Now

// what I'm doing now · updated June 2026

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

Ideas#

It has been (at least) a minute since I last touched this page.¹ I have been feeling somewhat guilty about taking so long to continue the series about derivative notation and the series about Calories In, Calories Out. I haven’t abandoned these projects; I have simply deprioritized completing them. I’ve got something north of 50,000 words of notes written for the derivative notation series, and maybe around half of that for the CICO series. I am simply struggling to find the time (and motivation) to string these words into a proper story, especially since I’ve got about twenty other open projects at the moment (more on this below). I have the tendency to work on projects in fits and bursts, rather than making steady progress on one project until it’s done. The blog posts have simply fallen out of the rotation.² They will be published in finite time, I promise.

Current research#

My recent research has been pretty solidly pure mathematics. The only relatively applied thing I’ve done these past couple of months is push a years-old project about cooperative transaction cost sharing to arXiv.³ I’ve sort of put an indefinite pause on the project mentioned in the previous now post, instead prioritizing some work I am doing on some extremal growth characteristics of multiplicative functions, and on some interesting constants in probability theory.

At least, those are the two projects that have had the most enduring presence in my day-to-day work. As mentioned, I’ve got something like twenty open projects. The issue is that I’m always coming up with new ideas for projects, or ways to deepen or extend existing projects, such that I never finish anything and I nevertheless continue to add to my plate. In the past, this used to paralyze me with indecision. I’d boot up my laptop and get nothing done because I could not decide where I wanted to dedicate my time and brainpower for the day. Nowadays, LLMs have become the great enabler for this terrible habit of mine. I’m now able to delegate work to LLMs, allowing me to switch between multiple projects at once and actually, at least ostensibly, make progress on them. The issue now is that LLMs are only able to get me around 80% of the way done, and the remaining 20% of work is, frankly, rather boring. It’s a lot of reviewing and polishing. That leaves me in a position where I’ve got a ton of projects that are “most of the way done”, where all the substantive work is done but the framing, documentation, and polish are atrocious. I suppose that this is a better situation than having a ton of woefully incomplete projects.

Teaching#

I have started teaching EE 364A (Convex Optimization) this summer! So far, the first two lectures went… not so according to plan. I prepared loads for the lectures; I wrote up notes, watched previous iterations of the course, and drafted annotated versions of the slides for reference and everything. I still feel that my first two lectures were not great. I tend to do best as an extemporaneous speaker, and that works really well when the talk or lecture is your own, purpose-built product. But I’m using the existing slide deck, and I did not realize when preparing for lecture just how often my preferred intuitions for things relied on ideas or definitions that were either not presented in the slides at all, or were introduced later in the course. Actually, the slides themselves were internally incoherent in places, using vocabulary and ideas that did not appear until later. Somehow Stephen Boyd makes it all work. His lectures are impeccable pedagogically, at least in my opinion. But the way I think about the subject is sufficiently different from him that I have found it impossible to make effective use of the existing slides, and I don’t have the time to put together new slides. Oh well. I’ll just continue to do my best, and I’ll try to make sure that my office hours are clearer.

Books, music, and film#

Films. I am not a cinephile by any stretch of the imagination. Until two weeks ago, I hadn’t gone to see a movie in theaters since 2024 when my family went to see Wicked. And before that it must’ve been pre-COVID. I went to see Backrooms with some friends and, while it was good, I was a little disappointed to be honest. It’s not the movie’s fault per se. It was definitely much more of a me issue. I’ve seen the full YouTube series at least three times,⁴ and I (having avoided the trailer) was anticipating that a lot more of the film would center on Async and government responses. I suppose I wasn’t expecting that the film would go the route of overt symbolism. At the very least, I am glad that the movie didn’t go the route of implying that the Backrooms were entirely a figment of the imagination.

But I did enjoy the movie. I realized after I saw Backrooms that Obsession (which I still have yet to see) was directed by another YouTube creator that I like (Curry Barker of that’s a bad idea). And then I remembered Markiplier also did a movie just recently, namely, Iron Lung, which YouTube soon after recommended. So then I watched that, and it was great!

And then YouTube recommended me Your Name (the English dub). And ho-ly. It’s been a remarkably long time since I last cried. This was simply a beautiful film and I would highly recommend that you give it a watch, ideally without reading anything about it beyond maybe the basic description. Such a scrumptious meal to the eyes and heart that I think I might have had my fill of film for a while now.⁵

Reading. I am currently reading… nothing. I’m currently in a bit of a mood where I have not been enjoying books. I’ve started a few, but I keep getting distracted or bored and giving up. Hopefully soon this will pass and I will resume the habit.

About two months ago I finished Ten Great Ideas About Chance by Persi Diaconis and Brian Skyrms, which I received as a birthday gift. It’s aimed at a general audience, which, in classic Diaconis fashion, means “acquainted with some measure theory”.⁶ I found the book enjoyable, and I will likely return to the book from time to time as I let some of the ideas marinate.

PHIL 288A (Explanation) concluded, gosh, almost 15 weeks ago now. We read Reasons Why by Bradford Skow, and subsequently read Calling for Explanation by Dan Baras. I audited the class hoping to understand if there were some structural, mind-independent reason that certain proofs feel explanatory while others do not (see, for instance, the two proofs of Euler’s partition identity presented in my post about mathematical phenomena). If so, then I further wondered why we should be able to so reliably detect this kind of structure. Although the course was interesting, it didn’t quite cover what I was expecting. Skow concerned himself chiefly with (facts about) so-called concrete events, and explicitly disclaims that his theory extends to mathematical facts.⁷ Baras was interested to understand what he calls the striking principle, which is, roughly, that the more striking a fact is, the more reason we have to believe it has an explanation of a special kind. Now this a priori seems to relate to the kind of mathematical explanation I was hoping to explore. On reading, it is indeed one subject of discourse, where strikingness of mathematical facts is sort of a barometer for deep structural properties of mathematics; but frankly the most compelling aspect of Baras’ observation concerns cases like the fine-tuning argument, or nonphysical theories of mind, where the striking principle serves as an epistemic principle. By epistemic I mean that it works as a principle of rational belief: a striking fact gives you reason to expect a special explanation, and so to discount any theory that can only write the fact off as coincidence. The fine-tuning argument, for instance, argues that the life-permitting values of the physical constants are striking, so we are pressed toward intelligent design or a multiverse theory rather than a brute coincidence. Likewise, the correlation between brain states and qualia is striking, so physicalist theories of mind seem inadequate.

Baras has three primary objectives in his investigation. First, he investigates whether the feeling that a fact “calls for explanation” serves as a valid truth-discovery mechanism, that if some theory renders a fact striking while being impotent to explain it, then that theory should be penalized. Second, he explores whether calling-for-explanation tracks strikingness. Third, he examines if strikingness is fundamental or reducible to something else. Ultimately, he fails to find a unified strikingness property, and he argues that the striking principle is good but not privileged, since it is derivable from ordinary probabilistic and inductive reasoning. He settles on the idea that we “are better off forgetting the idea that there are facts that call for explanation and focus instead on the details of each individual case” (ch. 6, p. 172). And I agree with this conclusion. The way in which the four-color theorem “calls for explanation” (it demands an illuminating proof) is quite different from the way in which the correlation between certain neural firing patterns and experienced qualia “calls for explanation” (it demands a reductive account).

While the course was different from expectations, I’m glad to have audited it. I have gained a better understanding of my own beliefs, which is what I aim to do through my studies of philosophy anyway.

Listening. My most recent earworms include

I’ve cycled through many, many more songs since my post in January, but I can’t list them all here (I’ve forgotten most of them anyway).

See past updates.

¹Does that mean the year of creativity is already over?
²It does go a bit deeper than this. I also have this tendency to be way, WAY overly ambitious about every one of my projects. Any time I investigate anything, I always find an endlessly branching tree of research, and it inevitably makes me unhappy to put my name publicly on anything that doesn’t try to capture the whole thing. I’ve struggled with perfectionism since elementary school. It’s a wonder I’ve been able to finish any project ever.
³Technically, my coauthor Nikhil Devanathan pushed it to arXiv.
⁴I have also seen a ton of other YouTube interpretations, like this one by Andy R Animations (who, by the way, also makes some banger documentaries), this one by Complex Research, this one by Crispy VFX, this one by ReverseLogic, and this one by Spectre, to name a few.
⁵Actually after this I rewatched Spaceballs for the fifth time, since it is free on YouTube!
⁶Somehow I imagine that a general audience will not be able to parse $P (A_{1}, A_{2}, \dots, A_{n}) = \int_{P} F (A_{1}) F (A_{2}) \dots F (A_{n}) μ (d F)$ as appears on page 138, even with a brief breakdown of the meaning of each symbol.
⁷I do find peculiar what he considers to be concrete and what he considers to be abstract. He defines concrete events by example only, refusing to even attempt a precise definition (and claiming it does not much matter). A firecracker exploded? Well, clearly that is concrete. $2 + 2 = 4$ ? Well, that is abstract. Sure, for these sort of basic mundane examples it’s pretty hard to contest the classification. But then take the example of a lone particle traveling at constant velocity in a perfectly Newtonian universe, or of the man in Benardete’s paradox standing still. These, to me, are sufficiently idealized as to render them abstract, yet Skow considers these to be concrete!⁸⁹ So, much as Eubulides of Miletus wondered where the boundary between heap and non-heap lies, I wonder about the boundary between concrete and abstract, or at least some necessary conditions for concreteness. Must an event be a change? Not to Skow: “Events don’t have to be changes […] If a room is completely empty for an hour, there is an event that occurs in that room” (p. 27). Must it be physical, located in spacetime? Also no: “a given non-physical mind (if there are any such things) thought ‘I think’” (p. 28) is a concrete event. Must it be physically possible? Nope, as Skow includes a variant of Benardete’s paradox as an example of a concrete event. Namely, he considers the halting of a point-ball at $0$ by a reverse-omega arrangement of infinitely many infinitely thin walls—that is, the $n$ th wall appears at $1/ 2^{n}$ and pops up only if every later wall has popped and the ball has cleared it—to be a concrete event. What renders $2 + 2 = 4$ abstract is that it is “concerning […] only mathematical objects”, which is to say abstracta, the very point at issue. Perhaps what distinguishes a concrete event from an abstract one is that an event is concrete if Skow’s theory applies, but then of course that gives no a priori handle on the distinction.
⁸Technically, Skow does not consider Benardete’s “paradox of the gods” directly, but a variant that involves a physical ball being obstructed by physical walls that are arranged in reverse-omega sequence. I discuss this more in a moment.
⁹Skow’s willingness to include the lone particle traveling in a perfectly Newtonian universe at constant velocity suggests that he would also be happy to recognize scenarios involving Norton’s dome as concrete. The idea is this: picture a point mass sitting exactly at the apex of a dome built so that, writing $r$ for the arc-length down the surface from the top, the tangential force pulling the mass downhill works out to $F = r$ . Newton’s second law then reads $\overset{r}{¨} = r$ , which admits the obvious solution (the mass remains stationary at the apex) but also a whole family in which the mass sits still until an arbitrary time $T$ and then slides off in any arbitrary direction, namely, $r (t) = \frac{1}{144} (t - T)^{4}$ for $t \geq T$ and $0$ for $t < T$ . There is no first instant of motion, no prior force, no privileged $T$ , and no privileged direction. So, if one considers the event that the point mass moves according to one of these nontrivial solutions, then presumably this is a concrete event, so falls under the jurisdiction of Skow’s theory. And yet this produces a strange answer under Skow’s theory, namely, that there is no reason why the mass moved at $T$ , none why then rather than ever, and none why in the particular direction that it did. I suppose there is nothing wrong with this. But I think it does sharpen the question of whether “explanation” really has any metaphysical substance at bottom, or is just a convenient organizing principle for us humans.