The World Record for the Shortest Math Article: 2 Words

in Math | May 16th, 2025

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

How a Papal Conclave Works, and Who Might Be the Next Pope

in History, Religion | May 7th, 2025

On Tues­day, the car­di­nals locked them­selves into the Sis­tine Chapel, offi­cial­ly begin­ning the con­clave to elect the 267th pope. First for­mal­ized by Pope Gre­go­ry X in 1274, the con­clave (a word derived from the Latin words cum clave, mean­ing “with a key”) fol­lows a high­ly script­ed process honed over the past 800 years. How the con­clave works, and how it came into being—all of that gets cov­ered in the Reli­gion for Break­fast video above. It’s host­ed by the reli­gious stud­ies schol­ar Dr. Andrew M. Hen­ry.

Below, you can also delve into the more recent his­to­ry of papal elec­tions. Cre­at­ed by Use­ful Charts, this video cov­ers every papal con­clave since 1958 and includes a pre­dic­tion for who the next pope will be once the white smoke ris­es. Who is the next like­ly pon­tiff? No spoil­ers here. You’ll have to watch the video to find out.

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 

Take a 3D Vir­tu­al Tour of the Sis­tine Chapel & Explore Michelangelo’s Mas­ter­pieces Up Close

When There Were Three Popes at Once: An Ani­mat­ed Video Drawn in the Style of Medieval Illu­mi­nat­ed Man­u­script

Pope Fran­cis Set to Release a Rock/Pop Album: Lis­ten to the First Sin­gle

Pope John Paul II Takes Bat­ting Prac­tice in Cal­i­for­nia, 1987

See Vermeer’s Girl with a Pearl Earring in 3D in a New 108-Gigapixel Scan

in Art, History | May 5th, 2025

You may believe that you’ve had a close enough view of Johannes Ver­meer’s Girl with a Pearl Ear­ring. You may have gone to The Hague and seen the paint­ing in per­son at the Mau­rit­shuis. You may have zoomed into the ten bil­lion-pix­el scan we fea­tured here on Open Cul­ture in 2021. But if you haven’t spent time with the new 108 bil­lion-pix­el scan, can you real­ly claim to have seen Girl with a Pearl Ear­ring at all?

At that 108-gigapix­el res­o­lu­tion, notes Jason Kot­tke, “each pix­el is 1.3 microns in size — 1000 microns is 1 mil­lime­ter.” You can learn more about the tech­nol­o­gy behind the project in this mak­ing-of video pro­duced by Hirox Europe, the local branch of the Japan­ese dig­i­tal micro­scope com­pa­ny respon­si­ble for both the ten bil­lion-pix­el scan and this 108 bil­lion-pix­el one, which neces­si­tat­ed 88 hours of non-stop scan­ning this rel­a­tive­ly small can­vas of 15 inch­es by 17.5 inch­es, a process that result­ed in 41,000 3D images.

Yes, 3D images: though Girl with a Pearl Ear­ring, known as “the Mona Lisa of the North,” may be known far and wide in flat rep­re­sen­ta­tions on pages, screens, posters, and T‑shirts, it is, after all, a work of oil on can­vas.

Ver­meer achieved his ultra-real­is­tic effects not just by putting the right col­ors in the right places, but apply­ing them at the right thick­ness­es and with the right tex­tures — all of which have been repli­cat­ed in a “mega-sized” phys­i­cal 3D print, 100 times larg­er than the orig­i­nal work, com­mis­sioned by the Mau­rit­shuis for its Who’s that Girl? exhi­bi­tion.

You can per­form your own topo­graph­i­cal exam­i­na­tion of sec­tions of the paint­ing — the eyes, the lips, a fold of the tur­ban, the ear­ring, and even the reflec­tion on the ear­ring — by click­ing the “3D” but­ton at the bot­tom of the scan’s view­ing inter­face.  A look this close reveals much about how Ver­meer cre­at­ed this world-famous image, as well as how it’s weath­ered the past 360 years. It does not reveal, of course, the answers to such long-stand­ing mys­ter­ies as the iden­ti­ty of the sub­ject or the moti­va­tions behind her strik­ing pre­sen­ta­tion. Whether or not the girl with the pearl ear­ring even exist­ed, we can, at this point, be sure of one thing: she must feel seen. Enter the new 108 bil­lion-pix­el scan here.

via Kot­tke

Relat­ed con­tent:

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.

Stream Online Monty Python and the Holy Grail Free on Its 50th Anniversary

in Comedy, Film | May 1st, 2025

This year, YouTube cel­e­brat­ed its twen­ti­eth anniver­sary, prompt­ing younger users to won­der what life could have been like before it. The fifti­eth anniver­sary of Mon­ty Python and the Holy Grail, which pre­miered in April of 1975, has inspired sim­i­lar reflec­tion among com­e­dy enthu­si­asts. It can be dif­fi­cult, at this point, to imag­ine one­self back in a cul­ture not yet dis­rupt­ed by Mon­ty Python’s rig­or­ous­ly absurd log­ic, scat­ter­shot satire, and delib­er­ate break­ing of nar­ra­tive and social con­ven­tion — a cul­ture, indeed, where that sort of thing could be feared too dan­ger­ous for tele­vi­sion and film.

It was their BBC sketch series Mon­ty Python’s Fly­ing Cir­cus that intro­duced this comedic sen­si­bil­i­ty first to Britain, and then to the world. Between that show’s third and fourth sea­sons, the Pythons — Gra­ham Chap­man, John Cleese, Eric Idle, Ter­ry Jones, Michael Palin, and Ter­ry Gilliam — took on the side project of cre­at­ing their own cin­e­mat­ic re-inter­pre­ta­tion of Arthuri­an leg­end.

With a mod­est bud­get fur­nished by Led Zep­pelin, Pink Floyd, Jethro Tul­l’s Ian Ander­son, and oth­er investors con­nect­ed to the music world, they plunged them­selves into a grimy, unglam­orous vision of the Mid­dle Ages, punc­tu­at­ed by inex­plic­a­ble anachro­nism and sat­u­rat­ed with an icon­o­clas­tic dis­re­gard for received wis­dom and trumped-up glo­ry.

There the Pythons told a sto­ry that, while per­haps lack­ing in nar­ra­tive struc­ture — to say noth­ing of his­tor­i­cal real­ism — more than com­pen­sates in sheer com­ic momen­tum. By all accounts, it holds up half a cen­tu­ry on, even for those view­ers who’ve already seen it so many times as to have invol­un­tar­i­ly com­mit­ted every joke to mem­o­ry. In cel­e­bra­tion of its anniver­sary, the film has become avail­able to stream free (albeit not in all regions of the world) on the offi­cial YouTube Movies & TV chan­nel, where the lat­est gen­er­a­tions of Mon­ty Python fans first dis­cov­ered their work. Even if lines like “I fart in your gen­er­al direc­tion” no longer raise any trans­gres­sive fris­son, there’s still lit­tle on that plat­for­m’s uni­verse of con­tent to match Mon­ty Python and the Holy Grail’s mul­ti­lay­ered silli­ness, whose place in the annals of com­e­dy leg­end has long since been assured.

Relat­ed con­tent:

Ter­ry Gilliam’s Lost Ani­ma­tions from Mon­ty Python and the Holy Grail Are Now Online

Mon­ty Python’s Eric Idle Breaks Down His Most Icon­ic Char­ac­ters

Mon­ty Python and the Holy Grail Cen­sor­ship Let­ter: We Want to Retain “Fart in Your Gen­er­al Direc­tion”

Mon­ty Python and the Holy Grail Re-Imag­ined as an Epic, Main­stream Hol­ly­wood Film

Mon­ty Python’s Best Phi­los­o­phy Sketch­es

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 1924 Soviet Chess Match Where The Chess Pieces Were Real Soldiers and Horses

in Games | April 23rd, 2025

Let’s time trav­el back to Leningrad (aka St. Peters­burg) in 1924. That’s when an uncon­ven­tion­al chess match was played by Peter Romanovsky and Ilya Rabi­novich, two chess mas­ters of the day.

Appar­ent­ly, they called in their moves over the tele­phone. And then real-life chess pieces—in the form of human beings and horses—were moved across a huge chess­board cov­er­ing Palace Square. Mem­bers of the Sovi­et Union’s Red Army served as the black pieces; mem­bers of the Sovi­et navy were the white pieces. 8,000 onlook­ers watched the action unfold.

Accord­ing to this online forum for chess enthu­si­asts, the 5‑hour match “was an annu­al event, designed to pro­mote chess in the USSR.” The first such match was held in Smolen­sk in 1921, fol­lowed by match­es in Kerch in 1922, Omsk in 1923 and then St. Peters­burg in 1924. You can catch a glimpse of the match in the footage below.

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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:

Man Ray Designs a Supreme­ly Ele­gant, Geo­met­ric Chess Set in 1920 (and It’s Now Re-Issued for the Rest of Us)

A Free 700-Page Chess Man­u­al Explains 1,000 Chess Tac­tics in Straight­for­ward Eng­lish

A Famous Chess Match from 1910 Reen­act­ed with Clay­ma­tion

A Brief His­to­ry of Chess: An Ani­mat­ed Intro­duc­tion to the 1,500-Year-Old Game

James Joyce, With His Eyesight Failing, Draws a Sketch of Leopold Bloom (1926)

in Art, Literature | April 21st, 2025

James Joyce had a ter­ri­ble time with his eyes. When he was six years old he received his first set of eye­glass­es, and, when he was 25, he came down with his first case of iri­tis, a very painful and poten­tial­ly blind­ing inflam­ma­tion of the col­ored part of the eye, the iris. A short time lat­er, he named his new­born daugh­ter “Lucia,” after the patron saint of those with eye trou­bles.

For the rest of his life, Joyce had to endure a hor­rif­ic series of oper­a­tions and treat­ments for one or the oth­er of his eyes, includ­ing the removal of parts of the iris, a reshap­ing of the pupil, the appli­ca­tion of leech­es direct­ly on the eye to remove fluid–even the removal of all of Joyce’s teeth, on the the­o­ry that his recur­ring iri­tis was con­nect­ed with the bac­te­r­i­al infec­tion in his teeth, brought on by years of pover­ty and den­tal neglect.

After his sev­enth eye oper­a­tion on Decem­ber 5, 1925, accord­ing to Gor­don Bowk­er in James Joyce: A New Biog­ra­phy, Joyce was “unable to see lights, suf­fer­ing con­tin­u­al pain from the oper­a­tion, weep­ing oceans of tears, high­ly ner­vous, and unable to think straight. He was now depen­dent on kind peo­ple to see him across the road and hail taxis for him. All day, he lay on a couch in a state of com­plete depres­sion, want­i­ng to work but quite unable to do so.”

In ear­ly 1926, Joyce’s sight was improv­ing a lit­tle in one eye. It was about this time (Jan­u­ary 1926, accord­ing to one source) that Joyce paid a vis­it to his friend Myron C. Nut­ting, an Amer­i­can painter who had a stu­dio in the Mont­par­nasse sec­tion of Paris. To demon­strate his improv­ing vision, Joyce picked up a thick black pen­cil and made a few squig­gles on a sheet of paper, along with a car­i­ca­ture of a mis­chie­vous man in a bowler hat and a wide mus­tache–Leopold Bloom, the pro­tag­o­nist of Ulysses. Next to Bloom, Joyce wrote in Greek (“with a minor error in spelling and char­ac­ter­is­ti­cal­ly skewed accents,” accord­ing to R. J. Schork in Greek and Hel­lenic Cul­ture in Joyce) the open­ing pas­sage  of Home­r’s Odyssey: “Tell me, muse, of that man of many turns, who wan­dered far and wide.”

NOTE: Joyce’s draw­ing of Bloom is now in the Charles Deer­ing McCormick Library of Spe­cial Col­lec­tions at North­west­ern Uni­ver­si­ty. Nut­ting was a sig­nif­i­cant source for the biog­ra­phy of Joyce that was writ­ten by Richard Ell­mann, a pro­fes­sor at North­west­ern. Accord­ing to Scott Krafft, a cura­tor at the library, Ell­mann bro­kered a deal in 1960 for the library to pur­chase Nut­ting’s oil paint­ings of James and Nora Joyce, his pas­tel draw­ings of the Joyce chil­dren Gior­gio and Lucia, along with Joyce’s sketch of Bloom, for a total of $500. The source for the Jan­u­ary 1926 date of the Bloom sketch is an arti­cle, “James Joyce…a quick sketch” from the July 1976 edi­tion of Foot­notes, pub­lished by the North­west­ern Uni­ver­si­ty Library Coun­cil. Our thanks to Scott Krafft.

Note: An ear­li­er ver­sion of this post appeared on our site in 2013.

Relat­ed Con­tent:

James Joyce: An Ani­mat­ed Intro­duc­tion to His Life and Lit­er­ary Works

What Makes James Joyce’s Ulysses a Mas­ter­piece: Great Books Explained

James Joyce’s Cray­on Cov­ered Man­u­script Pages for Ulysses and Finnegans Wake

Read the Orig­i­nal Seri­al­ized Edi­tion of James Joyce’s Ulysses (1918)

The Ark Before Noah: Discover the Ancient Flood Myths That Came Before the Bible

in History, Religion | April 15th, 2025

The Lord said to Noah, there’s going to be a floody, floody; then to get those chil­dren out of the mud­dy, mud­dy; then to build him an arky, arky. This much we heard while toast­ing marsh­mal­lows around the camp­fire, at least if we grew up in a cer­tain mod­ern Protes­tant tra­di­tion. As adults, we may or may not believe that there ever lived a man called Noah who built an ark to save all the world’s inno­cent ani­mal species from a sin-cleans­ing flood. But unless we’ve tak­en a deep dive into ancient his­to­ry, we prob­a­bly don’t know that this espe­cial­ly famous Bible sto­ry was­n’t the first of its par­tic­u­lar sub­genre. As explained in the Hochela­ga video above, there are even old­er glob­al-del­uge tales to be reck­oned with.

In fact, one such myth appears in the old­est known work of lit­er­a­ture in human his­to­ry, the Epic of Gil­gamesh. “In it, the god Ea learns of this divine flood, and secret­ly warns the humans about this com­ing dis­as­ter,” says Hochela­ga cre­ator Tom­mie Trelawny. Thus informed, the king Utnapish­tim builds a giant cor­a­cle, a kind of cir­cu­lar boat “used to nav­i­gate the rivers of Mesopotamia for cen­turies.”

Like Noah, Utnapish­tim brings his fam­i­ly and a host of ani­mals aboard, and after rid­ing out the worst of the storm, finds that his craft has come to rest on a moun­tain­top. Also like Noah, he then sends birds out to find dry land. But ulti­mate­ly, “the sto­ry takes a strange turn: instead of being pleased, the gods are angry,” though Ea does step in to take respon­si­bil­i­ty and make sure that Utnapish­tim is reward­ed.

There are oth­er ver­sions with oth­er gods, floods, and ark-builders as well. In the Reli­gion for Break­fast video just above, reli­gious stud­ies schol­ar Andrew Mark Hen­ry com­pares the Bib­li­cal sto­ry of Noah and the Utnapish­tim episode of the Epic of Gil­gamesh with the “Sumer­ian flood sto­ry” from the sec­ond mil­len­ni­um BC and the two-cen­turies-old­er “Atra­ha­sis epic.” All of these ver­sions have a good deal in com­mon, not least the exec­u­tive deci­sion by an exas­per­at­ed high­er being (or beings) to wipe out almost entire­ly the human­i­ty they them­selves cre­at­ed. Iron­i­cal­ly, we mod­erns are like­ly to have first encoun­tered this tale of god­ly wrath and sub­se­quent mass destruc­tion in light­heart­ed, even cheer­ful pre­sen­ta­tions. Whether ancient Sume­ri­ans also sang about it in youth groups, no clay tablet has yet revealed.

Relat­ed con­tent:

Dis­cov­er Thomas Jefferson’s Cut-and-Paste Ver­sion of the Bible, and Read the Curi­ous Edi­tion Online

Lit­er­ary Crit­ic Northrop Frye Teach­es “The Bible and Eng­lish Lit­er­a­ture”: All 25 Lec­tures Free Online

A Map of All the Coun­tries Men­tioned in the Bible: What The Coun­tries Were Called Then, and Now

Isaac Asimov’s Guide to the Bible: A Wit­ty, Eru­dite Atheist’s Guide to the World’s Most Famous Book

Did the Tow­er of Babel Actu­al­ly Exist?: A Look at the Archae­o­log­i­cal Evi­dence

The Epic of Gil­gamesh, the Old­est-Known Work of Lit­er­a­ture in World His­to­ry

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.

What Was Smoot-Hawley, and Why Are We Doing It Again? Anyone? Anyone?

in Economics, History | April 14th, 2025

When most Amer­i­cans think of the Smoot-Haw­ley Tar­iffs, they think of eco­nom­ic dis­as­ter. But if you ask why, most Amer­i­cans may need a short refresh­er course. Below, you will find just that. Appear­ing on Derek Thomp­son’s Plain His­to­ry pod­cast, Dou­glas Irwin (an econ­o­mist and his­to­ri­an at Dart­mouth) revis­its the 1930 Smoot-Haw­ley Tar­iff Act, which raised tar­iffs on over 20,000 prod­ucts import­ed into the Unit­ed States. The law was passed despite warn­ings from exec­u­tives like Hen­ry Ford (who called the tar­iff act “an eco­nom­ic stu­pid­i­ty”) and a peti­tion signed by 1,028 Amer­i­can econ­o­mists, who argued that the tar­iffs would raise prices and spark a trade war, leav­ing the Unit­ed States iso­lat­ed. Their con­cerns were ulti­mate­ly well-found­ed. The Smoot-Haw­ley Tar­iffs, sup­port­ed by a Repub­li­can pres­i­dent and Con­gress, had the unin­tend­ed con­se­quence of deep­en­ing, not end­ing, the Great Depres­sion.

Mark Twain alleged­ly said that “His­to­ry doesn’t repeat itself, but it often rhymes.” But some­times his­to­ry may well repeat itself or come very close, and that’s where we seem to be head­ed right now. As in 1930, we have Repub­li­cans imple­ment­ing new tar­iffs, but this time with the hope of re-engi­neer­ing the world econ­o­my and bring­ing man­u­fac­tur­ing back to Amer­i­ca. Mean­while, econ­o­mists (even con­ser­v­a­tive ones) warn that these poli­cies risk repeat­ing the mis­takes of Smoot-Haw­ley.

Below you can hear the assess­ment of the eco­nom­ic his­to­ri­an Niall Fer­gu­son, who, in speak­ing with Bari Weiss, explains why Don­ald Trump’s tar­iffs will fail to re-indus­tri­al­ize Amer­i­ca. The gold­en age of man­u­fac­tur­ing in Amer­i­ca is long gone, and it’s not com­ing back, part­ly thanks to automa­tion. (Mor­gan Housel has more to say on that.) But even worse, the chaot­ic imple­men­ta­tion of these poli­cies risks trig­ger­ing a trade war, “a major finan­cial cri­sis com­pa­ra­ble in scale to 2008,” or even a mil­i­tary cri­sis that an iso­lat­ed Amer­i­ca would be ill-equipped to han­dle. Speak­ing on Meet the Press this week­end, investor Ray Dalio omi­nous­ly voiced very sim­i­lar con­cerns, say­ing “some­thing worse than reces­sion” may be on the hori­zon.

For anoth­er take, you can hear Preet Bharara’s con­ver­sa­tion with Justin Wolfers, where the Aus­tralian econ­o­mist warns that Trump’s tar­iffs may have few ben­e­fits and most­ly costs, some quite pro­found. By launch­ing a trade war, Amer­i­ca will trade less and find its glob­al influ­ence dimin­ished, leav­ing a void that Chi­na can fill. Echo­ing Niall Fer­gu­son, Wolfers also cau­tions that you can’t turn back the eco­nom­ic clock. He notes:

A hun­dred years ago, we had actu­al­ly the same debate, but it was because we were mov­ing from the land, from a pre­dom­i­nant­ly agri­cul­tur­al econ­o­my, to a man­u­fac­tur­ing-based econ­o­my. And we moved from an enor­mous share of the pop­u­la­tion work­ing in agri­cul­ture to work­ing in man­u­fac­tur­ing, and that raised the Amer­i­can mid­dle class.

There was a lot of nos­tal­gia. Why aren’t we back on the land? And the sub­se­quent stage of eco­nom­ic devel­op­ment is we move out of the fac­to­ries, and we move and become engi­neers and com­put­er sci­en­tists and soft­ware design­ers. And we’re in a much more cog­ni­tive econ­o­my.

And we are not inhal­ing black soot in our mines or in our fac­to­ries dur­ing the day. And that’s the future of the Amer­i­can econ­o­my. And it’s one that speaks well to the skills that Amer­i­cans have.

We’re the most edu­cat­ed work­force in the world. And so pre­sum­ably the jobs of the future are those, the jobs we want are those that cater to the extreme pro­duc­tiv­i­ty and edu­ca­tion of Amer­i­can work­ers.

How have we reached the point where we’re run­ning the same failed exper­i­ments again, all to reclaim an illu­so­ry bygone eco­nom­ic age? It’s a hard ques­tion to con­tem­plate, but I ask that ques­tion again. Any­one? Any­one? Any­one?

Relat­ed Con­tent 

The Steps a Pres­i­dent Would Take to Destroy His Nation, Accord­ing to Elon Musk’s AI Chat­bot, Grok

Free Online Eco­nom­ics & Finance Cours­es

Strik­ing Poster Col­lec­tion from the Great Depres­sion Shows That the US Gov­ern­ment Once Sup­port­ed the Arts in Amer­i­ca

Actor John Lithgow Reads 20 Lessons on Tyranny, Penned by Historian Timothy Snyder

in Current Affairs | April 10th, 2025

In 2017, his­to­ri­an Tim­o­thy Sny­der wrote the con­cise book On Tyran­ny: Twen­ty Lessons from the Twen­ti­eth Cen­tu­ry, which went on to become a New York Times best­seller. A his­to­ri­an of fas­cism (then at Yale, now at U. Toron­to), Sny­der want­ed to offer Amer­i­cans a use­ful guide for resist­ing the coun­try’s drift towards author­i­tar­i­an­ism. It was handy then and even hand­i­er now–especially as the feds bear down on dif­fer­ent insti­tu­tions under­gird­ing Amer­i­can civ­il soci­ety. Law firms, uni­ver­si­ties, cor­po­ra­tions, media outlets–they’re all get­ting squeezed, and many have already vio­lat­ed the first of Sny­der’s 20 lessons: “Do not obey in advance.” Above, you can hear actor John Lith­gow read a con­densed ver­sion of Sny­der’s lessons. You can order a copy of his book online, or explore here a relat­ed video series that Sny­der pro­duced a few years back. Find a cheat sheet below.

1. Do not obey in advance
2. Defend insti­tu­tions
3. Beware the one-par­ty state
4. Take respon­si­bil­i­ty for the face of the world
5. Remem­ber pro­fes­sion­al ethics
6. Be wary of para­mil­i­taries
7. Be reflec­tive if you must be armed
8. Stand out
9. Be kind to our lan­guage
10. Believe in truth
11. Inves­ti­gate
12. Make eye con­tact and small talk
13. Prac­tice cor­po­re­al pol­i­tics
14. Estab­lish a pri­vate life
15. Con­tribute to good caus­es
16. Learn from peers in oth­er coun­tries
17. Lis­ten for dan­ger­ous words
18. Be calm when the unthink­able arrives
19. Be a patri­ot
20. Be as coura­geous as you can

Relat­ed Con­tent 

20 Lessons from the 20th Cen­tu­ry About How to Defend Democ­ra­cy from Author­i­tar­i­an­ism, Accord­ing to Yale His­to­ri­an Tim­o­thy Sny­der

His­to­ri­an Tim­o­thy Sny­der Presents 20 Lessons for Defend­ing Democ­ra­cy Against Tyran­ny in a New Video Series

Umber­to Eco’s List of the 14 Com­mon Fea­tures of Fas­cism

Yale Pro­fes­sor Jason Stan­ley Iden­ti­fies 10 Tac­tics of Fas­cism: The “Cult of the Leader,” Law & Order, Vic­tim­hood and More

Toni Mor­ri­son Lists the 10 Steps That Lead Coun­tries to Fas­cism (1995)

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

in Math | April 8th, 2025

Back in Decem­ber, you hope­ful­ly thor­ough­ly immersed your­self in The Map of Physics, an ani­mat­ed video–a visu­al aid for the mod­ern age–that mapped out the field of physics, explain­ing all the con­nec­tions between clas­si­cal physics, quan­tum physics, and rel­a­tiv­i­ty.

You can’t do physics with­out math. Hence we now have The Map of Math­e­mat­ics. Cre­at­ed by physi­cist Dominic Wal­li­man, this video explains “how pure math­e­mat­ics and applied math­e­mat­ics relate to each oth­er and all of the sub-top­ics they are made from.” Watch the new video above. You can buy a poster of the map here. And you can down­load a ver­sion for edu­ca­tion­al use here.

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Relat­ed Con­tent 

Com­plex Math Made Sim­ple With Engag­ing Ani­ma­tions: Fouri­er Trans­form, Cal­cu­lus, Lin­ear Alge­bra, Neur­al Net­works & More

John Coltrane Draws a Pic­ture Illus­trat­ing the Math­e­mat­ics of Music

The Ele­gant Math­e­mat­ics of Vit­ru­vian Man, Leonar­do da Vinci’s Most Famous Draw­ing: An Ani­mat­ed Intro­duc­tion

The Math Behind Beethoven’s Music

Free Online Math Cours­es