Samuel Choi

math/cs @ stanford

[Luna Lyu @lunanaboonana]

OpenAI released 722 math manuscripts in a day.
Will mathematicians read them?

A proof can settle a question. Understanding it can open up a thousand more.

Introducing Readable Intelligence: making AI-generated math easier to understand and build on. https://t.co/mk9raefnbf

[Samuel Choi @slamthatmule]

@mostrovs Extremely convincing coming from you, I think I might take it 🙂

[Samuel Choi @slamthatmule]

https://t.co/JuHOyHPceU

[Samuel Choi @slamthatmule]

@frbilo @gaoooric (I also think I may be using the word metacognition differently, in that it must be an active, conscious process as almost disjoint to the idea of intuition - maybe it should not be treated as disjoint)

[Samuel Choi @slamthatmule]

Thanks for reading! Your paper looks super interesting, and it seems to conclude that most students lack sufficient metacognition to be able to know what problems they have a better chance at solving.

I want to make the case (please prove me wrong) that knowing what problems to skip at face value is an intuition outside of metacognition.

In the context of competition math, I think everyones' first thought after looking at a problem is to consciously or subconsciously generate a probability distribution on confidence of success over a variety of different approaches.

There are some problems you *immediately* know how to solve with conviction, those that you have to play around with in order to form a distribution, and then everything in between.

If you define some metric of how optimal it is to skip a problem, I think it should be a (roughly, forget about arduous problems with easy intuition) monotonically increasing function f of t=E[time it takes to come up with a solution sketch]. Hence, to rank problems in order of how much you should skip them, it suffices to rank them by magnitude of t. So let us analyze the value of metacognition at every value of t.

If t is sufficiently close to 0, I would call this an "instasolve" that definitely doesn't require metacognition. You'd expect the value of metacognition to increase the more unsure your initial "approach" distribution is. But simultaneously, I believe being completely unsure on how to approach a problem (t sufficiently large) gives less leeway for metacognition and forces you to get your hands dirty with shots of pure intuition in the dark.

In that weird middle gray area where you have a few possible approaches that you *think* might work well, I'm bearish on metacognition serving much utility for several reasons. I think it's extremely difficult to:

1. determine this as a prime gray area to use metacognition (as discussed, it's often not very helpful) if you do so correctly...
2. analyze how your initial intuition about the problem reveals anything about f(t)
3. have enough self-control and *conviction* in your judgement to avoid some kind of gambler's ruin

Essentially, I think it's a skill that is difficult to know when to use, difficult to master, and relies on top of a completely different psychological strength. By the time you've mastered this process, I'd think you'd have mastered instantly sketching out the problems themselves.

Where I definitely do think metacognition is EXTREMELY helpful and underrated is in the process of learning and reflecting after you've solved a problem.

[Samuel Choi @slamthatmule]

@abhishekm1636 @dylann4500 @OpenAI @Citadel @sequoia 🫡

[Dylan Nguyen @dylann4500]

@slamthatmule and i recently competed in the no limit pokerbot tourney hosted by @OpenAI, @Citadel, and @sequoia.

we finished 6th of 148, missing finals (and $5,000) by 1 place (rip).

i still had so much fun, and wanted to share a write up of our bot: https://t.co/ZjEXbV0Slg.

[Samuel Choi @slamthatmule]

@dylann4500 @OpenAI @Citadel @sequoia tragic ☹️😔

[Samuel Choi @slamthatmule]

@gaoooric Not in depth! My grandfather was an economist and I’ve always looked up to him, though :)

[Samuel Choi @slamthatmule]

@justintsato Thanks!

[Samuel Choi @slamthatmule]

I think I missed the point in the last section [2] that some inference must be drawn from external variables outside of the individuals’ current state of mind - this probably does matter a ton and you’re right. Modeling their mind should definitely require variables that describe their environment

[Samuel Choi @slamthatmule]

very interesting piece and i really enjoy your writing.

> thank you so much! I appreciate that you took the time to read and think about it

there's this conflation between awareness and modeling. awareness is a fairly neutral term while the use of the word “model” implies you’d want to operationalize it for some end. ie a model is only so good as to what you can do with it.[0]

> definitely did not intend to make that conflation. Awareness is a goal that my methods of thought to predicting traits may or may not contribute to. You definitely don’t a model-like thought process to become aware!

the equivalence you draw between awareness and modeling makes awareness merely a means to an end--a prerequisite to minimizing irrationality. your iterative algorithm is fundamentally predictive, but you seem to derive a normative ideal from it.

> awareness seems to definitionally become both a prerequisite to good prediction (i wouldn’t call it minimizing irrationality) and an independent goal. Also, I do tend to derive normative ideals, and I do think this is bad - this was what I attempted to say in bringing up the third section.

[1] and i think this is contrary to DFW’s conception of awareness. the reason he mourns the unconscious individual is exactly because they are not aware enough to choose how they relate to the parts of ourselves and others that resist determination, those that are infinite in nature. i think he is all but explicit that you can’t find solace in some finite rationality, precisely because what it’s set against is infinite.

>I want to point out that finiteness is a strange concept. I don’t exactly understand what you mean by a finite rationality. For sake of discussion, I assume this to be my method of thinking in a finite number of core variables.

awareness is there as an end--that very act of attending to it is the goal. i think trying to "minimize" it only makes that harder, since you’d have to pretend it’s the kind of thing that can get smaller. i feel as if you have not squared the inherent irreducibility of irrationality with this imperative to minimize it.

> awareness is definitely a goal in itself, I think I’d also factor in some metric of accuracy if not already implicit. And in achieving this accuracy, I think being able to intentionally distill your thoughts is necessary, which I think fits into your idea of minimization?

> I also think both the fault of thinking in finite subsets of these infinite variables and the solution (to remember not to delude yourself into solace) is encapsulated in my discussion of inconsiderate people.

> I claim that potential higher model accuracy is akin to reducibility. higher accuracy is definitely possible in predicting many classes of events including my Avalon example.

[1] i also somewhat have problems with the algorithm,…you've correctly identified most actions are somewhat autonomic, but the most important ones are rare and highly interdependent.

> maybe the written architecture implied this because I didn’t want to make it sound convoluted and needlessly technical, but I feel you could account for these memoryless actions. For tendencies to be influenced, you can take functions of multiple actions to draw conclusions about influence patterns (which exist for sure!) For spontaneity, I believe it is governed by a deeper subconscious rather than being pure chaos.

[Samuel Choi @slamthatmule]

@cindehaa Tysm! Really appreciate it.

[Samuel Choi @slamthatmule]

@jdlichtman Well said! I like the term intellectual ownership here.

[Samuel Choi @slamthatmule]

@matthewyuart Bro thought he was niche