To add to this, I find talking to it about code quality or architecture issues can work quite well. Just treating it like another developer. Saying, “I’m not happy with the way the project is going because of X, and Y” and then making a plan for how to get things back on track. Maybe putting a complete rewrite on the table, or maybe just having it record the agreed code style principles in CLAUDE.md, etc
I think I have almost the opposite intuition. The fact that attention models are capable of making sophisticated logical constructions within a recursive grammar, even for a simple DSL like SQL, is kind of surprising. I think it’s likely that this property does depend on training on a very large and more general corpus, and hence demands the full parameter space that we need for conversational writing.
Concrete Mathematics is probably the best single book that you could read to prepare you for some the problems beyond the first 50. It’s extremely fun, and also mathematically serious. A large portion of PE problems are exactly in the cross sections of number theory, combinatorics, and computation that is covered in this book.
I mean, you can just do that in the browser too. "Enter ID" allows you to enter the MusicBrainz UUID (or just full URL). You can even do in the command itself.
It's just a good set of models to use to think about all sorts of different mathematical systems, kind of like a unified vocabulary. Beyond undergraduate level, category theory these days plays a huge role within many vast fields - e.g., algebraic geometry, algebraic topology, or representation theory.
I think your reply overstates the importance of category theory in mathematics and doesn't give any hint on what it is about.
IMO a better reply would be: category theory appeared to unify the concepts around using discrete objects to prove the properties of continous objects in topology, like fundamental groups, homology groups and homothopy groups. It is only practically useful for very advanced proofs like 2nd Weil Conjecture. Any usage of it in programming is only an analogy and is not mathematically rigorous (see https://math.andrej.com/2016/08/06/hask-is-not-a-category/)
I do this at the moment in my hand rolled personal assistant experiment built out of Claude code agents and hooks. I describe my workouts to Claude (among other things) and they are logged to a csv table. Then it reads the recent workouts and makes recommendations on exercises when I plan my next session etc. It also helps me manage projects, todos, and time blocked schedules using a similar system. I think the calorie counter that the OP describes would be very easy to add to this sort of set up.
In my experience, complicated rules like this are extremely unreliable. Claude just ignores it much of the time. The problem is that when Claude sees a failing test it is usually just an obstacle to completing some other task at hand - it essentially never chooses to branch out into some new complicated workflow and instead will find some other low friction solution. This is exactly why subagents are effective: if Claude knows to always run tests via a testing subagent, then the specific testing workflow can become that subagent’s whole objective.
This would mean moving to 100% weighted exams, and there's good reasons why there has been a general trend away from that over recent decades. For one thing, some students simply perform better under pressure than others, independent of their preparedness and knowledge of the material.
Mind you, I don't really have any alternative suggestions.
> Mind you, I don't really have any alternative suggestions.
This is thing.
If this choice is between:
1. A gameable system that will be gamed by most students.
2. An ungameable system that will unfairly punish those bad under pressure and time constraints.
There isn't really a choice at all.
One option would be a school-provided proctoring system, allowing teachers to outsource the actual test-taking times. It could be done outside of class time, at the student's convenience, and they could have 3-4 hours if they chose.
"Can they do this under pressure?" might in fact be a good question to test for and train for. A lot of real-life activity after graduation will involve some pressure.
But we could do what I'll call a "monastic exam".
You've got a week, not an hour, but it's in a little monastery and you don't have your phone or other unapproved tools.
One of my freshman professors accidentally did nearly that. The final exam was 3 hours. This was normal at my school although many students finish in 1-2 house. After realizing nobody was close to finishing after 2 hours and he had greatly underestimated the difficulty, he expanded the time limit to 6 hours!
I will say it's not practical to have exams that long. In this case, the dorm required me to move out immediately after the exam and my parents were waiting to pick me up, so I decided to leave after 4 hours to avoid unnecessary panic or having to drive overnight. In hindsight, the professor probably would have let me make a phone call, but that didn't occur to me at the time.
Fair point, but the solution I propose would only apply to those parts of the assessment involving solo writing assignments -- so excluding class participation, group assignments, etc. (Which is not to say that students can't use AI to cheat on these, but they have other solutions.)
I mean, the real answer is that the other students were cheating on their assignments. It's that simple. We keep making up excuses for all of this shit. Some people don't "test well". Turns out those people don't know shit.
Let's get real here. I know why these nonsensical memes keep propagating but dear god. People will just believe anything these days, including that gas stoves cause asthma or whatever other bullshit is being peddled.
This isn't true. I'm one of those people who tested remarkably well, and back in college would do fine on exams despite frantically copying all of my own (non-comp Sci) assignments. Better than my peers who knew more and helped me cram. Test anxiety is real.
I was a great test taker, I used to make a sort of game out finishing tests in half the time as almost everybody else and acing it at the same time. I also never crammed, never attended pre-test study groups, and sometimes made a show of drinking beers right before the test just to annoy the people cramming in the last minute.
But I'm not particularly brilliant, in fact I wouldn't be terribly surprised if I have undiagnosed ADHD. My test taking performance trick, which I freely told everybody to their annoyance, was very simple. I knew the material! Read the assigned texts, do the optional homework, pay attention in class. If you know the material you don't have to try to cram it into your brain in the last half hour before the test. If you know the material you don't have to try to reason it out from first principles during the test. You just go in, fill out the easy answers straight away, go back and do a second pass for the tricky questions, and that's it. If you have to sit there wracking your brain for 30 minutes on a single problem it's because you already fucked up with how you approached the course weeks ago.
Again, I'm not special for this. There were a handful of other students who were as fast as me. We'd sit in the hall waiting for our friends, look at each other and say "you knew all this stuff too, huh?""yeah of course"
It is definitely not the case that if student A performs better on a timed high-stakes test than student B, that means A must have worked harder / prepared better / know the material better / etc. than B. Some people are very skilled at bullshitting their way through stupid school tests, and others are not. Very few school tests are well enough designed that they can effectively measure the intended target of how well someone understands the topic, content, and course-specific skills which are being intentionally trained in the course.
Bullshitting though tests is a learnable / trainable skill, but schools generally do not teach it very coherently or well and most students do not deliberately practice it. It generally doesn't have that much to do with the content or other skills intentionally taught by any particular course or by schools in general (there's decent overlap with the skills involved in competitive debate and extemporaneous speech, which some students participate in as an extracurricular activity). Rating students on how good they are at bullshitting their way through exams is sadly a significant part of the way our education system is focused and organized, but in my opinion it is not a valuable or particularly valid approach. There are certain professional contexts/tasks where this kind of skill is useful, but developing it per se shouldn't be the focus of the education system.
Sometimes this and related skills are summarized as "intelligence" ("oh she aced the test without studying, she must just be really smart", etc.), but in my opinion it's quite a misleading use of the word.
This perspective is the inspiration for much of lattice theory. When you consider implication as an ordering, then "x and y" becomes max(x, y), "x or y" becomes min(x, y). True becomes the top term, False becomes the bottom. One of the neat implications is that much of what we think of as being propositions in boolean algebra also work in the wider setting of Heyting algebras i.e., any lattice that also has implication.
