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

Instagram: http://www.instagram.com/electricpants

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/

related Numberphile videos:

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

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 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://skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.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
http://dgleahy.com/p47.html
https://www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml

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

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

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

http://www.audionetwork.com

source

Fahad Hashmi is one of the known Software Engineer and blogger likes to blog about design resources. He is passionate about collecting the awe-inspiring design tools, to help designers.He blogs only for Designers & Photographers.

### 37 thoughts on “The Banach–Tarski Paradox”

• November 10, 2017 at 4:16 am

My nigga lost 3 dollars making this video

• November 10, 2017 at 4:16 am

The dollar thing was a joke, right? You tryna make people rip up money?

• November 10, 2017 at 4:16 am

Things can grow to infinity but infinity itself doesn't exist in this universe.

• November 10, 2017 at 4:16 am

• November 10, 2017 at 4:16 am

Makes me think of how we exist…our universe replicating itself from one moment in time to the next…in an infinite amount of ways…leaving our previous copy in the past…continually…for an infinite amount of time………………Huh…Everything exists in a single moment of time…all focusing in with my perception of my moment in reality….

• November 10, 2017 at 4:16 am

this should be named "how to go insane"

• November 10, 2017 at 4:16 am

You spelled explanations wrong in the description.

• November 10, 2017 at 4:16 am

Did anyone notice how he drew his eight?

• November 10, 2017 at 4:16 am

what is the difference between RUL and U?

• November 10, 2017 at 4:16 am

I don't think our language is able to even explain these things

• November 10, 2017 at 4:16 am

This paradox explains exactly how parallel universes could exist.
The sphere is a 3 dimensional object, but When the points move, they are experiencing time. You can use any set of points to create an entire sphere separate from the original by introducing them to time.
If you apply this to life, each point represents a person — no two are exactly alike and the reproduction is infinite. There are infinite possibilities to how a single point could navigate the sphere through time, just like there are infinite ways one person could experience their life.
Then, to take it farther, if you look at each point on the sphere as being a galaxy in the universe, the entire universe can exist in a different sequence an infinite amount of times all at once.

Good day.

• November 10, 2017 at 4:16 am

The serial numbers are different from each other…

• November 10, 2017 at 4:16 am

Wait, I have watched this video like 10 times, and the one thing I never understand is that, while you are creating matter, you are still using energy to create it. I don't know if some has done the math on it, but it seems that to separate the spheres, rotate them, and put them back together would use more energy than the spheres would contain. It is still a net-loss of energy. You may be able to create matter, but what good does that do if it uses up energy? This is not my territory by any means and I might not be understanding how energy is used. Like, would the energy used to create the second sphere be altered in some way? I know that the first law of thermodynamics is that matter cannot be created and destroyed, which obviously the Banach-Tarski paradox breaks this rule, but that's the point of the video, that is why it is a paradox.

So I guess question is this, can the paradox be used to stop the heat-death of the universe? Can you use this paradox to create an object with more potential energy than it took to create it? I know that question is impossible to answer right now, but it is just a thought that crossed my mind.

• November 10, 2017 at 4:16 am

What if you take infinity away from infinity? Is it 0?

• November 10, 2017 at 4:16 am

I just saw a man rip up 2 fresh dollars right infront of my eyes…

• November 10, 2017 at 4:16 am

I thought that made sense, but then I realized "whaaaaaaat"

• November 10, 2017 at 4:16 am

For this mathematical theorie the dots you name have to be infinitly small right?
Because not only our measurements, but also the particles that make up any object, have a certain size and thus are larger than infinitly small, making this theorie unapplicable in any practical application.

• November 10, 2017 at 4:16 am

mind got blown infinte amount of times during this video

• November 10, 2017 at 4:16 am

It's just an argument is not a prove.

• November 10, 2017 at 4:16 am

So everything is ….. everything? Our reality?

• November 10, 2017 at 4:16 am

man I really love your long videos

• November 10, 2017 at 4:16 am

"I really appreciate who all of you are"
how can something so simple make me feel so much..

• November 10, 2017 at 4:16 am

I was doing well up to when he said vsauce michael here, it all went downhill from there.

• November 10, 2017 at 4:16 am

Alright guys. Let's duplicate earth and we're done with over populations

• November 10, 2017 at 4:16 am

And the point is ? Infinity means infinity ,no beginning,no ending, no mathematical solution period.

• November 10, 2017 at 4:16 am

great video and all, but is there still a way to make more chocolate out of the chocolate you have?

• November 10, 2017 at 4:16 am

Hey Vsauce! Micheal here… or am I?

• November 10, 2017 at 4:16 am

I love this guy and this channel. But the word infinite does not contain a third letter N after the final I and before the letter T. As such and by general consensus, at least here in the UK, the word is not pronounced IN-FIN-NINT.

It's IN-FI-NIT or IN-FY-NITE (depending on context).

• November 10, 2017 at 4:16 am