The course covered the basics of group theory, with a little bit about rings at the end of the semester. The textbook was Joseph A. Gallian's _Contemporary Abstract Algebra_, which I found to be in insultingly poor taste. The contrast between "Modern Algebra I" ("MATH 335") and "Theory of Functions of a Complex Variable" ("MATH 730") that semester did persuade me that the course numbers did have semantic content in their first digit (3xx = insulting, 4xx or cross-listed 4xx/7xx = requires effort, 7xx = potentially punishing).
-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. 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.
-
-[TODO: Python program calculations]
+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.
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 of an effort to be transparent that it just 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 all the reasons I've laid out, and that there's something real about some parts of the existing institutions that makes them potentially worth participating in. Part of the tragedy of my story is that because I had 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 sought them out at Santa Cruz.
+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 all 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 because having wasting 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.
+
+[TODO—
+ * I think I'm latching on to math as something legible where the school model is tolerable; non-math school _could_ be real; it just isn't, empirically; math is so unnatural and writing is natural
+]
None of this is to justify credentialism, of course. Chris Olah never got his Bachelor's degree, and anyone who thinks less of him because of that is telling on themselves.
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.
-
[TODO—
* without justifying the credentialist menace, the fact that I was ill-calibrated, is why coercion is functional; it's possible to do worse
* it was chance that I ended up deciding to finish before moving; finishing at Reno would be harder
]
-[TODO—
- * I think I'm latching on to math as something legible where the school model is tolerable; non-math school _could_ be real; it just isn't, empirically
-]
+
+#### 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
* the struggle and external resources are probably normal
]
+
+### Denouement
+
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_.)
Dishonest disagreements end up looking like conflicts [because they are disguised conflicts](https://www.lesswrong.com/posts/e4GBj6jxRZcsHFSvP/assume-bad-faith). The parties to a dishonest disagreement are competing to get their preferred belief accepted, where beliefs are being preferred for some reason other than their accuracy: for example, because acceptance of the belief would imply actions that would benefit the belief-holder. If it were _true_ that my company is the best, it would follow logically that customers should buy my products and investors should fund me. And yet a discussion with me about whether or not my company is the best probably doesn't feel like a discussion about bus arrival times or the theory of functions of a complex variable. You probably expect me to behave as if I thought my belief is better "because it's mine", to treat attacks on _the belief_ as if they were attacks on my person: a conflict rather than a disagreement.
-"My company is the best" is a particularly stark example of a dishonest belief, but the pattern is very general: when people are attached to their beliefs for whatever reason—which is true for most of the beliefs that people spend time disagreeing about, as contrasted to math and bus-schedule disagreements that resolve quickly—neither party is being rational (which doesn't mean neither party is right on the object level). Attempts to improve the epistemic situation should take into account that the typical situation is not that of truth-seekers who can do better at their shared goal if they learn to trust each other, but rather of people who don't trust each other because each _correctly_ perceives that the other is _not_ truth-seeking.
+"My company is the best" is a particularly stark example of a dishonest belief, but the pattern is very general: when people are attached to their beliefs for whatever reason—which is true for most of the beliefs that people spend time disagreeing about, as contrasted to math and bus-schedule disagreements that resolve quickly—neither party is being rational (which doesn't mean neither party is right on the object level). Attempts to improve the situation should take into account that the typical case is not that of truth-seekers who can do better at their shared goal if they learn to trust each other, but rather of people who don't trust each other because each _correctly_ perceives that the other is _not_ truth-seeking.
Again, "not truth-seeking" here is meant in a functionalist sense. It doesn't matter if both parties subjectively think of themselves as honest. The "distrust" that prevents Aumann-agreement-like convergence is about how agents respond to evidence, not about subjective feelings. It applies as much to a mislabeled barometer as it does to a human with a functionally-dishonest belief. If I don't think the barometer readings correspond to the true atmospheric pressure, I might still update on evidence from the barometer in some way if I have a guess about how its labels correspond to reality, but I'm still going to disagree with its reading according to the false labels.
Cooperative approaches are particularly dangerous insofar as they seem likely to produce a convincing but false illusion of rationality, despite the participants' best of subjective conscious "intentions". It's common for discussions to involve more than one point of disagreement. An apprarently productive discussion might end with me saying, "Okay, I see you have a point about X, but I was still right about Y."
-This is a success if the reason I'm saying that is downstream of you in fact having a point about X but me in fact having been right about Y. But another state of affairs that would result in me saying that sentence, is that we were functionally playing a social game in which I implicitly agreed to concede on X (which you visibly care about) in exchange for ceding ground on Y (which I visibly care about).
+This is a success if the reason I'm saying that is downstream of you in fact having a point about X but me in fact having been right about Y. But another state of affairs that would result in me saying that sentence, is that we were functionally playing a social game in which I implicitly agreed to concede on X (which you visibly care about) in exchange for you ceding ground on Y (which I visibly care about).
-Let's sketch out a toy model to make this more concrete. "Truth or Dare" [provides an illustration of confirmation bias](https://www.lesswrong.com/posts/TQ4AXj3bCMfrNPTLf/truth-or-dare#Scene_III__Patterns__Projections__and_Preconceptions): if you've been primed to make the color yellow salient, it's easy to perceive an image as being yellower than it is.
+Let's sketch out a toy model to make this more concrete. "Truth or Dare" [uses color perception an illustration of confirmation bias](https://www.lesswrong.com/posts/TQ4AXj3bCMfrNPTLf/truth-or-dare#Scene_III__Patterns__Projections__and_Preconceptions): if you've been primed to make the color yellow salient, it's easy to perceive an image as being yellower than it is.
Suppose Jade and Ruby consciously identify as truthseekers, but really, Jade is biased to perceive non-green things as green 20% of the time, and Ruby is biased to perceive non-red things as red 20% of the time. In our functionalist sense, we can model Jade as "wanting" to misrepresent the world as being greener than it is, and Ruby as "wanting" to misrepresent the world is being redder than it is.
Cooperative human relationships result in everyone getting more of what they want. If Jade wants to believe that the world is greener than it is and Ruby wants to believe that the world is redder than it is, then naïve attempts at "cooperation" might involve Jade making an effort to see things Ruby's way at Ruby's behest, and _vice versa_. But Ruby is only going to insist that Jade make an effort to see it her way when Jade says an item isn't red. (That's what Ruby cares about.) Jade is only going to insist that Ruby make an effort to see it her way when Ruby says an item isn't green. (That's what Jade cares about.)
-If the two (perversely) succeed at seeing things the other's way, they would end up converging on believing that the sequence of objects is 20% green and 20% red (rather than the 0% green and 0% red that it actually is). They'd be happier, but they would also be wrong. In order for the pair to get the correct answer, then without loss of generality, when Ruby says an object is red, Jade needs to _stand her ground_: "No, it's not red; no, I don't trust you and won't see things your way; let's break out the Pantone swatches", but that doesn't seem very "cooperative" or "trusting".
+If the two (perversely) succeed at seeing things the other's way, they would end up converging on believing that the sequence of objects is 20% green and 20% red (rather than the 0% green and 0% red that it actually is). They'd be happier, but they would also be wrong. In order for the pair to get the correct answer, then without loss of generality, when Ruby says an object is red, Jade needs to _stand her ground_: "No, it's not red; no, I don't trust you and won't see things your way; let's break out the Pantone swatches." But that doesn't seem very "cooperative" or "trusting".
------
-At this point, a proponent of the high-trust, high-cooperation dynamics that Sabien champions is likely to object that the absurd "20% green, 20% red" mutual sycophancy outcome in this toy model is clearly not what they meant. (As Sabien [takes pains to clarify in "Basics of Rationalist Discourse"](https://www.lesswrong.com/posts/XPv4sYrKnPzeJASuk/basics-of-rationalist-discourse-1#5__Aim_for_convergence_on_truth__and_behave_as_if_your_interlocutors_are_also_aiming_for_convergence_on_truth_), "If two people disagree, it's tempting for them to attempt to converge _with each other_, but in fact the right move is for both of them to _try to see more of what's true_.")
+At this point, a proponent of the high-trust, high-cooperation dynamics that Sabien champions is likely to object that the absurd "20% green, 20% red" mutual-sycophancy outcome in this toy model is clearly not what they meant. (As Sabien [takes pains to clarify in "Basics of Rationalist Discourse"](https://www.lesswrong.com/posts/XPv4sYrKnPzeJASuk/basics-of-rationalist-discourse-1#5__Aim_for_convergence_on_truth__and_behave_as_if_your_interlocutors_are_also_aiming_for_convergence_on_truth_), "If two people disagree, it's tempting for them to attempt to converge _with each other_, but in fact the right move is for both of them to _try to see more of what's true_.")
-I agree that the mutual sycophancy outcome is clearly not what proponents of trust and cooperation consciously intend. The problem is that mutual sycophancy seems to be the natural outcome of treating interpersonal conflicts as analogous to epistemic disagreements and trying to resolve them both using cooperative practices, when in fact the decision-theoretic structure of those situations are very different. The text of "Truth or Dare" seems to treat the analogy as a strong one; it wouldn't make sense to spend so many thousands of words discussing gift economies and the eponymous party game it it weren't relevant to what constitutes productive discourse.
+Obviously, the mutual sycophancy outcome is clearly not what proponents of trust and cooperation consciously intend. The problem is that mutual sycophancy seems to be the natural outcome of treating interpersonal conflicts as analogous to epistemic disagreements and trying to resolve them both using cooperative practices, when in fact the decision-theoretic structure of those situations are very different. The text of "Truth or Dare" seems to treat the analogy as a strong one; it wouldn't make sense to spend so many thousands of words discussing gift economies and the eponymous party game it it weren't relevant to what constitutes productive discourse.
"Truth or Dare" seems to suggest that it's possible to escape the Dark World by excluding the bad guys. "[F]rom the perspective of someone with light world privilege, [...] it did not occur to me that you might be hanging around someone with ill intent at all," Sabien imagines a denizen of the light world saying. "Can you, um. Leave? Send them away? Not be spending time in the vicinity of known or suspected malefactors?"
-If we're talking about holding my associates to a standard of ideal truthseeking (as contrasted to the standard of "not using this truth-or-dare game to blackmail me"), then, no, I think I'm stuck spending time in the vicinity of people who are known or suspected to be biased. I can try to mitigate the problem somewhat by choosing _less_ biased friends, but when we do disagree, I [have no choice](https://www.lesswrong.com/posts/eY45uCCX7DdwJ4Jha/no-one-can-exempt-you-from-rationality-s-laws) but to approach that using the same rules of reasoning that I could use with a possibly-mislabeled barometer, which do not have a particularly cooperative character. Telling us that the right move is for both of us to try to see more of what's true is tautologically correct but non-actionable; I don't know how to _do_ that except by the same methodology that Sabien has criticized as characteristic of living in a dark world.
+If we're talking about holding my associates to a standard of ideal truthseeking (as contrasted to a lower standard of "not using this truth-or-dare game to blackmail me"), then, no, I think I'm stuck spending time in the vicinity of people who are known or suspected to be biased. I can try to mitigate the problem somewhat by choosing _less_ biased friends, but when we do disagree, I [have no choice](https://www.lesswrong.com/posts/eY45uCCX7DdwJ4Jha/no-one-can-exempt-you-from-rationality-s-laws) but to approach that using the same rules of reasoning that I could use with a possibly-mislabeled barometer, which do not have a particularly cooperative character. Telling us that the right move is for both of us to try to see more of what's true is tautologically correct but non-actionable; I don't know how to _do_ that except by my usual methodology, which Sabien has criticized as characteristic of living in a dark world.
That is to say: I do not understand how high-trust, high-cooperation dynamics work. I've never seen them. They are utterly outside my experience and beyond my comprehension. What I do know is how to keep my footing in a world of people with different goals from me, which I try to do with what skill and tenacity I can manage.
projects / An_Algorithmic_Lucidity.git / commitdiff