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

in Math, Music | May 13th, 2021

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.

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

in Art, Math, Technology, TED Talks | March 23rd, 2021

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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Three Amateur Cryptographers Finally Decrypted the Zodiac Killer’s Letters: A Look Inside How They Solved a Half Century-Old Mystery

in History, Math | December 18th, 2020

If we envi­sion ser­i­al killers as fig­ures who taunt law enforce­ment with cryp­tic mes­sages sent to the media, we do so in large part because of the Zodi­ac Killer, who ter­ror­ized north­ern Cal­i­for­nia in the late 1960s and ear­ly 70s. Though he seems to have stopped killing more than half a cen­tu­ry ago, he remains an object of great fas­ci­na­tion (and even became the sub­ject of David Fincher’s acclaimed film Zodi­ac in 2007). As thor­ough­ly as the case has been inves­ti­gat­ed, much remains unknown — not least what he actu­al­ly said in some of his cod­ed let­ters. But just this month, a team of three cryp­tog­ra­phy enthu­si­asts man­aged to break one of the Zodi­ac’s ciphers, final­ly reveal­ing the con­tents of a 51-year old let­ter.

The Zodi­ac wrote this par­tic­u­lar com­mu­niqué in a trans­po­si­tion cipher, which, as Ars Tech­ni­ca’s Dan Good­in writes, uses “rules to rearrange the char­ac­ters or groups of char­ac­ters in the mes­sage.” In the case of the 340, named for the num­ber of sym­bols, the con­tent “was prob­a­bly rearranged by manip­u­lat­ing tri­an­gu­lar sec­tions cut from mes­sages writ­ten into rec­tan­gles.” For the past half-cen­tu­ry, nobody could suc­cess­ful­ly return the text to its orig­i­nal arrange­ment, but in 2020, there’s an app for that. Or rather, a soft­ware engi­neer named David Oran­chak, a math­e­mati­cian named Sam Blake, and a pro­gram­mer named Jarl Van Eycke made an app for that. Good­in quotes Oran­chak as say­ing the three had been “work­ing on and off on solv­ing the 340 since 2006.”

You can see Oran­chak explain how he and his col­lab­o­ra­tors final­ly cracked the 340’s cipher in the video at the top of the post, the final episode of his five-part series Let’s Crack the Zodi­ac. This was­n’t a mat­ter of sim­ply whip­ping up the right piece of arti­fi­cial intel­li­gence and let­ting it rip: they had to gen­er­ate hun­dreds of thou­sands of per­mu­ta­tions of the mes­sage as well as attempts at decryp­tions of those mes­sages. And even when rec­og­niz­able words and phras­es began to emerge in the results — “TRYING TO CATCH ME,” “THE GAS CHAMBER” — quite a bit of tri­al, error, and thought, remained to be done. It helped that Oran­chak knew his Zodi­ac his­to­ry, such as that some­one claim­ing to be the killer men­tioned not want­i­ng to be sent to the gas cham­ber when he called in to a local tele­vi­sion show on Octo­ber 20, 1969, two weeks before the 340 was received.

Was it real­ly him? The 340, when final­ly decod­ed — a process com­pli­cat­ed by the mis­takes the Zodi­ac made, not just in spelling but in exe­cut­ing his labo­ri­ous, ful­ly ana­log encryp­tion process — seems to pro­vide the answer:

I HOPE YOU ARE HAVING LOTS OF FUN IN TRYING TO CATCH ME
THAT WASNT ME ON THE TV SHOW
WHICH BRINGS UP A POINT ABOUT ME
I AM NOT AFRAID OF THE GAS CHAMBER
BECAUSE IT WILL SEND ME TO PARADICE ALL THE SOONER
BECAUSE I NOW HAVE ENOUGH SLAVES TO WORK FOR ME
WHERE EVERYONE ELSE HAS NOTHING WHEN THEY REACH PARADICE
SO THEY ARE AFRAID OF DEATH
I AM NOT AFRAID BECAUSE I KNOW THAT MY NEW LIFE IS
LIFE WILL BE AN EASY ONE IN PARADICE DEATH

“The mes­sage does­n’t real­ly say a whole lot,” admits Oran­chak. “It’s more of the same atten­tion-seek­ing junk from Zodi­ac. We were dis­ap­point­ed that he did­n’t put any per­son­al­ly iden­ti­fy­ing infor­ma­tion in the mes­sage, but we did­n’t expect him to.” The Zodi­ac Killer remains uniden­ti­fied, and indeed remains one of recent his­to­ry’s more com­pelling vil­lains, not just to those with an inter­est in true crime, but to those with an inter­est in cryp­tog­ra­phy as well. For two more mes­sages still remain to be decod­ed, and in one of them he offers a short cipher that, he writes, con­tains his name — but then, if there’s any cor­re­spon­dent we should­n’t rush to take at his word, it’s this one.

Relat­ed Con­tent:

Arti­fi­cial Intel­li­gence May Have Cracked the Code of the Voyn­ich Man­u­script: Has Mod­ern Tech­nol­o­gy Final­ly Solved a Medieval Mys­tery?

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

How British Code­break­ers Built the First Elec­tron­ic Com­put­er

The Ser­i­al Killer Who Loved Jazz: The Infa­mous Sto­ry of the Axe­man of New Orleans (1919)

The Grue­some Doll­house Death Scenes That Rein­vent­ed Mur­der Inves­ti­ga­tions

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, on Face­book, or on Insta­gram.

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This Is What an 1869 MIT Entrance Exam Looks Like: Could You Have Passed the Test?

in Education, Math, MIT | May 27th, 2020

The late 19th Cen­tu­ry was the time of Charles Dar­win and James Clerk Maxwell, of Thomas Edi­son and Alexan­der Gra­ham Bell. It was a gold­en age of sci­ence and tech­nol­o­gy. So you might won­der how hard it was to get into one of the top tech­ni­cal uni­ver­si­ties in that era.

The answer, accord­ing to this video? Not very hard.

At least that was the case in 1869 at the Mass­a­chu­setts Insti­tute of Tech­nol­o­gy, or MIT,  as the young Aus­tralian sci­ence and math teacher Toby Hendy explains on her excel­lent YouTube chan­nel, Tibees. MIT was brand new and des­per­ate for tuition rev­enue in 1869, so the object of the test was­n’t to whit­tle a mas­sive field of appli­cants down to a man­age­able size. It was sim­ply to make sure that incom­ing stu­dents could han­dle the work.

MIT opened in 1865, just after the end of the Civ­il War. The idea was to cre­ate a Euro­pean-style poly­tech­nic uni­ver­si­ty to meet the demands of an increas­ing­ly indus­tri­al econ­o­my. The orig­i­nal cam­pus was in Boston, across the Charles Riv­er from its cur­rent loca­tion in Cam­bridge. Only 15 stu­dents signed up in 1865. Tuition was $100 for the whole year. There was no for­mal entrance test. Accord­ing to an arti­cle from the school’s Archives and Spe­cial Col­lec­tions,

The “con­di­tions for admis­sion” sec­tion of MIT’s cat­a­logue for 1865–66 indi­cates that can­di­dates for admis­sion as first year stu­dents must be at least six­teen years old and must give sat­is­fac­to­ry evi­dence “by exam­i­na­tion or oth­er­wise” of a com­pe­tent train­ing in arith­metic, geom­e­try, Eng­lish gram­mar, geog­ra­phy, and the “rudi­ments of French.” Rapid and leg­i­ble hand­writ­ing was also stressed as being “par­tic­u­lar­ly impor­tant.” By 1869 the hand­writ­ing require­ment and French had been dropped, but alge­bra had been added and stu­dents need­ed to pass a qual­i­fy­ing exam in the required sub­ject areas. An ancil­lary effect was to pro­tect unqual­i­fied stu­dents from dis­ap­point­ment and pro­fes­sors from wast­ing their time.

A cou­ple of years ear­li­er, in 1867, the MIT Exec­u­tive Com­mit­tee report­ed that fac­ul­ty mem­bers had felt it nec­es­sary to ask par­ents of “some incom­pe­tent and inat­ten­tive stu­dents to with­draw them from the school, wish­ing to spare them the mor­ti­fi­ca­tion of an exam­i­na­tion which it was cer­tain they could not pass.”

Nowa­days, the stu­dents who make it into MIT have aver­age SAT and ACT scores in the 99th per­centile. Of 21,312 first-year appli­cants hop­ing to join the Class of 2023, only 1,427 made it. That’s an admis­sion rate of 6.7 per­cent. What a dif­fer­ence 150 years can make!

To take the 1869 entrance exam­i­na­tion in Eng­lish, Alge­bra, Geom­e­try and Arith­metic, and to see the cor­rect answers, vis­it this cached arti­cle from the MIT web­site.

Relat­ed Con­tent:

Free Online Math Cours­es

Albert Ein­stein’s Grades: A Fas­ci­nat­ing Look at His Report Cards

Teacher Calls Jacques Der­ri­da’s Col­lege Admis­sion Essay on Shake­speare “Quite Incom­pre­hen­si­ble” (1951)

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The Shortest-Known Paper Published in a Serious Math Journal: Two Succinct Sentences

in Math | February 27th, 2020

shortest math paper

Euler’s con­jec­ture, a the­o­ry pro­posed by Leon­hard Euler in 1769, hung in there for 200 years. Then L.J. Lan­der and T.R. Parkin came along in 1966, and debunked the con­jec­ture in two swift sen­tences. Their arti­cle — which is now open access and can be down­loaded here — appeared in the Bul­letin of the Amer­i­can Math­e­mat­i­cal Soci­ety. If you’re won­der­ing what the con­jec­ture and its refu­ta­tion are all about, you might want to ask Cliff Pick­over, the author of 45 books on math and sci­ence. He brought this curi­ous doc­u­ment to the web back in 2015.

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:

60 Free Online Math Cours­es

Free Math Text­books

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

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

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Discover Kōlams, the Traditional Indian Patterns That Combine Art, Mathematics & Magic

in Art, Math, Religion | May 20th, 2019

Have accom­plished abstract geo­met­ri­cal artists come out of any demo­graph­ic in greater num­bers than from the women of South Asia? Not when even the most demand­ing art-school cur­ricu­lum can’t hope to equal the rig­or of the kōlam, a com­plex kind of line draw­ing prac­ticed by women every­where from India to Sri Lan­ka to Malaysia to Thai­land. Using hum­ble mate­ri­als like chalk and rice flour on the ground in front of their homes, they inter­weave not just lines, shapes, and pat­terns but reli­gious, philo­soph­i­cal, and mag­i­cal motifs as well — and they cre­ate their kōlams anew each and every day.

“Feed­ing A Thou­sand Souls: Kōlam” by Thacher Gallery at the Uni­ver­si­ty of San Fran­cis­co is licensed under CC BY-SA 2.0

“Tak­ing a clump of rice flour in a bowl (or a coconut shell), the kōlam artist steps onto her fresh­ly washed can­vas: the ground at the entrance of her house, or any patch of floor mark­ing an entry­point,” writes Atlas Obscu­ra’s Rohi­ni Cha­ki.

“Work­ing swift­ly, she takes pinch­es of rice flour and draws geo­met­ric pat­terns: curved lines, labyrinthine loops around red or white dots, hexag­o­nal frac­tals, or flo­ral pat­terns resem­bling the lotus, a sym­bol of the god­dess of pros­per­i­ty, Lak­sh­mi, for whom the kōlam is drawn as a prayer in illus­tra­tion.”

Col­or­ful Kolam — Sivasankaran — Own work

Kōlams are thought to bring pros­per­i­ty, but they also have oth­er uses, such as feed­ing ants, birds, and oth­er pass­ing crea­tures. Cha­ki quotes Uni­ver­si­ty of San Fran­cis­co The­ol­o­gy and Reli­gious Stud­ies pro­fes­sor Vijaya Nagara­jan as describ­ing their ful­fill­ing the Hin­du “karmic oblig­a­tion” to “feed a thou­sand souls.” Kōlams have also become an object of gen­uine inter­est for math­e­mati­cians and com­put­er sci­en­tists due to their recur­sive nature: “They start out small, but can be built out by con­tin­u­ing to enlarge the same sub­pat­tern, cre­at­ing a com­plex over­all design,” Cha­ki writes. “This has fas­ci­nat­ed math­e­mati­cians, because the pat­terns elu­ci­date fun­da­men­tal math­e­mat­i­cal prin­ci­ples.”

“Kolam” by resakse is licensed under CC BY-ND 2.0

Like any tra­di­tion­al art form, the kōlam does­n’t have quite as many prac­ti­tion­ers as it used to, much less prac­ti­tion­ers who can meet the stan­dard of mas­tery of com­plet­ing an entire work with­out once stand­ing up or even lift­ing their hand. But even so, the kōlam is hard­ly on the brink of dying out: you can see a few of their cre­ators in action in the video at the top of the post, and the age of social media has offered kōlam cre­ators of any age — and now even the occa­sion­al man — the kind of expo­sure that even the busiest front door could nev­er match. Some who get into kōlams in the 21st cen­tu­ry may want to cre­ate ones that show ever more com­plex­i­ty of geom­e­try and depth of ref­er­ence, but the best among them won’t for­get the mean­ing, accord­ing to Cha­ki, of the for­m’s very name: beau­ty.

Read more about kōlams at Atlas Obscu­ra.

Relat­ed Con­tent:

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

New Iran­ian Video Game, Engare, Explores the Ele­gant Geom­e­try of Islam­ic Art

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

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, on Face­book, or on Insta­gram.

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Why the World’s Best Mathematicians Are Hoarding Japanese Chalk

in Math | May 7th, 2019

Here’s the lat­est from Great Big Sto­ry: “Once upon a time, not long ago, the math world fell in love … with a chalk. But not just any chalk! This was Hagoro­mo: a Japan­ese brand so smooth, so per­fect that some won­dered if it was made from the tears of angels. Pen­cils down, please, as we tell the tale of a writ­ing imple­ment so irre­place­able, pro­fes­sors stock­piled it.”

Head over to Ama­zon and try to buy it, and all you get is: “Cur­rent­ly unavail­able. We don’t know when or if this item will be back in stock.” Indeed, they’ve stock­piled it all.

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:

Stephen Hawking’s Lec­tures on Black Holes Now Ful­ly Ani­mat­ed with Chalk­board Illus­tra­tions

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

Free Online Math Cours­es

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Pioneering Computer Scientist Grace Hopper Shows Us How to Visualize a Nanosecond (1983)

in Computer Science, Math, Physics | May 7th, 2019

Human imag­i­na­tion seems seri­ous­ly lim­it­ed when faced with the cos­mic scope of time and space. We can imag­ine, through stop-motion ani­ma­tion and CGI, what it might be like to walk the earth with crea­tures the size of office build­ings. But how to wrap our heads around the fact that they lived hun­dreds of mil­lions of years ago, on a plan­et some four and a half bil­lion years old? We trust the sci­ence, but can’t rely on intu­ition alone to guide us to such mind-bog­gling knowl­edge.

At the oth­er end of the scale, events mea­sured in nanosec­onds, or bil­lionths of a sec­ond, seem incon­ceiv­able, even to some­one as smart as Grace Hop­per, the Navy math­e­mati­cian who invent­ed COBOL and helped built the first com­put­er. Or so she says in the 1983 video clip above from one of her many lec­tures in her role as a guest lec­tur­er at uni­ver­si­ties, muse­ums, mil­i­tary bod­ies, and cor­po­ra­tions.

When she first heard of “cir­cuits that act­ed in nanosec­onds,” she says, “bil­lionths of a sec­ond… Well, I didn’t know what a bil­lion was…. And if you don’t know what a bil­lion is, how on earth do you know what a bil­lionth is? Final­ly, one morn­ing in total des­per­a­tion, I called over the engi­neer­ing build­ing, and I said, ‘Please cut off a nanosec­ond and send it to me.” What she asked for, she explains, and shows the class, was a piece of wire rep­re­sent­ing the dis­tance a sig­nal could trav­el in a nanosec­ond.

Now of course it wouldn’t real­ly be through wire — it’d be out in space, the veloc­i­ty of light. So if we start with a veloc­i­ty of light and use your friend­ly com­put­er, you’ll dis­cov­er that a nanosec­ond is 11.8 inch­es long, the max­i­mum lim­it­ing dis­tance that elec­tric­i­ty can trav­el in a bil­lionth of a sec­ond.

Fol­low the rest of her expla­na­tion, with wire props, and see if you can bet­ter under­stand a mea­sure of time beyond the reach­es of con­scious expe­ri­ence. The expla­na­tion was imme­di­ate­ly suc­cess­ful when she began using it in the late 1960s “to demon­strate how design­ing small­er com­po­nents would pro­duce faster com­put­ers,” writes the Nation­al Muse­um of Amer­i­can His­to­ry. The bun­dle of wires below, each about 30cm (11.8 inch­es) long, comes from a lec­ture Hop­per gave muse­um docents in March 1985.

Pho­to via the Nation­al Muse­um of Amer­i­can His­to­ry

Like the age of the dinosaurs, the nanosec­ond may only rep­re­sent a small frac­tion of the incom­pre­hen­si­bly small units of time sci­en­tists are even­tu­al­ly able to measure—and com­put­er sci­en­tists able to access. “Lat­er,” notes the NMAH, “as com­po­nents shrank and com­put­er speeds increased, Hop­per used grains of pep­per to rep­re­sent the dis­tance elec­tric­i­ty trav­eled in a picosec­ond, one tril­lionth of a sec­ond.”

At this point, the map becomes no more reveal­ing than the unknown ter­ri­to­ry, invis­i­ble to the naked eye, incon­ceiv­able but through wild leaps of imag­i­na­tion. But if any­one could explain the increas­ing­ly inex­plic­a­ble in terms most any­one could under­stand, it was the bril­liant but down-to-earth Hop­per.

via Kot­tke

Relat­ed Con­tent:

Meet Grace Hop­per, the Pio­neer­ing Com­put­er Sci­en­tist Who Helped Invent COBOL and Build the His­toric Mark I Com­put­er (1906–1992)

The Map of Com­put­er Sci­ence: New Ani­ma­tion Presents a Sur­vey of Com­put­er Sci­ence, from Alan Tur­ing to “Aug­ment­ed Real­i­ty”

Free Online Com­put­er Sci­ence Cours­es 

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

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