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Mind-wandering (sometimes referred to as task unrelated thought) is the experience of thoughts not remaining on a single topic for a long period of time, particularly when people are not engaged in an attention-demanding task. It is the topic of research in the study of attention and consciousness, as it relates to attentional lapses, or digression due to lack of focus on the task in hand.
Mind-wandering tends to occur during driving, reading and other activities where vigilance may be low. In these situations, people report having no memory of what happened in the surrounding environment while pre-occupied with their thoughts. This is known as the decoupling hypothesis. Studies using event-related potentials (ERPs) have quantified the extent that mind-wandering reduces the cortical processing of the external environment. When thinking is not focused on the task in hand, the brain processes both task relevant and unrelated sensory information in a less detailed manner.
Mind-wandering appears to be both a stable trait of people and a transient state. Studies have linked performance problems in the laboratory and in daily life. Mind-wandering is also intimately linked to states of affect; studies indicate that task unrelated thought is common in states of low or depressed mood. Mind-wandering is also common when drunk through the consumption of alcohol.
It is common during mind-wandering to engage in mental time travel—the consideration of personally relevant events from the past and the anticipation of events in the future. Poet Joseph Brodsky described it as a “psychological Sahara,” a cognitive desert “that starts right in your bedroom and spurns the horizon.” The hands of the clock seem to stop; the stream of consciousness slows to a drip. We want to be anywhere but here.
Studies have demonstrated a prospective bias to spontaneous thought because individuals tend to engage in more future than past related thoughts during mind-wandering.
The history of mind wandering research dates back to 18th century England. British philosophers struggled to determine whether this phenomenon was occurring within the mind or whether there were outside sources affecting it. It wasn’t until the 1960s that the first documented studies were completed on mind wandering. John Antrobus and Jerome Singer created a study with a questionnaire and discussed the experience of mind wandering in their article “Mind Wandering and Cognitive Structure”.  This questionnaire is called the Imaginal Processes Inventory (IPI). The IPI is the only known method to measure mind wandering and it concludes three things: 1. How vivid the thoughts are. 2. How many of those thoughts are guilt or fear based, and 3. How deep into the though do they go. Since very few studies have been done on the subject and very little is known about mind wandering it is still a developing topic in psychology.
Mind-wandering is studied using thought sampling, or simply asking participants what they are thinking about at any given moment. Another way in which mind-wandering has been studied is through the use of behavioral indicators of a lapse in external attention. A common technique is to use the sustained attention to response (SART) task originally developed by Ian Robertson and his colleagues at Trinity College, Dublin to explore deficits in executive control after lesions to the frontal lobe. Since there is no scientific way to measure mind wandering researchers have had to improvise to collect the data they needed. One process used was to simply give patients something to focus on and then at different times ask them what they were thinking about. Those who were not thinking about what was given to them were considered “wandering”. Other researchers tried to use technology such as an fMRI to see the changes in brain function and to plot in the brain where this phenomenon occurs, but the results were inconclusive. In the 1980s Eric Klinger conducted a study on what people day dreamed about. In his findings he concluded that in the event of mind wandering people think of ordinary everyday events. He also concluded that people with boring jobs tend to do the most mind wandering most of it to pass the time. He stated that less than 5% of those thoughts involved sexual or violent acts. 
Mind-wandering is important in understanding how the brain produces what William James called the train of thought and the stream of consciousness. This aspect of mind-wandering research is focused on understanding how the brain generates the spontaneous and relatively unconstrained thoughts that are experienced when the mind wanders. One candidate neural mechanism for generating this aspect of experience is a network of regions in the frontal and parietal cortex known as the default network. This network of regions is highly active even when subjects are resting with their eyes closed suggesting a role in generating spontaneous internal thoughts. One relatively controversial result is that periods of mind wandering are associated with increased activation in both the default and executive system a result that implies that mind-wandering may often be goal oriented.
In addition to neural models, computational models of consciousness based on Bernard Baars' Global Workspace theory suggest that mind-wandering, or "spontaneous thought" may involve competition between internally and externally generated activities attempting to gain access to a limited capacity central network.
One important question facing the study of mind-wandering is how it relates to working memory capacity. Generally, reports of task unrelated thought are less frequent when performing tasks that do not demand continuous use of working memory than when performing tasks which do [e.g. 11]. Moreover, individual difference studies demonstrate that when tasks are non-demanding, high levels of working memory capacity are associated with more frequent reports of task unrelated thinking  especially when it is focused on the future .. By contrast, when performing tasks that demand continuous external attention, high levels of working memory capacity are associated with fewer reports of task unrelated thought . Together these data are consistent with the claim that working memory capacity helps sustain a train of thought whether it is generated in response to an perceptual event or is self-generated by the individual themselves. Thus, at least under certain circumstances, the experience of mind-wandering is supported by working memory resources ..