The title of this book, “Quod Erat Demonstrandum” (Q.E.D.), is a Latin term which roughly translates to “that which has been demonstrated”. In mathematics, it is used to indicate that a proof is complete. In general use, it refers to a fact or experience which proves some claim to be true.
With the pieces in this year’s volume, we noticed that our writers were grappling with topics to which there was no clear answer and revealing the limitations of our ability to contend with these issues. In this book, we hope to demonstrate and explore these limitations and to show how, unlike our title suggests, there are many things that cannot be proven, at least within our human capabilities.
As this year’s Editors-in-Chief, we wanted to explore this topic through the dual lenses of mathematics and literature. Julia is a third-year English student with a passion for critical analysis and for asking an annoying amount of questions, while Stephanie identifies as would-be English student, having always intended to study the subject until a pesky (and wonderful) high school math teacher led her astray. Now, she’s a fourth-year honours student in math with a minor in English. What we share, however, is an ardent curiosity and a desire to use our respective disciplines to better understand the world.
Godel’s Incompleteness Theorem is an important result in mathematics that states that there is no set of basic truths, known as axioms, that can be used to prove every mathematical fact. Given any system of axioms, there will always be some statements that are undecidable, meaning they cannot be proven to be true or false. Moreover, it is impossible to prove that a system is consistent — that is, that a system contains no fact that can be proven to be both true and false — using only the axioms of that system. In other words, we cannot prove the consistency of a system from within the system itself.
Mathematics and literature are often seen as incompatible entities, as different from one another as opera and monster truck rallies. Mathematics is your standoffish officemate who always seems to know every single answer at trivia, whereas your pal Literature in marketing — “but, there isn’t just one right answer, you guys” — is the reason your team lost three Wednesdays in a row. But, as demonstrated by Godel’s Theorem, even mathematics, our most rigorous way of categorizing and dissecting the universe, contains significant and unrectifiable ambiguities. For example, within our standard set of mathematical axioms, it is impossible to prove whether any set of numbers has a cardinality (size) larger than the natural numbers (the counting numbers 1, 2, 3…) but smaller than the real numbers (the set of all possible decimal values along an infinite line), even though we know this fact to be false, as it can be proven so using other systems. As a species, we are constantly striving to (and failing at) understanding our lives, our minds, our relationships, our society, and our universe. In this impossible quest, we wield mathematical tools and theorems, but we also brandish books, investigate ideas, and even, on occasion, probe poetry. It won’t be enough, of course — we are too small, too fragile to unravel the universe — but the story of humanity is our ability to try, and that is also the story of this book.
Writing is another way in which we try, and often fail, to comprehend our realities. Science Fiction, as a genre, frequently contends with the unknown. Whether it be interstellar life forms, rogue technological possibilities, or visions of the future, this genre allows its readers to explore possibilities. In this way, Science Fiction highlights how we will never understand all that exists in our universe while simultaneously encouraging its readers and writers to imagine the possibilities and never stop striving for understanding. In this volume of the Arts Review, many of our pieces use their writing similarly to explore the unknown and the various reactions that encountering it can elicit. As such, the introductions to the four chapters of our book use quotes from notable works of Science Fiction to illuminate central ideas and themes. Our minds are fragile, but so too are our lives, our relationships, and our civilizations, and each of these fragilities contribute to our inability to understand both that particular aspect of our world and the wider universe.
The first chapter of this book deals with “The Fragility of the Mind.” This section speaks to the notion that we can’t understand our minds because of the limits of our minds. The pieces here contend with the difficulty in understanding our own limitations as we ourselves are so limited. Whether it be memory, fixation, persuasion, or imagination, these capacities and limitations make it difficult to ever fully understand our own minds. Yet, despite this difficulty, these pieces do not shy away from asking these questions.
Our temporal limitations as human beings are questioned in the second section of this book: “The Fragility of Life.” Here, our writers explore the themes of loss and grief, all the while, keeping in mind the fact that we can never fully understand death because of the limits of our own lives.
In the next chapter, “The Fragility of Relationships,” we move from inside ourselves and look at the often-complex nature of mediating relationships between the self and others. The authors in this chapter use a variety of experiences to explore this theme. In addressing these particular experiences with relationships, complexities and uncertainties are ever-present.
Our final chapter is “The Fragility of Civilization.” The pieces in this section address our world and how we structure it while maintaining the notion that these structures are fragile, unstable, and subject to significant change. In this way, even when looking at that which we have built, we can see how there is great uncertainty in our place in nature and the universe.
There are multiple ways to contend with our inability to understand the universe. We can react with despair, apathy, curiosity, delight, or wonder. We can travel to the far reaches of our understanding, nudging the outer boundaries ever further. Alternatively, we can retreat into its comfortable center, fueled by fear, eyes turned away from the stars. Still too, we can retreat, not into hopelessness, but into ourselves, celebrating and lending meaning to our smallness. Our writers explore these divergent responses in diverse ways. As you read through these pieces, you focus on the writers’ responses but also begin to question you own. If you do choose to grapple with these questions, consider what tools you use to understand the world. What are your axioms? What are the questions that you can’t prove? Much remains to be said before we can claim Q.E.D.