Humans, through both their embedding in cognitive social
networks, and their secondary epigenetic inheritance system
of culture, are even more than ‘simply’ individual animals.
Equation (24) implies the possibility of extending the global
neuronal workspace model of consciousness to include both
internal cognitive physiological systems and embedding cog-
nitive and other structures, providing a natural approach to
evading that fallacy.
Equation (24) is itself subject to significant generalization.
The single information source Z is seen here as invariant,
not affected by, but affecting, cross talk with the informa-
tion sources for which it serves as the driving context. Sup-
pose there is an interacting system of contexts, acting more
slowly than the global neuronal workspace, but communicat-
ing within itself. It should be possible, at first order, to divide
the full system into two sections, one ‘fast’, containing the
Yj , and the other ‘slow’, containing the series of information
sources Zk. The fast system instantiates the conscious neu-
ronal workspace, including crosstalk, while the slow system
constitutes an embedding context for the fast, but one which
engages in its own pattern of crosstalk. Then the extended
splitting criterion, which we write as
I(Y1, ..., Yj |Z1 , ..., Zk),
(25)
becomes something far more complicated than equation
(24). This must be expressed in terms of sums of appropriate
Shannon uncertainties, a complex task which will be individ-
ually contingent on the particular forms of context and their
interrelations.
Our approach, while arguably more general than dynamic
systems theory, can incorporate a subset of dynamic systems
models through an appropriate ‘coarse graining’, a concept
which can further illuminate matters. The procedure is best
understood through an example.
We use a simplistic mathematical picture of an elementary
predator/prey ecosystem for illustration. Let X represent the
appropriately scaled number of predators, Y the scaled num-
ber of prey, t the time, and ω a parameter defining the in-
teraction of predator and prey. The model assumes that the
system’s ‘keystone’ ecological process is direct interaction be-
tween predator and prey, so that
dX/dt = ωY
dY/dt = -ωX
Thus the predator populations grows proportionately to the
prey population, and the prey declines proportionately to the
predator population.
After differentiating the first and using the second equation,
we obtain the differential equation
d2X/dt2 + ω2X = 0
having the solution
X(t) = sin(ωt); Y (t) = cos(ωt).
with
X (t)2 + Y (t)2 = sin2(ωt) + cos2 (ωt) ≡ 1.
Thus in the two dimensional ‘phase space’ defined by X(t)
and Y (t), the system traces out an endless, circular trajectory
in time, representing the out-of-phase sinusoidal oscillations
of the predator and prey populations.
Divide the X — Y ‘phase space’ into two components - the
simplest ‘coarse graining’ - calling the halfplane to the left of
the vertical Y -axis A and that to the right B . This system,
over units of the period 1∕(2πω), traces out a stream of A’s
and B’s having a very precise ‘grammar’ and ‘syntax’, i.e.
ABABABAB...
Many other such ‘statements’ might be conceivable, e.g.
AAAAA...,BBBBB...,AAABAAAB...,ABAABAAAB...,
and so on, but, of the obviously infinite number of possi-
bilities, only one is actually observed, is ‘grammatical’, i.e.
ABABABAB....
More complex dynamical system models, incorporating dif-
fusional drift around deterministic solutions, or even very
elaborate systems of complicated stochastic differential equa-
tions, having various ‘domains of attraction’, i.e. different
sets of grammars, can be described by analogous ‘symbolic
dynamics’ (e.g. Beck and Schlogl, 1993, Ch. 3).
The essential trick is to show that a system has a ‘high
frequency limit’ so that an appropriate coarse graining catches
the dynamics of fundamental importance, while filtering out
‘high frequency noise’.
Taking this analysis into consideration, the model of equa-
tion (25) can be seen, from a dynamic systems theory per-
spective, as constituting a ‘double coarse-graining’ in which
the Zk represent a ‘slow’ system which serves as a driving
conditional context for the ‘fast’ Yj of the global neuronal
workspace.
We can envision a ‘multi’ (or even distributed) coarse grain-
ing in which, for example, low, medium, and high, frequency
phenomena can affect each other. The mathematics of such
extension appears straightforward but is exponentially com-
plicated. In essence we must give meaning to the notation
I(Y1,...,Yj|X1,...,Xk|Z1,...,Zq)
(26)
where the Yj represent the fast-acting cognitive modules of
the global neuronal workspace, the Xk are intermediate rate
effects such as emotional structure, long-term goals, immune
and local social network function, and the like, and the Zq are
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