# Fixed Points

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• Published on Sep 28, 2016
• My video on Sesame Studios: thexvid.com/video/BTjAiyyG2sw/video.html
The Curiosity Box by Vsauce: www.curiositybox.com/
My instagram: instagram.com/electricpants
DONG: thexvid.com/user/dong
Moon Museum:
en.wikipedia.org/wiki/Moon_Museum
E.A.T. en.wikipedia.org/wiki/Experiments_in_Art_and_Technology
Brouwer’s fixed point theorem:
mathforum.org/mathimages/index.php/Brouwer_Fixed_Point_Theorem
simanaitissays.com/2015/01/19/combed-coconut-must-have-cowlicks/
en.wikipedia.org/wiki/Brouwer_fixed-point_theorem
thexvid.com/video/86uarqPBJ9s/video.html
Excellent interactive wolfram demo of Brouwer: demonstrations.wolfram.com/BrouwerFixedPointTheorem/
Online graphing calculator used was: www.desmos.com/
fixed points more generally:
www.math.uri.edu/~kulenm/mth381pr/fixedpoint/fixedpoint.html
en.wikipedia.org/wiki/Fixed_point_(mathematics)
en.wikipedia.org/wiki/Fixed-point_iteration
Gullible
9s: mathforum.org/library/drmath/view/62561.html
Babylonian method:
en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
Iterated equation solver you can use to run the Babylonian method: www.wolframalpha.com/widgets/view.jsp?id=e4a9b48a942efefa14b2773c31982c29
aleph fixed point:
lukepalmer.wordpress.com/2007/06/14/the-lesser-of-infinitely-many-evils/
cantorsattic.info/Aleph
My video on counting past infinity: thexvid.com/video/SrU9YDoXE88/video.html
map projections:
www.gis.osu.edu/misc/map-projections/
www.jasondavies.com/maps/transition/
antipodes: geographer-at-large.blogspot.co.uk/2011/10/where-is-your-antipode.html
antipode-finders:
www.jasondavies.com/maps/antipodes/
www.findlatitudeandlongitude.com/antipode-map/#.V-nBkZMrIUF
Pacific antipode image: i.imgur.com/dyJQ3EW.jpg
Borsuk-Ulam:
thexvid.com/video/5Px6fajpSio/video.html
thexvid.com/video/_sA3c0AhK34/video.html
thexvid.com/video/EhAs-vZDQG0/video.html
“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!! thexvid.com/video/LYKn0yUTIU4/video.html
theweeklyriddle.blogspot.com/2010/09/cosmic-number.html

“Idempotent”: en.wikipedia.org/wiki/Idempotence
Other topology pages:
en.wikipedia.org/wiki/Homeomorphism
wiki images:
commons.wikimedia.org/wiki/File:Robert_Rauschenberg_(1968).jpg
en.wikipedia.org/wiki/Claes_Oldenburg#/media/File:Claes_Oldenburg_(1970).jpg
Globe is from Ballerby & Co. Globemakers
www.bellerbyandco.com/
instagram.com/globemakers/
music from
thexvid.com/user/JakeChudnow
and www.audionetwork.com
Any VFX that actually look cool are by thexvid.com/user/ericlanglay -- I did the rest the best I could :)
• Science & Technology

• Sam O'Brien Day ago

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

• Brian Lallement Day ago

2:43 Is that Desmos?

• Arsh Tewari Day ago

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

• firebeast 654 2 days ago

7:27 me on.my scooter

• Michael Yang 2 days ago

Andy warhol is a legend

• Daniël Mao 2 days ago +1

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

• Law Berry 2 days ago

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

• PC room 3 days ago

That 4 is in slovakia 3

• BrotherSquidman 3 days ago +1

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

• 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 - 4 days ago

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

• 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 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 6 days ago

Fuck them those damn artists, damn engineer was a retard

• MintyFreshness4 6 days ago

Hey,

VSauce

• Hitler after trying the addition subtraction thing:
NINE NINE NINE NINE NINE NINE NINE NINE

• 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 6 days ago

But the circles can rotate
/music plays

• Tyler Chen 8 days ago

the fours are coming

• 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 8 days ago +1

12:14

• AA12 Fordays 8 days ago

Is his globe always upside down?

• tumšsCuška77 8 days ago

12:15 the reference

• TheGoldenTank TGT 9 days ago

man the moon is male? thats gnarly

• Kapitan Niño 10 days ago

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

• MrTingles 10 days ago

It's just Alephs, all the way down.

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

• 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 12 days ago

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

• fivenightsofben 12 days ago

π,2,3,5,4
100,8,5,4
e,12,6,3,5,4

• Fickle Pickle 12 days ago +1

?

• Is Yeboi 13 days ago

7:30 this is basically my life

• Oetze Broek 14 days ago

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

• 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 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 10 days ago

Gravity keeps the liquid inside, so there basically is one

• 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 14 days ago

14:05
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 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 15 days ago

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

• Amber Mature 15 days ago

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

• 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 15 days ago

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

• clout boi 16 days ago

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

• Pixel Blast 17 days ago

THERES A DICC ON DA MOON

• Pixel Blast 17 days ago

I WONDER WHAT ALIENS WILL SAY-

• 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 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 17 days ago

Michael your music makes everything scary

• 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

• Fr_87 17 days ago

• Liam Grohs 17 days ago

I was eating walnuts while watching.

• Huang Ou 17 days ago

I wanna know what’s past OMEGA

• Shaun Chabikwa 18 days ago

Content

• Whysy Boy 18 days ago

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

• qweryt 18 days ago

12:15

• Jakc Skelimgton 18 days ago

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

• Xavier Mikol 18 days ago

I'll never fourgive him four those terrible jokes.

• Un Known 19 days ago

I bet you it's empty 4:23

• Hudson Truitt 19 days ago

Haha piens is on the moon hahaha

• 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 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 19 days ago

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

Ohhhhhhh good point , even irl

• 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 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 20 days ago

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

• This video was very infourmative.

• Madhav Raghu 20 days ago

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

• Goomboi 20 days ago

1:58 lol

• Roman Gamer 20 days ago

I own a FOURklift.

• Shikimoribito 20 days ago

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

• Martijn Noordermeer 20 days ago

Four.

• Zach The Ripper 20 days ago

Lol the description has the word gullible in it

• 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 20 days ago

M O O N P E N I S ?

• RALPH JAYAMANNE 20 days ago +1

Cool intro

• Alavoi 20 days ago +1

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

• 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
More!
Twenty seven = ยี่สิบเจ็ด
Ten letters
Ten = สิบ
Three letters.

• ex aid zombie 21 day ago

(0:05)

• 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 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 21 day ago

• Johan Boserup 21 day ago

This is one of your best. Absolutely brilliant!!

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

• Olivier Thibault 22 days ago

YES ANDY ! LEGENDARY !

• BrainyBrian 22 days ago

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

• Fingers 57 22 days ago

Hey, that’s pretty good :D

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

• 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 22 days ago

Desmos FTW. Love that tool!!

• BeatStreat JB 22 days ago

In Germany we say Vier

• MackAreYouShaw 23 days ago

Subscribe to Vsause for more scooter trick montages

• 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 23 days ago

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

• ABNTGeneric 23 days ago

What’s the song at the end?

• Dumaflatchi 23 days ago

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

• 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. imgur.com/a/Z3kgK8V (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 23 days ago

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

• Albert Sephardi 23 days ago

5:00

• Razl Gazl 23 days ago