Max Cooper - Aleph 2 (Official Video by Martin Krzywinski)

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This isn’t a traditional music video. As part of my new AV show I’ve been working on different ways of visualising the infinite. In collaboration with Martin Krzywinski, we set out to explore some of Georg Cantor’s ground-breaking ideas on different sizes of infinity.
What you see is an authentic numerical rendering of Cantor’s work, and if you’re willing to spend the time reading about what each part shows it should provide real insight into some exotic ideas.
The video begins by counting the natural numbers 1, 2, 3, and so on. This list continues forever, but can be thought of as a single entity: the infinite “set” of natural numbers.
We next look at the set of integers (whole numbers including negative numbers), and pair naturals off with integers.This process is called a bijection. Two sets with a bijection have the same size, or “cardinality”. A set with a bijection to the naturals is considered “countable”.
Even though the cardinalities of the naturals and integers are infinite, they’re the same “kind” of infinity. This first (and smallest) infinity is called Aleph 0 (Aleph numbers and section labels shown top left).
Cantor's diagonal progression between fractions (rationals) and natural numbers is demonstrated next. We build up an infinite table of fractions and then apply his pairing function, which snakes across the table, to match up every fraction with a unique natural. A bijection. So, the cardinality of rationals is the same as naturals, and we see that the rationals are countable.
Our story of infinity now expands in scope to include uncountable infinite sets-those that are infinite but for which there is no bijection with the naturals. Cantor’s diagonal argument is visualized to make this proof by contradiction. First, we assume that there is bijection between the naturals and the “reals” (numbers with decimal expansions), and write a list of reals each assigned a natural number to count them. But we can see that whatever our countable list of real numbers contains, we can always change one digit of each member of the list and work through them all diagonally, to construct a new number which is not on the list. This proves that bijection between the naturals and the reals cannot exist, and the reals, the numbers with (infinite) decimal digits, are uncountably infinite - a bigger type of infinity.
There are many sets that, like the reals, are larger than the naturals. We can use the naturals to construct one such set: the power set, which is the set of all possible combinations of natural numbers. We build up the power set by sampling from the first few naturals-a process that rapidly explodes in complexity.
The size of the set of reals, the so-called cardinality of the continuum is the same as the size of the power set of naturals. But we don’t know if any other sizes of infinity exist between the countable naturals and the uncountable continuum of the reals. This question is settled via the “Continuum Hypothesis”. If it’s true, then the cardinality of the continuum is Aleph 1, which is the next smallest infinity after Aleph 0. But because we don’t know whether the Continuum Hypothesis is true, all we can say is that the cardinality of the continuum is equal to or larger than Aleph 1.
In fact, the Continuum Hypothesis is apparently formally undecidable and our mathematics can work regardless whether it is true or false. Each assumption leads to different and contradictory-but internally consistent-outcomes. There is no doubt that this formal undecidability of the continuum hypothesis led to bouts of anxiety and instability in the minds of its early pioneers. Imagine working hard to prove something is true one day, only to prove that it is false the next.
We go past Aleph 1 and reach the lofty infinite heights of Aleph 2, which we visually show by power sets of reals, whose cardinality is Aleph 2 if the Continuum Hypothesis is true (as we assume it is for the animation). We can keep going to Aleph 3 (power sets of power sets of reals) and beyond, but Aleph 2 seems to capture the basic incomprehensible nature of the whole thing for me, and musically I maxed out my distortion chaos just getting to Aleph 2 so I had to end there!
That may sound a little impenetrable explained so briefly, but the point is that the essence of the techniques which put the infinite onto firm mathematical grounds by Cantor have been visualised. And they form their own equally intense aesthetic for storytelling in the live show context. It’s annoying it came out looking a bit Matrix, but there you go, that’s what it looked like, and the idea had to be shown as clearly as possible.
For a more quantitative explanation of all of this, see Martin’s pages at: mkweb.bcgsc.ca/...
www.yearningfo...

[@maxcoopermax]

Buy/stream: ffm.to/yearningfortheinfinite Subscribe: bit.ly/sub2maxcooper and enable alerts 🛎️

[@CaptainPilipinas]

music aside from this. Hrm.... so the [Sky] vs the *[Deep]* kind of cosmologies then.... (fictional-wise and a kind of reminder that I see here).

[@alystair]

No option to buy video?

[@NullifierMotion]

KZbin video compression can’t keep up with the pace of this gorgeousness

[@sugnasugna]

Karen Nullifier Grigorean actually looks surprisingly good maybe they white listed this guy for compression

[@martin-krzywinski]

You're right. The compression is shrinking the color gamut. The red was richer RGB(255,30,30) in our master mix but gets washed out by the chroma subsampling.

[@sugnasugna]

Martin Krzywinski that’s interesting it still looked amazing man

[@NullifierMotion]

Angus menegon yeah, it seems that the quality got better, can’t see any artifacts anymore

[@daveachuk]

@@martin-krzywinski I suspect if you spent a few million years trying out different timings, you might be able to get the blank screen -> number screen strobes to align with the I-frames in the KZbin re-compression, and that would get a better result. Right now I think in many of those strobing sections it is having to generate the image for the text/numbers with P-frames which are basically a video version of a diff, but are given much-reduced bandwidth compared to I-frames, so they'll never be able to keep up (which will affect both the chroma and luma). I had problems with a couple of my vids not playing nice with YT so did a custom-tuned encode and made them available for download for a couple bucks... I would happily pay a few dollars for 4K high-quality renders of yours and other videos from Max's collaborators!

[@Spawningtriplets]

Never seen anyone so simply, intuitively, beautifully, yet coldly express the orders of infinity. Music fits brilliantly too on many levels. Absolutely amazing.

[@midknight1339]

Vi Hart has some great intuitive explanations, although they are certainly not cold

[@mrpicky1868]

watch weavals new clip

[@daxtronus]

I’d absolutely love to see a sci-fi movie scored by you. Wouldn’t matter what it was about or who it stars, I’d just know that with music THIS good, it would be an amazing film.

[@ABDALLAHJu199]

The visuals are unreal, I keep on introducing my friends to these videos and they always get astonished. EDIT: Please consider 4k for future work

[@billB101]

4K render times with motion graphics take a lot longer for not a lot of difference. Bit pointless for youtube releases.

[@FunctionGermany]

@@billB101 these aren't very complicated motion graphics. and even without the scene being 4K, an upscaled 4K upload would increase the bitrate that KZbin supplies for it's conversion, so individual frames like in the flashing parts of the animation would pop a bit more, with less noise / blocking.

[@billB101]

@@FunctionGermany This one maybe, some of the other videos for Max Copper are pretty complicated though. You can always watch on Vimeo.

[@FunctionGermany]

@@billB101 good point

[@martin-krzywinski]

We can render at 4k pretty easily but KZbin compression kills the effect. Not just time compression but also chroma: the red was designed to be much (255,30,30) richer than what you see here. You have to see it live at one of Max's shows ;p

[@quaidcarlobulloch9300]

the next generation of art, and I want to be a part of it

[@markmarkmark_]

Company: We are sorry we have to make some budget cuts and can't afford another month of Adobe CC subscription Editor: It's fine, I will just use the command prompt

[@Hrosade]

Max, please never stop doing this! Your music is so remarkably beautiful, it eases my mind .

[@MsSovereign1214]

this is one of the most beautiful things ive ever seen and i dont know why

[@kogbechie123]

probs should have a seizure warning but this vid was absolutely amazing

[@louper3002]

Thought you were joking until I got to the halfway mark lol

[@RishiPurkayastha-it4jz]

Oh shoot this is a problem. People with photosensitive epilepsy will have to avoid seeing this video or they could end up having a seizure.

[@ethancrowe280]

@Danny Boy Jango well aren't you edgy. I hope you know that you made yourself out be pathetic.

[@user-md3is4dq2d]

@@ethancrowe280 nobody actually cares

[@user-md3is4dq2d]

There's a long build up before the flashing, people with epilepsy can usually tell a video like this could contain flashing images

[@xmasu]

ASCII Art on a whole new level...made me nearly trippin'

[@Shnowz]

check out t69 collapse by aphex twin for some crazy ascii visuals

[@Mithrimil]

@Melanie Boots You do realize thats how a lot of the oldest games were made, right?

[@romanenkostas]

I cried while watching this. Just a masterpiece both musically and visually! I immediately remembered the "Pi" movie.

[@wugu42]

«Пи» отличный, кстати.

[@Bladavia]

You sir are a man of culture. Pi is so good. Also featuring the game of Go, which is a plus.

[@blackknightsatellite3847]

I cried Tears of Joy when listening to "Says" from Nils Frahm for the first Time :-)

[@L-in-oleum]

12:50, press return.

[@junkyarddog303]

Jesus Christ this is what I’ve unknowingly been waiting for. A tune hasn’t hit me the same way as this since 1997’s ‘High Noon’ by DJ Shadow. Cheers big time Max.

[@mcbpete]

* Flashbacks of repeatedly failing at TIS-100 challenges *

[@tenet-rotas]

can relate

[@SuperGheppio]

My God XD

[@UncoveredTruths]

what a mood

[@futrey9353]

who even won

[@TR13400]

Incredibly beautiful song and visual.

[@sab1229]

this is one of the most awe-inspiring, beautiful things i've ever seen

[@matveyboayr]

Stunning work of art

[@stnkr_5508]

Indredible, I was completely hypnotized by the video and the music, both match perfectly.

[@martin-krzywinski]

Thanks! I took great care to match the animation and scene phrasing to the beat (118 bpm).

[@nickpiovesan4361]

“This may sound a little impenetrable, explained so briefly...” Yup

[@Mority90]

Great!

[@vanakryptaaphrodisia1435]

That synchronizing glitch and music was totally astounding to me. Excellent work! I should remember your work into my Hall of Fame!

[@olfmombach260]

3:05 Love that visualisation of the diagonality proof

[@zmliore]

This drums 😍

[@rusnor]

Just. a. masterpiece. Listening to this music and watching this art gives me the same feeling of being interested, inspired, lively and sensual, that a good poem or painting can give. I feel happy to be involved in it. The language of art is changing, but its deep inner content is staying the same. It's all about us. Electronic music and digital art are proved not to be just toys for playing, but to be the same fully informative languages as were the traditional languages of art.

[@susakreuzuxinformationdesi4311]

🖤♥️🖤 love the laconic ending after the climax🎈

[@martin-krzywinski]

A happy ending is a laconic ending. :)

[@maraoz]

Holy crap this is a masterpiece

[@TzadikTheManic]

Fantastic!! “Aleph 2” is also the title of one in a series of compositions by the one & only John Zorn

[@TzadikTheManic]

Yes indeed, nice reference. And, PIHKAL as you likely know is an acronym: *Phenethylamines I Have Known And Loved* ;)

[@eulerpie]

I was looking to see about finding an explanation on higher cardnality and found this. Completely blown away, very well made.

[@stephenwalker4723]

Hey max love your music and visuals! From South Africa🐆

[@camerontubb895]

Without a doubt the best music videos are by Max cooper! Whenever I get a notification for a release I always wait so I can sit in a dark room speaker up and sit back and enjoy!

[@CatzNGaz]

The commitment to discovering truths in Set Theory is remarkable by itself.

[@mindremapping-themindsmirr3679]

YES!!!!

[@MichaNovako]

Sitting back and just watching this on full screen was an absolute journey. Late to the party but I am here to stay.

[@twentysevenkey]

This just gave me the most intensive Nerdgasm i've ever had!

[@mees8711]

The Buzz Lightyear theme song. To Infinity... and Beyond!

[@pattyluss]

Gorgeous

[@dischargedarrowgetback4322]

I saw a movie with diagonal theory for the first time! ! Super Amazing!

[@thestuffedman]

Super... !

[@acidmer]

Це щось неймовірне!

[@Kalledussin]

Fantastic music and the best videos in the business! Love your style max!

[@ZomgGames]

i think this may be best video on channel

[@TheChazas]

Drop 4:01 honestly sounds like done on "M83 - This Bright Flash" song, you can literally hear it in the background.

[@chris-hayes]

Super cool! I love the description into how thought-out everything is. As a web developer I feel a bit inspired by the beautiful animations and curious how this was rendered.

[@chris-hayes]

Martin Krzywinski actually has a in-depth explanation how the video was rendered at mkweb.bcgsc.ca/infinity/method.mhtml Super interesting, the video can be succinctly described as a 192 × 83 × 9,473 matrix. 192 chars across, 83 vertical, 9,473 frames in total. Timing however, sounds like the real pain with this one.

[@chris-hayes]

Wish we could experience this video in its original terminal glory. Or something like asciinema.org/ would be amazing.

[@climbtheladder9440]

A visual representation of what numbers can/are doing. Awesome.

[@blobby750]

Went to a special place first time i heard this. Then I come hear to listen again and all everyone talks about is the video.

[@jonathanjoly9677]

A deep jump in the Matrix !!! I almost had a epileptic crisis !!! Nice job

[@georginabyrom8844]

The combined effect of track and vid was mindblowing....what a trip.

[@gardikagigih5704]

this music and this video is sooo sick!

[@Phntm213]

As someone who read the book Aleph by Paul blablabla, and someone that is into chakras and spirituality, this is something fine to listen to, to watch to

[@Nytra_]

I love this. Even after initially just watching the video I was blown away by the music and how the numbers reacted. Then I learn that I actually just watched some mathematically sound representations of infinity? Bravo. I applaud the time and effort that must've gone into creating this beauty.

[@tsuaretehn_espira]

Definitely going in my "Best videos that fail the Harding test" list

[@anassaccente1322]

I just learned to code!!! The fastest way to learn it.

[@Lone_wolf--br7fi]

Surpass thy inner boundaries.

[@lagduck2209]

This is beautiful video about some beautiful concept, visualised perfectly. As always, gets better and better. (I researched this area a lot, and found some fractal objects with like phi^N cardinality that seemed to be between A0 and 2^N, and a lot of similar objects, but in the end I believe they're all still countable, anything below 2^N probably could be counted , and even cardinality of set of similar objects is fo 1^N cardinality; and at exactly 2 it becomes "orthogonal" and collapses into new dimension, something like that).

[@lagduck2209]

and power set of reals, and bigger cardinalities, that's surely a way to blow someones mind.

[@martin-krzywinski]

The Continuum Hypothesis states that there are no cardinalities between A0 and 2^A0. As a consequence, A1 = 2^A0. But we just dont' know since CH is independent of ZFC.

[@billB101]

Innovative, as always.

[@diracflux]

Have i just been uploaded with a mind virus? BY YOUR COMMAND IMPERIOUS LEADER MAX COOPER

[@mrjothescholar1149]

Waaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa beautiful sound track Max, and amazing video clip Martin !!! 😍😍😍

[@owenkjartanson7476]

Absolutely amazing. Thank you.

[@campingrom]

Thank you .

[@duncanlgeoghegan6333]

Such an amazing song and video. So so goooood.

[@Hummelsbusch]

Beautiful work!

[@MrMaksimi]

This is it.

[@quentin2368]

Next level "Man Machine" visuals. Awsome.

[@davidr2421]

That's an excellent and very well-articulated summary of the orders of infinity and Cantor's diagonal method -- this coming from a software engineer who double majored in computer science and discrete mathematics. Nicely done!

[@philippjohn555]

wow, nothing more to say... that's a freaky awesome presentation of the infinity

[@Raniu]

HOLY SHIAZO, THIS IS AN ABSOLUTE MIRACLE thankyouvm

[@CatzNGaz]

You created a marvelous visualization, showing how the reals are uncountable; for rigor, by demonstrating that the mapping from naturals to (0,1) is not surjective via contriving a decimal such that for every respective f(i) diagonal decimal element, there always exists one decimal place in the contrived decimal that's different; and thus the contrived element is neglected from the (0,1) infinite subset you listed (Cantor's famous, at first contentious proof by contradiction). Set theory is awe-inspiring

[@lilllilill6033]

Amazing Work!! Love & Gratitude!

[@funkysexy69]

Loving new track! 💖 Awesome use of digital visuals + love the drum-kicks! 🥁 Can see ur music used in film scores + soundtracks! Epic sounds!! 💗🔊🔊 😎🖤👊🏽

[@agerven]

Fascinating video, and majestic track. Great!

[@Maefreric]

dude all of this work is so good. the sounds meld with everything so perfectly. im really excited about this stuff for you.

[@s-upper]

i'm crying. i was always afraid of numbers and the whole thing about to imagine eternity in numbers, but now i can feel true numerophobia inside me

[@dragvarrenegade9363]

This was the whole ride.

[@flyfemale13]

Whaoo!

[@davidmcgough8736]

Fantastic track and visuals wonderful soundscapes reached

[@Remedynr]

Mindblowing spectacle. Reminded me of the movie Pi in the best possible sense :) my respect to both of You and Martin

[@dantegrabowski1109]

Another Piece of Art showing me my bundaries and possibilities. Ur a Muse to me as an artist

[@squalllionheart5127]

i finished to unzoom my eyes of the numbers and saw the wave of sound

[@Jadamhodges]

That felt very good to watch.

[@zoehead8029]

i love your music so much. i feel as though i have been looking for it for a long time.

[@nlg9763]

Outstanding work

[@TheTrip333]

E1010011T !!!

[@JDTheJuggleope]

Oh. Ok. Wow. I have a new favorite video now. Thanks. There are no words for this (pun intended)

[@user-ss7ht8nq2m]

The video is a masterpiece, it gives me goosebumps, I remember my first year at the university on Vasilyevsky Island, not far from the house where Cantor was born. But you can’t define a natural number through itself))) At least in ZFC. It would be more correct to write P(1)={0,{0}}={{},{{}}} because 1:={0}

[@user-mo3ux9ne7p]

예술이네요

[@MatthieuLebas1968]

Fascinating !

[@temps_triste]

YES this is awesome, the music and the video

[@StevenLightning]

It’s so cool how even the disintegrating text is still made up of actual text characters.

[@kenshi21]

❤️ hashing visualisations for music 👍

[@MrSamuelconway]

Still one of the most beautiful tracks ever.

[@ErugoPurakushiOne]

Sick. Almost bring a tear in my eye... Great work!

[@dimitris.theodoridis]

Such an emotional breeze...

[@M1gas]

no words (almost literally no words, in the video xD) amazing work with the video truly amazing masterpiece thank you so much for this

[@notnow2364]

Kryptisch und melodisch 😊😁😀😃😆😇💕💕💕

[@surroundgatari]

That was a trip, I gotta check out this guys album now, thoroughly intrigued

[@carolinecalisto7551]

So different. Vibe et.al. digging it.

[@ettoremariotti4280]

BEST. VIDEO. EVER.

[@funkysexy69]

Max's gig at #Printworks, London was Epic!! Absolutely phenomenal + awesome graphic show!! 🌌✨⚡ Need to play again at #Printworks!! 🙏🏽🙏🏽🖤💗

[@romanrst8092]

это прекрасно.

[@stephanmobius1380]

I want to see this in cinema.