The Map of Mathematics: An Animated Video Shows How All the Different Fields in Math Fit Together

If you’re a reg­u­lar Open Cul­ture read­er, you have hope­ful­ly thor­ough­ly immersed your­self in The Map of Physics, an ani­mat­ed video–a visu­al aid for the mod­ern age–that mapped out the field of physics, explain­ing all the con­nec­tions between clas­si­cal physics, quan­tum physics, and rel­a­tiv­i­ty.

You can’t do physics with­out math. Hence we now have The Map of Math­e­mat­ics. Cre­at­ed by physi­cist Dominic Wal­li­man, this new video explains “how pure math­e­mat­ics and applied math­e­mat­ics relate to each oth­er and all of the sub-top­ics they are made from.” Watch the new video above. You can buy a poster of the map here. And you can down­load a ver­sion for edu­ca­tion­al use here. Enjoy.

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Relat­ed Con­tent 

Jour­ney to the Cen­ter of a Tri­an­gle: Watch the 1977 Dig­i­tal Ani­ma­tion That Demys­ti­fies Geom­e­try

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

How to Defeat the US with Math: An Ani­mat­ed North Kore­an Pro­pa­gan­da Film for Kids

Free Online Math Cours­es, a sub­set of our col­lec­tion, 1,700 Free Online Cours­es from Top Uni­ver­si­ties

A Retired Math Teacher Helps Students Learn Geometry Through Quilting

Some real talk from retired geom­e­try teacher Wendy Licht­man, above, the author of sev­er­al math-themed YA nov­els:

Not many 15-year-olds care that two par­al­lel lines are crossed by a trans­ver­sal.

“But right here are two par­al­lel lines,” she con­tin­ues, point­ing to a pink and orange quilt. “and these are trans­ver­sals, and they are at a 90º angle and it feels real. You’ve got­ta get it to look right.”

The teenaged par­tic­i­pants in the Oak­land, Cal­i­for­nia pro­gram she found­ed to demys­ti­fy geom­e­try through hands-on quilt­mak­ing get it to look right by plot­ting their designs on graph paper, care­ful­ly mea­sur­ing and cut­ting shapes from bright cal­i­co of their own choos­ing. (Lic­th­man has com­mit­ted to but­ton­ing her lip if their favored print is not to her taste.)

Licht­man came up with this cre­ative approach to help a bright stu­dent who was in dan­ger of not grad­u­at­ing, hav­ing flunked geom­e­try three times.

She details their jour­ney in How to Make a Geo­met­ric Quilt, an essay for­mat­ted as step-by-step instructions…not for quilt­mak­ing but rather how those in the teach­ing pro­fes­sion can lead with humil­i­ty and deter­mi­na­tion, while main­tain­ing good bound­aries.

Some high­lights:

6. Some­time after the sewing has begun, and the math note­book is ignored for weeks, begin to wor­ry that your stu­dent is not real­ly learn­ing geom­e­try.  She’s learn­ing sewing and she’s learn­ing to fix a bro­ken bob­bin, but real­ly, geom­e­try?

7. Remind your­self that this kid needs a quilt as much as she needs geom­e­try.

8. Remem­ber, also, the very, very old woman who taught you hat-mak­ing one night long ago.  She had gone to school only through 5th grade because, she said, she was a Black child in the deep south and that’s how it was back then.  Think about how she explained to the hat-mak­ing class that to fig­ure out the length of the hat’s brim, you need­ed to mea­sure from the cen­ter to the edge with a string and then do “three of those and a lit­tle bit more,” and remem­ber how you sat in awe, because three radii and a lit­tle bit more is the def­i­n­i­tion of pi, and this hat-mak­er had evi­dent­ly dis­cov­ered for her­self the for­mu­la for cir­cum­fer­ence.

As the two become bet­ter acquaint­ed, the stu­dent let her guard down, reveal­ing more about her sit­u­a­tion while they swapped sto­ries of their moth­ers.

But this was no easy A.

In addi­tion to expect­ing reg­u­lar, punc­tu­al atten­dance, Lict­man stip­u­lat­ed that in order to pass, the stu­dent could not give the fruits of her labor away.

(Sol­id advice for cre­ators of any craft project this ambi­tious. As Deb­bie Stoller, author of Stitch ‘n Bitch: The Knit­ter’s Hand­book coun­sels:

…those who have nev­er knit some­thing have no idea how much time it took. If you give some­one a sweater, they may think that you made that in an evening when you were watch­ing a half-hour sit­com. It’s only when peo­ple actu­al­ly attempt to knit that they final­ly get this real­iza­tion, this light bulb goes on over their heads, and they real­ize that, “Wow, this actu­al­ly takes some skill and some time. I’ve got new­found respect for my grand­ma.”)

Ulti­mate­ly, Licht­man con­cludes that the five cred­its she award­ed her stu­dent could not be reduced to some­thing as sim­ple as geom­e­try or quilt-mak­ing;

You are giv­ing her cred­it for some­thing less tan­gi­ble.  Some­thing like pride.  Five cred­it hours for feel­ing she can accom­plish some­thing hard that, okay, is slight­ly relat­ed to geom­e­try.

Exam­ples of the cur­rent cohort’s work can be seen on Rock Paper Scis­sors Col­lec­tive’s Insta­gram.

Once com­plet­ed, these quilts will be donat­ed to Bay Area fos­ter chil­dren and pedi­atric patients at the local Chil­dren’s Hos­pi­tal.

via Boing­Bo­ing

Relat­ed Con­tent 

The Solar Sys­tem Quilt: In 1876, a Teacher Cre­ates a Hand­craft­ed Quilt to Use as a Teach­ing Aid in Her Astron­o­my Class

17-Year-Old Ade­line Har­ris Cre­at­ed a Quilt Col­lect­ing 360 Sig­na­tures of the Most Famous Peo­ple of the 19th Cen­tu­ry: Lin­coln, Dick­ens, Emer­son & More (1863)

Bisa Butler’s Beau­ti­ful Quilt­ed Por­traits of Fred­er­ick Dou­glass, Nina Simone, Jean-Michel Basquiat & More

Via Boing Boing

– Ayun Hal­l­i­day is the Chief Pri­ma­tol­o­gist of the East Vil­lage Inky zine and author, most recent­ly, of Cre­ative, Not Famous: The Small Pota­to Man­i­festo and Cre­ative, Not Famous Activ­i­ty Book. Fol­low her @AyunHalliday.

Why Algorithms Are Called Algorithms, and How It All Goes Back to the Medieval Persian Mathematician Muhammad al-Khwarizmi

In recent decades, a medieval Per­sian word has come to promi­nence in Eng­lish and oth­er major world lan­guages. Many of use it on a dai­ly basis, often while regard­ing the con­cept to which it refers as essen­tial­ly mys­te­ri­ous. The word is algo­rithm, whose roots go back to the ninth cen­tu­ry in mod­ern-day Greater Iran. There lived a poly­math by the name of Muham­mad ibn Musa al-Khwariz­mi, whom we now remem­ber for his achieve­ments in geog­ra­phy, astron­o­my, and math­e­mat­ics. In that last field, he was the first to define the prin­ci­ples of “reduc­ing” and “bal­anc­ing” equa­tions, a sub­ject all of us came to know in school as alge­bra (a name itself descend­ed from the Ara­bic al-jabr, or “com­ple­tion”).

Today, a good few of us have come to resent algo­rithms even more than alge­bra. This is per­haps because algo­rithms are most pop­u­lar­ly asso­ci­at­ed with the deep, unseen work­ings of the inter­net, a sys­tem with ever increas­ing influ­ence over the things we do, the infor­ma­tion we receive, and even the peo­ple with whom we asso­ciate.

Pro­vid­ed suf­fi­cient data about us and the lives we lead, so we’re giv­en to under­stand, these algo­rithms can make bet­ter deci­sions for us than we can make for our­selves. But what exact­ly are they? You can get one answer from “Why Algo­rithms Are Called Algo­rithms,” the BBC Ideas video at the top of the post.

For West­ern civ­i­liza­tion, al-Khwarizmi’s most impor­tant book was Con­cern­ing the Hin­du Art of Reck­on­ing, which was trans­lat­ed into Latin three cen­turies after its com­po­si­tion. Al-Khwarizmi’s Latinized name “Algo­rit­mi” gave rise to the word algo­ris­mus, which at first referred to the dec­i­mal num­ber sys­tem and much lat­er came to mean “a set of step-by-step rules for solv­ing a prob­lem.” It was Enig­ma code­break­er Alan Tur­ing who “worked out how, in the­o­ry, a machine could fol­low algo­rith­mic instruc­tions and solve com­plex math­e­mat­ics. This was the birth of the com­put­er age.” Now, much fur­ther into the com­put­er age, algo­rithms “are help­ing us to get from A to B, dri­ving inter­net search­es, mak­ing rec­om­men­da­tions of things for us to buy, watch, or share.”

The algo­rithm giveth, but the algo­rithm also taketh away — or so it some­times feels as we make our way deep­er into the twen­ty-first cen­tu­ry. In the oth­er BBC Ideas video just above, Jon Stroud makes an inves­ti­ga­tion into both the nature and the cur­rent uses of this math­e­mat­i­cal con­cept. The essen­tial job of an algo­rithm, as the experts explain to him, is that of pro­cess­ing data, these days often in large quan­ti­ties and of var­i­ous kinds, and increas­ing­ly with the aid of sophis­ti­cat­ed machine-learn­ing process­es. In mak­ing or influ­enc­ing choic­es humans would once have han­dled them­selves, algo­rithms do present a risk of “de-skilling” as we come to rely on their ser­vices. We all occa­sion­al­ly feel grat­i­tude for the bless­ings those ser­vices send our way, just as we all occa­sion­al­ly blame them for our dis­sat­is­fac­tions — mak­ing the algo­rithm, in oth­er words, into a thor­ough­ly mod­ern deity.

Relat­ed con­tent:

Algo­rithms for Big Data: A Free Course from Har­vard

Advanced Algo­rithms: A Free Course from Har­vard Uni­ver­si­ty

This Is Your Kids’ Brains on Inter­net Algo­rithms: A Chill­ing Case Study Shows What’s Wrong with the Inter­net Today

The Prob­lem with Face­book: “It’s Keep­ing Things From You”

The Com­plex Geom­e­try of Islam­ic Art & Design: A Short Intro­duc­tion

How Youtube’s Algo­rithm Turned an Obscure 1980s Japan­ese Song Into an Enor­mous­ly Pop­u­lar Hit: Dis­cov­er Mariya Takeuchi’s “Plas­tic Love”

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities, 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.

Bach on a Möbius Strip: Marcus du Sautoy Visualizes How Bach Used Math to Compose His Music

“A math­e­mati­cian’s favorite com­pos­er? Top of the list prob­a­bly comes Bach.” Thus speaks a reli­able source on the mat­ter: Oxford math­e­mati­cian Mar­cus du Sautoy in the Num­ber­phile video above. “Bach uses a lot of math­e­mat­i­cal tricks as a way of gen­er­at­ing music, so his music is high­ly com­plex,” but at its heart is “the use of math­e­mat­ics as a kind of short­cut to gen­er­ate extra­or­di­nar­i­ly com­plex music.” As a first exam­ple du Sautoy takes up the “Musi­cal Offer­ing,” and in par­tic­u­lar its “crab canon,” the genius of which has pre­vi­ous­ly been fea­tured here on Open Cul­ture.

Writ­ten out, Bach’s crab canon “looks like just one line of music.” But “what’s curi­ous is that when you get to the end of the music, there’s the lit­tle sym­bol you usu­al­ly begin a piece of music with.” This means that Bach wants the play­er of the piece to “play this for­wards and back­wards; he’s ask­ing you to start at the end and play it back­wards at the same time.” His com­po­si­tion thus becomes a two-voice piece made out of just one line of music going in both direc­tions. It’s the under­ly­ing math­e­mat­ics that make this, when played, more than just a trick but “some­thing beau­ti­ful­ly har­mon­ic and com­plex.”

To under­stand the crab canon or Bach’s oth­er math­e­mat­i­cal­ly shaped pieces, it helps to visu­al­ize them in uncon­ven­tion­al ways such as on a twist­ing Möbius strip, whose ends con­nect direct­ly to one anoth­er. “You can make a Möbius strip out of any piece of music,” says du Sautoy as he does so in the video. “The stun­ning thing is that when you then look at this piece of music” — that is the fifth canon from Bach’s Gold­berg Vari­a­tions — “the notes that are on one side are exact­ly the same notes as if this thing were see-through.” (Nat­u­ral­ly, he’s also pre­pared a see-through Bach Möbius strip for his view­ing audi­ence.)

In 2017 du Sautoy gave an Oxford Math­e­mat­ics Pub­lic Lec­ture on “the Sound of Sym­me­try and the Sym­me­try of Sound.” In it he dis­cuss­es sym­me­try as present in not just the Gold­berg Vari­a­tions but the twelve-tone rows com­posed in the 20th cen­tu­ry by Arnold Schoen­berg and even the very sound waves made by musi­cal instru­ments them­selves. Just this year, he col­lab­o­rat­ed with the Oxford Phil­har­mon­ic Orches­tra to deliv­er “Music & Maths: Baroque & Beyond,” a pre­sen­ta­tion that draws math­e­mat­i­cal con­nec­tions between the music, art, archi­tec­ture, and sci­ence going on in the 17th and 18th cen­turies. Bach has been dead for more than a quar­ter of a mil­len­ni­um, but the con­nec­tions embod­ied in his music still hold rev­e­la­tions for lis­ten­ers will­ing to hear them — or see them.

Relat­ed Con­tent:

Take an Intel­lec­tu­al Odyssey with a Free MIT Course on Dou­glas Hofstadter’s Pulitzer Prize-Win­ning Book Gödel, Esch­er, Bach: An Eter­nal Gold­en Braid

The Genius of J.S. Bach’s “Crab Canon” Visu­al­ized on a Möbius Strip

Visu­al­iz­ing Bach: Alexan­der Chen’s Impos­si­ble Harp

How a Bach Canon Works. Bril­liant

The Math Behind Beethoven’s Music

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities, 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.

Take an Intellectual Odyssey with a Free MIT Course on Douglas Hofstadter’s Pulitzer Prize-Winning Book Gödel, Escher, Bach: An Eternal Golden Braid

In 1979, math­e­mati­cian Kurt Gödel, artist M.C. Esch­er, and com­pos­er J.S. Bach walked into a book title, and you may well know the rest. Dou­glas R. Hof­s­tadter won a Pulitzer Prize for Gödel, Esch­er, Bach: an Eter­nal Gold­en Braid, his first book, thence­forth (and hence­forth) known as GEB. The extra­or­di­nary work is not a trea­tise on math­e­mat­ics, art, or music, but an essay on cog­ni­tion through an explo­ration of all three — and of for­mal sys­tems, recur­sion, self-ref­er­ence, arti­fi­cial intel­li­gence, etc. Its pub­lish­er set­tled on the pithy descrip­tion, “a metaphor­i­cal fugue on minds and machines in the spir­it of Lewis Car­roll.”

GEB attempt­ed to reveal the mind at work; the minds of extra­or­di­nary indi­vid­u­als, for sure, but also all human minds, which behave in sim­i­lar­ly unfath­omable ways. One might also describe the book as oper­at­ing in the spir­it — and the prac­tice — of Her­man Hesse’s Glass Bead Game, a nov­el Hesse wrote in response to the data-dri­ven machi­na­tions of fas­cism and their threat to an intel­lec­tu­al tra­di­tion he held par­tic­u­lar­ly dear. An alter­nate title (and key phrase in the book) Mag­is­ter Ludi, puns on both “game” and “school,” and alludes to the impor­tance of play and free asso­ci­a­tion in the life of the mind.

Hesse’s eso­teric game, writes his biog­ra­ph­er Ralph Freed­man, con­sists of “con­tem­pla­tion, the secrets of the Chi­nese I Ching and West­ern math­e­mat­ics and music” and seems sim­i­lar enough to Hof­s­tadter’s approach and that of the instruc­tors of MIT’s open course, Gödel, Esch­er, Bach: A Men­tal Space Odyssey. Offered through the High School Stud­ies Pro­gram as a non-cred­it enrich­ment course, it promis­es “an intel­lec­tu­al vaca­tion” through “Zen Bud­dhism, Log­ic, Meta­math­e­mat­ics, Com­put­er Sci­ence, Arti­fi­cial Intel­li­gence, Recur­sion, Com­plex Sys­tems, Con­scious­ness, Music and Art.”

Stu­dents will not study direct­ly the work of Gödel, Esch­er, and Bach but rather “find their spir­its aboard our men­tal ship,” the course descrip­tion notes, through con­tem­pla­tions of canons, fugues, strange loops, and tan­gled hier­ar­chies. How do mean­ing and form arise in sys­tems like math and music? What is the rela­tion­ship of fig­ure to ground in art? “Can recur­sion explain cre­ativ­i­ty,” as one of the course notes asks. Hof­s­tadter him­self has pur­sued the ques­tion beyond the entrench­ment of AI research in big data and brute force machine learn­ing. For all his daunt­ing eru­di­tion and chal­leng­ing syn­the­ses, we must remem­ber that he is play­ing a high­ly intel­lec­tu­al game, one that repli­cates his own expe­ri­ence of think­ing.

Hof­s­tadter sug­gests that before we can under­stand intel­li­gence, we must first under­stand cre­ativ­i­ty. It may reveal its secrets in com­par­a­tive analy­ses of the high­est forms of intel­lec­tu­al play, where we see the clever for­mal rules that gov­ern the mind’s oper­a­tions; the blind alleys that explain its fail­ures and lim­i­ta­tions; and the pos­si­bil­i­ty of ever actu­al­ly repro­duc­ing work­ings in a machine. Watch the lec­tures above, grab a copy of Hofstadter’s book, and find course notes, read­ings, and oth­er resources for the fas­ci­nat­ing course Gödel, Esch­er, Bach: A Men­tal Space Odyssey archived here. The course will be added to our list, 1,700 Free Online Cours­es from Top Uni­ver­si­ties.

Relat­ed Con­tent: 

How a Bach Canon Works. Bril­liant.

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

The Mir­ror­ing Mind: An Espres­so-Fueled Inter­pre­ta­tion of Dou­glas Hofstadter’s Ground­break­ing Ideas

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

An Introduction to Nicolas Bourbaki, One of the Most Influential Mathematicians of All Time … Who Never Actually Lived

In 20th-cen­tu­ry math­e­mat­ics, the renowned name of Nico­las Bour­ba­ki stands alone in its class — the class, that is, of renowned math­e­mat­i­cal names that don’t actu­al­ly belong to real peo­ple. Bour­ba­ki refers not to a math­e­mati­cian, but to math­e­mati­cians; a whole secret soci­ety of them, in fact, who made their name by col­lec­tive­ly com­pos­ing Ele­ments of Math­e­mat­ic. Not, mind you, Ele­ments of Math­e­mat­ics: “Bourbaki’s Ele­ments of Math­e­mat­ic — a series of text­books and pro­gram­mat­ic writ­ings first appear­ing in 1939—pointedly omit­ted the ‘s’ from the end of ‘Math­e­mat­ics,’ ” writes JSTOR Dai­ly’s Michael Barany, “as a way of insist­ing on the fun­da­men­tal uni­ty and coher­ence of a dizzy­ing­ly var­ie­gat­ed field.”

That’s mere­ly the tip of Bour­bak­i’s ice­berg of eccen­tric­i­ties. Formed in 1934 “by alum­ni of the École nor­male supérieure, a sto­ried train­ing ground for French aca­d­e­m­ic and polit­i­cal elites,” this group of high-pow­ered math­e­mat­i­cal minds set about rec­ti­fy­ing their coun­try’s loss of near­ly an entire gen­er­a­tion of math­e­mati­cians in the First World War. (While Ger­many had kept its bright­est stu­dents and sci­en­tists out of bat­tle, the French com­mit­ment to égal­ité could per­mit no such favoritism.) It was the press­ing need for revised and updat­ed text­books that spurred the mem­bers of Bour­ba­ki to their col­lab­o­ra­tive­ly pseu­do­ny­mous, indi­vid­u­al­ly anony­mous work.

“Yet instead of writ­ing text­books,” explains Quan­ta’s Kevin Hart­nett, “they end­ed up cre­at­ing some­thing com­plete­ly nov­el: free-stand­ing books that explained advanced math­e­mat­ics with­out ref­er­ence to any out­side sources.” The most dis­tinc­tive fea­ture of this already unusu­al project “was the writ­ing style: rig­or­ous, for­mal and stripped to the log­i­cal studs. The books spelled out math­e­mat­i­cal the­o­rems from the ground up with­out skip­ping any steps — exhibit­ing an unusu­al degree of thor­ough­ness among math­e­mati­cians.”  Not that Bour­ba­ki lacked play­ful­ness: “In fan­ci­ful and pun-filled nar­ra­tives shared among one anoth­er and allud­ed to in out­ward-fac­ing writ­ing,” adds Barany, “Bourbaki’s col­lab­o­ra­tors embed­ded him in an elab­o­rate math­e­mat­i­cal-polit­i­cal uni­verse filled with the abstruse ter­mi­nol­o­gy and con­cepts of mod­ern the­o­ries.”

You can get an ani­mat­ed intro­duc­tion to Bour­ba­ki, which sur­vives even today as a still-pres­ti­gious and at least nom­i­nal­ly secret math­e­mat­i­cal soci­ety, in the TED-Ed les­son above. In the decades after the group’s found­ing, writes les­son author Pratik Aghor, “Bour­rbak­i’s pub­li­ca­tions became stan­dard ref­er­ences, and the group’s mem­bers took their prank as seri­ous­ly as their work.” Their com­mit­ment to the front was total: “they sent telegrams in Bour­bak­i’s name, announced his daugh­ter’s wed­ding, and pub­licly insult­ed any­one who doubt­ed his exis­tence. In 1968, when they could no longer main­tain the ruse, the group end­ed their joke the only way they could: they print­ed Bour­bak­i’s obit­u­ary, com­plete with math­e­mat­i­cal puns.” And if you laugh at the math­e­mat­i­cal pun with which Aghor ends the les­son, you may car­ry a bit of Bour­bak­i’s spir­it with­in your­self as well.

Relat­ed Con­tent:

Beau­ti­ful Equa­tions: Doc­u­men­tary Explores the Beau­ty of Ein­stein & Newton’s Great Equa­tions

The Math­e­mat­ics Behind Origa­mi, the Ancient Japan­ese Art of Paper Fold­ing

The Unex­pect­ed Math Behind Van Gogh’s Star­ry Night

Can You Solve These Ani­mat­ed Brain Teasers from TED-Ed?

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

Why the World’s Best Math­e­mati­cians Are Hoard­ing Japan­ese Chalk

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities, 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.

Pink Floyd’s David Gilmour Composes a Soundtrack to Arthur C. Clarke’s Documentary Fractals: The Colors of Infinity

An observ­er once called the Man­del­brot Set “The Thumbprint of God,” the sim­ple equa­tion that led to the dis­cov­ery of frac­tal geog­ra­phy, chaos the­o­ry, and why games like No Man’s Sky even exist. In 1994, Arthur C. Clarke, writer of both sci­ence fic­tion and sci­ence fact, nar­rat­ed a one-hour doc­u­men­tary on the new math­e­mat­ics, called Frac­tals: The Col­ors of Infin­i­ty. If that sounds famil­iar, dear read­er, it’s because we’ve told you about it long ago. But it’s worth revis­it­ing, and it’s worth men­tion­ing that the sound­track was cre­at­ed by Pink Floyd’s David Gilmour.

To be hon­est, at first I wasn’t real­ly hear­ing that Floyd vibe, just some pleas­ant synth-strings you could find on any num­ber of doc­u­men­taries. But then Clarke explains the impli­ca­tion of the Man­del­brot equa­tion, end­ing it with “This real­ly is infin­i­ty.” And then Boom, the acid hit.

Or rather, the rain­bow com­put­er graph­ics of the end­less zoom hit, and it was unmis­tak­ably Gilmour—cue up 5:19 and be care­ful with that frac­tal, Eugene. This hap­pens again at 14:30, 25:12, 31:07, 35:46, 38:22, 43:22, 44:51, and 50:06 for those with an itchy scrub­bing fin­ger. But stick around for the whole doc, as the his­to­ry of how we got to the equa­tion, its prece­dents in nature and art, and the impli­ca­tions only hint­ed at in the pro­gram, all make for inter­est­ing view­ing.

The music will remind you in places of “Shine On Your Crazy Dia­mond”, “Obscured by Clouds,” and “On the Run.” When a DVD was released years lat­er, a spe­cial fea­ture iso­lat­ed just Gilmour’s music and the frac­tal ani­ma­tion.

Gilmour has con­tributed sound­track work to oth­er pro­grams. He has an uncred­it­ed per­for­mance on Guy Pratt’s sound­track from 1995’s Hack­ers; inci­den­tal music for 1992’s Ruby Takes a Trip with Ruby Wax; and a 1993 doc­u­men­tary on the arts and drug use called The Art of Trip­ping.

There are no offi­cial releas­es of this sound­track work, but one user has put up 16 min­utes of the Colours of Infin­i­ty music over at Sound­Cloud.

 

Relat­ed Con­tent:

David Gilmour, David Cros­by & Gra­ham Nash Per­form the Pink Floyd Clas­sic, “Shine on You Crazy Dia­mond” (2006)

Watch David Gilmour Play the Songs of Syd Bar­rett, with the Help of David Bowie & Richard Wright

Arthur C. Clarke Pre­dicts the Future in 1964 … And Kind of Nails It

Ted Mills is a free­lance writer on the arts who cur­rent­ly hosts the Notes from the Shed pod­cast and is the pro­duc­er of KCR­W’s Curi­ous Coast. You can also fol­low him on Twit­ter at @tedmills, and/or watch his films here.

The Mathematics Behind Origami, the Ancient Japanese Art of Paper Folding

The two char­ac­ters at the core of origa­mi (折り紙), one of the best-known Japan­ese words around the world, mean “fold­ing” and “paper.” You might well have guessed that, but giv­en the vari­ety and elab­o­rate­ness of the con­struc­tions pro­duced by origa­mi mas­ters over the past few cen­turies, the sim­plic­i­ty of the prac­tice’s basic nature bears repeat­ing. Those mas­ters must devel­op no slight degree of man­u­al dex­ter­i­ty, it goes with­out say­ing, but also a for­mi­da­ble math­e­mat­i­cal under­stand­ing of their medi­um. In many cas­es that under­stand­ing is intu­itive; in the TED-Ed les­son above, origa­mi artist Evan Zodl makes it explic­it.

Zodl’s les­son explains that “though most origa­mi mod­els are three-dimen­sion­al, their crease pat­terns are usu­al­ly designed to fold flat, with­out intro­duc­ing any new creas­es or cut­ting the paper.”(Incidentally, the Japan­ese word for paper art involv­ing cuts is kiriga­mi, or 切り紙.)

An “abstract, 2D design” thus becomes, in the origa­mi mas­ter’s hands, “a 3D form,” but only in accor­dance with a set of four sim­ple rules Zodl explains. He does so clear­ly and under­stand­ably — and in a way that for many of us may exhume buried geom­e­try-class mem­o­ries — but like actu­al works of origa­mi, they’re bet­ter shown than described: hence the vivid accom­pa­ny­ing ani­ma­tions of Char­lotte Arene.

Origami’s prin­ci­ples and prod­ucts may be fas­ci­nat­ing to con­tem­plate, but “the abil­i­ty to fold a large sur­face into a com­pact shape” has also proven to have seri­ous real-world appli­ca­tions. Zodl points to an origa­mi-based re-imag­i­na­tion of “the tra­di­tion­al stent graft, a tube used to open and sup­port dam­aged blood ves­sels.” This in addi­tion to “airbags, solar arrays, self-fold­ing robots, and even DNA nanos­truc­tures” — as well as a mas­sive “star shade” for space tele­scopes that blocks the glare of near­by stars. If you’d like to get start­ed on your own tac­tile under­stand­ing of all this, do have a look at Zodl’s own Youtube chan­nel, as well as oth­ers like Origa­mi Instruc­tions. Don’t let the elab­o­rate­ly fold­ed flow­ers, boats, or ani­mals you’ve seen intim­i­date you; start with a sim­ple box and work your way up from there. If origa­mi shows us any­thing, after all, it’s that com­plex­i­ty begins with sim­plic­i­ty.

Relat­ed Con­tent:

An Origa­mi Samu­rai Made from a Sin­gle Sheet of Rice Paper, With­out Any Cut­ting

A Data­base of Paper Air­plane Designs: Hours of Fun for Kids & Adults Alike

MIT Cre­ates Amaz­ing Self-Fold­ing Origa­mi Robots & Leap­ing Chee­tah Robots

Design­er Cre­ates Origa­mi Card­board Tents to Shel­ter the Home­less from the Win­ter Cold

The Art of Let­ter­lock­ing: The Elab­o­rate Fold­ing Tech­niques That Ensured the Pri­va­cy of Hand­writ­ten Let­ters Cen­turies Ago

The Mak­ing of Japan­ese Hand­made Paper: A Short Film Doc­u­ments an 800-Year-Old Tra­di­tion

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities, lan­guage, and cul­ture. His projects include the Sub­stack newslet­ter Books on Cities, 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.

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Open Culture was founded by Dan Colman.