Wang, Xiwen 2021 English Thesis A Neighborhood of the Missing Knot Advisor Cassandra Cleghorn Additional Advisor Access None of the above Contains Copyrighted Material? No Release Restrictions release now Authenticated Access A NEIGHBORHOOD OF THE MISSING KNOT by XIWEN WANG Cassandra Cleghorn, Advisor A thesis submitted in partial fulfillment of the requirements for the Degree of Bachelor of Arts with Honors in English WILLIAMS COLLEGE Williamstown, Massachusetts February 22, 2021 Contents #1 Eversion Proposition .................................................................................................................. 1 #2 When Knots Becomes Personal ............................................................................................... 13 #3 On Sleeping on It ..................................................................................................................... 27 #4 Aloft the Confirmed Knot Tier ................................................................................................ 39 #5 A Neighborhood of the Missing Knot ..................................................................................... 55 Acknowledgements ....................................................................................................................... 69 Bibliography ................................................................................................................................. 70 knot n. complex 46.2 v. join 47.5 tangle, tangled skein, mess, snarl; couple, pair, accouple, copulate, knot, Gordian knot; maze, meander, conjugate, marry, link, yoke, knot, Chinese puzzle, labyrinth; Rube splice, tie, chain, bracket; put Goldberg contraption, wheels within together, fix together, lay together, wheels; rat’s nest, can of worms, piece together, clap together, tack snake pit. together, stick together, lump connection 47.3 together, roll into one. attachment; binding, bonding, gluing, sticking, tieing, lashing, trussing, girding, hooking, clasping, zipping, buckling, buttoning. dilemma 731.6 paradox, oxymoron; asses’ bridge, pons asinorum. puzzle 549.8 knotty point, crux, point to be solved; puzzler, poser, brain twister or teaser, sticker; mind-boggler, floorer or stumper; nut to crack, hard or tough nut to crack; tough proposition, “a perfect nonplus and baffle to all human understanding” [Southey]. —Roget’s International Thesaurus, fourth edition #1 Eversion Proposition If you want to study Zen, you should forget all your previous ideas and just practice zazen and see what kind of experience you have in your practice. That is naturalness. Sometimes we say nyu nan shin, “soft or flexible mind.” As long as you have some fixed idea or are caught by some habitual way of doing things, you cannot appreciate things in their true sense. —Shunryu Suzuki, Zen Mind, Beginner’s Mind On Tuesday nights, I attend a knot theory research group. My Knot Friend and I bike to the math building after dinner, plonk our bags on the floor of the common room, and join the group huddled before the board. It’s only the third time we’ve met, but already I’m not sure what I’m doing there. I’m staring blankly at the flurry of chalk when Professor Adams asks me, “Do you buy this?” I open my mouth, seconds of silence elapse. He smiles and says, “You haven’t decided yet.” We’re supposed to be theorizing virtual triple crossing knots, a new type of knot which grew out of an office hour conversation between Professor Adams and his thesis student Jonah. Questions about its definition and properties were deemed sufficiently interesting to warrant exploration in a paper. The next week in Intro to Knot Theory, Professor Adams passed around a sign-up sheet. I was curious what a mathematician’s work looked like, how math is made. I would lurk, for journalistic purposes, I convinced myself. At our first meeting, Professor Adams 1 said that there were no stupid questions, that he knew about virtual triple crossing knots as much as we did. Our help was enlisted. Passive observation, it seemed, was not an option. But so far I’ve made no contribution. I’m still tripping over the very idea of virtual knots, the imaginary numbers of knot theory. How to wrap one’s head around it? Bear with me: take a rope, put a knot in it, and glue the two ends together. There, we have one of the simplest knots, the trefoil. That’s knot theory 101. At each point where the rope intersects in the diagram, one strand must go over, and another strand must go under. These intersections are called classical crossings. A virtual crossing, however, looks like this: We can never realize a virtual knot out of a rope in the real world, but mathematicians have knitted an entire field out of these virtual knots. The strands in a virtual crossing are neither under nor over. But what on earth does this mean? Knots continue to flash in the back of my eyes as I hurry across campus to the Zendo for my meditation session. Students and townies on zafus and wooden seiza benches already line the small, dim room. Our teacher, Bernie kneels in the center, his eyes closed. I tuck myself into a corner, and notice the resemblance he bears in his thin, shaved-headed equanimity to the buddha in a drawing on the wall, loosely robed, meditating with eyes closed, the back of one hand resting in the palm of the other, thumbs lightly pointed together before a protruding belly. 2 As usual, the session begins with a guided meditation: To settle into your posture, take a few deep breaths. Let your shoulders rise and fall. As you inhale, imagine a string running along your spine, extending out from the top of your head, pulling you upward; as you exhale, imagine your spine as a coat rack, and let your whole body just hang. Here we go. Do not fall asleep again today. Let the sludge settle . In the next minute or so, I’d like you to open yourself up to all the sounds in the environment. Just hear, let all the sounds pass through your body. Well, I hear laughter from the interfaith common room. A guy is speaking and girls are laughing. Whirl of the ventilation system. Breathing of the lady to my right. Breathing. A rustle of clothes. A swallow. What else . a cough. More laughter. Bernie’s deep voice—I really need to start my essay later tonight. Why am I doing this at this hour? When you notice that you are carried away by a thought, just label it with the phrase “having a thought” and repeat, as verbatim as you can, the thought you just had. “Having a thought: Meditation is hard.” “Having a thought: I can’t do this.” Then, gently return to the open listening, to the sounds of the environment. Having a thought: planning, planning. A deep breath. Having a thought: what was going on there with that isotopy problem? Having a thought: this is not the time to think about knots. Another: at least wait until you have pen and paper. And: mechanical revving in the room . So now I’d like you to bring your awareness to your breath. Feel the passage of the air over the soft tissue inside your nose. See how granular and moment-by-moment you can make your sensation. Sense the difference of the beginning, the middle, and the end of each inhalation and exhalation. 3 Okay . Breathing in, a cool, minty sensation. Breathing out, warmth. Breathing in, a prick, discomfort, stretchiness. Breathing out, not much to note. How much more granular can I go? Here’s a question: why are these two nubbins isotopic? When Bernie rings the bell at the end of the meditation, the string running up my spine has long tied itself into a knot. I thought I had an inkling of a solution to the isotopy problem— thinking of the two nubbins as extremely malleable rubber, a way to deform one into the other without cutting and gluing. Maybe I can just pinch in here, bring that part over . But then my mind’s eye isn’t convinced this is legal . In the infinite catch and throw of meditation, that night I failed. ! The recent Tuesday night series marks my third attempt at getting into meditation, and I must admit, what I’ve most enjoyed this time round is the logic behind it, though I hesitate to use this word. Meditation is about seeing what I otherwise cannot see. Let me explain: it took me a while to make peace with the fact that my mind wanders during sitting. But that’s what the mind does, and in fact, it is never the point of meditation to suppress thinking. Instead, meditation is largely about entering a state where we can best observe not just the thoughts themselves, but their patterns. When I attune my attention to sounds in the environment and sensations in my body, I invite the agitated glass of river water that is my mind to settle. When thoughts float up and swim into my consciousness, I try to label each with curiosity. I say, having a thought. This 4 tag is a gentle reminder that whatever the thought is, however gripping and compelling it may seem, in the end it is just a thought. “Having a thought: I suck at math.” This micro-exercise returns our thought-beliefs to their proper status. It is not about disbelieving; it is about awareness of the possibility that “I suck at math” might not be true. Thought labeling aims to dissociate thoughts from beliefs. The hope is that, if we can just notice such self-beliefs for what they are, instead of believing them as truth, we can start to imagine a roomier relationship between our judgements and ourselves. Eventually, I might see that I am not the whirlpool in the glass; I am the water where grit and dirt and sand act out their little drama. I am the empty sky where clouds drift through. And Annie Dillard’s formulation: “I am the skin of water the wind plays over.” It seems that I resort to the word “see” a lot when I describe meditation, when in fact it is hardly visual as a practice. We close our eyes and privilege the other senses: the chill of a breeze, the sting near a knee cap, the tingle in the nostrils, the buzz of a bug.