the incorporation, in a natural manner, of constraints on in-
dividual consciousness, i.e. what Baars calls contexts. Using
information theory methods, extended by an obvious homol-
ogy between information source uncertainty and free energy
density, it is possible to formally account for the effects on
individual consciousness of parallel physiological modules like
the immune system, embedding structures like the local social
network, and, most importantly, the all-encompassing cul-
tural heritage which so uniquely marks human biology (e.g.
Richerson and Boyd, 2004). This embedding evades the mere-
ological fallacy which fatally bedevils brain-only theories of
human consciousness (Bennett and Hacker, 2003).
Transfer of phase change approaches from statistical
physics to information theory via the same homology gen-
erates the punctuated nature of accession to consciousness
in a similarly natural manner. The necessary renormaliza-
tion calculation focuses on a phase transition driven by varia-
tion in the average strength of nondisjunctive weak ties (Gra-
novetter, 1973) linking unconscious cognitive submodules. A
second-order universality class tuning allows for adaptation of
conscious attention via rate distortion manifolds which gen-
eralize the idea of a retina. The Baars model emerges as an
almost exact parallel to hierarchical regression, based, how-
ever, on the Shannon-McMillan rather than the Central Limit
Theorem.
Wallace (2005b) recently proposed a somewhat different ap-
proach, using classic results from random and semirandom
network theory (Erdos and Renyi, 1960; Albert and Barabasi,
2002; Newman, 2003) applied to a modular network of cogni-
tive processors. The unconscious modular network structure
of the brain is, of course, not random. However, in the spirit
of the wag who said “all mathematical models are wrong,
but some are useful”, the method serves as the foundation
of a different, but roughly parallel, treatment of the Global
Workspace to that given in Wallace (2005a), and hence as
another basis for a benchmark model against which empirical
data can be compared.
The first step is to argue for the existence of a network of
loosely linked cognitive unconscious modules, and to charac-
terize each of them by the richness of the canonical language
- information source - associated with it. This is in some con-
trast to attempts to explicitly model neural structures them-
selves using network theory, e.g. the neuropercolation ap-
proach of Kozma et al. (2004, 2005), which nonetheless uses
many similar mathematical techniques. Here, rather, we look
at the necessary conditions imposed by the asymptotic limits
of information theory on any realization of a cognitive pro-
cess, be it biological wetware, silicon dryware, or some direct
or systems-level hybrid. All cognitive processes, in this formu-
lation, are to be associated with a canonical dual information
source which will be constrained by the Rate Distortion Theo-
rem, or, in the zero-error limit, the Shannon-McMillan Theo-
rem, both of which are described further in the Mathematical
Appendix. It is interactions between nodes in this abstractly
defined network which will be of interest here, rather than
whatever mechanisms, social or biological system, or mixture
of them, actually constitute the underlying cognitive modules.
The second step is to examine the conditions under which
a giant component (GC) suddenly emerges as a kind of phase
transition in a network of such linked cognitive modules, to
determine how large that component is, and to define the rela-
tion between the size of the component and the richness of the
cognitive language associated with it. This is the candidate
for Baars’ shifting Global Workspace of consciousness.
While Wallace (2005a) examines the effect of changing the
average strength of nondisjunctive weak ties acting across
linked unconscious modules, Wallace (2005b) focuses on
changing the average number of such ties having a fixed
strength, a complementary perspective whose extension via
a kind of ‘renormalization’ leads to a far more general ap-
proach.
The third step, following Wallace (2005b), is to tune the
threshold at which the giant component comes into being, and
to tune vigilance, the threshold for accession to consciousness.
Wallace’s (2005b) information theory modular network
treatment can be enriched by introducing a groupoid formal-
ism which is roughly similar to recent analyses of linked dy-
namic networks described by differential equation models (e.g.
Golubitsky and Stewart, 2006; Stewart et al., 2003, Stewart,
2004; Weinstein, 1996; Connes, 1994; Bak et al., 2006). Inter-
nal and external linkages between information sources break
the underlying groupoid symmetry, and introduce more struc-
ture, the global workspace and the effect of contexts, respec-
tively. The analysis provides a foundation for further mathe-
matical exploration of linked cognitive processes.
The generalization of interest here is to examine the condi-
tions under which cognitive modules may multitask, engaging
in more than one giant component at the same time, i.e. syn-
chronously. This is something which individual consciousness
does not permit under normal circumstances. The obvious
tradeoff, of course, is the very rapid flow of individual con-
sciousness, a matter of a few hundred milliseconds, as opposed
to the much slower, if considerably more comprehensive, op-
erations of institutional cognition.
The conjecture, of course, is that machines can be built
which would carry out complex processes of multiple global
workspace cognition at rates approaching those of individual
conscious animals.
2. Cognition as language
Cognition is not consciousness. Most mental, and many
physiological, functions, while cognitive in a formal sense,
hardly ever become entrained into the Global Workspace of
individual consciousness: one seldom is able to consciously
regulate immune function, blood pressure, or the details of
binocular tracking and bipedal motion, except to decide ‘what
shall I look at’, ‘where shall I walk’. Nonetheless, many cog-
nitive processes, conscious or unconscious, appear intimately
related to language, broadly speaking. The construction is
fairly straightforward (Wallace, 2000, 2005a, b).
Atlan and Cohen (1998) and Cohen (2000) argue, in the
context of immune cognition, that the essence of cognitive
function involves comparison of a perceived signal with an
internal, learned picture of the world, and then, upon that
comparison, choice of one response from a much larger reper-