Choices

The Banach–Tarski Paradox

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Q: “What’s an anagram of Banach-Tarski?”
A: “Banach-Tarski Banach-Tarski.”

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Field Day: https://www.youtube.com/channel/UCRPktNf5vnBR1J4e7t1RUVg

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If you like it, you’ll love this video also by Nader: https://www.youtube.com/watch?v=fJ9j_z2kXI0

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

Chocolate illusion video: https://www.youtube.com/watch?v=dmBsPgPu0Wc

related Numberphile videos:

sizes of infinity (includes diagonal argument): https://www.youtube.com/watch?v=elvOZm0d4H0
infinity paradoxes: https://www.youtube.com/watch?v=dDl7g_2x74Q

Vi Hart on types of infinity: https://www.youtube.com/watch?v=23I5GS4JiDg
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

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Missile Dude RPG is an “Editor’s Choice” idle clicker where we slay endless rounds of wacky monsters by tapping the screen to fire hilariously-designed missiles (I’m looking at you, Penguin missile!), deploy troops to attack for us, and upgrade existing missiles and launchers to increase the damage per second.

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Total game size: 217 MB – Offline Playable

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Grim Soul Dark Fantasy Survival is a brand new game and it is amazing! This video gives you all kinds of tips for the new game. It is a last Day on Earth Copy Cat Game, but it is amazing.

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‘Beast’ cracks billions of passwords a second, Dr Mike Pound demonstrates why you should probably change your passwords…

Please note,at one point during the video Mike suggests using SHA512. Please check whatever the recommended process is at the time you view the video.

How NOT to Store Passwords: https://youtu.be/8ZtInClXe1Q
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