by mutual
information less than that value will be unable to participate,
will be locked out and not active. ω becomes an epigenet-
ically syntactically-dependent detection limit, and depends
critically on the instantaneous topology of the giant compo-
nent defining the interaction between possible gene interaction
MM networks.
Suppose, now, that a set of such giant components exists
at some generalized system ‘time’ k and is characterized by
a set of parameters Ωk ≡ ωk, ...,ωm. Fixed parameter values
define a particular giant component set having a particular
set of topological structures. Suppose that, over a sequence
of times the set of giant components can be characterized by
a possibly coarse-grained path γn = Ω0, Ω1,..., Ωn-ι having
significant serial correlations that, in fact, permit definition
of an adiabatically, piecewise stationary, ergodic (APSE) in-
formation source Γ.
Suppose that a set of (external or internal) epigenetic sig-
nals impinging on the set of such giant components can also be
characterized by another APSE information source Z that in-
teracts not only with the system of interest globally, but with
the tuning parameters of the set of giant components char-
acterized by Γ. Pair the paths (γn , zn) and apply the joint
information argument above, generating a splitting criterion
between high and low probability sets of pairs of paths. We
now have a multiple workspace cognitive genetic expression
structure driven by epigenetic catalysis.
11 ‘Coevolutionary’ development
The model can be applied to multiple interacting information
sources representing simultaneous gene expression processes,
for example across a spatially differentiating organism as it
develops. This is, in a broad sense, a ‘coevolutionary’ phe-
nomenon in that the development of one segment may affect
that of others.
Most generally we assume that different cognitive develop-
mental subprocesses of gene expression characterized by infor-
mation sources Hm interact through chemical or other signals
and assume that different processes become each other’s prin-
cipal environments, a broadly coevolutionary phenomenon.
We write
Hm = Hm(K1 ...Ks, ...Hj ...), j 6= m,
(18)
where the Ks represent other relevant parameters.
The dynamics of such a system is driven by a recursive
network of stochastic differential equations, similar to those
used to study many other highly parallel dynamic structures
(e.g., Wymer, 1997).
Letting the Kj and Hm all be represented as parameters
Qj , (with the caveat that Hm not depend on itself), one can
define, according to the generalized Onsager development of
the Appendix,
Sm ≡ Hm - X Qi∂Hm∕∂Qi
i
to obtain a complicated recursive system of phenomenolog-
ical ‘Onsager relations’ stochastic differential equations,
dQj = ∑[Lj,i(t, ...∂Sm∕∂Qi...)dt+σj,i(t, ...∂Sm∕∂Qi...)dBti],
i
(19)
where, again, for notational simplicity only, we have ex-
pressed both the Hj and the external K’s in terms of the
same symbols Qj .
11