Watch Werner Herzog’s Very First Film, Herakles, Made When He Was Only 19-Years-Old (1962)

Rebel­lious dwarfs, crazed con­quis­ta­dors, delu­sion­al tycoons, wood-carv­ing ski jumpers: Wern­er Her­zog schol­ars who attempt to find a pat­tern in the film­mak­er’s choic­es of sub­ject mat­ter are vir­tu­al­ly guar­an­teed an inter­est­ing search, if an ulti­mate­ly futile one. But they must all start in the same place: Her­zog’s very first film Her­ak­les, which mash­es up the spec­ta­cles of body build­ing, auto rac­ing, and destruc­tion. It does all that in nine min­utes to a sound­track of sax­o­phone jazz, and with fre­quent ref­er­ences to the tit­u­lar hero of myth, whom you may know bet­ter by his Roman name of Her­cules.

“Would he clean the Augean sta­bles?” ask Her­ak­les’ sub­ti­tles over footage of one young Ger­man man show­ing off his well-shaped tor­so. “Would he dis­pose of the Ler­naean Hydra?” they ask of anoth­er as he strikes a pose.

Between clips of these body­builders per­form­ing their labors and ques­tions about whether they could per­form those of Her­cules, we see mil­i­taris­tic march­es, falling bombs, heaps of rub­ble, and a 1955 race­car crash at Le Mans that killed 83 peo­ple. All this jux­ta­po­si­tion tempts us to ask what mes­sage the nine­teen-year-old Her­zog want­ed to deliv­er, but, as in all his sub­se­quent work, he sure­ly want­ed less to make an artic­u­la­ble point than to explore the pos­si­bil­i­ties of cin­e­ma itself.

More recent­ly, in Paul Cron­in’s inter­view book Her­zog on Her­zog, the film­mak­er looks back on “my first blun­der, Her­ak­les” and finds it “rather stu­pid and point­less, though at the time it was an impor­tant test for me. It taught me about edit­ing togeth­er very diverse mate­r­i­al that would not nor­mal­ly sit com­fort­ably as a whole,” and in a sense pre­pared him for an entire cin­e­mat­ic career of very diverse mate­r­i­al that would not nor­mal­ly sit com­fort­ably as a whole. “For me it was fas­ci­nat­ing to edit mate­r­i­al togeth­er that had such sep­a­rate and indi­vid­ual lives. The film was some kind of an appren­tice­ship for me. I just felt it would be bet­ter to make a film than go to film school” — of the non-rogue vari­ety, any­way.

Relat­ed Con­tent:

Wern­er Her­zog Teach­es His First Online Course on Film­mak­ing

Wern­er Herzog’s Rogue Film School: Apply & Learn the Art of Gueril­la Film­mak­ing & Lock-Pick­ing

Por­trait Wern­er Her­zog: The Director’s Auto­bi­o­graph­i­cal Short Film from 1986

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities and cul­ture. He’s at work on the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les, the video series The City in Cin­e­ma, the crowd­fund­ed jour­nal­ism project Where Is the City of the Future?, and the Los Ange­les Review of Books’ Korea Blog. Fol­low him on Twit­ter at @colinmarshall or on Face­book.

The Map of Computer Science: New Animation Presents a Survey of Computer Science, from Alan Turing to “Augmented Reality”

I’ve nev­er want­ed to start a sen­tence with “I’m old enough to remem­ber…” because, well, who does? But here we are. I remem­ber the enor­mous­ly suc­cess­ful Apple IIe and Com­modore 64, and a world before Microsoft. Smart phones were sci­ence fic­tion. To do much more than word process or play games one had to learn a pro­gram­ming lan­guage. These ancient days seemed at the time—and in hind­sight as well—to be the very dawn of com­put­ing. Before the per­son­al com­put­er, such devices were the size of kitchen appli­ances and were hid­den away in mil­i­tary instal­la­tions, uni­ver­si­ties, and NASA labs.

But of course we all know that the his­to­ry of com­put­ing goes far beyond the ear­ly 80s: at least back to World War II, and per­haps even much far­ther. Do we begin with the aba­cus, the 2,200-Year-Old Antikythera Mech­a­nism, the astro­labe, Ada Lovelace and Charles Bab­bage? The ques­tion is maybe one of def­i­n­i­tions. In the short, ani­mat­ed video above, physi­cist, sci­ence writer, and YouTube edu­ca­tor Dominic Wal­li­man defines the com­put­er accord­ing to its basic bina­ry func­tion of “just flip­ping zeros and ones,” and he begins his con­densed his­to­ry of com­put­er sci­ence with trag­ic genius Alan Tur­ing of Tur­ing Test and Bletch­ley Park code­break­ing fame.

Turing’s most sig­nif­i­cant con­tri­bu­tion to com­put­ing came from his 1936 con­cept of the “Tur­ing Machine,” a the­o­ret­i­cal mech­a­nism that could, writes the Cam­bridge Com­put­er Lab­o­ra­to­ry “sim­u­late ANY com­put­er algo­rithm, no mat­ter how com­pli­cat­ed it is!” All oth­er designs, says Walliman—apart from a quan­tum computer—are equiv­a­lent to the Tur­ing Machine, “which makes it the foun­da­tion of com­put­er sci­ence.” But since Turing’s time, the sim­ple design has come to seem end­less­ly capa­ble of adap­ta­tion and inno­va­tion.

Wal­li­man illus­trates the com­put­er’s expo­nen­tial growth by point­ing out that a smart phone has more com­put­ing pow­er than the entire world pos­sessed in 1963, and that the com­put­ing capa­bil­i­ty that first land­ed astro­nauts on the moon is equal to “a cou­ple of Nin­ten­dos” (first gen­er­a­tion clas­sic con­soles, judg­ing by the image). But despite the hubris of the com­put­er age, Wal­li­man points out that “there are some prob­lems which, due to their very nature, can nev­er be solved by a com­put­er” either because of the degree of uncer­tain­ty involved or the degree of inher­ent com­plex­i­ty. This fas­ci­nat­ing, yet abstract dis­cus­sion is where Walliman’s “Map of Com­put­er Sci­ence” begins, and for most of us this will prob­a­bly be unfa­mil­iar ter­ri­to­ry.

We’ll feel more at home once the map moves from the region of Com­put­er The­o­ry to that of Com­put­er Engi­neer­ing, but while Wal­li­man cov­ers famil­iar ground here, he does not dumb it down. Once we get to appli­ca­tions, we’re in the realm of big data, nat­ur­al lan­guage pro­cess­ing, the inter­net of things, and “aug­ment­ed real­i­ty.” From here on out, com­put­er tech­nol­o­gy will only get faster, and weird­er, despite the fact that the “under­ly­ing hard­ware is hit­ting some hard lim­its.” Cer­tain­ly this very quick course in Com­put­er Sci­ence only makes for an intro­duc­to­ry sur­vey of the dis­ci­pline, but like Wallman’s oth­er maps—of math­e­mat­ics, physics, and chem­istry—this one pro­vides us with an impres­sive visu­al overview of the field that is both broad and spe­cif­ic, and that we like­ly wouldn’t encounter any­where else.

As with his oth­er maps, Wal­li­man has made this the Map of Com­put­er Sci­ence avail­able as a poster, per­fect for dorm rooms, liv­ing rooms, or wher­ev­er else you might need a reminder.

Relat­ed Con­tent:

Free Online Com­put­er Sci­ence Cours­es

How Ada Lovelace, Daugh­ter of Lord Byron, Wrote the First Com­put­er Pro­gram in 1842–a Cen­tu­ry Before the First Com­put­er

Watch Break­ing the Code, About the Life & Times of Alan Tur­ing (1996)

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

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

The Map of Chem­istry: New Ani­ma­tion Sum­ma­rizes the Entire Field of Chem­istry in 12 Min­utes

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

The Top 100 American Films of All Time, According to 62 International Film Critics

Enter­tain­ment first, and art sec­ond? Has­n’t that always been the Amer­i­can way when it comes to film? And is that how the rest of the world sees it, espe­cial­ly con­sid­er­ing France’s love of Jer­ry Lewis, Germany’s obses­sion with David Has­sel­hoff, and Chi­na tak­ing Nicholas Cage’s career choic­es more seri­ous­ly than he does him­self?

In this list of The 100 Great­est Amer­i­can Films, the BBC polled 62 inter­na­tion­al film crit­ics to see what they thought were the Unit­ed States’ endur­ing con­tri­bu­tions to cin­e­ma cul­ture. The films only need­ed to be fund­ed by Amer­i­can companies—the direc­tors could be from oth­er coun­tries. (If not, about a third of these choic­es would be dis­qual­i­fied. Five are by Hitch­cock alone.)

As for oth­er favorite direc­tors, Spiel­berg gets five (although the high­est entry, Jaws, comes in at 38) and Bil­ly Wilder gets five, with The Apart­ment the high­est ranked at 24. The most pop­u­lar decade for film is the 1970s, the top two being Coppola’s first two God­fa­ther films. (It would be inter­est­ing to know the medi­an age of these 62 crit­ics, just to see if their for­ma­tive years align with the decade.)

Of the 100, here’s the Top 10:

10. The God­fa­ther Part II (Fran­cis Ford Cop­po­la, 1974)
9. Casablan­ca (Michael Cur­tiz, 1942)
8. Psy­cho (Alfred Hitch­cock, 1960)
7. Sin­gin’ in the Rain (Stan­ley Donen and Gene Kel­ly, 1952)
6. Sun­rise (F.W. Mur­nau, 1927)
5. The Searchers (John Ford, 1956)
4. 2001: A Space Odyssey (Stan­ley Kubrick, 1968)
3. Ver­ti­go (Alfred Hitch­cock, 1958)
2. The God­fa­ther (Fran­cis Ford Cop­po­la, 1972)
1. Cit­i­zen Kane (Orson Welles, 1941)

Com­par­ing this list to BFI’s 2012 list of the Top 100 films of all time, there isn’t much dif­fer­ence in the top spots. And, in the years to come, I sus­pect those top four films will switch places occa­sion­al­ly but nev­er real­ly leave.

Instead, the sur­pris­es come fur­ther down the list. Gone with the Wind used to be con­sid­ered a clas­sic, no doubt bol­stered by its box office suc­cess at the time. But its pol­i­tics have weak­ened its posi­tion, and, along with Birth of a Nation, it might not last anoth­er decade on such lists. On the flip side, black film­mak­ers have four films on the list and women direc­tors only one (Mesh­es of the After­noon one of the best exper­i­men­tal films of all time).

Oth­er inter­est­ing choic­es include The Lion King (the only ani­mat­ed film on the list), Sternberg’s The Shang­hai Ges­ture, and Minnelli’s The Band Wag­on (one of two musi­cals by the direc­tor on the list). What films would you like to see added or tak­en away? Is this a fair assess­ment of America’s worth? Let us know in the com­ments.

Above, you can watch a some­what idio­syn­crat­ic pre­sen­ta­tions of the films on the BBC list.

Relat­ed Con­tent:
The 100 Fun­ni­est Films of All Time, Accord­ing to 253 Film Crit­ics from 52 Coun­tries

The 10 Great­est Films of All Time Accord­ing to 358 Film­mak­ers

The 10 Great­est Films of All Time Accord­ing to 846 Film Crit­ics

Ted Mills is a free­lance writer on the arts who cur­rent­ly hosts the FunkZone Pod­cast. You can also fol­low him on Twit­ter at @tedmills, read his oth­er arts writ­ing at tedmills.com and/or watch his films here.

The Addams Family Dance to The Ramones’ “Blitzkrieg Bop”

In the spir­it of Andrew Sul­li­van’s Men­tal Health Break, we give you this: The Addams Fam­i­ly Danc­ing to The Ramones’ 1976 track, “Blitzkrieg Bop.” For a brief moment, for­get the hur­ri­canes, the threat of nuclear war, the fires burn­ing in LA, Mon­tana, Wash­ing­ton, DC and the hearts of white suprema­cists. Breathe in. Breathe out. And repeat after me. “Hey Ho.…..Let’s go!”

If you would like to sign up for Open Culture’s free email newslet­ter, please find it here. Or fol­low our posts on Threads, Face­book and BlueSky.

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:

John Astin, From The Addams Fam­i­ly, Recites “The Raven” as Edgar Allan Poe

Talk­ing Heads Per­form The Ramones’ “I Wan­na Be Your Boyfriend” Live in 1977 (and How the Bands Got Their Start Togeth­er)

The Ramones’ First Press Release: We’re Part Musi­cians, Den­tists & Degen­er­ates (1975)

Hear Joey Ramone Sing a Piece by John Cage Adapt­ed from James Joyce’s Finnegans Wake

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Watch Steve Martin Make His First TV Appearance: The Smothers Brothers Comedy Hour (1968)

“What if there were no punch lines?” asks Steve Mar­tin in his auto­bi­og­ra­phy Born Stand­ing Up. “What if there were no indi­ca­tors? What if I cre­at­ed ten­sion and nev­er released it? What if I head­ed for a cli­max, but all I deliv­ered was an anti­cli­max?” These ques­tions moti­vat­ed him to devel­op the dis­tinc­tive style of stand-up com­e­dy — in a sense, an anti-stand-up com­e­dy — that rock­et­ed him to super­star­dom in the 1970s. But before the world knew him as a ban­jo-play­ing fun­ny­man, Mar­tin worked for a cou­ple of his espe­cial­ly notable come­di­an-musi­cian elders: Tom and Dick Smoth­ers, bet­ter known as the Smoth­ers Broth­ers.

“We hap­pened to be walk­ing through the writer area of the show, and there he was, sit­ting at one of our writ­ers’ desks,” Tom says of Mar­tin on the 1968 broad­cast of The Smoth­ers Broth­ers Com­e­dy Hour above. “Lat­er we found out that he actu­al­ly was one of our writ­ers. Since he has­n’t been paid for his work, we thought we’d let him come out tonight and make a few dol­lars.”

So intro­duced, the 22-year-old Mar­tin begins his tele­vi­sion debut by re-intro­duc­ing him­self: “As Tom just said, I’m Steve Mar­tin, and I’ll be out here in a minute. While I’m wait­ing for me, I’d like to jump into kind of a socko-bof­fo com­e­dy rou­tine.” With his prop table ready, he then launch­es into “the fab­u­lous glove-into-dove trick.”

Though the stu­dio audi­ence may look pret­ty square by today’s stan­dards (or even those of the late 1960s), The Smoth­ers Broth­ers Com­e­dy Hour had already built a rep­u­ta­tion for push­ing the enve­lope of main­stream tele­vi­sion com­e­dy. Still, it’s safe to say that its audi­ence had nev­er seen any per­former – and cer­tain­ly not any prop com­ic — quite like Mar­tin before. In this short set, he per­forms a num­ber of delib­er­ate­ly botched or oth­er­wise askew mag­ic tricks, using his tone to gen­er­ate the humor. “If I kept deny­ing them the for­mal­i­ty of a punch line,” as he writes more than 40 years lat­er in Born Stand­ing Up, “the audi­ence would even­tu­al­ly pick their own place to laugh, essen­tial­ly out of des­per­a­tion. This type of laugh seemed stronger to me, as they would be laugh­ing at some­thing they chose, rather than being told exact­ly when to laugh.”

Watch­ing today, Mar­t­in’s fans will rec­og­nize his trade­mark sen­si­bil­i­ty more quick­ly than his appear­ance, since the clip pre­dates both the white suit and the white hair. Even then, he want­ed to per­form in a way that, in the words of The Guardian’s Rafael Behr, “would unnerve and alien­ate the audi­ence, but also, through self-dep­re­ca­tion, engage them in con­spir­a­cy against him­self.” Mar­tin seems to take a dim view of his own ear­ly tele­vi­sion work, hav­ing described him­self in a 1971 Vir­ginia Gra­ham Show appear­ance as “man­nered, slow and self-aware. I had absolute­ly no author­i­ty,” a qual­i­ty that he has since devel­oped in abun­dance, and of which “the art of hav­ing an act so bad it was good,” as Behr puts it, demands a sur­pris­ing amount.

Relat­ed Con­tent:

Steve Mar­tin Will Teach His First Online Course on Com­e­dy

Steve Mar­tin & Robin Williams Riff on Math, Physics, Ein­stein & Picas­so in a Heady Com­e­dy Rou­tine (2002)

Steve Mar­tin on the Leg­endary Blue­grass Musi­cian Earl Scrug­gs

Steve Mar­tin Writes a Hymn for Hymn-Less Athe­ists

Steve Mar­tin, “Home Crafts Expert,” Explains the Art of Paper Wadding, Endors­es Bob Ker­rey

Steve Mar­tin Releas­es Blue­grass Album/Animated Video

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities and cul­ture. He’s at work on the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les, the video series The City in Cin­e­ma, the crowd­fund­ed jour­nal­ism project Where Is the City of the Future?, and the Los Ange­les Review of Books’ Korea Blog. Fol­low him on Twit­ter at @colinmarshall or on Face­book.

Watch John Lennon’s Last Live Performance (1975): “Imagine,” “Stand By Me” & More


After each heart­break­ing loss of a musi­cal icon this past year and a half, we have turned to their great­est moments onstage, not nec­es­sar­i­ly their last, because their final shows weren’t always all that mem­o­rable. Declin­ing health, bad record­ings… and not every gig is a good one even in the best of times and with the best of per­form­ers. But when it comes to John Lennon’s last pub­lic appear­ance, I like to think he might have left the stage exact­ly the way he want­ed to, as a rock­er, a provo­ca­teur, and a pis­stak­er in a can­dy-apple red jump­suit, backed by a nine-piece mim­ing band of bald men in black leather with masks paint­ed on the back of their heads.


Cred­it­ed as “John Lennon, Etc.,” the band’s true name, giv­en to them by Lennon him­self, is abbre­vi­at­ed on their bass drum: B.O.M.F., or “Broth­ers of Moth­er Fuck­ers.” It was Lennon’s send off to his own career as much as it was a Salute to Sir Lew, as the pro­gram was called. Just a few months lat­er Sean was born, and Lennon declared he would retire to raise his son. At the time of his trag­ic death five years lat­er, he had begun record­ing again, releas­ing Dou­ble Fan­ta­sy and plan­ning a sec­ond dou­ble album, Milk and Hon­ey. But we nev­er got to see him per­form those songs.

The hon­oree for Lennon’s last gig was Sir Lew Grade, “a pow­er­ful media mogul,” notes Dan­ger­ous Minds, “with roots in cabaret and vari­ety shows.” A man known as much for his ruth­less­ness in busi­ness as for his Charleston, which he per­formed on table­tops when­ev­er the mood struck him. In 1969 Grade bought up the rights to over a hun­dred Lennon and McCart­ney songs, after some very tense nego­ti­a­tions. Lennon sued Grade in 1974 and set­tled out of court, and Grade remained the co-pub­lish­er of all of his new songs.


As part of the set­tle­ment, Lennon record­ed his album of cov­ers of clas­sic rock ‘n’ roll songs, appro­pri­ate­ly titled Rock ‘n’ Roll. When he appeared at the trib­ute con­cert for Sir Lew at the Hilton Hotel in New York—on the bill with Julie Andrews, Tom Jones, and Peter Sellers—he played Lit­tle Richard’s “Slip­pin’ and Slidin,” and Ben E. King’s “Stand by Me” for “a “who’s who of the old Hol­ly­wood elite,” includ­ing Lau­ren Bacall, Kirk Dou­glas, Gene Kel­ly, and Orson Welles. The show, record­ed for TV broad­cast, cut his ren­di­tion of “Stand by Me” (hear the audio above), but they did air his final song, “Imag­ine,” which turned out to be the last song he ever sang live onstage (top).


Lennon is in very good form, and seem­ing­ly in good spir­its. The year pre­vi­ous, he’d scored a num­ber one hit with “What­ev­er Gets You Thru the Night.” Accord­ing at least to Paul McCart­ney and Lennon’s girl­friend May Pang, he had even con­sid­ered reunit­ing the Bea­t­les. In Novem­ber of 1974, Lennon joined Elton John onstage at Madi­son Square Gar­den for rol­lick­ing ver­sions of “I Saw Her Stand­ing There,” “Lucy in the Sky with Dia­monds,” and “What­ev­er Gets You Thru the Night” on which Elton had played in the stu­dio. You can see a recre­ation of that per­for­mance above. It was tech­ni­cal­ly Lennon’s last live con­cert appear­ance.

His final appear­ance on stage, on the oth­er hand, while it might have been an odd way to say good­bye, whether he meant to do so or not, may not be what we revis­it when we revis­it Lennon. Why did he agree to do a trib­ute con­cert “for a man he had been embroiled in law­suits with?” With a stage show that many have thought was delib­er­ate­ly designed to antag­o­nize the hon­oree? We’ll nev­er know. But I’m grate­ful that his final live song was one that still speaks to us of hope and pos­si­bil­i­ty. Maybe bow­ing to cen­sors, Lennon changes “Imagine”’s con­tro­ver­sial line about reli­gion. Instead, he sings, “Noth­ing to kill or die for, no immi­gra­tion, too,” refer­ring both to his trou­bles with the U.S. immi­gra­tion author­i­ties and to the bor­der­less world the song projects. “Imag­ine there’s no coun­tries… Imag­ine all the peo­ple shar­ing all the world.”

Relat­ed Con­tent:

The Night John Lennon & Yoko Ono Jammed with Frank Zap­pa at the Fill­more East (1971)

Get a Fly-on-the-Wall View of John Lennon Record­ing & Arrang­ing His Clas­sic Song, “Imag­ine” (1971)

John Lennon’s Solo Albums Now Stream­ing for Free on Spo­ti­fy

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

NASA Lets You Download Free Posters Celebrating the 40th Anniversary of the Voyager Missions

A quick fyi: Last year, NASA released 14 Free Posters That Depict the Future of Space Trav­el in a Cap­ti­vat­ing­ly Retro Style. Now, on the 40th anniver­sary of the Voy­ager mis­sions (Aug. 20 and Sept. 5, 1977), the space agency has issued three attrac­tive new posters to cel­e­brate our “ambas­sadors to the rest of the Milky Way.” All are free to down­load and print here. Writes Space.com: “One of the Voy­ager posters is an image of a star­ry night sky [see above], and anoth­er adver­tis­es the mis­sion using the flam­boy­ant design style of the 1970s, the decade when the probes launched. A third poster hon­ors the probes’ ‘grand tour’ of the plan­ets, on their way to the edge of the solar sys­tem.” Hap­py down­load­ing!

If you would like to sign up for Open Culture’s free email newslet­ter, please find it here. Or fol­low our posts on Threads, Face­book and BlueSky.

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:

How the Icon­ic 1968 “Earth­rise” Pho­to Was Made: An Engross­ing Visu­al­iza­tion by NASA

NASA Archive Col­lects Great Time-Lapse Videos of our Plan­et

Ray Brad­bury Reads Mov­ing Poem on the Eve of NASA’s 1971 Mars Mis­sion

NASA Presents “The Earth as Art” in a Free eBook and Free iPad App

NASA Sends Image of the Mona Lisa to the Moon and Back

Free Inter­ac­tive e‑Books from NASA Reveal His­to­ry, Dis­cov­er­ies of the Hub­ble & Webb Tele­scopes

Leonard Nimoy Nar­rates Short Film About NASA’s Dawn: A Voy­age to the Ori­gins of the Solar Sys­tem

The Best of NASA Space Shut­tle Videos (1981–2010)

 

Trigonometry Discovered on a 3700-Year-Old Ancient Babylonian Tablet

One pre­sump­tion of tele­vi­sion shows like Ancient Aliens and books like Char­i­ots of the Gods is that ancient people—particularly non-west­ern people—couldn’t pos­si­bly have con­struct­ed the elab­o­rate infra­struc­ture and mon­u­men­tal archi­tec­ture and stat­u­ary they did with­out the help of extra-ter­res­tri­als. The idea is intrigu­ing, giv­ing us the huge­ly ambi­tious sci-fi fan­tasies woven into Rid­ley Scott’s revived Alien fran­chise. It is also insult­ing in its lev­el of dis­be­lief about the capa­bil­i­ties of ancient Egyp­tians, Mesopotami­ans, South Amer­i­cans, South Sea Islanders, etc.

We assume the Greeks per­fect­ed geom­e­try, for exam­ple, and refer to the Pythagore­an the­o­rem, although this prin­ci­ple was prob­a­bly well-known to ancient Indi­ans. Since at least the 1940s, math­e­mati­cians have also known that the “Pythagore­an triples”—inte­ger solu­tions to the theorem—appeared 1000 years before Pythago­ras on a Baby­lon­ian tablet called Plimp­ton 322. Dat­ing back to some­time between 1822 and 1762 B.C. and dis­cov­ered in south­ern Iraq in the ear­ly 1900s, the tablet has recent­ly been re-exam­ined by math­e­mati­cians Daniel Mans­field and Nor­man Wild­berg­er of Australia’s Uni­ver­si­ty of New South Wales and found to con­tain even more ancient math­e­mat­i­cal wis­dom, “a trigono­met­ric table, which is 3,000 years ahead of its time.”

In a paper pub­lished in His­to­ria Math­e­mat­i­ca the two con­clude that Plimp­ton 322’s Baby­lon­ian cre­ators detailed a “nov­el kind of trigonom­e­try,” 1000 years before Pythago­ras and Greek astronomer Hip­parchus, who has typ­i­cal­ly received cred­it for trigonometry’s dis­cov­ery. In the video above, Mans­field intro­duces the unique prop­er­ties of this “sci­en­tif­ic mar­vel of the ancient world,” an enig­ma that has “puz­zled math­e­mati­cians,” he writes in his arti­cle, “for more than 70 years.” Mans­field is con­fi­dent that his research will fun­da­men­tal­ly change the way we under­stand sci­en­tif­ic his­to­ry. He may be over­ly opti­mistic about the cul­tur­al forces that shape his­tor­i­cal nar­ra­tives, and he is not with­out his schol­ar­ly crit­ics either.

Eleanor Rob­son, an expert on Mesopotamia at Uni­ver­si­ty Col­lege Lon­don has not pub­lished a for­mal cri­tique, but she did take to Twit­ter to reg­is­ter her dis­sent, writ­ing, “for any his­tor­i­cal doc­u­ment, you need to be able to read the lan­guage & know the his­tor­i­cal con­text to make sense of it. Maths is no excep­tion.” The trigonom­e­try hypoth­e­sis, she writes in a fol­low-up tweet, is “tedious­ly wrong.” Mans­field and Wild­berg­er may not be experts in ancient Mesopotami­an lan­guage and cul­ture, it’s true, but Rob­son is also not a math­e­mati­cian. “The strongest argu­ment” in the Aus­tralian researchers’ favor, writes Ken­neth Chang at The New York Times, is that “the table works for trigo­nom­ic cal­cu­la­tions.” As Mans­field says, “you don’t make a trigo­nom­ic table by acci­dent.”

Plimp­ton 322 uses ratios rather than angles and cir­cles. “But when you arrange it such a way so that you can use any known ratio of a tri­an­gle to find the oth­er side of a tri­an­gle,” says Mans­field, “then it becomes trigonom­e­try. That’s what we can use this frag­ment for.” As for what the ancient Baby­lo­ni­ans used it for, we can only spec­u­late. Rob­son and oth­ers have pro­posed that the tablet was a teach­ing guide. Mans­field believes “Plimp­ton 322 was a pow­er­ful tool that could have been used for sur­vey­ing fields or mak­ing archi­tec­tur­al cal­cu­la­tions to build palaces, tem­ples or step pyra­mids.”

What­ev­er its ancient use, Mans­field thinks the tablet “has great rel­e­vance for our mod­ern world… prac­ti­cal appli­ca­tions in sur­vey­ing, com­put­er graph­ics and edu­ca­tion.” Giv­en the pos­si­bil­i­ties, Plimp­ton 322 might serve as “a rare exam­ple of the ancient world teach­ing us some­thing new,” should we choose to learn it. That knowl­edge prob­a­bly did not orig­i­nate in out­er space.

Relat­ed Con­tent:

How the Ancient Greeks Shaped Mod­ern Math­e­mat­ics: A Short, Ani­mat­ed Intro­duc­tion

Ancient Maps that Changed the World: See World Maps from Ancient Greece, Baby­lon, Rome, and the Islam­ic World

Hear The Epic of Gil­gamesh Read in the Orig­i­nal Akka­di­an and Enjoy the Sounds of Mesopotamia

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

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