The Banach–Tarski Paradox

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  • Published on:  Friday, July 31, 2015
  • Q: "What's an anagram of Banach-Tarski?"
    A: "Banach-Tarski Banach-Tarski."

    twitter: https://www.twitter.com/tweetsauce
    Instagram: http://www.instagram.com/electricpants

    Kevin’s Field Day video: https://www.vuiclip.net/video/1zARMZ08ums/video.html

    Field Day: https://www.vuiclip.net/channel/UCRPktNf5vnBR1J4e7t1RUVg

    Deep dream animation by http://instagram.com/NaderMakki/

    If you like it, you'll love this video also by Nader: https://www.vuiclip.net/video/fJ9j_z2kXI0/video.html

    Chocolate illusion: http://mathandmultimedia.com/2014/07/22/explanation-infinite-chocolate-bars/

    Chocolate illusion video: https://www.vuiclip.net/video/dmBsPgPu0Wc/video.html

    related Numberphile videos:

    sizes of infinity (includes diagonal argument): https://www.vuiclip.net/video/elvOZm0d4H0/video.html
    infinity paradoxes: https://www.vuiclip.net/video/dDl7g_2x74Q/video.html

    Vi Hart on types of infinity: https://www.vuiclip.net/video/23I5GS4JiDg/video.html
    Countable & uncountable definitions:

    http://mathinsight.org/definition/uncountable
    https://en.wikipedia.org/wiki/Countable_set
    https://en.wikipedia.org/wiki/Uncountable_set

    Banach-Tarski on wikipedia: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox

    Banach-Tarski proofs:

    http://math.uchicago.edu/~may/REU2014/REUPapers/Robinson.pdf
    https://www.math.hmc.edu/~su/papers.dir/banachtarski.pdf
    http://people.math.umass.edu/~weston/oldpapers/banach.pdf

    Banach-Tarski explinations online:

    http://www.irregularwebcomic.net/2339.html
    http://www.kuro5hin.org/comments/2003/5/23/134430/275?pid=5#10
    http://skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.html
    http://austinrochford.com/posts/2014-05-14-banach-tarski-paradox.html
    http://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
    http://rachellevanger.com/index_files/BT%20Animated%20Presentation%20Web.pdf
    http://quibb.blogspot.co.uk/2013_03_01_archive.html
    http://blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html
    https://geopolicraticus.wordpress.com/tag/banach-tarski-paradox/
    http://dgleahy.com/p47.html
    https://www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml

    Cayley graph animated gif: https://twitter.com/GIFsofWikipedia/status/624202342259240960

    Hilbert’s hotel on wikipedia: https://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel

    types of infinity: http://www.xamuel.com/levels-of-infinity/

    set theory and quantum physics: http://link.springer.com/article/10.1007/BF02213427#page-1

    LHC gif: http://cms.web.cern.ch/news/lhc-data-be-made-public-open-access-initiative

    Zermelo-Fraenkel axioms of mathematics: http://mathworld.wolfram.com/Zermelo-FraenkelAxioms.html

    Is math invented or discovered?

    http://phys.org/news/2013-09-mathematics-effective-world.html
    http://www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/

    more deep dream images: https://www.reddit.com/r/deepdream/

    BOOKS:

    The Pea and the Sun: http://www.amazon.com/The-Pea-Sun-Mathematical-Paradox/dp/1568813279
    The Outer Limits of Reason: http://www.amazon.com/Outer-Limits-Reason-Science-Mathematics/dp/0262019353
    Why Beliefs Matter: http://www.amazon.com/Why-Beliefs-Matter-Reflections-Science/dp/0198704992
    Things to Make and do in the Fourth Dimension: http://www.amazon.com/Things-Make-Fourth-Dimension-Mathematicians/dp/0374275653

    Music by http://www.youtube.com/JakeChudnow and
    http://www.audionetwork.com
  • Source: https://youtu.be/s86-Z-CbaHA
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Comment

  • Roy Patton

    Roy Patton

     an hour ago

    You added a rotation. That isn't nothing.

  • PHOENIX

    PHOENIX

     an hour ago

    How many of you just stared at the screen for a while and totally zoned out.......multiple times?......and then pressed rewind?......multiple times? So it wasn't just me then?

  • no not gonna enter a name

    no not gonna enter a name

     3 hours ago

    If you make it an uncountably infinite number of points and color each of them a different color then you have an uncountably infinite amount of colors

  • Rad_itya 2

    Rad_itya 2

     4 hours ago

    Are point itself infinite???

  • rikyboy345

    rikyboy345

     5 hours ago

    Nigga what?

  • zudeyix

    zudeyix

     5 hours ago

    I guess it was patched

  • Vänni Urponen

    Vänni Urponen

     5 hours ago +1

    Me: does a backflip.
    Also me: you look just like me.

  • dr horseface

    dr horseface

     6 hours ago

    i lost like all my brain cells watching this

  • Atlas

    Atlas

     6 hours ago

    Doctor:Sir you have an incurable form of cancer
    Micheal:Or do i?
    (Continues to explain the impossible)

  • TheBendablespoons

    TheBendablespoons

     7 hours ago

    This shit is gonna be the key to a post scarcity society

  • anmol bhatti

    anmol bhatti

     7 hours ago

    I don't understand that circle thing

  • Leong Ka Hou Daniel 梁家豪 P5C13

    Leong Ka Hou Daniel 梁家豪 P5C13

     8 hours ago

    This just ended my sanity

  • drache444444

    drache444444

     9 hours ago

    and theres the mistake : youre betting an infinite amound of numbers agains a finite amount: you basically say that the amount of full numbers is finite. it isnt.
    let me explain :
    when ever you add another zero into the 0.00..1 i simply add 1 to the full numbers.
    you could now say "but then i have another infinite amound that i could count!" and yes , thats true , but i still wont be able to reach an end to the full numbers. infinite times infinity is infinity. no infinity². infinity minus whatever is infinity. infinity plus whatever is infinity. it doesnt end.
    what ever you try to explain that one infinity is bigger then the other i simply object -> where does one end for the other to go on further?.
    its a paradox that isnt a paradox. its faulty thinking.

  • SCORPION FIRE

    SCORPION FIRE

     10 hours ago

    ? If infinity exists, then the odds are that I WILL see my dead parents again! Infinite times... And an infinite amount of those experiences will be heaven, and an infinite amount of those experiences will be hell. If infinity exists, then infinite infinities will likely exist (true infinity), (or no?!). And then all things aren't only possible, but WILL, and WILL HAVE already happened (?) And if that's the case, then why don't I remember just one of them? God dammit!

  • zacharie slimosine

    zacharie slimosine

     10 hours ago

    michael's third eye is held open with a toothpick at all times

  • FOOKIN HALE

    FOOKIN HALE

     11 hours ago

    Just when you thought you escaped linear algebra... Here we go again.

  • Mobile Builds :D

    Mobile Builds :D

     11 hours ago

    I’m learning too much, Better stop.

  • Art Vein

    Art Vein

     12 hours ago +1

    1+1 always equalled 3
    That's how I was born

  • Paul Kevin Koehler

    Paul Kevin Koehler

     12 hours ago

    James Bond: Forever Isn't Enough

  • Xiomeria Rogers the mermaid

    Xiomeria Rogers the mermaid

     13 hours ago

    This makes so much sense. Like it really does I now understands the number system of infinity ♾