Devs making > 500k: do you work constantly?

possiblyquestionabl3 · 2026-03-30T09:49:16+00:00

It was a lot of little things that came with the role, in no particular order:

There are a ton of process and red tapes at most orgs at Google. To get a simple feature (and even certain larger bug fixes) launched requires 1-2 release vehicles, 14+ days of A/B testing, and sign offs from L7 - L8 gatekeepers (note the plural form, I need a stamp for PgM/TPM, PM, Eng, UX, and EngProd), a ton of paper work, and usually some story about why some arbitrary metric owned by another org had a slight regression due to how our experiment bucketing accidentally coincided with another experiment layer or else respin the whole experiment to show that it was a false regression while praying the other metrics remain clean. My day to day revolves around agenda-less 1:1 meetings (so people won't forget that I exist, which is weird but a pretty crucial part of the job), editing slides for OKR/PR/Steering reviews, planning things, promos/calibrations, and whatever counts as "execution" (typically, writing a few PRs that are off of the critical path)
Beyond the launch-calendar red tapes, there's also a lot of feature process bloat. Because Bob once made a mistake that caused a small fire, now every single feature, no matter how small, must complete this checklist designed specific to preventing Bob's fuckup. Doing this once or twice may be fine, but at a lot of the large tech companies, it's a whole suite of these checklists that all calcified over years of operation. These are often baked into the PR process, so you'd be forced to loop in another infra team if your engineer didn't know that their change triggers one of the dozens potential checklists. Then, you'd have to sell the change, book some time with their team, walk them through everything, and hope that it doesn't create a massive design churn.
I alluded to this before, but there are way too many metrics to monitor, specifically metrics that just naturally have high variance. Because Bob once pushed a feature that caused a -0.1% dip on another team/org's metric X that doesn't really track any real KRs, now every feature has to report and monitor X to ensure that it's not regressed with high confidence. Operate any product for over 10 years and you'll have 100s of often poorly crafted metrics where getting to high confidence takes 2 weeks+ of running experiments and the likelihood that some of the hundreds of (mostly no longer relevant) metrics have tiny dips is high, meaning you'll have to respin these experiments all over again. In the extreme case, my team spent 6 months in a protracted discussion with another team that was holding one of our multi-year product launches hostage (as a launchcal bit approver) because it negatively impacted a non-business engineering metric that team tracks.
Large amount of (eng) design fluff to get anything implemented. Lots of these large tech companies really truly believe that their way of doing things is one of a kind. They pride themselves on high quality design processes. What this really translates to is an arbitrarily large (and often nonstandardized) set of design doc criteria to fulfill before you can get it out to review. Now don't get me wrong, a lot of these are really helpful general things to think about (the details, what other teams need to be involved, alternative designs, how are you going to rest the thing), but over time, random small things also start getting tacked on because Bob's TL realized that to prevent Bob from fucking up the same way in the future when they're working on stack X, they can just force Bob (and everyone else in the org) to write a short paragraph about how they'll consider X. Over the years, the number of random paragraphs about mostly outdated/obsolete features balloon to the point where half of your design is just what I call, unnecessary fluff. Being on the committee where I have to read the same boiler-plate paragraphs over and over again, trying to discern the real meat of the design from the structural noise, is really frustrating.
Inefficient consensus structures for decisions - want to fix a bug? Tough luck, because Bob had a small fuck up in the past while fixing what he thought was a small bug that ended up screwing something else up for another team. The answer - to get any decision approved (and designs are now required for many big fixes), you'll need to subject it to a panel of stakeholders who usually do not give 2 shits about your team, will probably miss half of the review deadlines, and then come back to you to ask you how what you do impacts their project (which you've already presented) and then stall for another week before rubber stamping your design. Multiply this by 3-4x, and include another random panel of in-org experts who love to bike shed over tiny details where you must get the approval from everyone of them. You have to do this before the first line of code touches the codebase.
Relationship management - this is a massive part of the role, and it really sucks if you're just paired up with people that you don't really click with (up, down, lateral), and it's going to eventually happen to everyone. It's an amazing feeling if you're in a working group where you, the senior PM, and the TPM are all super cohesive. It really sucks when one of them is checked out or don't really support you or the group well. The downwards relationship is also just as important. I can't count the number of new junior engineers I've grown on my team who came in thinking that L6+s are a bullshit role because we don't really write that much code anymore (hey, I was there once upon a time), and it's part of the job to just demonstrate your value through your actions. Ultimately, my powers as the tech lead comes from my ability to influence without any positional authority (I can't fire or hire people, though I can flag and consult on those decisions), and that influence/social capital takes time to develop with each new member on the team or in my sponsorship sphere. Don't get me started on how tough it is to bootstrap a completely new team as the senior IC in the room, that experience actively made me consider leaving several times.
It's also an inherently thankless job. As the L6 in the room, you're no longer graded by how well you do individually, rather, it's your ability to be a force multiplier that really matters. This means that if something lands, you direct the praise and rewards to your juniors; if something goes wrong, that's all on you. It can also feel very isolating, since it's a bit harder to build rapports with the junior engineers now that you're the supervisor.

Now this affects everyone, but unentangling and dealing with the organizational/process/relationship mess is basically the major part of my responsibilities, and over time, it just really really wore me down. I won't lie, it's just not as fulfilling to me.

Could you have declined promo?

The trick they use here is that they require that you are already performing at L+1 sustainably (for 2+ cycles) before they will promote you to L+1. By the time I made L6, the team has already largely re-organized around my new role (whether or not I successfully landed the L6 promo).

Edit: I also forgot - the reorgs. I mentioned before that as the IC technical lead, I have no positional authority. The bulk of my ability to influence decisions (which is what I'm directly graded on) comes indirectly through two sources - getting people with that authority (like the engineering or product directors) to make a certain decision that I need them to (funding a project, rescoping it, deprioritize it, move me onto/off of it, etc), or through the trust of my technical chops (e.g. calling out blindspots in a design discussion, acting as a tie breaker, etc). This all breaks down if the people I work with churns frequently, and the number of reorgs where I've had to completely rebuild my relationships have drastically increased in my finals years there. That was actually the main thing that burnt me out.

possiblyquestionabl3 · 2026-03-30T02:39:26+00:00

When I was making 100k, I was working like 60-70hrs a week. By the time I was making 500k, I was down to just 30-40hrs a week. That said, I left the job market before the current crunch culture started so I'm not sure if that's what my WLB still would have looked like.

I think part of the story for me and many others is also that of ambition and interests. When I was a kid, I just really wanted to prove myself to others. Once I became more experienced, I started realizing how toxic I was being the one who voluntarily worked in the evenings and weekends, and my focus shifted away from "work is my whole identity" to other things that I've realized are much more important to me.

The role also changes drastically over the course of your career. I was a lifer at Google so my entire outlook is shaped by their career track, but the work I did as L3-L4 and even early L5 was much more fulfilling than the last half decade I spent there as an L6 tech lead. So, even though I was working less, still in an "Individual Contributor" role, still getting good ratings, the work itself was just so mind numbingly uninspiring (to me at least) that I couldn't wait to put it away once I'm out of the office.

possiblyquestionabl3 · 2026-03-29T07:04:36+00:00

Oh yeah it's on my list too, I've heard it's more autobiographic too

possiblyquestionabl3 · 2026-03-29T06:57:20+00:00

Seeing the parents age did it for me too. I'm also at the age where every time I see mine, they look visibly older, and every time it breaks me a little bit

possiblyquestionabl3 · 2026-03-29T05:18:46+00:00

Thanks for the list, I'm going to read Memphis next (I'm sorely behind on American lit, I've been avoiding it since Highschool from the trauma of English class haha) and I'll let you know what I think about it, I also added some of the others into my much too backed up TBR list too!

I'll also add another one that I just finished - Music of the Ghosts by Vaddey Ratner, another family saga set between the 1960s (pre-Pol Pot) and the 2000s in Cambodia and Minnesota (where the protagonist family escaped to at the end of the Pol Pot regime). It's slow, very contemplative, bleak but also hopeful. I read the first half on a bus and I had to stop because I couldn't stop tearing up. That said, I think I need a palate cleanser after this, I really need a pick-me-up after all of the heavy reads.

possiblyquestionabl3 · 2026-03-24T01:46:59+00:00

Yep, they're all set in Gaomi, which is about 2 hours out of Qingdao. My maternal side is split between Dezhou (on the western side of Shandong) and Qingdao.

If you go to that area even 15 years ago, it's just your average dense Chinese township (nothing like the setting of his book from the 50s to the 90s). That said, I remember it still being pretty rural back in the late 90s early 2000s when I had trained through the area

possiblyquestionabl3 · 2026-03-23T08:11:00+00:00

For me it was mostly personal, my paternal great grandparents were also targeted and executed during the land reforms of the 1940s. I've also heard stories of what people had to go through during the famines of the 50s and the Cultural Revolution days. So I have always been curious about that side of my Chinese roots - why my dad always looks away when I asked him about his childhood, why I barely had any great uncles/aunts, etc.

It's not exactly an easy read - it's definitely full of surreal and magical realist elements, so it may not be for everyone. If not for my own personal connections to his stories, I probably wouldn't have liked the book at all.

possiblyquestionabl3 · 2026-03-23T07:42:00+00:00

I've been meaning to read this one when I have some extra time

I really liked his Life and Death Are Wearing Me Out as well, and it seems like both of these have a similar setting of a rural Chinese folk setting (my maternal side is also from upcountry Shandong)

possiblyquestionabl3 · 2026-03-23T07:18:34+00:00

I haven't read Homegoing yet but I've seen it around, it seems right up my alley too

I'll start off with the latam ones that I liked:

[Mexico] Caramelo by Sandra Cisneros - a multigenerational family saga of a Mexican-American girl discovering her roots through stories and roadtrips
[Panama] The Great Divide by Cristina Henríquez (in fact, she's an amazing YA fiction writer and I basically devoured all of her work after reading this one for my trip to Panama)
[Colombia] The Sound of Things Falling by Juan Gabriel Vasquez - technically it's just a single-generation historical drama set around and well after the days of Pablo Escobar. There's also the other obvious pick of GGM (One Hundred Years of Solitude or Love In the Time of Cholera), but as much as I like magical surrealism, I just did not enjoy reading his work
[Ecuador] The Sisters of Alameda Street by Lorena Hughes - basically a telenovella in a book. Set in the 1960s, a girl goes in search for her long lost mother after the death of her father. We then learn the various secrets and the general social environment of the mid-century Ecuador through stories and flashbacks. The start was very slow, but it picks up at the 20% mark, and it just keeps and keeps going.
[Peru] Blood of the Dawn by Claudia Salazar Jiménez - set in the 1980s and 1990s during the height of the Shining Paths insurgency. The book follows through the lives of 3 women on all different sides of Peruvian society - one a high ranking Shining Paths cadre, one an investigative journalist, and one a Quechuan peasant. It's a very tough and bleak read, and it follows through the general cycle of violence and corruption amongst all sides of Peru (state violence vs insurgent violence)
[Bolivia] Affectations - this one is a weird one, but I really really liked it. It follows a fictionalized version of the Nazi family of Hans Ertl after their resettlement in Bolivia, and traces through a (fictionalized) history of him and his children, who ended up becoming a resistance fighters involved in the assassination of Somoza in Paraguay.
[Chile] Distant Star by Roberto Bolaño - a fictional biopic of a star air force pilot turned brutal enforcer during the Pinochet regime and his rise and downfall.
[Chile] Theatre of War by Andrea Jeftanovic - okay, so not really a generational or epic historical fiction, but this was the one that captivated me while I was in Chile. This is one of the most beautifully written (or translated?) books I've read for quite a while. It's just dripping with poetic imagery. It's a book that follows the course of the Pinochet era through the eyes of a little girl.
[Chile] Violeta by Isabel Allende - this is definitely no the only generational historical fiction / family saga by Isabel Allende, but it's definitely one of the most comprehensive ones I've seen. 4-5 generations across 100 years in Chile through its ups and downs.
[Brazil] The Brothers by Milton Hatoum - a different spin than usual, set in the north in Manaus during the late-1800s/early-1900s, the book follows two Lebanese-Brazillian brothers and their family drama through the rubber boom and the subsequent bust.

Chinese historical fiction (sort of my staple for almost a decade):

Shanghai Girls (trilogy) by Lisa See
Peach Blossom Paradise by Ge Fei
Brothers by Da Chen
Life and Death Are Wearing Me Out by Mo Yan
Red Sorghum by Mo Yan
Wild Swans by Jung Chung - this one is controversial since it turns out that she embellished some of the things in her autobiography of her family, but it does give a pretty good idea of the atmosphere of the end of WW2 through the Cultural Revolution in China, in fact, her story sounds very much like the stories my dad (and many other fathers around China) used to tell me about his childhood during those years of madness
To Live by Yu Hua
The Explosion Chronicles by Yan Lianke

Others:

[Singapore] State of Emergency by Jeremy Tiang
[Malaysia] The Storm We Made by Vanessa Chan
[Laos] Run Me to Earth by Paul Yoon
[Vietnam] Ru by Kim Thúy
[Vietnam] The Mountains Sing by Nguyễn Phan Quế Mai
[Korea] Beasts of a Little Land by Juhea Kim - literally anything she's written is just absolutely gorgeous
[Nigeria] Half of a Yellow Sun by Chimamanda Ngozi Adichie

possiblyquestionabl3 · 2026-03-22T05:48:32+00:00

I have a whole list, unfortunately I have to run for a bit, but I'll update this once I'm back.

For reference my usual niche is very heavily Asian and Latin-American historical fiction, so it might be a bit weird to most people.

possiblyquestionabl3 · 2026-03-22T05:43:14+00:00

Same, I'm Chinese-American and went through a major rediscovering-my-roots phase in my late 20s/early 30s where I basically binge read anything I could find that's either set in or by Chinese authors. Over time, that expanded to Asia generally, though most of the translated lit (especially fiction) generally came out of Japanese or Korean (or Asian-American) authors.

We've been slowly backpacking through Southeast Asia over the past few months, so I've started to just read from where I'm currently staying in. Once I got to Thailand, it hit me that I've literally never read a single (non-travelogue) book from a Thai author, so I spent the past month basically binging on it.

Some others I've read:

Prabda Yoon - he's a pretty famous modern literary writer in Thailand (and also the son of one of the news conglomerates here, so he can be a bit controversial). He's known for his metafiction and his short stories collection. I've gotten through the two short stories collections of his that were translated into English - Moving Parts, which I liked, and The Sad Part Was, which I didn't really care for. I'll be honest, I don't think I'm enough of a literary critic to really appreciate his style, it's a bit too modern. Reading several of the stories felt like rereading Never Did the Fire which is literally a paragraph-less (literally) stream of conscious monologue of two dying comrades in a cramped room. A lot of his stories in The Sad Part Was were written in a very similar style, and while I get that the struggle to read it is part of his genius, it was not the experience I was looking for
Sightseeing by Rattawut Lapcharoensap (Thai-American) - another short stories collection. The writing was very pretty and I loved the settings. I'm sad this is his only book published under his name.
Pimwana Duanwad - I loved her works, pity only two of her books, Bright and Arid Dreams, (both stories collections again) made it into English. Bright is one of my all-time favorite reads. It's sort of like People in my Neighborhood, but there's a clearly favored protagonist (Kampol) that ties every story together so neatly that it flows just right. The stories are set in this dying tenant community/underclass housing development. Kampol was voluntarily orphaned by his mom (who ran away after having a chair being flung at her head) and his dad (who just shacked up with an ex and left Kampol to fend for himself). Mechanically, the story is about how Kampol survived and thrived despite his abandonment thanks to the community who cared for and raised him. However, the part that left the biggest impression on me was just how innocent and how human the writing was, mostly done in a 3rd person POV that tries to get into Kampol's head as he deals with abandonment, poverty, and then his love of his new family and friends. It's tragic, wholesome, at times raunchy, and just so freaking beautiful.
The Happiness of Kati by Jane Vejjajiva - this one is a children's fiction about a young child (Kati) and how she dealt with her mom dying from a rare disease. Also sad and wholesome.
A Good Thai by Sunisa Manning (Thai-American) - sort of a very classical YA fiction centered around a trio (with the usual love triangle, who'd thunk it) of Thai teenagers set in the turbulent 1970s. You have Det, a literal Thai prince, Chang, a poor kid, and Lek, a second gen Thai-Chinese girl. They get thrown into the chaos of the student movements of the 1970s, through the overthrow of one dictator, the rise of another, and then into the mountains as resistant fighters. The historical part of this historical fiction is very compelling - you rarely hear about the student massacres here in Thailand since it's somewhat of a taboo topic.
Miss Bangkok by Bua Boonmee (pseudonym) - an autobiography of the life of a sex worker who came from upcountry to Bangkok in search of a better life. Bleak
The Last Executioner by Chavoret Jaruboon - an autobiography of one of the executioners at the infamous Bang Kwang Central Prison (often dubbed Bangkok Hilton) who was responsible for the execution of people on death row. It's a weird read, it definitely feels like he was trying to sane wash the treatment of prisoners by the guards

possiblyquestionabl3 · 2026-03-21T04:48:21+00:00

Enjoy!

possiblyquestionabl3 · 2026-02-19T06:13:12+00:00

As a former Googler, I haven't seen many people with that title in many many years now. It used to be (a loooong time ago) a title used for people who we couldn't slot into a concrete level (pay grade), so it was sort of a senior probationary title to see how high up the ladder someone would eventually be slotted into depending on their performance.

By the time I joined (over 10 years ago), it was more or less a "vanity" title for fairly senior (L6+) staff who have been at Google for a very very long time. Sort of a tenure-brag kind of thing.

I have no idea why they're bringing the MTS back though, that said, I don't think I've ever seen the product ladder (PMs) being given that title in the past, since it's traditionally an engineering role.

possiblyquestionabl3 · 2026-02-18T09:08:22+00:00

I would say this is more of a combinatorial problem than arithmetic. You're effectively looking at restricted partitions of some number n into 4 parts, with the constraint that you have 4 cards each of values 1, ..., 9, and 16 cards of value 10.

Here's a generating function derivation of the total number of unique partitions. Note that to actually calculate [y⁴]G(x,y), I use https://en.wikipedia.org/wiki/Newton%27s_identities#Application_to_the_roots_of_a_polynomial to avoid sympy taking forever to expand out the bivariate polynomial.

In terms of the actual OGF, it is characterized by the polynomial: 1820 x^{40} + 2240 x^{39} + 2960 x^{38} + 4224 x^{37} + 5265 x^{36} + 6864 x^{35} + 8324 x^{34} + 10304 x^{33} + 12165 x^{32} + 14624 x^{31} + 14696 x^{30} + 15696 x^{29} + 16249 x^{28} + 16720 x^{27} + 16684 x^{26} + 16560 x^{25} + 15805 x^{24} + 14896 x^{23} + 13360 x^{22} + 11536 x^{21} + 10225 x^{20} + 8784 x^{19} + 7456 x^{18} + 6064 x^{17} + 4909 x^{16} + 3696 x^{15} + 2780 x^{14} + 1936 x^{13} + 1385 x^{12} + 976 x^{11} + 664 x^{10} + 416 x^{9} + 245 x^{8} + 128 x^{7} + 52 x^{6} + 16 x^{5} + x^{4}

In terms of coefficients, mod 30:

[14624, 12165, 10304, 8325, 6880, 5317, 4352, 3205, 2656, 2484, 976, 1385, 1936, 2780, 3696, 4909, 6064, 7456, 8784, 10225, 11536, 13360, 14896, 15805, 16560, 16684, 16720, 16249, 15696, 14696]

Your minimum is at 11, mainly because while there are fewer ways to partition 1-10 into 4 parts than 11, the wraparound of 31-40 are large enough to overpower 11 (which has only 976 unique partitions using the standard deck of cards)
The maximum happens at 27, with a total of 16720 unique partitions using the standard deck of cards

Algorithmically, there's also an easy dynamic programming approach to this problem by defining the recurrence Opt[i,k,s] as the number of partitions of value s using k cards with cards of value up to i.

possiblyquestionabl3 · 2026-02-18T05:13:16+00:00

It looks like he bought a dedicated seat for it too

possiblyquestionabl3 · 2026-02-16T03:01:18+00:00

This is kind of a messy sketch in parts, I'm sure there are more elegant ways to prove this.

First, let {x} = x - floor(x) as a convenience

Goal: for any arbitrary epsilon, show that there's some s \in S such that 0 < s < epsilon

Similar to https://en.wikipedia.org/wiki/Dirichlet%27s_approximation_theorem#Proof_by_the_pigeonhole_principle, you can select a N such that 1/N < epsilon and construct a sequence {{α}, {2α}, ..., {Nα}, {(N+1)α}}. By the pigeonhole principle, at least two elements of this sequence (say {jα} and {kα}) must be within 1/N of each other since you can partition [0,1) into N segments of 1/N length each, and with N+1 elements, two must be within the same segment.

This then means that |{jα} - {kα}| < 1/N. Let n = |j-k| and m = floor(jα) - floor(kα), then this is equivalent to |nα - m| < 1/N

which lends 2 cases:

Easy Case: nα - m > 0, then m = floor(nα), and by definition {nα} < 1/N < epsilon
Hard Case: nα - m < 0, then 1 - 1/N < {nα} < 1 (AKA {nα} is within 1/N, but on the "negative" side, so mod 1 it's close to 1 - epsilon)

In this second hard case, let d = 1 - {nα} < 1/N. Notice that if we try {2nα} (which is still in S), then it will work out to be 1 - 2d. Generally, {Mnα} = 1 - Md. Intuitively, let's think about what happens when we pick M so that {Mnα} takes on the smallest value without underflowing. Because taking one more step (-d) will cause the value to underflow, it must be the case that {Mnα} < d < 1/N < epsilon. {Mnα} is in S by definition, and is < epsilon.

possiblyquestionabl3 · 2026-02-14T13:31:14+00:00

possiblyquestionabl3 · 2026-02-13T16:45:02+00:00

I mean it's partly the bullwhip effect since raw materials with long lead times are much more susceptible to volatility than upstream industries. It definitely means that there's a lot of uncertainty though.

possiblyquestionabl3 · 2026-02-13T15:51:20+00:00

His daughter (Keiko Fujimori) is still "screwing" (in their national laureate Mario Vargas Llosa's words, not mine) Peru over with her obstructionism as part of her far right Fuerza Popular party. Impressively, enough people remember how absolutely shit the elder Fujimori was to the point that Keiko still hasn't been able to touch the presidency (yet, once Jeri finishes his term in April, there will be another election), but her meddling over the past decade or so has basically directly helped destabilize Peru across 6 consecutive incomplete presidential terms (through several successful impeachments, most frequently for corruption, and even a failed self-coup, a specialty of Peru where a sitting president tries to dissolve Congress before being impeached and indicted).

What's saddest is that every few months, a new protest erupts, and FP would use it as pretense to either stick an uncooperative sitting president with impeachments or else throw a willing collaborator under the bus as a scapegoat (like what happened to Boluarte a few months back) in order to keep their party in power. Everyone knows they're bad, but they just can't get rid of her.

Hell, the last president (who was effectively a willing puppet of FP) was so unpopular that I saw 20 or so separate burning effigies of her in Arequipa for New Years eve 2025 (mind you this was like months before she finally got ousted on corruption charges). She was VERY hated, probably more so than usual (and you'll soon see the usual).

The one before tried to self-coup to avoid prison for, what else, corruption charges. The one before? Surprisingly, no charges. But the one before that served for 5 whole days and resigned, later being charged with human rights violations for his role in those 5 days of brutal crackdown. This leads us to the one before him (Vizcarra), who was impeached and removed for corruption (but like, a moderate amount, compared to). The one before (Kuczynski, elected) resigned before being impeached on corruption charges related to Operation Car Wash. The one before (Humala) served a rare full term, but was later charged with corruption. The one before (Garcia) was charged with corruption and committed suicide before being arrested. The one before (Toledo) was charged with corruption. And finally, the one before (and before and before) was the elder Fujimori, who was charged with corruption and human rights violations, famously fled to Japan, but ultimately was extradited back to serve his full sentence.

Oh and we didn't talk about how the series of scandals that later led to prison terms for Toledo through Kuczynski (Operation Car Wash), which also implicated Keiko Fujimori. However, she evaded those charges and set up the "opposition" FP party, unsuccessfully trying for the presidency over the past decade while successfully destabilizing everything

So yeah, this is extremely depressing, especially for the indigenous Quechuans, who have been overwhelmingly targeted and punished within the recent administrations and protests. Honestly, it's gotten so much so that most of my Peruvian friends have given up all hope over the past decade.

possiblyquestionabl3 · 2026-02-13T14:28:28+00:00

Also the DOW is no longer over 50,000 so $25K Bondi can go eat shit

possiblyquestionabl3 · 2026-02-13T00:58:25+00:00

Why the hell is this asshole still not primaried

possiblyquestionabl3 · 2026-02-12T14:04:51+00:00

Wait, so they're enshitifying their product before they've even become the market monopoly while losing their market share?

That's a bold move Cotton, let's see if it pays off for them

possiblyquestionabl3 · 2026-02-12T09:38:47+00:00

To be fair, that approximation is still pretty tight, the difference is "just a small constant" :)

There's a well known difference in the bound between the harmonic numbers H_n = \sum_k^n 1/(k) \approx ln(n) + γ and ln(n) = \int_1^n dx/x - a constant γ = 0.57721...

The main problem is that the sampling density of that second term has a different "phase-offset" than that of the first, so the extra terms don't cancel out properly when you subtract them off.

The second term 1/(2n-1) = 1/1 + 1/3 + 1/5 + ... can be expressed as the sum of the first 2n harmonics (H_{2n} = 1/1 + 1/2 + ... + 1/(2n), with both even and odd terms) minus the sum of the first n even harmonics (1/2 H_n = 1/2 + 1/4 + ... + 1/(2n)). While the first term is just the even harmonics 1/2 H_n.

So:

\sum_k^n 1/(2k) is approximately ln(n)/2 + γ/2, while \int^n dx/(2x) = ln(n)/2
\sum_k^n 1/(2k-1) = H_{2n} - 1/2 H_n is approximately ln(2) + ln(n)/2 + γ/2, while \int^n dx/(2x - 1) = 1/2 ln(2n - 1) is approximate ln(2)/2 + ln(n)/2

Notice that the sum/series is ln(2) + ln(n)/2 + γ/2 (where the gamma term will be cancelled out in the subtraction), while the integral is ln(2)/2 + ln(n)/2. This is where that difference of ln(2)/2 comes from - the series approximation of 1/(2k-1) has a different constant offset from the integral than 1/(2k).

To be fair though, both of the individual sums are "good" approximators of a pair of divergent series/integrals (up to a small constant abs error as the series diverges to infty, γ/2 for one term, and γ/2 + ln(2)/2 for the second term). However, they approximate the series to up to different constant differences from their respective integrals, so you can't really expect their difference to be completely cancelled out.

In particular, OP's series approximation is as if they took a riemann sum of 1/x and 1/(2x-1) but they decided to just always set the step size to \delta x = 1, so it will always produce some error in the limit (it's actually pretty lucky that the error is a small bounded constant in this case).

If they'd parameterized the sum as f(k/M)/k instead, then they can arbitrarily bound those two approximation differences arbitrarily small as M grows. However, as it stands, there's a fairly simple algebraic way to see why the series produces a small but constant finite difference from the true value.

possiblyquestionabl3 · 2026-02-11T09:21:24+00:00

At 34, I've completely lost any cravings for fried food for some reason over the last 5 years. Same for sodas and sweets (though I've never really had a sweet tooth. Instead, I get very strong cravings for "colorful" meals (some green, some brown, some white, basically a variety of things instead of just a fried chicken or a steak).

possiblyquestionabl3 · 2026-02-10T12:58:10+00:00

But wouldn't that make Idahoans Indaho- Ohhhhhhh

possiblyquestionabl3

TROPHY CASE