GENE EXPRESSION AND ITS DISCONTENTS Developmental disorders as dysfunctions of epigenetic cognition

channel, that is, the best algorithm turning a problem into
a solution, will necessarily be highly problem-specific. Thus
there can be no best algorithm for all equivalence classes of
problems, although there may well be an optimal algorithm
for any given class. The tuning theorem form of the No Free
Lunch theorem will apply quite generally to cognitive bio-
logical and social structures, as well as to massively parallel
machines.

Rate distortion, however, occurs when the problem is col-
lapsed into a smaller, simplified, version and then solved.
Then there must be a tradeoff between allowed average dis-
tortion and the rate of solution: the retina effect. In a very
fundamental sense - particularly for real time systems - rate
distortion manifolds present a generalization of the converse of
the Wolpert/Macready no free lunch arguments. The neural
corollary is known as inattentional blindness (Wallace, 2007).

We are led to suggest that there may well be a considerable
set of no free lunch-like conundrums confronting highly par-
allel real-time structures, including epigenetic control of gene
expression, and that they may interact in distinctly nonlinear
ways.

14 Developmental disorders

14.1 Network information theory

Let U be an information source representing a systematic em-
bedding environmental ‘program’ interacting with the pro-
cess of cognitive gene expression, here defined as a compli-
cated information set of sources having source joint uncer-
tainty H(Z1, ..., Zn) that guides the system into a particular
equivalence class of desired developmental behaviors and tra-
jectories.

Most simply, one can directly invoke results from network
information theory, (Cover and Thomas, 1991, p. 388). Given
three interacting information sources, say Y1 , Y2 , Z, the split-
ting criterion between high and low probability sets of states,
taking Z as the external context, is given by

I(Y1,Y2|Z) =H(Z)+H(Y1|Z)+H(Y2|Z) -H(Y1,Y2,Z),

where, again, H (...|...) and H (..., ..., ...) represent condi-
tional and joint uncertainties. This generalizes to the relation

n

I(Y1,...,Yn|Z) =H(Z)+^XH(Yj|Z)-H(Y1,...,Yn,Z)
j=1

Thus the fundamental splitting criterion between low and
high probability sets of joint developmental paths becomes

I(Z1,...,Zn|U) =H(U)+^Xn H(Zj|U)-H(Z1,...,Zn,U).

j=1

(21)

Again, the Zi represent internal information sources and U
that of the embedding environmental context.

The central point is that a one step extension of that sys-
tem via the results of network information theory (Cover and
Thomas, 1991) allows incorporating the effect of an exter-
nal environmental ‘farmer’ in guiding cognitive developmental
gene expression.

14.2 Embedding ecosystems as information
sources

The principal farmer for a developing organism is the ecosys-
tem in which it is embedded, in a large sense. Following
the arguments of Wallace and Wallace (2008) fairly closely,
ecosystems, under appropriate coarse graining, often have re-
conizable grammar and syntax. For example, the turn-of-the-
seasons in a temperate climate, for most natural communities,
is remarkably similar from year to year in the sense that the
ice melts, migrating birds return, trees bud, flowers and grass
grow, plants and animals reproduce, the foliage turns, birds
migrate, frost, snow, the rivers freeze, and so on in a pre-
dictable manner from year to year.

Suppose, then, that we can coarse grain an ecosystem at
time t according to some appropriate partition of the phase
space in which each division Aj represents a particular range
of numbers for each possible species in the ecosystem, along
with associated parameters such as temperature, rainfall, hu-
midity, insolation, and so on. We are interested in longitudi-
nal paths, statements of the form

x(n) = A0, A1, ..., An

defined in terms of some ‘natural’ time unit characteristic
of the system. Then n corresponds to a time unit T , so that
t = T, 2T, ..., nT. Our interest is in the serial correlation along
paths. IfN(n) is the number of possible paths of length n that
are consistent with the underlying grammar and syntax of the
appropriately coarse grained ecosystem, for example, spring
leads to summer, autum, winter, back to spring, etc., but
never spring to autumn to summer to winter in a temperate
climate.

The essential assumption is that, for appropriate coarse
graining, N (n), the number of possible grammatical paths,
is much smaller than the total conceivable number of paths,
and that, in the limit of large n,

H ≡ lim ^lOg[N(n)]
n→∞   n

both exists and is independent of path.

Not all possible ecosystem coarse grainings are likely to lead
to this result, as is sometimes the case with Markov models.
Holling (1992) in particular emphasizes that mesoscale ecosys-
tem processes are most likely to entrain dynamics at larger

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