Crossing the Theshold Paradox:
Modelling Creative Cognition in the Global Workspace
Geraint A. Wiggins
Centre for Digital Music
School of Electronic Engineering and Computer Science
Queen Mary University of London
Mile End Road, London E1 4NS, UK
geraint.wiggins@eecs.qmul.ac.uk
Abstract
I present a hypothetical global model of everyday creative
cognition located within Baars’ Global Workspace Theory,
based on theories of predictive cognition and specific work on
statistical modelling of music perception. The key idea is a
proposal for regulating access to the Global Workspace, overcoming
what Baars calls the Threshold Paradox. This idea is
motivated as a general mechanism for managing the world,
and an argument is given as to its evolutionary value. I then
show how this general mechanism produces effects which are
indistinguishable from spontaneous creative inspiration, best
illustrated by Wallas’ (1926) “Aha!” moment. I argue that
W. A. Mozart’s introspective account of compositional experience
closely matches the proposed process, and refer to a
computational system which will form the basis of an implementation
of the ideas, for musical composition.
Introduction
Computational Creativity is mired, practically speaking, in
the problem of evaluation. Artefacts created by computer
cannot be judged by the computer’s aesthetic, for that is obscure,
and evaluating them in terms human aesthetics has
been shown to be unreliable due to negative preconceptions
(Moffat and Kelly, 2006). One solution to this might be to
compensate for that bias statistically, given the necessary
models. Another is to avoid the issue of artefact evaluation
altogether, and focus on process, and on building systems
that apply it. Colton (2009) catchily entitles this point
“Paradigms Lost”, making the point that AI sometimes overtheorises,
and paints itself into a corner by the application of
problem solving methods to a domain in the abstract, instead
of getting on and building something that concretely
explores it: the subtext may be that this tendency arises from
rigour envy. Colton raises a point that benefits from emphasis:
he finishes the section with “the production of beautiful,
interesting and valuable artefacts”, and this occludes the key
point in the final sentence: “the need to embrace entire intelligent
tasks” (my italics).
The vexed question is “how?” Modelling an entire, novel
creative process, evaluation, reflection, and all, in the abstract
leads us back to the initial problem: the only way
to judge it from outside is in terms of its outputs (Ritchie,
2001).
The rest of the paper is structured as follows. First, I explain
the theoretical methods used, and make and important
distinction between what I shall call inspiration and creative
reasoning; the current proposal addresses only the first of
these. Next, I describe some of the extended background to
the thinking presented here, and in terms of the surrounding
and supporting cognitive theory, including an apparent inherent
paradox identified by its creator. Then I present the
evolutionary argument for the theoretical stance taken here,
and derive the (simple) principles on which my proposal is
based from it. Next, turning to implementation, I summarise
earlier modelling work, explain its connection with the current
proposal, and describe what is necessary to extend it
into the model proposed here.
The technical contributions of the paper are a variant notion
of AI Agent, based on prediction from sense data, rather
than on sensing, and a mechanism for deployment of that
agent in a particular kind of reasoning system. The key
philosophical contribution is the fact that, once this mechanism
is deployed, the kind of creativity that is addressed
here, inspiration, is explained within the basic reasoning,
and needs no further explanation.
Methodology
To overcome the methodological problem introduced above,
my approach is to attempt to replicate an existing creative
process. The only existing creative process ready available
for inspection is that of humans; these have the built-in advantage,
mostly, of being able to explain what (they thought)
they did, and elegant paradigms exist to empirically deconstruct
that majority of aspects of human behaviour of which
introspective reports are unreliable. I therefore aim to apply
cognitive modelling theory and technology to human creative
process, and then to evaluate the success of the enterprise
with respect not only to the outputs of the computational
systems produced, but to compare the various aspects
of their operation with human creators. While this
approach solves only part of the general problem of computational
creativity, it is an area where refutable hypotheses
can be made, and so demonstrable progress in a research
programme (Lakatos, 1970) may take place.
For this attempt to succeed in a scientific sense, before one
even considers the artefacts that the replicant creative system
may produce, the theory and its associated computational
International Conference on Computational Creativity 2012 180
system must conform to at least the following constraints, to
be said to model human creative cognition.
1. Falsifiability The system must not behave in ways which
are arguably or demonstrably different from human creators
while it is operating. Since we cannot, currently,
know how human creators create, this is the strongest falsifiability
constraint that can be applied.
2. Evolutionary context There must be an account of the
evolutionary advantage conferred by the mechanisms proposed,
a corresponding order of development, and an
analysis of their appearance in successive species over
evolutionary time. This account cannot be verifiable, but
the lack of one leaves the biological development of the
proposed solution unavailable to scientific scrutiny.
3. Learning capability The system must be capable of
learning its creative domain. Learning should be appropriate
to the domain: for example, in music, perceptual
aspects should be implicit—that is, teaching or supervision
should not be required; however, in some domains,
such as mathematics, minimal supervision is evidently
unavoidable, because of the need to know the meaning
of symbols, to give semantics to what is being learned1.
4. Production capability The system must be able to produce
artefacts that are demonstrably within its creative domain,
whether or not they are of quality comparable with a
human creator’s output. While the judgement of whether
an artefact is or is not a particular kind of thing is subjective,
it is not as difficult as the subjectivity of quality.
For the purposes of experiment, restricted domains with
clear tests must be set up, using appropriate theory from
the corresponding human-creative domain.
5. Reflection The system must be capable of reflecting on
its behaviour, modifying it, and explaining it—where necessary
via indirect indicators such as those used for understanding
the behaviour of humans.
In this paper, I present a hypothetical, but partly implemented,
computational model of a particular kind of human
creativity, and suggest that it conforms to criteria 3–4, and
partly to criterion 2, though further research is required to
provide more evidence against criterion 1. Criterion 5, Re-
flection, is conferred by location of the model within Baars’
(1988) Global Workspace Theory, whose focus is consciousness;
so it falls beyond the scope of the present proposal.
Background
Creativity: Inspiration and Reasoning
Wiggins (2012) introduces a distinction between two kinds
of creativity: on one hand, inspiration and, on the other, creative
reasoning. Respectively, these terms are intended to
distinguish what appears spontaneously in consciousness—
the “Aha!” moment that Wallas (1926) suggests follows
1
To ask the system to learn the semantics of the symbols to
which it is exposed from context is not, in principle, unreasonable,
as there is every evidence that humans do so. However, to require
the system to do so when the scientific research focus is creativity
seems unnecessarily difficult.
“incubation”—from what is produced by the deliberate application
of creative method. The spectrum between the
two allows us to make distinctions between conscious creation
in the deliberate planning of a formalist composer, the
semi-spontaneous but cooperative and partly planned creation
of the jazz improviser in a trio, and entirely spontaneous
singing in the shower. Note that a non-polar position
on this spectrum necessarily entails a combination of
explicit technique and implicit imagination: there is not a
smooth transition in kind between the two, but rather a mixture
containing some of each in varying proportion.
Having made this point, I reserve creative reasoning for
future work, not least because it entails that we address consciousness,
which is difficult, but also because Baars’ theory
already provides a framework in which it may be considered,
given a mechanism for inspiration. This is not to dismiss the
deliberate end of the scale, nor to suggest that it does not
exist, but merely to focus the current work on a separable
aspect of the complex.
Global Workspace Theory
Bernard Baars (1988) introduces a theory of conscious
cognition called the Global Workspace Theory. There is
not space to describe this wide-ranging and elegant theory
here, so I summarise the relevant important points.
The theory posits a framework within which consciousness
can take place, based around a multi-agent architecture
(Minsky, 1985) communicating via something like an
AI blackboard system (Corkill, 1991), but with particular
constraints, which I outline below. The approach taken is
to avoid Chalmers’ “hard” question of “what is conscious?”
(Chalmers, 1996) and instead ask “what is it conscious of,
and how?” This is especially appropriate in cases such as
the current paper, where consciousness is not the central issue,
but presentation of information to it is.
Baars casts the non-conscious mind as a large collection
of expert generators (not unlike the multiple experts in Minsky’s
Society of Mind, 1985), performing tasks by applying
algorithms to data in massive parallel, compete for access
to a Global Workspace via which (and only via which) information
may be exchanged; crucially, information must
cross a notional threshold of “importance” before it is allowed
access. The Global Workspace is always visible to
all generators, and contains the information of which the organism
is conscious at any given time. However, it is capable
of containing only one “thing” at a time, though the
scope of what that “thing” might be is variable. The Global
Workspace is highly contextualised, and meaning contained
therein is context sensitive and structured; contexts can contain
goals, desires, etc., of the kind familiar from broader
AI. Aside from further discussion of the “threshold” idea,
below, this is all that is needed to understand the purpose of
the competition mechanism proposed here. Baars mentions
the possibility of creativity within this framework in passing,
implicitly equating entry of a generator’s output into consciousness
with the “Aha!” moment (Wallas, 1926). However,
he does not develop this idea further beyond noting that
a process of refinement may be implemented as cycling of
information into the Workspace and out again; that process
International Conference on Computational Creativity 2012 181
Global Workspace
Generator
Generator
Generator
Generator
Generator
Access threshold
Generator
Coalition of agreement
Generator
Figure 1: Illustration of Baars’ Threshold Paradox. Generators
generate, but need a means of recruiting support for
their outputs. Individuals cannot break in; they must recruit
coalitions, as shown. The only way to do so is via the Global
Workspace, but before they can do so, they need the support
they are trying to recruit, and therein lies the paradox.
may be equivalent to my creative reasoning. To the best of
my knowledge, however, creativity in the Global Workspace
has not been addressed elsewhere in the related literature.
In the later developments of the theory, Baars proposes
that information integration may take place in stages, via
something that one might (but he does not) call local
workspaces, that integrate information step by step in a sequence,
rather than all in one go as it arrives in the Global
Workspace. This information integration approach has been
extended by Tononi and Edelman (1998), who propose
information-theoretic measures of information integration as
a measure of consciousness of an information-processing
mechanism. Baars has embraced the information-theoretic
stance, too, and the three authors have jointly proposed to
begin implementing a conscious machine (Edelman, Gally,
and Baars, 2011) based on their ideas. The current work may
contribute to this endeavour, though probably at a level more
abstract from neurophysiology than these authors intend.
The Threshold Paradox
Baars (1988, pp. 98–99) addresses what he acknowledges
is a problem for his theory. He proposes a threshold for
input access to the Global Workspace, crossing of which
is thought of in terms of recruiting sufficient generators to
produce information that is somehow coordinated, or synchronised
between them: it must be metaphorically “loud”
enough to be “audible” in the Workspace. However, in terms
of the Global Workspace alone, there is no means of doing
this: generators can only be coordinated (whatever that
means) via the Global Workspace, and so the generators are
faced with the beginning artist’s dilemma: you have to be famous
to show your work, but you have to show your work to
become famous. This form of the Workspace is illustrated in
Figure 1. Baars presents two possible solutions to the paradox,
which is the motivation of the current paper, but both
are presented somewhat half-heartedly, leaving a gap in the
theory. Here, I present a possible solution, in terms of the
evolutionary argument required by my criterion 2, above.
Perception, Anticipation, and Evolution
Reaction vs. Anticipation
I now present a mechanism for managing the competition
between generators in Baars’ system. This mechanism may
be implemented either directly or indirectly (that is, by
means of some other effect)—the difference is immaterial
at the current theoretical level. The key distinctions are a)
between the information content and entropy (defined below)
of various stimuli; and b) between organisms that react
and organisms that anticipate. The design of this mechanism
is motivated by evolutionary thinking: that is, by consideration
of the evolutionary advantage conferred by the resulting
behaviours, in humans and other animals. Thus, the evolutionary
argument presented here is part of the design, not
merely an example.
Russell and Norvig (1995), in their well-known AI text
book, define an AI agent (of which an AI creative agent
is presumably an instance) as a program or robot with a
behaviour cycle that consists of perceiving the world and
then acting on the perceptions. It seems not unreasonable to
present this as a model of lower organisms, such as insects,
which seem to do nothing more than react to environmental
conditions, coping poorly when their evolved reactive program
is interrupted. However, to model higher cognitive development,
one can propose a more predictive system, in
which an organism is predicting continually, from a learned
model of previous sensory data, what is likely to come next,
and comparing this with current sensory input. Doing so
gives a simple but effective mechanism for spotting what
is unusual, what, therefore, constitutes a potential new opportunity
or threat, and what deserves cognitive resource, or
attention. In the simplest case, the anticipatory agent can in
principle avoid a threat before it becomes apparent, while the
reactive one has to experience the threat in order to respond.
The consequence of sequence: managing
uncertainty with expectation
The most important feature of an autonomous agent is not,
as sometimes supposed in AI, that it is able to identify or
categorise a situation from available data. What gives it the
edge is that it can, in some sense, imagine what is to come
next, and react, or perhaps preact, in advance. Of course,
the word “imagine” is loaded, and suggests the involvement
of consciousness and even volition; I use it here deliberately
to draw attention to the point that consciousness need not be
implicated in this process, which can be described in completely
mechanistic terms, of prediction alone.
In order to predict usefully in a changing world, it is necessary
for an organism to learn. It must be able to learn not
just categorisations (to understand what something is), but
also associations (to associate co-occurrence of events with
reward or threat), and, crucially here, sequence.
However, a simple statistical learning mechanism is not
subtle enough (Huron, 2006). Since evolutionary success
entails that an organism breeds, a mechanism which allows
International Conference on Computational Creativity 2012 182
that organism to learn only from potentially fatal consequences
does not suffice: if the organism dies as the result of
an experience, it does not benefit from the experience (or, at
least, not for long). An effective strategy here lies at a metalevel
with respect to a learned body of experience: if an organism
is aware that it is in circumstances that it cannot predict
reliably, it can behave more cautiously, its metabolism
can be aroused to prepare for flight, and it can devote more
attention than normal to its surroundings; thus, the effective
strategy is also affective. Huron convincingly argues
that this process is exapted to produce part of the aesthetic
effect of music; however, for the purposes of the current section,
the mere adaptation suffices: self-evidently, there is a
mechanism that allows uncertainty to affect behaviour in humans
and other animals, and that mechanism does not rely
on explicit reasoning: indeed, the converse is the case: we
feel nervous in uncertain situations, and the feeling serves
to make us wonder why, as well as to heighten our attention
to appropriate sensory inputs and to prepare for flight. This
mechanism, and the associated affective response, is not the
same as fear, but can lead there in extremis.
Finally, any kind of learning of this nature is inadequate
unless it includes generalisation. It is necessary to be able to
generalise from both co-occurrence and sequence that similar
consequences arise from similar events, encounters, etc.
Without this, mere tension cannot lead to the fear that is
appropriate at the sight of the bared fangs of a previouslyunexperienced
large animal. This accords with proposals
such as that of Gardenfors (2000), that perceptual learning ¨
systems are motivated by the need to understand similarities
and differences between perceived entities in the world,
and to place observations at the appropriate point between
previously experienced referents.
Prediction, Prioritisation and Selection
Given a model of the world, suitably subcategorised into
types, situations, etc., one can imagine a set of generators
using the model with recent and current perceptual inputs
matched against precursors of sequential associations, making
predictions, on a basis that is stochastic, and conditioned
by the model. Making such predictions quickly, one at a
time, would be valuable, but, given the nature of brains,
slow, multiple predictions, in parallel, are a more likely candidate
for evolutionary success, and the more the better—
as in Baars’ proposal. But this begs a question: arbitrarily
many predictions occurring simultaneously will be an impossible,
incomprehensible babble, so how will useful candidates
for prediction be selected? Baars’ solution is the
problematic threshold, described above.
Another shortcoming of the Global Workspace Theory is
unclarity about precisely what the notion of generators “recruiting”
one another means. The effect is something like
an additive weight: the more generators that are “recruited”,
the greater the impact of their output. In my proposal, we
will avoid answering this question, by approximating the effect
of the recruitment, rather more simply. I return to this
below; in the argument that follows, I will use the analogy
of sound volume to refer to this property: “loud” predictions
come from many generators, “quiet” ones do not.
My proposal here is based on statistical, frequentist notions
of learning, and so my reasoning is couched in terms
of statistical models; however, I do not think that the reasoning
is in principle exclusive to such models, and it should not
be supposed that the proposal is restricted in this way. In this
view of the system surrounding the Global Workspace, there
are many independent subsystems, which are making multiple
predictions by biased sampling from a predictive statistical
model of (assumedly) reasonable quality. It is also
appropriate to assume imperfect models: each of these generating
subsystems will have a fragmentary, partial view of
its world and its predictions, as to model everything all the
time in massive-parallel would be prohibitively expensive. It
follows from the use of frequentist models that the more expected
occurrences are the more likely ones to be predicted:
the commonest predictions will be the most expected ones.
This means there are relatively “loud” groups of contributions,
reinforcing each other. Conversely, extremely unlikely
predictions will be proposed by only a very small number of
generators, and as such will never be “audible”.
In a model of prediction and action based solely on this
frequentist principle, an organism will tend do the commonest
thing, even when inappropriate, and therefore will
be doomed to failure: it will not “imagine” unlikely and
surprising situations, and will not therefore prepare itself
against necessary eventualities. To see this, consider a territorial
animal, on patrol, and let it be a high enough species
to learn its reactions. Today, our animal senses the things it
usually senses, and the vast majority of things in the world
today are the same as they were the last time it passed this
way. One tiny difference is a scent that it does not recognise,
that it has not experienced before. Since this difference
is small in comparison to the rest of the data in the world,
and it has not been experienced before, in purely frequentist
terms, it will be ignored: it is unlikely, and it has no known
consequences and determines little or no probability mass.
In Baar’s theory, the pure frequentist approach, where the
most likely outcome is chosen, corresponds with multiple
generators in coalition generating that outcome. The likelihood
of each generator predicting an outcome is proportional
to the “volume” of that outcome across the set of generators.
Therefore, we can neatly draw a veil over the mechanistic
gap left by Baars’ idea of coalition formation, and
simply use the likelihood of the outcome, p, to model its
outcome.
In reality, though, we know well that to carry on as normal
will not be the reaction of an animal in these circumstances:
it will experience Huron’s proposed affective response,
described above. Therefore, it is necessary to hypothesise
a mechanism to cause that response. In our current
simple context of abstracted statistical modelling, the obvious
choice for such a mechanism is the notion of entropy,
as formalised by Shannon (1948). MacKay (2003) makes a
distinction between information content, h, which is defined
as an estimate of the number of bits required to describe an
event, e, given a context, c, or its unexpectedness:
h(e | c) = ! log2 p(e | c),
and entropy, H, which is defined as an estimate of the uncertainty
inherent in the distribution of the set of events E
International Conference on Computational Creativity 2012 183
from which that e might be selected, given the context, c:
H(c) = X
e2E
p(e | c) h(e | c) = !
X
e2E
p(e | c) log2 p(e | c).
H is maximised when all outcomes are equally likely, and
minimised when a single outcome is certain. Both h and H
are useful to our hypothetical animal.
First, consider ht, the unexpectedness of a partial model
of the actual on-going experience in a particular state, t. If
the experience is likely (in particular, if it is readily predictable
from what has gone before), it is not unexpected,
and therefore ht is low; if it is unlikely, it is unexpected, and
so ht is high. An experience such as encountering a new
scent is maximally unlikely, in frequentist terms. To model
this, I propose that individual generators are sensitive to their
own ht value, and decrease their notional “volume” when it
is low. Thus, the likelihood of models of the experience in
which the new scent is included being heard in the theatre is
positively related (possibly in a non-trivial way) to its unexpectedness.
I call this the recognition-h case. It may explain
why unexpected things are noticed.
Now, consider, ht+1, the unexpectedness of a predicted
situation. It is maximally unlikely that a prediction will be
made including a scent that has not been encountered before,
and, as above, we would therefore expect ht+1 to be very
high, causing alarm. Excess of such predictions, or repeated
occurrence of a single one, would lead to a state of constant
anxiety2. I call this the prediction-h case. It may explain
why surprising predictions are more likely to draw attention
than prosaic ones.
Of course, in a simplistic frequentist account, predictions
introducing new percepts or concepts cannot arise, because
they entail the creation of new symbols. This is why it is
necessary to include generalisation and/or interpolation in
the theory (see above). Gardenfors (2000) presents a the- ¨
ory that explicates the symbolic representations more commonly
used in statistical AI modelling in terms of an underlying,
sometimes continuous, geometrical layer, and, at least
at perceptual levels, places cognitive semantics at the centre
of mind. In particular, an outline mechanism is supplied
whereby previously unencountered stimuli may be assigned
first non-symbolic, and then symbolic, representations. It is
important to understand that the semantics in these theories
are internal to the organism experiencing them, and have no
definition in terms of the external word; rather they have external
associations, which can serve to allow intersubjective
meaning, but they themselves are ineffable.
The problem of over-active prediction-h is mitigated by
the mechanism supplied above, in which prediction is probabilistic
and (broadly) additive across predictors, modelled
by p. There are two opposing forces here, one of which
changes inversely relative to the other, and because they are
co-occurrent, their effects should (broadly) multiply. Therefore,
the overall outcome audible in the global workspace
2
Indeed, some humans who suffer from anxiety, in the clinical
sense, report intrusive, repetitive thoughts predicting problems or
worries of one sort or another, the anxiety being aroused by fear of
what might happen. Their situation would be explicable in terms
of a breakdown of this mechanism.
Likelihood/Information Content
<references_biblio/>
Preference
Figure 2: Illustration of the interaction between likelihood
and unexpectedness. The overall likelihood (solid) is formed
by the multiplication of two monotonic functions: the unexpectedness
of a generated item (dashed) and the number of
generators likely to agree on it, according to its likelihood
(dotted).
can be estimated by multiplying the probability, p of an
event (which estimates the likely number of generators predicting
it) by h (which estimates the volume at which they
are predicting). The resulting likelihood is illustrated by the
unit-free diagram in Figure 2. This creates a bias away from
predictions which are either very likely or very unexpected,
reducing the power of the very unlikely or the very obvious
to attract attention. This may explain why unlikely possibilities
do not prevent action by overwhelming the acting
organism with choice.
It is important to see the difference between recognitionh
and prediction-h in the context of the Global Workspace.
I propose that generators may generate structures of either
kind, and that the two will be in competition for the resource
of attention. Thus, clear and present danger or benefit will
outweigh predicted likelihoods, because the distribution of
potential predictions is over a much wider range of possibilities
than that over actual perceptions, and therefore, comparatively,
probability mass is spread more thinly. Conversely,
for example, likely but unexpected predicted benefits can
outweigh less seriously dangerous present circumstances—
thus, prioritising an unusual positive opportunity can be
mechanistically explained as an emergent behaviour.
Given that there are now two kinds of generator (or generator
output), I must propose a means of distinguishing between
them, though this is not a key focus of the current
argument. Without such a means, consciousness would be
unable to distinguish between the perceived world and the
predicted one3.
Sensing Certainty
Shannon’s H is interesting here in a different way. As explained
above, H is the expected value of the information
3
Coupled with a deficit in suppression of less likely outcomes,
as above, this situation might lead to some root symptoms of
schizophrenia: hallucinations, delusions and cognitive disorganisation.
International Conference on Computational Creativity 2012 184
content of a given distribution, so it is different in kind
from h, which deals with individual situations, actual or predicted.
It is best characterised as the uncertainty inherent in a
distribution, and, indeed, a uniform distribution always gives
the maximum entropy for a given alphabet size. Unlike h,
H really only has meaning in the predictive context: once
one knows which possibility of a range is the right one, only
information content is really relevant. However, in the predictive
context, a predicted outcome of which one is certain
is much more useful than one of which one is unconfident:
H measures this difference.
I propose, therefore, that, in the predictive generators,
higher H also predicts lower volume, so that less certain
generated outputs are de-emphasised. This, then, I call
prediction-H. It may explain how it is possible to feel certain
about intuitions (as opposed to be convinced of reasoned
argument). It also prevents the Global Workspace
from being flooded out with predicted information that is
not strongly supported, allowing the important material to
shine through. A particularly interesting point is this: should
a generator make an unlikely prediction, that has sufficient
prediction-h to be “audible”, in the absence of other explanations,
that prediction will have low prediction-H, and so
will not be suppressed by this final mechanism. Increasing
the range of possibilities over which the distribution holds,
even if they are unlikely, increases prediction-H and thus
decreases certainty. Under this regime an organism that has ´
less experience is more likely to admit unlikely predictions
to consciousness; this might be taken to account for the tendency,
for example, of children to be more affected by imagined
fears than adults.
No straightforward diagram can be drawn of the effect of
prediction-H on the overall likelihood of a generator taking
over the Global Workspace, because the numbers depend
heavily on the multidimensional distributions from which
the various Hs are calculated.
This leaves us with a “volume” value for each generator,
T, which is estimated by the following, for either kind of h,
above:
T = p ⇥ h
H .
I propose that, at any given moment, this “volume” value
is used in deciding which of the range of possible inputs,
derived from matching sensory input to statistical models in
memory, enters the Global Workspace. This is illustrated in
Figure 3.
Generation, Creativity and Intuition
In the previous section, I outlined a simple, comparative
mechanism by which statistically likely and informationtheoretically
rich structures can emerge from a multi-agent
system furnished with high-quality models of a domain of
knowledge. With such a mechanism, the Threshold Paradox
disappears. I should also note that it is possible that such a
mechanism is one of Baars’ own proposals; however, if so,
it is not clearly specified as such. The remaining question
is then: how does this mechanism for choosing access to
consciousness help to simulate creativity?
Generator Generator Generator Generator Generator
Access competition
Global Workspace
Memory
model
Memory
model
Sensory
input
. . .
Figure 3: Schematic diagram of my proposal for the Global
Workspace. In this version, there is no need for a threshold
of access. Instead, the generators compete, one against another,
and probability and information content determine the
winner.
Perhaps surprisingly, an answer may be found in the writing
of Wolfgang Amadeus Mozart (quoted by Holmes, 2009,
pp. 317–8):
When I am, as it were, completely myself, entirely
alone, and of good cheer – say traveling in a carriage,
or walking after a good meal, or during the night when
I cannot sleep; it is on such occasions that my ideas
flow best and most abundantly. Whence and how they
come, I know not; nor can I force them. Those ideas
that please me I retain in memory, and am accustomed,
as I have been told, to hum them to myself.
One might paraphrase the opening sentence here as “when
I am not being bothered, and when I have no worries and
no particular goals”, which in turn means “when I have no
distractions” or “when I have no information-rich input to
consciousness from outside or within”. This accords with
a situation when the Global Workspace is occupied only by
weakly-informative ephemera, and when generators are receiving
little or no external stimulus.
Recall now my earlier proposal that effective animals will
base their actions not only on received stimuli, but on the results
of the comparison of received stimuli with predictions
about the current state of the world made from the previous
state(s). Suppose that those generators continue to generate,
even when there is very little informative input. Given the
appropriate knowledge and tendencies in a particular individual
(music—and, by all accounts, scatology—in Mozart),
generators will begin to freewheel, within the same statistical
framework as above, but lacking the statistical prior of
a particular stimulus. The outputs, one might expect, will
be rather more diffuse and perhaps less highly rated than
when directly stimulated, but this is not a brake on their
progress towards the Global Workspace, because there is little
or no competition. At this point, the diagram in Figure
2 becomes recognisable as the Wundt curve, as it defines a
International Conference on Computational Creativity 2012 185
sweet spot of balance between dullness and over-complexity
in information-theoretic terms.
Mozart, above, describes a particular kind of musical approach,
where one essentially enters a quiescent state, in order
deliberately to allow Baars’ generators to freewheel; I
find that the same method works for writing. But this is
only one case of many. For example, the mechanism above
also accounts for why hearing a musical phrase, or even a
non-musical pitch sequence, may give rise to new musical
phrase: the percept conditions the generators in a particular
way, and so affects the likely outcomes, which are generated
all the time. The ones with the right statistical properties
make it into the Global Workspace, and so can be further
elaborated.
Note that this mechanism can apply to any statistical
model available to the generators, so it need not be restricted
to music (as it is in the system components summarised in
the next section). In principle, the same idea can work with
any model from which statistical likelihoods can be computed.
This means, for example, that it can account for
the generation of sentences, and therefore possibly internal
speech. If internal speech is equated with essential thought,
as commonly, then the current approach can account for
general creative thought and for the emergence of particular
thoughts into consciousness as intuition. It can also,
via prediction-H, account for the (sometimes inappropriate)
feeling of certainty associated with thoughts and intuitions.
Thus, I suggest that “Threshold Paradox” as a name for
this issue needs to be reinterpreted. The paradox is not in the
nature of the threshold, but in the formulation of the Global
Workspace as requiring one. The current theory reformulates
entry to the Workspace as purely competitive, without
a particular boundary, so, one might say, the paradox arose
from the assumption that the Threshold exists.
What is more, in the present theory, there is no longer
any need to search for an explanation of creativity as a distinct
phenomenon. In my approach, non-conscious creativity
is happening all the time as a result of on-going anticipation
in all sensory (and other) modalities. When conditions
are right, this essential survival mechanism is not so much
exapted for creativity, but gives rise to creativity as a side
effect.
Towards a Creative System
To ground this theory in a technical base, I now summarise
research that has already been conducted towards building a
system of the kind proposed here, in the domain of musical
creativity. Pearce and Wiggins (2006)4 describe a statistical
model of musical learning, based on, but extending, statistical
language learning methods. Wiggins (2011) has shown
that the extensions to the musical model can also benefit language
models. Pearce and Wiggins (2007) showed how the
model could generate entire musical melodies, though the
requirements of the current proposal are less stringent, as
fragmentary musical ideas are all that is required: in this
4
A fuller presentation of the modelling work published up to
2007 is given in Pearce’s (2005) PhD thesis.
case short sequences of notes that might be consciously assembled
into melodies. Most importantly, the model has
been used to demonstrate that high information content corresponds
with increased beta-band synchrony in human listeners
(Pearce et al., 2010), providing at least circumstantial
evidence that cognitive resource (i.e., attention) does indeed
follow information content, which would accord with that
information’s entry into the Global Workspace when the circumstances,
as described above, are right.
Ponsford, Wiggins, and Mellish (1999), Whorley, Pearce,
and Wiggins (2008), Whorley, Wiggins, and Pearce (2007)
and Whorley et al. (2010) have presented more complex
models for dealing with deeper aspects of music than
melody.
A crucial piece of evidence for the model of creativity
proposed above is embedded in the workings of Pearce’s
perceptual model—recalling that perception and prediction
are closely linked in the view of the world presented here.
There are two sub-models, both of which contain multiple
predictors. The distributions output by the two sub-models
are combined multiplicatively, with weightings derived their
relative information entropy. The distributions output by the
multiple predictors within each of the two sub-models are
combined in the same way. Other configurations (for example,
a one-stage combination of all of the distributions,
instead of this two-stage combination) produce a less successful
model of human behaviour. This system matches exactly
against the multi-stage version of Baars’ Global Work
Space, described above, coupled with my proposal for a
competition mechanism based on information content and
entropy.
There is still substantial work to be done on this model
before the simulation of creativity can be claimed. The next
threshold to cross is not a paradox, but the engineering task
of implementing the integrated multiple generators in the
model described above, to test out the this particular approach
to competitive generation in the Global Workspace.
Acknowledgments
I gratefully acknowledge the contribution of the ISMS
group, most particularly Roger Dean, Ollie Bown, Jamie
Forth and Marcus Pearce, of Joydeep Bhattacharya, and
of three anonymous referees, to the thinking presented
here. Funding was provided by EPSRC Research Grant
EP/H01294X/2, “Information and neural dynamics in the
perception of musical structure”.
References
Baars, B. J. 1988. A cognitive theory of consciousness.
Cambridge University Press.
Chalmers, D. J. 1996. The Conscious Mind: in search of a
fundamental theory. OUP.
Colton, S. 2009. Seven catchy phrases for computational
creativity research: A position paper. In Proceedings
of the Dagstuhl Workshop on Computational Creativity.
Germany: Schloss Dagshtul.
Corkill, D. D. 1991. Blackboard systems. AI Expert
6(9):40–47.
International Conference on Computational Creativity 2012 186
Edelman, G. M.; Gally, J. A.; and Baars, B. J. 2011. Biology
of consciousness. Frontiers in Psychology 2.
Gardenfors, P. 2000. ¨ Conceptual Spaces: the geometry of
thought. Cambridge, MA: MIT Press.
Holmes, E. 2009. The Life of Mozart: Including his Correspondence.
Cambridge Library Collection. Cambridge
University Press.
Huron, D. 2006. Sweet Anticipation: Music and the Psychology
of Expectation. Bradford Books. Cambridge,
MA: MIT Press.
Lakatos, I. 1970. Falsification and the methodology of scientific
research programmes. In Lakatos, I., and Musgrave,
A., eds., Criticism and the Growth of Knowledge.
Cambridge, UK: Cambridge University Press. 91–196.
MacKay, D. J. C. 2003. Information Theory, Inference,
and Learning Algorithms. Cambridge, UK: Cambridge
University Press.
Minsky, M. 1985. The Society of Mind. New York, NY:
Simon and Schuster Inc.
Moffat, D., and Kelly, M. 2006. An investigation into people’s
bias against computational creativity in music compositio.
In Proceeings of the International Joint Workshop
on Computational Creativity.
Pearce, M. T., and Wiggins, G. A. 2006. Expectation in
melody: The influence of context and learning. Music
Perception 23(5):377–405.
Pearce, M. T., and Wiggins, G. A. 2007. Evaluating cognitive
models of musical composition. In Cardoso, A.,
and Wiggins, G. A., eds., Proceedings of the 4th International
Joint Workshop on Computational Creativity, 73–
80. London: Goldsmiths, University of London.
Pearce, M. T.; Herrojo Ruiz, M.; Kapasi, S.; Wiggins,
G. A.; and Bhattacharya, J. 2010. Unsupervised statistical
learning underpins computational, behavioural and
neural manifestations of musical expectation. NeuroImage
50(1):303–314.
Pearce, M. T. 2005. The Construction and Evaluation of
Statistical Models of Melodic Structure in Music Perception
and Composition. Ph.D. Dissertation, Department of
Computing, City University, London, UK.
Ponsford, D.; Wiggins, G. A.; and Mellish, C. 1999. Statistical
learning of harmonic movement. Journal of New
Music Research 28(2):150–177.
Ritchie, G. 2001. Assessing creativity. In Proceedings
of the AISB’01 Symposium on Artificial Intelligence and
Creativity in the Arts and Sciences, 3–11. Brighton, UK:
SSAISB.
Russell, S., and Norvig, P. 1995. Artificial Intelligence – a
modern approach. New Jersey: Prentice Hall.
Shannon, C. 1948. A mathematical theory of communication.
Bell System Technical Journal 27:379–423, 623–56.
Tononi, G., and Edelman, G. M. 1998. Consciousness and
complexity. Science 282(5395):1846–1851.
Wallas, G. 1926. The Art of Thought. New York: Harcourt
Brace.
Whorley, R.; Wiggins, G. A.; Rhodes, C.; and Pearce, M.
2010. Development of techniques for the computational
modelling of harmony. In Ventura, et al., eds., Proceedings
of the First International Conference on Computational
Creativity.
Whorley, R. P.; Pearce, M. T.; and Wiggins, G. A. 2008.
Computational modelling of the cognition of harmonic
movement. In Proceedings of the 10th International Conference
on Music Perception and Cognition.
Whorley, R. P.; Wiggins, G. A.; and Pearce, M. T. 2007. Systematic
evaluation and improvement of statistical models
of harmony. In A. Cardoso, and G. A. Wiggins., eds.,
Proceedings of the 4th International Joint Workshop on
Computational Creativity, 81–88.
Wiggins, G. A. 2011. “I let the music speak”: cross-domain
application of a cognitive model of musical learning. In
Rebuschat, P., and Williams, J., eds., Statistical Learning
and Language Acquisition. Amsterdam, NL: Mouton De
Gruyter.
Wiggins, G. A. 2012. Defining inspiration? Modelling nonconscious
creative process. In Collins, D., ed., The Act of
Musical Composition – Studies in the Creative Process.
Aldershot, UK: Ashgate.
International Conference on Computational Creativity 2012 187