The Banach-Tarski Paradox

Nauka i technika

Want more brain food? Want your house to become a museum? Now you're thinking:
Q: "What's an anagram of Banach-Tarski?"
A: "Banach-Tarski Banach-Tarski."
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Kevin’s Field Day video:
Field Day:
Deep dream animation by NaderMakki
If you like it, you'll love this video also by Nader:
Chocolate illusion:
Chocolate illusion video:
related Numberphile videos:
sizes of infinity (includes diagonal argument):
infinity paradoxes:
Vi Hart on types of infinity:
Countable & uncountable definitions:
Banach-Tarski on wikipedia:
Banach-Tarski proofs:
Banach-Tarski explinations online:
Cayley graph animated gif: GIFsofWikipedia/status/624202342259240960
Hilbert’s hotel on wikipedia:
types of infinity:
set theory and quantum physics:
LHC gif:
Zermelo-Fraenkel axioms of mathematics:
Is math invented or discovered?
more deep dream images:
The Pea and the Sun:
The Outer Limits of Reason:
Why Beliefs Matter:
Things to Make and do in the Fourth Dimension:
Music by and


  • Tanish Singh
    Tanish SinghGodzinę temu

    A minecraft world is infinite

  • Raccoon Balls
    Raccoon Balls2 godzin temu

    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.

  • Ebenezer Sam
    Ebenezer Sam2 godzin temu

    The homely attack orly complain because cup contrastingly owe besides a homely dinosaur. tested, heady italy

  • Logan Kaminski
    Logan Kaminski3 godzin temu

    mabye I will try to make something out of one thing

  • Khanh Do
    Khanh Do4 godzin temu

    I came for universe/alien stuff and I left feeling dumb. 😭😭

    BLAISE MUHUNE5 godzin temu

    1+1 = 1

  • Lil Strats
    Lil Strats5 godzin temu

    “First we have to ask a few questions..” No one: Not a soul: Vsauce: “wHaT iS iNfInIty?”

  • izuku medoriya
    izuku medoriya6 godzin temu

    Why use money to rip

  • Joe Boike
    Joe Boike6 godzin temu

    I would like to observe infinity

  • mike robinson
    mike robinson8 godzin temu

    that dollar bill trick does not work

  • Gabe
    Gabe8 godzin temu

    Who else really wants to rip up a dollar now?

  • Gabe


    8 godzin temu

    If you did it, Let me know if it works

  • simpson cornish
    simpson cornish10 godzin temu

    The curious east unfortunately matter because heat aesthetically unfasten anenst a childlike case. stupid, fallacious cowbell

  • Suthernhillbilly
    Suthernhillbilly10 godzin temu

    If there was a hotel with never ending rooms who the hell is making the other rooms

  • Henrique Machado Moreira
    Henrique Machado Moreira10 godzin temu

    there is an infinite number of bla bla bla. me: bla bla bla bla bla...

  • Ned Hannon
    Ned Hannon10 godzin temu

    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

    крест Лапотников

    10 godzin temu

    Whoever made these numbers must be magnificent. God

  • Jubby Custard
    Jubby Custard11 godzin temu

    It explains quark radio decay and probably photosynthesis. And probably messenger rna. Good work

  • Jamie Lacourse
    Jamie Lacourse14 godzin temu

    Wow.......brain like........

  • Gary Diamond
    Gary Diamond16 godzin temu

    The chivalrous duck anaerobically delight because addition affectively unfasten amid a drab saudi arabia. cloudy, eager grasshopper

  • Jacob Bijo Daniel
    Jacob Bijo Daniel16 godzin temu

    13:59 my mind stopped listening at this point, but I still continued till the end

  • Abhishek
    Abhishek17 godzin temu

    It means that a super accurate clock never comes exactly at 12 because it's irrational

  • Rabbit Kati
    Rabbit Kati18 godzin temu

    Bruh he just cut money wtf

  • Cubic s Discord
    Cubic s Discord19 godzin temu

    I was gonna comment something smart, but after seeing other peoples comments I don't feel like doing it anymore.

  • Cubic s Discord
    Cubic s Discord20 godzin temu

    5:46 the way he did that creeps me out

    K-POP STATION22 godzin temu

    Me explaining why i should get a piece of food from my friend:

  • Tai Nguyen
    Tai NguyenDzień temu

    Holy shit, i'm a Asian and i can't even get it lol

  • Fappy da Bear
    Fappy da BearDzień temu

    My head hurts, and I still don't get it. Lol.

  • Comrade #0001
    Comrade #0001Dzień temu

    Im skeptical that you could yet intrigued that you may

  • Khi Turner
    Khi TurnerDzień temu

    _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_

  • Hulfe
    HulfeDzień temu


  • Alexander Berg
    Alexander BergDzień temu

    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

    Tom Svoboda

    3 godzin temu

    it wasn't meant seriously

  • maverick email
    maverick emailDzień temu

    The one dollar into 2 separate dollars is a lie.

  • Eric is Waiting
    Eric is WaitingDzień temu


  • some thing
    some thingDzień temu

    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.

  • Brian T. Johnston
    Brian T. JohnstonDzień temu

    If we are strange then the universe is strange as we are part of it, etc....

  • legomation adventures!
    legomation adventures!Dzień temu

    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

  • karma for all
    karma for allDzień temu

    What an infinte load of shit

  • K6HR
    K6HRDzień temu

    The two dollar bills have different serial numbers...of course.

  • Five Point 5 Sicks
    Five Point 5 SicksDzień temu

    My head hurts...

  • Dioptre Obscura
    Dioptre ObscuraDzień temu

    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

    Dioptre Obscura

    53 minut temu

    @Tom Svoboda Don't be a pussy, you can have 5 apples on a tree.

  • Tom Svoboda

    Tom Svoboda

    3 godzin temu

    that doesn't say anything. numbers are also just concepts. there's no number 5 in nature.

  • Not a garden gnome
    Not a garden gnomeDzień temu

    15:40 The track is "Moonwish" by Christian Marsac

  • Philly Cheesesteak
    Philly CheesesteakDzień temu

    Thank you for showing us how a quantum computer needs to function

  • Levi Andrea Ciccone
    Levi Andrea Ciccone2 dni temu

    14:06. Our and u are the same

  • Cursor EU
    Cursor EU2 dni temu


  • Kent Reece
    Kent Reece2 dni temu

    Duh!!! Why is this news? Or a video? Bunch of idiots

  • FNix
    FNix2 dni temu

    Isn't it illigal to destroy currency...?

  • AlphaVettelNova5
    AlphaVettelNova52 dni temu


  • Brandon
    Brandon2 dni temu

    The sphere part is infinite because you can go left or right up or down infinite times.....

  • Florida Man
    Florida Man2 dni temu

    This hurts my brain and I’m half way done with the video

  • Silli


    2 dni temu

  • Oliver Palma
    Oliver Palma2 dni temu

    Michael: ...the universe may be infinite in size and...FLAT Flat Earthers: I told you!!!

  • Azamarr
    Azamarr2 dni temu


  • Symple _UT
    Symple _UT2 dni temu

    4:25 i am going fucking insane

  • parkyfnr
    parkyfnr2 dni temu

    I have a headache

  • Swat Turltle
    Swat Turltle2 dni temu

    13:49 *Nervous sweating*

  • Taha Yousaf
    Taha Yousaf2 dni temu

    This is more scary than a horror movie.

  • DontHatemusiK
    DontHatemusiK2 dni temu

    Infinite* not "infininte"... Thumbs down for this

  • james fiaco
    james fiaco3 dni temu

    🍒💙judgment that is not physically, mentally, naturally financially and spiritually beneficial is useless therefore has no true value. Without judgment progress cannot be made. For no one can express or receive love or any other desired emotion in its entirety if the don't know themselves. We are all not created equal however we all have a equal obligation in living up to the pleasure, potential, and responsibility of femininity and masculinity. So don't miss the deadline on doing your best to become physically fit, mentally sound, and spiritually balanced being able to express physical freedom. Which can be accomplished through clean air, water, fitness, that specializes in overall functionality combined with high sources of nutrition organic non-genetically modified would be best. Plus formal education and real hands-on experience. When one learns the body's capabilities and limitations by fully engaging with all their bodies senses to their extreme limits in the most efficient way that is humanly possible. The subconscious then begins to naturally subconsciously systematically coincide with the mind-body souls spirit mother Earth nature and all the various different forms of life that live within this world and the most efficient way that is humanly possible. Thus yielding the best spiritual kickback for one's efforts accomplishments experiences. You might want to take these points to heart Considering the simple logic basic concept that if life is not free, why the hell would death be any cheaper? It's not the question the common, basic, average, normal man or woman may be able to wonder is what is the spiritual cost to one's own soul and spirit for freely living dying off having only used the smallest percentage of a fraction of the true potential they are first born with. Not to add insult to injury for the last hundred and 50 years or so the mass majority of the population from coast-to-coast globally more so here in America. has been living and dying yielding the worst spiritual kickback that has ever been manifested since the beginning of life only getting worse. And that has nothing to do with everybodys so-called charming personality and everything to do with the standards of quality pertaining to our air, water, foods, landscapes, working/living environment, every day home products, habitats, and ecosystems. This lack of comprehension conscious physical participation in solutions is ignorant beyond retarded (no offense to any disabled people was intended.) When you consider for the last 490 years Give or take we have had the manpower woman influence or vice versa to have created clean high paying jobs from coast-to-coast globally that would constantly consistently be improving upon and maintaining the quality of our life in such a manner. That the mass majority of the population from coast-to-coast globally would constantly consistently naturally, gradually, and systematically almost effortlessly start becoming stronger, smarter, healthier, happier, better off physically, mentally, and financially possibly spiritually then the previous generation. Now I would like to resurrect the wish and prayer I made prior to my 8th birthday which was to be held spiritually accountable to the statements I proclaim to the way I'm living personally and professionally. I guarantee you never see or hear another body, man or woman in power, persons of legal, religious authority, or leaders ever freely validate the statements they proclaim with that level of certainty one reason they don't have the best interest of the majority of the population's needs at heart a another reason could be they cum from a bloodline of cowards or simply have a lifestyle that suggests, confirms, and validates them as being feebleminded physically inadequate submissive subservient which it doesn't get any worse than that. One is genetically inherited and the other is a simple generic learned behavior. Quite possible to be a combination of these worst-case scenarios combined is one to say the least. Nonetheless either way it is physically, mentally, and spiritually useless to freely live and die in such a low quality manner. Especially if that ignorant stupidity, weak, lonely desperation stems from being soft, lazy, out of shape, over fed, undernourished, overworked, and underpaid with a dirty low-paying job that comes from outdated power sources, inferior materials, poisonous, toxic substances, pesticides, and chemicals that never change their killing composition. Which means simpletons whether it is a solid, liquid, or burnt off into our airways atmosphere as a vapor it is always going to be poisonous, debilitating, and deadly to the body at the same time polluting, corrupting, and devastating to mother Earth and all the various different forms of life that live within this world. There is no cash profit to be made in the demise of the planet. Thanks to those dirty low-paying jobs we are in the mist of environmental financial global collapse. The good news souls and spirits have paid out are picking up the tab on the end results of those dirty low-paying jobs And so much more. The even better news that the common, basic, average, normal man woman may be able to comprehend is souls and spirits have been are being managed, directed, maintained, and implemented with all the disease, sickness, illness, pain, suffering, injury, abuse, neglect, hunger, addiction, sadness, anger, and hyper- aggressive violent criminal conduct. That has been allowed to occur manifesting throughout the history of mankind into what it is today thanks to people like Donald Trump who have the false belief if the mass majority of the population is at their worst they will feel less afraid scared inferior to the true potentials of love, honor, and the creation of life. Here's the deal you're either part of the world solutions or exacerbating the planets problems there is no safe in between. Either way no matter how you look at it each and every moment of every life has been spiritually accounted for. S.R.F.

    RAVI POHANI3 dni temu

    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

  • Lutterot
    Lutterot3 dni temu

    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?

  • Todd Nickell
    Todd Nickell3 dni temu

    Wait, what?...

  • Jeffrey Keffer
    Jeffrey Keffer3 dni temu

    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

  • Kyle John NJUE
    Kyle John NJUE3 dni temu

    I can just duplicate a £5 note, till I'm rich

  • decapitationnated
    decapitationnated3 dni temu

    You said left up right but your arrows points the opposite way......right up left...🤔

  • Gloria Wan
    Gloria Wan3 dni temu

    The ablaze sandwich anatomically roll because chimpanzee perioperaively tick except a capable thursday. second-hand, kind opera

  • gege culu
    gege culu3 dni temu

    The elegant event acceptably puncture because factory kinetically surprise alongside a sweet vessel. parched, scarce fahrenheit

  • Gamer person
    Gamer person3 dni temu

    “Hyperwebster” sounds like it would be a cool band name

  • allen gormley
    allen gormley3 dni temu

    5 years later I still can't follow it.

  • That Fire Inside
    That Fire Inside3 dni temu

    So guys, who is still wondering what happened to that chocolate?

  • agent puro
    agent puro3 dni temu

    1:47 infinite gold glitch IRL

  • Lusio
    Lusio3 dni temu

    me not understanding a single thing: *interesting*

  • Arindam
    Arindam3 dni temu

    Did he put half in between 1 and 2?

  • Adrian brunette
    Adrian brunette3 dni temu

    Conservation of mass kind of overrules that.

  • Vinicius Oliveira
    Vinicius Oliveira3 dni temu

    Você acabou de rasgar 5,46 reais na minha frente cara ;-;

  • Vinicius Oliveira

    Vinicius Oliveira

    3 dni temu


  • mortiz von nassau
    mortiz von nassau4 dni temu


  • NooB NooB
    NooB NooB4 dni temu

    Im scared..

  • Brock Jamal
    Brock Jamal4 dni temu

    The dazzling himalayan interestingly peep because rose separately kick aside a rainy litter. secretive, abiding interviewer

  • Karl
    Karl4 dni temu

    damn my mind blowing so hard,

  • Sandeep Kaur
    Sandeep Kaur4 dni temu

    If I watched this anymore this is going to result in my brain death paradox

  • Sandeep Kaur

    Sandeep Kaur

    20 godzin temu

    @Thanh N Ok now I realise what you meant

  • Sandeep Kaur

    Sandeep Kaur

    21 godzinę temu

    @Thanh N No man it’s a joke

  • Sandeep Kaur

    Sandeep Kaur

    21 godzinę temu

    No man it’s a joke

  • Thanh N

    Thanh N

    4 dni temu

    You mean this video?

  • Sandeep Kaur
    Sandeep Kaur4 dni temu

    Why do human’s tend to make things out of imagination that makes no sense

  • Tom Ford
    Tom Ford4 dni temu

    Infinity is not a number. Neither is zero.

  • Metalhead640
    Metalhead6404 dni temu


  • Tia Daniel
    Tia Daniel4 dni temu

    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.

  • chief 1 redwolf
    chief 1 redwolf4 dni temu

    Heaven and earth will pass away Jesus said, but my Words 📖 will never pass away, Matthew 24:35. There will be a new heaven and a new earth Revelation 21:1 HOPE ✨🪐💫🌎🙌 Salvation is found in no one else, no other name under heaven given among men where by we must be saved. Saved from the punishment of sin. I’m trying to offer people Hope in absolute perfection !!! No more pain, dying, lies, decay, depression, anxiety, crying, sickness, rotten food, broken things , etc... offering the Hope of Eternity in heaven with Jesus Christ. We must be willing to turn from sin to receive Jesus forgiveness. And to know and live out his teachings. He who does the will of God abides for eternity 1 John 2:17 Visual Bible movies on PLclip ❤️👑✝️📖nkjv 🧎‍♂️🙂 ♥️🇺🇸🤍🇺🇸💙🇺🇸 🍫🍫🍫🍫🍫🍫🍫

  • Malik baldwin
    Malik baldwin4 dni temu

    The harmonious quilt principally report because grey probably wait past a coherent rub. observant, obese pendulum

  • Th3 Night Lion
    Th3 Night Lion4 dni temu

    Is this the answer to the matter vs antimatter? Is this the answer to quantum physics?

  • Th3 Night Lion

    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

  • Hisyam Ahmad
    Hisyam Ahmad4 dni temu

    Sir this is a mcdonald's drive thru

  • Dick McCarthy
    Dick McCarthy4 dni temu

    Sir, there's a glitch in matrix..or is there?

  • General Acquisitions
    General Acquisitions4 dni temu

    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.

  • Ikit Claw
    Ikit Claw4 dni temu

    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

  • larry larry
    larry larry4 dni temu

    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

  • Dissoson
    Dissoson5 dni temu

    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.

  • Dissoson
    Dissoson5 dni temu

    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

  • Glenn Davey
    Glenn Davey5 dni temu

    Why do we need to know this when humanity is going extinct anyway?

  • Gabriel MENDOZA
    Gabriel MENDOZA5 dni temu

    Wait wouldn’t” up”and” Left, up ,right “ land on the same point..?

  • Camden Ritter

    Camden Ritter

    2 dni temu

    Good point

  • Bielcrippa
    Bielcrippa5 dni temu

    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.

  • Emma Clyman
    Emma Clyman5 dni temu

    whenever i DOUBT that i'm smart, i think of this video and remember that i understood everything he said

  • ax Öllner
    ax Öllner5 dni temu

    everybody gangsta till michael almost drawed a swastika :D

  • The Doctor
    The Doctor5 dni temu

    this is a dupe glitch in real life lol

  • Khia Higgs
    Khia Higgs5 dni temu

    Can we talk about how he drew the line with the shade of a piece of paper? 8:16

  • Danny
    Danny5 dni temu

    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

  • Racoon God
    Racoon God5 dni temu

    Did-did my guy just commit a crime by defacing money? Damn, this man said ‘frick twelve, or can I?’