Fixed Points

  • Published on Sep 28, 2016
  • My video on Sesame Studios:
    The Curiosity Box by Vsauce:
    My twitter:
    My instagram:
    Moon Museum:
    Brouwer’s fixed point theorem:
    Excellent interactive wolfram demo of Brouwer:
    Online graphing calculator used was:
    fixed points more generally:
    Babylonian method:
    Iterated equation solver you can use to run the Babylonian method:
    aleph fixed point:
    My video on counting past infinity:
    map projections:
    Pacific antipode image:
    “four” is the cosmic number:
    Standupmaths video about how four has four letters. So bummed I only found this AFTER I made this vid, check it out!!

    protocol_7’s comment:
    Other topology pages:
    wiki images:
    Globe is from Ballerby & Co. Globemakers
    music from
    Any VFX that actually look cool are by -- I did the rest the best I could :)
  • Science & TechnologyScience & Technology

Comments • 24 813

  • Sam O'Brien
    Sam O'Brien Day ago

    Someone could use four to create a code, the encryption levels are theoretically endless, I think

  • Brian Lallement
    Brian Lallement Day ago

    2:43 Is that Desmos?

  • Arsh Tewari
    Arsh Tewari Day ago

    michael: *drops scooter*
    michael: that's pretty cool.

  • firebeast 654
    firebeast 654 2 days ago

    7:27 me scooter

  • Michael Yang
    Michael Yang 2 days ago

    Andy warhol is a legend

  • Daniël Mao
    Daniël Mao 2 days ago +1

    7:28 the first thing i noticed is the upside down globe.

  • Law Berry
    Law Berry 2 days ago

    Six hundred eighty four thousand, eight hundred ninety two
    Forty nine
    god dammit

  • PC room
    PC room 3 days ago

    That 4 is in slovakia 3

  • BrotherSquidman
    BrotherSquidman 3 days ago +1

    it's the time of the day to watch vsauce and ruin my brain

  • Kayo Takeda
    Kayo Takeda 4 days ago

    *pushes elevator button once, elevator arrives. Door closes and leaves, punches it twice, elevator hurts through the wall* OKAY...

  • - Emerealm -
    - Emerealm - 4 days ago

    Brewer's Fixed Point Theorem. I'm sorry.

  • flow
    flow 4 days ago +1

    you won't end up at four every time if you take an irrational number! Wtf? proof that he said it: 13:00

  • Terry Cornelius
    Terry Cornelius 4 days ago

    If it's in English you'll be stuck at 4, but if it's in Indonesian you'll be stuck going between 4 and 5. (4 = empat and 5 = lima, lima has 4 letters and empat has 5 letters).

    SMACKY PANTS 5 days ago

    hey subscribe to me and ill subscribe back

  • Basel
    Basel 6 days ago

    Fuck them those damn artists, damn engineer was a retard

  • MintyFreshness4
    MintyFreshness4 6 days ago



  • Lord Habitaxe of Prydonia

    Hitler after trying the addition subtraction thing:

  • Nícolas Ferreira Gruenwaldt Ribeiro

    um(1) -> dois(2) -> quatro(4) -> cinco(5) -> cinco(5)...
    três(3) -> quatro(4) -> cinco(5) -> cinco(5)...
    seis(6) -> quatro(4) -> cinco(5) -> cinco(5)...
    sete(7) -> quatro -> cinco -> cinco...
    oito(8) -> quatro -> cinco -> cinco...
    nove(9) -> quatro -> cinco -> cinco...
    dez(10) -> três(3) -> quatro(4) -> cinco...
    onze -> 4 -> 5
    doze -> 4 -> 5
    treze -> 5
    quatorze -> 8 -> 4 -> 5
    quinze -> 5
    dezesseis -> 9 -> 4 -> 5
    dezessete -> 9 -> 4 -> 5
    dezoito -> 7 -> 4 -> 5
    dezenove -> 8 -> 4 -> 5
    vinte -> 5

  • Nilsber
    Nilsber 6 days ago

    But the circles can rotate
    /music plays

  • Tyler Chen
    Tyler Chen 8 days ago

    the fours are coming

  • Saul Di Bari
    Saul Di Bari 8 days ago +1

    Why do you have to do the “I’m not a robot” tests when trying to create an account on something

  • Gregory Chen
    Gregory Chen 8 days ago +1


  • AA12 Fordays
    AA12 Fordays 8 days ago

    Is his globe always upside down?

  • tumšsCuška77
    tumšsCuška77 8 days ago

    12:15 the reference

  • TheGoldenTank TGT
    TheGoldenTank TGT 9 days ago

    man the moon is male? thats gnarly

  • Kapitan Niño
    Kapitan Niño 10 days ago

    Woah i was an artist al my life like the line of robert

  • MrTingles
    MrTingles 10 days ago

    It's just Alephs, all the way down.

  • Werner and Ella Gamers and Creators

    If aliens go to the moo , they’ll see that song on the moon and just turn right back

  • Kiwi
    Kiwi 11 days ago +3

    3:55 Yeah but if that grid was for example 4x4, you could just turn it 180 degrees and there would be none of these original overlapping areas.

  • Obliteration Studios
    Obliteration Studios 12 days ago

    11:12 is my favorite vsauce “experiment” or cool concept that he’s ever shown

  • fivenightsofben
    fivenightsofben 12 days ago


  • Fickle Pickle
    Fickle Pickle 12 days ago +1


  • Is Yeboi
    Is Yeboi 13 days ago

    7:30 this is basically my life

  • Oetze Broek
    Oetze Broek 14 days ago

    The coffee is not true, there is no boundarie on top

    • Shirokröte
      Shirokröte 10 days ago

      +Oetze Broek he's talking about a normal cup of coffee held upright so the coffee doesn't get out. Anything else wouldn't be called a transformation.

    • Oetze Broek
      Oetze Broek 10 days ago

      +Shirokröte but you could remove the coffee from the mug, completely mess it up. Then put it back. I think gravity is not a boundarie

    • Shirokröte
      Shirokröte 10 days ago

      Gravity keeps the liquid inside, so there basically is one

  • Striker Bass
    Striker Bass 14 days ago

    I hadnt thought this was goong to happen, 8976.6869782645 is a bit too long to count the number of letters in it's name

  • Ubo
    Ubo 14 days ago

    The sentence "The absolute value to the solution of the quadratic formula in which 'a' is equal to positive fifteen, 'b' is equal to zero, and 'c' is equal to sixty-three point five," is 127 and has 127 letters.

  • Dan The Meme Man
    Dan The Meme Man 14 days ago

    there's too many fucking fours oh four k

    ALAAP SARKAR 14 days ago

    Stirring would not follow the fixed point theorem if the spoon touches the walls of the cup during stirring since it would create a hole and all points can then move around the spoon.

  • Daan Sentjens
    Daan Sentjens 15 days ago

    13:08 wait, infinite isn't a number. Or is it?

  • Amber Mature
    Amber Mature 15 days ago

    6 by 6 checkerboard of different colors
    JUST ROTATE 180░!!!

  • JSR _154
    JSR _154 15 days ago

    Not true 28 for example 2+8=10, 28-10=18, 18-10=8, 8 is not 9

  • Chirag Mantri
    Chirag Mantri 15 days ago

    That moment when 15:11 ..........................

  • clout boi
    clout boi 16 days ago

    1:56 tfw you see a bigger penis than yours.

  • Pixel Blast
    Pixel Blast 17 days ago


    • Pixel Blast
      Pixel Blast 17 days ago


  • stavros psaroudakis
    stavros psaroudakis 17 days ago

    I am 13 and i prefer this channel. I can't even imagine how i would enjoy sessemy studios.

  • Johan Klovsjö
    Johan Klovsjö 17 days ago

    When you introduce the spoon to the cup of coffee, do you not in fact create a hole in the coffee? And thus there would not have to be any point remaining in its exact position. Appreciate answers, thanks :)

  • WeirdozChannel
    WeirdozChannel 17 days ago

    Michael your music makes everything scary

  • s Script
    s Script 17 days ago

    this video correspond to your other video that explains randomness, probability and coincidences. and i think this is how the universe is built upon

  • Sophisticated Salamander

    1:58 Sponsored by pornhub

  • Fr_87
    Fr_87 17 days ago

    Andy Warhol you little madlad

  • Liam Grohs
    Liam Grohs 17 days ago

    I was eating walnuts while watching.

  • Huang Ou
    Huang Ou 17 days ago

    I wanna know what’s past OMEGA

  • Shaun Chabikwa
    Shaun Chabikwa 18 days ago


  • Whysy Boy
    Whysy Boy 18 days ago

    "And as for always thanks for watching" then he blinked four times

  • qweryt
    qweryt 18 days ago


  • Jakc Skelimgton
    Jakc Skelimgton 18 days ago

    positive fifteen has the same value of letters as 15/+15

  • Xavier Mikol
    Xavier Mikol 18 days ago

    I'll never fourgive him four those terrible jokes.

  • Un Known
    Un Known 19 days ago

    I bet you it's empty 4:23

  • Hudson Truitt
    Hudson Truitt 19 days ago

    Haha piens is on the moon hahaha

  • Ryan Kelly
    Ryan Kelly 19 days ago

    In the thumbnail you might think that the middle one is is the biggest but they're actually all the same size

  • Omar Issa
    Omar Issa 19 days ago

    mankind will never change, there are ancient arts of dicks, modern arts of dicks, and now, space arts. dicks are in almost every part of art. The immaturity of men has no bounds XD

  • lilBean15
    lilBean15 19 days ago

    What is the closest number to infinity without being it or above it

  • KaskaVenom
    KaskaVenom 19 days ago

    Ohhhhhhh good point , even irl

  • LavaError_LP
    LavaError_LP 19 days ago

    But you can do that whift the glowing Pixels make the Little thing so small Like 1 Pixel of the big one Then move IT to the green one ON the legt Side and rotate it 180° wola Not 1 Glowing!!!

  • Phantom Blade
    Phantom Blade 19 days ago

    Sorry but you need to fourtify the fact that I'll see you next time, how do I know you are really thanking us four watching.... stop being so fourward....

  • Eonde Nobrow
    Eonde Nobrow 20 days ago

    Hey Vsauce, please make an awesome video(as always) on "The Other Dimensions"(4th and 5th).

  • Александр Бантьев

    This video was very infourmative.

  • Madhav Raghu
    Madhav Raghu 20 days ago

    I was gonna make a four pun, but I fourgot what it was.

  • Goomboi
    Goomboi 20 days ago

    1:58 lol

  • Roman Gamer
    Roman Gamer 20 days ago

    I own a FOURklift.

  • Shikimoribito
    Shikimoribito 20 days ago

    "4 is a cosmic number" only in English you cuck.

  • Martijn Noordermeer
    Martijn Noordermeer 20 days ago


  • Zach The Ripper
    Zach The Ripper 20 days ago

    Lol the description has the word gullible in it

    • Cd-iLozytp
      Cd-iLozytp 5 days ago

      Holy shit it does
      I thought this was a jape but no
      Edit: Holy shit I was just japing and trying to get you to check the description, then I checked it and it did say gullible
      This is meta-levels i wasn't ready for

  • Chromiia YT
    Chromiia YT 20 days ago

    M O O N P E N I S ?

    RALPH JAYAMANNE 20 days ago +1

    Cool intro

  • Alavoi
    Alavoi 20 days ago +1

    14:55 anyone else notice he did FOUR blinks to end the video.

  • P.C.P
    P.C.P 21 day ago

    7 in Thai เจ็ด
    Four letters
    Four = สี่
    Three letters
    Three = สาม
    Three letters, alternative?
    Let's try another
    Infinite = อนันต์
    Six letters
    Six = หก
    Two letters
    Two = สอง
    Three letters
    Twenty seven = ยี่สิบเจ็ด
    Ten letters
    Ten = สิบ
    Three letters.

  • ex aid zombie
    ex aid zombie 21 day ago


  • That Asshole
    That Asshole 21 day ago

    Here I was thinking I could watch a v-sauce video without him talking about infinity
    What a fool I was.

    KAMIKAZEKITTIES 21 day ago

    I wonder what watching your videos after eating magic mushrooms while smoking pot and inhaling nitrous oxide would be like.

  • MagicDoorMan 23
    MagicDoorMan 23 21 day ago

    I haven't read through the comments and I'm rather late but did anyone else notice him blink four times at the end? At 14:50

  • Coo Coo Cat
    Coo Coo Cat 21 day ago

    what about a GOx(10^100)Gle?

  • Johan Boserup
    Johan Boserup 21 day ago

    This is one of your best. Absolutely brilliant!!

  • Рената Сабирова

    The loop in Russian language contains of three numbers:
    4 (четыре) = 6
    6 (шесть) = 5
    5 (пять) = 4
    And so on 👌

  • Olivier Thibault
    Olivier Thibault 22 days ago


  • BrainyBrian
    BrainyBrian 22 days ago

    So we are low key drawing penises on the moon, we have reached the peak of human evolution

  • Fingers 57
    Fingers 57 22 days ago

    Hey, that’s pretty good :D

  • Acella, Multiverse Dweller

    Oh fork, there is a Four-hal penus on the moon

  • gedstrom
    gedstrom 22 days ago

    I cringe every time I hear them talk about the various types of infinities. Infinity is a concept and NOT a number. Therefore, any sort of comparison of infinite sets is meaningless. This also makes many of the so-called infinity paradoxes meaningless because they are treating infinity as a number.

  • SweetSpotGuitar
    SweetSpotGuitar 22 days ago

    Desmos FTW. Love that tool!!

  • BeatStreat JB
    BeatStreat JB 22 days ago

    In Germany we say Vier

  • MackAreYouShaw
    MackAreYouShaw 23 days ago

    Subscribe to Vsause for more scooter trick montages

  • Tiffany Croone
    Tiffany Croone 23 days ago

    5:02-522 what about numbers with a 0 in the ones place? Does that make this a theory? Example, 10. If you add 1 to 0 you will get 1. Not 9. 20. 2+0=2.

  • Peanut B
    Peanut B 23 days ago

    14:59 , that outro reminds me of the outro from Numberphile's "The Four Color Map Theorem" video

  • ABNTGeneric
    ABNTGeneric 23 days ago

    What’s the song at the end?

  • Dumaflatchi
    Dumaflatchi 23 days ago

    Anybody else check those globes and see that the smallest one is over a thousand dollars

  • Eternal Dog
    Eternal Dog 23 days ago

    3:35 Take the whole square, Rotate it 180 Degrees and place it where the first line of squares on the left is on the darker square at the bottom left of the main image, and the rest are within the light grey area of the bottom right. (image is not perfect, but the idea is that the grey and dark grey squares do not overlap. They swap sides at the exact point they touch Dark|Gray to Gray|Dark. All other colours/squares are irrelevant at that point.)
    If i am getting the concept wrong, could someone please explain it more in depth.
    Also at 3:44 the bottom square is lighting up in the presentation when it shouldn't. It's not the middle square.

  • TJHammer28 - PSN/PC
    TJHammer28 - PSN/PC 23 days ago

    Have I ever told you the definition of insanity? "Four."

  • Albert Sephardi
    Albert Sephardi 23 days ago


  • Razl Gazl
    Razl Gazl 23 days ago

    Part 5 is confirmed, lads!

    Sorry for that...