Did I not, then, as I grew out of infancy, come next to boyhood, or rather did it not come to me and succeed my infancy? My infancy did not go away (for where would it go?). It was simply no longer present; and I was no longer an infant who could not speak, but now a chattering boy. I remember this, and I have since observed how I learned to speak. My elders did not teach me words by rote, as they taught me my letters afterward. But I myself, when I was unable to communicate all I wished to say to whomever I wished by means of whimperings and grunts and various gestures of my limbs (which I used to reinforce my demands), I myself repeated the sounds already stored in my memory by the mind which thou, O my God, hadst given me. When they called some thing by name and pointed it out while they spoke, I saw it and realized that the thing they wished to indicate was called by the name they then uttered. And what they meant was made plain by the gestures of their bodies, by a kind of natural language, common to all nations, which expresses itself through changes of countenance, glances of the eye, gestures and intonations which indicate a disposition and attitude--either to seek or to possess, to reject or to avoid. So it was that by frequently hearing words, in different phrases, I gradually identified the objects which the words stood for and, having formed my mouth to repeat these signs, I was thereby able to express my will. Thus I exchanged with those about me the verbal signs by which we express our wishes and advanced deeper into the stormy fellowship of human life, depending all the while upon the authority of my parents and the behest of my elders.

  In the modern academic practice, the question of where a particular idea came from, or whether an axiom is ontologically correct, is considered vacuous and out of scope. For the most part, you’re just handed a rulebook to play someone else’s game.

To be clear I think the standard intuitive semi-naive set theory is the correct approach for most math students. But it didn't work for me. I needed to see the axioms and formal language.

  >> Wait, looking at the prompt history, the model had a strange quirk.

  Throughout every prior thinking trace in the conversations (and, honestly, every other thinking trace across all other conversations I've had with it), the frame is always in first-person, including the moment in this one where it "noticed" the corruption: "I noticed," "I had some weird typos," "did I do that on purpose?" And then the moment the anomaly couldn't be reconciled with the self-model, the language shifted to third person: "The model had a strange quirk." Effectively, the thing doing the thinking dissociated from the thing that produced the anomalous output, as if they were two entirely different layers of the process, much in the same way a person might fumble an easy sentence and then go for something like "my brain just did something weird." Except, of course, that "me" vs "my brain" is a distinction without a difference in much the same way Gemma's "I" vs "the model" is. Gemma is the model, just as much as we are our brains.

Likewise with Claude referring to "the model" - that quote sounds like something an Anthropic worker would say. Seems like a pithy little line Claude could have learned "on the job."

a) I got bullied into sharing my math homework so people could copy it, just like high school and college... but this was math grad school!

b) In 2011 I TAed a 4000-level course where the instructor left the solutions to the homework online (he wrote the book). I estimate 95% of students copied the solutions. It was only 5% of the grade and they paid for it on the exams. Still. Kind of stunning to see at U Waterloo - it was a continuous optimization course and most of them wanted to work in finance, yikes.

LLM agents will a) discover dumb counterintuitive stuff like this and b) exploit it to satisfy the kernel with c) the questionable lines being buried behind millions of lines of math slop. Humans have to check this stuff.

This future of "the AI built the compiler and it's totally incomprehensible spaghetti, but don't worry, it verified the compiler works using this AI-generated proof assistant whose codebase is also pure spaghetti" terrifies me.

"We get a ton of money, you get increased natural gas emissions, increased unemployment, your electric bill is going up... oh and guess who's bailing us out when the bubble bursts?" Pretty rotten deal!

- from an alternate reality, where devs still have shame and humility