The Banach–Tarski Paradox
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 Published on: Friday, July 31, 2015
 Q: "What's an anagram of BanachTarski?"
A: "BanachTarski BanachTarski."
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/explanationinfinitechocolatebars/
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
BanachTarski on wikipedia: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
BanachTarski 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
BanachTarski 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/doublingsphere.html
http://austinrochford.com/posts/20140514banachtarskiparadox.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_BanachTarski.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/whatdidbanachswifethinkofbanach.html
https://geopolicraticus.wordpress.com/tag/banachtarskiparadox/
http://dgleahy.com/p47.html
https://www.math.hmc.edu/funfacts/ffiles/30001.138.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/levelsofinfinity/
set theory and quantum physics: http://link.springer.com/article/10.1007/BF02213427#page1
LHC gif: http://cms.web.cern.ch/news/lhcdatabemadepublicopenaccessinitiative
ZermeloFraenkel axioms of mathematics: http://mathworld.wolfram.com/ZermeloFraenkelAxioms.html
Is math invented or discovered?
http://phys.org/news/201309mathematicseffectiveworld.html
http://www.scientificamerican.com/article/istheuniversemadeofmathexcerpt/
more deep dream images: https://www.reddit.com/r/deepdream/
BOOKS:
The Pea and the Sun: http://www.amazon.com/ThePeaSunMathematicalParadox/dp/1568813279
The Outer Limits of Reason: http://www.amazon.com/OuterLimitsReasonScienceMathematics/dp/0262019353
Why Beliefs Matter: http://www.amazon.com/WhyBeliefsMatterReflectionsScience/dp/0198704992
Things to Make and do in the Fourth Dimension: http://www.amazon.com/ThingsMakeFourthDimensionMathematicians/dp/0374275653
Music by http://www.youtube.com/JakeChudnow and
http://www.audionetwork.com  Source: https://youtu.be/s86ZCbaHA
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Roy Patton
an hour agoYou added a rotation. That isn't nothing.
PHOENIX
an hour agoHow 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
3 hours agoIf 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
4 hours agoAre point itself infinite???
rikyboy345
5 hours agoNigga what?
zudeyix
5 hours agoI guess it was patched
Vänni Urponen
5 hours ago ^{+1}Me: does a backflip.
Also me: you look just like me.
dr horseface
6 hours agoi lost like all my brain cells watching this
Atlas
6 hours agoDoctor:Sir you have an incurable form of cancer
Micheal:Or do i?
(Continues to explain the impossible)
TheBendablespoons
7 hours agoThis shit is gonna be the key to a post scarcity society
anmol bhatti
7 hours agoI don't understand that circle thing
Leong Ka Hou Daniel 梁家豪 P5C13
8 hours agoThis just ended my sanity
drache444444
9 hours agoand 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
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
10 hours agomichael's third eye is held open with a toothpick at all times
FOOKIN HALE
11 hours agoJust when you thought you escaped linear algebra... Here we go again.
Mobile Builds :D
11 hours agoI’m learning too much, Better stop.
Art Vein
12 hours ago ^{+1}1+1 always equalled 3
That's how I was born
Paul Kevin Koehler
12 hours agoJames Bond: Forever Isn't Enough
Xiomeria Rogers the mermaid
13 hours agoThis makes so much sense. Like it really does I now understands the number system of infinity ♾