Alan Turing, Brilliant Mathematician and Code Breaker, Will Be Finally Pardoned by British Government

in Life, Math | July 19th, 2013

turing pardon“Alan Tur­ing, the Enig­ma code­break­er who took his own life after being con­vict­ed of gross inde­cen­cy under anti-homo­sex­u­al­i­ty leg­is­la­tion, is to be giv­en a posthu­mous par­don,” writes The Guardian today. One of the great math­e­mati­cians of the last cen­tu­ry, Tur­ing laid the foun­da­tions for com­put­er sci­ence and played a key role in break­ing the Nazi Enig­ma code dur­ing World War II. Despite his con­tri­bu­tions to defend­ing Britain, Tur­ing was pros­e­cut­ed in 1952 for engag­ing in homo­sex­u­al acts under an 1885 law that led to the con­vic­tions of 49,000 gay men, includ­ing Oscar Wilde. It’s a sad tale that gets recount­ed by anoth­er com­put­er pio­neer Jaron Lanier here:

For years, sup­port­ers have called upon the British gov­ern­ment to issue a posthu­mous par­don. And while British Prime Min­is­ter Gor­don Brown apol­o­gized in 2010 for “the appalling way [Tur­ing] was treat­ed,” mem­bers of the House of Lords resist­ed issu­ing an actu­al par­don as recent­ly as last year. But, accord­ing to The Guardian, leg­is­la­tors are pre­pared to pass a new bill as ear­ly as this Octo­ber. As many of our read­ers will be quick to point out, the con­cept  of a par­don is a bit strange, see­ing that Tur­ing did noth­ing wrong. But the will­ing­ness of the gov­ern­ment to effec­tive­ly nul­li­fy the con­vic­tion and reject an archa­ic law is a wel­comed piece of news.

via @phi­los­o­phy­bites

Relat­ed Con­tent:

Watch the 1996 Film, Break­ing the Code, Star­ring Derek Jaco­bi

The Enig­ma Machine: How Alan Tur­ing Helped Break the Unbreak­able Nazi Code

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Vi Hart Uses Her Video Magic to Demystify Stravinsky and Schoenberg’s 12-Tone Compositions

in Literature, Math, Music, Random | July 8th, 2013

Hav­ing one of those morn­ings where you wake up think­ing it’d be “awe­some” if you jazzed up Stravin­sky’s aton­al musi­cal set­ting of Edward Lear’s famous non­sense poem, “The Owl and the Pussy­cat”?

You are? Wow! What luck! Appar­ent­ly Recre­ation­al Math­e­mu­si­cian Vi Hart had the exact same kind of morn­ing recent­ly, and used it as the spring­board for address­ing the 12-Tone Tech­nique orig­i­nal­ly devised by Arnold Schoen­berg. Unini­ti­at­ed philistines may want to dou­ble down on the caf­feinat­ed bev­er­age of their choice, as this stuff is dense, and Hart talks the way a hum­ming­bird flies.

But as she notes at the 15 minute mark, “Cre­ativ­i­ty means fear­less­ly embrac­ing things that seem odd, even ran­dom, know­ing that if you keep your brain open you’ll even­tu­al­ly find the con­nec­tions.”

Ergo, those of us whose ref­er­ence lev­el (or, it must be said, inter­est) is no match for a 30 minute trea­tise on the his­to­ry and log­ic of order­ing the twelve pitch-class­es of the chro­mat­ic scale into numer­i­cal­ly des­ig­nat­ed sets should find some­thing to chew on, too: copy­right and Fair Use Law, for starters; the con­straint-bound exper­i­men­tal fic­tion of French lit­er­ary group Oulipo, not to men­tion Borges’ “Library of Babel” and the orga­nized ran­dom­ness of Rorschach blots and con­stel­la­tions; zom­bies… John Cage…

(Easy to imag­ine the sort of jacked-up, expla­na­tion-crazed, bed-resis­tant child she must have been.)

As ever, her sharpie-on-spi­ral stop-motion visu­als add dimen­sion, espe­cial­ly now that she seems to be exper­i­ment­ing with giv­ing her on-the-fly stick fig­ures a cer­tain Hyper­bole-and-a-Half exu­ber­ance.

For good mea­sure, we’ve added a con­ven­tion­al video primer on the 12 Tone Tech­nique by The New York Times below.

H/T Hannes

Relat­ed Con­tent:

Math­e­mu­si­cian Vi Hart Explains the Space-Time Con­tin­u­um With a Music Box, Bach, and a Möbius Strip

Math Doo­dling

Inter­views with Schoen­berg and Bartók

Ayun Hal­l­i­day would’ve resort­ed to Vi Hart’s snake draw­ing tech­nique had this been a live lec­ture. Fol­low her @AyunHalliday

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Does Math Objectively Exist, or Is It a Human Creation? A New PBS Video Explores a Timeless Question

in Math, Philosophy | June 5th, 2013

In a famous scene from Boswell’s Life of Samuel John­son, the biog­ra­ph­er and his sub­ject come to dis­cuss the bizarre the­o­ries of Bish­op Berke­ley, who posit­ed that every­thing is immaterial—nothing has any real exis­tence; it’s all just ide­al con­cepts held togeth­er by the mind of God. If God should lose his mind or fall asleep or die, every­thing would fall to pieces or cease to exist. Boswell insists there’s no way to refute the idea. John­son, kick­ing a large stone with such force that his foot rebounds, cries, “I refute it thus.”

Johnson’s lit­tle demon­stra­tion doesn’t actu­al­ly refute Berkeley’s rad­i­cal ide­al­ism. It’s a conun­drum still with us, like Plato’s Euthy­phro stumper, which asks whether the rules gov­ern­ing human behav­ior exist inde­pen­dent­ly of the gods, who sim­ply enforce them, or whether the gods make the rules accord­ing to their whims. In oth­er words, is moral­i­ty objec­tive or sub­jec­tive?

A sim­i­lar prob­lem occurs when we con­sid­er the exis­tence of the rules that gov­ern phys­i­cal laws—the rules of math­e­mat­ics. Where does math come from? Does it exist inde­pen­dent­ly of human (or oth­er) minds, or is it a human cre­ation? Do we dis­cov­er math­e­mat­i­cal prob­lems or do we invent them?

The ques­tion has engen­dered two posi­tions: math­e­mat­i­cal real­ism, which states that math exists whether we do or not, and that there is math out there we don’t know yet, and maybe nev­er can. This posi­tion may require a degree of faith, since, “unlike all of the oth­er sci­ences, math lacks an empir­i­cal com­po­nent.” You can’t phys­i­cal­ly observe it hap­pen­ing. Anti-real­ists, on the oth­er hand, argue that math is a lan­guage, a fic­tion, a “rig­or­ous aes­thet­ic” that allows us to mod­el reg­u­lar­i­ties in the uni­verse that don’t objec­tive­ly exist. This seems like the kind of rel­a­tivism that tends to piss off sci­en­tists. But no one can refute either idea… yet. The video above, from PBS’s Idea Chan­nel, asks us to con­sid­er the var­i­ous dimen­sions of this fas­ci­nat­ing and irre­solv­able ques­tion.

Relat­ed Con­tent:

The Math in Good Will Hunt­ing is Easy: How Do You Like Them Apples?

Incred­i­ble Men­tal Math Gym­nas­tics on “Count­down”

Math Doo­dling

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

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Learn How Richard Feynman Cracked the Safes with Atomic Secrets at Los Alamos

in Math, Physics, Technology | April 17th, 2013

The sto­ry has become part of physics lore: A young Richard Feyn­man, future Nobel win­ner, was bored with life in the remote New Mex­i­co desert while work­ing on the atom­ic bomb dur­ing World War II, so he amused him­self by learn­ing to pick the com­bi­na­tion locks in the sup­pos­ed­ly secure fil­ing cab­i­nets con­tain­ing Amer­i­ca’s nuclear secrets. As Feyn­man would lat­er write in his essay, “Safe­crack­er Meets Safe­crack­er”:

To demon­strate that the locks meant noth­ing, when­ev­er I want­ed some­body’s report and they weren’t around, I’d just go in their office, open the fil­ing cab­i­net, and take it out. When I was fin­ished I would give it back to the guy: “Thanks for your report.”

“Where’d you get it?”

“Out of your fil­ing cab­i­net.”

“But I locked it!”

“I know you locked it. The locks are no good.”

So the offi­cials at Los Alam­os installed cab­i­nets with bet­ter locks. But Feyn­man stud­ied the new ones sys­tem­at­i­cal­ly, and even­tu­al­ly, giv­en a lit­tle time, he could open any lock at will. As a joke, he left a note in one cab­i­net that said, “I bor­rowed doc­u­ment no. LA4312–Feynman the safe­crack­er.”

I opened the safes which con­tained all the secrets to the atom­ic bomb: the sched­ules for the pro­duc­tion of the plu­to­ni­um, the purifi­ca­tion pro­ce­dures, how much mate­r­i­al is need­ed, how the bomb works, how the neu­trons are gen­er­at­ed, what the design is, the dimensions–the entire infor­ma­tion that was known at Los Alam­os: the whole schmeer!

To learn a bit about how Feyn­man did it, watch this fas­ci­nat­ing lit­tle video by jour­nal­ist Brady Haran of the YouTube-fund­ed Num­ber­phile. Haran inter­views Roger Bow­ley, emer­i­tus pro­fes­sor of physics at the Uni­ver­si­ty of Not­ting­ham, who explains sev­er­al of the inge­nious meth­ods used by Feyn­man to solve the prob­lem of crack­ing a lock with (sup­pos­ed­ly) a mil­lion pos­si­ble com­bi­na­tions. And to learn more about Feyn­man’s adven­ture as a safe­crack­er, be sure to read “Safe­crack­er Meets Safe­crack­er,” which is includ­ed in his book Sure­ly You’re Jok­ing, Mr. Feyn­man! and can be read on PDF by click­ing here.

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: Richard Feynman’s Physics Course from Cor­nell (1964)

Richard Feynman’s Ode to a Flower: A Short Ani­ma­tion

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Tom Lehrer’s Mathematically and Scientifically Inclined Singing and Songwriting, Animated

in Math, Music, Physics | April 12th, 2013

I went through child­hood lis­ten­ing to Tom Lehrer’s “New Math”. The 1965 song, per­formed in part like stan­dard spo­ken-word com­e­dy, made me laugh every time. “In the new approach,” the satirist says of the rev­o­lu­tion­ary math­e­mat­ics he pur­ports to teach us, “the impor­tant thing is to under­stand what you’re doing rather than to get the right answer.” Work­ing aloud through a sub­trac­tion prob­lem at the piano, Lehrer sings the oper­a­tions: “And so you’ve got thir­teen tens and you take away sev­en and that leaves five. Well, six, actu­al­ly, but the idea’s the impor­tant thing.” This struck me at the time as noth­ing more than an amus­ing­ly goofy numer­ic riff, and per­haps one with harsh impli­ca­tions for the flaky edu­ca­tion­al fads of the nineties my peers and I then endured. Only years lat­er did I find out that Cold War Amer­i­ca of the ear­ly six­ties actu­al­ly went through a New Math phase, shak­en hard enough by Sput­nik to des­per­ate­ly foist abstract, set the­o­ry-dri­ven math text­books upon its ele­men­tary school­ers.

Lehrer, who turned 85 on Tues­day, knows the sub­ject well: he holds degrees in math­e­mat­ics from Har­vard, has co-authored such papers as “Ran­dom walks with restrain­ing bar­ri­er as applied to the biased bina­ry counter” and “The dis­tri­b­u­tion of the num­ber of local­ly max­i­mal ele­ments in a ran­dom sam­ple”, and, after retir­ing from music in the ear­ly sev­en­ties, taught math class­es at the Uni­ver­si­ty of Cal­i­for­nia, San­ta Cruz. Leg­end has it that he would incor­po­rate rel­e­vant songs from his cat­a­log into lec­tures. But he nev­er sang only about math­e­mat­ics; he also sang about physics, as you can see in the ani­mat­ed ver­sion of his 1959 song “The Ele­ments” above, a trib­ute simul­ta­ne­ous­ly to the peri­od­ic table and The Pirates of Pen­zance. Nobody can deny the impor­tance of learn­ing how to sub­tract or how to tell one ele­ment from anoth­er, but we’d do well to keep Lehrer’s sharp human insights, present implic­it­ly in all his music and explic­it­ly in some of it, in mind. So put one of his records on the next time you have a birth­day of your own, tak­ing a brac­ing shot of his wit before you con­tin­ue, as he put it in “Bright Col­lege Days”, “slid­ing down the razor blade of life.”

Col­in Mar­shall hosts and pro­duces Note­book on Cities and Cul­ture and writes essays on lit­er­a­ture, film, cities, Asia, and aes­thet­ics. He’s at work on a book about Los Ange­les, A Los Ange­les Primer. Fol­low him on Twit­ter at @colinmarshall.

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How Pi Was Nearly Changed to 3.2 … and Copyrighted!

in History, Math | March 22nd, 2013

The sto­ry above—from our old friend James Grime of Num­ber­phile and Cam­bridge Uni­ver­si­ty—has all the mak­ings of weirdo Amer­i­cana: bad ama­teur sci­ence, com­mer­cial ven­tures based upon the same, and a state leg­is­la­ture eager to embrace it all. In 1897, an ama­teur math­e­mati­cian named Edwin Good­win believed he’d solved an ancient prob­lem ruled insol­u­ble fif­teen years ear­li­er. He thought that he had squared the cir­cle and could rea­son­ably copy­right Pi as 3.2. Yes, that’s right, after his “dis­cov­ery,” Good­win, a native of Indi­ana, decid­ed to copy­right his proof so that any­one using it out­side of the state would have to pay him roy­al­ties.

But kind­ly, in a ges­ture of nativist good­will (or polit­i­cal oppor­tunism), Good­win decid­ed he would let his home state of Indi­ana use his proof for free for edu­ca­tion­al pur­pos­es. In fact, he said as much when he intro­duced a bill to the Indi­ana House of Rep­re­sen­ta­tives to rule his proof cor­rect and grant him sole pro­pri­etor­ship. And, as some­times hap­pens in sto­ries like this, the bill passed, unan­i­mous­ly, and the leg­is­la­tors were impressed. But one man wasn’t. By sheer chance, a pro­fes­sor of math­e­mat­ics hap­pened to be in atten­dance. While he declined to meet math­e­mat­ics hero Edwin Good­win, he did take it upon him­self to warn the Indi­ana Sen­ate of what was com­ing its way. Luck­i­ly for the state’s school­child­ren, the Sen­ate threw the bill out, but not before a half-hour spent  mock­ing its silli­ness.

But is the idea of squar­ing a cir­cle ridicu­lous? Dr. Grime cites one Indi­an math­e­mati­cian who pro­posed a some­what fea­si­ble solu­tion. And what exact­ly does it mean to “square a cir­cle”? If you don’t know (and I don’t), you’ll have to wait till next time on Num­ber­phile, when Grime and his team promise to explain it to us rubes.

Relat­ed Con­tent:

The Math in Good Will Hunt­ing is Easy: How Do You Like Them Apples?

The Enig­ma Machine: How Alan Tur­ing Helped Break the Unbreak­able Nazi Code

Incred­i­ble Men­tal Math Gym­nas­tics on “Count­down”

Josh Jones is a writer, edi­tor, and musi­cian based in Wash­ing­ton, DC. Fol­low him @jdmagness

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The Math in Good Will Hunting is Easy: How Do You Like Them Apples?

in Film, Math | March 13th, 2013

Per­haps you remem­ber the scene (above) in Gus Van San­t’s 1997 film, Good Will Hunt­ing. MIT pro­fes­sor Ger­ald Lam­beau, win­ner of the cov­et­ed Fields Medal, chal­lenges his grad­u­ate stu­dents to solve a math prob­lem that he, him­self, spent two years try­ing to crack. That set the bar pret­ty high. So, imag­ine every­one’s sur­prise when Will Hunt­ing, a jan­i­tor at MIT played by Matt Damon, wres­tles the prob­lem to the ground with­out break­ing a men­tal sweat.

?t=13s

Well, not quite every­one was sur­prised, espe­cial­ly not the math­e­mati­cians behind the Num­ber­phile video series. Right above James Grime, who resides at the Depart­ment of Math­e­mat­ics and The­o­ret­i­cal Physics at Cam­bridge Uni­ver­si­ty, breaks down the famous “Home­o­mor­phi­cal­ly Irre­ducible Trees of Degree Ten” prob­lem. And, it turns out, it’s a prob­lem mere mor­tals can solve fair­ly eas­i­ly at home.

Num­ber­phile also offers a quick bonus video that tries to answer anoth­er tough ques­tion: Who was the real Will Hunt­ing? Who was the char­ac­ter mod­eled after? There are a few prime can­di­dates.…

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:

Math­e­mat­ics in Movies: Har­vard Prof Curates 150+ Scenes

Cal­cu­lus Life­saver: A Free Online Course from Prince­ton

Math: Free Cours­es

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In Under Three Minutes, Hans Rosling Visualizes the Incredible Progress of the “Developing World”

in Economics, Math | February 18th, 2013

Hans Rosling knows how to make a con­cise, pow­er­ful point. His mas­tery of sta­tis­tics and visu­al aids does­n’t hurt. Behold, for instance, the Karolin­s­ka Insti­tute Pro­fes­sor of Inter­na­tion­al Health visu­al­iz­ing the health of 200 coun­tries over 200 years with 120,000 data points. His abil­i­ty to con­dense vast amounts of infor­ma­tion into short bursts while pro­vid­ing the widest pos­si­ble con­text for his points nat­u­ral­ly endears him to the TED audi­ence, which val­ues coun­ter­in­tu­itive intel­lec­tu­al impact deliv­ered with the utmost suc­cinct­ness. We pre­vi­ous­ly fea­tured a TED Talk from where­in the excitable pro­fes­sor explains world pop­u­la­tion growth and pros­per­i­ty with props bought at IKEA. (The man comes from Swe­den, after all. One must rep­re­sent.) Now, on Bill Gates’ Youtube chan­nel, you can watch Rosling’s short­est and slick­est video yet: “The Riv­er of Myths.”

Open­ing with a visu­al­iza­tion of 1960’s world child mor­tal­i­ty num­bers graphed against the num­ber of chil­dren born per woman, Rosling uses his sig­na­ture method of sta­tis­ti­cal-ani­ma­tion show­man­ship to explode myths about the poten­tial of devel­op­ing nations. We see that, as a coun­try’s wealth ris­es, its health ris­es; as its health ris­es, its child mor­tal­i­ty drops; and as its child mor­tal­i­ty drops, so does its num­ber of chil­dren born per woman, which leads to a sus­tain­able over­all pop­u­la­tion size. He then exam­ines the sep­a­rate regions of Ethiopia, for­mer­ly a devel­op­men­tal lag­gard, show­ing that the cap­i­tal Addis Aba­ba ranks repro­duc­tive­ly among the devel­oped nations, while only remote regions lag behind. “Most peo­ple think the prob­lems in Africa are unsolv­able, but if the poor­est coun­tries can just fol­low the path of Ethiopia, it’s ful­ly pos­si­ble that the world will look like this by 2030.” We then see a pro­jec­tion of all the world’s nations clus­tered in the small-fam­i­ly, low-mor­tal­i­ty cor­ner of the graph. “But to ensure this hap­pens, we must mea­sure the progress of coun­tries. It’s only by mea­sur­ing we can cross the riv­er of myths.” Have you heard a more pow­er­ful argu­ment for the use­ful­ness of sta­tis­tics late­ly?

Relat­ed con­tent:

Hans Rosling Uses Ikea Props to Explain World of 7 Bil­lion Peo­ple

200 Coun­tries & 200 Years in 4 Min­utes, Pre­sent­ed by Hans Rosling

Col­in Mar­shall hosts and pro­duces Note­book on Cities and Cul­ture and writes essays on lit­er­a­ture, film, cities, Asia, and aes­thet­ics. He’s at work on a book about Los Ange­les, A Los Ange­les Primer. Fol­low him on Twit­ter at @colinmarshall.

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