Now

This is my take on a now page. Last updated: August 2026.

AI and my research#

It’s been about, what, two months since GPT 5.6 Sol was released? And it’s been absolutely groundbreaking for my own research. It’s hard for me even to express just how capable the model is for the kind of projects that I’d been building. In fact, my original idea for what my PhD thesis might be has possibly been made effectively trivial to do with GPT 5.6. I can’t quite comment on that just yet since I haven’t begun working on it in earnest, but I can give two examples of what I’ve been doing with this model.

First, you might remember from some of my previous now posts (January, June) that I was working on a project called “quadratic reasoning”, which I now call “Quadarith”. The exact goal and scope remained unclear during the entirety of the first year of my PhD. Upon release of GPT 5.6 Sol, however, I decided to see what would happen if I tasked it with building the most aspirational version of the idea. Namely, suppose that you’d like to decide the truth of a first-order sentence over the reals, whose atomic formulas are (or can be provably reduced to) equations or inequalities between polynomial expressions with exact coefficients and total degree at most two in the quantified variables. This is obviously NP-hard (in fact, PSPACE-hard). For a given expression, however, there may be some hidden structure that could be exploited to more efficiently conclude if the sentence is true or false. For instance, there could be some hidden convexity, or perhaps the relevant quadratic forms are simultaneously diagonalizable in a way that exposes a simpler exact reformulation. The project formalizes a calculus for searching over these formulations while checking every accepted step exactly. The question we wish to answer is whether we can design a routing policy that, given a specific sentence and some computation budget, inspects formula structure and probes the space of problem formulations and reductions to as efficiently as possible assemble evidence for the sentence’s truth or falsity. If neither the sentence nor its negation is established within that budget, then we report unknown.

GPT 5.6 Sol in Codex’s Ultra mode really cooked. I’ll make the highly preliminary code and paper repos public once Jaewook and I are ready, but it did not disappoint. It assembled a large library of solver and certificate routes, built substantial Python IR and formulation graph infrastructure, and even built a separate Lean tactic called quadarith, similar in spirit to the linarith tactic for linear arithmetic. The Python frontend currently handles quantifier-free formulas. A numerical solver can suggest a point or bound, but Python checks the resulting claim with exact arithmetic before accepting it. Lean separately accepts only kernel-checked proofs. No trained routing policy exists yet, but it did build the training and evaluation infrastructure, including the ability to probe structure, extract features, and do some graph searching. I am excited to see how a properly trained policy performs on realistically large problems.

Granted, it did a rather abysmal job at drafting a comprehensible initial version of the paper to communicate the core idea (it did, indeed, write one, and it sort of looks OK if you skim it, but I think that draft is horribly unclear once you start to actually read the thing), and I think the codebase is kind of a sprawling mess. But it did all of this initial work in just about two weeks.¹

Second, I’ve been building out a Scrabble-like game that lets you specify arbitrary board layouts and topologies, along with customizing a ton of other rules. You’ve probably never played Scrabble on a donut, or a Möbius strip, or on (a “tracked” version of) the Petersen graph. You’ve also probably never played a game of Scrabble where you can play English words only and your opponent can play, say, French words only. And I imagine most of you have never played a game of Scrabble with various handicaps, like some of your rack being visible to opponents or your bingo bonuses being nullified. Now you can do all of these, at the same time! The game engine and a local web version are public on GitHub.

The actual game logic was very fast and easy for GPT 5.6 Sol to implement. I’ve spent much of the rest of my usage building an AI opponent that can handle arbitrary game configurations, lexicons, and to some extent, game objectives. It will also adapt to user play style. This component of the project is not ready for public consumption yet. The next time my hyperfixation roulette lands on this project, however, I’ll be sure to prioritize polishing up the AI component enough that it wouldn’t be a complete waste of space on GitHub.

Besides just enabling me to pursue larger projects, the speed with which these frontier models are able to take an idea and build a damn good prototype has forced me to reconsider the economics of ideas. There used to be strong reason to keep an idea private until you could turn it into something substantial enough to demonstrate value. The barrier to entry was work, and the work took long enough that priority was easy to establish (in the sense that usually you wouldn’t have much competition). Now anyone with an idea (or anyone who merely overhears someone else’s idea) can generate a mediocre implementation almost immediately by sloppily dropping in a few relevant keywords into Codex or Claude Code.²

Since I’ve probably never had a fully unique research or project idea in my life, I reckon that the best response I could have to the collapse of the barrier to entry is to stop hoarding work and start making as much of my projects publicly visible from the start. That way, I establish publicly, from the start, what I think the right abstraction is, what are the questions worth asking, and what I think is the “right” way to do something, hopefully before someone else’s quick prototype or preliminary result (that I think is obviously deficient in some number of ways) becomes the nucleation site. In principle, this is how I should’ve been approaching things already, but I think I was psychologically not ready to show things that I knew were incomplete and flawed.

There are some risks involved in this approach, of course. I can’t say, for instance, that I’ll be particularly proud of any of these projects until they are verifiably done and I can fully endorse the contents of the project. But they’ll nevertheless have my name attached from the start, which to anyone who doesn’t know me could be interpreted as a signal of broader endorsement than may be true. Moreover, since many of these projects will, indeed, begin with AI-generated prototypes, it’s possible I’ll be written off by some people as some kind of lazy AI slop researcher. Fine. I’ll have to just not care. I am doing these projects for fun anyway.³

Slow writing#

Some of you reading might have noticed a new page on my blog, namely, the work-in-progress (WIP) page. This is sort of the same idea as above, but for blog posts! I intend there to maintain reasonably coherent public snapshots of thoughts that I am still working through. Besides leaving a public trace of what I’ve been pondering, the WIP page will help resolve the great duress created by my inability to express myself clearly. Let me explain.

I spent much of July writing and rewriting an updated now page as I tried to articulate some thoughts that began to crystallize as I interrogated the kinds of anxieties I and others were feeling after learning about all the open problems being resolved by Anthropic and OpenAI models. I went through at least five or six revisions of this post, and almost gave up after one revision read as nothing more than a pretentious overexplanation of a pithyism everyone already understood. (A partial working draft will soon appear on the WIP page.) It is incredibly distressing and frustrating to have some bundle of intuitions that appear as clear as day, but which I can’t for the life of me seem to write down cogently. I’ve had this problem for as long as I can remember. Writing assignments were hell for me starting in fourth grade and continuing through undergrad.⁴

I’ve never been a great bullshitter. I don’t have that kind of valve I can open and just firehose my thoughts as words onto a page. Even if I did, I don’t think it would matter all that much, since the word supply seems to be rate-limiting. My thoughts aren’t natively linguistic, and whatever part of my brain is responsible for translating them into English (Broca’s area?) is either woefully incompetent, just as distractible as me, or both. Expressing one thought cleanly is a challenge, and anything more substantive means that I have to translate thought to English and untangle a big knotted ball of raw intuition. It never yields, never unravels to become a nice linear string of ideas to feed through my brain’s decoder.⁵ Writing even relatively short pieces takes me sometimes hours. And boy do I also have a knack for circumlocution. (This section, for instance, is about eleven hundred words that say “writing is hard”.)

Whatever I lack in thought-to-English translation, I make up for it in my sensitivity to thought-to-English mistranslation. I am acutely, painfully aware of the gap between an idea as I understand it internally and the nonsense that ends up spilling out of my brain. Just about every time I write anything at all, I’ll read it back, and it’ll activate some neurons, and I can palpably feel the gulf between the pattern of neurons just activated and the pattern of neurons that fire off when I think about the idea intuitively.⁶ So I keep writing, and rewriting, and rewriting, and soon enough it’s been five-and-a-half hours and I’ve, in fact, made negative progress. I started with a paragraph or two and now the page is blank again.

Surely part of this is perfectionism. I always imagine the grandest versions of every project I start, including essays and blog posts, and I really struggle to publicly endorse what I view as an incomplete draft. I don’t quite know why. Part of it could be some phobia of the exposure that comes along with publication. If I don’t even interpret my words the way I intended, then how can anyone else? Perhaps I am afraid of being associated with ideas that aren’t really mine, especially on topics that invite the least charitable possible interpretation. On the other hand, I reckon that even if I were alone on a deserted island and for whatever reason kept a journal, I would probably drive myself mad trying to make myself clear to myself.⁷

I think there is more to this than mere perfectionism, though. I’m not a psychologist nor a neuroscientist, though, so I may never be able to diagnose for myself precisely what makes it so hard for me to emit tokens. I have some speculations, which perhaps I will write about some other day.

So I shall sincerely try to course correct and engage with ideas more publicly in my academic work, recreational work, and writing. I’m still not going to dump every half-formed note onto the Internet (I’m no Xitter user) but I am going to try to lower my threshold for what I am comfortable making visible. If something is coherent enough that another person could usefully understand what I am trying to do, then I would rather expose a dated, revisable snapshot than keep it hidden for another year (or two or three, depending on when the hyperfixation roulette wheel in my brain decides to land on it again) while I inspect every remaining corner, nook, and cranny trying to make it fully comprehensive and perfectly polished. Some of these thoughts might turn into proper posts and “finished” projects (and in the process they might mutate beyond recognition); others might remain in limbo, unfinished for eternity; and still others might be disowned and nuked. That’s all fine. I just want the ideas to be more visible, more quickly.

Books and music#

Reading. I most recently read The Grasshopper by Bernard Suits, and it connected to a lot of thoughts I have had for a while, so much so that I was inspired to write at least two proper blog posts that should soon appear on the WIP page. For now, it captured very well an intuition I’ve had since at least middle school, which is that in a world where nobody ever has to do anything except because they want to, people would devote their lives to something like playing games. And I don’t mean board games or video games necessarily. In defiance of Wittgenstein,⁹ Suits captures quite well what I think is meant by playing a game: it is the voluntary attempt to overcome unnecessary obstacles. You pursue some goal that can be described independently of the game (the prelusory goal), you accept rules that forbid the most efficient means of achieving it (the constitutive rules, which permit just the lusory means), and you accept those rules just because they make the activity (the game) possible (the lusory attitude).

Just to qualify his argument a bit further, Suits stipulates, as a limiting case, a Utopia of such extreme plenitude that not only is productive labor unnecessary, but material wants can be satisfied instantaneously by “mental telepathy”, all possible interpersonal problems have been resolved, and all possible knowledge is but a query away. Many of my thoughts about the Suitsian Utopia will be documented in the full blog post about work and purpose. Here I want to document some thoughts about other aspects of the treatise.

Much of The Grasshopper is spent defending the Suitsian definition of a game against purported false positives and false negatives. One of the counterexamples Suits claims to dispose of is Ring Around the Rosie:

G: […] Things like Ring Around the Rosie, too, are referred to […] as games. But I think you will agree with me that Ring Around the Rosie is simply a kind of dance to vocal accompaniment, or a choreographed song. It is no more a game than Swan Lake is.

This passage bothered me right away. First of all, there seems to be some equivocation of two different things called Ring Around the Rosie. There is the choreographed sequence of moves, and there is the practice of actually enacting that choreography. Suits appears to classify the former and take himself thereby to have classified the latter.

In the appendix, Suits gives further defense of this classification:

[…] I can more convincingly assign Ring Around the Rosie to a class other than the class game, and I cannot do the same with the hundred yard dash. […] I excluded [Ring Around the Rosie] by finding another class to put it into […]

Now, it may be that dance to vocal accompaniment is disjoint from game. Prima facie I do not see why it should be, since race and game do not seem disjoint, as his own admission of the hundred yard dash attests, but even granting it, the choreographed sequence might be a dance to vocal accompaniment while the activity of enacting it is a game. In fact I think it is.

The performance of Ring Around the Rosie consists in a particular sequence of coordinated bodily configurations and vocal sounds. So suppose that I had in mind the goal of producing this prescribed sequence. Notice that in setting this goal, I have not a priori determined how those configurations and sounds are to be produced. I can produce them myself in the familiar way, but I could also imagine a sufficiently elaborate robot, puppet apparatus, or neurological controller that moves my meat suit in exactly the desired fashion. In the Suitsian Utopia, these alternative means would be, I imagine, substantially more reliable than my own mental and physical exertions. However, to play Ring Around the Rosie suggests to me that these more efficient alternative means are proscribed, and that I must perform the dance with vocal accompaniment myself, using my own brain to control my own body and voice.

Does this not render Ring Around the Rosie, possibly, as a game? I’ve just described it as having something like a prelusory goal (to produce such and such bodily configurations), with constitutive rules (use voluntary motor control), and my observance of the constitutive rules is voluntary; I follow them precisely because I want to play Ring Around the Rosie.

Let’s revisit the actual criteria Suits sets for some specification to identify a prelusory goal, since if anything is wrong, then it’s what I’ve stated as being the prelusory goal for Ring Around the Rosie. Suits demands that the prelusory goal be a “specific achievable state of affairs” that omits “how the state of affairs in question is to be brought about”. For instance, the prelusory goal of golf might be get a ball into a hole in the ground, but it cannot be something like get a ball into a hole in the ground by hitting it with golf clubs, since the latter prescribes a method and not just a state of affairs. Allowed methods belong to the constitutive rules.

Does my description of Ring Around the Rosie violate this restriction? Maybe, but not obviously. There is a difference between specifying the trajectory that my body and voice are to trace out and specifying the means by which that trajectory is produced. If you observed that my body passed through exactly the prescribed sequence of configurations, then that alone does not tell you whether I moved it through ordinary voluntary motor control, or if I instead was merely a conscious passenger in my meat suit while electrodes invisible to you stimulated the relevant nerves in just the right way to puppeteer my body and voice through the sequence for me. In the latter case, I think it would be absurd to claim that I “played” Ring Around the Rosie. I think, therefore, that the description I gave is not really analogous to get a ball into a hole in the ground by hitting it with golf clubs, since I did not specify the means by which I produce the sequence.

While that may be true, my stated description does feel dissimilar to prelusory goals like get a ball into a hole in the ground or be on the other side of the finish line. What exactly is the dissimilarity?

Perhaps I baked in too much of the activity into the desired state of affairs. I’ve put the entire choreographed sequence into the state of affairs. Yet I think this is actually not forbidden. Chess is certainly considered a game, and as Skepticus and the Grasshopper discuss in chapter 4, its prelusory goal can be described as put the chess pieces into a checkmate arrangement, where a checkmate arrangement is defined as either a member of some innumerable set¹⁰ or in reference to the rules of chess.

Perhaps the issue is that Suits intended “state of affairs” to be more like an instantaneous snapshot of some physical state. The state of affairs I described has a continuum of instantaneous states of affairs.¹¹ This is a plausible objection, but I think it can be avoided by modifying my description a bit so it adheres more closely to Suits’s idea of open games, whose members are systems of “reciprocally enabling moves whose purpose is the continued operation of the system”.

Suits asks us to imagine two people engaged in a ping-pong rally where neither is trying to score. They are simply trying to keep the ball in play. Skepticus objects to this scenario as being a non-game:

S: But Grasshopper, how can that be? The original definition requires that players of games be seeking to bring about a specific state of affairs, but for players of open games, as we have seen, there is no state of affairs they are striving to achieve. They are simply committed to striving indefinitely.

The Grasshopper responds:

G: I think you say that, Skepticus, only because you are taking an unnecessarily narrow view of what constitutes a state of affairs. In a ping-pong rally there is a perfectly clear state of affairs that the players are striving to achieve. It is the state of affairs which consists in the ball’s being in play.

He then extends this principle elsewhere. Cops and Robbers is an open game whose prelusory goal is keep a dramatic episode (involving roles of cops and robbers) going with the constitutive rules forbidding means such as using a script. Why not describe Ring Around the Rosie similarly? The relevant goal could be something like keep a successful performance of Ring Around the Rosie in progress. At any given moment, the performance is either proceeding successfully or it is not. If somebody forgets what comes next, wanders away, or sufficiently mangles the choreography, then the performance breaks down. Just as in the ping-pong rally or Cops and Robbers, it is kept going by the participants’ successive actions. (If one objects that I’ve again done too much prescription in the prelusory goal by specifying Ring Around the Rosie, then remember the earlier chess example!)

Granted, Ring Around the Rosie is distinct from the everlasting ping-pong rally or Cops and Robbers in the sense that there is a definite endpoint. But I think the useful feature from these examples, and from the definition of open games, is that Suits admits as games activities whose prelusory goals involve the maintenance of a presently obtaining condition rather than describing a timeless, static state of affairs.

I think that if this critique is successful, then there are new problems that emerge. For instance, now it seems plausible to me that we could smuggle in constitutive rules to the prelusory goal. Define the lightly choreographed performance Qolf, in which one or more actors are to execute a sequence of moves that result in a ball being whacked by a club into a hole in the ground. Now set the prelusory goal to be perform a sequence of moves in accordance with Qolf or keep a successful performance of Qolf in progress, and stipulate constitutive rules like use voluntary motor control only. This seems very much like the descriptions I have provided for Ring Around the Rosie, so if that is a game, then so too is this new one. Call the new game qolf. Now, players of golf look very much like players of qolf. How can we be sure which game is being played? (Does it matter?)

If the critique does not succeed, then I punt it back to you: if playing Ring Around the Rosie (i.e., enacting the choreography of Ring Around the Rosie) is to be excluded from the class of games, then I think something more is needed than the observation that the name refers also to a choreographed song. What is that something more?

There is another part that I found myself disagreeing with Suits. In chapter 15, Suits considers the fate of art. The initial instinct expressed by the Grasshopper is:

I believe that [artistic] skills would not exist in Utopia because art would not exist there. Art has a subject matter which consists in the actions and passions of men: with human aspirations and frustrations, hopes and fears, triumphs and tragedies, with flaws of character, moral dilemmas, joy and sorrow. But it would seem that none of these necessary ingredients of art could exist in Utopia.

Later, the Grasshopper changes his mind, after realizing that games create a platform for these passions to persist:

And with the re-introduction of the emotions associated with striving—the joy of victory, you know, and the bitterness of defeat—emotional content is provided for art.

I believe that, yes, in a Suitsian Utopia, art would continue. And here I do mean art in I think the way Suits intends, not as simply the (re)production of some sensory forms. (It would be very easy to suggest, say, that painting persists as a game, whose prelusory goal is to produce imprints obeying some pattern, and whose constitutive rules require that you do so with a paintbrush; I think that is not what Suits is calling art here.) However, I think Suits took a circuitous and wrong route to this conclusion.

His initial instinct seems to have been that Utopia removes the ordinary external causes of strife, and a fortiori the disappearance of the kinds of human affect on which art depends. I don’t buy this. Even absent scarcity or externally imposed striving, I see no inherent reason why humans would no longer experience the kinds of emotion represented by art. It seems Suits doesn’t quite believe this either:

John Striver has spent his first decade in Utopia doing all the things that newcomers to Utopia usually do. He has travelled round the world several times, loafed a good deal in the sun, and so on, and now, having become bored, he wants some activity to be engaged in.

John Striver has become bored, has he? Could that be an emotion, one which could be depicted visually in something like a painting?

This is still arguably presented as a product of circumstance. But I also doubt that such material circumstances are necessary conditions for these emotions. Perhaps emotions are not principally responses to deficits in the world at all, and that part of being human is to be continuously affective. (It’s possible, anyway. I’m not ready to make a claim one way or the other.) At most, games supply one new source of affective material. I understand this wasn’t a particularly important part of his argument and it could have been elided entirely without changing the thrust of the book, but it did stick out to me that Suits needs some much stronger argument that the affects from which art draws its content are exhausted by responses to material scarcity and externally imposed striving.

Listening. My most recent earworms include

• Genre Police by S3RL feat. Lexi;
• Sledgehammer by USAO & Yuta Imai; and
• Shake Ya Shimmy by Da Tweekaz & Code Black.

See past updates.