## College Was Not That Terrible Now That I'm Not That Crazy
-Previously, [I wrote about how I was considering going back to San Francisco State University for two semesters](http://zackmdavis.net/blog/2024/05/should-i-finish-my-bachelors-degree/) to finish up my math B.A.
+Previously, [I wrote about how I was considering going back to San Francisco State University for two semesters](http://zackmdavis.net/blog/2024/05/should-i-finish-my-bachelors-degree/) to finish up my Bachelor's degree in math.
So, I did that. I think it was a good decision! I got more out of it than I expected.
### Past Prologue
+I wasn't always like this. Until I quit college the first time, I had had a pretty normal school experience for my social background: public elementary school, then Jewish day school from 5th to 8th grades, then back to public high school, then to the University of California at Santa Cruz before everything changed. It's only in retrospect that there were clues that something was wrong.
+
+It started out fine. I remember in first grade getting a sequence of arithmetic workbooks and going through them much faster than most of the other children, like being on chapter 30 when Chelsea was only on chapter 6. I needed help from the teacher when I got to multi-digit subtraction with borrowing. I remember in second grade, Mrs. Wright had a practice of "reading stars"—for every so many minutes of reading, the name of the book would be written by one of the points of a yellow construction paper five-point star. I earned _so many stars_.
+
+At some point, they stopped giving me workbooks and reading stars, and just had classes, which was obviously worse
+
[TODO—
- * I would say I had a pretty normal school experience—public elementary school, then Jewish day school from 5th–8th grades after my parents thought I was sad in normal school, then public high school.
* I had accepted the necessity of school==education because everyone said so; looking back, there are clues.
* Reading stars and workbooks in 1st–2nd grade (they should have kept doing that!)
* Time in middle school where they let us play games and I thought less of it; the time in high school where he had a class party and I described high school life as "easy" in my Diary
I told myself not to worry about it. The purpose of the "assignment" was to help us to learn about the theory of functions of a complex variable, and I was doing that. Prof. Lai had said in class and in office hours that he trusted us, that he trusted me. If I had wanted to avoid this particular source of moral ambiguity at all costs, but still wanted a Bachelor's degree, I could have taken easier classes for which I wouldn't need so much external assistance. (I didn't even need the credits from this class to graduate.)
-But that would be insane. The thing I was doing now, of jointly trying to maximize math knowledge while also participating in the standard system to help with that, made sense. Minimizing perceived moral ambiguity (which was all in my head) would have been a really stupid goal. Now, so late in life at age 37, I wanted to give myself fully over to not being stupid, even unto the cost of perceived moral ambiguity which was all in my head.
+But that would be insane. The thing I was doing now, of jointly trying to maximize math knowledge while also participating in the standard system to help with that, made sense. Minimizing perceived moral ambiguity (which was all in my head) would have been a really stupid goal. Now, so late in life at age 37, I wanted to give myself fully over to not being stupid, even unto the cost of self-perceived moral ambiguity.
Prof. Lai eschewed in-person exams in favor of take-homes for both the midterm and the final. He said reasonable internet reference usage was allowed, as with the assignments. I didn't ask for further clarification because I had already neurotically asked for clarification about the policy for the assignments once more than was necessary, but resolved to myself that for the take-homes, I would allow myself static websites but obviously no LLMs. I wasn't a grade-grubber; I would give myself the authentic 2010s take-home exam experience and accept the outcome.
Prof. Ross is an outstanding schoolteacher, the best I encountered at SFSU. I choose my words here very carefully. I don't mean he was my favorite professor. I mean that he was good at his job. His lectures were clear and well-prepared, and puncutated with group work on well-designed worksheets (pedogogically superior to the whole class just being lecture). The assignments and tests were fair, and son on.
-On the first day, he brought a cardboard square with color-labeled corners to illustrate the dihedral group. When he asked us how many ways there were to position the square, I said: eight, because the dihedral group for the _n_-gon has 2<em>n</em> elements. On Monday of the second week, Prof. Ross stopped me after class to express disapproval with how I had brought out my copy of Dummit & Foote and referred to Lagrange's theorem during the group worksheet discussion about subgroups of cyclic groups; we hadn't covered that yet. He also criticized my response about the dihedral group from the previous week; those were just words, he said.
+On the first day, he brought a cardboard square with color-labeled corners to illustrate the dihedral group. When he asked us how many ways there were to position the square, I said: eight, because the dihedral group for the _n_-gon has 2<em>n</em> elements. On Monday of the second week, Prof. Ross stopped me after class to express disapproval with how I had brought out my copy of Dummit & Foote and referred to Lagrange's theorem during the group worksheet discussion about subgroups of cyclic groups; we hadn't covered that yet. He also criticized my response about the dihedral group from the previous week; those were just words, he said. I understood the criticism that there's a danger in citing results you or your audience might not understand, but resented the implication that knowledge that hadn't been covered in class was therefore inadmissible.
I asked whether he cared whether I attended class, and he said that the answer was already in the syllabus. (Attendance was worth 5% of the grade.) After that, I mostly stayed home on Mondays, Wednesdays, and Fridays unless there was a quiz (and didn't show up to topology again), which seemed like a mutually agreeable outcome to all parties.
I mostly treated the algebra coursework as an afterthought to the analysis courses I was devoting most of my focus to. I tried to maintain a lead on the weekly algebra assignments (five problems hand-picked by Prof. Ross, not from Gallian), submitting them an average of 5.9 days early—in the spirit of getting it out of the way. [On](http://zackmdavis.net/docs/davis-algebra-assignment02.pdf) [a](http://zackmdavis.net/docs/davis-algebra-assignment05.pdf) [few](http://zackmdavis.net/docs/davis-algebra-assignment07.pdf) [assignments](http://zackmdavis.net/docs/davis-algebra-assignment07.pdf), I wrote some Python to compute orders of elements or cosets of permutation groups in preference to doing it by hand. One week [I started working on the prequisite chapter on polynomial rings](http://zackmdavis.net/docs/polynomial_rings_1.pdf) from the algebraic geometry book Prof. Ross had just written with his partner Prof. Emily Clader, but that was just to show off to Prof. Ross at office hours that I had at least looked at his book; I didn't stick with it.
-The Tutoring and Academic Support Center (TASC) offered tutoring for "Modern Algebra I", so I signed up for weekly tutoring sessions with the TA for the class, not because I needed help to do well in the class, but it was nice to work with someone. Sometimes I did the homework, sometimes we talked about some other algebra topic (from Dummit & Foote, or Ross & Clader that one week), one week I tried to explain my struggles with measure theory. TASC gave out "loyalty program"-style punch cards that bribed students with a choice of between two prizes every three tutoring sessions, which is as patronizing as it sounds, but wondering what the next prize options would be provided a source of anticipation and mystery; I got a pen and a button and a tote bag over the course of the semester.
+The Tutoring and Academic Support Center (TASC) offered tutoring for "Modern Algebra I", so I signed up for weekly tutoring sessions with the TA for the class, not because I needed help to do well in the class, but it was nice to work with someone. Sometimes I did the homework, sometimes we talked about some other algebra topic (from Dummit & Foote, or Ross & Clader that one week), one week I tried to explain my struggles with measure theory. TASC gave out loyalty program–style punch cards that bribed students with a choice of between two prizes every three tutoring sessions, which is as patronizing as it sounds, but wondering what the next prize options would be provided a source of anticipation and mystery; I got a pen and a button and a tote bag over the course of the semester.
I posted a somewhat disappointing 79/90 (87.8%) on the final, mostly due to stupid mistakes or laziness on my part; I hadn't prepped that much. Wracking my brain during a "Give an example of each the [_sic_] following" question on the exam, I was proud to have come up with the quaternions and "even-integer quaternions" as examples of noncommutative rings with and without unity, respectively.
#### "Self, Place, and Knowing: An Introduction to Interdisciplinary Inquiry" (Spring 2025)
-I was able to satisfy the "Area E: Lifelong Learning and Self-Development" gen-ed requirement with an asynchronous online-only class, Prof. Mariana Ferreira's "Self, Place, and Knowing". Whatever expectations I had of a lower-division social studies gen-ed class at San Francisco State University, this felt like a parody of that.
+I was able to satisfy the "Area E: Lifelong Learning and Self-Development" gen-ed requirement with an asynchronous online-only class, Prof. Mariana Ferreira's "Self, Place, and Knowing: An Introduction to Interdisciplinary Inquiry". Whatever expectations I had of a lower-division social studies gen-ed class at San Francisco State University, this felt like a parody of that.
The first few weekly assignments were quizzes on given readings. This already annoyed me: in a synchronous in-person class, a "quiz" is typically closed-book unless otherwise specified. The purpose is to verify that the student did the reading. It would be a perversion of that purpose for the quiz-taker to read the question, and then Ctrl-F in the PDF to find the answer without reading the full text, but there was no provision for stopping that eventuality here.
The first quiz was incredibly poorly written: some of the answers were obvious just from looking at the multiple choice options, and some of them depended on minutiae of the text that a typical reader couldn't reasonably be expected to memorize. (The article quoted several academics in passing, and then the quiz had a question of the form "[name] at [university] expresses concerns about:".) I took it closed-book and got 7/10.
-I posted a question on the class forum asking for clarification on the closed-book issue, and gently complaining about the terrible questions (Subject: "Are the quizzes supposed to be 'open book'? And, question design"). No one replied; I was hoping Prof. Ferreira kept an eye on the forum. I could have inquired with her more directly, but the syllabus said Zoom office hours were by appointment only at 8 _a.m._ Tuesdays—just when I was supposed to be out the door to be on time for "Measure and Integration." I decided not to bother.
+I posted a question on the class forum asking for clarification on the closed-book issue, and gently complaining about the terrible questions (Subject: "Are the quizzes supposed to be 'open book'? And, question design"). No one replied; I was hoping Prof. Ferreira kept an eye on the forum. I could have inquired with her more directly, but the syllabus said Zoom office hours were by appointment only at 8 _a.m._ Tuesdays—just when I was supposed to be out the door to be on time for "Measure and Integration." I didn't bother.
You might question why I even bothered to ask on the forum, given my contempt for grade-grubbing: I could just adhere to a closed-book policy unilaterally and eat the resulting subpar scores. But I had noticed that my cumulative GPA was sitting at 3.47 (down from 3.49 in Spring 2013 because of that C− in "Queer Literatures and Media" last semester), and 3.5 would classify my degree as _cum laude_. Despite everything, I think I did want an A in "Self, Place, and Knowing", and my probability of getting an A was lower if I handicapped myself with moral constraints perceived by myself and probably not anyone else.
-My forum post got no responses. I also did the next two quizzes closed book—except that on the third quiz, I think I succumbed to the temptation to peek at the PDF once, but didn't end up changing my answer as the result of the peek. Was that contrary to the moral law? Was this entire endeavor of finishing the degree now morally tainted by that one moment, however inconsequential it was to any outcome?
+I also did the next two quizzes closed book—except that on the third quiz, I think I succumbed to the temptation to peek at the PDF once, but didn't end up changing my answer as the result of the peek. Was that contrary to the moral law? Was this entire endeavor of finishing the degree now morally tainted by that one moment, however inconsequential it was to any outcome?
-I think part of the reason I peeked was because, in that moment, I was feeling doubtful that the logic of "the word 'quiz' implies closed-book unless otherwise specified" held any force outside of my own head. Maybe "quiz" just meant "collection of questions to answer", and referring back to the reading was expected. The syllabus had been very clear about LLM use being plagiarism, despite how hard that was to enforce. If Prof. Ferreira had expected the quizzes to be closed book on the honor system, wouldn't she have said that in the syllabus, too? The fact that no one had shown any interest in clarifying what the rules were even after I had asked in the most obvious place, suggested that no one cared. I couldn't be in violation of the moral law if "Self, Place, and Knowing" was not a place where the moral law applied.
+I think part of the reason I peeked was because, in that moment, I was feeling doubtful that the logic of "the word 'quiz' implies closed-book unless otherwise specified" held any force outside of my own head. Maybe "quiz" just meant "collection of questions to answer", and it was expected that students would refer back to the reading while completing it. The syllabus had been very clear about LLM use being plagiarism, despite how hard that was to enforce. If Prof. Ferreira had expected the quizzes to be closed book on the honor system, wouldn't she have said that in the syllabus, too? The fact that no one had shown any interest in clarifying what the rules were even after I had asked in the most obvious place, suggested that no one cared. I couldn't be in violation of the moral law if "Self, Place, and Knowing" was not a place where the moral law applied.
It turned out that I needn't have worried about my handicapped quiz scores (cumulative 32/40 = 80%) hurting my chances of making _cum laude_. Almost all of the remaining assignments were written (often in the form of posts to the class forum, including responses to other students), and Prof. Ferreira awarded full or almost-full credit for submissions that met the prescribed wordcount and made an effort to satisfy the (often unclear or contradictory) requirements.
I felt a little bit nervous about that afterwards: my conscious intent with the "Nigerian manservant" simile was to allude to the story about ChatGPT's affinity for the word _delve_ being traceable to the word's prevalence among the English-speaking Nigerians that OpenAI employed as data labelers, but given the cultural milieu of an SFSU social studies class, I worried that it would be called out as racist. (And whatever my conscious intent, maybe at some level I was asking for it.)
-I definitely shouldn't have worried. Other than the fact that Prof. Ferreira gave me credit for the assignment, I have no evidence that any human being read what I wrote.
+I definitely shouldn't have worried. Other than the fact that Prof. Ferreira gave me credit for the assignment, I have no evidence that any human read what I wrote.
My final paper was an exercise in bullshit and malicious compliance: over the course of an afternoon and evening (and finishing up the next morning), I rambled until I hit the wordcount requirement, [titling the result, "How Do Housing Supply and Community Assets Affect Rents and Quality of Life in Census Tract 3240.03? An Critical Microeconomic Synthesis of Self, Place, and Knowing"](http://zackmdavis.net/docs/davis-ls200-final_paper.pdf). My contempt for the exercise would have been quite apparent to anyone who read my work, but Prof. Ferreira predictably either didn't read it or didn't care. I got my A, and my Bachelor of Arts in Mathematics (Mathematics for Liberal Arts) _cum laude_.
Even so, it would have been better for everyone if I had either bullshitted to meet the pagecount, or just turned in a too-short paper without having a total mental breakdown about it. The total mental breakdown didn't help anyone! It was bad for me, and it imposed costs on everyone around me.
-I wish I had known that the kind of integrity I craved could be had in other ways. I think I did better for myself this time by mostly complying with the streams of natural language instructions, but not throwing a fit when I didn't comply, and writing this blog post afterwards to clarify what happened. If anyone has any doubts about the meaning of my Bachelor of Arts in Mathematics for Liberal Arts, they can read this post and get a pretty good idea of what that entailed. I've put in more than enough effort into being transparent that it doesn't make sense for me to be neurotically afraid of accidentally being a fraud.
+I wish I had known that the kind of integrity I craved could be had in other ways. I think I did better for myself this time by mostly complying with the streams of natural language instructions, but not throwing a fit when I didn't comply, and writing this blog post afterwards to clarify what happened. If anyone has any doubts about the meaning of my Bachelor of Arts in Mathematics for Liberal Arts from San Francisco State University, they can read this post and get a pretty good idea of what that entailed. I've put in more than enough effort into being transparent that it doesn't make sense for me to be neurotically afraid of accidentally being a fraud.
I think the Bachelor of Arts in Mathematics does mean something, even to me. It can simultaneously be the case that existing schools are awful for the reasons I've laid out, and that there's something real about some parts of them. Part of the tragedy of my story is that having wasted too much of my life in classes that were just obedience tests, I wasn't prepared to appreciate the value of classes that weren't just that. If I had known, I could have deliberately sought them out at Santa Cruz.
-Separately, I think I've latched on to math as something legible enough and unnatural enough (in contrast to writing) that the school model is tolerable. My primary contributions to the world are not as a mathematician. If I have to prove my intellectual value to Society in some way that doesn't depend on people intimately knowing my work, this is a way that makes sense, because math is too difficult and too pure to be ruined by the institution. Maybe other subjects could be studied in school in a way that's not fake. I just haven't seen it done.
+I think I've latched on to math as something legible enough and unnatural enough (in contrast to writing) that the school model is tolerable. My primary contributions to the world are not as a mathematician, but if I have to prove my intellectual value to Society in some way that doesn't depend on people intimately knowing my work, this is a way that makes sense, because math is too difficult and too pure to be ruined by the institution. Maybe other subjects could be studied in school in a way that's not fake. I just haven't seen it done.
+
+There's also a sense of grief and impermanence about only having my serious-university-math experience in the GPT-4 era rather than getting to experience it in the before-time while it lasted. If I didn't have LLM tutors, I would have had to be more aggressive about collaborating with peers and asking followup questions in office hours.
My grudging admission that the degree means something to me should not be construed as support for credentialism. Neural net interpretability pioneer Chris Olah never got his Bachelor's degree, and anyone who thinks less of him because of that is telling on themselves.
-At the same time, I'm not Chris Olah. For those of us without access to the feedback loops entailed by a research position at Google Brain, there's a benefit to being calibrated about the standard way things are done. (Which, I hasten to note, I could in principle have gotten from MIT OpenCourseWare; my accounting of benefits from happening to finish college is not an admission that the credentialists were right.) Obviously, I knew that math is not a spectator sport: in the years that I was filling my pages of notes from my own textbooks, I was attempting exercises and not just reading (because just reading doesn't work). But was I doing _enough_ exercises, correctly, to the standard that would be demanded in a school class, before moving on to the next topic? It's not worth the effort to do an exhaustive audit of my 2008–2024 private work, but I think in many cases, I was not. Having a better sense of what the mainstream standard is will help me adjust my self-study practices going forward.
+At the same time, I'm not Chris Olah. For those of us without access to the feedback loops entailed by a research position at Google Brain, there's a benefit to being calibrated about the standard way things are done. (Which, I hasten to note, I could in principle have gotten from MIT OpenCourseWare; my accounting of benefits from happening to finish college is not an admission that the credentialists were right.) Obviously, I knew that math is not a spectator sport: in the years that I was filling my pages of notes from my own textbooks, I was attempting exercises and not just reading (because just reading doesn't work). But was I doing _enough_ exercises, correctly, to the standard that would be demanded in a school class, before moving on to the next shiny topic? It's not worth the effort to do an exhaustive audit of my 2008–2024 private work, but I think in many cases, I was not. Having a better sense of what the mainstream standard is will help me adjust my self-study practices going forward.
When I informally audited honors analysis at UC Berkeley in 2017, Prof. Charles C. Pugh agreed to grade my midterm, and I got a 56/100. I don't know what the class's distribution was. Having been given to understand that many STEM courses offered a generous curve, I would later describe it as me ["[doing] fine on the midterm"](/2024/Mar/agreeing-with-stalin-in-ways-that-exhibit-generally-rationalist-principles/#it-matters-whether-peoples-beliefs-about-themselves-are-actually-true). Looking at the paper after having been through even SFSU's idea of an analysis course, I think I was expecting too little of myself: by all rights, a serious analysis student in exam shape _should_ be able to prove that the minimum distance between a compact and a connected set is achieved by some pair of points in the sets, or the product of connected spaces is connected (as opposed to merely writing down relevant observations that fell short of a proof, as I did).
In a July 2011 Diary entry, yearning to finally be free of school, I fantasized about speedrunning SF State's "advanced studies" track in two semesters: "Six classes a semester sounds like a heavy load, but it won't be if I study some of the material in advance," I wrote. That seems delusional now. That's not actually true of real math classes, even if it were potentially true of "Self, Place, and Knowing"-tier bullshit classes.
-It doesn't justify the scourge of credentialism, but the fact that I was ill-calibrated about the reality of the mathematical skill ladder helps explain why the coercion of credentialism is functional, why the power structure survives instead of getting competed out of existence. As terrible as school is along so many dimensions, it's tragically possible for people to do worse for themselves in freedom along some dimensions.
+It doesn't justify the scourge of credentialism, but the fact that I was ill-calibrated about the reality of the mathematical skill ladder helps explain why the coercion of credentialism is functional, why the power structure survives instead of immediately getting competed out of existence. As terrible as school is along so many dimensions, it's tragically possible for people to do worse for themselves in freedom along some key dimensions.
There's a substantial component of chance in my coming to finish the degree. The idea presented itself to me in early 2024 while I was considering what to work on next after a writing project had reached a natural stopping point. People were discussing education and schooling on Twitter in a way that pained me, and it occurred to me that I would feel better about being able to criticize school from the position of "... and I have a math degree" rather than "... so I didn't finish." It seemed convenient enough, so I did it.
-But a key reason it seemed convenient enough is that I still happened to live within commuting distance of SF State. That may be more due to inertia than anything else; when I needed to change apartments in 2023, I had considered moving to Reno, NV, but ended up staying in the East Bay because it was less of a hassle. If I had fled to Reno, then finishing the degree on a whim at University of Nevada–Reno would have been less convenient. I probably wouldn't have done it—and I think it was ultimately worth doing.
-
-The fact that humans are such weak general intelligences that so much of our lives come down to happenstance, rather than people charting an optimal path and not deviating from it, helps explain why there are institutions that shunt people down a standard track with a known distribution of results. I don't like it and still think it deserves to be competed out of existence, but I can respect it a little more now.
-
-
-#### It's Going to Be the Future Soon
-
-[TODO—sorrow in not having the hard college math experience before the GPT-4 era
- * I would have leaned on office hours more if LLMs didn't exist
- * LLM use and citing it
- * sorrow that autodidacticism was less feasible before the GPT-4 era _and I didn't realize it_ (I thought I was doing OK from just books, and maybe I wasn't); grief that learning is easier now is arguably perverse, but it's real
- * the struggle and external resources are probably normal
-]
-
+But a key reason it seemed convenient enough is that I still happened to live within commuting distance of SF State. That may be more due to inertia than anything else; when I needed to change apartments in 2023, I had considered moving to Reno, NV, but ended up staying in the East Bay because it was less of a hassle. If I had fled to Reno, then transferring credits and finishing the degree on a whim at the University of Nevada–Reno would have been less convenient. I probably wouldn't have done it—and I think it was ultimately worth doing.
-### Denouement
+The fact that humans are such weak general intelligences that so much of our lives come down to happenstance, rather than people charting an optimal path for themselves, helps explain why there are institutions that shunt people down a standard track with a known distribution of results. I still don't like it, and I still think people should try to do better for themselves, but it seems somewhat less perverse now.
Afterwards, Prof. Schuster encouraged me via email to at least consider grad school, saying that I seemed comparable to his peers in the University of Michigan Ph.D. program (which was ranked #10 in the U.S. at that time in the late '90s). I demurred: I said I would consider it if circumstances were otherwise, but in contrast to the last two semesters to finish undergrad, grad school didn't pass a cost-benefit analysis.
-(Okay, I did end up crashing Prof. Clader's "Advanced Topics in Mathematics: Algebraic Topology" the following semester, but I didn't _enroll_.)
+(Okay, I did end up [crashing Prof. Clader's "Advanced Topics in Mathematics: Algebraic Topology"](http://zackmdavis.net/docs/algebraic_topology-01.pdf) the following semester, but I didn't _enroll_.)
-What was significant (but not appropriate to mention in the email) was that now the choice to pursue more schooling _was_ a matter of cost–benefit analysis, and not a prospect of torment or betrayal.
+What was significant (but not appropriate to mention in the email) was that now the choice to pursue more schooling _was_ a matter of cost–benefit analysis, and not a prospect of torment or betrayal of the divine.
I wasn't that crazy anymore.
projects / An_Algorithmic_Lucidity.git / commitdiff