As for how cognition exists within a larger social environment, this would largely depend on the particular civilization in which the social environment is situated. In a highly developed, technologically advanced society such as the United States, cognition is largely shared via the Internet, the mass media, and hard copy books. Moreover, much of the education of children and adolescents has been entrusted to a specialized class of teaching professionals. In a less advanced society, however, the existence of cognition within a larger social environment would largely be found within oral traditions that are shared among the members of the society; also, much of the dogma that is found within traditional religious scripture might be referred to as a form of "shared cognition." After all, parts of the Old Testament read as though they are instructions for how to survive and prosper in the Iron Age; the consumption of undercooked pork and shellfish in that era could easily lead to an untimely death. Moreover, engaging in "immoral" behaviors such as theft and adultery could easily lead to a prolonged war between different tribal groups in that era. When it comes to the influence that culture exerts upon cognition, this can be seen in the various emphases that different cultures place on certain types of knowledge, and which types of people have the right to certain forms of cognition.
As for contemporary information processing systems that have the potential to make a strong argument for individual level cognitive processing rather than collective processing, one such system would be that of the neural networks that are utilized in deep learning technology. According to Jones (2014): In the 1980s, one better way seemed to be deep learning in neural networks. These systems promised to learn their own rules from scratch, and offered the pleasing symmetry of using brain-inspired mechanics to achieve brain-like function." However, comparing information processing systems that were developed in the late twentieth century with human brains is a bit of a logical fallacy which seems to ignore the fact that human cognition arose as a result of complex evolutionary process, and that humans evolved as a social animal.
As for the claims that have been made about how people learn, this has changed dramatically in the last few decades. According to Sawyer, the predominant educational paradigm until the 1970's was that of "instructionism." In the instructionist paradigm, the student is essentially an "empty vessel" to be "filled" with knowledge passed down to them from established scholars and experts. During this period, the predominant mode of thinking was that students simply needed to be provided with a large volume of facts and formulas for solving common problems, and that there was little active cognitive agency within most students. However, these notion began to quickly change in the 1970's, when the educational sector began to consider that students of all ages learn best when they are given problems to solve on their own, as well as being given information that relates to other bodies of knowledge that they have acquired. Thus began a new framework of student centered learning that was better adapted to the cognitive development of the student, rather than simply passing on large chunks of "accumulated wisdom" to them.
As for how people come to believe what they believe, this is a complex social, cultural, and cognitive process. For instance, if a child is told from birth that there is a "sky god" who watches over all of us, and makes it rain from time to time in order to keep us alive, the young child will probably not question that. Moreover, when they see evidence of this belief, in the form of periodic rainfall that does seem to "perk up" all of the surrounding greenery, they will process this as "empirical confirmation" of the existence of a sky god who sends rations of water to people from time to time.
As for how cognitive science can be applied to current real world problems, one of the most apparent arenas of contribution is in the realm of criminal justice. Often, law enforcement and the courts rely on eyewitness testimony of victims or passersby to convict people of crimes, but as it turns out, they often convict and sentence the wrong individual. In these cases, the witnesses are not out to get the defendant or being malicious in any way, but it is clear that human memory is subject to numerous distortions. As Loftus (2003) observes, "Today, hundreds of studies have been published documenting memory distortion induced by exposure to misinformation. In these studies, not only have people recalled stop signs as yield signs but they have also recalled nonexistent broken glass and tape recorders, a blue vehicle used in a crime scene as white, Minnie Mouse when they really saw Mickey Mouse, and, most recently, wounded animals (that were not there) near the scene of a tragic terrorist bombing that actually had occurred in Russia a few years earlier. Taken together, these studies show that misinformation can change an individual's recollection in predictable, and sometimes very powerful, ways."
One of the strengths of the contribution of cognitive science to this real world problem is that it will lead to fewer people being wrongfully convicted. On the other hand, it could lead to perfectly legitimate criminal cases being dismissed simply because a witness has a slight distortion in their recall of the event. As for which of the contemporary information processing systems appears to have the most potential for helping to solve real world problems, that would be embodied cognition. Since embodied cognition is the type of system that is most fundamentally similar to actual human thought processes, it has more capacity for understanding the complexity of real world issues.
Bermúdez, J. L. (2014). Cognitive science: An introduction to the science of the mind. Cambridge University Press.
Chalmers, D. J. (1995). The puzzle of conscious experience. Scientific American, 273(6), 80-86.
Jones, N. (2014). Computer science: The learning machines. Nature News, 505(7482), 146.
Loftus, E. F. (2003). Make-believe memories. American Psychologist, 58(11), 867.
Sawyer, R. K. (2006). The new science of learning. The Cambridge handbook of the learning sciences, 1, 18.
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Brain and learning scientist at an international university.