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Mathematical structures of natural intelligence
Neuman Y., Springer International Publishing, New York, NY, 2017. 173 pp. Type: Book (978-3-319682-45-7)
Date Reviewed: Sep 10 2019

The author of this enthusiastically written book does not promote fashionable buzzwords; furthermore, he clearly distinguishes natural intelligence from artificial intelligence (AI). He emphasizes that “our world should be considered in terms of relational patterning,” and notes that “it is much more reasonable to assume that the mind is grounded in some basic ability to form structures from which all types of structures grow and adapt in real time.” Thus, Neuman appropriately considers category theory to be the mathematical basis of natural intelligence and, more generally, a powerful tool for building models since “objects/elements [in category theory] are to be defined through ... relations and not vice versa.” The book is terse but self-contained and does not assume any prior knowledge of category theory. Neuman explains some important category theory concepts using quite a few nice and varied examples.

Neuman is not alone in this approach to modeling complex phenomena. Conceptually, when he properly observes that the main benefit of his book is a “better understanding [of] the way natural intelligence identifies and forms orders existing in the world,” F. A. Hayek’s outstanding contributions (assembled, for example, in [1]) immediately come to mind (regretfully, however, Neuman does not mention Hayek). Category theory as a mathematical foundation for the study of complex orders has been convincingly demonstrated, for example, in an excellent (and also self-contained) book [2] with a wealth of interesting examples from biological and social systems (noted but not further discussed in the book under review), and also in a more recent collection [3]. Furthermore, proper observations such as this may remind readers of the definitions of abstraction and viewpoints in the Reference Model of Open Distributed Processing (RM-ODP)--an international standard successfully used in business and other system modeling:

When we ... model the behavior of a complex modeling system, such as the immune system or the human brain, we usually do so by focusing on a limited spectrum of this modeling activity and by using a simplified model of [this] modeling process.

Neuman discusses at length emergent properties of the whole that “cannot be deduced from the sum of its parts” (compare also with [1,2,3]), and also presents articulated surveys of existing work, for example, on the concept of local integration of information “before being propagated ... to higher levels of the network assembly” (in this context, I would like to refer to another great contribution by Hayek [4]). Regretfully, these concepts, while essential for understanding and modeling, may not be too popular in the worlds of automation and tool-based approaches. On a somewhat conceptually similar note, the author observes:

Increasing complexity is highly important as it is through this expanding field of possibilities that creativity, novelty, and the potential for new solutions become possible. [...] [T]he discourse concerning artificial intelligence systems is usually occupied with reducing the combinatorial complexity of well-defined tasks. Natural intelligence ... involves both a decrease and an increase in complexity.

For another example of an approach that cannot and should not be automated, Neuman refers to and explains Bateson’s concept of “difference that makes a difference” [5]--“the basic unit of the mind,” observing again that,

The path chosen by natural intelligence is to focus on meaningful relations ... and to consider the “objects” ... as secondary, in such a way that they can be substituted ... without tricking the mind.

This corresponds very well with the concept of “structure over content,” used, for example, in RM-ODP for template definition and instantiation, as well as with Manin’s bipartite structure of scientific theories [6]. When the author compares natural intelligence with machine learning, he observes that “[t]he starlings have not developed theories about flying in a flock ... and they don’t have to justify their flying empirically in academic conferences with other birds.” Finally, one can only agree with Neuman’s suggestion that “[t]he idea that the laws of probability theory are somehow encoded in the mind may not be the first hypothesis we want to generate” (compare with Hayek’s observation that statistics is incapable of dealing with phenomena of organized complexity [1]), as well as with Neuman’s emphasis on varying and potentially incongruent pictures of the world that, again, exemplifies the difference between natural and artificial intelligence.

In summary, I would like to agree with Neuman’s “old definition of intelligence” as “the ability to know ‘general truths,’ here interpreted as patterns, holds both for the virus and the human being,” and with his proposal that “reader[s] may find the theoretical Lego blocks provided herein relevant for modeling processes ..., for addressing real-world challenges, and for developing practical solutions to those challenges.”

Reviewer:  H. I. Kilov Review #: CR146687 (1912-0422)
1) Hayek, F. A.; Caldwell, B. (Ed.) The market and other orders. The University of Chicago Press, Chicago, IL, 2014.
2) Ehresmann, A. C.; Vanbremeersch, J.-P. Memory evolutive systems: hierarchy, emergence, cognition. Elsevier, Boston, MA, 2007.
3) Landry, E. (Ed.) Categories for the working philosopher. Oxford University Press, Oxford, UK, 2017.
4) Hayek, F. A.; Vanberg, V. J. (Ed.) The sensory order and other writings on the foundations of theoretical psychology. The University of Chicago Press, Chicago, IL, 2017.
5) Hoffmeyer, J. (Ed.) A legacy for living systems: Gregory Bateson as precursor to biosemiotics. Springer, New York, NY, 2008.
6) Manin, Y. Cognition and complexity. In: Information and complexity. 338-352, World Scientific, 2017.
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