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

In many an audio engi­neer­ing course, I’ve come across the Fouri­er Trans­form, an idea so fun­da­men­tal in sound pro­duc­tion that it seems essen­tial for every­one to know it. My lim­it­ed under­stand­ing was, you might say, func­tion­al. It’s some kind of math­e­mat­i­cal reverse engi­neer­ing machine that turns wave­forms into fre­quen­cies, right? Yes, but it’s much more than that. The idea can seem over­whelm­ing to the non-math­e­mat­i­cal­ly-inclined among us.

The Fouri­er Trans­form, named for French math­e­mati­cian and physi­cist Jean-Bap­tiste Joseph Fouri­er, “decom­pos­es” any wave form into fre­quen­cies, and “vir­tu­al­ly every­thing in the world can be described via a wave­form,” writes one intro­duc­tion to the the­o­ry. That includes not only sounds but “elec­tro­mag­net­ic fields, the ele­va­tion of a hill ver­sus loca­tion… the price of  your favorite stock ver­sus time,” the sig­nals of an MRI scan­ner.

The con­cept “extends well beyond sound and fre­quen­cy into many dis­parate areas of math and even physics. It is crazy just how ubiq­ui­tous this idea is,” notes the 3Blue1Brown video above, one of dozens of ani­mat­ed explo­rations of math­e­mat­i­cal con­cepts. I know far more than I did yes­ter­day thanks to this com­pre­hen­sive ani­mat­ed lec­ture. Even if it all seems old hat to you, “there is some­thing fun and enrich­ing,” the video assures us, “about see­ing what all of its com­po­nents look like.”

Things get com­pli­cat­ed rather quick­ly when we get into the dense equa­tions, but the video illus­trates every for­mu­la with graphs that trans­form the num­bers into mean­ing­ful mov­ing images.

3Blue1Brown, a project of for­mer Khan Acad­e­my fel­low Grant Sander­son, has done the same for dozens of STEM con­cepts, includ­ing such sub­jects as high­er dimen­sions, cryp­tocur­ren­cies, machine learn­ing, and neur­al net­works and essen­tials of cal­cu­lus and lin­ear alge­bra like the deriv­a­tive para­dox and “Vec­tors, what even are they?”

In short­er lessons, you can learn to count to 1000 on two hands, or, just below, learn what it feels like to invent math. (It feels weird at first.)

Sander­son­’s short cours­es “tend to fall into one of two cat­e­gories,” he writes: top­ics “peo­ple might be seek­ing out,” like many of those men­tioned above, and “prob­lems in math which many peo­ple may not have heard of, and which seem real­ly hard at first, but where some shift in per­spec­tive makes it both doable and beau­ti­ful.” These puz­zles with ele­gant­ly clever solu­tions can be found here. Whether you’re a hard­core math-head or not, you’ll find Sanderson’s series of 3Blue1Brown ani­ma­tions illu­mi­nat­ing. Find them all here.

Relat­ed Con­tent:

Free Online Math Cours­es

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

Cit­i­zen Maths: A Free Online Course That Teach­es Adults the Math They Missed in High School

Free Math Text­books 

Math Mag­ic

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

Making Sense of White Paintings: A Short Art History Lesson on Minimalism and the All-White Painting

“I could do that” goes the refrain of philistines at mod­ern art gal­leries, some­times fol­lowed by a “Hell, my dog/cat/baby/elephant could do that!” Sophis­ti­cates smirk know­ing smirks. Oh no, sir or madam, they most cer­tain­ly could not. But maybe every­one, at some lev­el, comes across Agnes Martin’s White Stone or Jo Baer’s Unti­tled (White Square Laven­der) and thinks it looks like some­one “just took a tube of white paint and spread it on a can­vas.”

It’s tempt­ing to imag­ine, notes Vox in the explain­er video above, but “it’s not actu­al­ly that easy.”

Oh, real­ly? Enlight­en us…. Why exact­ly did Robert Ryman’s all-white paint­ing Bridge sell for $20.6 mil­lion dol­lars? This ques­tion may be answered in anoth­er video. Here, we get a lit­tle bit of art history—on the ori­gins of the all-white paint­ing in the min­i­mal­ism of Kaz­imir Male­vich (he pre­ferred to call it “Supre­ma­tism”) and the devel­op­ment of Min­i­mal­ism, cap­i­tal “M.”

Elis­a­beth Sher­man, assis­tant cura­tor at the Whit­ney Muse­um in New York says that “white isn’t ever a pure thing, white is always tint­ed in some way.” Of course we know this, she acknowl­edges, because we’ve mar­veled at the dozens of shades of white in the paint sec­tion of the hard­ware store. Attend to the sub­tle gra­da­tions of white, from warm to cool, and the range of tex­tures, lines, pat­terns, shapes, and “sub­tle intri­ca­cies,” and the all-white paint­ing begins to reveal itself as an almost liv­ing, breath­ing thing rather than a piece of dec­o­ra­tive dry­wall.

Art his­tor­i­cal­ly, the vari­ety of white paint­ings came about prin­ci­pal­ly in the 50s as a response to Abstract Expressionism’s emo­tion­al excess­es and the out­sized ges­tur­al per­son­al­i­ties of De Koon­ing and Pol­lock. Artists like Bauhaus alum Josef Albers and Min­i­mal­ist purist Frank Stel­la pro­posed that “the art object” should “be as far removed from the author as pos­si­ble.” No greater an attack could be launched on the idea of art as per­son­al expres­sion than the all-white paint­ing.

This ten­den­cy toward total abstraction—reducing art to fields of col­or, non-col­or, and sim­ple shapes—has made a lot of peo­ple very upset. Vox includes sev­er­al clips of “men get­ting angry” at Min­i­mal­ist art. The word “pre­ten­tious” pops up a lot. The all-white paint­ing has even inspired a play, Yas­mi­na Reza’s Art, about “a group of life­long friends who are torn apart when one of them buys an all-white paint­ing for $200,000.”

As for “I could do that”… in near­ly every show she’s worked on in her career as a cura­tor, Sher­man remarks, “some­one has said that.” Well, she says, yes, maybe you could. “But you didn’t.” So there. If look­ing at an all-white paint­ing (or an all-black paint­ing) makes you feel angry, annoyed, or dis­mis­sive, maybe, she says, try and get beyond that first impres­sion and engage with the sub­tleties of the work. And maybe don’t ask how much the muse­um paid for it.

Relat­ed Con­tent:

Har­vard Puts Online a Huge Col­lec­tion of Bauhaus Art Objects

Watch At the Muse­um, MoMA’s 8‑Part Doc­u­men­tary on What it Takes to Run a World-Class Muse­um

The Tree of Mod­ern Art: Ele­gant Draw­ing Visu­al­izes the Devel­op­ment of Mod­ern Art from Delacroix to Dalí (1940)

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

The Strange Dancing Plague of 1518: When Hundreds of People in France Could Not Stop Dancing for Months

If you find your­self think­ing you aren’t a vic­tim of fash­ion, maybe take anoth­er look. Yes, we can con­scious­ly train our­selves to resist trends through force of habit. We can declare our pref­er­ences and stand on prin­ci­ple. But we aren’t con­scious­ly aware of what’s hap­pen­ing in the hid­den turn­ings of our brains. Maybe what we call the uncon­scious has more con­trol over us than we would like to think.

Inex­plic­a­ble episodes of mass obses­sion and com­pul­sion serve as dis­qui­et­ing exam­ples. Mass pan­ics and delu­sions tend to occur, argues author John Waller, “in peo­ple who are under extreme psy­cho­log­i­cal dis­tress, and who believe in the pos­si­bil­i­ty of spir­it pos­ses­sion. All of these con­di­tions were sat­is­fied in Stras­bourg in 1518,” the year the Danc­ing Plague came to the town in Alsace—an invol­un­tary com­mu­nal dance fes­ti­val with dead­ly out­comes.

The event began with one per­son, as you’ll learn in the almost jaun­ty ani­mat­ed BBC video below, a woman known as Frau Trof­fea. One day she began danc­ing in the street. Peo­ple came out of their hous­es and gawked, laughed, and clapped. Then she didn’t stop. She “con­tin­ued to dance, with­out rest­ing, morn­ing, after­noon, and night for six whole days.” Then her neigh­bors joined in. With­in a month, 400 peo­ple were “danc­ing relent­less­ly with­out music or song.”

We might expect that town lead­ers in this late-Medieval peri­od would have declared it a mass pos­ses­sion event and com­menced with exor­cisms or witch burn­ings. Instead, it was said to be a nat­ur­al phe­nom­e­non. Draw­ing on humoral the­o­ry, “local physi­cians blamed it on ‘hot blood,’” History.com’s Evan Andrews writes. They “sug­gest­ed the afflict­ed sim­ply gyrate the fever away. A stage was con­struct­ed and pro­fes­sion­al dancers were brought in. The town even hired a band to pro­vide back­ing music.”

Soon, how­ev­er, bloody and exhaust­ed, peo­ple began dying from strokes and heart attacks. The danc­ing went on for months. It was not a fad. No one was enjoy­ing them­selves. On the con­trary, Waller writes, “con­tem­po­raries were cer­tain that the afflict­ed did not want to dance and the dancers them­selves, when they could, expressed their mis­ery and need for help.” This con­tra­dicts sug­ges­tions they were will­ing mem­bers of a cult, and paints an even dark­er pic­ture of the event.

Cer­tain psy­cho­nauts might see in the 1518 Danc­ing Plague a shared uncon­scious, work­ing some­thing out while drag­ging the poor Stras­bour­gians along behind it. Oth­er, more or less plau­si­ble expla­na­tions have includ­ed ergo­tism, or poi­son­ing “from a psy­chotrop­ic mould that grows on stalks of rye.” How­ev­er, Waller points out, ergot “typ­i­cal­ly cuts off blood sup­ply to the extrem­i­ties mak­ing coor­di­nat­ed move­ment very dif­fi­cult.”

He sug­gests the danc­ing mania came about through the meet­ing of two pri­or con­di­tions: “The city’s poor were suf­fer­ing from severe famine and dis­ease,” and many peo­ple in the region believed they could obtain good health by danc­ing before a stat­ue of Saint Vitus. They also believed, he writes, that “St. Vitus… had the pow­er to take over their minds and inflict a ter­ri­ble, com­pul­sive dance. Once these high­ly vul­ner­a­ble peo­ple began to antic­i­pate the St. Vitus curse they increased the like­li­hood that they’d enter the trance state.”

The mys­tery can­not be defin­i­tive­ly solved, but it does seem that what Waller calls “fer­vent super­nat­u­ral­ism” played a key role, as it has in many mass hys­te­rias, includ­ing “ten such con­ta­gions which had bro­ken out along the Rhine and Moselle rivers since 1374,” as the Pub­lic Domain Review notes. Fur­ther up, see a 1642 engrav­ing based on a 1564 draw­ing by Peter Breughel of anoth­er danc­ing epi­dem­ic which occurred that year in Molen­beek. The 17th cen­tu­ry Ger­man engrav­ing above of a danc­ing epi­dem­ic in a church­yard fea­tures a man hold­ing a sev­ered arm.

We see mass pan­ics and delu­sions around the world, for rea­sons that are rarely clear to schol­ars, psy­chi­a­trists, his­to­ri­ans, anthro­pol­o­gists, and physi­cians dur­ing or after the fact. What is med­ical­ly known as Saint Vitus dance, or Sydenham’s Chorea, has rec­og­nized phys­i­cal caus­es like rheumat­ic fever and occurs in a spe­cif­ic sub­set of the pop­u­la­tion. The his­tor­i­cal Saint Vitus Dance, or Danc­ing Plague, how­ev­er, affect­ed peo­ple indis­crim­i­nate­ly and seems to have been a phe­nom­e­non of mass sug­ges­tion, like many oth­er social-psy­cho­log­i­cal events around the world.

Episodes of epi­dem­ic manias relat­ed to out­mod­ed super­nat­ur­al beliefs can seem espe­cial­ly bizarre, but the mass psy­chol­o­gy of 21st cen­tu­ry west­ern cul­ture includes many episodes of social con­ta­gion and com­pul­sion no less strange, and per­haps no less wide­spread or dead­ly, espe­cial­ly dur­ing times of extreme stress.

via Pub­lic Domain Review

Relat­ed Con­tent:

Oliv­er Sacks Explains the Biol­o­gy of Hal­lu­ci­na­tions: “We See with the Eyes, But with the Brain as Well”

Behold the Mys­te­ri­ous Voyn­ich Man­u­script: The 15th-Cen­tu­ry Text That Lin­guists & Code-Break­ers Can’t Under­stand

A Free Yale Course on Medieval His­to­ry: 700 Years in 22 Lec­tures

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

The Musical Instruments in Hieronymus Bosch’s The Garden of Earthly Delights Get Brought to Life, and It Turns Out That They Sound “Painful” and “Horrible”

Wel­come to The Gar­den of Earth­ly Delights.

You’ll find no angel­ic strings here.

Those are reserved for first class cit­i­zens whose vir­tu­ous lives earned them pas­sage to the upper­most heights.

Down below, stringed instru­ments pro­duce the most hell­ish sort of cacoph­o­ny, a fit­ting accom­pa­ni­ment for the horn whose bell is befouled with the arm of a tor­tured soul.

How do we know that’s what they sound­ed like?

A group of musi­col­o­gists, crafts­peo­ple and aca­d­e­mics from the Bate Col­lec­tion of Musi­cal Instru­ments at the Uni­ver­si­ty of Oxford, took it upon them­selves to actu­al­ly build the instru­ments depict­ed in Hierony­mus Bosch’s action-packed trip­tych—the hell harp, the vio­lat­ed lute, the gross­ly over­sized hur­dy-gur­dy

…And then they played them.

Let us hope they stopped shy of shov­ing flutes up their bums. (Such a place­ment might pro­duce a sound, but not from the flute’s gold­en throat).

The Bosch exper­i­ment added ten more instru­ments to the museum’s already impres­sive, over-1000-strong col­lec­tion of wood­winds, per­cus­sion, and brass, many from the stu­dios of esteemed mak­ers, some dat­ing all the way back to the Renais­sance.

Unfor­tu­nate­ly, the new addi­tions don’t sound very good. “Hor­ri­ble” and “painful” are among the adjec­tives the Bate Col­lec­tion man­ag­er Andrew Lamb uses to describe the aur­al fruits of his team’s months-long labors.

Might we assume Bosch would have want­ed it that way?

Bran­don McWilliams, the wag behind Bosch’s wild­ly enthu­si­as­tic, f‑bomb-laced review of thrash met­al band Slayer’s 1986 Reign in Blood album, would sure­ly say yes, as would
Alden and Cali Hack­mann, North Amer­i­can hur­dy-gur­dy mak­ers, who note that Bosch’s painter­ly des­e­cra­tions were not lim­it­ed to their per­son­al favorite instru­ment:

Bosch and his con­tem­po­raries viewed music as sin­ful, asso­ci­at­ing it with oth­er sins of the flesh and spir­it. A num­ber of oth­er instru­ments are also depict­ed: a harp, a drum, a shawm, a recorder, and the met­al tri­an­gle being played by the woman (a nun, per­haps) who is appar­ent­ly impris­oned in the key­box of the instru­ment. The hur­dy-gur­dy was also asso­ci­at­ed with beg­gars, who were often blind. The man turn­ing the crank is hold­ing a beg­ging bowl in his oth­er hand. Hang­ing from the bowl is a met­al seal on a rib­bon, called a “gaber­lun­zie.” This was a license to beg in a par­tic­u­lar town on a par­tic­u­lar day, grant­ed by the nobil­i­ty. Sol­diers who were blind­ed or maimed in their lord’s ser­vice might be giv­en a gaber­lun­zie in rec­om­pense.

To the best of our knowl­edge, no gaber­fun­zies were grant­ed, nor any sin­ners eter­nal­ly damned, in the Bate Collection’s caper. Accord­ing to man­ag­er Lamb, expand­ing the bound­aries of music edu­ca­tion was rec­om­pense enough, well worth the tem­po­rary affront to ten­der ears.

via Metafil­ter

Relat­ed Con­tent:

Take a Vir­tu­al Tour of Hierony­mus Bosch’s Bewil­der­ing Mas­ter­piece The Gar­den of Earth­ly Delights

The Hierony­mus Bosch Demon Bird Was Spot­ted Rid­ing the New York City Sub­way the Oth­er Day…

Hierony­mus Bosch Fig­urines: Col­lect Sur­re­al Char­ac­ters from Bosch’s Paint­ings & Put Them on Your Book­shelf

Ayun Hal­l­i­day is an author, illus­tra­tor, the­ater mak­er and Chief Pri­ma­tol­o­gist of the East Vil­lage Inky zine.  See her onstage in New York City tonight as host of The­ater of the Apes book-based vari­ety show, Necro­mancers of the Pub­lic Domain. Fol­low her @AyunHalliday.

A Fender Stratocaster Made Out of 1200 Colored Pencils

Alder and Ash. These woods have tra­di­tion­al­ly made up the body of the Fend­er Stra­to­cast­er. Cray­ola col­ored pen­cils? They were nev­er part of the mix … at least until now.

Above, Burls Art gives it a go. In nine min­utes, they take you through the mak­ing and play­ing of the Cray­ola Strat, from start to fin­ish. Afi­ciona­dos, feel free to argue over the tonal qual­i­ties of this new fan­gled cre­ation.

Relat­ed Con­tent:

Behold the First Elec­tric Gui­tar: The 1931 “Fry­ing Pan”

Bri­an May’s Home­made Gui­tar, Made From Old Tables, Bike and Motor­cy­cle Parts & More

Oxford Sci­en­tist Explains the Physics of Play­ing Elec­tric Gui­tar Solos

Repair­ing Willie Nelson’s Trig­ger: A Good Look at How a Luthi­er Gets America’s Most Icon­ic Gui­tar on the Road Again

A New Edition of Ray Bradbury’s Fahrenheit 451 That’s Only Readable When You Apply Heat to Its Pages: Pre-Order It Today

Ray Brad­bury’s Fahren­heit 451, a nov­el of a near­ly book­less dystopi­an future in which “fire­men” go around burn­ing any last vol­umes they can find, lends itself well to high­ly phys­i­cal spe­cial edi­tions. Last year we fea­tured an asbestos-bound, fire­proof ver­sion, 200 copies of which were pub­lished at the book’s first print­ing in 1953. The year before we fea­tured an exper­i­men­tal edi­tion per­haps even more faith­ful­ly reflec­tive of the sto­ry’s premise, one whose all-black pages only reveal the neg­a­tive space around the text with the appli­ca­tion of heat.

“Graph­ic design stu­dio Super Terrain’s edi­tion of Ray Bradbury’s sci-fi clas­sic Fahren­heit-451 took the inter­net by storm,” writes Elec­tric Lit­er­a­ture, “thanks to a video show­ing how its all-black pages become read­able text when exposed to an open flame.

Now, “for only $451  —  get it?  —  you can pre­order one to keep on a spe­cial­ly-heat­ed shelf in your home!” As not­ed in that post, you could also expose its text using some­thing oth­er than an open flame (a hair dry­er, for exam­ple), but that would hard­ly put you as much in the mind of the nov­el­’s “fire­men” with their book-erad­i­cat­ing flamethrow­ers. What­ev­er you use to heat up the pages, they revert right back to their car­bonized-look­ing black as soon as they cool down.

In Fahren­heit 451, says Super Ter­rain’s man­i­festo for this unusu­al edi­tion of the nov­el, Brad­bury “ques­tions the cen­tral role played by books in cul­ture and expos­es the pos­si­ble drifts of a soci­ety ruled by imme­di­a­cy. This tyran­ny of hap­pi­ness pre­vents any form of con­tes­ta­tion that could be nur­tured by reflex­ion, mem­o­ry or cul­ture in books or works of art.” This black-paged book “could be part of Bradbury’s fic­tion as a trick to keep and hide away the books from the pyro­ma­ni­ac fire­men. By set­ting the book on fire, the read­er plunges into the nov­el and becomes the hyphen between real­i­ty and fic­tion.” How rel­e­vant has all of this remained in our “time of con­tin­u­ous flow of images, self­ies, fake news, tweets and oth­er ‘digest-digest-digests’ ”? Strike a match, flick on your lighter, or pow­er up your hair dry­er — all, of course, under adult super­vi­sion if nec­es­sary — and find out for your­self.

via Elec­tric Lit­er­a­ture

Relat­ed Con­tent:

To Read This Exper­i­men­tal Edi­tion of Ray Bradbury’s Fahren­heit 451, You’ll Need to Add Heat to the Pages

Ray Brad­bury Reveals the True Mean­ing of Fahren­heit 451: It’s Not About Cen­sor­ship, But Peo­ple “Being Turned Into Morons by TV”

Father Writes a Great Let­ter About Cen­sor­ship When Son Brings Home Per­mis­sion Slip to Read Ray Bradbury’s Cen­sored Book, Fahren­heit 451

An Asbestos-Bound, Fire­proof Edi­tion of Ray Bradbury’s Fahren­heit 451 (1953)

Hear Ray Bradbury’s Clas­sic Sci-Fi Sto­ry Fahren­heit 451 as a Radio Dra­ma

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les and the video series The City in Cin­e­ma. Fol­low him on Twit­ter at @colinmarshall or on Face­book.

150 Courses Starting at Stanford Continuing Studies Next Week: Explore the Catalogue of Campus and Online Courses

Quick fyi: I spend my days at Stan­ford Con­tin­u­ing Stud­ies, where we’ve devel­oped a rich line­up of online cours­es for life­long learn­ers, many of which will get start­ed next week. The cours­es aren’t free. But they’re first rate, giv­ing adult students–no mat­ter where they live–the chance to work with ded­i­cat­ed teach­ers and stu­dents.

The cat­a­logue includes a large num­ber of online Cre­ative Writ­ing cours­es, cov­er­ing the Nov­el, the Mem­oir, Cre­ative Non­fic­tion, Trav­el Writ­ing, Poet­ry and more. For the pro­fes­sion­al, the pro­gram offers online busi­ness cours­es in sub­jects like Fun­da­men­tals of Project Man­age­mentVal­ue Invest­ing: An Intro­duc­tionHow to Build Suc­cess­ful Star­tups: Learn Lessons Straight from Sil­i­con Val­ley Entre­pre­neurs and Lead­er­ship by Design: Using Design Think­ing to Trans­form Com­pa­nies and CareersAnd there’s a grow­ing num­ber of online Lib­er­al Arts cours­es too. Take for exam­ple The Geol­o­gy and Wines of Cal­i­for­nia and FranceDraw­ing Inspi­ra­tion: Devel­op­ing a Cre­ative Prac­tice, and The Dai­ly Pho­to­graph: Devel­op­ing Your Cre­ative Intu­ition.

If you live in the San Fran­cis­co Bay Area, check out the larg­er cat­a­logue. Stan­ford Con­tin­u­ing Stud­ies has 150 cours­es get­ting start­ed this Win­ter quar­ter (next week), many tak­ing place in Stan­ford’s class­rooms. The two flag­ship cours­es of the quar­ter include: Piv­otal Moments That Shaped the Mod­ern World and The Ethics of Tech­no­log­i­cal Dis­rup­tion: A Con­ver­sa­tion with Sil­i­con Val­ley Lead­ers and Beyond.

Relat­ed Con­tent:

Free: A Crash Course in Design Think­ing from Stanford’s Design School

Stan­ford Uni­ver­si­ty Launch­es Free Course on Devel­op­ing Apps with iOS 10

How Walk­ing Fos­ters Cre­ativ­i­ty: Stan­ford Researchers Con­firm What Philoso­phers and Writ­ers Have Always Known

Take a Free Course on Dig­i­tal Pho­tog­ra­phy from Stan­ford Prof Marc Lev­oy

How to Start a Start-Up: A Free Course from Y Com­bi­na­tor Taught at Stan­ford

130,000 Pho­tographs by Andy Warhol Are Now Avail­able Online, Cour­tesy of Stan­ford Uni­ver­si­ty

Philip Glass Finishes His David Bowie Trilogy, Debuting His Lodger Symphony

Some­times I feel
The need to move on
So I pack a bag
And move on
Move on

–David Bowie, “Move On”

We might have been call­ing it the Lake Gene­va Tril­o­gy, giv­en David Bowie’s recu­per­a­tive sojourn in Switzer­land after the empti­ness he felt in L.A. The first album in the Berlin Tril­o­gy, Low, was most­ly record­ed in France, and the last album of the tril­o­gy, Lodger, in Mon­treaux in 1979. But they were almost all writ­ten in, around, and about Berlin, where Bowie found what he was look­ing for—a more rar­i­fied form of isolation—or as he puts it, “vir­tu­al anonymi­ty…. For some rea­son Berlin­ers just didn’t care. Well, not about an Eng­lish rock singer, any­way.”

Bowie’s wife Angela remem­bers that “he chose to live in a sec­tion of the city as bleak, anony­mous, and cul­tur­al­ly lost as pos­si­ble…. He took an apart­ment above an auto parts store and ate at the local workingman’s café. Talk about alien­ation.” The feel­ing per­vades all three albums to dif­fer­ent effect, but Lodger takes things in a far edgi­er, more cacoph­o­nous direc­tion. Removed from Bowie’s time of soak­ing up krautrock and pro­duc­ing his room­mate Iggy Pop’s solo albums, record­ed as his mar­riage dis­solved, it is the sound of jad­ed cul­tur­al and rela­tion­al dis­lo­ca­tion.

“A lot more chaos was intend­ed” on Lodger says Tony Vis­con­ti, and it is on these rocks that com­pos­er Philip Glass foundered for 23 years. In the 90s, he began his own tril­o­gy, of sym­phonies based on the renowned Bowie/Eno/Visconti col­lab­o­ra­tions. Lodger hung him up because it “didn’t inter­est me at all,” he tells the Los Ange­les Times. Despite its wild exper­i­men­tal­ism, he heard “no orig­i­nal ideas on that record.”

Glass grav­i­tat­ed towards the melodies of the first two albums, releas­ing his Low sym­pho­ny in 1993 and the equal­ly inspired Heroes in ’96. Final­ly, just this week, he pre­miered Lodger, with ven­er­a­ble Amer­i­can com­pos­er John Adams con­duct­ing, in Los Ange­les on what would have been Bowie’s birth­day, Jan­u­ary 8th.

Though Glass nev­er shared his thoughts about Lodger with Bowie, he may not have need­ed to. Bowie him­self felt that “Tony [Vis­con­ti] lost heart a lit­tle” dur­ing the record­ing “because it nev­er came togeth­er as eas­i­ly as both Low and “Heroes” had. This had a lot to do with my being dis­tract­ed by per­son­al events in my life,” he says, though “I would still main­tain thought that there are a num­ber of real­ly impor­tant ideas on Lodger.” It is on the ideas that Glass seized. “The writ­ing was remark­able. It was some­one who had cre­at­ed a polit­i­cal lan­guage for them­selves.”

While Glass’s oth­er Bowie sym­phonies drew direct­ly from the albums’ music (the Low sym­pho­ny opens with the cin­e­mat­ic theme from “Sub­ter­raneans”), “What I was going to do on Lodger,” says Glass, “had noth­ing to do with the music that was on the record.” He real­ized that he had been giv­en “a whole piece by a very accom­plished writer and artist who had a vision of the world” in the lyrics. Employ­ing the unique voice of singer Angélique Kid­jo, Glass made what he calls “a song sym­pho­ny” using sev­en of the “texts” (he left off “Look Back in Anger,” “D.J.” and “Red Mon­ey”).

Glass takes these “poems” as he calls them and weaves them into his own musi­cal fab­ric. He’s “uncon­cerned,” writes Ran­dal Roberts at the L.A. Times “with what Bowie would have thought of his method,” but he remem­bers Bowie was most struck in his oth­er sym­phonies by “the parts that didn’t sound very much like the orig­i­nal.” At the top of the post, hear “Warsza­wa” from Glass’s Low sym­pho­ny and lis­ten to his oth­er Bowie-inspired pieces on Spo­ti­fy. The Lodger sym­pho­ny will make its Euro­pean pre­mier at the South­bank Cen­tre in Lon­don in May of this year, and we should hope to see a record­ing released soon.

Relat­ed Con­tent:

The “David Bowie Is” Exhi­bi­tion Is Now Avail­able as an Aug­ment­ed Real­i­ty Mobile App That’s Nar­rat­ed by Gary Old­man: For David Bowie’s Birth­day Today

Stream David Bowie’s Com­plete Discog­ra­phy in a 19-Hour Playlist: From His Very First Record­ings to His Last

David Bowie’s Top 100 Books

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

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