Chuck Jones’ The Dot and the Line Celebrates Geometry & Hard Work: An Oscar-Winning Animation (1965)

The ani­mat­ed short above, The Dot and the Line, direct­ed by the great Chuck Jones and nar­rat­ed by Eng­lish actor Robert Mor­ley, won an Oscar in 1965 for Best Ani­mat­ed Short Film. Based on a book writ­ten by Nor­ton Juster, â€śThe Dot and the Line” tells the sto­ry of a romance between two geo­met­ric shapes—taking the arche­typ­al nar­ra­tive tra­jec­to­ry of boy meets girl, los­es girl, wins girl in the end (find­ing him­self along the way) and inject­ing it with some fas­ci­nat­ing social com­men­tary that still res­onates almost fifty years lat­er. One way of watch­ing “The Dot and the Line” is as a “tri­umph of the nerd” sto­ry, where an anx­ious square (as in “uncool”) Line has to com­pete with a hip­ster beat­nik Squig­gle of a rival for the affec­tions of a flighty Dot.

The Line begins the film “stiff as a stick… dull, con­ven­tion­al and repressed” (as his love inter­est says of him) in con­trast to the groovy Squig­gle and his groovy bebop sound­track. With the pos­si­ble sug­ges­tion that this love trans­gress­es mid-cen­tu­ry racial bound­aries, the Line’s friends dis­ap­prove and tell him to give it up, since “they all look alike any­way.” But the Line per­sists in his fol­ly, indulging in some Wal­ter Mit­ty-like rever­ies of hero­ic endeav­ors that might win over his Dot. Final­ly, using “great self-con­trol,” he man­ages to bend him­self into an angle, then anoth­er, then a series of sim­ple, then very com­plex, shapes, becom­ing, we might assume, some kind of math­e­mat­i­cal wiz. After refin­ing his tal­ents alone, he goes off to show them to Dot, who is “over­whelmed” and delight­ed and who “gig­gles like a school­girl.”

Here the sub­text of the nerd-gets-the-girl sto­ry­line man­i­fests a fair­ly con­ser­v­a­tive cri­tique of the “anar­chy” of the Squig­gle, whom the Dot comes to see as “undis­ci­plined, grace­less, coarse” and oth­er unflat­ter­ing adjec­tives while the line—who pro­claimed to him­self ear­li­er that “free­dom is not a license for chaos”—is “daz­zling, clever, mys­te­ri­ous, ver­sa­tile, light, elo­quent, pro­found, enig­mat­ic, com­plex, and com­pelling.” I can almost imag­ine that George Will had a hand in the writ­ing, which is to say that it’s enor­mous­ly clever, and enor­mous­ly invest­ed in the val­ues of self-con­trol, hard work, and dis­ci­pline, and dis­trust­ful of spon­tane­ity, free play, and gen­er­al groovi­ness. At the end of the film, our Dot and Line go off to live “if not hap­pi­ly ever after, at least rea­son­ably so” in some cozy sub­urb, no doubt. The moral of the sto­ry? “To the vec­tor belong the spoils.”

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!

Josh Jones is a doc­tor­al can­di­date in Eng­lish at Ford­ham Uni­ver­si­ty and a co-founder and for­mer man­ag­ing edi­tor of Guer­ni­ca / A Mag­a­zine of Arts and Pol­i­tics.

The Mathematics of Spiderman and the Physics of Superheroes

I have not seen the new Spi­der­man reboot, so I’ll have to reserve judg­ment on the virtues of the movie. But, in gen­er­al, super­hero movies suc­ceed or fail for me based on how plau­si­ble and con­sis­tent the physics of the alter­nate uni­verse they cre­ate are. In the above video from the “Emory [Uni­ver­si­ty] Looks at Hol­ly­wood” series, Skip Garibal­di, pro­fes­sor of math­e­mat­ics (who pre­vi­ous­ly exam­ined the math of rock climb­ing) explains that the new Spi­der­man film does, with a minor excep­tion, por­tray the feats of Spi­der­man in a math­e­mat­i­cal­ly pos­si­ble way—granted that we’re will­ing to believe in super­pow­ers. For exam­ple, Spi­der­man’s grace­ful swings through the city on long strands of web­bing don’t just serve a cin­e­mat­ic pur­pose; they also keep him from pos­si­bly dis­lo­cat­ing his shoul­ders while com­ing to a full-stop from a free-fall.

Ana­lyz­ing the sci­ence of super­heroes is a fun side­line for pop cul­ture-mind­ed sci­en­tists. In some cas­es, it can be an effec­tive teach­ing tool as well. Uni­ver­si­ty of Min­neso­ta physi­cist and com­ic book fan James Kakalios devotes an entire lec­ture to “The Uncan­ny Physics of Super­hero Com­ic Books.” Kakalios, who has writ­ten a book called the Physics of Super­heroesworked as a sci­ence con­sul­tant on the Spi­der­man reboot and on Zack Snyder’s adap­ta­tion of Watch­men, which he dis­cuss­es below.

Many great physics cours­es (some intro­duc­to­ry, some advanced) can be found in the Physics sec­tion of our col­lec­tion of 500 Free Online Cours­es.

Mathematics Made Visible: The Extraordinary Mathematical Art of M.C. Escher

The eye and the intel­lect play off one anoth­er in sur­pris­ing and beau­ti­ful ways in the art of M.C. Esch­er. Where the Renais­sance mas­ters used shad­ing and per­spec­tive to cre­ate the illu­sion of three-dimen­sion­al depth on two dimen­sion­al sur­faces, Esch­er turned those tricks in on them­selves to cre­ate puz­zles and para­dox­es. He manip­u­lat­ed our fac­ul­ties of per­cep­tion not sim­ply to please the sens­es, but to stim­u­late the mind.

His cool, ana­lyt­ic ten­den­cy was appar­ent from the start. “Mau­rits Esch­er is a good graph­ic artist,” wrote the head­mas­ter of the Haar­lem School of Archi­tec­ture and Dec­o­ra­tive Arts in 1922, the year of Escher’s grad­u­a­tion, “but he lacks the right artis­tic tem­pera­ment.

His work is to too cerebral–neither emo­tion­al nor lyri­cal enough.” Escher’s work became even more cere­bral over time, as it grew in geo­met­ric sophis­ti­ca­tion. In describ­ing what went into the cre­ation of his wood­cuts and engrav­ings, Esch­er wrote:

The ideas that are basic to them often bear wit­ness to my amaze­ment and won­der at the laws of nature which oper­ate in the world around us. He who won­ders dis­cov­ers that this is in itself a won­der. By keen­ly con­fronting the enig­mas that sur­round us, and by con­sid­er­ing and ana­lyz­ing the obser­va­tions that I had made, I end­ed up in the domain of math­e­mat­ics. Although I am absolute­ly inno­cent of train­ing or knowl­edge in the exact sci­ences, I often seem to have more in com­mon with math­e­mati­cians than with my fel­low artists.

The affin­i­ty between Esch­er and math­e­mati­cians is described in the scene above from the the BBC doc­u­men­tary, The Math­e­mat­i­cal Art of M.C. Esch­er. “Math­e­mati­cians know their sub­ject is beau­ti­ful,” says Ian Stew­art of the Uni­ver­si­ty of War­wick. “Esch­er shows us that it’s beau­ti­ful.”

If the BBC clip whets your appetite, be sure to watch Meta­mor­phose: M.C. Esch­er, 1898–1972, a 2002 doc­u­men­tary by Jan Bro­driesz. The one-hour film gives an excel­lent overview of the Dutch artist’s life and work, and fea­tures a rare inter­view with Esch­er, along with scenes of him cre­at­ing his art. If you’re a fan of Esch­er, this film is a must-see.

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:

Free Online Math Cours­es

M.C. Escher’s Per­pet­u­al Motion Water­fall Brought to Life: Real or Sleight of Hand?

Inspi­ra­tions: A Short Film Cel­e­brat­ing the Math­e­mat­i­cal Art of M.C. Esch­er

Udacity to Launch 5 New Courses, from Statistics to Physics. Shooting for Largest Online Class Ever.

This week­end, the Wall Street Jour­nal pub­lished a gush­ing lit­tle pro­file on Sebas­t­ian Thrun. By now, you prob­a­bly know his bio. Thrun helped invent the self-dri­ving car at Google and taught arti­fi­cial intel­li­gence at Stan­ford, before ditch­ing his tenured teach­ing posi­tion and launch­ing Udac­i­ty, a new ven­ture that offers MOOCs (Mas­sive Open Online Cours­es) to stu­dents every­where.

Also this week­end, Thrun kicked off an effort to “break the stu­dent record for the largest online class ever taught” with his new class, Intro­duc­tion to Sta­tis­tics: Mak­ing Deci­sions Based on Data. It starts June 25, and above you can watch Thrun give a short (Hans Rosling-like) intro­duc­tion to the class.  The course is entire­ly free and open to stu­dents every­where. Stu­dents will receive dynam­ic feed­back along the way, and dili­gent stu­dents will get a cer­tifi­cate of com­ple­tion at the end. So what’s stop­ping you? Cer­tain­ly not mon­ey or geog­ra­phy. Oth­er cours­es start­ing on June 25 include:

Intro to Physics: Land­marks in Physics

Algo­rithms: Crunch­ing Social Net­works

Log­ic & Dis­crete Math­e­mat­ics: Foun­da­tions of Com­put­ing

Soft­ware Test­ing: How to Make Soft­ware Fail

Relat­ed Con­tent:

Cours­era Adds Human­i­ties Cours­es, Rais­es $16 Mil­lion, Strikes Deal with 3 Uni­ver­si­ties

Har­vard and MIT Cre­ate EDX to Offer Free Online Cours­es World­wide

Why the Uni­ver­si­ty Sys­tem, as We Know It, Won’t Last …. and What’s Com­ing Next

Free Online Cer­tifi­cate Cours­es from Great Uni­ver­si­ties: A Com­plete List

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Inspirations: A Short Film Celebrating the Mathematical Art of M.C. Escher

Almost two years ago, Span­ish film­mak­er CristĂłbal Vila shot an exquis­ite lit­tle film, Nature by Num­bers, which cap­tured the ways in which math­e­mat­i­cal con­cepts (Fibonac­ci Sequence, Gold­en Num­ber, etc.) reveal them­selves in nature. And the short then clocked a good 2.1 mil­lion views on YouTube alone.

This week, Vila returns with a new film called Inspi­ra­tions. In this case, the inspi­ra­tion is M.C. Esch­er (1898–1972), the Dutch artist who explored a wide range of math­e­mat­i­cal ideas with his wood­cuts, lith­o­graphs, and mez­zot­ints. Although Esch­er had no for­mal train­ing in math­e­mat­ics beyond sec­ondary school, many math­e­mati­cians count­ed them­selves as admir­ers of his work. (Vis­it this online gallery to get bet­ter acquaint­ed with Escher’s art, and be sure to click on the thumb­nails to enlarge the images). As Vila explains, Inspi­ra­tions tries to imag­ine Escher’s work­place, “what things would sur­round an artist like him, so deeply inter­est­ed in sci­ence in gen­er­al and math­e­mat­ics in par­tic­u­lar.” It’s a three min­utes of unbri­dled imag­i­na­tion.

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!

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

Updat­ed on Decem­ber 24, 2013: Yes­ter­day the British gov­ern­ment brought a sad chap­ter to a close when it final­ly issued a posthu­mous par­don to Alan Tur­ing, who was con­vict­ed in 1952 of break­ing laws that crim­i­nal­ized homo­sex­u­al­i­ty. The post you see below was orig­i­nal­ly writ­ten in Feb­ru­ary, 2012, when the ques­tion of Tur­ing being par­doned was still up for debate. The film fea­tured above is still very much worth your while.

This week the British gov­ern­ment final­ly par­doned Alan Tur­ing. One of the great­est math­e­mati­cians of the 20th cen­tu­ry, Tur­ing laid the foun­da­tions for com­put­er sci­ence and played a key role in break­ing the Nazi Enig­ma code dur­ing World War II. In 1952 he was con­vict­ed of homo­sex­u­al­i­ty. He killed him­self two years lat­er, after being chem­i­cal­ly cas­trat­ed by the gov­ern­ment.

On Mon­day, Jus­tice Min­is­ter Tom McNal­ly told the House of Lords that the gov­ern­ment of Prime Min­is­ter David Cameron stood by the deci­sion of ear­li­er gov­ern­ments to deny a par­don, not­ing that the pre­vi­ous prime min­is­ter, Gor­don Brown, had already issued an “unequiv­o­cal posthu­mous apol­o­gy” to Tur­ing. McNal­ly was quot­ed  in the Guardian:

A posthu­mous par­don was not con­sid­ered appro­pri­ate as Alan Tur­ing was prop­er­ly con­vict­ed of what at the time was a crim­i­nal offense. He would have known that his offense was against the law and that he would be pros­e­cut­ed. It is trag­ic that Alan Tur­ing was con­vict­ed of an offense which now seems both cru­el and absurd–particularly poignant giv­en his out­stand­ing con­tri­bu­tion to the war effort. How­ev­er, the law at the time required a pros­e­cu­tion and, as such, long-stand­ing pol­i­cy has been to accept that such con­vic­tions took place and, rather than try­ing to alter the his­tor­i­cal con­text and to put right what can­not be put right, ensure instead that we nev­er again return to those times.

The deci­sion came as a dis­ap­point­ment to thou­sands of peo­ple around the world who had peti­tioned for a for­mal par­don dur­ing the cen­te­nary year of Tur­ing’s birth. The Guardian also quot­ed an email sent by Amer­i­can math­e­mati­cian Den­nis Hejhal to a British col­league:

i see that the House of Lords reject­ed the par­don Feb 6 on what are for­mal grounds.

if law is X on date D, and you know­ing­ly break law X on date D, then you can­not be par­doned (no mat­ter how wrong or flawed law X is).

the real rea­son is OBVIOUS. they do not want thou­sands of old men say­ing par­don us too.

Efforts to obtain a par­don for Tur­ing are con­tin­u­ing. British cit­i­zens and UK res­i­dents can still sign the peti­tion.

To learn more about Tur­ing’s life, you can watch the 1996 BBC film Break­ing the Code (above, in its entire­ty), fea­tur­ing Derek Jaco­bi as Tur­ing and Nobel Prize-win­ning play­wright Harold Pin­ter as the mys­te­ri­ous “Man from the Min­istry.” Direct­ed by Her­bert Wise, the film is based on a 1986 play by Hugh White­more, which in turn was based on Andrew Hodge’s 1983 book Alan Tur­ing: The Enig­ma.

Break­ing the Code moves back and forth between two time frames and two very dif­fer­ent codes: one mil­i­tary, the oth­er social. The film runs 91 min­utes, and has been added to our col­lec­tion of Free Movies Online.

 

Three Passions of Bertrand Russell (and a Collection of Free Texts)

“Three pas­sions, sim­ple but over­whelm­ing­ly strong, have gov­erned my life,” wrote Bertrand Rus­sell in the pro­logue to his auto­bi­og­ra­phy: “the long­ing for love, the search for knowl­edge, and unbear­able pity for the suf­fer­ing of mankind.”

This five minute video, a pre­view of a three-part series pro­duced in 2005 for Ontario pub­lic tele­vi­sion called “The Three Pas­sions of Bertrand Rus­sell,” fea­tures a record­ing of Rus­sell read­ing pas­sages from the pro­logue, enti­tled “What I Have Lived For.” You can read the orig­i­nal text at the Bertrand Rus­sell Soci­ety, an excel­lent online resource, that also makes avail­able free books by Rus­sell, includ­ing:

You can also down­load the first edi­tion of Rus­sel­l’s land­mark 1910–13 col­lab­o­ra­tion with Alfred North White­head, Prin­cip­ia Math­e­mat­i­ca, as well as many of Rus­sel­l’s essays, includ­ing:

To explore the full list of avail­able resources, and to learn how you can sup­port the soci­ety’s activ­i­ties, vis­it the Bertrand Rus­sell Soci­ety web­site.

Also don’t miss some great Rus­sell mate­r­i­al in our own archives, includ­ing all six of his 1948 BBC Rei­th Lec­tures, a clip from a Cana­di­an tele­vi­sion inter­view fea­tur­ing his views on God, and his elo­quent 1959 mes­sage to the future.

Incredible Mental Math Gymnastics on “Countdown”

Count­down is a British TV game show revolv­ing around words and num­bers. In the num­bers round, con­tes­tants select six of twen­ty-four shuf­fled tiles with num­bers on them. Next, a com­put­er gen­er­ates a ran­dom three-dig­it tar­get num­ber and the con­tes­tants have thir­ty sec­onds to get as close to that num­ber as pos­si­ble by com­bin­ing the six num­bers through addi­tion, sub­trac­tion, mul­ti­pli­ca­tion and divi­sion. This mem­o­rable episode of Count­down aired in March 1997 and starred James Mar­tin and his rather unusu­al way of arriv­ing at the tar­get num­ber of 952.

One YouTube user sug­gest­ed a dif­fer­ent way: 6 x 75 = 450; 450 Ă· 50 = 9; 100 + 3 = 103; 9 x 103 = 927; 927 + 25 = 952

I found yet anoth­er way: 100 + 3 = 103; 103 x 6 = 618; 618 x 75 = 46,350; 46,350 Ă· 50 = 927; 927 + 25 = 952

What about you? Any more sug­ges­tions?

By pro­fes­sion, Matthias Rasch­er teach­es Eng­lish and His­to­ry at a High School in north­ern Bavaria, Ger­many. In his free time he scours the web for good links and posts the best finds on Twit­ter.

Relat­ed Con­tent:

Free Math Cours­es

Math­e­mat­ics in Movies: Har­vard Prof Curates 150+ Scenes

Mul­ti­pli­ca­tion: The Vedic Way

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