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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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25 minutes agoda shit12:19 lef [CC]

28 minutes agoExotic MenaceOkay

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

40 minutes agoExotic Menace^{+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

an hour agoDarkFlameHe was then arrested for destroying currency.

an hour agoThomas Cahill^{+1}1:50 : FBI OPEN UP

an hour agoYCode Devhahaha thats it! we are strange in all things!! I love that!!

an hour agoJason GreenSeriously, it's 0449hrs and I'm watching this.

...why?

2 hours agoDanny DetreetoMe explaining this to my friend for 30 minutes:

Them: huh

Me: 🤬

2 hours agobob knar010000101100001010011011100100101010010010001100100100100100100100000111101011010001110100001010010011001001011

2 hours agoKramSo..... can I make infinite chocolate????

2 hours agoKimberly Simpsoni don’t think my brain is capable of retaining this information

3 hours agoOk OkVsauce: infinity+1= infinity

Elementary kids: impossible

4 hours agoDiana AbarcaThis 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 ,-,

4 hours agoBrooks YeagerDig it Bro !! Sounds like some nice Brazillian musica in the background...

5 hours agoParasar BhattacharyaThanks 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.

7 hours agodAlexbWho buy a chocolate to try this

7 hours agoPirogI feel that the name of this video has been modified

could it be Mandela effect?

8 hours agoJenő Zsolt DudásHyper(loop)webster is Swami Venkateshanad: Yoga Vasishtha...

8 hours agoProxima Centauri117Ugh 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.

9 hours agohifiveJust imagine having to vacuum the hallway of the Hilbert's Grand Hotel.