The Banach-Tarski Paradox
Nauka i technika
Want more brain food? Want your house to become a museum? Now you're thinking: www.curiositybox.com
Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."
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Kevin’s Field Day video: plclip.info/show/Y7B1tYG_ZXDZpaQ/wideo
Field Day: plclip.info/run/RPktNf5vnBR1J4e7t1RUVg
Deep dream animation by NaderMakki
If you like it, you'll love this video also by Nader: plclip.info/show/mIBtzZPfZ6O8gWE/wideo
Chocolate illusion: mathandmultimedia.com/2014/07/22/explanation-infinite-chocolate-bars/
Chocolate illusion video: plclip.info/show/lqN21oTMha2Uj5Q/wideo
related Numberphile videos:
sizes of infinity (includes diagonal argument): plclip.info/show/l6Kqso7SZZyYgGE/wideo
infinity paradoxes: plclip.info/show/lnqgmpvEZ7CbbII/wideo
Vi Hart on types of infinity: plclip.info/show/ZGl9mHu4aYLNfJg/wideo
Countable & uncountable definitions:
mathinsight.org/definition/uncountable
en.wikipedia.org/wiki/Countable_set
en.wikipedia.org/wiki/Uncountable_set
Banach-Tarski on wikipedia: en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
Banach-Tarski proofs:
math.uchicago.edu/~may/REU2014/REUPapers/Robinson.pdf
www.math.hmc.edu/~su/papers.dir/banachtarski.pdf
people.math.umass.edu/~weston/oldpapers/banach.pdf
Banach-Tarski explinations online:
www.irregularwebcomic.net/2339.html
www.kuro5hin.org/comments/2003/5/23/134430/275?pid=5#10
skepticsplay.blogspot.co.uk/2010/05/doubling-sphere.html
austinrochford.com/posts/2014-05-14-banach-tarski-paradox.html
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
rachellevanger.com/index_files/BT%20Animated%20Presentation%20Web.pdf
quibb.blogspot.co.uk/2013_03_01_archive.html
blog.computationalcomplexity.org/2011/04/what-did-banachs-wife-think-of-banach.html
geopolicraticus.wordpress.com/tag/banach-tarski-paradox/
dgleahy.com/p47.html
www.math.hmc.edu/funfacts/ffiles/30001.1-3-8.shtml
Cayley graph animated gif: GIFsofWikipedia/status/624202342259240960
Hilbert’s hotel on wikipedia: en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Grand_Hotel
types of infinity: www.xamuel.com/levels-of-infinity/
set theory and quantum physics: link.springer.com/article/10.1007/BF02213427#page-1
LHC gif: cms.web.cern.ch/news/lhc-data-be-made-public-open-access-initiative
Zermelo-Fraenkel axioms of mathematics: mathworld.wolfram.com/Zermelo-FraenkelAxioms.html
Is math invented or discovered?
phys.org/news/2013-09-mathematics-effective-world.html
www.scientificamerican.com/article/is-the-universe-made-of-math-excerpt/
more deep dream images: www.reddit.com/r/deepdream/
BOOKS:
The Pea and the Sun: www.amazon.com/The-Pea-Sun-Mathematical-Paradox/dp/1568813279
The Outer Limits of Reason: www.amazon.com/Outer-Limits-Reason-Science-Mathematics/dp/0262019353
Why Beliefs Matter: www.amazon.com/Why-Beliefs-Matter-Reflections-Science/dp/0198704992
Things to Make and do in the Fourth Dimension: www.amazon.com/Things-Make-Fourth-Dimension-Mathematicians/dp/0374275653
Music by plclip.info and
www.audionetwork.com
Komentarze
A minecraft world is infinite
I think infinity is real. The Universe needed a beginning, but the beginning of the Universe needed a beginning. This sort of thing makes me question reality. This would raise questions on the Big Bang.
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mabye I will try to make something out of one thing
I came for universe/alien stuff and I left feeling dumb. 😭😭
1+1 = 1
“First we have to ask a few questions..” No one: Not a soul: Vsauce: “wHaT iS iNfInIty?”
Why use money to rip
I would like to observe infinity
that dollar bill trick does not work
Who else really wants to rip up a dollar now?
Gabe
8 godzin temu
If you did it, Let me know if it works
The curious east unfortunately matter because heat aesthetically unfasten anenst a childlike case. stupid, fallacious cowbell
If there was a hotel with never ending rooms who the hell is making the other rooms
there is an infinite number of bla bla bla. me: bla bla bla bla bla...
Tbh, how do people think this stuff up? I mean how do you go about even considering this, I suppose that's why we have maths Geniuses. It got complicated after 5 mins for me..
крест Лапотников
10 godzin temu
Whoever made these numbers must be magnificent. God
It explains quark radio decay and probably photosynthesis. And probably messenger rna. Good work
Wow.......brain like........
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13:59 my mind stopped listening at this point, but I still continued till the end
It means that a super accurate clock never comes exactly at 12 because it's irrational
Bruh he just cut money wtf
I was gonna comment something smart, but after seeing other peoples comments I don't feel like doing it anymore.
5:46 the way he did that creeps me out
Me explaining why i should get a piece of food from my friend:
Holy shit, i'm a Asian and i can't even get it lol
My head hurts, and I still don't get it. Lol.
Im skeptical that you could yet intrigued that you may
_Whenever I think of infinite, I think of forever, and when I think of forever I think of death, which makes my life slightly shorter_
EVERY WORD I'VE EVER SAID, WRITTEN AND THOUGHT IS IN THERE
The dollar trick is so fake lmao. The original dollar literally has a different Fed Reserve letter than both of the "duplicates." C'mon Michael, youre better than this.
Tom Svoboda
3 godzin temu
it wasn't meant seriously
The one dollar into 2 separate dollars is a lie.
E
I have watched this video more than five times. And every time I see it in my recommended, I know that I have watched it many times, but I can never remember what it's about, so I watch it again. That's because I'm a dummy. Just a, a stupid little dum-dum.
If we are strange then the universe is strange as we are part of it, etc....
blah blah blah isn't not blah blah blah and that is a lie ''solves'' - i am soooo smart! Vsauce - hold my quantum neutrino fusion
What an infinte load of shit
The two dollar bills have different serial numbers...of course.
My head hurts...
Infinity is a concept and NOT a number. Also there is no such thing (in nature) as a quantity, you can't have a tree with -5 apples. Subtraction beyond 0 is false.
Dioptre Obscura
53 minut temu
@Tom Svoboda Don't be a pussy, you can have 5 apples on a tree.
Tom Svoboda
3 godzin temu
that doesn't say anything. numbers are also just concepts. there's no number 5 in nature.
15:40 The track is "Moonwish" by Christian Marsac
Thank you for showing us how a quantum computer needs to function
14:06. Our and u are the same
Dumb
Duh!!! Why is this news? Or a video? Bunch of idiots
Isn't it illigal to destroy currency...?
hi
The sphere part is infinite because you can go left or right up or down infinite times.....
This hurts my brain and I’m half way done with the video
Silli
2 dni temu
plclip.info/show/gJ6fzGq6rn7SqKg/wideo
Michael: ...the universe may be infinite in size and...FLAT Flat Earthers: I told you!!!
Wot
4:25 i am going fucking insane
I have a headache
13:49 *Nervous sweating*
This is more scary than a horror movie.
Infinite* not "infininte"... Thumbs down for this
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the dictionary in A will have to end in an infinite no. of Zs with an A preceding it then only the short cut will be possible
I understand the whole video, except for the part about the poles. With the prescribed rotations (around the x-axis and z-axis) no matter what the starting point is, the only poles seems to be on these axes. That's 4 poles for the sphere, hence 4 yellow point on the sphere. Why then is there countably infinite number of yellow points? "Each sequence has 2 poles." seems to be the key, but to me it seems that all these poles coincide with the 4 poles I mentioned above. What am I missing?
Wait, what?...
I have been reading the hyperwebster .... I just got to Abaa... of course it caused a black hole to tear through the known universe, which caused all of my "Berenstain bears" books to turn into "Berenstein bears" books and all hell is breaking loose
I can just duplicate a £5 note, till I'm rich
You said left up right but your arrows points the opposite way......right up left...🤔
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The elegant event acceptably puncture because factory kinetically surprise alongside a sweet vessel. parched, scarce fahrenheit
“Hyperwebster” sounds like it would be a cool band name
5 years later I still can't follow it.
So guys, who is still wondering what happened to that chocolate?
1:47 infinite gold glitch IRL
me not understanding a single thing: *interesting*
Did he put half in between 1 and 2?
Conservation of mass kind of overrules that.
Você acabou de rasgar 5,46 reais na minha frente cara ;-;
Vinicius Oliveira
3 dni temu
1:37
Sexy
Im scared..
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damn my mind blowing so hard,
If I watched this anymore this is going to result in my brain death paradox
Sandeep Kaur
20 godzin temu
@Thanh N Ok now I realise what you meant
Sandeep Kaur
21 godzinę temu
@Thanh N No man it’s a joke
Sandeep Kaur
21 godzinę temu
No man it’s a joke
Thanh N
4 dni temu
You mean this video? plclip.info/show/m5-flWncpoHZfqA/wideo
Why do human’s tend to make things out of imagination that makes no sense
Infinity is not a number. Neither is zero.
what?
Would this apply to humans? They would more or less the same as before except for mass. The mass would decrease for both spheres, right? Now the best way that I can mentally somewhat comprehend what I learned from this video; I had to compare it to how babies are created. Taking pieces (dna) from parents and creating a new human with those pieces or dna. They’re their own beings and separate from the mother and father, but only with the expense of energy which is equal to mass. But the mother is still whole despite giving her dna to the baby and so is the father because we use energy to produce new cells, so it’s as if our cells are infinite as long as we’re using energy to produce them. Also, it takes energy to turn the sphere in some way shape or form, so that’s similar to using the energy to create new cells. It’s like picking new starting points on the sphere. I don’t know, but that’s the best way that I understand this paradox without my brain melting.
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Is this the answer to the matter vs antimatter? Is this the answer to quantum physics?
Th3 Night Lion
4 dni temu
@Релёкс84 yeah, but it's fun to think it is
Релёкс84
4 dni temu
No, it really isn't
Sir this is a mcdonald's drive thru
Sir, there's a glitch in matrix..or is there?
Banach-Tarski is an example of the law of universal abundance. Not necessarily the same thing, nevertheless, an example for people who have trouble imagining how to gain wealth and success when so much wealth and success flows to the top 1%..... These videos (and directed education/knowledge in general) help the mind understand the concepts it needs to manifest infinite possibilities or for itself "better or worse" imho.
Hilbert's hotel probably has a huge amount of negative feedback considering the amount of times ppl are moved from rooms. hahahahaha
Релёкс84
4 dni temu
If youre clever you can find ways to statistically make 0% of customers move, or even garantee a customer will never be moved more than once during their stay
this be how i would start my onveatigation before u knew it my endless sided figure that copied itself forever pulled in every reality and expanded copying its self like the orders u give it if it ment anything to you too bad it didnt is ordered and i stayed to make sure i kept hunt8ng down idiots
Mathematically with the sphere part, that's actually how Pain's universal pull works in real terms. Same thing with the force in star wars. It renders a infinite plane and adds/subtracts you to/from it in order to project you either towards or away through the sudden orbit.
This is pretty much what happened to my mind when Soul Calibur 2 HD Remastered came out, it had more characters but to me looked the same as the previous versions space wise. Look it up lol it's pretty neat
Why do we need to know this when humanity is going extinct anyway?
Wait wouldn’t” up”and” Left, up ,right “ land on the same point..?
Camden Ritter
2 dni temu
Good point
Straight up dropped the video in 2017, didn't understand anything in 2018, neither in 2019, in 2020 didn't even try. But now, after 5 years, at 16 years old, I have finally begun to start understanding this, and I'm oh so happy I can't describe it.
whenever i DOUBT that i'm smart, i think of this video and remember that i understood everything he said
everybody gangsta till michael almost drawed a swastika :D
this is a dupe glitch in real life lol
Can we talk about how he drew the line with the shade of a piece of paper? 8:16
A theorie about as a example matching even numbers to both even and uneven numbers while yes it is possible due to there being infinite of both the same would be true about matching even numbers to true numbers the only difference is how far you would have to go down the list of numbers unless at some point there would be a point where you can no longer continue that is not just limitet bye our understanding of Language logic or the time of existence of matter/consiusness and having the same ammount of even numbers as Uneven+ even numbers would assume there is no such limit while the idea of there being more real numbers would assume that there is Otherwise both could go on until past the point of what existence itself could even hold with the only difference in matching them being the speed of progress that in and of itself would only exist if there would be a hardcap since otherwise you would never have made any progress (atleast in Relative terms if we speak in absolute terms there of course would be progress but that once agein is different for both matching metods) Another thing backing that up is that as you mentioned infinitie divided bye 2 is still infinitie Meaning no matter what you match (true numbers to even numbers or uneven the result is always infinitie) Then agein all of these things are merely ideas and so defining right and wrong accurately is probably pretty hard or atleast hard to explain
Did-did my guy just commit a crime by defacing money? Damn, this man said ‘frick twelve, or can I?’