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 • 24 642

  • Crassen Mlg Scopez
    Crassen Mlg Scopez 6 hours ago

    Love that the video has a fixed point where i had to close the vidoe and scip that exact second

  • Michael T
    Michael T 18 hours ago

    Hey! That's pretty good!

  • BlazingBlace
    BlazingBlace Day ago

    I cant believe someone actually drew a penis

  • Ultracrepidarian
    Ultracrepidarian Day ago +1

    But you can completely stir your coffee completely since it exists in a 3 dimensional space

  • Jamieson Lawrence
    Jamieson Lawrence 2 days ago

    buzzfeed unsolved music

  • Giglefreakz
    Giglefreakz 2 days ago

    Does anybody know an interactive version of the checkerboard? Because looking at it, it almost seems as if it’s possible to resize it, fit it into a corner and not have any square light up.

  • Hell's Pain
    Hell's Pain 2 days ago

    look those tabs at 10:19

  • John Shumate
    John Shumate 4 days ago

    The absolute value of negative thirty seven has thirty seven letters in its name maybe that means something

  • swagdog100
    swagdog100 4 days ago


  • redfong
    redfong 5 days ago


  • Nick Korkodylas
    Nick Korkodylas 5 days ago

    You get an airman out of earth but you can never get the Air Force out of the airman.

  • Mario Hanna
    Mario Hanna 5 days ago +1

    to the coffemug analogy wouldnt the droplets you takeout with the spoon cause it to be possible to complete mix the coffe?

    • Walter Robinson
      Walter Robinson 3 days ago

      We assume frictionless coffee
      But i was thinking, if the spoon touches the bottom of the cup, doesnt it introduce a hole/cut?
      Allowing us to completely mix up the coffee?

  • RED Engineer
    RED Engineer 6 days ago +4

    aleph naught

  • Toe Knee
    Toe Knee 6 days ago

    12:15 idubbbz is that you?

  • Денис Кулініч

    Four 4

  • Ignacio Aguilera
    Ignacio Aguilera 7 days ago

    2:48 : 3am i died.

  • co8222
    co8222 7 days ago

    1:33 lol

  • RowingNoob
    RowingNoob 8 days ago

    Well, Vsauce, I'm sorry, but I do not want to dig straight down, I think none of us do. Not because we are, scared, or, it being impossible, but because we dont want to dig straight down just to loose 5 hours worth of strip mining for diamonds, just to fall into lava. It sounds fun, but you're in your own boat, sorry.

  • Captain Oblivious
    Captain Oblivious 8 days ago

    "Well, of course you can... NOT!"

  • Vielheim
    Vielheim 9 days ago


  • Berken Tekin
    Berken Tekin 9 days ago

    So what if I put a cylinder inside the coffee before stirring?

  • ja9395
    ja9395 9 days ago

    I'm not sure what you says about the coffee is true cause i don't know if a liquid a compact or not. Are orbjects open or closed? Actually they're just molecules


    what the 15:56. See her mouth.

  • Gautam Nag
    Gautam Nag 10 days ago

    life lesson #965 13:58

  • amy liu
    amy liu 10 days ago

    This is like the bane of OCD...

  • Evendo Sean D'mello
    Evendo Sean D'mello 10 days ago

    i came here because i was searching for md4/md5 fixed points ..... damn you google. wrong.

  • Job Muiles
    Job Muiles 11 days ago

    Trying to find information about numerical fixed point iterations. I got lost

  • KSR3
    KSR3 11 days ago

    *innconetly* puts his initials on the moon

  • Elnathan Ayanam
    Elnathan Ayanam 11 days ago

    Andy Warhol the savage😂😂

  • Graham Cartwright
    Graham Cartwright 11 days ago

    who else thinks the Apollo 12 team leaving the moon was full of confetti?

  • Yami
    Yami 11 days ago

    What is this, Vsauce 4?

  • Incompetence Logistics

    12:15 is iconic, but the context is so much better

  • Major Johnson
    Major Johnson 12 days ago

    Hold up, stirring coffee *can't* follow the fixed point law. It allows for "cutting and pasting": its a liquid.

    Take a toroidal shaped grouping of the liquid (that contains all of it) and rotate it around the circle defining the torroid, then rotate around the center of that circle. No points will remain fixed in place: the first rotation leaves only the points on the circle where they started, but the second rotation moves all of those points without moving any other point back to its start.

  • MissKisKis
    MissKisKis 12 days ago +1

    In Russian, the words for 6, 5 and 4 loop and never reach a fixed point. Someone should check that no such loop exists in English

  • the cool koopa
    the cool koopa 12 days ago

    At least we know he doesn't work four the illuminati

  • Zachary Sukovaty
    Zachary Sukovaty 12 days ago


  • Vol100000
    Vol100000 12 days ago +1

    13:52 but Michael, if you push enough, you break the button.

  • blablubb
    blablubb 13 days ago

    FOUR is language-specific, isn#t it?

  • MasterODisguise
    MasterODisguise 13 days ago

    It somehow comforts me that a poorly drawn penis was graffitied on an art museum that is on the moon

  • Saswat Padhi
    Saswat Padhi 13 days ago

    @Vsauce - The number shown at 9:00 doesn't make sense. The subscript for an Aleph number is always an "ordinal number", not a "cardinal number". So, an Aleph subscript doesn't make sense. I think you wanted to use Omega instead of Aleph.

  • Mohammed Qutu
    Mohammed Qutu 13 days ago


  • Ben Huston
    Ben Huston 13 days ago +3

    1:57 "Kill me please."-Vsauce, 2016

  • ZeroGeo
    ZeroGeo 14 days ago

    1:52 r/madlad

  • GameBossBot
    GameBossBot 14 days ago

    I love the puns

  • Joshua Martin
    Joshua Martin 14 days ago

    I think it was covered up because it looked like a d###

  • CefBlueware
    CefBlueware 15 days ago +1

    1:57 I need a 10 hour version of that stare

  • [MeMe] Lord Blitz of Crusades

    It's a space dick

  • Andrew Davis
    Andrew Davis 15 days ago

    How can you say that temperature, t, dependent upon some position, p, modeled by the function t(p) is continuous? If it is discontinuous, wouldn't the reasoning there fall apart?

  • Nibbs
    Nibbs 15 days ago

    Lmao he put a peen on the moon😂

  • Spedur
    Spedur 15 days ago

    Even Michael is mortified about the fact that there is a d*ck on the moon.

  • MrAcuriteOf1337
    MrAcuriteOf1337 16 days ago

    "Twelve plus one more than a score", including spaces, is twelve plus one more than a score letters long

  • cheezslice
    cheezslice 16 days ago +1

    Mista must hate the end of this

  • Unique Azrael' Gaming
    Unique Azrael' Gaming 16 days ago

    1:56 when you're job was simply to make the first art in another celestial body
    And you fucked up
    (Kids in school for be soo proud they're NATURAL thing to do is done by a professional scientist that works in nasa and is for the MOON)
    A dick form

  • Bohn Jarker
    Bohn Jarker 16 days ago

    Dick on a chip

  • dom cusano
    dom cusano 16 days ago +1

    2:50 is it just me or did anyone else’s eyes bug out

  • Nuada the silver hand
    Nuada the silver hand 16 days ago +6

    Anybody else notice, at the end... He blinked FOUR times.

  • Yellowstone The Pony
    Yellowstone The Pony 16 days ago

    God dammit Andy...

  • Kane A
    Kane A 17 days ago

    7:30 - everything falls over wheil you just ignore it i love it

  • PaperClip Studios
    PaperClip Studios 17 days ago

    “it’s the year 2030, we discovered a way to transport people to the moon. We discovered a penis”

  • Sir HoBo
    Sir HoBo 17 days ago +18

    Im sorry for posting this so late...but did ANYONE else notice that he blinked four times? @Vsauce

  • Noel Probst
    Noel Probst 17 days ago



  • Extraterrestrial Alien

    14:56 he blinks FOUR times.

  • PerriErri
    PerriErri 17 days ago +1

    I feel fixed... these videos

  • Jim Halpert
    Jim Halpert 18 days ago

    I'm lost

  • Sniper_Kid_308
    Sniper_Kid_308 18 days ago

    Four heavens sake, he blinked four times four you in the end two

  • Mage
    Mage 18 days ago


  • Sammi Zhang
    Sammi Zhang 18 days ago

    *Fixed Points* *Four*

  • Antonio Elua
    Antonio Elua 19 days ago

    Doesn't work in Spanish you can get either Cinco or a loop between seis and cuatro

  • Jiří Janoušek
    Jiří Janoušek 19 days ago

    Except coffe is a liquid so you are basically "cutting" it with the spoon...

  • Bennett Vergara
    Bennett Vergara 19 days ago

    I just think this is wrong because at 3:50 when he’s doing that thing I can make it where none of them are touching

  • Crunchy Guy
    Crunchy Guy 20 days ago

    Notice how he blinked four times at the end of the video.

  • Dick Longflop
    Dick Longflop 20 days ago

    I miss vsauce 💔😢

  • Tobias Johansen
    Tobias Johansen 20 days ago

    I do not get why the temperature and pressure has to flip when moving the meters around the earth. Since they are only moving half a globe isn't there a chance one might never go up, and the other might never go down thus they don't ever cross?

  • SydTheGoat
    SydTheGoat 21 day ago

    Fixed points in the sky

  • Prathamesh Sirmalla
    Prathamesh Sirmalla 22 days ago

    The coffee cup example of fixed point does not satisfy all of the conditions of brouwer's theorem, the 'cutting and gluing condition'.

  • JheyDraws
    JheyDraws 22 days ago

    * Glides in *
    *_Hey, Vsauce, Michael here_*

  • Marius Schiller
    Marius Schiller 24 days ago

    That ending would’ve killed Mista with bad luck...

  • Alex Neal
    Alex Neal 25 days ago

    It says gullible in the description

  • AE Universe
    AE Universe 25 days ago +1

    When he ask you to say any number you can think of and you choose a regular plain one 😭

  • Daniel Howerth
    Daniel Howerth 25 days ago


  • Immortal Potato
    Immortal Potato 26 days ago

    F O U R

  • Chris O
    Chris O 26 days ago

    I like how when his smile faded mine grew

  • AndreeH
    AndreeH 26 days ago


  • Donkey
    Donkey 26 days ago +1


  • Aiden Andre
    Aiden Andre 26 days ago +1

    The smartest and most creative people of earth are most often the most mentally questionable and crazy, same with the opposite, if you go into some insane asylums, you find some genius’ and extremely creative minds, Michael here is the perfect example

  • Almost Brilliant
    Almost Brilliant 26 days ago

    Stirring Coffee is almost certainly not a continuous transformation.

  • Shailesh Rana
    Shailesh Rana 26 days ago +1

    Michael FOUR sure referenced iDubbz

  • Shailesh Rana
    Shailesh Rana 26 days ago +1

    Bro, Michael legit showed a dick in a video

  • Andrej Patak
    Andrej Patak 27 days ago

    In my lenguage cosmic number is 3
    It has 3 letters

  • John Gallentine
    John Gallentine 27 days ago

    You can get anything you want, at a alephs restaurant.

  • tory mountain
    tory mountain 27 days ago

    Warhol is a leftist degenerate. Pardon the tautology.

  • GamingSiblings
    GamingSiblings 28 days ago

    Doing things over and over again, expecting a insanity...some guy on an island told me that.

  • Prikshit Garg
    Prikshit Garg 29 days ago

    There is a pee pee on the moon. This made my day

  • christian Saldaña
    christian Saldaña 29 days ago

    And,∞=≠∞,because,even what fraction you give over infinity,whatever you add or subtract,whatever you divide or multiply,even what operation you do to it(like powers,square roots,cube roots,etc.),it's still infinity,but is a different number.

    Therefore,it is in a state of superposition,though,it is "numerical superposition", and,∞ can't be 0,because ∞-1=∞,but 0-1=-1.

  • KAUR4
    KAUR4 29 days ago

    Don't show this video to Mista.

  • Tixein •
    Tixein • 29 days ago

    "Bobs or vegana? Whichever will it be?"

    Jokes on you pewds we chose the *pp lol*

  • TurtleBoy Comedy
    TurtleBoy Comedy Month ago

    12:15 Idubbz has entered the chat

  • canadianbacon1199
    canadianbacon1199 Month ago

    4:00 what if you were to shrink the pixel lin small enough that it would fit inside of one square of the origional. move it over to the left edge flip it 180 degrees and position it on top of the gree square then youy slide it over to the right to the right enough so that the edges are perfectly lined up with the edge line of the green square, with one collum outside of the gree square?

  • Pirrad The Vault Hunter

    Yeah, that's a dick

  • Katie Giles
    Katie Giles Month ago +2

    I wonder if TheXvid would break if vsauce uploaded a video like this in 2019...