New Ideas in Psychology 28 (2010) 274–282
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New Ideas in Psychology
journal homepage: www.elsevier.com/locate/
newideapsych
Emergence and reduction in dynamical cognitive science
Joel Walmsley
Department of Philosophy, University College Cork, Ireland
a r t i c l e i n f o
a b s t r a c t
Article history:
Available online 9 October 2009
This paper examines the widespread intuition that the dynamical
approach to cognitive science is importantly related to emergentism about the mind. The explanatory practices adopted by
dynamical cognitive science rule out some conceptions of emergence; covering law explanations require a deducibility relationship between explanans and explanandum, whereas canonical
theories of emergence require the absence of such deducibility.
A response to this problem – one which would save the intuition
that dynamics and emergence are related – is to reconstrue the
concept of emergence as a relationship between laws. I call this
‘‘nomological emergence’’ and comment on the extent to which
dynamicists would find it acceptable. Alternatively, dynamical
cognitive science might be viewed as fitting better with the kind of
‘‘functional reductionism’’ which has recently been developed by
authors such as Jaegwon Kim. Which of these two alternatives is
preferable remains an open question pending the further development of dynamical cognitive science, particularly in its ‘‘nonclassical’’ forms.
Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction
Although its historical roots stretch back to cybernetics and ecological psychology, the so-called
‘‘dynamical approach’’ to cognitive science really came to prominence in the mid-1990s with a series of
influential papers in philosophy, psychology, neuroscience and AI. Yet despite the initial flurry of
interest, the consequences of such a development have not yet been fully worked out. Although many
of the insights afforded by the dynamical approach, (such as the importance of time and timing and the
significance of the body and the environment) have been largely taken on board, many of its philosophical consequences have not been pursued. In this paper, I want to take a look at how the dynamical
E-mail address: [email protected]
0732-118X/$ – see front matter Ó 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.newideapsych.2009.09.003
J. Walmsley / New Ideas in Psychology 28 (2010) 274–282
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approach to cognitive science might shed light on the mind-body problem. It seems to me that there is
a tension here; whilst many authors are happy to make claims about the relation between dynamics
and emergence, their statements may also be interpreted in a way that lends support to a kind of
reductionism about the mind. For now, at least, my aim is simply to set out this tension, comment on
how it arises, and point towards some potential future developments.
Before starting, I should mention a couple of caveats. First of all, I am concerned specifically with the
relation between dynamical cognitive science and emergentism in philosophy of mind. The extent to
which my discussion will extend to the relationship between dynamical systems theory and the
concept of emergence more generally is a topic that lies beyond the scope of this paper. Secondly, the
following discussion takes as its starting point a small set of relatively well-developed dynamical
models in cognitive science, such as those of Kelso (1995) and Thelen and Smith (1994), and their
philosophical interpreters. These examples operate with a restricted set of the tools available in
dynamical systems theory – what we might think of as ‘‘classical’’ DST – and thus, they set aside issues
such as chaos, entropy, autopoiesis and far-from-equilibrium dynamics. For that reason, my conclusions will be similarly restricted – indeed, in the final section, I comment on how ‘‘non-classical’’
dynamics may offer additional insights.
In any case, many authors seem to think that even these kinds of dynamical models significantly bolster a non-reductive physicalist view of mind and cognition. In particular, there are
many expressions of the claim (or intuition) that dynamical cognitive science is importantly
related to the doctrine of emergentism. Tim van Gelder, for example, sees the two as related,
writing:
‘‘From a broadly dynamical perspective, cognition is seen as the emergent outcome of the
ongoing interaction of sets of coupled quantitative variables rather than as sequential discrete
transformations from one data structure to another.’’1
Other authors, such as Jeff Elman, make a slightly stronger claim – that the dynamical approach
might explain emergence – thus:
‘‘The dynamical systems approach is also concerned with interaction and emergentism; more
generally it can be viewed as a mathematical framework for understanding the sort of emergentism and the high-order interactions which are found in both connectionist and artificial life
models.’’2 (My emphasis)
Despite all this, there also seems to be a kind of reductionism lurking in the dynamical literature. In
particular, as we shall see, many dynamicists see the mathematics of dynamical systems theory as
a language for describing both psychological and physiological aspects of cognition. Insofar as it’s
supposed to unify different levels of description, therefore, dynamical systems theory may be seen as
underwriting a kind of reductionism akin to that found in the so-called ‘‘unity of science’’ movement in
the first half of the twentieth century.
2. Dynamical explanation
Let’s start by examining a complication for the emergentist intuition that arises because of the
kind of explanation found in dynamical cognitive science. The explanatory goals of dynamicism are
relatively clear. Dynamicists want to uncover differential equations that describe or govern cognitive
phenomena, since these are better suited for capturing the essentially temporal and interactive
nature of cognition. This aim is often contrasted with classical cognitive science, which seeks
something like computer programs – lines of algorithmic code which describe discrete transitions
between static states.
1
2
van Gelder (1999) p. 12.
Elman (1998) p. 504.
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J. Walmsley / New Ideas in Psychology 28 (2010) 274–282
In general, a dynamical system is ‘‘a system that evolves in time through the iterated application of
an underlying dynamical rule.’’3 Applying this picture to cognitive systems, Van Gelder and Port, two of
the most famous advocates of the dynamical approach to cognition, write:
‘‘[Dynamical] models specify how change in state variables at any instant depends on the current
values of those variables themselves and other parameters. Solutions to the governing equations
tell you the state that the system will be in at any point in time, as long as the starting state and
the amount of elapsed time are known.’’4
In a similar vein, Andy Clark writes:
‘‘The mathematics typically specifies a dynamical law that determines how the values of a set of
state variables evolve through time. (Such a law may consist, for example, in a set of differential
equations.) Given an initial state, the temporal sequence of states determined by the dynamical
law constitutes one trajectory through the space.’’5
So, on the dynamical conception of cognition, the laws of psychology are differential equations, and
psychological explanation consists of showing how the phenomenon in question unfolds in accordance
with them. To the extent that they’re successful, some dynamical models have achieved this goal.
Kelso’s famous (1995) model of rhythmic finger movement co-ordination is arguably an attempt to
show how the complexities of an observed phenomenon can be elegantly captured using the mathematical resources of dynamical systems theory. At the heart of the model is a differential equation, the
details of which we need not go into, that permits one to derive the observed behaviour, given
knowledge of the initial values of the variables (i.e., given the initial state of the system). Depending on
our interests, we can insert the value of the variables we know, and derive the values of the variables
we want to predict or explain. Thus, in predicting and explaining rhythmic finger movement using
Kelso’s model, one is, it seems, using a covering-law explanation.6
Very briefly, the covering-law model views explanation as deduction from a law in conjunction with
statements of the antecedent conditions. As Hempel (1965) puts it:
‘‘A [covering-law] explanation answers the question ‘‘Why did the explanandum phenomenon
occur?’’ by showing that the phenomenon resulted from certain particular circumstances,
specified in C1, C2,.Ck, in accordance with the laws L1, L2,.Lr. By pointing this out, the argument
shows that, given the particular circumstances and the laws in question, the occurrence of the
phenomenon was to be expected; and it is in this sense that the explanation enables us to
understand why the phenomenon occurred.’’7
Thus, according to the famous view put forward by Hempel and Oppenheim (1948),
explanations have the structure of a valid deductive argument in which the explanans is the
conjunction of two premisses – a statement of initial conditions and a statement of a general law –
and the explanandum is the conclusion, consisting of a description of the empirical phenomenon
to be explained.
The covering-law model of explanation has been very closely associated with the account of
reduction developed by Nagel (1961) since both take deductive relations as central. According to
Nagel’s model of reduction, if the laws of theory T1 can be deduced from the laws of theory T2, then T1 is
said to be reducible to T2 – reducibility is deducibility. In fact, it is sometimes even said that cases of
Nagel-reduction are cases where the reduced theory is explained by the reducing theory.8 This close
relationship between covering-law explanation and Nagel-reduction gives rise to an interesting
3
Jost (2005) p. 1.
van Gelder and Port (1995), p. 19.
5
Clark (1997) p. 100.
6
A similar story can, I think, be told for Thelen & Smith’s famous model of infant perseverative reaching, given that the model
consists of a ‘‘grand equation’’ (van Gelder’s term). (See Walmsley (2008))
7
Hempel (1965) p. 337 Italics in original. Note how this description assimilates explanation and prediction.
8
Silberstein (2002) writes that the Nagel-reduction model ’’. treats intertheoretic reduction as deductive, and as a special
case of [covering law] explanation.’’ (p. 85).
4
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277
problem for the dynamical cognitive scientist; covering law explanations require a kind of deducibility
relation between explanans and explanandum, whereas most theories of emergence (insofar as they’re
non-reductive views) require the absence of such deducibility.
Let’s pause to consider the implications of the adoption of this explanatory model. For one thing, it
no longer seems feasible to talk about the behaviour of a dynamical system as ‘‘emergent’’ in the
traditional technical sense that puts it directly at odds with the Nagel model of reduction. If
a description of your finger wagging behaviour is deducible from a conjunction of the law (e.g., Kelso’s
equation), and the initial state (i.e., a specification of the initial values of the variables), it seems more
appropriate to say that finger wagging is reducible, in the Nagelian sense, to the underlying theory of
dynamics. With this tension in mind, let us look at one potential response.
3. Nomological emergence
One way to overcome the apparent tension between the explanatory practices of dynamical
cognitive science and the intuition that it will support a non-reductive view of the mind, is to
reconstrue the notion of emergence. In this section, I want to suggest that one might do so by
understanding emergence as a relationship between laws themselves. Thus, even if cognitive behaviour is deducible from cognitive-level laws, the possibility remains open that those cognitive-level laws
are not in turn deducible from physical laws. We’d therefore still have a viable conception of emergentism (qua non-deducibility) on the table.
This idea is suggested by van Gelder (1991). Discussing the relationship between the equations of
dynamical cognitive science, and the underlying laws of physics, he writes:
‘‘In principle, of course, one supposes that the equations are ultimately derivable from general
physical laws, and it may even be possible to provide such a derivation. However, the crucial
point is that as long as one has the equations for the system, such a derivation is not in practice
part of the actual explanation of the behaviour of the system, and none of the explanatory force
is lost if no such derivation is forthcoming.’’
Van Gelder’s point here is that dynamical explanations can still be good explanations, even if
dynamical cognitive laws can’t be derived from lower-level physical laws. So although dynamical
explanations require deducibility at the cognitive level, they permit non-deducibility between
levels; there is still scope for emergence in some sense, despite the considerations of the previous
section.
This view – which I’ll call ‘‘nomological emergence’’ – amounts to saying that the laws of
dynamical cognitive science are emergent with respect to the laws of physics or physiology. If
nomological emergence applies to cognitive systems, a given cognitive behaviour could be derived or
predicted on the basis of some higher-level law, but this higher-level law itself could not be derived
or predicted from statements about (say) neurophysiology or physics. There would still be a kind of
emergence compatible with dynamical cognitive science, it is just that the emergence would have
happened, as it were, before the dynamical explanation got started. One might picture nomological
emergence by supplementing the classical diagrammatic representation of the covering law model of
explanation:
P1, P2 ... Pz
Laws of Physics or Physiology
Nomological Emergence
L1, L2 …Lx
C1, C2 …Cy
—————
E
Dynamical cognitive Laws
Initial Conditions
——————
Conclusion
Dynamical (Covering-law)
Explanation
Fig. 1. Diagrammatic representation of nomological emergence.
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J. Walmsley / New Ideas in Psychology 28 (2010) 274–282
Take your favourite case of dynamical cognitive science. The law qua differential equation found
in the example would correspond to the L1.Lx in Fig. 1, and emergence would be needed in order
to get from the laws of physics or physiology, which govern the underlying machinery, to the
dynamical laws, which govern the cognitive behaviour. In the case of Kelso’s model, for example,
observed rhythmic finger movement could still be explained by the equation, but we might say that
the equation itself is nomologically emergent with respect to the laws of physics or
neurophysiology.
One advantage of this picture of emergence is that it remains neutral on a number of metaphysical
questions that cause trouble for other accounts. For example, nomological emergence is compatible
with both substance- and process-metaphysical views. All that matters for this view of emergence is
that the laws standing in the emergent relation are not deducible from one another. It does not matter
whether the laws range over substances or processes, so nomological emergence is a conception of
emergence which may be suitable for both metaphysical views.
As noted, this conception of nomological emergence is compatible with the kind of explanation
found in and sought by dynamical cognitive science. As such, it presents one way to sustain the weaker
version of the intuition that dynamics and emergence are related or compatible. It’s not so clear,
however, that this conception of emergence could sustain the stronger intuition that dynamical
cognitive science could explain emergentism about the mind.
Fig. 1 is particularly helpful in spelling out this point. Here, the nomological emergence takes place
prior to the dynamical explanation. In this sense, nomological emergence is something external to
dynamical cognitive science. Dynamical cognitive science could not explain or illuminate nomological
emergentism about the mind – it could not tell us why it is that we cannot in principle deduce the laws
of cognition from the laws of physics/physiology – because the explanation for such in principle
undeducibilty is not itself part of cognitive science. As such, the stronger version of the intuition is
unwarranted; given the nature of explanation in dynamical cognitive science, and the kind of emergence with which it is compatible, the former can not illuminate, or provide evidence, for the latter.
The question remains as to whether this kind of emergence is one that dynamicists would want.
I suspect that many would not. At the very least this conception of emergence seems to place some
fundamental limits on the extent to which we can understand the world, with perhaps disheartening
consequences for the possibility of conducting fruitful interdisciplinary scientific research. Indeed, such
a point was noted by C.D. Broad:
‘‘On the emergent theory we have to reconcile ourselves to much less unity in the external world
and a much less intimate connexion between the various sciences.’’9
Further, unless we can give an account of emergence itself, this kind of picture makes the
dynamical law look something like an inexplicable brute fact, reminiscent of Samuel Alexander’s
famous phrase:
‘‘The existence of emergent qualities thus described is something to be noted, as some would say,
under the compulsion of brute empirical fact, or, as I should prefer to say in less harsh terms, to
be accepted with the ’natural piety’ of the investigator. It admits no explanation.’’10
Whether the positing of ‘‘brute facts’’ is ever acceptable is a topic outside the scope of this paper.
For now, however, it is worth noting that this view bears a striking resemblance to the so-called
‘‘mysterianism’’ advanced by, for example, Colin McGinn, according to which, the mind-body problem
is a mystery which cannot, in-principle, be solved. Suffice to note that the name ‘‘mysterianism’’ was
not intended as a compliment when attributed to McGinn’s view. McGinn’s detractors may well take
a correspondingly dim view of the mysterianism involved in nomological emergence, and presumably, those who express the dynamical-emergentist intuition would want to avoid being tarred with
the same brush.
9
10
Broad (1925) p. 77.
Alexander (1920) p. 46.
J. Walmsley / New Ideas in Psychology 28 (2010) 274–282
279
4. Functional reductionism
Many dynamical cognitive scientists will want to avoid this fundamental disunity – in fact, ‘‘unity’’
between different cognitive scientific subdisciplines, or between different modes of discourse is
explicitly sought in many cases. To quote Randall Beer, dynamical cognitive science aims to provide
a ‘‘common language for cognition, for the neurophysiological processes that support it, for noncognitive human behaviour, and for the adaptive behaviour of simpler animals.’’ As such, it is
a ‘‘unified theoretical framework for cognitive science.’’11
But this unificationist view in fact has a great deal in common with Nagel-reduction. In particular,
the attempt to unify different levels (in this case, cognitive and neural) by characterising them using
the same vocabulary seems to fall under what Michael Silberstein has called the ‘‘semantic approach’’
to reduction. On this view, the ‘‘reduction relation might be conceived of as some kind of ‘isomorphism’
or ‘expressive equivalence’ between models.’’12
The unificationist idea, it seems, lies behind Kelso’s studies of the dynamics of co-ordination. His
considered view is that the same kind of theoretical apparatus can be used to explain both neural
and cognitive dynamics; the same equations that characterise the pattern of finger wagging abilities will also characterise the neural basis for that ability. In the epilogue to his 1995 book, he
writes:
‘‘My aim here was to join together neural processes at one end of the scale and mental or
cognitive processes at the other, in a common language. This is the language of dynamic patterns
[which provides] the linkage across levels of neural and cognitive function.’’13
Thus, Kelso holds an ideal – that a common vocabulary can capture more than one level of
description – which is similar to the ‘unity of science’ thesis famously held by reductionists in the
first half of the 20th century. He goes on to express this point in a way which simultaneously
incorporates the technical vocabulary of DST with the traditional vocabulary of the mind-body
problem:
‘‘. an order parameter isomorphism connects mind and body, will and brain, mental and neural
events. Mind itself is a spatiotemporal pattern that molds the metastable dynamic patterns of
the brain. Mind-body dualism is replaced by a single isomorphism, the heart of which is
semantically meaningful pattern variables.’’14
We can make sense of this using some of the terminology from DST itself. A useful distinction is
often drawn between a ‘real’ or ‘concrete’ dynamical system, such as the solar system or a Watt
centrifugal governor, and a ‘mathematical’ or ‘abstract’ dynamical system, such as the set of equations
used to characterize the changes in a real system. (See Giunti, 1997). The interesting feature of this
distinction is that it allows that more than one real dynamical system can be described by the same
mathematical dynamical system. The same equations could describe a number of different concrete
systems.
So Kelso’s form of reductionism could be understood as the claim that what unifies mind and brain
is the fact that both are described by differential equations with the same form. This claim is not so
much that cognition can be reduced to neurophysiology, but rather that both can be ‘reduced’ to the
same, shared, underlying dynamics.
Despite their work being one locus of the emergentist intuition I mentioned above, Thelen and
Smith ultimately seem to espouse a similar view to Kelso’s. Again, they are concerned with trying to
unify dynamical explanations of the same phenomenon at different levels – especially behavioural and
neural levels. In the preface to their 1994 book, they write:
11
Beer (2000) p. 97.
Silberstein (2002) p. 88. I assume here that Silberstein intends ‘isomorphism’ literally, meaning ‘having the same form.’
More on this below.
13
1995, p. 289.
14
1995, 288–289.
12
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J. Walmsley / New Ideas in Psychology 28 (2010) 274–282
‘‘We are especially dedicated to showing that behaviour and development are dynamic at many
levels of explanation, in particular, that phenomena described at the level of behaviour are
congruent with what is known about the brain and how it works.’’15
Thelen and Smith go on to draw an analogy with the relationship between quantum mechanics and
classical physics. They claim that
‘‘Quantum mechanics does not explain the action of objects as objects at the macrolevel. But
quantum mechanics does explain transitions and changes in the objects. The interactions, the
dynamics of quanta, explain how the objects of the macrolevel change. [T]he power of explanation is in the dynamics of the processes, in the view from below examined from above. The
explanatory power is in the joint consideration of the micro- and macrolevels. This is not
traditional reductionism.’’16
Now, it is certainly the case that Thelen et al.’s view is not ‘‘traditional reductionism,’’ if by that they
mean Nagelian derivational reductionism. Nonetheless, if one can explain the changes at the macrolevel using the theoretical machinery of the micro-level, we do have some kind of reductionism. Again
we have the situation where, rather than the macro-level being reduced to the micro-level, both levels
of explanation are unified by their common emphasis on change in time and the mathematical
formalism which describes and explains it.
Again, the question arises of how we are to understand this new form of non-Nagelian reductionism. I think it bears a striking resemblance, at least in spirit, to the model of ‘‘functional reduction’’
advanced by Kim (1997, 1998). Kim’s model is explicitly designed to be an alternative model of
reduction to that of Nagel, in particular, because it avoid the kinds of problems that plague the latter
concerning multiple realisability.
Very briefly, a Kim-style functional reduction consists of two stages. The first is a specification of the
target (i.e., reduced) property or behaviour in terms of its functional role (i.e., its law-like causal
relations) with respect to other properties or behaviour. An example that Kim gives of this kind of
functional reconstrual is the gene. Instead of thinking of a gene in terms of its intrinsic properties, Kim
argues, we need to specify its causal-nomic relations by saying something like ‘‘the gene is that
mechanism in a biological organism which is causally responsible for the transmission of heritable
characteristics from parents to offsprings.’’17 The kinds of equations provided by the canonical
dynamical models in cognitive science can be viewed as analogous; they specify the causal-nomic
relationships between the important variables in a cognitive system.
The second stage is to ‘‘find properties or mechanisms, often at the microlevel, that satisfy these
causal/nomic specifications and thereby fill the specified causal roles.’’18 In the case of the gene, the
DNA molecule fills the causal role of being responsible for the transmission of heritable characteristics
from parents to offspring. According to Kim, this is why we can justifiably say that the gene has been
reduced to DNA. In the case of dynamical cognitive science, this kind of functional reductionism would
require that we find brain systems which obey the same equations as those which govern higher-level
behaviours (and that would permit us to take Kelso’s and Silbertein’s use of the term isomorphism
literally; the equations which characterize both cognitive and neural dynamics would have the same
form.)If that were possible, we could say that the dynamics of cognition had been reduced to the
dynamics of the brain.
This kind of two-step process seems to be what Kelso and Thelen and Smith are hinting at. They
would, I suspect, be willing to bet that if we could find the differential equations which governed the
high-level behavioural and low-level neural aspects of a given task, we would find that they were
(literally) isomorphic. Thus the job of dynamical cognitive science – one which van Gelder admits,
when he describes the approach as ‘‘catholic’’ – is to investigate the same phenomena at multiple levels
of explanation with a view to effecting this kind of unification. Needless to say, this is the kind of stuff of
15
16
17
18
Thelen & Smith, 1994, p. 14.
Thelen & Smith, 1994, p. 39.
Kim 1998, p. 25.
Kim 1998, p. 25.
J. Walmsley / New Ideas in Psychology 28 (2010) 274–282
281
which cognitive scientific dreams are made. It should be noted, however, that adopting the functional
reductionist perspective is effectively to abandon both versions of the emergentist intuition. For this
reason, although some dynamical cognitive scientists elliptically suggest it, functional reductionism
may not be a palatable option for those that wish to retain goal of pursuing a ‘‘non-reductive’’ account
of mind and cognition.
5. Concluding remarks
We therefore have a dilemma, and thus, an open question. On the one hand, if the dynamical
cognitive scientist wants to retain links to emergentism in philosophy of mind, that view will be
coupled with the compulsion to accept ‘‘brute facts’’ shrouded with an aura of mystery. Such a view
would also place significant barriers in the way of interdisciplinary research in cognitive science. On
the other hand, the dynamical cognitive scientist can abandon the link to ‘‘emergentism’’ (in any strong
sense), but thus acquire a (perhaps admirable) unificatory aim that’s consistent with the kind of
interdisciplinary work they want to do.
Of course, the resolution of this dilemma is dependent in large part upon future developments in
dynamical cognitive science, not least because I have restricted the foregoing discussion to the canon of
relatively well-developed classical dynamical models. As the use of dynamical systems theory in
cognitive science expands to include what we might think of as ‘‘non-classical’’ dynamics (for example,
issues concerning chaos, autopoiesis and far-from-equilibrium dynamics), a different story may have to
be told.
Jost (2005) for example, points out that, in these cases,
‘‘The underlying rule may be rather simple, but its iterated application may still create an
asymptotic behaviour as time goes to infinity that is not so easy to predict from the dynamical
rule itself.’’19
In these situations, therefore, since there are significant barriers to carrying out prediction and
derivation from dynamical laws, the clash between dynamical explanation and non-deducibility may
not materialise. Indeed, Jost goes on to point out that, in these cases, ‘‘.there is no simpler way to
obtain or predict the final result than to let the dynamical system run itself.’’20 This point is reminiscent
of Bedau’s (1997) account according to which a macrostate of a system is ‘‘weakly emergent’’ if it can be
derived from the conjunction of the laws governing a system together with its initial conditions, but
only by simulation. It’s not clear whether this ‘‘run-it-and-see’’ account of emergence amounts to more
than a merely epistemological point, but nonetheless, since non-classical dynamical models seem to fit
the definition, there’s yet further scope for retaining the emergentist intuition.
As I mentioned, then, the resolution of the issue is contingent upon the development of the
discipline, and so we must wait for an answer until such time as dynamical cognitive science is
developed enough to provide it. At the very least, I hope to have shown that we presently stand at
a bifurcation point, and, although the direction in which our trajectory will be pushed is not clear, we
can at least see the shape of some of the attractors ahead .
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