Against All Odds: A Gentle Introduction to Statistics Hosted by Harvard Geneticist Pardis Sabeti (Free Online Course)

in Harvard, Math | January 10th, 2014

Worth a quick men­tion: Dr. Par­dis Sabeti, a media-savvy com­pu­ta­tion­al geneti­cist at Har­vard, has teamed up with the Annen­berg Foun­da­tion, to cre­ate a new intro­duc­tion to sta­tis­tics. In 32 nice­ly-pro­duced videos, Against All Odds: Inside Sta­tis­tics guides “view­ers through the wide range of sta­tis­ti­cal appli­ca­tions used by sci­en­tists, busi­ness own­ers, and even Shake­speare schol­ars, in their work and dai­ly lives.” It’s all about “real peo­ple work­ing on real prob­lems.”

The series starts with What Is Sta­tis­tics?. And then, along the way, the course cov­ers top­ics like Stan­dard Devi­a­tion, Cor­re­la­tion, Sam­ples and Sur­veys, and more. The clip above comes from the unit called Check­ing Assump­tion of Nor­mal­i­ty. And do note that each video mod­ule is com­ple­ment­ed by a Stu­dent Guide and Fac­ul­ty Guide spe­cif­ic to the unit.

Against All Odds: Inside Sta­tis­tics has been added to our col­lec­tion of Free Math Cours­es, a sub­set of our larg­er col­lec­tion, 1,700 Free Online Cours­es from Top Uni­ver­si­ties.

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, BlueSky or Mastodon.

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:

Sta­tis­tics Explained Through Mod­ern Dance: A New Way of Teach­ing a Tough Sub­ject

Cal­cu­lus Life­saver: A Free Online Course from Prince­ton

The Math of Rock Climb­ing

Math: Free Cours­es Online

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How Benoit Mandelbrot Discovered Fractals: A Short Film by Errol Morris

in Film, Math | November 18th, 2013

Even if you know lit­tle of math­e­mat­ics, you prob­a­bly have some aware­ness of frac­tals. You’ve almost cer­tain­ly heard them invoked, cor­rect­ly or oth­er­wise, to describe things that look or act the same at the large scale as they do at the small. You may even know the name Benoit Man­del­brot, the much-lau­reled Pol­ish-French-Amer­i­can “father of frac­tal geom­e­try.” Hard sci­ence-fic­tion titan Arthur C. Clarke called his epony­mous set of math­e­mat­i­cal points “one of the most aston­ish­ing dis­cov­er­ies in the entire his­to­ry of math­e­mat­ics.”

Nas­sim Nicholas Taleb, the famous­ly dis­crim­i­nat­ing author of The Black Swan, called him “the only per­son for whom I have had intel­lec­tu­al respect.” Even for­mer French pres­i­dent Nico­las Sarkozy gave Man­del­brot his props, cred­it­ing his dis­cov­er­ies of the geo­met­ri­cal reg­u­lar­i­ties of “rough” things, from coast­lines to stock-mar­ket fluc­tu­a­tions, as antecedent to mod­ern infor­ma­tion the­o­ry. He also acknowl­edged Man­del­brot’s hav­ing car­ried on his work “entire­ly out­side main­stream research,” and the math­e­mati­cian’s rep­u­ta­tion as an unusu­al­ly insight­ful intel­lec­tu­al mav­er­ick sur­vives him.

Who bet­ter to reveal the mind of an intel­lec­tu­al mav­er­ick, insight­ful or oth­er­wise, than Errol Mor­ris, the doc­u­men­tar­i­an behind such head-on inter­view-dri­ven fea­ture films as A Brief His­to­ry of Time, about astro­physi­cist Stephen Hawk­ing; Mr. Death, about elec­tric-chair design­er and Holo­caust-denial mav­er­ick Fred A. Leuchter Jr.; and The Fog of War, about for­mer Defense Sec­re­tary and Viet­nam War engi­neer Robert S. McNa­ma­ra? His five-minute pro­file of Man­del­brot comes cour­tesy of IBM, where the father of frac­tals worked for 35 years — and whose then-cut­ting-edge com­put­ers he used to father those frac­tals in the first place. “A for­mu­la can be very sim­ple,” he says, sum­ming up one impact of the Man­del­brot set in this inter­view shot 19 days before his death in 2010, “and cre­ate a uni­verse of bot­tom­less com­plex­i­ty.” To find out more about just how that hap­pens, vis­it to IBM’s page on Man­del­brot and frac­tal geom­e­try as well as their ongo­ing frac­tal-themed Tum­blr.

Relat­ed Con­tent:

Arthur C. Clarke Nar­rates Film on Mandelbrot’s Frac­tals; David Gilmour Pro­vides the Sound­track

Watch A Brief His­to­ry of Time, Errol Mor­ris’ Film About the Life & Work of Stephen Hawk­ing

“They Were There” — Errol Mor­ris Final­ly Directs a Film for IBM

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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Statistics Explained Through Modern Dance: A New Way of Teaching a Tough Subject

in Math | October 1st, 2013

You want a gen­tle intro­duc­tion to sta­tis­tics, and maybe those Khan Acad­e­my videos aren’t quite work­ing out for you. Well, here’s anoth­er approach: sta­tis­tics explained with mod­ern dance. That’s the nov­el approach explored by Lucy Irv­ing (Mid­dle­sex Uni­ver­si­ty) and Andy Field (Uni­ver­si­ty of Sus­sex), who pro­duced four short films demon­strat­ing dif­fer­ent sta­tis­ti­cal con­cepts through dance. The films touch on Cor­re­la­tion, Fre­quen­cy Dis­tri­b­u­tions, Sam­pling and Stan­dard Error, and Vari­ance. Speak­ing about the project, Irv­ing explained: “We worked with the chore­o­g­ra­ph­er and exper­i­ment­ed with the dancers to find ways of com­mu­ni­cat­ing the con­cepts.  Our hope is that, as well as being fun and edu­ca­tion­al, the films will demys­ti­fy and take some of the fear out of sta­tis­tics.  Stu­dents often report that ‘the stats’ are the most dif­fi­cult part of their psy­chol­o­gy degree and these the films aim to chal­lenge this by demon­strat­ing that think­ing about them in new ways may make them eas­i­er to com­pre­hend.” You can fol­low Lucy on Twit­ter at @statsdancer.

Fre­quen­cy Dis­tri­b­u­tions:

Sam­pling and Stan­dard Error

Vari­ance

Relat­ed Con­tent:

Free Math Cours­es from Great Uni­ver­si­ties

Cal­cu­lus Life­saver: A Free Online Course from Prince­ton

Har­vard Thinks Big 4 Offers TED-Style Talks on Stats, Milk, and Traf­fic-Direct­ing Mimes

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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 sign up for Open Culture’s free email newslet­ter, please find it here. Or fol­low our posts on Threads, Face­book, BlueSky or Mastodon.

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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