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.thvideos.net/video/1zARMZ08ums/video.html

    Field Day: https://www.thvideos.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.thvideos.net/video/fJ9j_z2kXI0/video.html

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

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

    related Numberphile videos:

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

    Vi Hart on types of infinity: https://www.thvideos.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

  • da shit

    da shit

     25 minutes ago

    12:19 lef [CC]

  • Exotic Menace

    Exotic Menace

     28 minutes ago

    Okay
    Say you are in Kansas. You start going down south at a constant rate. After a period of time, you would be going north.

  • Exotic Menace

    Exotic Menace

     40 minutes ago +1

    What if the universe is a sphere? And instead of it going on and on, it just repeats and there just happens to be another earth farther superior or more inferior than us?


    Mind blowing

  • DarkFlame

    DarkFlame

     an hour ago

    He was then arrested for destroying currency.

  • Thomas Cahill

    Thomas Cahill

     an hour ago +1

    1:50 : FBI OPEN UP

  • YCode Dev

    YCode Dev

     an hour ago

    hahaha thats it! we are strange in all things!! I love that!!

  • Jason Green

    Jason Green

     an hour ago

    Seriously, it's 0449hrs and I'm watching this.

    ...why?

  • Danny Detreeto

    Danny Detreeto

     2 hours ago

    Me explaining this to my friend for 30 minutes:

    Them: huh

    Me: 🤬

  • bob knar

    bob knar

     2 hours ago

    010000101100001010011011100100101010010010001100100100100100100100000111101011010001110100001010010011001001011

  • Kram

    Kram

     2 hours ago

    So..... can I make infinite chocolate????

  • Kimberly Simpson

    Kimberly Simpson

     2 hours ago

    i don’t think my brain is capable of retaining this information

  • Ok Ok

    Ok Ok

     3 hours ago

    Vsauce: infinity+1= infinity
    Elementary kids: impossible

  • Diana Abarca

    Diana Abarca

     4 hours ago

    This is the first Vsauce video I've ever seen and at the end I just expected you to say "Stay saucy." Much sadness after it wasn't said ,-,

  • Brooks Yeager

    Brooks Yeager

     4 hours ago

    Dig it Bro !! Sounds like some nice Brazillian musica in the background...

  • Parasar Bhattacharya

    Parasar Bhattacharya

     5 hours ago

    Thanks boss you just enlightened me. If i give up my 99%of power to some one i am left with 1% of my power, but that person will think he has my 99%power, but i have to realise that my 1% consists of 10×10 % as i know i about my powers, so even after giving my 99%power i am left with 100% my power... So thats what god feels even after giving his or hers 99%infinite power to some one he or she is left with 100% infinite power. Its amazing. The feeling of being unbeatable even after giving your 99% of infinite power.

  • dAlexb

    dAlexb

     7 hours ago

    Who buy a chocolate to try this

  • Pirog

    Pirog

     7 hours ago

    I feel that the name of this video has been modified

    could it be Mandela effect?

  • Jenő Zsolt Dudás

    Jenő Zsolt Dudás

     8 hours ago

    Hyper(loop)webster is Swami Venkateshanad: Yoga Vasishtha...

  • Proxima Centauri117

    Proxima Centauri117

     8 hours ago

    Ugh this is why you don’t come up with imaginary shapes. Of course you can take it apart and create it again. It’s imaginary. Something created by humans. It’s not perfect. If we are talking about a physical sphere (let’s pretend it’s possible) then it isn’t possible to do this. There are a limited number of atoms in it. Also a limited number of quarks. Same with anything smaller than them.

  • hifive

    hifive

     9 hours ago

    Just imagine having to vacuum the hallway of the Hilbert's Grand Hotel.