I have a grow­ing ha­tred for AI-generated im­ages in blogs. It makes me won­der if the text in the blog posts is AI-generated to some ex­tent. It’s al­ways dis­ap­point­ing see­ing these im­ages in blogs run by in­di­vid­u­als. I ex­pect this from cor­po­rate blogs but not in­die blogs.

I’d rather see a shitty Microsoft Paint draw­ing as op­posed to some AI im­age.

I know there are plenty of things you can roast my blog for but at least you know for a fact you’re get­ting the thoughts of a real hu­man be­ing and not some LLM.

If you run a per­sonal blog, please avoid AI-generated im­ages.

Discussion over at Hacker News

Something ter­ri­ble just hap­pened. My wife, Elise Cawley, was re­cov­er­ing from heart surgery and had just at­tended vir­tu­ally a cel­e­bra­tion for one of our chil­dren when she had a freak, vast car­dio­vas­cu­lar event—and died in­stantly. We had been to­gether for 36 years. The pic­ture above was taken just hours be­fore she died.

In all the writ­ing and pub­lic speak­ing I have done, I have cho­sen, as a mat­ter of pri­vacy, to say lit­tle about my fam­ily. But now that Elise is gone I can­not re­strain my­self from telling the world some­thing about the re­mark­able per­son with whom I shared the past 36 years of my life.

It was September 17, 1990, and I was in New York City. The event I had been at­tend­ing fin­ished a lit­tle early, so I de­cided to drop in on a friend of mine. And there, sit­ting styl­ishly on the floor, was Elise, a some­what bash­ful but ob­vi­ously bril­liant young pure math­e­mati­cian. It took me a cou­ple of weeks to call her. But from that mo­ment on we talked es­sen­tially every day for 36 years—un­til the day she died a week ago.

Somehow in the shock of what has hap­pened it feels as if I just met Elise, and now she is gone. But ac­tu­ally there were 36 won­der­ful years in be­tween, in which my life was lit up by Elise’s in­tel­lect, love and en­ergy. She was deeply the­matic, able to get, with re­mark­able ease, to the essence of things. Truth, beauty and our fam­ily and four chil­dren were her great themes. She al­ways told me that truth and beauty were ul­ti­mately the same thing, and that one day I would un­der­stand that. What I could see is that she her­self loved to cre­ate beauty—whether in math­e­mat­ics, in­te­rior de­sign, ar­chi­tec­ture or per­sonal style. She was a force­ful in­tel­lect, kind and sweet, but per­sis­tent and of­ten feisty in ar­gu­ing for what she thought was true.

Despite her deep knowl­edge and ca­pa­bil­ity in ab­stract math­e­mat­ics, she was at some level fun­da­men­tally a hu­man­ist, think­ing about the world in hu­man terms. She de­cried dry mod­ernism and was drawn to the hu­man con­nec­tions of clas­si­cism. In re­cent years she thought in­creas­ingly about the foun­da­tions of math­e­mat­ics, tak­ing a Platonic view of truth and lament­ing the twen­ti­eth-cen­tury tran­si­tion to a more for­mal­is­tic ap­proach.

There was al­ways a cer­tain lively spon­tane­ity to Elise, mixed with a drive to­wards the high­est stan­dards of in­tel­lec­tual and aes­thetic rigor. People’s first im­pres­sions of Elise tended to be of her per­sonal en­ergy, her lively style and her keen in­tel­lect. But as they got to know her, they would also come to see how much she cared about the peo­ple around her and how much lov­ing thought and ef­fort she would put into things she did for them. Whether it was a gift or the in­te­rior de­sign of a space, Elise would ap­ply her cre­ativ­ity and go back and forth un­til it was just right.

Our four chil­dren were a defin­ing part of Elise’s life, and she was im­mensely proud of all of them (as am I!). She had her own unique re­la­tion­ship with each of our chil­dren that helped them each de­velop in their own way. She also built us a won­der­ful home, full of warmth, ar­chi­tec­tural beauty and cre­ative de­sign. She took great plea­sure in per­fect­ing every de­tail, main­tain­ing re­mark­able over­all co­her­ence, with dashes of the un­ex­pected.

Elise was a very fine math­e­mati­cian, top flight in tech­ni­cal mas­tery but, more im­por­tantly, able to the­mat­i­cally pull to­gether grand con­cep­tual arcs. She was al­ways drawn to el­e­gance, of­ten with an ab­stract geo­met­ri­cal bent, and by the time I met her she had al­ready es­tab­lished her­self with re­sults that con­tinue to be cited to­day. Later in life Elise would re­fer to her­self as a “retired math­e­mati­cian”, but if ex­posed to her kind of math, she would im­me­di­ately en­gage with great en­thu­si­asm.

In all my years with Elise we never di­rectly worked to­gether on in­tel­lec­tual pro­jects. Perhaps we were both too strong willed, and with her quick mind, it did not take long for her to get im­pa­tient with the dif­fer­ences in our styles of think­ing. Still, I would of­ten tell her about work I was do­ing. And it was re­mark­able how ef­fort­lessly she would see deeper themes, which she would then ex­plain back to me, with vary­ing de­grees of pa­tience.

She liked my con­cept of com­pu­ta­tional ir­re­ducibil­ity, and I think was pleased that the ef­forts in sci­ence on which I had spent so many of our years to­gether had led to a place that high­lighted the lim­i­ta­tions of sci­ence and of sci­en­tism, and aligned well with her hu­man­is­tic world­view. When I be­gan to form ideas about ob­servers and the ru­liad, she was far ahead of me in see­ing their philo­soph­i­cal and meta­phys­i­cal im­pli­ca­tions.

For years, the foun­da­tions of math­e­mat­ics were some­thing of a sore point be­tween us (and our chil­dren were highly amused that one of the most vig­or­ous ar­gu­ments they ever saw be­tween us was about the meta­phys­i­cal char­ac­ter of the con­cept of a cir­cle). Elise main­tained that raw ax­iomatic for­mal­iza­tion can­not be the true essence of math and that math is re­ally some­thing much more hu­man. And fi­nally, just a few years ago, by a long and cir­cuitous route, I came to re­al­ize that—de­spite my ob­sti­nate in­sis­tence to the con­trary—she’d been right about this all along. But then she made other as­ser­tions too, that she thought were quite sig­nif­i­cant. Like that the fun­da­men­tal ab­strac­tions from which we build math as we know it are the con­cept of point (which she viewed as equiv­a­lent to space, con­ti­nu­ity and in­fin­ity), and the con­cept of num­ber. She also as­serted that physics dif­fers from math mainly in its in­tro­duc­tion of the con­cept of time.

While Elise could be a very orig­i­nal thinker, she also be­lieved in the value of ex­ist­ing wis­dom and ex­ist­ing ways of do­ing things—and was con­stantly telling me that I should­n’t try to fig­ure out ab­solutely every­thing (including about every­day life) from first prin­ci­ples. Being with Elise was al­ways some­thing of an ad­ven­ture. There was spon­tane­ity (“no plan; let’s play it by ear”), yet also pre­ci­sion and per­fec­tion. And there were the force­fully de­liv­ered bursts of in­sight, not just about math and ab­strac­tion, but also about the hu­man con­di­tion and the way the world works. Elise would say that there were peo­ple of ac­tion, and there were philoso­phers. She saw her­self more as the lat­ter. She had strong opin­ions about how things should be in the world. But she was much more in­ter­ested in fig­ur­ing out what should be than in what she saw as the grind of try­ing to make it ac­tu­ally hap­pen.

Elise was a per­son who had both great con­fi­dence and great hu­mil­ity. While she was al­ways con­vinced that she was right in things she thought (and in fact usu­ally was), she was never one to ad­ver­tise her ca­pa­bil­i­ties. Still, if ever a con­ver­sa­tion turned to things she knew or cared about, she would­n’t re­strain her­self from mak­ing what was of­ten a deeply in­sight­ful con­tri­bu­tion.

I al­ways thought Elise and I were an out­stand­ing match—sim­i­lar in many ways, yet also com­ple­men­tary. We both val­ued the­matic think­ing (though in many do­mains she was bet­ter at it than me), and we shared an ap­pre­ci­a­tion for aes­thet­ics and work well done. But for ex­am­ple our ways of in­ter­act­ing with peo­ple were some­what dif­fer­ent. My chil­dren say I have only one mode of in­ter­ac­tion: full on. Elise was at some level more in­tro­verted and would imag­ine her­self to be shy—though once en­gaged she would be­come highly talk­a­tive and an­i­mated. And when it was just Elise and me on our own, we al­ways seemed to have things to talk about, in fact an in­fi­nite num­ber of things.

Elise was born in 1961 in Urbana, IL—ironically not far from the head­quar­ters of our com­pany—when her fa­ther was a physics grad­u­ate stu­dent at the University of Illinois. The sec­ond of four chil­dren, she grew up mostly in Columbia, MD, as a top stu­dent, par­tic­u­larly rec­og­nized for her math and her the­matic es­says. As she of­ten men­tioned to our chil­dren, in 6th grade her teacher char­ac­ter­ized her writ­ing as “the cat’s pa­ja­mas”—and for a while she imag­ined grow­ing up to be a writer. In high school she had the for­ma­tive ex­pe­ri­ence of go­ing to the Hampshire sum­mer math pro­gram, where for the first time she met other peo­ple who were in­tensely in­ter­ested in math.

She went to MIT for col­lege, falling in with a group that in­cluded sev­eral later promi­nent math­e­mati­cians. She al­ways told me that what re­ally ig­nited her in­ter­est in con­cep­tual pure math­e­mat­ics was an epiphany she had in a class she took about topol­ogy. At MIT, she sup­ported her­self by work­ing in the the­sis bindery, us­ing her cal­li­graphic skills to la­bel the­ses. She also made up lan­guage puz­zles for a lan­guage ac­qui­si­tion study and had a sum­mer job work­ing on al­go­rithms at an early speech recog­ni­tion com­pany. A fam­ily cri­sis took her back to Maryland, where she fin­ished de­grees in both math and physics at the University of Maryland. She also had an in­tern­ship work­ing on a PET scan­ner at NIH, vol­un­teered at some hos­pi­tals and con­sid­ered go­ing to med­ical school. But in the end she de­cided on grad­u­ate school.

She could­n’t make her mind up be­tween physics and math but ended up ap­ply­ing in physics. One of her physics pro­fes­sors had said she was the best stu­dent he’d ever seen but would be most suited to very the­o­ret­i­cal physics. She had her choice be­tween Harvard and Berkeley. And in her ever-typ­i­cal fash­ion she waited un­til the last minute, pick­ing Berkeley be­cause she was told she’d be able to switch to math there.

After an in­tense “think on your feet” in­ter­view process, she re­ceived a Hertz Foundation fel­low­ship, which gen­er­ously sup­ported her grad­u­ate stud­ies. Before even ar­riv­ing at Berkeley she’d set­tled on math, and hav­ing im­pressed peo­ple with her el­e­gant so­lu­tion to a small open prob­lem, she joined a group work­ing on geo­met­ri­cal ap­proaches to dy­nam­i­cal sys­tems. After four years in grad­u­ate school she com­pleted her PhD the­sis on “Smooth Markov Partitions and Toral Automorphisms”. It was quin­tes­sen­tial Elise. An el­e­gant the­matic idea im­ple­mented with clean tech­ni­cal pro­fi­ciency.

It made her a hot­shot young math­e­mati­cian, sought af­ter by many uni­ver­si­ties. She ended up with two jobs: a tenure-track pro­fes­sor­ship at Stony Brook and an NSF post­doc spon­sored by the promi­nent math­e­mati­cian Dennis Sullivan. She chose to de­fer the pro­fes­sor­ship and take the post­doc for a year, partly at CUNY in New York City and partly at IHES near Paris.

While at IHES, Elise lived in the very cen­ter of Paris, only steps from the Jardin du Luxembourg, in an un­used stu­dio owned by an artist who was the sis­ter of an­other math­e­mati­cian. It was a pe­riod of in­tense math­e­mat­i­cal work for Elise about which she was very en­thu­si­as­tic. And her the­matic and aes­thetic sen­si­bil­i­ties drew her to the study of Teichmüller spaces, which are spaces of pos­si­ble geo­met­ri­cal ob­jects, or in a sense spaces of pos­si­ble spaces. It was also at this time that she em­barked on what would be a long-term in­ter­est in the so-called ther­mo­dy­namic for­mal­ism, or Gibbs the­ory.

With con­nec­tions to math­e­mat­i­cal physics, Gibbs the­ory pro­vides a way to talk about in­fi­nite col­lec­tions of in­fi­nite struc­tures, and their de­vel­op­ment, for ex­am­ple through time. (Ironically enough—as Elise would re­peat­edly men­tion—con­cepts such as trans­ver­sals that ap­pear in Gibbs the­ory are now di­rectly rel­e­vant to my own work on in­fra­geom­e­try and the foun­da­tions of physics.)

Rather un­typ­i­cally for a math­e­mati­cian, Elise was al­ways no­table for her dis­tinc­tive per­sonal style—of­ten an in­ter­pre­ta­tion of cur­rent fash­ion, but with her own spunky and col­or­ful touches. As one of my daugh­ters tells it, Elise’s in­ter­est in style be­gan to ex­pand with the fund­ing she re­ceived from her Hertz fel­low­ship and de­vel­oped fur­ther dur­ing her time in New York City and Paris.

Upon re­turn­ing from Paris, Elise was about to start at Stony Brook, but while wait­ing for her apart­ment to be ready, was stay­ing with her long-time friend Lisa Goldberg in New York City. And that’s how, on September 17, 1990, Elise and I first met.

Lisa’s apart­ment was an el­e­gant one, but I was not quite so el­e­gant that day. I had been at a tech in­dus­try event where I had re­ceived a rather bulky award, which was in my jacket pocket weigh­ing it down. Elise was sit­ting on the floor, with her bangs flopped across her face, in a pose that I thought might be yoga. We talked just a bit, but it was enough.

The next day I went back to Champaign, IL, where I was based at the time. It had been two and a half years since we’d re­leased Mathematica 1.0 and our com­pany was grow­ing rapidly. I had started my ca­reer young, so even though I was only two years older than Elise (she was close to 29 and I had just turned 31), I had al­ready done quite a bit, both in acad­e­mia and the tech in­dus­try.

Early ver­sions of Mathematica came with a book, that I had to write. And in September 1990 I was rush­ing to fin­ish the sec­ond edi­tion of that book, to ac­com­pany Mathematica 2.0. Two weeks af­ter I re­turned to Champaign, I did fin­ish, though promptly got sick with a high fever. And that was when I fi­nally called Elise.

Soon I was tak­ing trips to Stony Brook, and she to Champaign. And when apart we were talk­ing by phone for hours each day. Lisa Goldberg made a point of telling me, “She’s a very fine math­e­mati­cian, you know”. Elise had met an­other per­son a lit­tle ear­lier, and Lisa had dis­missed them as un­suit­able. But—as I just now learned from one of my chil­dren—when Elise asked Lisa about me she im­me­di­ately re­sponded with en­thu­si­asm.

One no­table trip was the re­sult of a call I got from Elise where she ex­plained that she’d mixed up con­tact lens so­lu­tion and hy­dro­gen per­ox­ide and now had to patch both her eyes for a few days. I im­me­di­ately got on the next flight. And while the only food I could cook at that time (and still to­day) was an omelette, she viewed this “rescue” as an act of chivalry that—as she told our chil­dren—was what de­fin­i­tively sold her on me.

On Elise’s 29th birth­day in December 1990 I sent some flow­ers. She re­sponded by email, now bit­ter­sweet:

Hi there. Some amaz­ing flow­ers just ar­rived. I think I can make to92. I’m head­ing off to aer­o­bics — tonight is the amaz­ing Margaret(who plays great mu­sic). I has some good math con­ver­sa­tion with­caro­line s. to­day. And got a lit­tle bit of real work done.

I’ll be back around 9pm.

elise

The very next email I re­ceived from her was about a bug in the Mathematica Residue func­tion.

My day job was (and still is) tech CEO. But what made me orig­i­nally de­velop our tech­nol­ogy was that I wanted to use it my­self—to do sci­ence. By the spring of 1991 I was get­ting frus­trated that I could in­ject new ideas into our com­pany faster than it could ab­sorb them. So I de­cided I should take some­thing of a sab­bat­i­cal and work on sci­ence for a while. Meanwhile, Elise still had time left on her NSF post­doc, that she could take any­where. And so it was that we de­cided to get a house to­gether in the hills above Oakland, CA, and she re­turned to Berkeley.

Before mov­ing into the house that she found for us, she came with me on an 18-city tour of Europe+Russia to pro­mote Mathematica 2.0. After that, we set­tled into a good rou­tine. She would go off each day to do math. I would stay home to be a re­mote CEO, and work on sci­ence. And from time to time she’d jet off to Texas, Montana, France or wher­ever to give talks.

By late 1992 we were think­ing about next steps. Elise was adamant that she could­n’t live in Champaign-Urbana (despite hav­ing been born there). But she thought the idea of liv­ing in the Chicago area was in­ter­est­ing. Meanwhile, she was highly in de­mand as a math­e­mati­cian, and there were mul­ti­ple op­por­tu­ni­ties for her there.

Elise took charge, and ex­plored many dif­fer­ent lo­ca­tions and houses around Chicago, even­tu­ally pick­ing a house in Hinsdale, IL. We moved there in the mid­dle of 1993, and Elise took up a po­si­tion at the University of Chicago. It was a nice house, but Elise thought it could be nicer, and set about ren­o­vat­ing it to have top-of-the-line in­te­rior de­sign. She started work­ing with a de­signer who she dis­cov­ered by read­ing mag­a­zines, and learned that her aes­thetic and geo­met­ric sen­si­bil­i­ties trans­lated well into cre­ative in­te­rior de­sign. Elise was par­tic­u­larly keen on in­te­grat­ing lively col­ors and un­ex­pected el­e­ments into tra­di­tional de­sign themes.

Meanwhile, at the University of Chicago, Elise was teach­ing a course about Gibbs the­ory. She wrote ex­ten­sive notes which she planned even­tu­ally to turn into a book. Over the years, peo­ple asked for the book many times, and Elise had re­cently started talk­ing about fi­nally fin­ish­ing it. Ironically enough, our daugh­ter Catherine, now her­self a math­e­mati­cian, has ended up work­ing in some­what re­lated ar­eas.

Elise in­ter­acted a lot with Bob Zimmer, who was then chair­man of the math de­part­ment (and would later be­come pres­i­dent of the University of Chicago). Together they de­vised the con­cept of a new ac­tiv­ity for the math de­part­ment: a pro­fes­sional mas­ter’s de­gree in fi­nan­cial math­e­mat­ics, ba­si­cally aimed at quants, and taught by math pro­fes­sors. Though Elise was never too in­ter­ested in the messi­ness of ac­tual mar­ket data, she liked the pure math­e­mat­ics of mar­ket mod­els, and helped de­velop a cur­ricu­lum around it. The mas­ter’s de­gree ended up be­ing highly suc­cess­ful and con­tin­ues to this day.

In the fall of 1994 Elise and I mar­ried. And then, in December 1995, as Elise would later de­scribe it, “the world overnight had a new cen­ter”: our first child, Alexander, was born. The next few years were dom­i­nated by the ar­rival of chil­dren, with Catherine be­ing born in 1997 and Christopher in 1998—leaving Elise, as she put it, with “three un­der three”.

With our fam­ily grow­ing—and our book col­lec­tion reach­ing over 5000 vol­umes—we were out­grow­ing our house in Hinsdale, and started look­ing for a new home. At first, Elise found real es­tate in Lake Forest, IL. But when the deal for it fell through we started think­ing more broadly and de­cided that since the Boston area was the place where to­gether we knew the most peo­ple, that was where we should go. But which town in par­tic­u­lar? Elise’s #1 ini­tial cri­te­rion was that it should al­ready have a Starbucks. From the list of such towns, she then started look­ing at USGS aer­ial pho­tographs (or what would now be satel­lite im­ages), and soon set­tled on Concord, MA. But find­ing no suit­able ex­ist­ing house to buy there, she set about de­sign­ing a house to build.

It was a com­plex process. The house had to ac­com­mo­date what was by then a li­brary of nearly 10,000 books, as well as space for my re­mote-CEO of­fice and for our three chil­dren. Elise had been scour­ing ar­chi­tec­ture books, and in­ter­viewed sev­eral top-of-the-line ar­chi­tects be­fore set­tling on one to work with. With her math­e­mat­i­cal and aes­thetic sen­si­bil­i­ties she eas­ily ab­sorbed prin­ci­ples of ar­chi­tec­ture and soon de­vel­oped her own in­tu­ition for it. Sometimes she’d bring in se­ri­ous math—like num­ber the­ory to de­sign a stair­case with aligned squig­gly ban­is­ters, or cir­cle pack­ing to lay out an Italian-inspired tiling based on cir­cles and Sierpinski pat­terns. She started off mak­ing sketches, but soon learned the lat­est CAD tools. And in the end her ideas de­fined much of the de­sign of the house. (At the be­gin­ning, I had tried mak­ing some “suggestions” about the plans, but quickly re­al­ized that this was an Elise pro­ject, and I should stay out of it.)

It took sev­eral years to build the house (with Elise reg­u­larly trav­el­ing to Boston to over­see the pro­ject) but in the spring of 2002 the pro­ject was fin­ished—co­in­ci­den­tally at ba­si­cally the same time as my 10-year pro­ject of writ­ing A New Kind of Science. Other than in CAD draw­ings I’d only seen the house once, early in its con­struc­tion, so when we drove from Hinsdale and ar­rived at the house I was in for a sur­prise. It was much big­ger than I ex­pected! And when we went in­side I could see that it was a mas­ter­piece, filled with per­son­al­ity: beau­ti­ful, el­e­gant, cre­ative—quin­tes­sen­tial Elise.

And then there was the in­te­rior de­sign. Bold and col­or­ful, yet clas­sic. Each room with a dis­tinct char­ac­ter, grace­fully flow­ing into the next. Over the years, Elise re­vised and up­dated the in­te­rior de­sign of the house many times. She was of­ten to be seen sketch­ing on graph pa­per new pos­si­ble de­signs based on new ideas. She kept the style fresh, con­stantly breath­ing new life into the house—even if it meant that our chil­dren would com­ment that every time they showed up the fur­ni­ture seemed to have been re­arranged. And 24 years af­ter I first saw the house, I still find my­self wowed by it.

By 2003, our old­est was en­cour­ag­ing us to have an­other child, not­ing, among other things, that the sym­me­try of the house had given it four chil­dren’s bed­rooms. And so it was that in the fall of 2004 our fourth child, Elizabeth, was born.

In her ear­lier years, Elise had al­ways said that she “couldn’t imag­ine her life not do­ing math”. But partly through me, and, more im­por­tantly through our chil­dren, her world had been broad­ened, and her per­spec­tives had shifted. She would later de­scribe her life as hav­ing sev­eral chap­ters, and this was a chap­ter about chil­dren.

Through her chil­dren show­ing in­ter­est in math, she ended up coach­ing some mid­dle-school MathCounts math com­pe­ti­tion teams. She was­n’t a fan of the way math was typ­i­cally taught in schools, com­plain­ing that the beauty of math was be­ing lost in the at­tempt to make math seem “applicable”, and not­ing that “most of math in mod­ern text­books is not re­ally math at all”. In an email to me in 2010 Elise spirit­edly went fur­ther:

What has hap­pened to beauty in math? The beauty de­rives­from the sim­plic­ity and el­e­gance. That has been lost in the­p­ro­lif­er­a­tion of ex­tra­ne­ous ter­mi­nol­ogy, meant to make things “moreconceptual”, from early end­less ex­cur­sions with “place value” to ab­sur­d­vari­a­tions on al­go­rithms, to gummy de­scrip­tions of every­thing us­ing­con­tor­tions of lan­guage, rather than the lan­guage of math­e­mat­ics it­self.

Elise did nev­er­the­less do some ap­pli­ca­tions of math her­self. During the pan­demic, for ex­am­ple, she de­vel­oped the idea that in­fec­tion was not a bi­nary phe­nom­e­non, but that in­stead each per­son had a con­stantly chang­ing vi­ral load and im­mu­nity, cre­at­ing a “viral field” at the pop­u­la­tion level. Elise was al­ways up to date on world af­fairs, and had a deep in­ter­est in un­der­stand­ing their the­matic arcs at work.

Elise loved the small-town at­mos­phere of Concord, MA, and en­joyed the feel­ing of be­ing in a place “where every­one knows your name”. She was a reg­u­lar at lo­cal cafes and ex­er­cise classes, bring­ing her live­li­ness wher­ever she went. She had a cir­cle of friends with many dif­fer­ent back­grounds, of­ten met through their chil­dren or sim­ply through re­peat­edly run­ning into them at Starbucks. She took great plea­sure in ap­ply­ing her knowl­edge and think­ing to help her friends in all sorts of ways. Whether it was do­ing re­search on med­ical is­sues, solv­ing in­te­rior de­sign prob­lems, or sim­ply us­ing her keen in­sight and judg­ment to pro­vide life ad­vice, she would re­li­ably go above and be­yond.

Our fam­ily had a def­i­nite rou­tine, with din­ner each day at about 6pm. Every Friday night—fol­low­ing a tra­di­tion from Elise’s own fam­ily grow­ing up—we would go out to a movie (and, yes, that meant we saw many ques­tion­able movies). Before our chil­dren were old enough, it was just Elise and me; later it in­cluded var­i­ous con­tin­gents of chil­dren too. Elise and I would talk af­ter each movie, with her of­ten be­ing quite ap­palled by my lack of un­der­stand­ing of what seemed to her like the movie’s ob­vi­ous the­matic el­e­ments. (Elise also gave me a hard time about my fail­ure to read fic­tion, claim­ing that many ideas, par­tic­u­larly about hu­man na­ture, are best com­mu­ni­cated in fic­tion.)

A dozen years ago two of our chil­dren were at the Stanford Online High School, and Elise was re­cruited as an in­au­gural mem­ber of the school’s Community Advisory Group. Originally this was just sup­posed to be for a year. But a decade later she was still there, a highly val­ued mem­ber of the group. She spent con­sid­er­able ef­fort think­ing about the over­all strat­egy and is­sues of the or­ga­ni­za­tion, and de­vel­oped many ideas and opin­ions. Despite this, she’d of­ten tell us that she did­n’t think she’d end up say­ing any­thing at a given meet­ing. But with great con­sis­tency it would later tran­spire that ac­tu­ally she had been the most talk­a­tive and en­gaged per­son there.

In the early 2000s, the Hertz Foundation, from which Elise had re­ceived her grad­u­ate school fel­low­ship, started reach­ing out to her, and she en­joyed en­gag­ing with the emerg­ing Hertz com­mu­nity, and meet­ing fel­lows from a wide range of fields. In 2018 she was also re­cruited to the board of the Hertz Foundation. And here again she be­came a key con­trib­u­tor, of­ten ex­pect­ing not to say any­thing, but then end­ing up as one of the most vo­cal peo­ple there.

By 2023, our three older chil­dren had all grad­u­ated from col­lege, but our youngest, Elizabeth, was just start­ing at Yale. Elizabeth has al­ways been in­volved in a great many ac­tiv­i­ties, and Elise took great plea­sure in at­tend­ing every pos­si­ble con­cert, sport­ing or other event—and also for ex­am­ple host­ing Elizabeth’s en­tire a cap­pella group for a re­treat at our house.

A bit more than a decade ago Elise also dis­cov­ered a love for the Southwest and for hik­ing. And with her brother Jason—with whom she was al­ways very close—liv­ing in the Phoenix, AZ, area, we started spend­ing time there each win­ter.

With Elizabeth off in col­lege we were fi­nally empty nesters, and Elise was ready for a new chap­ter in her life. She con­sid­ered re­turn­ing to where she’d left off in Gibbs the­ory 30 years ago, be­ing told by an old col­league that her work there was still very cur­rent. She also con­sid­ered get­ting more deeply in­volved in the phi­los­o­phy of math­e­mat­ics and was on the brink of writ­ing a piece about it. She was also quite en­gaged in think­ing about the pur­pose and di­rec­tion of higher ed­u­ca­tion, and the im­por­tance of free ex­pres­sion in the search for truth.

In some ways Elise and I were be­com­ing “the old mar­ried cou­ple”, with her ad­mon­ish­ing me about my messi­ness in eat­ing ice cream cones or her de­sire that I switch on self-dri­ving to avoid her be­ing sub­jected to my own sub­stan­dard hu­man dri­ving.

Elise had al­ways been a fit and healthy per­son, and was also very med­ically knowl­edge­able. So when she started notic­ing jaw pain when hik­ing in Colorado and Arizona, she was con­cerned. Tests at first showed noth­ing alarm­ing, though, as she al­ready knew, she had a small con­gen­i­tal heart is­sue that was grad­u­ally wors­en­ing. But just a few weeks ago her symp­toms wors­ened and more in­va­sive tests re­vealed that she needed ur­gent open heart surgery. She had an out­stand­ing team of top doc­tors, the com­plex surgery went very well, and she was soon con­tin­u­ing her re­cov­ery from home.

Meanwhile there was a long-planned cel­e­bra­tion for one of our chil­dren that Elise hoped to at­tend. But though it was not pos­si­ble for her to be there in per­son, we arranged for her to at­tend vir­tu­ally. It was a won­der­ful event, and Elise could be seen via video call beam­ing through all of it. But then, soon af­ter, dis­as­ter struck, and she col­lapsed, the vic­tim of a mas­sive car­dio­vas­cu­lar event. My only so­lace in this tragedy is that the end came in­stantly, af­ter a day filled with noth­ing but joy.

There is so much that Elise was look­ing for­ward to. The im­mi­nent ar­rival of our first grand­child. Elizabeth’s grad­u­a­tion from col­lege. The next chap­ter of her life. But Elise will not be here for any of these.

Elise had no idea the end was near. And even though she ex­pected more, she had al­ready had many chap­ters in her life, and many achieve­ments of which she was proud. Elise had a beau­ti­ful life, full of things she val­ued greatly, es­pe­cially her chil­dren. That she is gone is a tragedy for us all; she will be deeply missed.

Thank you, Elise, for all those won­der­ful years.

Jay Peters: Xbox’s huge out­age even blocked games on disc

An ex­tended Xbox out­age that be­gan Sunday evening has­n’t just caused is­sues for peo­ple try­ing to play dig­i­tal games — it blocked peo­ple from play­ing their disc-based games, too.

When Sony an­nounced that they were dis­con­tin­u­ing phys­i­cal discs for PlayStation, I was less out­raged than many. The rea­son I felt this way was­n’t be­cause I loved what Sony was do­ing. I think it came from an un­der­stand­ing that phys­i­cal me­dia ain’t what it used to be.

I got an ana­log pocket a cou­ple years ago, and I think it’s an awe­some prod­uct. I was able to in­sert my Game Boy car­tridges from 20 years ago and was able to play them im­me­di­ately, just like I did back then. Well, on a back­lit screen with 10x the pixel den­sity, but still.

The im­pres­sion I get is that a lot of peo­ple have this vi­sion in their head for what phys­i­cal me­dia still is to­day, and it sim­ply is­n’t. Sure, I tech­ni­cally did­n’t own Golden Sun on the GBA. I tech­ni­cally had a li­cense, but for all in­tents and pur­poses, I owned that game. And the ev­i­dence is, with­out Nintendo au­tho­riz­ing any­thing, I’m able to play it on a new piece of hard­ware, and it works great. No net­work down­time is gonna pre­vent me from do­ing that.

But own­ing a game on a disc to­day is­n’t re­ally the same thing. It’s still just a li­cense, and Microsoft, Sony, and Nintendo can ei­ther in­ten­tion­ally or, in this case, un­in­ten­tion­ally pre­vent you from play­ing that game, even if you own the phys­i­cal copy. This is­n’t even to men­tion the fact that when you pop the disc in your drive, you’re not play­ing from the disc. It’s in­stalling it to your in­ter­nal hard drive and is prob­a­bly in­stalling a bunch of up­dates that are re­quired to make the game ac­tu­ally work at all.

All I’m say­ing is it’s all dig­i­tal on the PC side of things, and has been for ages, but we have means of main­tain­ing ac­cess to the games we love over here, and it’s one of the rea­sons I’ve grav­i­tated to the PC for quite a while now.

In the liv­ing room the voice-clock sang, Tick-tock, seven o’­clock, time to get up, time to get up, seven o’­clock! As if it were afraid that no­body would.

Seven-nine, break­fast time, seven-nine!

In the kitchen the break­fast stove ejected eight pieces of per­fectly browned toast, eight eggs sun­ny­side up, six­teen slices of ba­con, two cof­fees, and two cool glasses of milk.

“Today is August 4, 2026, the city of Allendale, California.”

Somewhere in the walls, re­lays clicked, mem­ory tapes glided un­der elec­tric eyes.

“”Eight-one, tick-tock, eight-one o’­clock, off to school, off to work, run, run, eight-one!” But no doors slammed. It was rain­ing out­side. The weather box on the front door sang qui­etly: “Rain, rain, go away; rub­bers, rain­coats for to­day…”

Outside, the garage chimed and lifted its door to re­veal the wait­ing car.

After a long wait the door swung down again.

At eight-thirty the eggs were shriv­eled and the toast was like stone. An alu­minum wedge scraped them into the sink. The dirty dishes were dropped into a hot washer and emerged twin­kling dry.

“Nine-fifteen,” sang the clock, “time to clean.”

Tiny ro­bot mice thud­ded against chairs, whirling their mus­tached run­ners, Kneading the rug nap, suck­ing gen­tly at hid­den dust. Then, they popped into their bur­rows. The house was clean.

“Ten o’­clock.” The sun came out from be­hind the rain. The house stood alone in a city of rub­ble and ashes. This was the one house left stand­ing. At night the ru­ined city gave off a ra­dioac­tive glow which could be seen for miles.

“Ten-fifteen.” The gar­den sprin­klers pelted the win­dow­panes,

run­ning down the charred west side where the house had been burned evenly

free of its white paint. The en­tire west face of the house was black, save for five places. Here the sil­hou­ette in paint of a man mow­ing a lawn. Here, as in a pho­to­graph, a woman bent to pick flow­ers. Still far­ther over, their im­ages burned on wood in one ti­tanic in­stant, a small boy, hands flung into the air; higher up, the im­age of a thrown ball, and op­po­site him a girl, hand raised to catch a ball which never came down.

The five spots of paint — the man, the woman, the chil­dren, the ball –

re­mained. The rest was a think char­coaled layer.

“Twelve noon.”

A dog whined on the front porch.

The front door rec­og­nized the dog voice and opened. The dog, once huge and fleshy, but now gone to bone and cov­ered with sores, moved in and through the house, track­ing mud.

The dog frothed at the mouth, ran wildly in cir­cles, bit­ing at its tail, spun in a frenzy, and died. It lay in the par­lor for an hour.

“Two-fifteen.”

The dog was gone.

In the cel­lar, the in­cin­er­a­tor glowed sud­denly and a whirl of sparks leaped up the chim­ney.

“Two thirty-five.”

Bridge ta­bles sprouted from pa­tio walls. Playing cards flut­tered. Martinis man­i­fested while mu­sic played.

But the ta­bles were silent and the cards un­touched.

At four o’­clock the ta­bles folded back through the pan­eled walls. “Four-thirty.”

The nurs­ery walls glowed.

Animals took shape: yel­low gi­raffes, blue li­ons, pink an­telopes, lilac pan­thers. Hidden films clocked through well-oiled sprock­ets, and the glas walls lived. It was the chil­dren’s hour.

“Six, seven, eight o’­clock.” The din­ner dishes ma­nip­u­lated like magic

tricks, and in the study a click.

“Nine-five.” A voice spoke from the study ceil­ing:

“Mrs. McClellan, which poem would you like this evening?”

The house was silent.

The voice said at last, “Since you ex­press no pref­er­ence, I shall se­lect a

poem at ran­dom.” “Sara Teasdale. As I re­call, your fa­vorite…

“There will come soft rains and the smell of the ground,

And swal­lows cir­cling with their shim­mer­ing sound;

And frogs in the pools singing at night, And wild plum trees in tremu­lous white;

Robins will wear their feath­ery fire, Whistling their whims on a low fence-wire;

And not one will know of the war, not one Will care at last when it is done,

Not one would mind, nei­ther bird nor tree If mankind per­ished ut­terly;

And Spring her­self, when she woke at dawn Would scarcely know that we were gone.

At ten o’­clock a falling tree bough crashed through the kitchen win­dow

shat­ter­ing clean­ing sol­vent over the stove. The room was ablaze in an in­stant.

“Fire!” screamed a voice. Water pumps shot wa­ter from the ceil­ings while the voices took it up in cho­rus: “Fire, fire, fire!”

The house tried to save it­self, but the wind blew and sucked upon the fire.

Scurrying wa­ter rats pis­toled their wa­ter, and ran for more. And the wall sprays let down show­ers of me­chan­i­cal rain.

But too late. The quench­ing rain ceased. The re­serve wa­ter sup­ply which had filled baths and washed dishes for many quiet days was gone.

From at­tic trap­doors gushed a green chem­i­cal.

But the fire was clever. It had sent flames out­side the house, up through The at­tic to the pumps there. An ex­plo­sion! The at­tic brain which di­rected the pumps was shat­tered.

The house shud­dered, its bared skele­ton cring­ing from the heat. And the voices wailed, “Fire, fire, run, run,” like a tragic nurs­ery rhyme, a dozen voices, high, low. One, two, three, four, five voices died.

Other cho­ruses could be heard an­nounc­ing the time, play­ing mu­sic, or cut­ting the lawn by re­mote-con­trol mower. A scene of ma­niac con­fu­sion, yet unity; singing, scream­ing, and one voice, read po­etry aloud in the firey study, un­til all the film spools burned.

In the kitchen the stove could be seen mak­ing break­fasts at a psy­cho­pathic rate, ten dozen eggs, six loaves of toast, twenty dozen ba­con strips, which eaten by the fire, started the stove work­ing again, hys­ter­i­cally hiss­ing!

The crash. The at­tic smash­ing into kitchen and par­lor. The par­lor into cel­lar, cel­lar into sub-cel­lar.

Smoke and si­lence.

Among the ru­ins, one wall stood alone. Within the wall, a last voice said,

over and over, “Today is August 5, 2026, to­day is August 5, 2026, to­day is …”

If you’re just look­ing for the re­sults, be­low is a cus­tom color picker based on the color space writ­ten in Javascript and a sam­ple pro­ce­dural gen­er­a­tion al­go­rithm in Python (Javascript equiv­a­lents are in the page source) - feel free to take this math and go have fun de­pict­ing our di­verse world!

The goal of this pro­ject was to de­fine a color space that makes it eas­ier to build in­clu­sive color tools for a va­ri­ety of con­texts - such as char­ac­ter cre­ators or dig­i­tal art. If you see some­thing here that sparks your cu­rios­ity, I would love for you to stick around and read be­low this sec­tion to learn more!

R² =

(What’s R²?)

│

Show Sphere

What is each di­rec­tion on the picker ad­just­ing? Jump to that ex­pla­na­tion here.

# Plug the out­put of one of the se­lec­t_­point im­ple­men­ta­tions into to_rgb(t, u, v)

def se­lec­t_­point(r_square: float = 2.) -> tu­ple[float, float, float]: “”″Uniformly sam­ple from the sphere de­ter­min­is­ti­cally”“” ra­dius = r_square ** (1. / 2)

phi = uni­form(0, 2 * math.pi) cos­theta = uni­form(-1, 1) n = uni­form(0, 1)

theta = math.acos(cos­theta) r = ra­dius * (n ** (1.0 / 3))

t = r * math.sin(theta) * math.cos(phi) u = r * math.sin(theta) * math.sin(phi) v = r * math.cos(theta)

re­turn (t, u, v)

def se­lec­t_­point(r_square: float = 2.) -> tu­ple[float, float, float]: “”″Uniformly sam­ple from the sphere us­ing re­jec­tion sam­pling”“” ra­dius = r_square ** (1. / 2) R = ra­dius + 1

while R > ra­dius: t = uni­form(-ra­dius, ra­dius) u = uni­form(-ra­dius, ra­dius) v = uni­form(-ra­dius, ra­dius)

R = (t**2 + u**2 + v**2) ** (1.0 / 2)

re­turn (t, u, v)

def to_rgb(t, u, v) -> tu­ple[int, int, int]: x = (t - 0.15) / 0.45 y = (v - 1.2 * t ** 2 + 0.2 * t + 0.655) / 1.84 z = u / 3.6

r = 28.77438370854 * x + 36.78307445559 * y - 19.69766918644 * z + 187.1436241611 g = 35.38327306318 * x - 2.009931981182 * y + 47.93462563172 * z + 137.1073825503 b = 36.14733717939 * x - 43.54346996173 * y - 28.50821294135 * z + 108.2241610738

re­turn int(r), int(g), int(b)

# Overview

What col­ors are we? The short an­swer is maybe some­thing like “brown” and the long an­swer is very, very long. Representing the broad range of hu­man skin tones dig­i­tally is a hard prob­lem. Often, a lim­ited set of col­ors is pre­sented as be­ing good enough to cover the full spec­trum of di­ver­sity. However, in us­ing a spe­cific set of col­ors, large groups of peo­ple are un­able to ac­cu­rately be rep­re­sented, or might be un­in­ten­tion­ally ex­cluded.

The goal of this work is to iden­tify the broad­est in­clu­sive range of col­ors in the RGB color space that cor­re­spond to plau­si­ble, but sim­pli­fied skin tones. In par­tic­u­lar, the aim was to iden­tify sim­ple, “good enough” equa­tions which de­fine that area, al­low­ing the range to be used in a va­ri­ety of con­texts. Calling the equa­tions “good enough” is in­tended to keep the lim­i­ta­tions of this work at the fore­front - the re­sults are a use­ful start­ing point, but should not be taken to be au­thor­i­ta­tive.

# Introduction

Although there have been im­prove­ments in the set of col­ors that are pre­sented as rep­re­sen­ta­tive of us, there’s still a gap that needs to be closed. Emojis say we’re 5 shades (or car­toon-yel­low); a makeup brand might say 50; and a char­ac­ter cre­ator might shrug and tell you to pick from all 16,777,216 op­tions. If you look out­side - or just at your­self - you’ll quickly no­tice that none of those can com­pare to the va­ri­ety of re­al­ity; one per­son is not just one color. Despite that, it can be use­ful to try to boil things down to fewer val­ues. The Unicode Consortium and makeup com­pa­nies can fig­ure out their own ranges, but I be­lieve we can find a bet­ter so­lu­tion that’s some­where be­tween “several” and “several mil­lion.”

Taking the dig­i­tal art world as an ex­am­ple, im­ages such as the one be­low are of­ten cir­cu­lated in an at­tempt to as­sist other artists in iden­ti­fy­ing plau­si­ble col­ors.

In the video game world, nowa­days the pre­set col­ors are of­ten wide rang­ing and sup­ple­mented with a gen­eral color picker, but it would be even bet­ter if the ini­tial ex­pe­ri­ence pre­sented bet­ter op­tions.

# Limitations

Taking a step back to re­al­ity, this work has a num­ber of in­her­ent lim­i­ta­tions.

As men­tioned be­fore, skin tones are much more com­pli­cated than a sin­gle color. They vary widely be­tween dif­fer­ent ar­eas of the body and are sub­ject to com­plex bi­o­log­i­cal processes. The per­ceived color of the skin is af­fected by blood flow, con­cen­tra­tions of melanin, com­plex scat­ter­ing of light through the lay­ers of the skin, as well as things like vi­tiligo, freck­les, hy­per­pig­men­ta­tion, scar­ring, and other com­mon vari­a­tions.

Secondly, a va­ri­ety of health con­di­tions can cause peo­ple to have skin tones that are well out­side what might be per­ceived as plau­si­ble. Argyria can of­ten lead to skin that is blue-gray in color; high biliru­bin can cause skin to be yel­low­ish or green­ish.

Additionally, it’s im­por­tant to note that I am one per­son, not a re­searcher, and sub­ject to my own gen­eral bi­ases on top of my own per­cep­tion of color. As far as I am aware I don’t have color vi­sion de­fi­ciency, but a lot of the choices I made are com­pletely sub­jec­tive.

Finally, col­ors are not per­ceived con­sis­tently across dis­play types and view­ing en­vi­ron­ments. RGB val­ues look dif­fer­ent be­tween dif­fer­ent screens, and peo­ple look com­pletely dif­fer­ent un­der dif­fer­ent light­ing con­di­tions.

Broadening this work to ad­dress some of these lim­i­ta­tions would be an in­ter­est­ing area of fur­ther in­ves­ti­ga­tion - a goal of this pro­ject was to be good enough for sim­ple use cases, but these lim­i­ta­tions might be more prob­lem­atic in other con­texts. The re­sults here will mainly be ap­plic­a­ble in con­texts that re­late to gen­er­at­ing sim­pli­fied rep­re­sen­ta­tions of peo­ple.

# Methodology

What are all of those num­bers, and how did you get them?

Content warn­ing - un­sci­en­tific method­ol­ogy be­low. In other words: good enough is fine if you’re an en­gi­neer.

Summary:

Manually la­bel col­ors in RGB in or­der to get a rough ap­prox­i­ma­tion of the dataset shape

Perform a prin­ci­pal com­po­nent analy­sis (PCA) with N=3 on the dataset to change the shape into some­thing eas­ier to work with

Use your pre­ferred graph­ing soft­ware to man­u­ally cre­ate equa­tions that map a sphere in the tar­get space onto the trans­formed data in the XYZ, or PCA space

# Manually Labeling Colors

Sometimes the best place to start is by do­ing a ton of te­dious work. I did­n’t la­bel every color in RGB, but there cer­tainly were a lot. This is the UI I built for la­bel­ing - just a sim­ple web­page where you click to move a face be­tween the yes and no side. Initially they were just squares, but I ended up draw­ing a face and slap­ping the col­ors onto it. Gazing into my lumpy re­search as­sis­tan­t’s eyes made it much eas­ier to quickly go “yeah I can imag­ine that per­son walk­ing around”.

Graphing that data, you get the fol­low­ing shape - for vi­su­al­iza­tion it’s kind of like a ba­nana shape that swoops be­tween 0, 0, 0 and 255, 255, 255. The curve is more to­wards red and away from blue.

This is where I got stuck for the longest. For your sake, I’m go­ing to skip over all of my dead ends and strug­gles along the way. There were many. Far too many. Things in­volv­ing con­vex hulls, re­gres­sion mis­ad­ven­tures, 4th de­gree poly­no­mi­als, and the worst look­ing code I’ve ever writ­ten.

The re­sult of all of that was that I de­cided I needed some way to trans­form the shape into some­thing eas­ier to work with: that’s when I learned about prin­ci­pal com­po­nent analy­sis and was im­me­di­ately in­spired.

# Humanities Intermission

Although all of the math and tech­nol­ogy here is fun, it’s im­por­tant to ad­dress the fact that tech­nol­ogy ex­ists in a so­cial con­text. Stating things plainly: lighter skin col­ors have both presently and his­tor­i­cally been cel­e­brated and pri­or­i­tized while darker skin col­ors have been mar­gin­al­ized and ma­ligned. Racism and col­orism are sys­tem­i­cally pre­sent in many cul­tures, in both overt and sub­tle ways.

Below are some great videos, es­says and pro­jects that ad­dress these is­sues through a va­ri­ety of lenses. I highly rec­om­mend tak­ing a look, es­pe­cially if you want a break be­fore we get into the math.

In her video se­ries The Darkest Shade, Nyma Tang re­views the dark­est shades from a va­ri­ety of makeup brands. In her own words, “It’s im­por­tant for makeup brands to make prod­ucts for all shades and as some­one with a darker skin tone, I want to be able to help oth­ers who strug­gle to find the same!”

In a sim­i­lar vein, Kat Blaque’s video (for in­tro­spec­tive hot peo­ple) Youthforia’s Blackface Foundation is about a makeup brand that re­leased a dark shade that was lit­er­ally black - far darker than what would be plau­si­bly use­ful.

Finally in the makeup space, the Vox video How beauty brands failed women of color talks about the his­tory of dis­crim­i­na­tion in the beauty in­dus­try and the lim­ited avail­abil­ity of deeper shades. There’s a lot of great ex­pert in­ter­views as well as a dis­cus­sion of the in­ter­sec­tion with Black his­tory.

Taking a look at video games, Me, On The Screen: Race in Animal Crossing: New Leaf by Austin Walker is an ex­cel­lent es­say about the au­thor’s strug­gle to see him­self rep­re­sented in video games. In the years since, Animal Crossing has got­ten much bet­ter about in­clu­siv­ity but the es­say also goes into his his­tory of not see­ing him­self - or see­ing char­ac­ters that look like him be stuck in racist tropes.

The Humanae pho­tog­ra­phy pro­ject by Angélica Dass is “an un­usu­ally di­rect re­flec­tion on the color of the skin, at­tempt­ing to doc­u­ment hu­man­i­ty’s true col­ors rather than the un­true la­bels “white”, “red”, “black” and “yellow” as­so­ci­ated with race.” In a way it’s re­ally sim­i­lar to the work here - ex­cept with a fo­cus on doc­u­ment­ing and con­vers­ing in­stead of de­scrib­ing, and us­ing Pantone shades over hex codes.

For more di­rect re­sources, the video It’s not a Coincidence. It’s Colorism. by Tee Noir gives a de­scrip­tion of what col­orism is, and a few ways it man­i­fests in mod­ern pop cul­ture.

Finally, Writing With Color is an ex­cel­lent blog with many re­sources about writ­ing var­i­ous kinds of di­ver­sity. The blog is run by a team with ex­per­tise in many dif­fer­ent ar­eas, and they of­ten take reader ques­tions. In par­tic­u­lar I found their post Words for Skin Tone | How to Describe Skin Color re­ally in­ter­est­ing. As more of a reader than a writer, it’s fas­ci­nat­ing to see be­hind the scenes on how to make bet­ter word choices.

# Principal Component Analysis

Briefly, prin­ci­pal com­po­nent analy­sis (PCA) is a way to ro­tate and stretch a dataset so that the main di­rec­tions of vari­a­tion lie along the axes of the co­or­di­nate sys­tem. To make that more con­crete - re­call the ba­nana shape of my dataset from be­fore. In its orig­i­nal form, the ba­nana was sort of float­ing in space. PCA took that shape and placed in on the ground so that it was sym­met­ri­cal about the axes and aligned nicely. It also did some slight stretch­ing and rescal­ing, but that’s less im­por­tant.

Aside from the mod­i­fied dataset, an­other out­put of the analy­sis is a ma­trix that can be used to take a point from RGB space and trans­late it into the rest­ing-on-the-floor space. I re­fer to this as PCA space, or XYZ space since those are the vari­ables I use for it.

# Manual Function Fitting

To sum­ma­rize what we’ve done so far: we started with data in RGB space (the man­u­ally la­beled dataset). PCA gives us a way to take points in that space and trans­form them into an­other space - XYZ space.

Now the goal is to fit some func­tion to all of these points. Because it’s a dense shape, if we can de­fine the sur­face of it with an equa­tion, we can mod­ify that equa­tion to in­clude the points on the in­side as well by switch­ing the equa­tion to be­ing an in­equal­ity (eg from x² + y² + z² = 2 to x² + y² + z² ≤ 2).

The process for fit­ting the func­tion is as fol­lows:

Start with a func­tion for a sphere: R² = t² + u² + v² (see Adjusting R² for why a sphere is used)

Define t, u, and v in terms of x, y, and z

Modify how t, u, and v are de­fined un­til the sphere stretches to match up with the ex­pected data

Invert the re­la­tion­ships in or­der to de­fine x, y, and z in terms of t, u, and v

If you have (t = x, u = y, v = z) as a start­ing point, you can start to play with those re­la­tions un­til you start to get an in­tu­ition for how changes to the equa­tions will end up shift­ing your sphere around.

So I did that! A lot. To put it plainly - I man­u­ally fit func­tions to my tar­get cloud of points. There is no re­gres­sion here, I lit­er­ally did guess and check and eye­balled the func­tion fit. I did this in Desmos 3D - if you haven’t used Desmos in a while it’s amaz­ing how good it was for this.

The func­tions that re­late (t, u, v) to (x, y, z) can be used to trans­late a point be­tween those two spaces. Principal com­po­nent analy­sis gave us a way to move be­tween RGB and XYZ, and then these new equa­tions give us a way to move be­tween XYZ and TUV. Linking up all the trans­for­ma­tions gives us the func­tions that take us be­tween TUV to RGB.

Am I en­dors­ing this method­ol­ogy? No. But also kind of. In this spe­cific sit­u­a­tion it’s what worked to get it done and get func­tional equa­tions. It would be great to see some­one do this prop­erly, with nice clean sym­bolic re­gres­sion and re­ally good train­ing data. But I fig­ured since the train­ing data I la­beled was mid­dling qual­ity at best, I’d prob­a­bly have a bet­ter time us­ing my guess and check and then eye­balling the re­sults.

And all that be­ing said, I think I would en­dorse the over­all method I used, if not the specifics. That be­ing “Label Data” → “PCA” → “Fit A Spherical Equation”.

# Results

From the equa­tions, the sam­ple code at the top of the page is just a short trans­la­tion away. The next sec­tion is the de­scrip­tion of the com­po­nents of the Picker UI, which also serves as an ex­pla­na­tion of what TUV space ac­tu­ally looks like, and what prop­er­ties it has.

# Picker UI

Just like how a typ­i­cal color picker al­lows you to ad­just red, green and blue val­ues (or hue, sat­u­ra­tion and value), this color picker also has 3 in­de­pen­dent val­ues to ad­just - re­ferred to in the code sam­ples as T, U and V.

What’s re­ally in­ter­est­ing about these con­trols is that the con­cept each is ad­just­ing is com­pletely an out­put of the prin­ci­pal com­po­nent analy­sis. Or in other words, I did­n’t know that these would be what the di­rec­tions con­trolled un­til af­ter I had made the picker. It’s a re­ally neat demon­stra­tion of what prin­ci­pal com­po­nent analy­sis does - it ro­tates data to max­i­mize how mean­ing­ful each axis is.

Now, if you’re ex­pe­ri­enced with color spaces you might be think­ing that this looks a lot like HSL/HSV. However, when I was do­ing my first ex­per­i­ments with the la­beled data those color spaces did­n’t quite cap­ture what I was look­ing for. I think in par­tic­u­lar that al­though T and U seem sim­i­lar to Value and Hue, they don’t com­pletely match up. And the biggest dif­fer­ence is be­tween V and Saturation. V ranges from blue to or­ange, while Saturation would look more like gray to or­ange; al­though at some (T, U) val­ues V might look a lot like Saturation, over­all it does­n’t quite cor­re­late.

# Adjusting R²

What is R²? R² is the ra­dius of a sphere in the skin tone color space. Because one of the steps of trans­la­tion from RGB to TUV in­volves a sphere, it makes spheres a nat­ural shape to work with in TUV space. A lot of the cool prop­er­ties that arise from that fact are just a side ef­fect of spheres hav­ing a lot of use­ful prop­er­ties.

To start with a vi­sual, be­low is a table of R² val­ues, and the re­sult of us­ing a sphere with that value:

So what’s go­ing on with that table? Because a sphere is de­fined by a ra­dius, you can de­fine use­ful sam­pling ranges us­ing only a sin­gle value and then eas­ily se­lect points from within that sphere. For ex­am­ple, in the sam­ple im­ple­men­ta­tion of the tone gen­er­a­tion func­tion I use a ra­dius of 2. This is the ra­dius that was used when de­vel­op­ing the color space and gen­er­ally will re­sult in a broad range of tones. However, if you find there are im­plau­si­ble re­sults gen­er­ated us­ing that ra­dius you can de­crease it by a bit in or­der to re­duce the vari­a­tion in gen­er­ated col­ors.

The fact that the sphere shrinks along a ra­dius means that the re­duc­tion in vari­a­tion ac­tu­ally does not re­sult in a large re­duc­tion in rep­re­sen­ta­tive­ness. In other words, re­duc­ing the ra­dius does­n’t lead to just chop­ping off deep or fair skinned col­ors - deep skin tones, fair skin tones, flush skin tones, ochre skin tones, cool skin tones and warm skin tones are uni­formly de­creased in vari­a­tion.

Taking R² all the way down to 0, we can iden­tify the ori­gin of the color space. If the space is well formed then this ori­gin point should be a very neu­tral am­bigu­ous tone. If the ori­gin seems bi­ased in a par­tic­u­lar di­rec­tion, then that would in­di­cate that the space needs more fine tun­ing. Essentially, the ori­gin point can be used to iden­tify bias in the space map­ping.

At the other ex­treme, you can in­crease R² in or­der to al­low for more vari­a­tion. As an ex­am­ple, I do this in the color picker UI. In a picker UI the user can ig­nore im­plau­si­ble col­ors, so there’s lit­tle is­sue with in­creas­ing the vari­a­tion too far. In a color gen­er­a­tion con­text you’d likely want to avoid hav­ing im­plau­si­ble col­ors pop­ping up. There is likely not an ideal R² value that works in all con­texts, but hav­ing a sin­gle pa­ra­me­ter to tweak makes it easy to ad­just the equa­tions to your needs.

# In Summary

We have a color space, we have a picker for it, we have a pro­ce­dural gen­er­a­tion al­go­rithm, and we have a method­ol­ogy for cre­at­ing new spaces or mod­i­fy­ing the ex­ist­ing one. Overall, I’m thrilled with this re­sult. It’s cer­tainly not per­fect, but I don’t think a sim­ple and com­pletely cor­rect so­lu­tion ex­ists. I’ve al­ready used the picker in a dig­i­tal paint­ing and it was ex­actly as I was hop­ing it’d be - and I’m look­ing for­ward to us­ing the gen­er­a­tor in my next pro­jects.

# What’s Next?

First is feed­back: if you at all found this in­ter­est­ing or use­ful, please let me know! Although I did this work for my own use, hear­ing from oth­ers is also so re­ward­ing. Also please reach out with any ques­tions or feed­back - es­pe­cially if you spot some­thing I did­n’t think about.

Although I would love to post an email ad­dress for ac­ces­si­bil­ity, I think the safest so­lu­tion is to use the is­sues page of the repo for this pro­ject to con­tact me. But open to sug­ges­tions on al­ter­na­tives for that as well!

A task for me is to clean up my code and post it to the repo for this page to make it easy for peo­ple to recre­ate and it­er­ate on this work.

# Future Work

# Refining The Space

In defin­ing the color space so pre­cisely and us­ing spe­cific R² val­ues, there is a risk that some col­ors have been ex­cluded or mar­gin­al­ized. However, that same con­crete­ness also al­lows for ex­tremely pre­cise cri­tiques of the color space, and there­fore ex­tremely pre­cise im­prove­ments. As men­tioned be­fore, my process in­volved a lot of sub­jec­tive eye­balling - a great it­er­a­tion on that would be to have mul­ti­ple peo­ple, per­haps ex­perts, la­bel­ing data and then mea­sur­ing the out­put more pre­cisely against that.

# Skin Variations and Conditions

A di­rec­tion men­tioned ear­lier would be to look into mod­el­ing sim­pli­fied ver­sions of var­i­ous con­di­tions. What mod­i­fi­ca­tion might you be able to ap­ply to base tones to sim­u­late that per­son hav­ing jaun­dice, or ar­gyria, or be­com­ing pal­lid? What col­ors are freck­les, vi­tiligo, scars, hy­per­pig­men­ta­tion, or stretch marks rel­a­tive to a per­son’s base tone?

# Technical Improvements

From a tech­ni­cal di­rec­tion, mak­ing the equa­tion gen­er­a­tion more for­mal­ized is an­other po­ten­tial di­rec­tion to go. Starting with the shape of equa­tions I man­u­ally de­ter­mined, sym­bolic re­gres­sion on those against bet­ter train­ing data might lead to an even bet­ter color space de­f­i­n­i­tion.

There’s also the po­ten­tial for op­ti­miz­ing the equa­tions for dif­fer­ent con­texts. I’ve cho­sen to write them out in code as they are to be the most read­able to a broad au­di­ence. However, keen math­e­mati­cians might no­tice that one of those steps looks a lot like a ma­trix mul­ti­pli­ca­tion, which can be rewrit­ten to be more ef­fi­cient in cer­tain con­texts.

It might also be in­ter­est­ing to see what the re­sults look like if you trans­form the data into an­other color space be­fore do­ing the prin­ci­pal com­po­nent analy­sis and equa­tion fit­ting. There’s a chance the equa­tions end up be­ing sim­pler or more rep­re­sen­ta­tive. Because of the sphere, the shape of the sur­face in the color space you build from will be main­tained and it will mainly scale with R² val­ues. For an il­lus­tra­tion of this idea, see the graph script in the re­po’s code.

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DeepSeek V4 Flash on a sin­gle AMD MI300X

This repos­i­tory con­tains the con­fig­u­ra­tion and patches I use to run deepseek-ai/​DeepSeek-V4-Flash-0731 on one AMD MI300X in pro­duc­tion. It in­cludes the Docker Compose stack, SHA-256-pinned file over­lays, ref­er­ence diffs against up­stream, and tun­ing ta­bles. The check­point runs as shipped, with­out ad­di­tional weight quan­ti­za­tion or of­fload.

Results from the pinned stack (vLLM ROCm nightly 0.26.1rc1.dev229+g124154a88.rocm723, AITER 0.1.19):

The of­fi­cial vLLM recipe tar­gets NVIDIA and newer AMD hard­ware. Running the model re­li­ably on MI300X re­quired fixes for its FP8 for­mat, MoE rout­ing at high con­cur­rency, causal spec­u­la­tive ver­i­fi­ca­tion, CPU-KV syn­chro­niza­tion, and sev­eral un­tuned ker­nel shapes. This repos­i­tory col­lects those fixes and pins the ver­sions used in pro­duc­tion.

Why MI300X

The MI300X has 192 GB of HBM3 and 5.3 TB/s of mem­ory band­width, with 2.4× the HBM ca­pac­ity of an H100 SXM5 (AMD). Doubleword’s write-up es­ti­mates that it costs roughly half as much at list price. For this 304B-parameter check­point, the mem­ory ca­pac­ity al­lows a sim­ple sin­gle-GPU de­ploy­ment:

The en­tire model fits in HBM with­out PCIe weight stream­ing or layer of­fload.

There is room for a 20 GB GPU KV pool and a 96 GiB CPU tier for evicted pre­fix-cache en­tries.

One card han­dles 2 – 8 typ­i­cal con­cur­rent streams and bursts of up to 64 streams.

MI300X (CDNA3) im­ple­ments the AMD/Graphcore fnuz vari­ant of E4M3, while MI325X and newer use OCP-standard FP8 (background). A ker­nel that as­sumes OCP se­man­tics on MI300X can be wrong by a fac­tor of two in the scale do­main. Correctness on this FP8 im­ple­men­ta­tion was the first pri­or­ity; per­for­mance tun­ing came af­ter­ward.

Prior art, and what this repo adds

Fergus Finn’s MI300X work­log and the ac­com­pa­ny­ing Doubleword repos­i­tory iden­ti­fied the FP8 in­com­pat­i­bil­ity, miss­ing AITER fast paths on gfx942, HIP-graph haz­ards in sparse MLA de­code, and MoE rout­ing bugs. The of­fi­cial vLLM recipe cov­ers NVIDIA hard­ware and newer AMD GPUs (MI325X at 4K con­text and MI355X), but not a sin­gle-MI300X pro­duc­tion con­fig­u­ra­tion for the 0731 check­point.

This repos­i­tory adds:

Correctness over­lays for the pinned ROCm nightly, in­clud­ing fixes not yet in up­stream vLLM.

A val­i­dated serv­ing con­fig­u­ra­tion with prob­a­bilis­tic DSpark draft­ing, block re­jec­tion, and sta­tic K=7. It uses a 2,048-token sched­uler bud­get and a 1,024-token long-pre­fill cap to pre­vent a cold prompt from stalling other streams.

AITER GEMM tun­ing ta­bles for the re­cur­ring gfx942 shapes the pack­aged ta­bles were miss­ing, plus a gfx942 OGS geom­e­try over­ride for the MXFP4 ex­perts.

A hy­brid KV strat­egy: 20 GB of fp8_d­s_mla GPU cache + 96 GiB na­tive CPU of­fload, with a load-path fenc­ing fix that up­stream is­sue #47282 doc­u­ments but PR #47291 never merged.

Repository lay­out

. ├── com­pose.yaml # The pro­duc­tion stack (vLLM ROCm + Caddy), di­gest-pinned ├── Caddyfile.example # Copy to Caddyfile; set host­name, email, and source CIDR ├── vllm-en­try­point.sh # Removes stale CPU-KV mmaps from /dev/shm be­fore start ├── SHA256SUMS # SHA-256 pins for every run­time ar­ti­fact ├── patches/ │ ├── *.py # Byte-for-byte pro­duc­tion over­lays (mounted read-only) │ ├── diffs/*.​patch # Unified diffs vs. the up­stream base re­vi­sion │ └── README.md # Provenance and re­gen­er­a­tion in­struc­tions └── tun­ing/ └── *.csv # AITER A8W8 blockscale tun­ing ta­bles for gfx942

Runtime con­fig­u­ra­tion

The stack uses a di­gest-pinned of­fi­cial vLLM ROCm nightly with:

–trust-remote-code and the DeepSeek V4 to­k­enizer, rea­son­ing, and tool parsers

fp8_d­s_mla KV cache (UE8M0 block-scaled FP8, not generic un­scaled FP8) with 256-token blocks

VLLM_ROCM_USE_AITER=1 and –moe-backend tri­ton; Triton OGS han­dles the grouped MXFP4 ex­perts, while AITER han­dles at­ten­tion and dense lin­ear lay­ers

DSpark-7 spec­u­la­tive de­cod­ing with prob­a­bilis­tic draft­ing and block re­jec­tion

full/​break­able CUDA graph cap­ture, giv­ing one graph launch per to­ken dur­ing steady de­code

Caddy as an IP-allowlisted HTTPS proxy

Deploying it

1. Host pre­req­ui­sites

One MI300X (gfx942, 304 CUs, ~192 GiB HBM), a work­ing AMD ker­nel dri­ver, re­cent Docker Compose, ~235 GiB RAM for the CPU KV tier, and ~500 GB disk (the model cache alone is ~156 GB).

2. Pull the pinned run­time and model

VLLM_IMAGE=‘vllm/vllm-openai-rocm@sha256:e68d18b2ba50298661bfc49baf01158fbf036645c2362cccf3e8a7a79fe6c69a’ MODEL=‘deepseek-ai/DeepSeek-V4-Flash-0731’ REVISION=‘7872f01b1d1fe23eabc4c98b48bffcef5a386062’

docker pull “$VLLM_IMAGE” docker run –rm –entrypoint hf \ -v /root/.cache/huggingface:/root/.cache/huggingface \ “$VLLM_IMAGE” down­load “$MODEL” –revision “$REVISION”

3. Prepare the files

cp Caddyfile.example Caddyfile # then set your host­name, email, and re­mote_ip CIDR mkdir -p aiter-cache crash-dumps chmod +x vllm-en­try­point.sh sha256­sum -c SHA256SUMS # ver­ify the over­lays be­fore first start

4. Start

docker com­pose con­fig -q docker com­pose up -d docker com­pose logs -f in­fer­ence

A healthy start takes ~5 min­utes and must show all of:

Model load­ing took 156.67 GiB DSpark draft model loaded: 96 params GPU KV cache size: 1,927,444 to­kens Maximum con­cur­rency for 262,144 to­kens per re­quest: 7.35x Created mmap file /dev/shm/vllm_offload_…mmap (103.08 GB) Capturing CUDA graphs (FULL) Application startup com­plete

After graph cap­ture, run rocm-smi –showmeminfo vram. The warmed high-wa­ter mark is ~204.5 GB of 205.8 GB. If only a few hun­dred MB re­main, the server may start but fail on the first re­quest.

5. Smoke-test

HOST=‘your-host.example.com’ curl -fsS “https://$​HOST/​v1/​mod­els” curl -sS “https://$​HOST/​v1/​com­ple­tions” \ -H ‘Content-Type: ap­pli­ca­tion/​json’ \ -d “{"model": "deepseek-ai/DeepSeek-V4-Flash-0731", "prompt": "Calculate 17 * 23. Answer with the num­ber only.", "temperature": 0, "max_tokens": 32}”

The patches

Each patches/*.​py file is a full-file over­lay mounted read-only over its coun­ter­part in the con­tainer; com­pose.yaml con­tains the tar­get paths. The cor­re­spond­ing diffs/*.​patch records the change from its up­stream base. The base im­age re­mains di­gest-pinned, so up­grades re­quire chang­ing the im­age ref­er­ence and reval­i­dat­ing the stack.

Two im­por­tant cor­rect­ness fixes

MXFP4 rout­ing. The MoE bit­ma­trix ker­nel pads its block columns to a Triton block size, but the padding lanes were masked against the global ten­sor bound in­stead of the log­i­cal block size. Under load, padded lanes cor­rupted the rout­ing ma­trix, caus­ing near-match tool names and for­got­ten schemas on long prompts. The one-line fix is mask = (offs_local < BLOCK_SIZE) & (offs_global < nonze­ro_in­dx_­size), taken from Doubleword com­mit c32932bb9. The over­lay also in­cludes fused-SiLU and fast-rout­ing changes for grouped MXFP4 ex­perts.

FP8 for­mat. DeepSeek V4′s Lightning Indexer cache uses FP8. The stock writer emits OCP E4M3 bytes in row-ma­jor or­der, while AITER on MI300X con­sumes AMD FNUZ E4M3 bytes in a preshuf­fled 16×16 tile lay­out. In the worst case, in­ter­pret­ing one for­mat as the other pro­duces a fac­tor-of-two scale er­ror. The over­lay se­lects float8e4b8 with FP8_MAX=224.0 and shuf­fled write off­sets on ROCm, while leav­ing the OCP path un­changed else­where.

Speculative de­cod­ing

This stack uses prob­a­bilis­tic draft­ing with block re­jec­tion. The two Gumbel over­lays keep draft-pro­posal noise in­de­pen­dent of re­jec­tion and re­cov­ery noise.

Performance

Key op­ti­miza­tions in the pro­duc­tion con­fig­u­ra­tion:

Final con­cur­rency sweep

Distinct ~400-word prompts, stream­ing, tem­per­a­ture=1.0, top_p=0.95; C1–C8 at 512 out­put to­kens, C64 at 256:

DSpark ac­cep­tance is prompt-de­pen­dent; treat these as gates for this ex­act im­age, not uni­ver­sal model bench­marks.

Prefill

With the tuned ker­nels, un­cached pre­fill reaches 7.9 – 8.5K tok/​s, de­pend­ing on sched­uler bud­get: 7.90 – 7.99K at C1 with an 8,192-token bud­get and 8.46 – 8.51K at C4. The pro­duc­tion pro­file uses a 2,048-token bud­get for la­tency iso­la­tion, giv­ing 6,988 – 7,019 tok/​s on fresh prompts. With the 1,024-token long-pre­fill cap, an 8.9K-token prompt reaches 5.20 – 5.29K tok/​s at C1. In ex­change, TTFT for a short re­quest queued be­hind a 52K cold pre­fill drops from 8.2 s to 0.5 s. Warm re­call of 380K cached to­kens takes 0.64 – 2.65 s af­ter a 120 – 125 s cold pre­fill.

Production notes

HBM head­room is lim­ited. The warmed high-wa­ter mark is 204.5 of 205.8 GB. A 30 GB KV pool loads but fails dur­ing graph cap­ture with HSA_STATUS_ERROR_OUT_OF_RESOURCES. Do not raise –kv-cache-memory-bytes; mon­i­tor HBM us­age for growth.

The CPU KV tier stores cache en­tries, not weights. –kv-offloading-size 96 –kv-offloading-backend na­tive maps ~103 GB in /dev/shm for evicted pre­fix-cache en­tries. The en­try­point re­moves stale map­pings af­ter crashes.

The 1,664-token sched­uler warn­ing is ex­pected. DSpark-7 re­serves draft slots from the 2,048-token bud­get. Raising the bud­get re­serves more in-flight slid­ing-win­dow state and re­duces us­able KV ca­pac­ity.

Warm the ker­nels af­ter restart. The first pre­fill ini­tial­izes ker­nels and takes 5.3 s for 8.9K to­kens; sub­se­quent runs take 1.7 s. Run one un­cached pre­fill be­fore ad­mit­ting traf­fic.

Test cor­rect­ness as well as through­put. The val­i­da­tion suite in­cludes two-turn tool-call­ing fix­tures, a BFCL sub­set (74 – 76/90 ex­act calls), OpenCode tool-schema checks, and 380K-token nee­dle re­call on both na­tive and DSpark paths. Cold and cached pre­fills can take dif­fer­ent float­ing-point paths, so test both.

License and prove­nance

The stack, doc­u­men­ta­tion, and vLLM-de­rived over­lays are Apache-2.0 (see LICENSE); the AITER-derived over­lay keeps its MIT header. Upstream base re­vi­sions for every diff are recorded in patches/​README.md. The model it­self is MIT-licensed.

References

All links ver­i­fied 2026 – 08-04.

DeepSeek-V4-Flash-0731 model card — of­fi­cial re­lease; 304B pa­ra­me­ters; fused DSpark mod­ule; rec­om­mended tem­per­a­ture=1.0, top_p=0.95; MIT li­cense

Official vLLM DeepSeek V4 Flash recipe — ref­er­ence launch con­fig­u­ra­tion, DSpark (num_speculative_tokens=7), FP8 KV, block size 256, deepseek_v4 parsers; AMD guid­ance for MI325X/MI355X

Bringing up DeepSeek-V4-Flash on AMD MI300X (Fergus Finn, Doubleword, June 2026) — the bring-up work­log this repo builds on: FNUZ vs. OCP FP8, AITER gaps on gfx942, HIP-graph haz­ards, rout­ing bugs

dou­ble­wor­dai/​vllm-amd-blog-dou­ble­word — demo PRs for the above, in­clud­ing com­mit c32932bb9 (“mask MXFP4 bit­ma­trix padding lanes by log­i­cal block size”)

vLLM com­mit 77469c9 — “[ROCm][MLA] Mask the AITER MLA small-head ver­ify flat­ten causally (#50476)”

vLLM is­sue #47282 — CPU-KV load path lacks cross-stream sync with com­pute (WAR gap)

vLLM PR #47291 — pro­posed WAR fix, not merged; car­ried as an over­lay here

AMD Instinct MI300X — 192 GB HBM3, 5.3 TB/s peak band­width, 2.61 PFLOPS peak FP8

ROCm/AITER — AMD tuned-ker­nel li­brary used for ROCm at­ten­tion and dense lin­ears

vLLM — the serv­ing run­time (ROCm nightlies un­der vllm/​vllm-ope­nai-rocm)

WINONA, Minn. (Valley News Live) - Every Flock li­cense plate reader cam­era op­er­ated by the Winona Police Department has been sawed off and stolen in what in­ves­ti­ga­tors be­lieve was a co­or­di­nated theft.

All eight cam­eras were taken Aug. 1, ac­cord­ing to the Winona Police Department. A pa­trol of­fi­cer first no­ticed the cam­eras had not sent any alerts in 24 hours. When of­fi­cers checked the lo­ca­tions, they found the cam­eras had been cut from their poles and taken. The poles were left be­hind.

Two ad­di­tional Flock cam­eras on the Mississippi River Bridge, owned by Buffalo County, were also stolen in the same man­ner.

Each cam­era is val­ued at ap­prox­i­mately $3,000, putting the to­tal loss at roughly $24,000. That cost falls di­rectly on the Winona Police Department’s bud­get.

The eight WPD cam­eras were po­si­tioned at key high­way en­try and exit points through­out the city: near Highway 61 and Bundy Boulevard, Highway 43 and Homer Road, Highway 14 and Knapp Valley Drive, and Highway 61 and Highway 14. Two cam­eras were sta­tioned at each lo­ca­tion.

Flock Safety cam­eras are au­to­mated li­cense plate read­ers that cap­ture im­ages of plates along with a ve­hi­cle’s make, model and color. Police use the tech­nol­ogy to in­ves­ti­gate crimes such as hit-and-runs and to lo­cate miss­ing per­sons. Camera data is owned by the po­lice de­part­ment and per­ma­nently deleted af­ter 30 days.

The thefts are part of a broader na­tional trend. Flock cam­eras have been van­dal­ized and cut down in com­mu­ni­ties across the coun­try. The tech­nol­ogy has drawn crit­i­cism from civil lib­er­ties ad­vo­cates who ar­gue the cam­eras ex­pand gov­ern­ment sur­veil­lance and raise con­cerns about data be­ing shared with third-party com­pa­nies or fed­eral agen­cies.

No sus­pects have been iden­ti­fied. The in­ves­ti­ga­tion is on­go­ing. Anyone with in­for­ma­tion is asked to con­tact the Winona Police Department.

Sources: News 8000 | Winona Post

Copyright 2026 KVLY. All rights re­served.

The U.S. Army has used up much of its stock­pile of highly ac­cu­rate long-range mis­siles dur­ing its five-month war with Iran, ac­cord­ing to three peo­ple fa­mil­iar ⁠with the data, rais­ing con­cerns about the mil­i­tary’s readi­ness for fu­ture con­flicts.

The mis­siles are prin­ci­pally the Army’s sur­face-to-sur­face weapons, known as Army Tactical Missile Systems (ATACMS) and Precision Strike Missiles (PrSM). The U.S. has used “virtually all” of these weapons, ac­cord­ing to two of the sources.

The de­gree to which the ​military is run­ning out of ATACMS and Precision Strike Missiles has not ​been pre­vi­ously re­ported. The long-range mu­ni­tions are an im­por­tant part ​the mil­i­tary’s ar­se­nal, al­low­ing ac­cu­rate strikes from a safe dis­tance. U.S.-supplied ATACMS have played a key role in the war in Ukraine, al­low­ing Ukrainian forces to at­tack tar­gets in­side Russia. The PrSM is a newer, more ad­vanced gen­er­a­tion that will re­place the ATACMS, which have a shorter range.

Analysts say such weapons — which cost over $1 mil­lion each — would also be im­por­tant in any con­flict with China.

The sources de­clined to say how many of each mu­ni­tion the U.S. had left.

President Donald Trump launched the ⁠Iran war ‌jointly with Israel in February, pre­dict­ing that the con­flict would last a short time.

But as the war drags on, the ⁠three peo­ple fa­mil­iar with the mat­ter ex­pressed worry that the falling mis­sile sup­plies could limit the U.S. abil­ity to de­ter ad­ver­saries, in­clud­ing Russia and China.

A fourth per­son fa­mil­iar with the mat­ter said that while Central Command — which over­sees U.S. forces in the Middle East — has nearly used up the land-based mis­siles it had be­fore the war be­gan, it has been able to re­load from U.S. mil­i­tary sup­plies else­where in the world.

The sources in­ter­viewed for this story spoke on the con­di­tion of anonymity.

Asked for com­ment on the stock­pile data, the White House is­sued a state­ment ‌from Trump, say­ing the U.S. had “far more mu­ni­tions than any­one in the world” and “far more than we need.”

“Our de­fense com­pa­nies are, at this mo­ment, mak­ing more mu­ni­tions than they have ever made be­fore, in ad­di­tion to ex­pand­ing their plants and equip­ment at record lev­els,” Trump said.

Analysts agree that cer­tain mu­ni­tions, in­clud­ing ar­tillery shells and sev­eral types of mis­siles, are be­ing pro­duced at record lev­els but cau­tion that ​supplies might far short of what is needed for a pro­longed war.

Lockheed Martin, which makes the ATACMs and PrSMs, along with the anti-bal­lis­tic mis­sile THAAD sys­tem, did not im­me­di­ately re­spond to ques­tions about Trump’s state­ments or about sup­ply lev­els. Raytheon, which makes Tomahawk mis­siles and Patriot in­ter­cep­tors, two im­por­tant U.S. weapons, also did not im­me­di­ately re­spond.

Responding to a re­quest for com­ment, chief Pentagon spokesper­son Sean Parnell said: “America’s mil­i­tary is the most pow­er­ful in the world and has every­thing it needs to ex­e­cute at the time and place of the President’s choos­ing. We have ex­e­cuted mul­ti­ple suc­cess­ful op­er­a­tions across com­bat­ant com­mands while en­sur­ing the U.S. mil­i­tary pos­sesses a ⁠deep ar­se­nal of ca­pa­bil­i­ties to pro­tect our peo­ple and our in­ter­ests.”

The sup­ply fig­ures have cir­cu­lated in­side the fed­eral gov­ern­ment over the last week dur­ing tense con­ver­sa­tions in­side the Trump ad­min­is­tra­tion about how much longer the U.S. can con­tinue strik­ing Iran with­out draw­ing down the ‌stockpile to lev­els that would limit the mil­i­tary’s abil­ity to re­spond to crises else­where.

Warnings over weapons sup­plies

One of the sources said the draw­down of the ‌ATACMS and PrSM stock­piles re­flected a de­ci­sion by the Trump ad­min­is­tra­tion to avoid riskier ways of at­tack­ing Iranian tar­gets, such as by us­ing pi­loted air­craft to drop bombs.

Because these weapons al­low the mil­i­tary to at­tack tar­gets from a dis­tance, an­a­lysts say they would be valu­able in a war against an ad­ver­sary with strong air de­fenses, such as China. They have been used to strike tar­gets in­side Iran, ac­cord­ing to a March re­port by the Center for Strategic and International Studies (CSIS).

According to the re­port, PrSM stock­piles were low to start with, since ⁠it is a rel­a­tively new mu­ni­tion, but the U.S. mil­i­tary has or­dered a large num­ber of them for 2027. The Army has said that ATACMS are be­ing phased out and that pro­duc­tion ⁠is shift­ing to the newer PrSM mis­siles.

Military lead­ers have for weeks warned the pres­i­dent that stock­piles of de­fen­sive weapons — in­clud­ing Patriot in­ter­cep­tors, which are ef­fec­tive against bal­lis­tic mis­siles — were dwin­dling, said two of ⁠the sources. Last week, sev­eral me­dia out­lets re­ported Trump had de­cided not to launch an­other mas­sive of­fen­sive in­side Iran in part be­cause his mil­i­tary ad­vis­ers had warned about the U.S. stock­pile.

A U.S. of­fi­cial dis­puted those ac­counts, say­ing Trump chose not to move for­ward with an­other at­tack be­cause of pres­sure from Gulf states.

The Middle East con­flict has sparked in­tense de­bate about Trump’s ​authority to pros­e­cute hos­til­i­ties against Iran with­out con­gres­sional au­tho­riza­tion. No re­quest for a de­c­la­ra­tion of war or an au­tho­riza­tion to ‌use mil­i­tary force has been sub­mit­ted to Congress.

Defensive weapon stocks are also di­min­ished

Last week, CSIS pub­lished a re­port es­ti­mat­ing that be­tween February and July about 65% of Patriot in­ter­cep­tors had been ex­pended and that the num­ber of THAAD bal­lis­tic mis­sile in­ter­cep­tors in U.S. stock­piles was at least 38% lower than at the start of the war. Patriots and THAADs are sys­tems that de­tect and de­stroy in­com­ing mis­siles and are among the most ef­fec­tive in the coun­try’s ar­se­nal.

While Reuters has not seen the sup­ply fig­ures, those num­bers match in­ter­nal U.S. data, two of the sources said.

The U.S. also burned through a lit­tle less than half of its global sup­ply of Tomahawk cruise mis­siles, which are gen­er­ally launched from ships, since the start of the war, one of the sources said.

Reuters could not ​independently ver­ify that num­ber.

The Tomahawk is a Navy weapon, launched from de­stroy­ers, cruis­ers and ‌submarines, and has long served as the sea ser­vice’s prin­ci­pal means of strik­ing heav­ily de­fended tar­gets with­out risk­ing pi­lots.

Raytheon, a unit of RTX, has reached a ten­ta­tive multi-year agree­ment with the Pentagon aimed at boost­ing Tomahawk pro­duc­tion, along­side in­creases in other mu­ni­tions, as Washington races to re­build stock­piles.

Apple is now seek­ing a pre­lim­i­nary in­junc­tion in its trade se­crets case against OpenAI, which aims to stop the AI model maker from mov­ing for­ward with de­vel­op­ing an AI de­vice or other prod­ucts based on Apple’s tech­nol­ogy. The iPhone maker also claims that more of its for­mer em­ploy­ees may be in­volved with the trade se­crets theft.

In a new fil­ing, Apple is re­quest­ing ex­pe­dited dis­cov­ery from the ac­cused OpenAI em­ploy­ees, se­nior sys­tems en­gi­neer Chang Liu and Chief Hardware Officer Tang Yew Tan; OpenAI, and its foun­da­tion; and io, the de­vice startup co-founded by Apple’s for­mer lead de­signer Jony Ive.

Apple also notes that its con­tin­ued in­ves­ti­ga­tion has so far re­vealed 11 other for­mer Apple em­ploy­ees be­yond Liu and Tan may have been wit­nesses or oth­er­wise in­volved in the case, and oth­ers who were pre­vi­ously named in the orig­i­nal com­plaint, like OpenAI em­ployee Yu-Ting Peng.

The fil­ing marks an es­ca­la­tion in Apple’s le­gal bat­tle with OpenAI, as it sug­gests Apple has un­cov­ered new ev­i­dence that the mis­con­duct goes be­yond the for­mer em­ploy­ees named in the orig­i­nal com­plaint.

“For ex­am­ple, an­other for­mer Apple em­ployee seems to have met with Mr. Liu and Ms. Peng in ad­vance of Ms. Peng’s in­ter­view at OpenAI and dis­cussed with them dur­ing that meet­ing Apple pro­pri­etary in­for­ma­tion re­lat­ing to unan­nounced prod­ucts,” the fil­ing states. “Yet an­other for­mer Apple em­ployee took screen­shots of con­fi­den­tial Apple doc­u­ments re­lat­ing to an unan­nounced Apple prod­uct be­fore an in­ter­view at OpenAI.”

“And, af­ter Apple filed its com­plaint, mul­ti­ple for­mer Apple em­ploy­ees now work­ing at OpenAI reached out to dis­cuss re­turn­ing Apple-issued work de­vices they kept when they left Apple,” Apple claims, sug­gest­ing there were more who were pos­si­bly in­volved with the scheme.

Apple is push­ing the court to al­low for ex­pe­dited dis­cov­ery be­cause it be­lieves it has good cause to sus­pect that there are oth­ers in­volved in the theft of its in­tel­lec­tual prop­erty. The com­pany noted that its mo­tion for a pre­lim­i­nary in­junc­tion is also pend­ing.

OpenAI re­sponded pub­licly to Apple’s lat­est, say­ing in a blog post that Apple’s re­quest for a pre­lim­i­nary in­junc­tion is “both based on false in­for­ma­tion and com­pletely un­nec­es­sary be­cause we do not have, nor want, any of their trade se­crets.”

“We’re much more in­ter­ested in build­ing in­no­v­a­tive prod­ucts and tech­nolo­gies that push the fron­tier,” OpenAI’s state­ment reads.

The AI model maker also pointed to ear­lier mis­takes Apple made, which had been re­ported, in­clud­ing that Apple emailed the wrong per­son when it made con­tact with OpenAI af­ter con­fus­ing two sim­i­lar sur­names. OpenAI also al­leges that Apple lied about dis­cussing mat­ters with its gen­eral coun­sel. And, the com­pany said that Apple did­n’t ad­mit to the claim that the “residual ac­cess” al­low­ing for­mer em­ploy­ees to ac­cess Apple’s sys­tem was the re­sult of poor se­cu­rity pro­ce­dures on Apple’s part.

When you pur­chase through links in our ar­ti­cles, we may earn a small com­mis­sion. This does­n’t af­fect our ed­i­to­r­ial in­de­pen­dence.

Sarah has worked as a re­porter for TechCrunch since August 2011. She joined the com­pany af­ter hav­ing pre­vi­ously spent over three years at ReadWriteWeb. Prior to her work as a re­porter, Sarah worked in I.T. across a num­ber of in­dus­tries, in­clud­ing bank­ing, re­tail and soft­ware.

You can con­tact or ver­ify out­reach from Sarah by email­ing sarahp@techcrunch.com or via en­crypted mes­sage at sarah­perez.01 on Signal.

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