Despite the desire of many high school juniors to "go against the system" at least when it comes to the college process, the fact is that our world is full of systems that we work in and with in order to make anything meaningful at all. Scientists define isolated systems to get a perfect constant of the law of conservation of energy, but even ballet dancers follow a system of dance moves and patterns in their artistic form. But why does any of this matter? Can't we just all destroy the "system" of rules and formalities and find the truest science and dance without it?
In his book Godel, Escher, Bach, Douglas Hofstadter explores the idea of an isomorphism, that is, (in the mathematical sense of the word) a one to one correspondent between two sets. In layman's terms, that's a system that helps you understand another system that is more cryptic.
For example, if I give you a pattern of a triangle followed by a square, a pentagon and a hexagon, you may understand that "system" as 3,4,5,6 in terms of the number of sides on the square. That system of numbers (3,4,5,6) itself is not the same as that pattern, but rather it is a separate system that helps you understand the pattern because it holds a one to one correspondence with the original. This is an isomorphism. Also loosely correlating to an analogy, isomorphic systems help you work within another. Just like I know that the next shape will have 7 sides, if given "cat:mouse is as "dog:--," I can know that the -- is cat. So now we know what an isomorphism is in a formal sense, but what does this mean for the "informal" things that (arguably) matter more? In the following lines I will argue that all systems we have in place are our isomorphic attempts to understand the system that is reality.
In his theory of language, linguist Ferdinand de Saussure (and later, in 1956, Roland Jakobson) argued that all language is actually metaphor or metonymy. Calling back to the title of this post, we may uses the example of a "cat." The English word "cat," as he argues, although attempting to use to the same idea as the Egyptian "mau," actually communicates a fundamentally different idea, that is, the idea of a graceful being whose values according to Egyptian culture is completely different from the Anglo-American conception of a "cat." Postmodern philosophers cite this phenomena to claim that language is utterly distinct from reality. However, these academics miss one key point, which is that while language as a system is distinct (or rather, separate) from reality, it is not indeed contrary to it. Otherwise, I believe we would see more significant differences between the nature of things and the labels we place upon them. Rather, any given system of language is our attempt to parallel and understand reality. Thus, I cite language as an example of our isomorphic attempts to grasp at the true nature of reality.
Art and literature are also clear examples of this. Throughout history, we see groups of people use stories to better comprehend principles and truths around them, ex. myths to explain the origins of the universe. But even on a daily basis this is true. The theory of Narrative Identity in Psychology and hermeneutic epistemology proposes that one's identity is formed by integrating individual life experiences into an over-arching and evolving story of the "self". This happens very early in childhood development and is something I have seen personally while babysitting toddlers, who when alone and/or going to sleep often recount to themselves their daily lives and their future plans for tomorrow. This same idea is spoken about by popular writer Malcom Gladwell. The historical and modern use of art forms such as painting and theater do this very thing either on an individual level or on a scale of a nation, event, or larger idea. Through the use of propagandistic pieces like Death of Marat or the Aeneid, nations and people groups define their identity via a story of courage and power. But aside from clear attempts to define identity, literature and art often reveal deeper truths about reality. In The Seven Basic Plots, Christopher Booker highlights key themes and characteristics present across a wide selection of books, a connection that suggests something greater than just coincidence or plagiarism. Rather, these plot types, which include "Rags to Riches" and "The Quest" are direct reflections of human nature and our connections with the universe.
What I have suggested here sounds like a pretty lofty idea, however, despite the fancy labeling of an "isomorphic system," you probably already realize this on some level. As humans, we crave understanding and use many forms in order to satisfy this craving. But my point is larger than this. In creating this deeply layered connection between all these "areas of knowledge" and our attempt to understand the universe, I have really suggested something greater. What all of these examples have in common is the idea of a system, a set of connected parts comprising a complex whole. If we are to take anything from these isomorphic systems, it is that the universe itself is a system– it is orderly, has sets of rules, and is able to be understood on some level. Whether this conclusion is true, or whether humanity has completely failed in creating accurate isomorphisms that can parallel reality... you decide.
Written by Alexandra Kytka.