The Banach–Tarski Paradox

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  • Published on:  7/31/2015
  • Want more brain food? Want your house to become a museum? Now you're thinking: http://www.curiositybox.com

    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.102tube.com/video/1zARMZ08ums/video.html

    Field Day: https://www.102tube.com/channel/UCRPktNf5vnBR1J4e7t1RUVg

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

    If you like it, you'll love this video also by Nader: https://www.102tube.com/video/fJ9j_z2kXI0/video.html

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

    Chocolate illusion video: https://www.102tube.com/video/dmBsPgPu0Wc/video.html

    related Numberphile videos:

    sizes of infinity (includes diagonal argument): https://www.102tube.com/video/elvOZm0d4H0/video.html
    infinity paradoxes: https://www.102tube.com/video/dDl7g_2x74Q/video.html

    Vi Hart on types of infinity: https://www.102tube.com/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
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