The 'Everything' Formula - Numberphile

[@jeffreycanfield1939]

"This is where it gets more interesting. 9, 8, 2..." "You'll notice this is one of the more boring parts of the number. 7, 6..." I love this guy

[@dino130395]

Matt Parker. I love him too. He even has his own channel: standupmaths

[@jeffreycanfield1939]

I know, he hardly uploads on his main channel, so it feels like a gift from the heavens when he is featured on Numberphile. Quality over quantity.

[@jrlepage2a03]

That used to be true, but not so much anymore. Matt actually uploads videos to his main channel somewhat regularly now.

[@jeffreycanfield1939]

jr lepage​​ Somewhat regularly, keyword there. I may just be used to most of the channels I watch uploading very frequently. The channels I subscribe to usually upload once every two to three times a day, so I guess I've set a standard when I subscribed to standupmaths.

[@bennylofgren3208]

MistaTwoJeffreyTwenty Yaay _"Once every two to three times a day"_ doesn't even make sense...

[@rogerszmodis]

I like how he can notice 4 incorrect digits in the middle of a giant wall of numbers, cross them out , then continue like nothing happened

[@whatisthis2809]

matt can do anything

[@genericusername4206]

What is this except make a magic square with square numbers.

but you know it was just a Matt's joke?

[@jalalshahini]

he is a show man

[@StormTheSquid]

@@whatisthis2809 Except some things. In which case he only Parker does them.

[@todroyas692]

I can't believe I'm procrastinating from doing my maths homework by learning about harder maths on the internet... Why am I like this?

[@guy_th18]

same

[@ghizlaane7]

Same

[@dexterrik]

Because Matt's videos are amazing! Always!!!

[@delicate6930]

T Thung u in 5th grade?

[@a-levelking8610]

FR

[@rakinazad]

"some of you might have come across this" yea, sure, OKAY.

[@chuckychuck8318]

Rakin Azad we did

[@aurilyx6084]

I would've liked this comment but it's on 666 likes

[@liabell675]

@@aurilyx6084 it's not now, so you can do it

[@aurilyx6084]

@@liabell675 ok thanks

[@raywilliams6717]

@@aurilyx6084 well comeback and add to the heap then

[@JOSHHMusic]

This formula contains your full name and the exact time you will die at some point in it.

[@willytb1]

+Josh Hoover im going to be that guy, also dicks, all of them

[@chiphead777]

+JOSHH Music but surely then it has my name and every other time that I won't die

[@frankx8739]

+JOSHH Music Youre freakin me out

[@YellowJelly13]

+JOSHH Music Not really. I'm immortal.

[@toadfrommariokart64]

Oh wow, you're right! 8263583755837812708269306612315086550161261465676621697191232299015555109530473991664298512605728238239971884193257992911988479264761223839731144237937037677601595042085060631575502286950807622498260341666536703268874083292839411102309775496585160713655771918911418658614525147648547269744638123703449667649106901730425073725871356176123630322283576528640839767243650827823155945461737174616919924091702793172230949715172669109477101683980103225542915133381652155692630611345042305744871378239161955200244747113368117810298880

[@ikaikaikaika2419]

So who here is going to reanimate an entire Spongebob episode by using different points on the graph and several screenshots

[@StarLink149]

You could write a computer program to do it. For each frame of the animation, get the corresponding number and draw a graph.

[@TheOfficialQU4KE]

Entire Bee Movie?

[@koyo4625]

They will need to then post the coordinates for each frame.

[@Gopherborn]

ME HOY MENOY

[@cameron719]

yes please

[@Icecicle83]

In the beginning, I almost thought he was going to say "and the reason this number is so great is because I just made it up" :P

[@eltyo340]

Icecicle83 Matt is such a great troll with things like that xD

[@standupmaths]

That was very tempting.

[@Icecicle83]

I think it would have been great.

[@QuasarRiceMints]

Icecicle83 That's exactly what I thought :D

[@Chrnan6710]

That's so Matt.

[@theodorekeezer877]

if you do the number he put in his book, it gives you the formula but under it, it says "matt was 'ere"

[@thomasbelcher6921]

No it doesn't. It has a picture of the Parker square with the caption, "never forget"

[@sevenred2803]

No it doesn't! It shows a pixelated image of him performing the goatse pose.

[@ramizchili8024]

Gosh. Confusions.

[@ChavvyChannel]

real gamer missed the joke dumbass

[@OrangeC7]

I thought I could look at the comments so I wouldn't have to get the book myself and plot the number but now I need to get the book so I can confirm what I've seen

[@isaacmiles-watt2758]

‘Tupper’s self-referential formula’ sounds like a D&D spell.

[@senorpepper3405]

tashas uncontrollable hideous laughter

[@alexnobody1]

"When cast, target must succeed on a Wisdom saving throw or recite this description."

[@Layotu]

"when cast, target creature must succeed a wisdom saving throw or be forced to cast tupper's self-referential formula", so it just drains spell slots.

[@weckar]

Any target that fails their Will save fails their next Will save.

[@word6344]

I've got a homebrew enemy wizard who's a senile mathematician. This is the perfect spell for him

[@LazoeJSCREI]

0:18 "This is where it gets quite interesting actually cause it goes:" *and the huge number continues*

[@justin_5631]

When you break it down, the equation is less complicated than it first appears. The (1/2) term is merely distinguishing between 0 and 1 - whether a pixel should appear at a given location in the image. The term floor( y / 17 ) will always represent the number of the grid-image itself ( before it was multiplied by 17 ). It is a binary encoding of the image. The term 2^( 17*floor(x) + mod( y, 17) ) selects each pixel of the image one at a time.. each x,y coordinate selects a different pixel. The exponent is then made negative so the grid number is divided by the pixel selection number. When there is a pixel in the given location, the selected-pixel number will be a factor of the image number and there will be a remainder of 1 (plus maybe a fraction). If not, there will be a fractional less than 1 and the floor of the value will be 0. There are a few tricky details, but this is the essence of the problem.

[@Fun_maths]

But why is it specifically 106 across? Doesn't that seem arbitrary? It doesn't appear in the equation so why is that how far it goes along the X axis?

[@weirdredstone42]

@@Fun_maths i think the points graphed with the formula keep going right, but you can just ignore them for a specific width.

[@henryginn7490]

@@Fun_maths you're right, there is no limit on how far across it goes, you would just need to go higher up

[@mumujibirb]

Putting the formula into desmos shows 1/2 is irrelevant I think, any k seems to suffice

[@suomeaboo]

Making your own formulas is basically coding, but your programming language is Math.

[@CannedMaths]

4:12 *looks at 1000 digits. “It’s not that far tho”

[@praneethmashetty591]

I was your 70th like, so close.

[@EHMM]

Dang he do be a 1000+ digits number fan bro

[@tinkerthinker4892]

"You're a long way up the Y-axis" ...I like that phrase

[@enricobianchi4499]

69th like.

[@TheProRedstoners]

yea i cried laughing at that

[@DeathBringer769]

Try that line in the bedroom sometime...

[@AlanKey86]

The images are 17 pixels tall - presumably "17" was a fairly arbitrary choice by Tupper? Tall enough to just fit the formula in I guess? Another formula might exist for making pictures 23 pixels tall, or 101 pixels tall.. or 720 pixels tall and 1080 pixels across... If so, every frame of this Numberphile video could, in principle, be encoded by a formula.... as well as every frame of every other video ever made. And every video that ever will be made.

[@mrphlip]

AlanKey86 Changing the size of the picture is pretty easy... there's three "17"s in the formula, just change all of those to, say, 23, or 720, and you have a formula that does the same thing for a different height. And the width isn't even a part of the formula, if you want to encode a wider picture it works just fine, you just end up with a larger number for k. Also, ultimately, everything on a computer _is_ encoded by a formula like this... every computer file could in principle be read as a single very large number, and it's the software on the computer that plays the role of the formula, turning that number into something useful... of course, (most) software is a bit more complicated than this particular formula, but the principle is the same.

[@unvergebeneid]

AlanKey86 Essentially that's the idea behind Gödelization, yes. Or digital computers for that matter. Everything in memory is a number, including both data and code. So your OS is a number, the KZbin server is a number, the videos are numbers, your Flash player is a number ... everything is a number, transformed into pretty pictures by other numbers.

[@Ddub1083]

AlanKey86 congrats on figuring out how animated gifs work. an animated gif is simply a series of bitmap images where bitmap images are simply the k values of this formula (or another one using any dimensions) so when plotted it gives the binary image, but also has a third dimension for color values.

[@Ddub1083]

Rawiri Hohepa hex is just a different base number system, it represents numbers (the same numbers) as binary just in a way that is easier for a human to interpret (to the computer its always binary at the machine level) you can represent a color image in binary, you would just need a third dimension to the formula where the values range from binary for black (00000....) to binary for white (111111....) and the range of colors would depend whether you use 8 bit, 16 bit, 32 bit colors etc. Of course these can be converted to hex but the hex and the binary both represent the same underlying numbers/colors.

[@SerBallister]

Ddub1083 Strictly speaking GIFs use LZW compression typically with 8 bits-per-pixel (palettised)

[@xCreide13x]

So you're telling me I can play doom in a 17 x 106 grid

[@gracefool]

If you're Cathy Newman, yes.

[@HashtagTSwagg]

You need more likes.

[@MisterYoda15]

let's stop at 420 likes cuz this is some high sheit

[@007MrYang]

I know this is real, but it felt like an April fools video. Especially, when he pulled out the pacman version XD

[@123unknownsoldier126]

007MrYang I know! I was thinking the same thing. As i was watching that part, i was about to comment asking if it was a joke.

[@chillsahoy2640]

Jordan Phillips Especially considering that Matt Parker is well-known for joking a lot, and delivering his jokes in a deadpan way that makes you question whether he's being serious or not. But this is actually real!

[@unvergebeneid]

007MrYang The Pac-Man one _was_ pretty great.

[@ThatLazyCrazyLady]

007MrYang Me too! I actually looked at the date to make sure it wasn't posted on April 1st. When he proved it was real, I was like okaaay... mind. blown.

[@JNCressey]

007MrYang If you pick the right k value, you'll find a section where it says "April Fool".

[@sayrith]

So you are saying that there is a K value for a screen shot of Half Life 3?

[@NathanTAK]

sayrith There's a k value for the phrase you'd need to speak to get them to release Half Life 3

[@NoriMori1992]

Nathan T I like you.

[@NathanTAK]

Sicarius Noctis Thank you for making me laugh :)

[@KnakuanaRka]

Well, there are also K values for images that look like a screen shot of HL3 but are not actually, and you can't tell what image is accurate until the game is released. You may as well say, "So there's an image that's a screenshot of HL3?", since any image can be encoded as a K number.

[@NathanTAK]

K1naku5ana3R1ka Any bitmap image within the size constraints, that is

[@Squobidal]

Matt Parker: this is the slowest longest running troll you will ever come across Fermat: am I a joke to you?

[@angelmendez-rivera351]

Squobidal 😂😂😂😂😂😂

[@michaelsaucier4396]

OMG now THAT is hilarious

[@higztv1166]

Who's Fermat?

[@Squobidal]

@@higztv1166 fermat was a mathematician who died before giving the proof of a stated theorem, which then took 300+ years to solve

[@pendrag2k]

@@Squobidal And used HUGELY advanced mathematics that weren't even dreamt of in Fermat's time. It's almost a certainty Fermat's 'proof' was one of the thousands of erroneous proofs that had been submitted prior to Andrew Wiles' finally proving his theorem in the 90s.

[@draheim90]

This video started off really boring and I wasn't sure where it was heading, but man did it deliver.

[@Banzybanz]

That 982 part was interesting.

[@PureZOOKS]

If that number isn't a giant pixel knob, I will be disappointed.

[@TeamDemoClan2]

***** 960939379918958884971672962127852754715004339660129306651505519271702802395266424689642842174350718121267153782770623355993237280874144307891325963941337723487857735749823926629715517173716995165232890538221619561473865746304976129424093469921873058694492149444647882055806603996307772920108275439090931487231139508469267169521581872227293630931364751681875244141639118844172571080588839278417813855101724217755801034516516847318278139146496085068307449373183066378525002863703739215155304174822734164455483814441481301873381703922338834284527

[@ClausTndering]

Vort3x When I convert that number to binary I get a 1804-digit number. But 106×17=1802, so there must be something strange going on. (By the way, I checked your number with the book, and it is correct.)

[@TeamDemoClan2]

Claus Tøndering Weird, it comes up with the correct image anyway :)

[@Binkophile]

Tru3Gamer I was kinda hoping it was the lyrics to "Never gonna give you up".Then Matt could have got the record for most convoluted rickroll ever :D

[@oqibidipo]

Claus Tøndering You have to divide it by 17 first.

[@elonmuskmtmt886]

"Things to make and do in the fourth dimension" is the book that sparked my obsession with mathematics. This instilled facination is literally why I am watching this channel to begin with!

[@Gofer925]

huh, so it's kind of the library of babel that's pretty neat

[@OrchidAlloy]

That's a fantastic comparison! This is the Library of Babel of formulas.

[@JeoshuaCollins]

It's more like a function which takes the k value as an argument, and turns that into a grid. The actual graph can be said to be "encoded" into the value you use for k. You can look at the value k as the actual image you want to be displayed, and the equation is actually the tool you use to render it.

[@roondarmurnig338]

Not necessarily formulas. You saw that he did "Numberphile," so really just the Library of Babel of anything that can fit in a 106*17 grid of pixels. xD

[@psionic0]

Actually the x size isn't limited to 106, it will go further with higher K's. And you can also increase the height with a slight modification of the formula.

[@lexscarlet]

BRO TEACH ME

[@Janders797]

When half the video was over, I thought this was a late April fools video. Now I'm just impressed.

[@simoncarlile5190]

106 * 17 = 1802, so there are 1802 pixels in each "grid". There are 2^1802 different possible grids with this logic. Since each grid has height 17, the max height of this function - based on the description within this video - is (17 * (2^1802)). So here's my question: what happens at higher y-values? That number is very large, but it's a drop in the pond of the infinite ocean lying above it. So how does the function behave at those far higher y-values? Is it periodic? Does it repeat the grids, exactly in order, for infinity? Does it start giving garbage? Is it blank; does it not display anything above that point?

[@alexyates7166]

Simon Carlile Do we know that it doesn't repeat itself even earlier? You can only call that the maximum height of the function if you know every block of 17 up to that point is unique. You would need to be prove that it won't start repeating until after it has exhausted all the distinct possibilities.

[@theaweary]

If a multiuniverse exists then those picrures which looks as garbage for us might have ordered structure in other worlds. By the way I rather think it's a trick than an explanation of how our world has been created. Someone could start thinking that it's a mistery but it's not. Tupper translated a picture to formula and that's all he did. LOL.

[@727iamsam]

It starts repeating but inverted - starts at the top right instead!! Pretty cool stuff, just tried it

[@europasib]

What happens at x>108? Does it repeat itself infinitely along the x-axis, or do something else?

[@garvielloken9510]

One thing, there are 2^1803 - 1, because you can have a binary number of 1802 1's which if you add one is 2^1803. Also it equals 5*10^543 or 5 Octogintacentillion or more specifically 57158678861384166688322083618419726931125849158791219735754653591148474629858302 9329307855601409760300747826776847499381492015935155358310368707377103728210100188785202981759809103290579875568916906279235071821145409548462543176216184507360998816271917014454116073103439318297642987304928618033941227386219089813017272961345788989281119720935756579294733327700663909734926341200602357242020202058745308528342595964074462982623785717895075051973515654339473200635760893294494091009288544445312098701587650328316415546394274036564639618598699007

[@S1lv3r_Flame]

This has truly amazed me. I've watched pretty much all Numberphile videos, and this is by far the most amazing video ever. When Matt brought up the plot, my jaw was literally wide open. Thank you for the excellent video!

[@kermanguy1877]

If I look hard enough, will I find the exact position of my goddamn car keys?

[@RussellTeapot]

Kerman Guy only a pixelated version of those filthy keys

[@snowberry3118]

and everywhere your keys aren't...

[@lukewatson8848]

878092144743601036050755526519512409743609013213694363450423579222198504825032290931305417025688609712993967554282623970424953235311665126946357353896133721225774739681694303824857856769467870456049364161556924431195356738205098398192574158268323021754386558528738911435423511900352239285034894227861339824931864863783878072358640768067180073112684135118485653967723048962183874467806189739293963867505212603587830794000219928129217074615702474450249684729664307009066375627636048836542899724531725768990448

[@chiyanyu553]

yeah but you won't know that you found it

[@fgvcosmic6752]

But youll also find where your car keys ARENT

[@WingnutEOD]

I love people. I love that people can come up with this stuff. And I'm grateful that you folks [The people that make Numberphile happen] bring amazing and interesting things into the forefront.

[@GBart]

Similar to how you can find your phone number in pi if you keep looking

[@oakenguitar3]

AndroidDoctorr lol my number occurs 20 times in the first 200 million digits.

[@mrphlip]

AndroidDoctorr It's similar, but it's more like how you can find your phone number in "0000000000000001000000020000000300000004"... it's not just easy to find, but it's also easy to figure out where to look to find it, once you know the pattern...

[@beeble2003]

AndroidDoctorr Actually, we don't know that you can find your phone number in pi. Numbers that contain every finite sequence of digits are called "normal" but we don't know if pi is normal or not.

[@oakenguitar3]

beeble2003 it might not work for every number or everyone but I did find that pi contains my number, I googled it and found a site that could tell me how many times my phone number or any number occurs (as long as it wasn't too large) in the first 200 million digits. it occurs 20 times. I didn't use area code though, I only used 7 digits. It couldn't do it with area code included.

[@MattMcIrvin]

AndroidDoctorr It's even more like how you can find an approximation as accurate as you like to any analytic function somewhere in the Riemann zeta function.

[@JLConawayII]

What?! What is...I don't even.....WHAT?!

[@Djorgal]

Indeed.

[@standupmaths]

Well said.

[@DahBlindNinja]

+RFC3514 actually, it plots every bitmap of height 16. It will not stop at length 106, it will go up to bitmaps of 16x1749395729 or even 16x374729273837373838383838363828284846 and up further

[@DahBlindNinja]

+The_Blind_Ninja actually replace all those 16s by 17s

[@NathanTAK]

RFC3514 Heh. Evil bit.

[@hanslee475]

We are number one but it is made using Tupper's formula

[@toastysauze]

Genious

[@old-bitprogaming4857]

Hans Lee if you wanna be mathematician number one you need to solve the formula on the run! Just do simple operation and do it quick be carefull not to make a mistake, no 1+1=2 not 1. Now look at this calculator that I just found, when I say go be ready to do the operation. Go! But that one doesn't have the mod function Ohh let's buy another one Now watch and learn here's the deal. Code and program with HTML. JA JA JA What are you doing! Lolol

[@ianpoe8704]

someone took time out of their day to make a mathy version of WANO. *faith in humanity lowers*

[@kylecow1930]

OLD-BIT ProGaming, HTML isnt a coding/progressing language its a markup language (its in the name. HyperText Markup Language)

[@TheGIANTgonads]

It has boolean and arithmetic operations so you could build anything really, it just not what it was made for.

[@Dapeepn1gg4]

So somewhere in there is everything you've ever said and done typed in comic sans.

[@UnityGamin]

if it fits in thar area of 17x106 YES

[@Monkyupurbutt]

+Dapeep Fonts probably have to have a higher resolution than that, so ... no.

[@lilman82111]

Monkyupurbutt it'll probably need to be found in separate parts

[@davr1]

Most fonts are just vector images, so u can't find any sharp pixels in it

[@deadaccount8022]

@@davr1 Vector yes, but prior to cleartype and AA, fonts like Comic Sans were designed to be rendered in an aliased manner. So yes, you'd be able to find Comic Sans text.

[@fraxinellla]

7:00 "..years from now..."? I expect it will be done before the day is through..

[@fraxinellla]

***** ...aaaand now I realize I need a copy of the book to sort it out.. Well played. Excellent marketing!

[@pooeyyeoop1]

***** If you do get the book and do it please do tell people what it is, I hope it is just the word 'trolol'

[@AceandDuce]

I would expect it to be don't now

[@wingbull2009]

***** I bet it's actually the correct plot and he's just a marketing genius.

[@TeamDemoClan2]

***** Here's a start: 96093937991895888 49716729621278527 54715004339660129 30665150551927170 28023952664246896 42842174350718121 26715378277062335 59932372808741443 07891325963941337

[@kalebbruwer]

at what number does it say parker's square?

[@anuradhakrishnan6040]

Daniel, I thought you'd just given a random number, but it does say "Parker square!" at that number!!

[@kalebbruwer]

Anurag Krishnan is there some kind of program to play with this that everyone except I know about?

[@GnuReligion]

Wonder if that web site is actually using big integer math, or merely deriving bitmaps from the binary conversion of the number? .... umm, well, yeah, duh, guess at least some big integers have to be involved just to derive the binary.

[@Tara_Li]

That's what the FLOOR function is doing in the formula - dropping off the decimal points.

[@prajnaprajna1923]

I have found the exact result of the formula Fermat case n = 3. y=1/{ [3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2 +2xy-2zy+2z^2 - 2Sx+2Sx -2Sz+ (x+y-z)/3 } / 2 However , B is an integer .So y< 1 does not accept Combine two formulas to solve Flt case n=3. Sx=1^2+2^2+3^2+....+x^2=(2x^3+3x^2+x) / 6. And x^2+y^2-z^2=(x+y-z)^2 +2xy-2zxz-2zy+2z^2 suppose x^3+y^3=z^3 so 3Sx-3/2x^2-x/2+3Sy-3/2y^2 - y/2 - (3Sz -3/2z^2-z/2)=0 so 2Sx-x^2-x/3+2Sy-y^2 - y/3 - (2Sz -z^2-z/3)=0 so (2Sx+2Sy-2Sz)-(x^2+y^2-z^2) =(x/3+y/3-z/3) so [Sx+S(x-1)+Sy+S(y-1)-Sz-S(z-1)]=(x+y-z)/3 so (x+y-z)^2=[3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2 because x^2+y^2-z^2=(x+y-z)^2 +2xy-2zxz-2zy+2z^2 so x^2+y^2-z^2=[3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2 +2xy-2zxz-2zy+2z^2 And there was x^2+y^2 - z^2=2Sx+2Sx -2Sz - (x+y-z)/3 compare 2Sx+2Sx -2Sz - (x+y-z)/3=[3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2 +2xy-2zx-2zy+2z^2 So x={ (2Sx+2Sx -2Sz) - (x+y-z)/3 - [3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2+2zx+2zy-2z^2 } / 2y z={ [3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2 +2xy-2zy+2z^2 - 2Sx+2Sx -2Sz+ (x+y-z)/3 } / 2x z={ [3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2 +2xy-2zx+2z^2 - 2Sx+2Sx -2Sz +(x+y-z)/3 } / 2y call { (2Sx+2Sx -2Sz) - (x+y-z)/3 - [3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2+2zx+2zy-2z^2 } / 2 is A So x=A/y { [3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2 +2xy-2zy+2z^2 - 2Sx+2Sx -2Sz+ (x+y-z)/3 } / 2 is B z=B/x { [3Sx+3S(x-1)+3Sy+3S(y-1)-3Sz-3S(z-1)]^2 +2xy-2zx+2z^2 - 2Sx+2Sx -2Sz +(x+y-z)/3 } /2 is C y=C/z Because x^3+y^3=z^3 So A^3/y^3+C^3/z^3=B^3/x^3 B^3/x^3=(A^3.z^3+C^3.y^3) / (zy)^3 B^3.(zy)^3=x^3A^3.z^3+x^3C^3.y^3 So (Bzy)^3=(Axz)^3+(Cxy)^3 This is x,y,z So z=Bzy So 1=By So y=1/B Because B is integer so y

[@Seltyk]

This is, without a doubt, the coolest formula I have ever seen. If you'll excuse me, I need to go find the k value for my own username which means I won't be back for a while

[@Seltyk]

DanTheStripe you are the greatest human alive. *thanks!!!*

[@DanTheStripe]

wundrweapon Haha, no worries mate.

[@Anankin12]

wundrweapon I can't see what he sent you :(

[@uhrguhrguhrg]

DaComputerNerd generating the binary number is super easy for any image. Translating it to dec is a bit harder but still easy.

[@hemakodaaa]

It's been a year, did you find it yet

[@alcesmir]

This equation makes so much more sense when you realize all these equations is just reducing the data to lattice points and doing some bit shifts and and'ing with 1 to get the data you want out of your chosen y start value. Really neat and fun to play around with. It also taught me that octave apparently doesn't support arbitrary size integers, while python does it easily.

[@car-keys]

This is my favorite Numberphile video, Matt Parker kills it.

[@corb805]

This would be an amazing way to hide codes. Just give someone the k coordinates and you can give someone any message

[@priyanshugoel3030]

No ,actually might as well just give them in writing.

[@jacobschiller4486]

@@priyanshugoel3030 But if someone else sees the number, they might not necessarily be well-informed on the context.

[@priyanshugoel3030]

@@jacobschiller4486 what i said might have been an overexaggeration. But still it is pretty inefficient for info transfer.maybe you could share a shortened link though.

[@coloneldookie7222]

When he brought out the sheet with Pac-Man, I thought this video was one giant joke of some sort. By the end, my brain finally wrapped around what and how this all worked, and I'm completely astounded by the complexity available for such a relatively "simple" formula (that isn't as lengthy as the k-value needed to define everything within).

[@spookyfbi8]

Colonel Dookie I thought it was a joke too and it was put up 2 weeks too late.

[@RussellTeapot]

Colonel Dookie If you are amazed with simple formulas or procedures that can create something really complex, I suggest you to search about fractals... I'm sure you could find that quite interesting

[@david203]

The long k value simply encodes the dots of the plot. Actually quite simple. But amazing the first time you see it when the number k has not been explained as yet.

[@piguy314159]

5:44 If that number encodes the Numberphile logo, isn't it illegal?

[@piguy314159]

/watch?v=wo19Y4tw0l8

[@SuperSilkyJohnson]

+piguy314159 Arrest that formula.

[@RadicalCaveman]

+AshyLarry No, society's to blame - we'll arrest them instead.

[@extrascript6622]

piguy314159 TWL!

[@Zaddis]

NumberWorld woooosh

[@enoughofyourkoicarp]

*looks around slowly* "That seven should be a two." (quick, run before he gets done checking)

[@jeremyrekier6124]

That's the kind of video that makes me check the day of original posting expecting it to be the 1st of April. That's astounding.

[@thelittleoctopus2353]

OK I thought I got maths but after that pacman I was just like nope someone's just making fun of me my whole life's been a lie

[@nathanhargreaves7071]

It is real, though.

[@thelittleoctopus2353]

yeah no I do believe it but I just think it's also amazingly hilarious XD

[@gracefool]

It's actually meaningless, like the library of Babel. It's just confusing people who don't understand how *all* information representation works. It's just one particular encoding.

[@PikalaxALT]

There are 2^1926 or 6078153291570505049950071276536638079404318120619847471539261205157450642348546168006770394132550721035068726296830713560389041699075758033545794462842837124927197605659660657814206393320816342070822997305553394052957504523655639148369650298525306301897561822259909700294109249193992132082636963801030910844946591834474977036099501761933577693294715247782869828358876835586348240220513290123228337041478835485477158320667250939610051764567232830698066368848946964033425097018126687442231039835221758080473219817014946335864250609802497581088885008037817468710693714003740395044864 possible plots using this scheme. A more general formula would look something like 1/2

[@RikyPerdana]

Can it mean that our whole universe is just a series of constants being plotted on space through this equation in timely manner? Mind blown

[@sahilsharma2952]

The best video I have seen till date. Hands down.

[@JugglingAnusJuggler]

oh ya youre right. i encounter that number practically every day of my life

[@araam688]

This formula has to be the most unique, natural, and mind-blowing equation I have encountered. Love math and love how this ties into binary meaning this is how images are made in computers I believe. Again, just mind blowing.

[@hairohukosu433]

Well, its more an abstract representation of all possible pixel permutations than how computers actually work, but yeah

[@souravzzz]

Huh what a coincidence! I was reading Tupper's original paper today and now you posted this :)

[@RainaRamsay]

It's possible this is the coolest thing ever done.

[@YuzuDrink]

Hah! That's super cool! And quite impressive. It's like a mathematical way to encode pixel data rather than the digital ways we currently have.

[@jackwalsh8601]

Very interesting but there is only a finite number of ways to colour a 17*106 graph. What happens when all of them have been graphed

[@davidsl118]

+Jack Walsh Must be repeating itself.

[@Gogetaofpersia]

that is like the best comment i've read till now.....

[@Treviisolion]

+Jack Walsh I believe there are 2^1802 different unique pictures you can make with this formula (2^1000 apparently has 301 digits), so yea.

[@Treviisolion]

+Jack Walsh That does make me curious though.

[@naota3k]

+Jack Walsh What happens? Nothing?

[@doid3r4s]

I'm sorry, I have to grab my brain from the ceiling, be right back.

[@aajjeee]

But what is beyond the k value for a completely black screen?

[@TheSpacecraftX]

aajjeee Maybe there isn't one. Maybe it's undefined.

[@CaesarsSalad]

TheSpacecraftX How could it possibly be undefined? Look at the formula.

[@xereeto]

aajjeee Try it and see

[@kyconny]

aajjeee the grid is 106 * 17, meaning there are 1802 squares, making for a 1802 bit number, thus the number holts 2^1802 possible values (including zero), so the number for a completely black screen would be 2^1802 - 1 285793394306920833441610418092098634655629245793956098678773267955742373149291514664653927800704880150373913388423749690746007967577679155184353688551864105050094392601490879904551645289937784458453139617535910572704774231271588108092253680499408135958507227058036551719659148821493652464309016970613693109544906508636480672894494640559860467878289647366663850331954867463170600301178621010101029372654264171297982037231491311892858947537525986757827169736600317880446647247045504644272222656049350793825164158207773197137018282319809299349503

[@philipjohansson3949]

kyconny You forgot to multiply by 17, but also, because of the mod() funcions, wouldn't -17 also be a black screen?

[@MrPatatogamer]

how to destroy your graphical calculator you had to buy for school xD

[@LunarEclypse]

It worked on mine

[@blocksofwater4758]

@@LunarEclypse you really type that number in?

[@adrianmoolman5255]

I dont think i will see anything cooler than this in any math class i have had, am having, or ever will have.

[@MegaZsolti]

Plot this, please. 9408928788638436073397719484541912079027883772177344090495082334914131517318234804104390228430351549078269334248551016667270814781207752121794763744166930316881129380042249811691535538095731067521739182945171239982281553282396067618909192276711649883646387408446333210067526748400389708161025959606958847356077907779033319194993348211890873810554512753922174049943465745841135008826184759245860432296143364030060503336420520411602441972077146080444396835484655908275955552316413205953482173141171470877758929620951462577138994933922005060

[@Skylar.vanderwoude]

curse you :P

[@bengineer8]

LOL!!!!!!

[@The_Green_Ghost]

477074188659101768156750670273788898386333499160967376261158418019968707389294626930556858011093390306037754345195556375445161500215690779153113781840030839964971886991609514916866140806171873533987565901709876441897732383973719416423161977393489395047131006567318132155519276760741414727190005950893317232749925978317016271246898321557134069574971428848

[@Onimirare]

There's a website to translate this? I couldn't find it.

[@bengineer8]

NomeInvalido tuppers-formula.tk

[@timvansurksum]

This is the coolest "semi hyperwebster" I've ever seen

[@KingLarbear]

I remember growing up in a time where they said, "you're not always going to have a calculator near by" and never learning this in school... i have never seen this before... I'm mesmerized

[@postbodzapism]

Is there anything like this in the 3D plot?

[@postbodzapism]

relike868p or sth to do in 4 dimensions lol

[@RFC3514]

relike868p There's no reason why you can't do it (i.e., make a voxel map printer instead of a bitmap printer), but the "K" numbers get a _lot_ bigger.

[@RFC3514]

FlyingJetpack1 Simulating what? You mean printing out every possible variation? Yes, that would take a long time (basically, it takes Z x T, where T is the time it takes to print every possible result of the 2-dimensional function and Z is the number of layers). Since the 2D version has 2^1802 possible variations, that does "add up", to put it mildly. But if you're just trying to print out _one_ voxel map, it's only Z x t, with t being the time it takes to print out _one_ 106x17 bitmap). In other words, pretty quick. Actually, 106 might not be enough (because the formula would be longer), but you get the picture. The real problem is that the size of the number K (which is what _actually_ encodes the "image") _also_ increases by a factor equal to the number of layers, even if you're just trying to print _one_ voxel map. So a 10-layer voxel (i.e., with a resolution of 106x17x10) would have a K number with 10x the digits of the number Matt used here. Basically, you're just "stacking" a series of bitmaps into that number, one after the other (and then using a modulo operation to split the layers while printing them out). And, of course, you can't really represent it with pen and paper (you'd need Lego bricks or something 3D), which limits its "party trick" potential, even if you managed to memorise the huge number.

[@oO_ox_O]

FlyingJetpack1 Nah, the number will be large (and you need quite some amount of space for storing it) but still will not take years because you don't need to try and guess something.

[@FlyingJetpack1]

o_O I missunderstood him, now that I know he ment rendering a certain K it's not as difficult as I thought it is. But in a 3D formula the numbers the K can get to are astronomically gigantic. As you said, it will take few GBs to storage all those numbers and extracting them to the formula will take a few mins.

[@kaselier1116]

I was pretty uninterested at first, but that has got to be one of the coolest things in all mathematics.

[@607]

This had been in my Watch later since 2016... I'm glad to have finally seen it, it was cool!

[@jamesonpayne3490]

This is so meta I just can't express how awesome it is

[@Hedning1390]

matt was 'ere

[@camerongray7767]

I just found a new favourite math KZbin video

[@gizmostudios]

New challenge: The input number that will plot out itself

[@staudinga]

I thought about that too, but many input numbers are so large, that you can't really fit them inside the grid, so I think it's probably impossible

[@guruhoro]

You could theoretically find a number that you could express as an equation that fit in the space, using exponents etc.

[@gizmostudios]

Make it happen :D

[@lucasvignolireis8181]

Gizmo Studios that's waaaay harder

[@JannikPitt]

Well that number doesn't necessarily exist. I'd even say that it is highly unlikely that such a number exists.

[@jaguarr314]

This video made me check the date for April 1st. Math becomes so incredible that you don't know if it's fake sometimes.

[@darkener3210]

NFT artist are shooken by watching this video

[@aadfg0]

Fun fact: Insane graphs like these have only come out in the past few decades or so. The Mandelbrot set was so hard to plot that this was literally the best picture they had of the set in the 70's and 80's: commons.wikimedia.org/wiki/File:Mandel.png Nowada Anyways, the main point is you gotta be thankful for computers which have made discovering things like these easier. It would be impossible to "discover" a Tupper Formula before the 1st century!

[@andrasfogarasi5014]

So there is everything... 4555091711244117493438346084238864012330730653781366947789267256009612609538736184658399545826367977013336345946058897680151095054837325582942694676552628780022918419835460511778760719504849199463816817005721123518840216773502064681553119738267243694399450411724138109368066507935990387059972100765633228580006046767388148421746923731855405112827176587307260473489333806726778469102150985525776485013579401581058555090879008179874854571975269491345876073081943198773575390962805787503109389590331030469084672858918253336723104095041330534678511

[@thomaskaldahl196]

+András Fogarasi kitty

[@jameswise9171]

+András Fogarasi There IS everything! 4049794512163849644978004481390526619142266047648863597623958365816687269099081642094961145691485350744232146762737614798707922377115841852472278876188557839484936374452248115984929179530271140325320443658149564594997323690097785841432003835824178520871415025399369566316265078571993942705219640850829061723439514482324924755123221163420411516128523214572846130634642108161189740544

[@Thomasynthesis]

Fixed it for ya. 4858487703217654168507377107565676789145697178497253677539145555247620343537955749299116772611982962556356527603203744742682135448820545638134012705381689785851604674225344958377377969928942335793703373498110479735981161931616997837568312568489938311294622859986621379234205529965392091893253288500432782862263410646820171439206408889517627953930924005233285455643232746873900205120036557171717499335122490912065694632935352302178602108137941774883061609026136356717962911449275408908448119205858928916227964752568083880766320836794510567391487

[@ProofOfDragons]

A complicated way to draw a bitmap trivially encoded in k.

[@nyalldavis]

Was about to ask if this could be used for some crazy compression, then I watched the bit where the K number is the uncompressed image... Back to square 1...

[@btat16]

Hi guy from 5 years ago! What if you found factors of those numbers and saved those instead?

[@WojtekCzaderna]

After you showed Pacman I checked if the release of the video was not 1st of April

[@JakubS]

The first mathematical formula that can graph a pornographic image

[@gro_skunk]

how these people memorize numbers that long will forever be a mystery to me

[@qwertyuiopazsd4253]

+Skunkdog Gro They put it next to where they are writing and copy them

[@leonardorezende106]

+Skunkdog Gro He put the wrong number in his book, what makes you think he actually wrote the correct version there?

[@ZweiSpeedruns]

+Clayton Fuhrman Due to a common misinterpretation of the fact that actual computer bitmaps work differently than this, the most common number used to represent the equation is plotted upside-down.

[@GeneralKenobi69420]

Furry cringe

[@owena7434]

@@ZweiSpeedruns Are you talking about endianness?

[@karlmachnow4961]

This formula is illegal in germany. Why? Because, at some point, it contains some not-so-nice-looking swastikas.

[@TimothyReeves]

C21H22 N2O2 wow

[@pickachu3739]

There are so many ways I could think of where we can use it. But I think the reason it is not used is because the memory needed to store the K value is more than the actual data needed to be represented.

[@morscoronam3779]

This is astounding... Absolutely confounding... Frankly, it's insane. Also, the first three lines are a haiku.

[@itsanumolu]

Mors Coronam wow that is beautiful

[@atanaciogarza7176]

No, for it to be a haiku, at some point in the poem you must reference a season or something seasonal.

[@davidforgeas2235]

Not really, it's just decoding the bits one my one with the modulo operations.

[@Seven111]

What's with this random brown paper that they always use?

[@kalebbruwer]

It's their thing, it looks nice.

[@cowlikenuts]

Sam Jacob ...

[@thorham1346]

It's not random if they ALWAYS use it.

[@Posiman]

It's just the basic color of paper that has not been dyed nor bleached (as it's the color of the wood pulp itself) and therefore slightly cheaper than white paper.

[@kiva8986]

It might actually be random. We've just not seen the other type of paper yet.

[@darthparallax5207]

i need that book now, because i want to experience the ultimate mastercraft of trolling ever....

[@guard13007]

Has anyone actually gone and figured out the plot from his book yet??

[@thomaskaldahl196]

+Guard13007 it has the words "matt was here"

[@DynamiteBacon]

Second time I've found you unintentionally outside your channel.

[@tilnation14]

No, it says "matt was 'ere"

[@L0LWTF1337]

How on earth did anyone ever find out that would happen?

[@Creaform003]

L0LWTF1337 started with the finished product and worked backward.

[@RFC3514]

L0LWTF1337 The formula just prints out bitmaps. There are equivalent (though more complex and more flexible) formulas in every digital paint program. This is more or less like using Photoshop to open a BMP file of the text "Photoshop", and then calling Photoshop "self-referential". The actual formula doesn't contain itself; what contains the bitmap of the formula is the K number (which is just a bitmap converted to decimal).

[@uncommonsense360]

If you change the "y" intercept of the function and change what the function can edit with respect to "x", then the function can be found at "y"=0 but to duplicate the function, it will go off very far in the "x" direction.

[@uPenguin]

This is insanely cool!

[@нескажунескажу-с8ц]

Ты меня поразил в самое сердце! Я первый раз в жизни с радостью на лице наблюдал за математикой. Меня первый раз в жизни заинтересовала математика! Это нечто!!! Спасибо! Так держать! Ты крут!

[@BaseSixBasics]

THIS IS SUPER USEFUL HOLY S*** I can imagine some circuitry in a computer monitor that decodes binary coordinate values to generate images

[@tggt00]

Am I the only one who thought this is a joke? It really seems like a great april fools joke.

[@oraz.]

I would love to see an animation of the plots as k increases quickly.

[@oakenguitar3]

orazdow kamacurus! :D

[@sethmitchell2176]

orazdow It actually looks pretty boring. Very little changes if you only increase by a increment of 100 digits or less, and most of what you'll see is a bunch of lines on the right hand side of the image and a bunch of garbage on the left, slowly changing as time goes on.

[@BlueSquad00]

You can't possibly make maths more interesting than this guy

[@Sylocat]

I'm confused at the "1/2

[@SomeRandomFellow]

+Rabbit Cube maybe if you wanted to do algebra to it and get everything on one side you would need to use 1/2

[@fizzicist7678]

+Rabbit Cube I don't know half of the key functions here, but as far as the mod function is concerned, the function you divide is that one that takes X and Y co ordinates, and does those many things you want it to do. Because it uses 2 as the base of it all, dividing it by 2 makes the mod return a 0 or a 1, because you either have an odd or an even number to divide by 2. Odds give remainder 1, so mod returns 1 for odds, and evens return 0. Think you have a point there for the 1/2< not being important and neither does the bigger floor function since the mod will give you 0 or 1 anyway. But wouldn't be plotting itself then now would it?

[@Sylocat]

+DarkBabyIon Well, it WOULD be plotting itself, because it plots everything, and they could just find where that was written out. Heck, since it's a floor function of a mod 2 function, they could just start it "1 =."

[@QwertyuiopThePie]

+Rabbit Cube In that case, you'd want to check this one: k = 153016202616638617152446647003205613599981464756945123501364320098017713905156881492682697332376227150372309520033482137529592674563223860831468029565267112858059457613314371589211602590697776649293897193922521297331223349187269154673136000122962790229393631480425629022486770086267963735018395718727367264503414661496293559422530848982844140255148194967047341549981366555660949891524452487183237441070454253250642346731490256955776761631210221209730658863424502193029575117804927143608280853026679311318841530214079089737740807632170761977839

[@QwertyuiopThePie]

+Rabbit Cube In that case, you'd want to check this one: k = 153016202616638617152446647003205613599981464756945123501364320098017713905156881492682697332376227150372309520033482137529592674563223860831468029565267112858059457613314371589211602590697776649293897193922521297331223349187269154673136000122962790229393631480425629022486770086267963735018395718727367264503414661496293559422530848982844140255148194967047341549981366555660949891524452487183237441070454253250642346731490256955776761631210221209730658863424502193029575117804927143608280853026679311318841530214079089737740807632170761977839

[@zerospin876]

So from this follows, that there is a mathematical formula, that plots every single state of the Universe in all n dimensions across all time slices, which means we are nothing but numbers.

[@pearse9116]

Not at all.

[@zinqtable1092]

Obviously.

[@thestarjon]

Time is a real number, real numbers are uncountable infinite, assertion refuted.

[@pearse9116]

Starjon No you haven't. You've said something pseudo-intelligent and pretend it relates to what we're talking about. I never even made an assertion. - Time isn't a number, it's a concept. - Two sets of numbers being uncountably infinite doesn't imply they're the same size, hence the existence of aleph-null

[@thestarjon]

Lopt The Treacherous My post replied to the original comment. It's impossible to create a formular that pictures every possible state of the universe, because the set of alle formulars is countable infinite and the set of alle possible state of the universe ist uncountable infinite. However, my post was certainly not very mathematically, I'm sorry about that.

[@Xonatron]

This formula contains all the digits of Pi. All of them! In groups albeit, all over, but with each group containing perfectly ordered digits of Pi that map it out to infinity.

[@FunOrange42]

i wish i could see what appears above and below k and k+17

[@FunOrange42]

***** ah, i expected as much

[@denny141196]

FunOrange Aren't you that osu freak? Had no idea you'd be into this kind of stuff.

[@Vodboi]

***** I think i understand binary, isnt 0000=0 0001=1 0010=2 0100=4 and 1000=8? these arent the numbers 0-4, but anyway, i get the point :D

[@trantix8251]

oh yea. oops. I feel stupid now. I'm a little surprised no one said something sooner. But yea, it still is relatively the same.

[@tiagovaladares2616]

***** 0000 = 0; 0001 = 1; 0010 = 2; 0011 = 3; 0100 = 4; 0101 = 5; 0110 = 6; 0111 = 7; 1000 = 8; 1001 = 9... etc*

[@anon8109]

"self referential" is a bit deceptive. A truly self referential formula would refer only to itself and not to anything else. Perhaps "partly self-referential" is closer to the truth. This poses the obvious question: does a truly self-referential formula exist? One where its plot is exactly the formula.

[@10ozPoundCake]

anon8109 If you accept computer programs as sort of mathematical formulas with additional symbols and operations, then a quine would be your answer. There's some really interesting and clever ones out there that are worth a google search.

[@anon8109]

Jakub Trávník Wonderful!

[@TheHuesSciTech]

Jakub Trávník Yeah, see what you've done there is actually clever, unlike the video.

[@unvergebeneid]

anon8109 I doubt there is one that is actually both self-referential _and_ elegant. BTW, Tupper himself did a couple of versions of such formulae. Just have a look at the Wikipedia article: en.wikipedia.org/wiki/Tupper%27s_self-referential_formula

[@xXsolar99Xx]

Jakub Trávník Very impressive!

[@1.4142]

This is like a mini version of the library of babel.

[@peaceistherealmuscle]

Anyone else who checked and found that he used the number k for the upside down version of the formula?

[@jacobschiller4486]

Yeah! I wonder how you can transform plots using that inequality for a given value of k...

[@raymondstheawesome]

i really like this one. it's one of the one's in all of human history! 8953414250588800289617325535280035162245185117643995475877506652422836705738415400906601754022056564829041902932330989371135024941302123326626468495565476455539347561034022819549348140453960859887976630352333484101093920833233872830424595791482328307303309721098929255345581398650281997298382341797645910016

[@zodiahk]

really?

[@Funnymoney101]

never did I expect

[@firegirl1287]

Great direction on this video - brilliant

[@GenericInternetter]

At first i was like "meh" But then i was like "wtf?!"

[@FederationStarShip]

What software could I use to play around with that formula? It's those massive K values which I guess will cause trouble

[@oscarsmith3942]

Python might be able to do it well as it's ints can get very big. (you would have to code it though)

[@davee7910]

Could you give me the code?

[@loliconofcyrene4463]

if you have access to a unix system (or have Cygwin installed on your computer) you can use the 'bc' program. it's an arbitrary-precision calculator that lets you play around with huge numbers in different bases. it doesn't support plotting though, so you still need to reformat/visualize the output digits in a separate program or manually using a text editor

[@davidforgeas2235]

@@loliconofcyrene4463 Indeed I've just used bc and I plot # or space for each point.

[@dougbrwn]

@@davee7910 it's at point number 8367727725256277625525627727652552556277727625567495995874772766262.... (Not really)

[@PyroManZII]

Next time I am programming a 106x17 LCD screen, instead of using inefficient GUI methods I will use this formula to generate every possible state of the screen!

[@TessaLucy]

It crashed my phone when I looked for the word "oatmeal"