Thus the effect of epigenetic regulation is to channel devel-
opment into pathways that might otherwise be inhibited by
an energy barrier. Hence the epigenetic information source
Z acts as a tunable catalyst, a kind of second order cognitive
enzyme, to enable and direct developmental pathways. This
result permits hierarchical models similar to those of higher
order cognitive neural function that incorporate Baars’ con-
texts in a natural way (e.g., Wallace and Wallace, 2008; Wal-
lace and Fullilove, 2008).
This elaboration allows a spectrum of possible ‘final’ pheno-
types, what Gilbert (2001) calls developmental or phenotype
plasticity. Thus gene expression is seen as, in part, responding
to environmental or other, internal, developmental signals.
West-Eberhard (2005) argues that any new input, whether
it comes from the genome, like a mutation, or from the ex-
ternal environment, like a temperature change, a pathogen,
or a parental opinion, has a developmental effect only if the
preexisting phenotype is responsive to it. A new input causes
a reorganization of the phenotype, or ‘developmental recom-
bination.’ In developmental recombination, phenotypic traits
are expressed in new or distinctive combinations during on-
togeny, or undergo correlated quantitative change in dimen-
sions. Developmental recombination can result in evolution-
ary divergence at all levels of organization.
Individual development can be visualized as a series of
branching pathways. Each branch point, in West-Eberhard’s
view, is a developmental decision, or switch point, governed
by some regulatory apparatus, and each switch point defines a
modular trait. Developmental recombination implies the ori-
gin or deletion of a branch and a new or lost modular trait.
It is important to realize that the novel regulatory response
and the novel trait originate simultaneously. Their origins
are, in fact, inseparable events. There cannot, West-Eberhard
concludes, be a change in the phenotype, a novel phenotypic
state, without an altered developmental pathway.
These mechanisms are accomplished in our formulation by
allowing the set B1 in section 3 to span a distribution of pos-
sible ‘final’ states S∞ . Then the groupoid arguments merely
expand to permit traverse of both initial states and possible
final sets, recognizing that there can now be a possible overlap
in the latter, and the epigenetic effects are realized through
the joint uncertainties H (XDi , Z), so that the epigenetic in-
formation source Z serves to direct as well the possible final
states of XDi .
Again, Scherrer and Jost (2007a, b) use information theory
arguments to suggest something similar to epigenetic cataly-
sis, finding the information in a sequence is not contained in
the sequence but has been provided by the machinery that
accompanies it on the expression pathway. They do not,
however, invoke a cognitive paradigm, its attendant groupoid
symmetries, or the homology between information source un-
certainty and free energy density that drives dynamics.
The mechanics of channeling can be made more precise as
follows.
7 Rate Distortion dynamics
Real time problems, like the crosstalk between epigenetic and
genetic structures, are inherently rate distortion problems,
and the interaction between biological structures can be re-
stated in communication theory terms. Suppose a sequence
of signals is generated by a biological information source Y
having output yn = y1, y2, .... This is ‘digitized’ in terms of
the observed behavior of the system with which it commu-
nicates, say a sequence of observed behaviors bn = b1, b2, ....
The bi happen in real time. Assume each bn is then determin-
istically retranslated back into a reproduction of the original
biological signal,
nn
b → y = ^1,y2, ••••
Here the information source Y is the epigenetic Z , and B
is XDi , but the terminology used here is more standard (e.g.,
Cover and Thomas, 1991).
Define a distortion measure d(y, y) which compares the
original to the retranslated path. Many distortion measures
are possible. The Hamming distortion is defined simply as
d(y,y) = 1,У = У
d(y,y) = 0,У = У
For continuous variates the squared error distortion is just
d(y,y) = (y - y)2.
There are many such possibilities. The distortion between
paths yn and yn is defined as
1n
d(yn,yn) ≡ - ]Td(yj,yj).
n j=1
A remarkable fact of the Rate Distortion Theorem is that
the basic result is independent of the exact distortion mea-
sure chosen (Cover and Thomas, -99-; Dembo and Zeitouni,
-998).
Suppose that with each path yn and bn-path retranslation
into the y-language, denoted yn, there are associated individ-
ual, joint, and conditional probability distributions
p(yn),p(yn),p(yn,yn),p(yn∣yn).
The average distortion is defined as
D ≡ ∑p(yn)d(yn,yn).
yn
(9)