The Banach-Tarski Paradox

  • Am Vor 5 years

    VsauceVsauce

    Dauer: 24:13

    Want more brain food? Want your house to become a museum? Now you're thinking: www.curiositybox.com
    Q: "What's an anagram of Banach-Tarski?"
    A: "Banach-Tarski Banach-Tarski."
    twitter: twitter.com/tweetsauce
    Instagram: instagram.com/electricpants
    Kevin’s Field Day video: de-film.com/v-video-1zARMZ08ums.html
    Field Day: de-film.com/ch-UCRPktNf5vnBR1J4e7t1RUVg
    Deep dream animation by instagram.com/NaderMakki/
    If you like it, you'll love this video also by Nader: de-film.com/v-video-fJ9j_z2kXI0.html
    Chocolate illusion: mathandmultimedia.com/2014/07/22/explanation-infinite-chocolate-bars/
    Chocolate illusion video: de-film.com/v-video-dmBsPgPu0Wc.html
    related Numberphile videos:
    sizes of infinity (includes diagonal argument): de-film.com/v-video-elvOZm0d4H0.html
    infinity paradoxes: de-film.com/v-video-dDl7g_2x74Q.html
    Vi Hart on types of infinity: de-film.com/v-video-23I5GS4JiDg.html
    Countable & uncountable definitions:
    mathinsight.org/definition/uncountable
    en.wikipedia.org/wiki/Countable_set
    en.wikipedia.org/wiki/Uncountable_set
    Banach-Tarski on wikipedia: en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
    Banach-Tarski proofs:
    math.uchicago.edu/~may/REU2014/REUPapers/Robinson.pdf
    www.math.hmc.edu/~su/papers.dir/banachtarski.pdf
    people.math.umass.edu/~weston/oldpapers/banach.pdf
    Banach-Tarski explinations online:
    www.irregularwebcomic.net/2339.html
    www.kuro5hin.org/comments/2003/5/23/134430/275?pid=5#10
    skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.html
    austinrochford.com/posts/2014-05-14-banach-tarski-paradox.html
    www.math.cornell.edu/~mec/Summer2009/Whieldon/Math_Explorers_Club%3A__Lesson_Links/Entries/2009/7/28_Lesson_6%3A__Whats_an_Anagram_of_Banach-Tarski.html
    rachellevanger.com/index_files/BT%20Animated%20Presentation%20Web.pdf
    quibb.blogspot.co.uk/2013_03_01_archive.html
    blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html
    geopolicraticus.wordpress.com/tag/banach-tarski-paradox/
    dgleahy.com/p47.html
    www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml
    Cayley graph animated gif: twitter.com/GIFsofWikipedia/status/624202342259240960
    Hilbert’s hotel on wikipedia: en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
    types of infinity: www.xamuel.com/levels-of-infinity/
    set theory and quantum physics: link.springer.com/article/10.1007/BF02213427#page-1
    LHC gif: cms.web.cern.ch/news/lhc-data-be-made-public-open-access-initiative
    Zermelo-Fraenkel axioms of mathematics: mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
    Is math invented or discovered?
    phys.org/news/2013-09-mathematics-effective-world.html
    www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/
    more deep dream images: www.reddit.com/r/deepdream/
    BOOKS:
    The Pea and the Sun: www.amazon.com/The-Pea-Sun-Mathematical-Paradox/dp/1568813279
    The Outer Limits of Reason: www.amazon.com/Outer-Limits-Reason-Science-Mathematics/dp/0262019353
    Why Beliefs Matter: www.amazon.com/Why-Beliefs-Matter-Reflections-Science/dp/0198704992
    Things to Make and do in the Fourth Dimension: www.amazon.com/Things-Make-Fourth-Dimension-Mathematicians/dp/0374275653
    Music by de-film.com/us/JakeChudnow and
    www.audionetwork.com

voidredstone
voidredstone

Me: trying to take the video seriously and learn something My brain: furry ball

Vor Stunde
click me
click me

0 divided by infinity equals- *Physics cannot predict what this number is*

Vor Stunde
Jamie Bainbridge
Jamie Bainbridge

If you ever think your job is pointless, some mathematician wrote a paper saying infinite numbers plus one is both a larger set than infinity and isn't a larger set than infinity. Thanks mate, really helpful, great work.

Vor 5 Stunden
Релёкс84
Релёкс84

infinity + 1 = infinity. Nobody writes papers to explain this relatively simple fact.

Vor 4 Stunden
Oyong Santoso
Oyong Santoso

If you rotate URRU to become DURRU it becomes RRU which has already been placed somewhere else in the circle. Right???

Vor 6 Stunden
Релёкс84
Релёкс84

Yes, which is why valid paths must not back track.

Vor 4 Stunden
Neon SWitchblade
Neon SWitchblade

"Blah, blah, blah" is not infinite. There is exactly 873,450,316,993,444,303 of them.

Vor 9 Stunden
Brian Arbenz
Brian Arbenz

Hundreds of thousands of your viewers are now tearing their dollar bills up, hoping to double their money. And wow, are they gonna be mad!

Vor 10 Stunden
Kim NANA The Artistic Masterpiece Whaley
Kim NANA The Artistic Masterpiece Whaley

This is just fascinating

Vor 12 Stunden
Mr. Johnson
Mr. Johnson

don't try the dollar shit it doesn't work.

Vor 12 Stunden
atrimus
atrimus

13:15 Red Dead Redemption!

Vor 13 Stunden
Ubaid Baig
Ubaid Baig

i dont understand shit but i watch to feel smart

Vor 14 Stunden
treelongated musk
treelongated musk

My brain hurts

Vor 17 Stunden
MagicReason
MagicReason

I'm only commenting here because the image for this video looks like a butthole, and I think that's what Michael really likes.

Vor 19 Stunden
Alinn
Alinn

I can’t not think with common sense, what does any of this mean?

Vor 19 Stunden
Johnny Espinoza
Johnny Espinoza

Think the dollar will still work in a machine

Vor 19 Stunden
Λευτερης
Λευτερης

you heard it guys no hole will be left unfilled

Vor 20 Stunden
Ryan Reyna
Ryan Reyna

this has given me more brain cells than ive had in my life

Vor 20 Stunden
Mohammed Tahmid
Mohammed Tahmid

5:46 that's a weird way to write 8

Vor 21 Stunde
Gromp
Gromp

Can't you do the same with Whole numbers just like you did with real numbers on that list? Take whole numbers, just remove the 0. so the first whole number is 5032164.... the second 7829136... and so on then add 1 to each part or deduce 1 if its a 9 and you'll have 68281.... which is obviously a new number isn't that also the case here?

Vor 22 Stunden
Релёкс84
Релёкс84

It doesn't work because whole numbers always have a finite amount of digits: an endless string of number does not generally correspond to a whole number, unless it ends in an endless string of zeros. And this is critical, because if you were to construct a string of number based on cantor's argument, it would necessarily end in an infinite string of non zero digits and therefore not desbrice a whole number.

Vor 19 Stunden
Ekata Satya
Ekata Satya

is there any practical use in this paradox, because life on Earth is practical..

Vor Tag
Jeff Bautista
Jeff Bautista

VSauce: What is infinity? Gojo Satouru: 😏

Vor Tag
Ricardo Ribeiro
Ricardo Ribeiro

This isnt properly explained in the sense that the whole sphere should be all the same color, a color that would be the mix of all the colors because each sphere of points contains all the points including the other sphere's points, so each of the decomposed spheres is equal to the combined sphere because its Just all the points on top of all the points, 6 layers of the same points

Vor Tag
eggynack
eggynack

No, every position on the sphere is hit exactly once. And they are thus each only a single color.

Vor 13 Stunden
Balou
Balou

Never have i had a bad customer service as now, changing people’s room everyday and stuff ... Never coming back To Hilbert’s Hotel 📌

Vor Tag
Mello Gee
Mello Gee

Good frickin' grief, dude. Just when I thought I was starting to finally grasp the Klein Bottle concept, someone on the 8chan discussion board decides to toss this Banach-Tarski concept at me, which ultimately led me here. You're a great teacher and you explain things very well in your videos, but this Banach-Tarski thing is hurting my brain. Next up: Quantum Entanglement and the Double-Slit experiment, for those of you who are not confused enough yet.

Vor Tag
Nghiep Luu
Nghiep Luu

11:53 arccoss

Vor Tag
_xiiaoyang
_xiiaoyang

I watch ur video when insomnia hits me

Vor Tag
MrDes1980
MrDes1980

Дык частицы жеж в вакууме возникают их ниоткуда и анигилируют постоянно. Похоже это явления одного порядка.

Vor Tag
CJVPlayz
CJVPlayz

Only death but live soul can pass though infinity = ∞

Vor Tag
masterpotato 120
masterpotato 120

1+1=1 I don't know any more

Vor Tag
Frances Hogg
Frances Hogg

Doesn't this paradox prove that infinity doesn't exist?

Vor Tag
ELISA MOYA
ELISA MOYA

that is how cels divide right?

Vor Tag
Miroslav Daniel Roshal
Miroslav Daniel Roshal

yutub be lik: twenti fiftin: nyet twenti sextin: nah twenti sebuntin: never twenti eiteen: not twenti neinteen: no TWENTI TWENTI: OKIE DOKIE LETS RECOMEND DIS TO EVERYWHUN!!!1 (P.S. Comment made in 2021) (P.S. This comment is a joke)

Vor Tag
Koji
Koji

I've watched this video maybe 25 times since I was 12 years old and I still don't understand how this works

Vor Tag
Samuel Magi locusts
Samuel Magi locusts

I stoped believing after the rip up a dollar gain 2 dollars thing. You can’t get something from nothing.

Vor Tag
Mr. Johnson
Mr. Johnson

@Samuel Magi locusts my exact thoughts when i saw the dollar thing

Vor 12 Stunden
Samuel Magi locusts
Samuel Magi locusts

@Klejnot Nilu check out 1:54 of the video. You can clearly see that he ripped those two bills differently than the one in his hand.

Vor Tag
Klejnot Nilu
Klejnot Nilu

Pls say you're baiting

Vor Tag
Klejnot Nilu
Klejnot Nilu

Wait wtf

Vor Tag
Jason Boyle
Jason Boyle

I lost him at "hey guys"

Vor Tag
Samuel Magi locusts
Samuel Magi locusts

It’s so hard to tell when he’s giving facts or making something up lol

Vor Tag
Roguewindow 758
Roguewindow 758

Him: literally does a duplication glitch in real life Gta player: I’m listening

Vor Tag
Market Socialist
Market Socialist

The gerog contour diagonal argument is proven incorrect via the true statement that there are as many even numbers as whole numbers, infinite will always match up with infinite for infinity contains all even the things infinity doesn't contain is contained in it... Otherwise it isnt infinite ;)

Vor Tag
eggynack
eggynack

Why would that prove the argument incorrect? There are as many even numbers as whole numbers, prime numbers, integers, rational numbers, and infinite others. There are more real numbers than any of those.

Vor Tag
Bashir Weheliye
Bashir Weheliye

9:15 no hole will be left unfilled

Vor Tag
unaura
unaura

1 fuzzy ball = 2 fuzzy balls

Vor Tag
Kunwar
Kunwar

What I learnt from genius people in these videos : *To become a genius one needs to write with a marker instead of a normal pen*

Vor Tag
tecHow
tecHow

The chocolate thing was easy

Vor Tag
Alexander Bozhilov
Alexander Bozhilov

The circel's name is Bob

Vor 2 Tage
cash man
cash man

Watch this guy if u want a big brain

Vor 2 Tage
Shirley .R.
Shirley .R.

guys i have a shower thought: how much is flat? or - how flat is flat

Vor 2 Tage
Loop Innovation
Loop Innovation

Am I the only deranged by how he write the 8 number ? 5:46

Vor 2 Tage
C-moon and Pucci
C-moon and Pucci

fun fact: none of fun fact is a fact then does that mean this fun fact is a fact?

Vor 2 Tage
Minecrafty Cam
Minecrafty Cam

Wait... Wut

Vor 2 Tage
Keana Dianne
Keana Dianne

the fuck

Vor 2 Tage
Farras Alghazy
Farras Alghazy

my brain:kaboom? me:yes rico kaboom

Vor 2 Tage
Zeke Korte
Zeke Korte

isnt the money thing illegal?....

Vor 2 Tage
Ar707x
Ar707x

THX MY BRAİN HURTS

Vor 2 Tage
Ar707x
Ar707x

he waste a dolar

Vor 2 Tage
Akash Krishnan U
Akash Krishnan U

@Legend oh ok my bad

Vor 12 Stunden
Legend
Legend

@Akash Krishnan U No its a literal crime to destroy US currency. it doesn't matter if its "his"

Vor 19 Stunden
Akash Krishnan U
Akash Krishnan U

@Legend no it is not,it is his money,he can do whatever he wants with it

Vor Tag
Legend
Legend

@Akash Krishnan U it’s a crime to destroy currency

Vor Tag
Akash Krishnan U
Akash Krishnan U

Bruh ,he gets a lot of money from these type of videos A dollar isnt really a big thing for him

Vor Tag
Prometheus
Prometheus

ive watched this video many, many times, and i never quite understand it, i guess part of it is the trouble i have connecting infinity to the real world. this problem, imo, only works when you assume that infinity is truly infinite, but that's sort of impossible for shapes outside mathematics i hope im wrong and something lights up in my head one day and suddenly i understand everything! that'd be better

Vor 2 Tage
Chili Ghost
Chili Ghost

So.. If it's possible to collide particles and get more particles, couldn't that mean it actually may be possible to build a machine that produces more energy than it uses?

Vor 2 Tage
Monti McShan
Monti McShan

Watching this while baked is a trip ..

Vor 2 Tage
Judah Speece
Judah Speece

You lost me at, “There’s a famous way to...”

Vor 2 Tage
Matthew Song
Matthew Song

I totally wasn't fooled by the infinite chocolate bar trick... i hope

Vor 2 Tage
scott turner
scott turner

Yes I'm retarded this proved it

Vor 2 Tage
Trevor Sabinson
Trevor Sabinson

I feel personally offended by all of this

Vor 2 Tage
Akash Krishnan U
Akash Krishnan U

@Trevor Sabinson he didnt draw it tho- Wtf is wrong with you

Vor Tag
Trevor Sabinson
Trevor Sabinson

Look how close he came to drawing a full blown swastica at 13:46

Vor 2 Tage
Louis Hazelwood
Louis Hazelwood

Who on earth would give this 20K thumbs down :(

Vor 2 Tage
vx vx
vx vx

This is how Blender UV spheres works

Vor 2 Tage
Zendusi
Zendusi

S w e l l

Vor 2 Tage
Zeli Mitchell-Hopmeier
Zeli Mitchell-Hopmeier

I just shat myself

Vor 2 Tage
John Marston
John Marston

My brain stopped functioning

Vor 2 Tage
Dr Silverium
Dr Silverium

1+1 equal 1 lol

Vor 2 Tage
Doug Steel
Doug Steel

There's no demonstrable relationship between maths and physics. That might sound crazy, but a relationship is stricter than tolerant correlation. On a practical level, I say practical, objects can't be closer together than the planck length the way they can in maths

Vor 2 Tage
Larry Pugsley
Larry Pugsley

For anyone who watches vsauce, there’s hope. Every one of his videos are amazing!

Vor 2 Tage
Midnattsol
Midnattsol

The doublicating sphere is an example of the difference between math and physics. While the description can be doublicated, not every described point contains matter. The matter of the object is not infinite, only the mathematical description of it is, as the description is an approximation, not an accurate representation. The more you zoom in, the bigger in relation will the distance become between described points which represent something real.

Vor 2 Tage
Panzerkampfwagen VI
Panzerkampfwagen VI

1:18 ohh yeah, that is the good shit

Vor 2 Tage
CoolSkeleton95
CoolSkeleton95

1:40 : Mean while michael: *internal suffering*

Vor 2 Tage
John0693
John0693

So, mathematical points are bullshit.

Vor 3 Tage
xaralampis_
xaralampis_

Me watching this video for the 5th time hoping that I am smarter enough to understand

Vor 3 Tage
J_Wolf_Cuber
J_Wolf_Cuber

bruh just use the bundle dupe glitch in the snapshots of 1.17 XD

Vor 3 Tage
Teodoro Marques
Teodoro Marques

OMG THE SONG ON THE END, LOOKS LIKE A COMMON OPENING OF A BRAZILLIAN NOVEL

Vor 3 Tage
Keelan Thornton
Keelan Thornton

Makes me think of Cellular mitosis.

Vor 3 Tage
javed ansari
javed ansari

Hey Michael, Do you think atoms and molecules or cells reproduce themselves like that

Vor 3 Tage
Yo The Profit
Yo The Profit

I’m running out of dollars are you sure I can make two dollars from a dollar lolololol

Vor 3 Tage
IVO
IVO

Música brasileira pra encerrar foi perfeita

Vor 3 Tage
robert bennett
robert bennett

Maybe it was through this process sub atomic particles multiplied during the big bang and began our universe.

Vor 3 Tage
JasonSpeeber
JasonSpeeber

I spose the flaw of the whole theory here is that we can't even measure infinity (countable or not). So trying to base any kind of functional mathematical or physical model on it is kinda moot.

Vor 3 Tage
Bob Forrest
Bob Forrest

the dollars Michael ripped apart have different letters, try again

Vor 3 Tage
ok ok
ok ok

Infinite money glitch but chocolate

Vor 3 Tage
Evan McDonald
Evan McDonald

Out of all the vsause videos if ever watched this one is by far my favorite. It gives me chills every time.

Vor 3 Tage
martin chagra
martin chagra

Me suffering when he cuts a dólar knowing that with that I could buy Tucumán

Vor 3 Tage
Asher Mastera
Asher Mastera

"Existence exists... or does it?". I promise you, that will be the next video.

Vor 3 Tage
Biscuit Tasty
Biscuit Tasty

17 paradoxes later

Vor 3 Tage
Case McDonald
Case McDonald

This is nothing but a demonstration of why mathematics is limited.

Vor 3 Tage
SpartanKnights DAD
SpartanKnights DAD

So if you believe in a Multi Universe then I believe this concept could be applied in the real world. If applied maybe a Universe/Dimension can exist on its own or within another Universe / Dimension to an Infinite degree.

Vor 3 Tage
Shogun FPV
Shogun FPV

Are we not going to talk about how he wrote the number 8?!

Vor 4 Tage
TEMPU
TEMPU

I AM WATCHING THIS VIDEO OR AM I ???

Vor 4 Tage
Aileen Laurel
Aileen Laurel

The rural direction unusually pretend because dress assembly question until a successful authorisation. precious, burly sugar

Vor 4 Tage
MESS
MESS

so what about the chocolate again?

Vor 4 Tage
Cynthia Estrada
Cynthia Estrada

Whaaat?

Vor 4 Tage
CellGames2006
CellGames2006

I don't think it's a good idea to annoy an infinite number of hotel guests by asking them to move to the next room... you might run into problems down the line.

Vor 4 Tage
Raw Hide
Raw Hide

Is this how we’ll be able to teleport ourselves to other planets?

Vor 4 Tage
DEVESH MORE
DEVESH MORE

If this banach tarki paradox applies to real world, we can create atoms and we can call ourselves God

Vor 4 Tage
Panders Person
Panders Person

Henry stickman: *breaks the bank* This guy: *breaks my brain*

Vor 4 Tage
Rik Raunaak
Rik Raunaak

https://youtu.be/mUraYXBwrk8

Vor 4 Tage
freeflight 42
freeflight 42

He could have used a pease of paper a stick a cloth but no he used money

Vor 4 Tage
Cool Bob
Cool Bob

Okay I can’t be the only one whose brain literally hurts right now

Vor 4 Tage

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