Psychological Bulletin
2013, Vol. 139, No. 3, 542–547
© 2013 American Psychological Association
0033-2909/13/$12.00 DOI: 10.1037/a0031019
REPLY
Searching for the Elements of Thought: Reply to Franklin, Mrazek,
Broadway, and Schooler (2013)
Jonathan Smallwood
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Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
Understanding thoughts with no perceptual basis is a complex problem, and the commentary by Franklin,
Mrazek, Broadway, and Schooler (2013) highlighted some of the difficulties that can occur when
theorizing about this topic. They argued that the suppression of external input during internal thought
arises from the selection of internal information. However, once a process of competition has been
resolved in favor of self-generated content, it is still necessary to explain the stability of that content over
time. It is proposed that perceptual decoupling and the associated attenuation of external input make
environmental information less likely to gain access to limited resources explaining how internal
thoughts persist over time. Franklin and colleagues also claimed that perceptual decoupling is unnecessary for an internal train of thought because statements of necessity cannot be drawn from correlational
evidence. However, experimentally induced internal trains of thought also compete with concurrent
external information, and this mutual inhibition is easily explained by assuming perceptual decoupling
is necessary for the integrity of a detailed internal train of thought. I argue that the fundamental advantage
of the process– occurrence framework is to highlight that self-generated thought is an emergent property
from a general-purpose cognitive architecture and that models such as these will deepen our understanding more effectively than those focused on describing specific mental states.
Keywords: perceptual decoupling, mind wandering, internal train of thought, task unrelated thought,
stimulus independent thought
In this response, I show that these criticisms reveal a misunderstanding of the central premises of the process– occurrence
framework and are inconsistent with the available data. For
example, it does not make sense to contrast selection and
decoupling accounts of the relation between an internal train of
thought and attenuated external attention. The result of a contest for limited cognitive resources requires other inputs to be
attenuated to ensure that the winner’s access to limited resources is stable over time (Section 1). Nor is evidence of
mutual inhibition between perception and internal attention
limited to correlational evidence, as Franklin and colleagues
(2013) claimed. Perceptual decoupling occurs when participants engage in a detailed internal train of thought as part of a
task. Furthermore, in these situations, the integrity of an internal train of thought can be compromised when perceptual input
is not attenuated. This pattern of mutual inhibition is parsimoniously explained by assuming that perceptual decoupling is
necessary for the persistence of an internal train of thought
(Section 2). These basic misunderstandings are one reason why
the alternative explanations that Franklin and colleagues proposed lack the specification of the process– occurrence framework (Section 3). This greater specificity emerges in part because the process– occurrence framework makes explicit the
assumption that specific mental states (such as mind wandering)
are emergent properties from within a general cognitive architecture and this underlying assumption provides important clarity when thinking about internal thought processes (Section 4).
The process– occurrence framework (Smallwood, 2013) offers a
comprehensive account of what is currently known about selfgenerated thought. This account goes beyond prior attempts
(Schooler et al., 2011; Smallwood & Schooler, 2006) by demonstrating the necessity to distinguish between the events that govern
the initiation or occurrence of self-generated thought and the
subsequent processes that transform these thought fragments into a
detailed train of thought that persist over time. In their commentary, Franklin, Mrazek, Broadway, and Schooler (2013) challenged
this framework on two counts. First, they claimed that perceptual
decoupling may not be necessary to allow the transformation of a
self-generated thought fragment into an internal train of thought.
Second, they argued that perceptual decoupling is not the only
account that specifies how an internal thought is maintained and
that many if not all of the available theories can be considered as
candidate explanations for the persistence of self-generated
thought persists in the absence of external stimulation.
The ideas in this article benefited from discussions with many people,
including Philip Kanske, Antoine Lutz, Daniel Margulies, Travis Proulx,
Nico Steinbeis, and Tania Singer. Particular thanks go to Haakon Engen,
Florence Ruby, and Cade McCall.
Correspondence concerning this article should be addressed to Jonathan
Smallwood, Department of Social Neuroscience, The Max Planck Institute
for Human Cognitive and Brain Sciences, Stephanstrasse 1A, Leipzig,
Germany. E-mail: smallwood@cbs.mpg.de
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PERCEPTUAL DECOUPLING AND THE ELEMENTS OF THOUGHT
Before considering these issues, it is important to clarify several
discrepancies in the description that Franklin and colleagues
(2013) offered for the concepts proposed in the process–
occurrence framework. They defined perceptual decoupling as
“the notion that mind wandering is associated with a reduction in
attention to the external environment” (Franklin et al., 2013, p.
536). This is incorrect: Perceptual decoupling is the process that
occurs when conscious thought becomes engaged in the detailed
processing of information that is not derived from immediate input
(Smallwood, 2013, p. 522). Perceptual coupling and decoupling
are what the mind does when it directs (or allocates) processing
resources in the service of maintaining a particular internal or
external train of thought. Franklin and colleagues also focused
almost exclusively on perceptual decoupling’s role in attenuating
perceptual information. However, the role of decoupling in the
process– occurrence framework is to stabilize an internal train of
thought by “ensuring continuity, as well as embellishing, selfgenerated mental activity” (Smallwood, 2013, p. 523).
Section 1: Maintaining an Internal Train of Thought
Depends on the Suppression of External Information
Leaving aside such inaccuracies, one source of Franklin and
colleagues’ (2013) problems with the process– occurrence framework can be paraphrased in the following manner: Does it make
sense to consider perceptual decoupling as an active process that
is responsible for attenuated external processing and hence ensuring continuity in an internal train of thought? This point is
made on numerous occasions and is stated clearly in a discussion
of why self-generated thought reduces perception in a multimodal
fashion (Kam et al., 2011): “However, such attenuations (of perceptual information) may simply reflect a change in the direction
of attention rather than an active insulation of the internal stream”
(Franklin et al., 2013, p. 538).
What is confusing about this statement is that in a competitive
system like the mind, and especially with respect to higher order
thought, processes of selection, suppression, and prioritization are
all necessary for a stable train of thought. Consider how the global
neural workspace (GNW) of consciousness is presumed to function: “If the stimulus is selected for its adequacy to current goals
and attention state, it is amplified in a top-down manner and
becomes maintained by sustained activity of a fraction of GNW
neurons, the rest being inhibited” (Dehaene, Changeux, & Naccache, 2011, p. 58). The outcome of selection by the GNW is a
facilitation of what is relevant and suppression of what is not; thus,
in competitive models, selected inputs require maintenance,
achieved through a specific balance of facilitation and inhibition.
Fully specified models such as the GNW explicitly acknowledge
this fact.
The argument that external information is suppressed because
attention has been redirected elsewhere is of course true; however,
self-generated thought by definition manifests content that is discrepant from perceptual input, and so, even after selection occurs,
it will be in continual competition with sensory information. This
is because perceptual input does not cease simply because we
focus internally. Thus, the extent to which an internal train of
thought persists over time depends upon its continuing to outcompete concurrent perceptual input, which is more likely to happen if
perceptual input is attenuated. The process– occurrence framework
543
uses the term perceptual decoupling to describe what takes place
after competition with perceptual input is resolved in favor of
self-generated information. From this, it follows that (a) if external
input is attenuated during self-generated thought and (b) if attenuated external input will be less likely to outcompete internal
input, then (c) perceptual decoupling will extend the duration of
self-generated thought. This logic underlies the claim that perceptual decoupling describes how an internal train of thought persists
over time but not why a specific set of mental contents was
generated in the first place (Smallwood, 2013).
It is because perceptual decoupling directly influences length,
but not the occurrence, of self-generated thought that the analogy
of insulation is appropriate. Insulation can keep a room warm by
keeping cool air out; it also keeps a room warm by preventing
external heat from escaping. However, without an initial discrepancy in temperature, insulation does nothing at all: It is simply a
process that helps stabilize a temperature differential between the
inside environment and the external world. Insulation explains
how a room’s temperature is relatively stable over time, but it does
not explain why the room was warm in the first place.
By analogy, therefore, the concept of insulation emphasizes that
the persistence of thought requires a process that can maintain
mental content. This process must be active in the sense that it
depends upon achieving a particular balance of facilitation and
inhibition of information, and its consequence is to stabilize the
process of competition for limited resources in favor of particular
mental content for a period of time. It is thus the proposal of the
process– occurrence framework that (a) a process analogous to
insulation governs continuity within any train of thought and (b)
when this process ensures stability in an internal train of thought,
it can do so at the cost of perceptual processing. Without a
mechanism such as insulation, internal thoughts would lack stability because they would readily be replaced by alternative mental
contents derived from the myriad perceptual inputs that are occurring concurrently.
Section 2: Perceptual Decoupling Is a Necessary
Condition for Self-Generated Thought
Franklin and colleagues (2013) also asked the following: Is the
co-occurrence of attenuated external input with self-generated
thought sufficient evidence to infer that perceptual decoupling is
dedicated to the continuation of internal thought? It is correct that
evidence of correlation does not indicate evidence of necessity;
however, statements of necessity can be made if (a) causal manipulation of state A is accompanied by the engagement of process B
and (b) the failure to engage in process B prohibits the instantiation
of state A. Under these circumstances, it is appropriate to claim
that process B may be necessary for state A to occur.
Studies of self-generated thought satisfy these conditions
(Smallwood, 2013), but there is also evidence that experimental
induction of an internal train of thought leads perceptual decoupling to occur. For example, Nathan Spreng, Dan Schacter, and
others have asked participants to make plans about their future
(such as how to get out of debt) and compared the neural state that
this produces with the one that occurs when planning a perceptual
task (Spreng & Schacter, 2012; Spreng, Stevens, Chamberlain,
Gilmore, & Schacter, 2010). During the perceptual planning task,
regions supporting visual processes were functionally coupled to
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544
SMALLWOOD
neural regions that are thought to allow control (dorsal anterior
cingulate [dACC], as well as the dorsolateral prefrontal cortex). By
contrast, during autobiographical planning, the same control system was coupled to the default mode network (including the
posterior cingulate cortex and the medial prefrontal cortex) rather
than to visual regions. As these experiments directly contrasted
whether participants produced a train of thought based on perception versus episodic memory, these and other data demonstrate that
the creation of an internal train of thought leads perceptual decoupling to occur.
There is also evidence that engaging in internal thought reduces
attention to perception. Kanske and colleagues have shown that if
participants perform mental arithmetic while being simultaneously
exposed to emotional pictures, self-reports of emotional responses
to the stimuli are reduced and image-related activity in the
amygdala is down-regulated (Kanske, Heissler, Schonfelder,
Bongers, & Wessa, 2011). Functional connectivity demonstrated
that this down-regulation of perceptual emotional information was
associated with greater activity in the dACC and other areas
engaged in attentional control, indicating engagement of the same
network as seen by Spreng and colleagues (2010).
Critically, it is also the case that the success with which cognition is dedicated to internal processes covaries with the extent that
perceptual processes are attenuated. Huijbers and colleagues asked
participants to learn a list of words; they were then presented with
the same words (plus new items) superimposed on top of pictures
and were asked to determine if the words were old or new (Huijbers, Pennartz, Cabeza, & Daselaar, 2009). Finally, the same
participants were shown the pictures (plus new items) and were
asked if the images had been seen before. When participants
correctly identified a word as old, they were less likely to subsequently remember the picture upon which it was presented. The
reverse was also true: If the participants correctly identified a
picture as old, they were less likely to identify that they had seen
the word previously. In a second experiment, functional magnetic
resonance imaging revealed that the retrieval-induced encoding
deficits were related directly to a suppression of learning-related
neural activity in visual areas. This work demonstrates that the
extent to which participants are able to perform a task based on
information retrieved from memory (e.g., an internal train of
thought) depends on whether or not their capacity for concurrent
encoding is or is not compromised.
A similar pattern of mutual inhibition between the integrity of
internal and external thought is observed in studies of pain. When
participants experience thermal pain while simultaneously performing a working memory task, subjective reports of pain are
decreased relative to baseline levels, and this effect can be dissociated from the belief that pain will be reduced (Buhle & Wager,
2010; Buhle, Stevens, Friedman, & Wager, 2012). Critically, when
more noxious pain stimulation was administered, working memory
task performance was compromised, demonstrating that painful
stimuli that are more difficult to ignore reduce the integrity of an
internal train of thought (Buhle et al., 2012). Buhle and Wager
(2010) proposed that this pattern of mutual inhibition between pain
and working memory performance occurs because both compete
for limited cognitive resources.
Evidence from a variety of different paradigms, therefore, demonstrates that there is a class of internal mental operations the
performance of which is accompanied by a reduction in perceptual
processing (both visual and somatosensory). Importantly, the reverse is also true: Conditions when perceptual input is especially
strong (e.g., high levels of noxious stimulation; Buhle & Wager,
2010) or when visual stimuli are responded to in an especially
strong manner (Huijbers et al., 2009) compromise an internal train
of thought. Thus, experimental inductions, just like studies of
self-generated thought, demonstrate mutual inhibition between
internal trains of thought and the concurrent response to external
stimulation. The process– occurrence framework suggests that this
pattern is parsimoniously explained by assuming that perceptual
decoupling is a necessary condition for ensuring integrity within
an internal train of thought. Inasmuch as causal manipulation can
demonstrate the necessity of mental operations, I contend that
Franklin and colleagues (2013) were simply wrong: Whereas other
theories of self-generated thought may conflate occurrence with
function, perceptual decoupling is necessary for continuity in an
internal train of thought.
Section 3: Alternative Resource-Allocation Accounts
Are Not Sufficiently Well Specified to Explain How an
Internal Train of Thought Is Maintained
Instead of the process of perceptual decoupling, Franklin and
colleagues (2013) proposed a resource-allocation account in which
internal thought gains access to limited-capacity domain-general
workspace (e.g., Smallwood & Schooler, 2006). This proposition
is reasonable as far as it goes; however, it leaves important
questions unanswered. For example, one question is to what are
the resources allocated; a second relates to the mechanism underlying resource allocation to self-generated mental content.
The answers to these questions form the starting point of the
process– occurrence framework. This framework assumes that it is
possible to distinguish those events that lead to the self-generation
of a thought fragment from the processes that allow it to persist
over time as a detailed internal train of thought. In this framework,
self-generated thought fragments gain access to limited resources
that then become decoupled from other sources of information
(e.g., sensory information), biasing subsequent competition in favor of the current internal train of thought (see Section 1). The
process of decoupling, therefore, is an explanation of how competition resolution is maintained in favor of either an external train
of thought (by coupling attention to perception) or an internal train
of thought (by coupling attention to self-generated information).
This action is made explicit in the process– occurrence framework
in the statement that the decoupling hypothesis simply extends
competitive models of the mind to include the “internal/external
dimension” (Smallwood, 2013, p. 523).
Although it is not necessarily a problem to use different terms to
describe the same psychological process, it is a problem to have a
theory that is underspecified, and this is especially true in this
particular area of research. Prior resource accounts of selfgenerated mental activity (e.g., Smallwood & Schooler, 2006)
were correctly criticized by McVay and Kane (2010) because they
lacked sufficient clarity to generate unambiguous experimental
predictions, and this is in part because it was unclear how selfgenerated thought is related to the competition between internal
and external information. The process– occurrence framework proposes a clearly specified answer: Once the process of competition
is resolved in favor of self-generated information, then perceptual
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PERCEPTUAL DECOUPLING AND THE ELEMENTS OF THOUGHT
decoupling allows domain-general resources to help support the
persistence of this mental content in the form of a detailed internal
train of thought.
Similar problems arise when considering the long list of alternative mechanisms that Franklin and colleagues (2013) raised as
alternatives to perceptual decoupling. Notwithstanding the fact that
a single unified account of a phenomenon is scientifically more
valuable than many different explanations, these suggestions are
generally a restatement in different terms and with less clarity of
the ideas proposed in the process– occurrence framework. For
example, what does it mean to use self-regulation “to modulate
whether attention remains on an internal stream” (Franklin et al.,
2013, p. 538)? In the process– occurrence framework, this would
be described as self-regulating the coupling between systems that
coordinate attention and those that represent internal information.
Likewise, what is entailed by the statement that executive functions work “to keep both perceptual and internal distractions at
bay” (Franklin et al., 2013, p. 538)? In terms of the process–
occurrence framework, this would involve ensuring that attention
is decoupled from information, either internal or external, that is
irrelevant to whatever the current train of thought is.
The lack of specification is perhaps most apparent when the
resource demands of processing distal goals (such as future
thought) are contrasted with the process– occurrence framework
(e.g., Franklin et al., 2013, pp. 537 & 538). Psychologically distant
cognitions are those that are not directly related to the here and
now (Liberman & Trope, 2008). Because the process– occurrence
framework aims to explain trains of thought based on selfgeneration rather than perception, it is fundamentally an account of
distal goal processing. Moreover, while Franklin and colleagues
simply stated that resources are allocated “in the service of thinking about distal goals” (Franklin et al., 2013, p. 538) or that future
thought is more resource demanding (Franklin et al., 2013, p. 537),
the process– occurrence framework argues that episodic thoughts
(such as prospection) emerge when competition for limited capacity is resolved in favor of information from memory leading to an
internal train of thought focused on a time period other than the
present.
Section 4: Explanations of Mental States Based on the
Underlying Cognitive Architecture Provide a Deeper
Understanding of the Mind
The things with which we concern ourselves in science appear in
myriad forms, and with a multitude of attributes . . . . Curiosity
demands that we ask questions, that we try to put things together and
try to understand this multitude of aspects as perhaps resulting from
the action of a relatively small number of elemental things and forces
acting in an infinite variety of combinations.
—Feynman, Leighton, and Sands (1964, p. 2-1)
One reason why the process– occurrence framework provides
the specificity that it does is because it makes explicit the assumption that mental states (such as mind wandering) can be best
understood as emerging through the interaction of discrete functional elements that serve specified cognitive processes. Just as in
the periodic table of elements, where the balance of protons and
neutrons determines the properties a substance has, the combination of different mental processes determines the psychological
features that any particular mental state has.1 As Franklin and
545
colleagues (2013) noted, one key advantage of thinking about
internal thought in this manner is that by highlighting the subprocesses that are engaged, it becomes clear what we do not yet know.
For example, because we are unable to identify when selfgenerated thought occurs, we are unable to determine basic information such as the frequency or duration of self-generated thought.
I believe that there are a number of additional advantages to
thinking about internal thought in this manner, and in what remains
of this response, I outline what I believe the most important ones
are.
First, specific subprocesses lend themselves to unambiguous
experimental measurement better than do the states that emerge
through their interaction (e.g., mind wandering). For example, the
process of mind wandering (e.g., shifting from a task to an unrelated though) can only be inferred indirectly by measuring the
occurrence of task-unrelated thought. By contrast, coupling and
decoupling can be quantified by examining the functional connectivity between different neural systems. For example, greater coupling between the default mode and the dACC has already been
observed during periods of self-generated thought (Christoff,
2012). Although the physiological changes indicating the onset of
self-generated thought are yet to be identified, they could be also
quantified using techniques such as change-point analysis (Robinson, Wager, & Lindquist, 2010) or dynamic connectivity regression (Cribben, Haraldsdottir, Atlas, Wager, & Lindquist, 2012). In
principle, therefore, the core elements of the process– occurrence
framework (namely, events that signify the onset and those that
serve to maintain or embellish the experience) could be measured
directly.
Second, the appropriate level to describe a phenomenon is one
in which statements can be made that are as close as possible to the
underlying process. The process– occurrence framework assumes
that the engagement of different mental states can be influenced by
many different parameters (see, e.g., the discussion in Smallwood,
2013, pp. 522 & 530). If this is the case, then states such as mind
wandering can arise for different reasons. To see how this works,
consider a recent demonstration that cultivating mindfulness reduces mind wandering (Mrazek, Franklin, Philips, Baird, &
Schooler, in press). In this experiment, a brief intervention of
breath training led to reductions in the report of task-unrelated
thought and improved performance on tasks in which a perceptual
focus is important (such as a measure of working memory span).
These reductions in mind wandering could arise for several reasons, including (a) an improvement in the capacity for external
concentration, (b) a reduction in the ability to self-generate thought
(in which the capacity to concentrate is less important), or (c)
decreases in the value that individuals place on self-generated
thoughts when they arise (in which case, concentration has not
changed, but the individual prioritizes perception over internal
thought, voluntarily reducing the amount of time spent engaged in
1
Although the process– occurrence framework proposes a number of
cognitive elements, it is not an exhaustive list. For example, given that
self-generated thought is intimately linked to mood (Killingsworth &
Gilbert, 2010; Smallwood, Fitzgerald, Miles, & Phillips, 2009; Smallwood
& O’Connor, 2011), processes may be required that provide emotional
color to cognition. Other processes may be required to determine the
system’s preference for the continuation of a particular train of thought
(Smallwood, Brown, Baird, & Schooler, 2011; Smallwood et al., 2012).
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546
SMALLWOOD
self-generated thought). It would be correct to describe each of
these changes as a reduction in mind wandering; however, because
they each occur for different reasons, these statements may not be
equivalent regarding the underlying change that takes place. Although mind wandering may suffice as a description of the general
phenomenon, it would be best if it was qualified by terms that are
closer to what we presume are the basic building blocks of thought.
Third, considering mental states as emerging from within a
general cognitive architecture allows many different experiential
states to be explained in a simple and parsimonious manner. This
property is apparent when the process– occurrence framework is
compared to the proposal that experience of mind wandering has a
specific sequence of stages—initiation, maintenance, and termination. This account seems reasonable, and with some fine-tuning, I
agree it could provide a description of the cognitive steps involved
in “mind-wandering from its initiation through its termination”
(Franklin et al., 2013, pp. 538 & 539). Whereas the stage model
can only describe the emergence of a specific phenomenon (mind
wandering), the process– occurrence framework can account for
this sequence of experience (Smallwood, 2013, pp. 519 & 520),
and it can also account for others. Perhaps most importantly, it
offers a framework in which both perceptually guided and selfgenerated trains of thought naturally emerge and so can flexibly
account for mental states that are often seen as in opposition. For
example, it allows for states of external distraction to be represented as situations when failure to insulate task-relevant cognition
from perceptual distraction has occurred. By focusing on the
interaction of basic cognitive elements, therefore, the processesoccurrence model can explain many different types of cognition
and so provides a comprehensive and hence deeper account of
mental states.
Finally, thinking about the production of different mental states
as emerging through the temporal interactions of a basic underlying architecture also provides a clear way to think about the
functions that self-generated thought serves. A section of the
commentary by Franklin and colleagues (2013, p. 539) was devoted to the ontological significance of mind wandering, where
they suggested caution in this line of reasoning, especially with
respect to understanding why it occurs. I agree: If all mindwandering episodes are not equivalent, there is unlikely to be a
single overarching function common to them all; thus, couching
questions in terms of what functions they serve could be counterproductive.2
Rather than asking what the function of mind wandering is, the
process– occurrence framework invites researchers to identify the
basic atoms of thought and to explore how in isolation, as well as
through their flexible combination across time, they are used to
navigate the challenges we all face in daily life. Functions would
be ascribed to particular processes (or their combination thereof),
and the value that these functions have emerges to the extent that
they are deployed effectively. For example, the fact that cognition
can be decoupled from perception allows thoughts to occur that are
not a direct response to an external stimulus. This capacity is the
basis for freedom from immediacy (e.g., Shadlen & Kiani, 2011)
and so explains our species’ capacity to engage in thought and
behavior that are not prescribed by the external environment.
Similarly, generating mental content based on episodic memory
allows the future or the mental states of other individuals to be
simulated (Amodio & Frith, 2006; Buckner & Carroll, 2007;
Mitchell, 2009a, 2009b). The capacity to self-generate thought
based on episodic memory thus conveys a very general benefit: It
allows the future to be simulated so that bad ideas can be “weeded
out before they’re hazarded in ‘real life’” (Dennet, 1996, p. 88).
Finally, the capacity to shift between different mental states allows
the agent to manage current and distal goals and so balance the
need between exploitation and exploration in goal pursuit (March,
1981). In this view, mind wandering would not be for anything—it
is just a way to describe a particular sequence of mental states that
emerge through the temporal interplay between a finite number of
functional elements within a cognitive architecture like that described in the process– occurrence framework.
2
It is possible that all mind-wandering episodes could depend on a single
underlying subprocess (such as self-generation). Under these circumstances, it
could be more parsimonious to argue that it is the subprocess, and not mind
wandering, that supports the function. For mind wandering to be attributed any
function at all, it is necessary to show (a) that this could not be explained by
a single process that is engaged in all mind-wandering episodes and (b) that
this function only emerges when this constellation of subprocesses occurs
during mind wandering and not when the same set of cognitive operations are
performed during a task. These conditions are not met by brain activation that
occurs during mind wandering (e.g., Spreng et al., 2010), nor is it true of the
process of decoupling because it can occur under experimentally induced
conditions (see Section 2).
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Received September 1, 2012
Revision received September 14, 2012
Accepted September 17, 2012 䡲