On the Interconnectedness of Knowledge

east of eden

Note: This piece has been adapted into a blog post from an essay I wrote earlier this year; therefore, parts of it are semi-academic in nature.

Introduction:

“’The weight of knowledge is too great for one mind to absorb.   He saw a time when one man would know only one little fragment, but he would know it well’”

– Lee from East of Eden

In his masterpiece, East of Eden (1952), John Steinbeck communicates these thoughts on knowledge and education in today’s western society: the age of specialization is on us in a way like never before.  The education system in the western world reflects this reality.  Though education differs slightly depending on culture and country, the current student proceeds through his academic life in much the same way.  The student begins in Primary school, more commonly known as elementary school.  At this stage, the student learns the basics of a wide range of subjects.  In other words, the breadth of the subjects is large while the depth of each subject remains fairly shallow.  The student follows Primary school with Secondary school (e.g. high school) where he is still taught a large number of subjects, going slightly deeper into each one.  However, the classes are still fairly basic: the math and science and English classes that are all necessary.  The student finally proceeds into the schooling that he sets his eyes on throughout his academic life: University level schooling.  When a student moves into a university, a near necessity in today’s working world, he must choose his academic discipline, or specialization.  Here, a shift occurs.  Now the classes the student takes cover a very small breadth, but each class goes into great depth and detail.  In essence, the education system forces a decision upon the student to choose one specific interest, typically in either the humanities or the sciences, to specialize in.  The pressure placed on students concerning their education reflects the separation of art and science in our culture through the forced specialization.

A more specific example of the separation of arts and sciences arrives when one takes a look at mathematics and literature.  Placed on opposite ends of the spectrum, math and literature seem to be nearly opposite in their nature; yet, surprising to many, several literary giants also excelled and delved deep into the field of mathematics.  In an attempt to bridge the gap between these two fields of study, I will take a brief look at the short story fiction of David Foster Wallace and Jorge Luis Borges, two men who embrace the seemingly contradictory disciplines of math and literature, and whose endeavors into these fields affect their short stories in both content and style.

David Foster Wallace

david FostWal

David Foster Wallace, a prominent figure in contemporary literature, never studied merely literature.  An avid student of mathematics, logic, and philosophy, Wallace became well versed in many academic disciplines.  D.T. Max, in his biography of David Foster Wallace Every Love Story is a Ghost Story (2012), describes Wallace as one who always excelled at math theory and logic despite his eventual decision to switch his major fields of study to solely philosophy and creative writing.  However, Wallace never fully left the realm of mathematical theory.  In an interview with Michael Silverblatt, a broadcaster in Los Angeles, Wallace admits to his dependence on a mathematical model for his masterpiece, Infinite Jest (1996): “It’s actually structured like something called a Sierpinski Gasket, which is a very primitive kind of pyramidical fractal.”  Though the influence may be less complex, Wallace’s short story “Good Old Neon” (2001) also possesses much mathematical and logical influence from its author.

In “Good Old Neon,” Wallace tells of the events leading up to a man’s suicide through the eyes of that man post mortem.  Wallace’s knowledge of mathematics and logic appears quickly in the content of this story.  As the narrator shares his warped thoughts, he traps himself in an endless number of paradoxes, or arguments producing inconsistencies.  The “fraudulence paradox” acts as the major paradox the narrator cannot avoid: “The fraudulence paradox was that the more time and effort you put into trying to appear impressive or attractive to other people, the less impressive or attractive you felt inside—you were a fraud.  And the more of a fraud you felt like, the harder you tried to convey an impressive or likable image of yourself.”  The narrator continues incessantly, “Logically, you would think that the moment a supposedly intelligent nineteen-year-old became aware of this paradox, he’d stop being a fraud and just settle for being himself….But here was the other, higher-order paradox which didn’t even have a form or name—I didn’t, I couldn’t.”  Wallace layers paradoxes here through his narrator, who, after writing about one of the major paradoxes in his life, trumps it with yet another paradox.

The paradoxes do not exist solely in the mind as Wallace embeds several paradoxes inside of the narrator’s actions.  For example, the narrator recounts his decision to go to counseling, or, as he calls it, analysis: “Later I was in analysis, I tried analysis like almost everybody else then in their late twenties who’d made some money or had a family or whatever they thought they wanted and still didn’t feel that they were happy.”  However, briefly following this statement the narrator admits, “I remember I spent maybe the first twenty times or so in analysis acting all open and candid but in reality sort of fencing with him or leading him around by the nose….And yet I wanted help and really was there to try to get help”  The narrator’s actions contradict each other: he goes to counseling for help yet does not look for help through this counseling for months.  Wallace plants another paradox through the narrator’s claims to be a complete fraud: “My whole life I’ve been a fraud.”  However, his writings, including his admittance to fraud, are brutally honest: “…If nothing else, you’re seeing how exhausting and solipsistic it is to be like this…Of Course, it’s also a really stupid and egotistical way to be, of course you can see this.”  Traditionally, honesty is a trait of an upstanding, respectable person; however, despite the narrator’s honesty, he still views himself as a fraud.

The sheer number of paradoxes in “Good Old Neon” grants the reader a glimpse into the mind of David Foster Wallace.  Paradoxes act as a key element of both math and logic, as they are often used in the critical thinking and creative aspects of these fields.  Understanding paradoxes and realizing the high number Wallace places in the story keys the way the story is read.  When proposed with a paradox, the student must enter into different proposed solutions to the contradiction.  Paradoxes challenge students to progress past mere problem solving and into creative thought to find answers.  Wallace places several paradoxes in this story’s content, thus creating a similar affect on the reader.  The paradoxes challenge the reader to process through the story in a creative mindset, causing one to propose answers to the paradox of the story itself.

Wallace’s mathematical and logical sides are also on display stylistically.  The narrator’s diction contains many mathematical terms: “I told him that was maybe a little simplistic but basically accurate.”  The narrator continues on to refer to a “fraudulent, calculating part of my brain firing away all the time.”  Wallace’s character bears influence from a mathematical creator, using words such as “simplistic,” “accurate,” and “calculating” frequently. Wallace also provides many paradoxes implicitly through the story’s style.  The first major paradox concerns the narrator’s timeline.  The narrator claims to be writing this after his death: “…it gets a lot more interesting when I get to the part where I kill myself and discover what happens immediately after a person dies.”  Time is linear, yet the narrator’s existence outside of time is a mathematical paradox.  Further, in comparison to the narrator’s existence outside of time, the actual reading of the story becomes paradoxical: the act of reading must have a beginning and an end, two traits of linear time.  Ultimately, Wallace presents the reader with a story riddled with paradoxes reflective of his studies in math and logic.

Jorge Luis Borges

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Jorge Luis Borges, an Argentine author, progressed far into the field of mathematics, an endeavor displayed in his short fiction as many of his stories stem from mathematical ideas.  In a lecture recorded in Borges and Mathematics (2011), Guillermo Martinez explains that Borges, at the very least, understood “the logical paradoxes, the question of the diverse orders of infinity, some basic problems in topology, and the theory of probability.”  Further, Martinez asserts the most vital fact about Borges involvement in mathematics: “…Borges showed that he was also aware of what at least in those days was a crucial, controversial, and keenly debated topic in the foundations of mathematics: the question of what is true versus what is demonstrable.”  Borges took mathematics seriously, and that interest weaves its way deeply into his writings.

In “The Book of Sand” (1975), Borges roots the very essence of the story in a mathematical idea: infinity, or something without limit or end.  The narrator purchases a book without beginning or end from a stranger who appears on his doorstep.  In other words, the book is infinite: “The stranger asked me to find the first page.  I laid my left hand on the cover and, trying to put my thumb on the flyleaf, I opened the book.  It was useless.  Every time I tried, a number of pages came between the cover and my thumb.”  Borges introduces infinity through this book, and translates this mathematical idea into real life as the character obsesses over this book: “I showed no one my treasure.  To the luck of owning it was added the fear of having it stolen, and then the misgiving that it might not truly be infinite.”  Borges uses infinity much like a mathematician experiments with a variable.  He introduces infinity into this character’s life, and then follows the variable to its end solution.  The variable sets the narrator on the path of obsession; attempting to comprehend his new reality, he states, “I set about listing them alphabetically in a notebook, which I was not long in filling up.”  Borges’ variable eventually leads the narrator to the only real solution to his problem, ridding himself of this book.

Though the idea of infinity is the most explicit presence of mathematics, it by no means stands alone as Borges also introduces problem solving.  In mathematics, many problems have answers; one answer is right, another is wrong.  However, other math problems, specifically in upper level mathematics, do not necessarily have exact answers.  Some problems have infinite answers, while others have no answers at all.  The narrator obtains this unique book for a seemingly small price, a pension check and a Bible, essentially the same price the stranger claims he obtained the book for.  The nature of these trades correlates to this mathematical idea of problem solving.  The Bible acts as a book many look to for specific answers on life; in both trades, a book of answers is exchanged for a book of endless questions.  The narrator’s account of the stranger hints at the ultimate result of the Book of Sand: “He paused awhile before speaking. A kind of gloom emanated from him—as it does now from me.”  The narrator, as he is led by this book into a life with no answers, eventually realizes the nature of this book: “Summer came and went, and I realized that the book was monstrous…I felt that the book was a nightmarish object, an obscene thing that affronted and tainted reality itself .”   The narrator finds himself with a truly infinite problem, one that has no answer, and acts in contrast to the book he trades, his Bible.  Problem solving becomes an important theme for this narrator as he loses himself in a place where nothing can be solved.

Stylistically, Borges employs technique reflective of his mathematical knowledge.  He opens the story with definitions of a line and plane, immediately placing mathematics, specifically the idea of infinity, on the mind of the reader: “The line is made up of an infinite number of points; the plane of an infinite number of lines; the volume of an infinite number of planes; the hypervolume of an infinite number of volumes.”  Borges also appropriates an interesting amount of the story to the encounter with the stranger in comparison to the narrator’s struggle with his infinite book.  Ironically, Borges spends a mere four paragraphs with the narrator once he enters the book of infinity, whereas the majority of the story takes place before this moment.  Quickly after obtaining the book, the narrator admits, “A prisoner of the book, I almost never went out anymore.”  Through the ironic allotment, Borges communicates just how quickly one can become lost in the realm of infinity, a place sparse with answers.

Conclusion

In western cultures at large, the academic disciplines have been separated.  The journalist Alexander Nazaryan puts it bluntly in his piece, “Why Writers Should Learn Math” (2012): “By the time you’re old enough to drive, you’ve likely decided which region of the brain you plan to use in your adult life, and which you want nothing to do with beyond the minimum requirements imposed by modern society.”  Experts of disciplines rarely seem to interest themselves in the apparent opposite academic field.  However, more similarities exist than one would see at first glance.  In similar fashion, math, science, and English all start at the same place: the basics.  For math, the basics are simple arithmetic; for science, knowledge of basic concepts such as elements and atoms; for English, grammar and spelling take on this title.  Yet all three disciplines end in similar places: discovery and creation.

Stephen King, in his half memoir, half how-to book On Writing (2000), describes the process of discovery in literature: “good story ideas seem to come quite literally from nowhere, sailing at you right out of the empty sky: two previously unrelated ideas come together and make something new under the sun.  Your job isn’t to find these ideas, but to recognize them when they show up.”  King’s description sounds eerily similar to the process of scientific or mathematical discovery: the science is present; the scientist’s job is not to create that science, but to merely recognize and uncover it when he sees it.  Specialization is a reality of the current world we live in.  As more students pursue graduate degrees, the trend will only continue, and I do not propose that this is necessarily a bad movement.  However, I do believe we would do well to look at the connections between fields of studies and attempt to be knowledgeable in more than merely one field.  Authors such as David Foster Wallace and Jorge Luis Borges shine as examples of men who pursued a breadth of knowledge, and that pursuit shaped and affected their art.

I return to East of Eden as I find Steinbeck’s thoughts on specialization particularly intriguing: “’Maybe the knowledge is too great and maybe men are growing too small,’ said Lee. ‘Maybe, kneeling down to atoms, they’re becoming atom-sized in their souls.  Maybe a specialist is only a coward, afraid to look out of his little cage.  And think what any specialist misses—the whole world over his fence.’”  Steinbeck writes from an extremist point of view here.  However, I urge everyone to lift your head up for a minute, take your eyes off what you’ve built your cage around, and turn your gaze to the rest of the world.  Who knows, you might just find something of value.

Source Material:

The Book of Sand by Jorge Luis Borges

Oblivion by David Foster Wallace

East of Eden by John Steinbeck

On Writing: A memoir of the Craft by Stephen King

Borges and Mathematics by Guillermo Martinez

Every Love Story is a Ghost Story: A Life of David Foster Wallace by D.T. Max

“Why Fiction Writers Should Learn Math” by Alexander Narzaryan

“Bookworm” Interview by Michael Silverblatt

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Posted on by Joseph Amagliani in Assorted Wisdom, Books, Featured, Misc. Posts

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