The World Record for the Shortest Math Article: 2 Words

In 2004, John Con­way and Alexan­der Soifer, both work­ing on math­e­mat­ics at Prince­ton Uni­ver­si­ty, sub­mit­ted to the Amer­i­can Math­e­mat­i­cal Month­ly what they believed was “a new world record in the num­ber of words in a [math] paper.”

Soifer explains: “On April 28, 2004 … I sub­mit­ted our paper that includ­ed just two words, ‘n2 + 2 can’ and our two draw­ings. [See one of them above.]” The sto­ry then con­tin­ues: “The Amer­i­can Math­e­mat­i­cal Month­ly was sur­prised, and did not know what to do about our new world record of a 2‑word arti­cle. Two days lat­er, on April 30, 2004, the Edi­to­r­i­al Assis­tant Mrs. Mar­garet Combs acknowl­edged the receipt of the paper”:

The Month­ly pub­lish­es expo­si­tion of math­e­mat­ics at many lev­els, and it con­tains arti­cles both long and short. Your arti­cle, how­ev­er, is a bit too short to be a good Month­ly arti­cle… A line or two of expla­na­tion would real­ly help.

Soifer writ­ers: “The same day at the cof­fee hour I asked John [Con­way], ‘What do you think?’ His answer was con­cise, ‘Do not give up too eas­i­ly.’ Accord­ing­ly, I replied [to] The Month­ly the same day”:

I respect­ful­ly dis­agree that a short paper in general—and this paper in particular—merely due to its size must be “a bit too short to be a good Month­ly arti­cle.” Is there a con­nec­tion between quan­ti­ty and qual­i­ty?… We have posed a fine (in our opin­ion) open prob­lem and report­ed two dis­tinct “behold-style” proofs of our advance on this prob­lem. What else is there to explain?

Soifer adds: “The Month­ly, appar­ent­ly felt out­gunned, for on May 4, 2004, the reply came from The Month­ly’s top gun, Edi­tor-in-Chief Bruce Pal­ka”:

The Month­ly pub­lish­es two types of papers: “arti­cles,” which are sub­stan­tive expos­i­to­ry papers rang­ing in length from about six to twen­ty-five pages, and “notes,” which are short­er, fre­quent­ly some­what more tech­ni­cal pieces (typ­i­cal­ly in the one-to-five page range). I can send your paper to the notes edi­tor if you wish, but I expect that he’ll not be inter­est­ed in it either because of its length and lack of any sub­stan­tial accom­pa­ny­ing text. The stan­dard way in which we use such short papers these days is as “boxed filler” on pages that would oth­er­wise con­tain a lot of the blank space that pub­lish­ers abhor. If you’d allow us to use your paper in that way, I’d be hap­py to pub­lish it.

Soifer con­cludes: “John Con­way and I accept­ed the ‘filler’, and in the Jan­u­ary 2005 issue our paper was pub­lished.” Vic­to­ry!

Get more of the back­sto­ry here.

Relat­ed Con­tent:

The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal: Two Suc­cinct Sen­tences

John Nash’s Super Short PhD The­sis: 26 Pages & Two Cita­tions

The Map of Math­e­mat­ics: Ani­ma­tion Shows How All the Dif­fer­ent Fields in Math Fit Togeth­er

The PhD Theses of Richard Feynman, Marie Curie, Albert Einstein & Others, Explained with Illustrations

Raise your chil­dren with a love of sci­ence, and there’s a decent chance they’ll grow up want­i­ng to be like Richard Feyn­man, Marie Curie, Albert Ein­stein, or any num­ber of oth­er famous sci­en­tists from his­to­ry. Luck­i­ly for them, they won’t yet have learned that the pur­suit of such a career will almost cer­tain­ly entail grind­ing out a PhD the­sis. But it’s also lucky for you that they con­se­quent­ly won’t ask you to explain the sub­jects of their idols’ the­ses. Maybe you tell them about quan­tum elec­tro­dy­nam­ics, radi­a­tion, and even the the­o­ry of rel­a­tiv­i­ty, but what can you recall of “The Prin­ci­ple of Least Action in Quan­tum Mechan­ics,” “Research on Radioac­tive Sub­stances,” or “Eine neue Bes­tim­mung der Moleküldimen­sio­nen”?

Per­haps “recall” isn’t quite the word. But if you want to get a han­dle on these papers, which con­sti­tute impor­tant parts of the foun­da­tion of the research that would ulti­mate­ly make their authors famous, you could do much worse than begin­ning with the expla­na­tions of sci­ence YouTu­ber Toby Hendy. In recent years, while build­ing up an ever-larg­er audi­ence with her chan­nel Tibees, she’s occa­sion­al­ly reached into the archives and pulled out a notable sci­en­tist’s PhD the­sis.

We’ve assem­bled all of her videos in that series into the playlist above, which also includes Hendy expla­na­tions of the­ses writ­ten by fig­ures not pri­mar­i­ly known to the pub­lic for their research: Carl Sagan and Neil DeGrasse Tyson, and Bri­an Cox (the physi­cist, not the Suc­ces­sion star), whose media work has inspired gen­er­a­tions of fans to go into sci­ence.

Though a young woman, Hendy has mas­tered old-school teach­ing tech­niques, such as draw­ing on a trans­paren­cy placed on an over­head pro­jec­tor, that may trig­ger Prous­t­ian mem­o­ries of sci­ence class, at least in those of us of a cer­tain age. With her calm­ness and clar­i­ty (not to men­tion her will­ing­ness to admit when she her­self strug­gles with the mate­r­i­al) she’d sure­ly have ranked among any of our favorite teach­ers, and if you intro­duce her chan­nel to your kids, she’ll prob­a­bly become one of theirs. Whether they go on to earn a sci­ence PhD is, of course, down to their own incli­na­tion and efforts. Like so many young peo­ple these days, they may ulti­mate­ly come away with a stronger desire to become a YouTu­ber — which, after all, is what Hendy quit her own PhD to do.

Relat­ed con­tent:

Marie Curie’s Ph.D. The­sis on Radioac­tiv­i­ty — Which Made Her the First Woman in France to Receive a Doc­tor­al Degree in Physics

John Nash’s Super Short PhD The­sis: 26 Pages & Two Cita­tions

Queen Gui­tarist Bri­an May Is Also an Astro­physi­cist: Read His PhD The­sis Online

Stephen Hawking’s Ph.D. The­sis, “Prop­er­ties of Expand­ing Uni­vers­es,” Now Free to Read/Download Online

Albert Einstein’s Grades: A Fas­ci­nat­ing Look at His Report Cards

This Is What an 1869 MIT Entrance Exam Looks Like: Could You Have Passed the Test?

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities and the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.

The Secret Link Between Jazz and Physics: How Einstein & Coltrane Shared Improvisation and Intuition in Common

Sci­en­tists need hob­bies. The gru­el­ing work of nav­i­gat­ing com­plex the­o­ry and the pol­i­tics of acad­e­mia can get to a per­son, even one as laid back as Brown Uni­ver­si­ty pro­fes­sor and astro­physi­cist Stephon Alexan­der. So Alexan­der plays the sax­o­phone, though at this point it may not be accu­rate to call his avo­ca­tion a spare time pur­suit, since John Coltrane has become as impor­tant to him as Ein­stein, Kepler, and New­ton.

Coltrane, he says in a 7‑minute TED talk above, “changed my whole research direc­tion… led to basi­cal­ly a dis­cov­ery in physics.” Alexan­der then pro­ceeds to play the famil­iar open­ing bars of “Giant Steps.” He’s no Coltrane, but he is a very cre­ative thinker whose love of jazz has giv­en him a unique per­spec­tive on the­o­ret­i­cal physics, one he shares, it turns out, with both Ein­stein and Coltrane, both of whom saw music and physics as intu­itive, impro­visato­ry pur­suits.

Alexan­der describes his jazz epiphany as occa­sioned by a com­plex dia­gram Coltrane gave leg­endary jazz musi­cian and Uni­ver­si­ty of Mass­a­chu­setts pro­fes­sor Yusef Lateef in 1967. “I thought the dia­gram was relat­ed to anoth­er and seem­ing­ly unre­lat­ed field of study—quantum grav­i­ty,” he writes in a Busi­ness Insid­er essay on his dis­cov­ery, “What I had real­ized… was that the same geo­met­ric prin­ci­ple that moti­vat­ed Einstein’s the­o­ry was reflect­ed in Coltrane’s dia­gram.”

The the­o­ry might “imme­di­ate­ly sound like untestable pop-phi­los­o­phy,” writes the Cre­ators Project, which show­cas­es Alexander’s physics-inspired musi­cal col­lab­o­ra­tion with exper­i­men­tal pro­duc­er Rioux (sam­ple below). But his ideas are much more sub­stan­tive, “a com­pelling cross-dis­ci­pli­nary inves­ti­ga­tion,” pub­lished in a book titled The Jazz of Physics: The Secret Link Between Music and the Struc­ture of the Uni­verse.

Alexan­der describes the links between jazz and physics in his TED talk, as well as in the brief Wired video fur­ther up. “One con­nec­tion,” he says, is “the mys­te­ri­ous way that quan­tum par­ti­cles move.… Accord­ing to the rules of quan­tum mechan­ics,” they “will actu­al­ly tra­verse all pos­si­ble paths.” This, Alexan­der says, par­al­lels the way jazz musi­cians impro­vise, play­ing with all pos­si­ble notes in a scale. His own impro­vi­sa­tion­al play­ing, he says, is great­ly enhanced by think­ing about physics. And in this, he’s only fol­low­ing in the giant steps of both of his idols.

It turns out that Coltrane him­self used Einstein’s the­o­ret­i­cal physics to inform his under­stand­ing of jazz com­po­si­tion. As Ben Ratliff reports in Coltrane: The Sto­ry of a Sound, the bril­liant sax­o­phon­ist once deliv­ered to French horn play­er David Amram an “incred­i­ble dis­course about the sym­me­try of the solar sys­tem, talk­ing about black holes in space, and con­stel­la­tions, and the whole struc­ture of the solar sys­tem, and how Ein­stein was able to reduce all of that com­plex­i­ty into some­thing very sim­ple.” Says Amram:

Then he explained to me that he was try­ing to do some­thing like that in music, some­thing that came from nat­ur­al sources, the tra­di­tions of the blues and jazz. But there was a whole dif­fer­ent way of look­ing at what was nat­ur­al in music.

This may all sound rather vague and mys­te­ri­ous, but Alexan­der assures us Coltrane’s method is very much like Einstein’s in a way: “Ein­stein is famous for what is per­haps his great­est gift: the abil­i­ty to tran­scend math­e­mat­i­cal lim­i­ta­tions with phys­i­cal intu­ition. He would impro­vise using what he called gedanken­ex­per­i­ments (Ger­man for thought exper­i­ments), which pro­vid­ed him with a men­tal pic­ture of the out­come of exper­i­ments no one could per­form.”

Ein­stein was also a musi­cian—as we’ve not­ed before—who played the vio­lin and piano and whose admi­ra­tion for Mozart inspired his the­o­ret­i­cal work. “Ein­stein used math­e­mat­i­cal rig­or,” writes Alexan­der, as much as he used “cre­ativ­i­ty and intu­ition. He was an impro­vis­er at heart, just like his hero, Mozart.” Alexan­der has fol­lowed suit, see­ing in the 1967 “Coltrane Man­dala” the idea that “impro­vi­sa­tion is a char­ac­ter­is­tic of both music and physics.” Coltrane “was a musi­cal inno­va­tor, with physics at his fin­ger­tips,” and “Ein­stein was an inno­va­tor in physics, with music at his fin­ger­tips.”

Alexan­der gets into a few more specifics in his longer TEDx talk above, begin­ning with some per­son­al back­ground on how he first came to under­stand physics as an intu­itive dis­ci­pline close­ly linked with music. For the real meat of his argu­ment, you’ll like­ly want to read his book, high­ly praised by Nobel-win­ning physi­cist Leon Coop­er, futur­is­tic com­pos­er Bri­an Eno, and many more bril­liant minds in both music and sci­ence.

Note: An ear­li­er ver­sion of this post appeared on our site in 2016.

Relat­ed Con­tent:

Free Online Physics Cours­es

The Musi­cal Mind of Albert Ein­stein: Great Physi­cist, Ama­teur Vio­lin­ist and Devo­tee of Mozart

CERN’s Cos­mic Piano and Jazz Pianist Jam Togeth­er at The Mon­treux Jazz Fes­ti­val

Bohemi­an Grav­i­ty: String The­o­ry Explored With an A Cap­pel­la Ver­sion of Bohemi­an Rhap­sody

Josh Jones is a writer and musi­cian based in Durham, NC. Fol­low him at @jdmagness

How Civilizations Built on Top of Each Other: Discover What Lies Beneath Rome, Troy & Other Cities

The idea of dis­cov­er­ing a lost ancient city under­ground has long cap­tured the human imag­i­na­tion. But why are the aban­doned built envi­ron­ments of those fan­tasies always buried? The answer, in large part, is that such places do indeed exist under our feet, at least in cer­tain parts of the world. When archae­ol­o­gists start­ed dig­ging under the Roman Forum, says the nar­ra­tion of the new Pri­mal Space video above, “they uncov­ered an entire world of ruins deep under­ground that had­n’t been seen for cen­turies.” The even old­er city of Troy “was rebuilt ten times, form­ing ten dis­tinct lay­ers, all built direct­ly on top of each oth­er.” A geo­log­i­cal dig is always a jour­ney back in time, but there even more so.

Each civ­i­liza­tion has its own rea­sons for this kind of phys­i­cal accre­tion. “After the great fire of Rome in the first cen­tu­ry, most of the city had to be rebuilt. But instead of clear­ing away the rub­ble, it was quick­er and eas­i­er to sim­ply flat­ten it out and build on top.” There­after, peri­od­ic dis­as­ters con­tin­ued to neces­si­tate peri­od­ic rais­ing of the streets, a process that would even­tu­al­ly bury old­er struc­tures com­plete­ly.

In the case of Troy, which began as a set­tle­ment built of mud bricks in 3,000 BC, nine civ­i­liza­tions grew and dis­solved (often lit­er­al­ly) on the very same mound, “going from the Per­sians to Alexan­der the Great, and even­tu­al­ly the Romans.” Some­thing sim­i­lar con­tin­ues to hap­pen in cer­tain parts of the world today: Shang­hai, for instance, which is now sink­ing at a rate of one cen­time­ter per year.

Hav­ing grown up around Seat­tle, I had more than one occa­sion to take its “under­ground tour,” which takes place amid the remains of a late-nine­teenth-cen­tu­ry town­scape pre­served just below the mod­ern streets. “In 1889, a dev­as­tat­ing fire ripped through the new­ly formed city, and just like Rome, almost every­thing had to be rebuilt,” the video explains. The after­math brought an oppor­tu­ni­ty to re-design the flood-prone city with streets ele­vat­ed above a sys­tem of drains. This put under­ground not just the low­er floors of the exist­ing build­ings, but also their sur­round­ing side­walks. At ele­men­tary-school age, one is some­how both fas­ci­nat­ed and not par­tic­u­lar­ly sur­prised by the exis­tence of a lost city beneath one’s home­town. For me and my class­mates, noth­ing was more mem­o­rable than the fact that there are still toi­lets down there.

Relat­ed con­tent:

The Lost Neigh­bor­hood Buried Under New York City’s Cen­tral Park

What’s Under Lon­don? Dis­cov­er London’s For­bid­den Under­world

How the “Lost Cities” of the Ama­zon Were Final­ly Dis­cov­ered

Under­ci­ty: Explor­ing the Under­bel­ly of New York City

Explore the Ruins of Tim­gad, the “African Pom­peii” Exca­vat­ed from the Sands of Alge­ria

Paris Under­ground

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities and the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.

The Cleanest Recordings of 1920s Louis Armstrong Songs You Will Ever Hear

On Youtube, jazz enthu­si­ast Jonathan Holmes declares: “I can guar­an­tee this is the clean­est sound­ing Louis Arm­strong record you’ll ever hear! With the orig­i­nal trans­fer sup­plied by Nick Del­low, here is the moth­er record which was shipped by Okeh to Ger­many for their Odeon press­ings. The sound is won­der­ful­ly imme­di­ate, and crys­tal clear.” No crack­le and pop. That’s how Holmes describes the pris­tine record­ing you can hear above of the Louis Arm­strong clas­sic, “Ain’t Mis­be­havin’.” Below, hear anoth­er “moth­er met­al” record­ing of anoth­er Arm­strong song, “Knee Drops.” Enjoy the ear­ly Satch­mo in all of its won­der­ful clar­i­ty.

If you would like to sign up for Open Culture’s free email newslet­ter, please find it here. It’s a great way to see our new posts, all bun­dled in one email, each day.

If you would like to sup­port the mis­sion of Open Cul­ture, con­sid­er mak­ing a dona­tion to our site. It’s hard to rely 100% on ads, and your con­tri­bu­tions will help us con­tin­ue pro­vid­ing the best free cul­tur­al and edu­ca­tion­al mate­ri­als to learn­ers every­where. You can con­tribute through Pay­Pal, Patre­on, and Ven­mo (@openculture). Thanks!

Note: An ear­li­er ver­sion of this post appeared on our site in 2016.

Relat­ed Con­tent:

An Aging Louis Arm­strong Sings “What a Won­der­ful World” in 1967, Dur­ing the Viet­nam War & The Civ­il Rights Strug­gle

1,000 Hours of Ear­ly Jazz Record­ings Now Online: Archive Fea­tures Louis Arm­strong, Duke Elling­ton & Much More

Watch the Ear­li­est Known Footage of Louis Arm­strong Per­form­ing Live in Con­cert (Copen­hagen, 1933)

Louis Arm­strong Remem­bers How He Sur­vived the 1918 Flu Epi­dem­ic in New Orleans

How Frank Lloyd Wright’s Architecture Evolved Over 70 Years and Changed America

In the new Archi­tec­tur­al Digest video above, Michael Wyet­zn­er talks about a fair few build­ings we’ve fea­tured over the years here on Open Cul­ture: the Impe­r­i­al Hotel, the Ennis House, Tal­iesin, Falling­wa­ter. These are all, of course, the work of Frank Lloyd Wright, who still stands as the embod­i­ment of Amer­i­can archi­tec­ture more than 65 years after his death. That’s a fair­ly long stretch by mod­ern stan­dards, but nev­er­the­less a short­er one than Wright’s career, which ran over 70 years. Dur­ing his long life, Wyet­zn­er explains, Wright wit­nessed the intro­duc­tion of indoor plumb­ing, elec­tric­i­ty, the tele­phone, the auto­mo­bile, the air­plane, the radio, tele­vi­sion, and space trav­el — and even giv­en that, his archi­tec­ture shows a dra­mat­ic evo­lu­tion.

Begin­ning with Wright’s appren­tice­ship in Chica­go under Louis Sul­li­van, “the father of mod­ernism,” Wyet­zn­er con­tin­ues on to his devel­op­ment of the hor­i­zon­tal indoor-out­door “Prairie Style” house; his Japan­ese com­mis­sions and sub­se­quent much-pho­tographed Los Ange­les hous­es; the emer­gence of his phi­los­o­phy of “organ­ic archi­tec­ture” meant to uni­fy the build­ing with its site and nat­ur­al envi­ron­ment; his dis­cov­ery of the desert; and his Depres­sion-era con­cep­tion of the “Uson­ian house,” which adapt­ed his refined spa­tial sen­si­bil­i­ty for Amer­i­can-style mass pro­duc­tion. This would be more than enough for even the most dis­tin­guished archi­tec­t’s career. Yet it does­n’t even get around to such projects as the Uni­ty Tem­ple, John­son Wax Head­quar­ters, the R. W. Lind­holm Ser­vice Sta­tion, the Solomon R. Guggen­heim Muse­um, or his first and last dog­house.

No mat­ter which peri­od of Wright’s career you exam­ine, you can find evi­dence for his belief in the inspi­ra­tion of place, in organ­ic aes­thet­ics, in struc­tur­al expres­sive­ness, and even in indi­rect moral instruc­tion. Yet it’s also pos­si­ble to imag­ine that, in some sense, a series of dif­fer­ent Frank Lloyd Wrights exist­ed, repeat­ed­ly destroyed and recre­at­ed by pro­fes­sion­al set­back, per­son­al dis­as­ter, for­eign sojourn, immer­sion in a new land­scape, or even acquain­tance with a new tech­nol­o­gy. Sure­ly no one could remain pro­duc­tive to the end of his 92 years with­out a lit­tle re-inven­tion. Dur­ing that time, he designed more than 1,000 projects, only about half of which were ever built. Young archi­tects who idol­ize Frank Lloyd Wright would do well to remem­ber that he, too, knew full well the sting of nev­er mak­ing it to con­struc­tion.

Relat­ed Con­tent:

How Frank Lloyd Wright Became Frank Lloyd Wright: A Video Intro­duc­tion

Frank Lloyd Wright Cre­ates a List of the 10 Traits Every Aspir­ing Artist Needs

That Far Cor­ner: Frank Lloyd Wright in Los Ange­les – A Free Online Doc­u­men­tary

Frank Lloyd Wright: America’s Great­est Archi­tect? – A Free Stream­ing Doc­u­men­tary

What Frank Lloyd Wright’s Unusu­al Win­dows Tell Us About His Archi­tec­tur­al Genius

What It’s Like to Work in Frank Lloyd Wright’s Icon­ic Office Build­ing

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities and the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.

David Bowie/Nirvana’s “The Man Who Sold The World” Played on the Gayageum, a Korean Instrument from the 6th Century

East meets West, and the Ancient, the Mod­ern. That’s what hap­pens every time Luna Lee plays one of your favorites on the Gayageum, a Kore­an instru­ment that dates back to the 6th cen­tu­ry. We’ve fea­tured her work in years past (see the Relat­eds below). Above, watch one of her stand­out performances—a cov­er of “The Man Who Sold The World,” the song first writ­ten by David Bowie in 1970, then famous­ly per­formed by Nir­vana on MTV Unplugged in 1993. An alter­nate video fea­tures Luna on vocals here. Enjoy!

If you would like to sign up for Open Culture’s free email newslet­ter, please find it here. It’s a great way to see our new posts, all bun­dled in one email, each day.

If you would like to sup­port the mis­sion of Open Cul­ture, con­sid­er mak­ing a dona­tion to our site. It’s hard to rely 100% on ads, and your con­tri­bu­tions will help us con­tin­ue pro­vid­ing the best free cul­tur­al and edu­ca­tion­al mate­ri­als to learn­ers every­where. You can con­tribute through Pay­Pal, Patre­on, and Ven­mo (@openculture). Thanks!

Relat­ed Con­tent:

Clas­sic Blues Songs By John Lee Hook­er, B.B. King & Mud­dy Waters Played on the Gayageum, a Tra­di­tion­al Kore­an Instru­ment

David Bowie and Klaus Nomi’s Hyp­not­ic Per­for­mance on SNL (1979)

Watch Jimi Hendrix’s ‘Voodoo Chile’ Per­formed on a Gayageum, a Tra­di­tion­al Kore­an Instru­ment

Three Pink Floyd Songs Played on the Tra­di­tion­al Kore­an Gayageum: “Com­fort­ably Numb,” “Anoth­er Brick in the Wall” & “Great Gig in the Sky”

Ste­vie Ray Vaughan’s Ver­sion of “Lit­tle Wing” Played on Tra­di­tion­al Kore­an Instru­ment, the Gayageum

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How Our Depiction of Jesus Changed Over 2,000 Years and What He May Have Actually Looked Like

Whether or not you believe Jesus Christ is the son of God, you prob­a­bly envi­sion him (or, if you pre­fer, Him) in much the same way as most every­one else does. The long hair and beard, the robe, the san­dals, the beatif­ic gaze: these traits have all man­i­fest­ed across two mil­len­nia of Chris­t­ian art. “How­ev­er, these depic­tions don’t exact­ly match the pro­file of a first-cen­tu­ry Jew­ish car­pen­ter from the Mid­dle East,” says Hochela­ga host Tom­mie Trelawny in the new video above, an inves­ti­ga­tion into how our mod­ern con­cept of how Jesus looked came to be — and into what we can know about his real appear­ance.

First, we must turn to the Bible. In the King James Ver­sion, Rev­e­la­tion describes Jesus thus: “His head and his hairs were white like wool, as white as snow; and his eyes were as a flame of fire; and his feet like unto fine brass, as if they burned in a fur­nace; and his voice as the sound of many waters. He had in His right hand sev­en stars, out of His mouth went a sharp two-edged sword, and His coun­te­nance was like the sun shin­ing in its strength.” That’s it for the New Tes­ta­ment. As for the Old Tes­ta­ment, Isa­iah describes a fig­ure that could pos­si­bly be Jesus by cred­it­ing him with “no form nor come­li­ness; and when we shall see him, there is no beau­ty that we should desire him.”

This scant Bib­li­cal evi­dence hard­ly aligns with the high-pro­file depic­tions of Jesus we’ve all seen. For many around the world today, the “default rep­re­sen­ta­tion” is the down­right glam­orous 1940 por­trait Head of Christ by the Amer­i­can painter Warn­er Sall­man (a Chicagoan, inci­den­tal­ly, much like the new­ly elect­ed Pope Leo XIV). One could see that art­work as the cul­mi­na­tion of a fair­ly long his­to­ry of visu­al depic­tions of Jesus, which first became abun­dant in the Roman Empire of the fourth cen­tu­ry under Con­stan­tine. Accord­ing to Gre­co-Roman mythol­o­gy, “hav­ing long hair and a beard were sym­bols of divine pow­er.” Ear­ly Chris­tians thus “want­ed to present their god using sim­i­lar artis­tic con­ven­tions,” plac­ing Jesus in a league with the likes of Zeus.

That’s the basic look Jesus has in most rep­re­sen­ta­tions, from the botched Span­ish fres­co that became a meme to the cru­ci­fied Mr. Uni­verse in South Korea, where I live, to Andy Warhol’s Christ $9.98. And yet, accord­ing to the dic­tates of Leviti­cus, “you shall not round the cor­ners of your heads, nei­ther shalt thou mar the cor­ners of thy beard.” Trelawny takes this into account when attempt­ing to recon­struct the his­tor­i­cal Jesus, also not­ing that, since Jesus could only be iden­ti­fied by Judas’ kiss of betray­al, he must have looked much like all the oth­er men around him. The result, when all of this is fed into an arti­fi­cial-intel­li­gence image gen­er­a­tor, is very much an every­man, which may be as his­tor­i­cal­ly accu­rate as we can get. But then, each time and place cre­ates its own Jesus — and now, with AI, each of us can do the same for our­selves.

Relat­ed con­tent:

The Ten Ear­li­est Depic­tions of Jesus: How Art Visu­al­ized Jesus in the First Cen­turies After His Death

What Makes Caravaggio’s The Tak­ing of Christ a Time­less, Great Paint­ing?

How Leonar­do da Vin­ci Paint­ed The Last Sup­per: A Deep Dive Into a Mas­ter­piece

The Real Sto­ry of East­er: How We Got from the First East­er in the Bible to Bun­nies, Eggs & Choco­late

Intro­duc­tion to New Tes­ta­ment His­to­ry and Lit­er­a­ture: A Free Yale Course

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities and the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.

John Nash’s Super Short PhD Thesis: 26 Pages & Two Citations

When John Nash wrote “Non-Coop­er­a­tive Games,” his Ph.D. dis­ser­ta­tion at Prince­ton in 1950, the text of his the­sis (read it online) was brief. It ran only 26 pages. And more par­tic­u­lar­ly, it was light on cita­tions. Nash’s diss cit­ed two texts: John von Neu­mann and Oskar Mor­gen­stern’s The­o­ry of Games and Eco­nom­ic Behav­ior (1944), which essen­tial­ly cre­at­ed game the­o­ry and rev­o­lu­tion­ized the field of eco­nom­ics; the oth­er cit­ed text, “Equi­lib­ri­um Points in n‑Person Games,” was an arti­cle writ­ten by Nash him­self. And it laid the foun­da­tion for his dis­ser­ta­tion, anoth­er sem­i­nal work in the devel­op­ment of game the­o­ry, for which Nash was award­ed the Nobel Prize in Eco­nom­ic Sci­ences in 1994.

The reward of invent­ing a new field is hav­ing a slim bib­li­og­ra­phy.

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Note: An ear­li­er ver­sion of this post appeared on our site in June, 2015.

Relat­ed Con­tent:

The Short­est-Known Paper Pub­lished in a Seri­ous Math Jour­nal: Two Suc­cinct Sen­tences

The World Record for the Short­est Math Arti­cle: 2 Words

Doc­tor­al Dis­ser­ta­tion as a Graph­ic Nov­el: Read a Free Excerpt of Nick Sou­sa­nis’ Unflat­ten­ing

How to Dance Your Dis­ser­ta­tion: See the Win­ning Video in the 2014 “Dance Your PhD” Con­test

Umber­to Eco’s How To Write a The­sis: A Wit­ty, Irrev­er­ent & High­ly Prac­ti­cal Guide Now Out in Eng­lish

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How a Student’s Phone Call Averted a Skyscraper Collapse: The Tale of the Citicorp Center

The Cit­i­group Cen­ter in Mid­town Man­hat­tan is also known by its address, 601 Lex­ing­ton Avenue, at which it’s been stand­ing for 47 years, longer than the medi­an New York­er has been alive. Though still a fair­ly hand­some build­ing, in a sev­en­ties-cor­po­rate sort of way, it now pops out only mild­ly on the sky­line. At street lev­el, though, the build­ing con­tin­ues to turn heads, placed as it is on a series of stilt-look­ing columns placed not at the cor­ners, but in the mid­dle of the walls. A vis­i­tor with no knowl­edge of struc­tur­al engi­neer­ing pass­ing the Cit­i­group Cen­ter for the first time may won­der why it does­n’t fall down — which, for a few months in 1978, was a gen­uine­ly seri­ous con­cern.

This sto­ry, told with a spe­cial explana­to­ry vivid­ness in the new Ver­i­ta­si­um video above, usu­al­ly begins with a phone call. An uniden­ti­fied archi­tec­ture stu­dent got ahold of William LeMes­suri­er, the struc­tur­al engi­neer of the Citi­corp Cen­ter, as it was then known, to relay con­cerns he’d heard a pro­fes­sor express about the still-new sky­scrap­er’s abil­i­ty to with­stand “quar­ter­ing winds,” which blow diag­o­nal­ly at its cor­ners. LeMes­suri­er took the time to walk the stu­dent through the ele­ments of his then-ground­break­ing light­weight design, which includ­ed chevron-shaped braces that direct­ed ten­sion loads down to the columns and a 400-ton con­crete tuned mass damper (or “great block of cheese,” as it got to be called) meant to coun­ter­act oscil­la­tion move­ments.

LeMes­suri­er was a proud pro­fes­sion­al, but his pro­fes­sion­al­ism out­weighed his pride. When he went back to check the Citi­corp Cen­ter’s plans, he received an unpleas­ant sur­prise: the con­struc­tion com­pa­ny had swapped out the weld­ed joints in those chevron braces for cheap­er bolt­ed ones. His office had approved the change, which made sense at the time, and had also tak­en into account only per­pen­dic­u­lar winds, not quar­ter­ing winds, as was then stan­dard indus­try prac­tice. Per­form­ing the rel­e­vant cal­cu­la­tions him­self, he deter­mined that the whole tow­er could be brought down — and much in the sur­round­ing area destroyed with it — by the kind of winds that have a one-in-six­teen chance of blow­ing in any giv­en year.

It did­n’t take LeMes­suri­er long to real­ize that he had no choice but to reveal what he’d dis­cov­ered to Citi­corp, whose lead­er­ship coop­er­at­ed with the accel­er­at­ed, semi-clan­des­tine project of shoring up their gleam­ing emblem’s struc­tur­al joints by night. The work could hard­ly fail to draw the atten­tion of the New York press, of course, but it received scant cov­er­age thanks to an impec­ca­bly timed news­pa­per strike, and on its com­ple­tion made the sky­scraper per­haps the safest in the city. In fact, the sto­ry of the Citi­corp Cen­ter dis­as­ter that was­n’t only came out pub­licly in a 1995 New York­er piece by Joseph Mor­gen­stern, which made LeMes­suri­er a kind of hero among struc­tur­al engi­neers. But it was the stu­dents who’d iden­ti­fied the build­ing’s faults, not just one but two of whom came for­ward there­after, who per­son­i­fied the life-sav­ing pow­er of ask­ing the right ques­tions.

Relat­ed con­tent:

How This Chica­go Sky­scraper Bare­ly Touch­es the Ground

New York’s Lost Sky­scraper: The Rise and Fall of the Singer Tow­er

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities and the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.

How Charlie Chaplin, Buster Keaton & Harold Lloyd Pulled Off Their Spectacular Stunts During Silent Film’s Golden Age

It can be tempt­ing to view the box office’s dom­i­na­tion by visu­al-effects-laden Hol­ly­wood spec­ta­cle as a recent phe­nom­e­non. And indeed, there have been peri­ods dur­ing which that was­n’t the case: the “New Hol­ly­wood” that began in the late nine­teen six­ties, for instance, when the old stu­dio sys­tem hand­ed the reins to inven­tive young guns like Peter Bog­danovich, Fran­cis Ford Cop­po­la, and Mar­tin Scors­ese. But lest we for­get, that move­ment met its end in the face of com­pe­ti­tion from late-1970s block­busters like Jaws and Star Wars, a new kind of block­buster that sig­naled a return to the sim­ple thrills of silent cin­e­ma.

Even a cen­tu­ry ago, many movie­go­ers expect­ed two expe­ri­ences above all: to be wowed, and to be made to laugh. No won­der that era saw visu­al come­di­ans like Harold Lloyd, Buster Keaton, and Char­lie Chap­lin become not just the most famous actors in the world, but some of the most famous human beings in the world.

Stay­ing on top required not just seri­ous per­for­ma­tive skill, but also equal­ly seri­ous tech­ni­cal inge­nu­ity, as explained in the new Lost in Time video above. It breaks down just how Lloyd, Keaton, and Chap­lin pulled off some of their career-defin­ing stunts on film, putting the actu­al clips along­side CGI recon­struc­tions of the sets as they would have looked dur­ing shoot­ing.

When Lloyd hangs from the arms of a clock high above down­town Los Ange­les in Safe­ty Last! (1923), he’s real­ly hang­ing high above down­town Los Ange­les — albeit on a set con­struct­ed atop a build­ing, shot from a care­ful­ly cho­sen angle. When the entire façade of a house falls around Keaton in Steam­boat Bill, Jr. (1928), leav­ing him stand­ing unharmed in a win­dow frame, the façade actu­al­ly fell around him — in a pre­cise­ly chore­o­graphed man­ner, but with only a cou­ple of inch­es of clear­ance on each side. When a blind­fold­ed Chap­lin skates per­ilous­ly close to a mul­ti­sto­ry drop in Mod­ern Times (1936), he’s per­fect­ly safe, the edge of the floor being noth­ing more than a mat­te paint­ing: one of those ana­log tech­nolo­gies of movie mag­ic whose obso­les­cence is still bemoaned by clas­sic-film enthu­si­asts, from whom CGI, no mat­ter how expen­sive, nev­er quite thrills or amus­es in the same way.

Relat­ed con­tent:

The Art of Cre­at­ing Spe­cial Effects in Silent Movies: Inge­nu­ity Before the Age of CGI

Watch the Only Time Char­lie Chap­lin & Buster Keaton Per­formed Togeth­er On-Screen (1952)

Safe­ty Last!, the 1923 Movie Fea­tur­ing the Most Icon­ic Scene from Silent Film Era, Just Went Into the Pub­lic Domain

30 Buster Keaton Films: “The Great­est of All Com­ic Actors,” “One of the Great­est Film­mak­ers of All Time”

How Char­lie Chap­lin Used Ground­break­ing Visu­al Effects to Shoot the Death-Defy­ing Roller Skate Scene in Mod­ern Times (1936)

Char­lie Chap­lin Does Cocaine and Saves the Day in Mod­ern Times (1936)

Based in Seoul, Col­in Marshall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities and the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les. Fol­low him on the social net­work for­mer­ly known as Twit­ter at @colinmarshall.


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