Several years ago I began a blog to document my pursuit of a math degree. I was sidetracked by other things more closely job-related (I wrote a book about libraries, among other things.) It has been three-ish years since I took my last math class. That pursuit, though not abandoned, has been tabled indefinitely. I’m renaming this site to something more generally professional where I can post things related to more than math. Although when math returns, this is where you’ll see it. This little note to for the few of you connected to this site, and serves as the milestone marker between what began here and what lives here now.
Category Archives: When I studied math
Calculus: Formula for inspiration
I started Calculus I this fall. We’re six weeks into the semester, and I just passed my first test (a surprise, considering I could only remember one formula so I used it on every single problem). I haven’t posted since the end of last semester because, honestly, I just wasn’t sure until today that I was going to keep going with this math shenanigan. This is a huge expenditure of time and, despite my enthusiasm, it still does not come naturally. And there are so many things going on.
But this morning a girlfriend told me today that I had inspired a mutual friend to take a class next semester. This made me happy to hear. I was flattered. My ego got a little bigger. My guess is, though, that this mutual friend would probably have taken the class anyway, because he’s that kind of person.
Then this afternoon, I ran into a math classmate on campus and we had a brief exchange about the class–she is struggling, too, but has to complete this class in order to get into grad school. And she inspired me, even though I’m (obviously) already taking the class. Inspiration is a funny thing.
Hebetude, and other words I learned this spring
I’ve had some glorious downtime recently and managed to read Combes, Finn, and Ronell. I looked up all the words I had never seen before, the words I could only make educated guesses about, and the words I wanted to confirm based on context. It’s what I tell my students to do, but it had been a long time since I’ve done it myself. Tedious but fruitful. Also, I’m a little gratified that, of the 37 words, spellcheck claimed 12 did not exist. Here’s my list, which includes the authors’ original sentences.
Anodyne: “Many poems seem to respond to their prompts with the same flat, affectless tone as the Mechanical Turk system itself, offering up anodyne confections of cliché and truism, completing the task of composition in as little as twelve seconds” (Finn 140).
Apeiron: “With this reference to nature, Simondon places himself in a pre-Socratic lineage, which is asserted explicitly in his definition of nature as ‘reality of the possible, in the form of this apeiron from which Anaximander generates all individuated forms.’“ (Combes 46).
Apophenia: “One of the most compelling aspects of games is precisely the seduction of algorithmically ordered universes–spaces where our apophenia can be deeply indulged, where every event and process operates according to a rule set” (Finn 123).
Arbitrage: “These companies are engaged in a form of algorithmic arbitrage, handling the messy details for us and becoming middlemen in every transaction” (Finn 97).
Autopoiesis: “This line of argument evolved into the theory of autopoiesis proposed by philosophers Humberto Maturana and Francisco Varela in the 1970s, the second wave of cybernetics which adapted the pattern-preservation of homeostasis more fully into the context of biological systems” (Finn 28).
Avuncular: “He leaps over the diegetic boundary of the story to touch us in a way that manages to be both avuncular and calculating” (Finn 107).
Badinage: “Algorithmic platforms now shape effectively all cultural production, from authors engaging in obligatory Twitter badinage to promote their new books to the sophisticated systems recommending new products to us” (Finn 53).
Catachrestic: “The point to be considered here, though, is that God needs the catachrestic maneuver in order to love” (Ronell 54).
Chiaroscuro: “The images show the data points of cars and office lights, buildings and structures, weather and movement patterns in long, unmoving chiaroscuro shots” (Finn 105).
Coelenterate: “Although the example of coelenterates on which Simondon bases his description of the individuation of living beings may appear surprising, or even poorly chosen in light of the difficulty in this case of precisely determining the site of individuality, it does not seem to me that the author made this choice lightly” (Combes 24).
Colloidal: “The clay can eventually be transformed into bricks because it possesses colloidal properties that render it capable of conducting a deforming energy while maintaining the coherence of molecular chains, because it is in a sense ‘already in form’ in the swampy earth” (Combes 6).
Concrescence: “Insofar as any technical individual is a system of elements organized to function together and characterized by its tendency toward concretization, we must distance ourselves from human intentionality and enter into the concrescence of technical systems in order to understand the mode of existence of technical objects” (Combes 58).
Consilient: “The spare utility of the search bar or the interfaces for Gmail, YouTube, and other essential services mask a deep infrastructure designed, ultimately, to construct a consilient model of the informational universe. (Finn 66).
Diegetic: “Like other elements of the diegetic background of the show, the Enterprise’s talking computer was meant to be unremarkable and efficient” (Finn 67).
Dyad: “To begin with the operation of individuation is to place oneself at the level of the polarization of a preindividual dyad (formed by an energetic condition and a structural seed)” (Combes, 7).
Elide: “Algorithmic systems and computational models elide away crucial aspects of complex systems with various abstracting gestures, and the things they leave behind reside uneasily in limbo, known and unknown, understood and forgotten at the same time” (Finn 51).
Farragoes: “We tell collective jokes and stories using comment threads and hashtags, building shared narratives and farragoes that can evolve into sophisticated techincal beings in their own right as Internet memes as superficial as #lolcats or as potent as #blacklivesmatter” (Finn 193).
Fiat: “The blockchain relies on a computational fiat by rewarding the miners who bring the most computational power to bear on calculating each new block” (Finn 166).
Fungible: “If software is a metaphor for metaphors, the algorithm becomes the mechanism of translation: “the prism or instrument by which the eternally fungible space of effective computability is focalized and instantiated in a particular program, interface, or user experience” (Finn 35).
Hebetude: “Back at his desk from the Orient, Flaubert famously bounces Charles Bovary’s hopeless hebetude against his wife’s destructive jouissance; the life span of the nonstupid, frustrated and shortened, considerably fades, whereas the dumbest, including the calculating pharmacist, survive” (Ronell 38).
Homeostasis: “Central to this upper ascent is the notion of homeostasis, or the way that a system responds to feedback to preserve its core patterns and identity” (Finn 28).
Hylomorphism: “In this respect, the philosophical tradition boils down to two tendencies, both of which are blind to the reality of being before all individuation: atomism and hylomorphism” (Combes 1).
Hypostasis: “Could we not avoid this hypostasis of a ‘sense of becoming’ wherein normativity culminates in the notion of ‘error against becoming’?” (Combes 62).
Imbrication: “Google’s near omni-presence online, its imbrication in countless cultural systems that do not merely enable but effectively define certain cultural fields of play for billions of people, make this more than just a suggestion service or even a sophisticated form of advertising” (Finn 74).
Inchoate: “Thus the animal appears to the observer of individuation as ‘an inchoate plant,’ that is, as a plant that was dilated at the very beginning of its becoming;” (Combes 22).
Isomorphic: “Thus, in super-cooled water” (i.e., water remaining liquid at a temperature below its freezing point), the least impurity with a structure isomorphic to that of ice plays the role of a seed for crystallization and suffices to turn the water to ice” (Combes 3).
Littoral: “Part of the work of the Netflix culture machine is to continually course-correct between that narrow aesthetic littoral and the vast ocean of abstraction behind it” (Finn 108).
Ontogenesis: “As is always the case with Simondon, philosophy will remain a philosophy of individuation, an ontogenesis” (Combes 58).
Parallelepipedic: “Now, the clay matter and the parallelepipedic form of the mold are only endpoints of two technological half-trajectories, of two half-chains that, upon being joined, make for the individuation of the clay brick” (Combes 5).
Predation: “The heroes of Lewis’s story are those trying to eliminate the ‘unfair’ predation of HFT algorightsm and create an equal playing field for the trading of securities as they imagine such things ought to be traded” (Finn 153).
Prenoetic: “The preindividual dyad is prenoetic as well, which is to say, it precedes both thought and individual” (Combes 7).
Propitiating: “Yet these tricks come with a script that Siri must learn–for Siri to deliver each punchline we must carefully set up the joke, propitiating the culture machine with appropriate rituals” (Finn 60).
Puerile: “There is something unquestionably Nietzschean about treating practically everyone as puerile and stupid” (though Nietzsche never did so–he credited them with cleverness and, at most, with acting stupid or like Christians, who introduced a substantially new and improved wave of stupidity, revaluating and honoring the stupid idiot: O sancta simplicitas!)” (Ronell 39).
Reticular: “And while ethics is said to be ‘sense of individuation,’ and there is ethics only ‘to the extent that there is information, that is, signification, ethics is simultaneously apprehended as reticular reality, the capacity to link the preindividual in many acts” (Combes 65).
Scholium: “Scholium: The intimacy of the common (chapter title)” (Combes 51).
Stochastic: “Computational systems are developing new capacities for imaginative thinking that may be fundamentally alien to human cognition, including the creation of inferences from millions of statistical variables and the manipulation of systems in stochastic, rapidly changing circumstances that are temporally behind our ability to effectively comprehend” (Finn 55).
Thanatological: “In sum, what confers separate individuality on a living being is its thanatological character–the fact of detaching from the original colony and, after having reproduced, dying at a distance from it” (Combes 24).
There’s a lot in this world about which I am not stupid: practically, I’ve navigated life more or less effectively so far. But more and more often I
notice am annoyed that there is someone at the table who professes to know more about [X] than I do. And the more I am expected to know, the more I question what I think I know. Maybe this is why I am enjoying the math classes: I’m allowed to be stupid* there. I am supposed to be stupid there.
Years ago, a professor was describing the idea of “lines of flight” from 1000 Plateaus, and he said (loosely paraphrased) that it means running headlong through a mountain rather than intentionally trying to go around it. His example was a 3¢ bank fee that you disagreed with. Rather than protesting and not paying it, which would ultimately benefit the bank, you should write a separate check for the 3¢ every time the fee is due. If we all wrote separate checks for these tiny fees, we could cripple the bank by costing it more money to process the fee than the fee itself is worth. Don’t avoid the fee. Force everyone to look at the fee in excruciating detail. Maybe this is what I’m doing with my own mathematical stupidity: running headlong into it and gazing on every horrifying crevice. To what end, I don’t know.
All of this to say: I have finally passed MATH 140: Introduction to Mathematical Analysis. It took me three tries, and I wasn’t entirely sure that I had passed until final grades were posted. I’m registered to take Calculus in the fall. Also, I’m getting better at finding textbook deals, so the book this time was only$180, and I bought the Student Solutions Manual up front, too–that might have saved me last semester, if only it had been “required” and not “recommended.”
The velocity of my stupidity is picking up steam. Maybe even accelerating?
*My use of stupidity is loosely based on what I vaguely remember of Derrida and Ronell. Probably stupidly misinterpreted.
Math as Corpse Pose
What a hiatus. Not long after my last post in October, the election cycle ramped up to such a level of screeching that many of us couldn’t hear ourselves think. And since the election itself, many of us have been struggling just to get out of bed and face the world, much less practice being in and being with the world. And since the inauguration, we’ve been too angry to focus on anything that hasn’t been overtly political or that might smack of self-indulgence in a time of crisis.
But last weekend I managed to pick up and open Manuel Castells’ Networks of Outrage and Hope. And I’m excited again to be on this math journey, even though it has stalled a little. I’m taking MATH 140 for the third time this semester. I dropped it this summer for a lot of good reasons. I took it again in the fall and saw it through all the way to the bitter (BITTER) end when the final exam knocked my barely-passing average down to a D.
So here I am, for, the third time. Things are vaguely familiar, and the repetition of material is replacing my frustration with a sense of calm. Muckelbauer in The Future of Invention talks about the “inventive singularity within repetition itself” (44). He says he is “not so much interested, for example, in getting Plato right,” but rather “in orienting toward the singular rhythms that circulate through his writing” (45). When I think about that, as I struggle to complete literally the same set of problems from the same book for the third time, unaware of everything except my pencil, the calculator, and that smooth, seductive graph paper (I LOVE IT SO MUCH), the repetition does not feel like a waste of time. Far from it. The two-hour block is functioning as a vacuum, as a sensory deprivation tank. Now that I in my third repetition, I can anticipate some quizzes and lectures as smoothly as if we were moving through a daily same-but-different sun salutation sequence. The logarithm as mode of unification, pencil grip as mudra. Trigonometric identities leading to Shavasana. This third-time math class has become a meditative chant through which a hidden rhythm is emerging.
When I am returned to the outside-math world and come face-to-face with (what feels to me like) political madness (for example the multiple readings of Coretta Scott King’s letter by Udall, Warren, Brown, Sanders, Merkley), I think I am able to focus on the emerging rhythm and repetition rather than the cacophony of certain voices and the attempted suppression of certain others. Even in my failure, especially in my failure, this third-time-around math experience is proving to be an especially valuable one when processing the multiple failures of the world around me.
WIDE-EMU: Writing wants reluctance
I’m preparing for the WIDE-EMU conference in a couple of weeks which has a theme of “What does writing want?” My colleague and I have chosen to tentatively answer this question with, “Writing wants reluctance.” For me, I reluctantly write about math (here, on this very blog). As part of the “Phase II: Respond” pre-conference work, this particular post details some of my reluctance toward the writing-via-math project in which I am engaged. This post ends with a plea for your input on my actual presentation at WIDE-EMU.
Reluctance 1: Majoring in math. When I decided last year to enroll at the institution where I teach English and to declare myself a math major, I did not have a very clear rationale for doing so. If I wanted to learn something new, why not attend a seminar in my own field that I could add to my CV? Why math? And if it had to be math, why not join a MOOC or audit a class? The best professional reason I had, as a composition instructor, was that I wanted to better relate to my students by remembering what it felt like to be uncomfortable in a classroom. Humanities classrooms (English, Spanish, history, philosophy) have been my go-to happy places for a long time, so I needed a subject that I had avoided academically. And I needed to feel the same kind of stress, commitment, and humility as students with a lot (only their entire futures) riding on their coursework. Enrolling as a degree-seeking Math major is well outside my comfort zone, costs money, and puts my real transcript at risk: three factors that make this a relatively authentic experience.
Reluctance 2: Blogging. The decision to blog about my math journey had a clearer rationale. I frequently ask my students to write publicly, I require that they share drafts, and I offer points for engaging in reflection. But many of them are as uncomfortable writing about my assignments as I am writing about math: I don’t know how to write about math. I don’t know how to relate basic math to the things I do know. I don’t know who my audience is, what they already know, or what they want to read. My attempts to make it “meaningful” are kludgy, stilted, and sophomoric, and posting these attempts online has been mortifying. And I have all of these doubts with every single post, despite the fact that I am an enthusiastic student and am thoroughly enjoying learning basic algebra. I hit “publish” with reluctance, every single time. For many of my students, the experience of writing publicly in a composition course probably feels similar. I’m not sure how to address yet the affective and effective role of reluctance on this writing, but I can feel it at work. Further down the road, I will work on expressing that more clearly.
Reluctance 3: Asking for help. I am approaching my few minutes at the front of a room during WIDE-EMU as my chance to give a “classroom presentation” in which I reluctantly-enthusiastically try to explain, in a meaningful and interesting way, a basic mathematical concept on which I have a tenuous grasp and that somehow relates to writing (maybe magnetic reluctance?). If you have any suggestions, requests, words of encouragement, or cautions, please feel free to comment on this blog post.
PS: I passed my first test of the semester and have almost-a-B in MATH 140 right now. Hooray!
Hope springs eternal.
I’m about halfway through Eagleton’s book, Hope Without Optimism. Optimism, it seems, is a vacuous, ungrounded belief that everything will be ok. Everything will work out for the best. It’s an attitude and an outlook. And when things don’t work out for the best, they have to be quickly recast as actually the best but we didn’t know it right away (the “what doesn’t kill you makes you stronger” kind of thing). Eagleton is not a fan of optimism. Neither am I.
Hope, on the other hand, requires a lot of work and for the most part, has very little to do with optimism. You can be hopeful without being optimistic. You can hope desperately for something, knowing full well that it likely won’t come to pass. And hope requires that we acknowledge that things might not work out for the best. That doesn’t mean we should quit. Not at all. There is a realism and a drive implied with hope that optimism doesn’t require. Hopeful people hold a certain fidelity to the virtue of hope. The whole idea is to forge ahead in a hopeful way, despite the presence or lack of optimism.
I’ve begun MATH 140 for the second time. So far, the material is familiar and I am passing, but I’m certainly not “acing” this course the way I expected–given that his is my second time through. And, of course, life is again getting in the way in all kinds of wonderful and insidious ways.
However: I will remain hopeful. Not optimistic. But unflaggingly hopeful.
Dropping like a hot potato (or: This was a Bad Plan.)
The summer math class ended in disaster, or what I (as a teacher) might have previously called “a teachable moment”: I dropped the class on the last day possible because I tried to build success on the foundation of a Bad Plan.
I ended up with this Bad Plan for Good Reasons. These Good Reasons may sound vaguely like excuses. But they’re not. Totally not. I’m detailing them here because they make me feel good.
- After registering for Math Class, I was invited to teach one of my favorite classes during the summer session. How could I NOT teach this class?? I love this class. It grew into two sections. And three concurrent summer classes, whether teaching or taking, is too many.
- Then, I was awarded a research grant to visit Ukraine during the fall. A colleague who speaks Ukrainian offered to travel there together, but she was going the week before the summer session. How could I NOT go with a native speaker who could help me translate?? So I flew home the day Math Class started and drove right to campus from the airport, jet-lagged and delirious.
- The week after this summer circus began, I was invited to participate in an edited collection directly related to my research. This was great news. How could I NOT agree?? But it included several summer deadlines, lots of intense thinking, and a few wine-infused conversations.
On top of all these Good Reasons, I was facing the Known Obstacles:
- Summer classes pack 15 weeks of content into 7 weeks of time.
- The class was held from 6:00PM to 10:00PM. PM. The middle of the night.
- Math takes me a long time.
- Math just really takes me a long time.
- Lots of time.
Looking at all this now, it’s obvious that I should have dropped the class right away. My math instructor could see it. He was very kind and after a five-quiz failure streak, he gently suggested that I could consider dropping so that my transcript wasn’t saddled with an F. He suggested that I come by his office to talk about my math goals, because maybe there was a better way for me to achieve whatever it is I’m hoping to achieve. He said I could continue to attend class even after dropping, so that when I did re-enroll into a long semester, I would be as prepared as possible.
Hearing the news that, despite your best efforts, you are very likely to fail is not easy. Delivering the news is worse. But in a world where a single course costs over $1,000 and an F can cause immeasurable problems in a competitive job market, it feels irresponsible not to have this conversation. I’ve discussed Bad Plans with several students over the years because I could see the writing on their walls much more clearly than I could see it on my own. As a chronic Bad Planner, I feel more than a little hypocritical offering others advice on this topic.
I do know, though, that failure for a Bad Planner is relative. Did I fail to meet the requirements of the course? You betcha. But look at all the other things I got done while I was fretting about failing math. Many of us do our best work when we’re looking at it peripherally. And that means the risk of failing whatever we’re looking at head-on.
The fall semester starts next week, and I’m again enrolled in MATH 140. Have I learned anything from this summer’s teachable moment? Debatable. I am again over-committed in a dozen other ways. And I am again underestimating the time commitment. Because technically, I’ve already taken this class once. And this time, it’s in the morning. And I have 15 whole weeks. So I’m pretty confident that this semester will be a success. It just might not be a success when it comes to math.
After a two month hiatus from learning anything new, the summer session careened into view. MATH 140: Introductory Mathematical Analysis started over two weeks ago, and only just now, today, do I have time to take a breath. Initial observation: summer class timelines are not to be taken lightly.
This is the course in which we finish up the algebra begun in MATH 120, and we start trigonometry. How did I not know that trigonometry was just Super Fantastic Geometry? I vaguely remember enjoying geometry in high school, although my only concrete memory is the gift of a pencil that said, “A logarithm is an exponent.”
In trigonometry, we’re learning how to calculate the speed of airplanes, the velocity of tsunami waves, and the ascent of hot air balloons. We can also calculate a ship’s bearings and a satellite’s orbit. Of course, algebra is simmering under the surface of it all: even if I get the concept and pick the right formula, I can’t complete the calculation without stupid PEDMAS poking me in the eye again.* But the ability to look at a triangle on the page and see movement and change in the physical world is powerful. I am in love.
The ability to see movement and change through language is powerful too, and it’s one reason I was an English major from the get-go. These days, I write a lot of things without knowing my words’ trajectories once launched. This blog is one of those things. Many of my social media posts are these things, too. Someone blocked me last week because of a comment I made related to #BlackLivesMatter and the Dallas sniper. Now that I’m blocked, I can’t access the comment to delete or amend it, I can’t respond, and I can’t see what anyone else has written. That ship has sailed, and in which direction I have no idea.
Who knows what other trajectories my writing has taken or what kind of change I have effected, I hope more often for better than for worse. But in just two short weeks of trigonometry, this power pops all over again, clearly and consistently. I am excited to have been reminded that it is sometimes possible to see a large chunk of the world on a relatively small piece of paper.
*Look! I just tried to express a relationship between algebra and trigonometry, which I couldn’t have done six months ago. Related: I still don’t know what calculus means.
Reflection with respect to the why-axis
Mercifully, the semester has ended. People keep asking me (because I keep bringing it up) why I took a math class. Originally, I wanted to better understand some of my favorite theorists and writers. While that’s still true, I don’t know now if it’s entirely true. I’m not at all sure why I’m doing this. With all the time I spent on this course, wouldn’t I have been smarter to do something overtly career-related? Maybe. Probably. I don’t know.
In January, I planned to work ahead so I could linger over important concepts and make astounding connections. But that never happened. It was all I could do to keep up with the basics. I had too much else going on. Everyone does. A writing student wrote something similar in his reflection on my English course. In fact, he described it as “crushing.” I empathize, but I also disagree: a particular course is not crushing. It’s just one variable within a larger societal structure designed to present “crushed” as our natural state of being. (In other words: If my course hadn’t crushed him, something else would have.) Same goes for math. And even when a course is pared down to make room for lingering, students (including myself) will likely absorb that extra time into other, more tangible and measurable commitments.
Despite the difficulty in assessing a good linger, I nonetheless believe in its value. A thoughtful reflection can far outweigh the more easily quantified skills. And so here’s mine:
From the perspective of teaching and student-ing: Doing math problems together in class is super helpful. Sitting on the back row is, generally, the bad idea I always knew it was. Offering to help a student during office hours has huge impact, even if the student never actually comes to office hours. Test anxiety is real, and “eating a good breakfast” doesn’t help. Grading math tests seems to be as labor-intensive as grading essays.
From the perspective of learning: THIS WAS SO HARD. It was a lot of trial-and-error, repetition, and memorization. I’m not advanced enough yet to understand the whys, the causes, or the “meaning” in most of what we learned, and that made it even harder to commit a formula or process to memory. Note to self: You felt the same way when you were learning to knit and could only make square things. Eventually, you did knit a sock. Be patient.
From the perspective of math: With only the very tippiest tip of the iceberg under my belt, I see now that basic math is not the tight narrative I was expecting. I knew the advanced stuff would be hairy and imaginary and unpredictable, but I was naively expecting to find a solid foundation in this basic algebra class–I guess because the last time I tried to learn algebra was in high school where ideas are often presented as immutable Truths. Instead, I see math has the same bunch of tiny little truths with which postmodernism has littered the humanities. I should have known: it’s always turtles all the way down. Not to be overly dramatic, but this is causing some existential angst to flare up. Note to self: Take a breath. The world isn’t any less stable than it was this time last year.
What’s next: I have passed MATH 120a: Algebraic Methods somewhere between the skin of my teeth and the hair on my chinny-chin-chin. In the upcoming summer session, I’m taking MATH 140: Introductory Mathematical Analysis. Despite the awesome course title, I think it’s really just Algebra II since we’re using the same book as 120a. My (likely faulty) expectation is that 140 won’t be as difficult: I won’t have to do so much legwork to get caught up, and the math classroom won’t feel so unfamiliar. However, it’s 15 weeks of material done in 7 weeks. So we’ll see. I’ll check in here during the first week of July.