In the fields of cognitive science and artificial intelligence, the most important unresolved problem concerns the methodology by which the human brain combines concepts from two or more disparate domains. The solution of this problem will result in a dramatic breakthrough in how we perceive human thought and how we can implement it in computing machines. To this day no scientist, technician, or engineer can claim to have a full view of how the human brain can take information about a musical composition for example and combine it with information detailing the rules of a chess game.
It is easy to see that a musical composition can be thought of as a series of symbols written down in a definite order under the constraint of certain rules of harmony. A chess game may be viewed as a series of moves on a chessboard under the constraint of the rules of chess. These movies can easily be transcribed in symbolic form. Musical compositions and chess games can therefore be viewed as a series of symbols written on paper or computer screen. In this way one can view musical composition and chess playing as part of the same category, namely the category that describes how entities in time, here musical notes or chess moves, can be represented by symbols.
But having this knowledge will not allow one to become a good composer and good chess player. For that one requires an understanding of the proper places in conceptual space that both of these activities lie, and how to combine these concepts in highly creative ways. What at first glance may be very disparate domains, musical composition and chess playing could be combined into one or more concepts that retain certain features of each domain but form a compact and effective knowledge base for which to compose music or play chess.
The authors of this book call this process "conceptual blending" and have done an excellent job of presenting to the reader their research and commentary on how the human mind performs this activity. Many readers, especially those who demand their support from cognitive neuroscience, will of course view their opinions as controversial. But as a whole they are a good first step in trying to understand what might be called the combinatorics of concepts. Readers in the artificial intelligence community, especially those that are determined to implement these ideas in real computing machines, may find the book helpful but will no doubt also realize after reading it that much remains to be done for a total understanding of domain-general human thinking.
Some of the examples that the authors use in the book are somewhat elementary but this was no doubt by design so as to make it more accessible to a general audience. There are places where this is not the case, as for example their use of the complex number system as being a "double-scoped network." Imagination plays a big role in conceptual blending, and this sets it apart from mere symbol manipulation, i.e. from the deceptions of the "Eliza" machine. They outline four different types of `blending' or `integration' networks and give real-world examples of each. As one might expect, the blending of concepts is a complex process, with the production of concepts never the result of applying just one mapping. It is also natural to expect that any logical inferences that take place in each of the domains may not survive when these domains are subjected to conceptual blending. The resulting blend may have vestiges (one might call them "shadows") of these inferences but the creative process involved in conceptual blending may result in inferences that are completely at odds with those in the original domains. Along these same lines it would seem that conceptual blending is irreversible, with this irreversibility even more apparent the more "entangled" the blended concepts are. This would raise the question as to the evolutionary advantage or energy requirements of conceptual blending, with the answer to this question no doubt arising from the view that a degree of compression is involved in it. Therefore the recollection/storage of huge knowledge bases becomes unnecessary, due to the ability to blend many ideas or concepts into a compact and useful form.
A natural question to ask is whether these networks can be embedded in the computational paradigm, and if so, how computationally complex this implementation would be in real computing machines. The authors emphasize strongly that conceptual blending is not algorithmic, and so any machine implementation may require new computing paradigms and data structures than what have been developed hitherto. There are many researchers in the artificial intelligence community who are working feverishly to implement conceptual blending in some form or another. These efforts have been classified as "artificial general intelligence" and although most of this activity is outside of the realm of the academia, it has attracted the attention of many highly talented (and courageous) individuals.
It might be tempting to view the theory of conceptual blending as outlined in this book as being one that could be easily viewed in terms of the field of category theory in mathematics. But in the latter concepts in one domain are related to another by "functors" that retain most the logic of each domain. Conceptual blending on the contrary mixes up this information and creates objects that could be very dissimilar to the ones in the starting domains. Of course, this does not mean that some sort of generalized category theory could not be invented that would emulate most of the features of conceptual blending. This would be an interesting research project for those who want to give the theory of conceptual blending a more rigorous mathematical foundation. In this regard a branch of mathematics called `topos theory' may be of assistance here.
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